比特派钱包网址|boson

作者: 比特派钱包网址
2024-03-07 17:29:58

玻色子_百度百科

百度百科 网页新闻贴吧知道网盘图片视频地图文库资讯采购百科百度首页登录注册进入词条全站搜索帮助首页秒懂百科特色百科知识专题加入百科百科团队权威合作下载百科APP个人中心玻色子播报讨论上传视频物理学术语收藏查看我的收藏0有用+10本词条由“科普中国”科学百科词条编写与应用工作项目 审核 。玻色子(英语:boson)是遵循玻色-爱因斯坦统计,自旋量子数为整数的粒子。玻色子不遵守泡利不相容原理,多个全同玻色子可以同时处于同一个量子态,在低温时可以发生玻色-爱因斯坦凝聚。和玻色子相对的是费米子,费米子遵循费米-狄拉克统计,自旋量子数为半整数(1/2,3/2,……)。物质的基本结构是费米子,而物质之间的基本相互作用却由玻色子来传递。中文名玻色子外文名Boson特    点不遵守泡利不相容原理属    性质量、电量和自旋例    子规范玻色子、希格斯粒子、氘核等现    象低温时发生玻色-爱因斯坦凝聚应用范围量子力学目录1分类2命名3科研分类播报编辑按照结构,可以分成基本粒子和复合粒子。基本玻色子有传递基本相互作用的胶子、光子、Z、引力子以及给其他基本粒子提供质量的希格斯粒子。复合玻色子由偶数个费米子组成,常见的有介子、氘核、氦-4等。按照自旋和宇称量子数,可以分成标量、赝标量、矢量和轴矢量粒子等。胶子-强相互作用的媒介粒子,质量为零,电中性,自旋量子数为1,有8种。光子-电磁相互作用的媒介粒子,质量为零,电中性,自旋量子数为1,只有1种。Z玻色子-弱相互作用的媒介粒子,自旋量子数为1。Z玻色子有一个,不带电,质量约为91.2GeV。W玻色子有两个,分别带正、负一个电子电量,质量约为80.4GeV。引力子-量子引力理论中传递引力相互作用的媒介粒子,质量为零,电中性,自旋量子数为2,只有1种,尚未被发现。希格斯玻色子(Higgs boson)- 又称为“上帝粒子”,在GSW电弱统一理论中引起规范对称性自发破缺并给其他基本粒子提供质量的自旋量子数为0的基本粒子,质量约为125GeV。2012年7月被欧洲核子中心(CERN)的大型强子对撞机(LHC)实验发现。介子- 由一个正夸克和一个反夸克组成的强子,常见的有π、ρ、K等。氘核、氦-4等由偶数个核子组成的原子核。因为质子和中子都是费米子,故含偶数个核子的原子核是自旋为整数的玻色子。声子-请参阅固体物理学命名播报编辑1924年,印度物理学家萨特延德拉·纳特·玻色(Satyendra Nath Bose)将电磁辐射作为光子气体来描述,考虑到全同粒子的不可分辨性和几率解释,建立了基于量子力学的光子气体的统计规律,得到了普朗克的黑体辐射公式。玻色的论文在投稿时被拒绝,后来求助于爱因斯坦。爱因斯坦意识到玻色这个工作的重要性,他将文章翻译成德文后发表在德国的Zeitschrift für Physik杂志上。随后爱因斯坦也在此领域做了研究工作,发展和推广了玻色的工作,因此人们把这个统计方法叫做玻色-爱因斯坦统计。1945年,著名物理学家保罗·狄拉克(Paul Dirac)为了纪念玻色在量子统计中的开创性贡献,将遵循玻色-爱因斯坦统计规律的粒子命名为玻色子。科研播报编辑2023年,麻省理工学院—哈佛大学超冷原子中心首次在超冷气体中观察到玻色子增强的光散射,或为玻色子系统的研究开辟新的可能性。 [1]新手上路成长任务编辑入门编辑规则本人编辑我有疑问内容质疑在线客服官方贴吧意见反馈投诉建议举报不良信息未通过词条申诉投诉侵权信息封禁查询与解封©2024 Baidu 使用百度前必读 | 百科协议 | 隐私政策 | 百度百科合作平台 | 京ICP证030173号 京公网安备110000020000

希格斯玻色子_百度百科

色子_百度百科 网页新闻贴吧知道网盘图片视频地图文库资讯采购百科百度首页登录注册进入词条全站搜索帮助首页秒懂百科特色百科知识专题加入百科百科团队权威合作下载百科APP个人中心希格斯玻色子播报讨论上传视频标准模型里的一种基本粒子收藏查看我的收藏0有用+10本词条由“科普中国”科学百科词条编写与应用工作项目 审核 。希格斯玻色子(英语:Higgs boson)是粒子物理学标准模型预言的一种自旋为零的玻色子(有异议),不带电荷、色荷,极不稳定,生成后会立刻衰变。1964年,英国科学家彼得·希格斯提出了希格斯场的存在,并进而预言了希格斯玻色子的存在。而在希格斯机制中,希格斯场引起自发对称性破缺,并将质量予规范传播子和费米子。希格斯粒子是希格斯场的场量子化激发,它通过自相互作用而获得质量。 [1]根据希格斯机制,基本粒子因与希格斯场耦合而获得质量。假若希格斯玻色子被证实存在,则希格斯场应该也存在,而希格斯机制也可被确认为基本无误。希格斯玻色子已被证实存在。 [4]2022年10月,希格斯玻色子的质量分布测量结果为:3.2兆电子伏特。 [5]2023年,欧洲核子研究中心(CERN)的实验团队找到了希格斯玻色子衰变为Z玻色子和光子的首个证据。 [6]7月22日,欧洲核子研究中心(CERN)超环面仪器实验(ATLAS)合作组报告了迄今最精确希格斯玻色子质量:125.11吉电子伏特。 [7]中文名希格斯玻色子外文名Higgs boson别    名希格斯粒子,希格斯子提出者彼得·希格斯(P.W.Higgs)类    型粒子提出时间1964年目录1粒子介绍2理论发展史3理论▪希子性质▪希子制备▪希子衰变▪另类模型4实验探索5上帝粒子6精确测量粒子介绍播报编辑综述本篇文章将希格斯玻色子简称为“希子”。 [2]标准模型在粒子物理学里,标准模型是一种被广泛接受的框架,可以描述强力、弱力及电磁力这三种基本力及组成所有物质的基本粒子。除了引力以外,标准模型可以合理解释这世界中的大多数物理现象。早期的标准模型所倚赖的规范场论阐明,基本力是源自于规范不变性,是由规范玻色子来传递。规范场论严格规定,规范玻色子必须不带有质量,因此,传递电磁相互作用的规范玻色子(光子)不带有质量。光子的质量的确经实验证实为零。借此类推,传递弱相互作用的规范玻色子(W玻色子、Z玻色子)应该不带有质量,可是实验证实W玻色子与Z玻色子的质量不为零,这显示出早期模型不够完善,因此须要建立特别机制来赋予W玻色子、Z玻色子它们所带有的质量。希格斯机制的场能效希格斯玻色子最早在1964年由彼得·希格斯和弗朗索瓦·恩格勒等在内的6位物理学家提出。希格斯玻色子能够利用自发对称性破缺来赋予基本粒子质量,同时又不会抵触到规范场论。这机制被称为希格斯机制,希格斯机制已被实验证实。但是,物理学者仍旧不清楚关于希格斯机制的诸多细节。 [3]这机制假定宇宙遍布着希格斯场,其能够与某些基本粒子相互作用,并且利用自发对称性破缺使得它们获得质量。相关理论在70年代被纳入粒子物理学的标准模型。希格斯玻色子的衰变希子是伴随着希格斯场的带质量玻色子,是希格斯场的量子激发。希格斯玻色子是在高能量的极端环境中的能量演变,并且伴随着衰变生成耦合粒子的对称,生成正负电子对撞的实粒子一种超对称性的超对称粒子耦合激发,正负电子对正反粒子耦合被称为"马约拉纳费米子天使粒子"手征粒子,激发态是检验这一种粒子能动的谱能。不仅如此,希格斯机制也可被确认为基本无误。在那时期,虽然还没有任何直接证据可以证实希格斯粒子存在,由于希格斯机制所给出的准确预测,物理学者认为,希格斯机制极有可能正确无误。到了1980年代,希格斯粒子的存在与否已成为在粒子物理学里最重要的未解决的物理学问题之一。标准模型明确指出,希子的存在很难证实。与其它粒子相比较,制造希子需要极大的碰撞能量,必须建造超级粒子加速器来提供这样大的能量,而且,每一次碰撞制造出其它粒子的可能性比制造出希子的可能性大很多,即使希子被制成,它也会非常迅速地衰变成别的粒子(平均寿命为1.56×10-22s),因此难以被检测到,只能倚靠辨认与分析衰变产物,才可推断出它们大概是源自于希子,而不是源自于其它粒子。此外,很多其它种衰变过程也会显示出类似的迹象,这使得寻找希子有如大海捞针。只有依靠先进的超级粒子加速器与精准的探测器,物理学者才可观测数之不尽的粒子碰撞事件,将获得的纪录数据加以分析,寻找出希子的蛛丝马迹,然后再进一步分析,计算希子存在的可能性,确定所得到的结果绝对不是来自偶发事件。再华丽、再精致的理论,也需要通过实验加以证实,才会被正式接受,否则只能视为高谈大论。物理学者很希望能够证实希子是否存在。但是,早先从实验得到的数据只能让他们判别希子是否可能存在于某个质量值域。为了弥补这不足,欧洲核子研究组织在瑞士建成了大型强子对撞机(LHC)。它是全世界最先进的粒子加速器。它的主要研究目标之一就是证实希子是否存在。2013年,LHC的物理学者已确定发现希子,这发现强烈支持某种希格斯场弥漫于空间。当今,LHC仍旧在如火如荼地搜集数据,试图明白希格斯场的性质。理论发展史播报编辑自1899年英国物理学家汤姆逊爵士发现电子开始,时至今日,在一个多世纪的时间里 ,人类一直孜孜不倦地探索着微观世界的奥秘。物理学者认为物质是由基本粒子组成,这些基本粒子彼此之间相互影响的基本力有四种。根据规范场论,为了满足定域规范对称性,必须引入传递基本力的规范玻色子。特别而言,传递电磁力的规范玻色子就是光子。怎样才能够使得传递短程力的规范玻色子获得质量?物理学者在凝聚态物理学的超导理论里找到重要暗示。1950年,苏联物理学者维塔利·金兹堡与列夫·郎道提出金兹堡-朗道理论,他们建议,在超导体里,弥漫着一种特别的场,能够使得光子获得有效质量,但他们并没有明确地描述这特别场。1954年,杨振宁与罗伯特·米尔斯试图将这关于电磁力的点子延伸至其他种基本力,他们提出了杨-米尔斯理论,但是规范场论预测规范玻色子的质量必须为零,而零质量玻色子传递的是类似电磁力的长程力,不适用于像弱核力或强核力一类的短程力。1957年,约翰·巴丁、利昂·库珀、约翰·施里弗共同创建了BCS理论,他们认为,由电子组成的库珀对,形成了这特别场。规范对称性被这特别场隐藏起来,因此造成自发对称性破缺──虽然对称性仍旧存在于描述这物理系统的方程,但是方程的某种解并不具有这对称性。南部阳一郎于1960年将自发对称性破缺的概念引入粒子物理学。他建议,假定夸克与反夸克的质量为零,则生成它们的能量成本很低,如同电子们在超导体里凝聚为库珀对,它们会在真空里凝聚为夸克对,使得强相对作用的手征对称性被打破,夸克会因此获得质量。他又指出,在这机制里,还会出现一种新的零质量玻色子,即π介子,由于上夸克、下夸克的质量不等于零,π介子的实际质量不等于零,只是比其他种介子的质量都轻很多。1962年,杰福瑞·戈德斯通提出戈德斯通定理,对于这类零质量玻色子的性质给予描述。根据这定理,当连续对称性被自发打破后必会生成一种零质量玻色子,称为戈德斯通玻色子。带质量粒子比较难制成,粒子加速器必须使用很高的能量来碰撞制成带质量粒子。零质量粒子案例跟重质量粒子案例不同,零质量粒子很容易制成,或者可从缺失能量或动量推测其存在。然而,事实并非如此,物理学者无法做实验找到其存在的任何蛛丝马迹,这事实意味着整个理论可能有瑕疵。1963年,菲利普·安德森发表论文指出,对于非相对论性的超导体案例,假若是规范对称性被打破,则不一定会出现戈德斯通玻色子,他进一步猜测,这机制应该可以加以延伸来处理相对论性案例,但他并没有明确地给出一个相对论性案例。这论述遭到未来诺贝尔化学奖得主沃特·吉尔伯特强烈反对。1964年,弗朗索瓦·恩格勒和罗伯特·布绕特领先于8月,紧接着,彼得·希格斯于10月,随后,杰拉德·古拉尼、卡尔·哈庚和汤姆·基博尔于11月,这三个研究小组分别独立地发表论文,宣布研究出相对论性模型。古拉尼于1965年、希格斯于1966年、基博尔于1967年,又分别更进一步发表论文探讨这模型的性质。这三篇1964年论文共同表明,假若将局部规范不变性理论与自发对称性破缺的概念以某种特别方式连结在一起,则规范玻色子必然会获得质量。1967年,史蒂文·温伯格与阿卜杜勒·萨拉姆各自独立地应用希格斯机制来打破电弱对称性,并且表述希格斯机制怎样能够并入稍后成为标准模型一部分的谢尔登·格拉肖的电弱理论。温伯格指出,这过程应该也会使得费米子获得质量。关于规范对称性的自发性破缺的这些划时代论文,最初并没有得到学术界的重视,因为大多数物理学者认为,非阿贝尔规范理论是个死胡同,无法被重整化。1971年,荷兰物理学者马丁纽斯·韦尔特曼与杰拉德·特·胡夫特发表了两篇论文,证明杨-米尔斯理论(一种非阿贝尔规范理论)可以被重整化,不论是对于零质量规范玻色子,还是对于带质量规范玻色子。自此以后,物理学者开始接受这些理论,正式将这些理论纳入主流。从这些理论孕育出的电弱理论与改善后的标准模型,正确地预测了弱中性流、W玻色子、Z玻色子、顶夸克、粲夸克,并且准确地计算出其中一些粒子的性质与质量。很多在这领域给出重要贡献的物理学者后来都获得了诺贝尔物理学奖与其它享有声望的奖赏。发表于《现代物理评论》的一篇1974年文章表示,至今为止,这些理论推导出的答案符合实验结果,但是,这些理论到底是否正确仍旧无法确定。权威著作《希格斯狩猎者指南》的作者指明,标准模型拥有惊人的成功。现今,粒子物理学的核心问题就是了解希格斯区的相关理论。物理评论快报1964年里程碑论文六位物理学者分别发表的三篇论文,在《物理评论快报》50周年庆祝文献里被公认为里程碑论文。2010年,他们又荣获理论粒子物理学樱井奖。同年,在他们之间,又发生了一点争执,万一因此获得诺贝尔物理学奖,由于每一年只能授予给三位杰出人士,而现在有六位人士做出了关键贡献,到底应该颁发物理学最荣誉的奖给哪三位人士?(结果,弗朗索瓦·恩格勒和彼得·希格斯获得了2013年诺贝尔物理学奖。)1964年8月,恩格勒团队发表了三页论文,他们假定存在有复值标量场(即希格斯场),其数值在量子真空里不等于零,然后使用费曼图方法演示出规范玻色子怎样获得质量。恩格勒团队并没有提到任何关于希子的信息。稍后,希格斯独立发表论文概述怎样能够应用定域规范对称性来回避戈德斯通定理,他并没有给出模型明确显示戈德斯通玻色子被抵销。不久之后,希格斯发表第二篇论文,他更仔细的表述这回避方法,给出一个可行模型,并且用这模型演示出规范矢量场怎样吃掉戈德斯通玻色子,因此获得质量。他将这篇论文被呈送给《物理快报》,但是令人惊讶地没有被接受。他无法理解,为什么同样的学术刊物,会接受一篇关于“带质量规范玻色子可能存在”的论文,又会否绝一篇描述“带质量规范玻色子实际模型”的文章。希格斯不因此而气馁,他又添加了一些内容,从他给出的模型,他预测另外存在一种带质量玻色子,后来知名为“希格斯玻色子”希格斯的1966年论文推导出希子的衰变机制;只有带质量玻色子可以衰变,假若找到衰变的迹象,就可以证实希子存在。古拉尼团队论文提到了恩格勒团队与希格斯先前分别独立发表的论文。古拉尼团队论文是唯一对于整个希格斯机制给出完整分析的论文。这论文也推导出希子的存在,但是希格斯的希子具有质量,而古拉尼团队的希子不具有质量,这结果令人疑问两种希子是否相同。在2009年与2011年发表的两篇论文中,古拉尼解释,在古拉尼团队给出的模型里,取至最低阶近似,玻色子的质量为零,但是这质量的数值没有被任何理论限制;取至较高阶,玻色子可以获得质量。希格斯机制不但解释了规范玻色子怎样获得质量,还预测这些玻色子与标准模型的费米子之间的耦合。经过在大型正负电子对撞机(LEP)和斯坦福线性加速器(SLAC)做精密测量实验,很多预测都已经核对证实,因此确认大自然实际存在这一机制。但物理学者仍旧不清楚希格斯机制到底是怎样发生,他们希望能从寻找希子所得到的结果获得一些这方面的证据。理论播报编辑希格斯势与希格斯场 的关系形状好似一顶墨西哥帽。帽顶为希格斯势的局域最大值,其希格斯场为零( );帽子谷底的任意位置为希格斯势的最小值,其希格斯场不为零( )。对于绕着帽子中心轴 的旋转,帽顶的位置不变,而帽子谷底的任意位置会改变,因此帽顶具有旋转对称性,而帽子谷底的任意位置不具有旋转对称性。主条目:希格斯机制量子力学的真空与一般认知的真空不同。在量子力学里,真空并不是全无一物的空间,虚粒子会持续地随机生成或湮灭于空间的任意位置,这会造成奥妙的量子效应。将这些量子效应纳入考量之后,空间的最低能量态,是在所有能量态之中,能量最低的能量态,又称为基态或“真空态”。最低能量态的空间才是量子力学的真空。描述物理系统的方程所具有的对称性,这最低能量态可能不具有,这现象称为自发对称性破缺。在标准模型里,为了满足定域规范不变性,规范玻色子的质量必须设定为零;但这不符合实验观察结果──W玻色子与Z玻色子都已经通过做实验检验确实拥有质量。因此,这些玻色子必须倚赖其它种机制或作用来获得质量。每一个最低能量态位置都不具有旋转对称性。在这无穷多个最低能量态之中,只有一个最低能量态能够被实现,旋转对称性因此被打破,造成自发对称性破缺,因此使规范玻色子获得质量,同时生成一种零质量玻色子,称为戈德斯通玻色子,而希子则是伴随着希格斯场的粒子,是希格斯场的振动。但这戈德斯通玻色子并不符合实际物理。通过选择适当的规范,戈德斯通玻色子会被抵销,只存留带质量希子与带质量规范玻色子。总括而言,利用自发对称性破缺,使得规范玻色子获得质量,这就是希格斯机制。在所有可以赋予规范玻色子质量,而同时又遵守规范理论的可能机制中,这是最简单的机制。按照希格斯机制,复值希格斯场(两个自由度)与零质量规范玻色子(横场,如同光子一样,具有两个自由度)被变换为带质量标量粒子(希子,一个自由度)与带质量规范玻色子(戈德斯通玻色子变换为一个纵场,加上先前的横场,共有三个自由度),自由度守恒。费米子也是因为与希格斯场相互作用而获得质量,但它们获得质量的方式不同于W玻色子、Z玻色子的方式。在规范场论里,为了满足定域规范不变性,必须设定费米子的质量为零。通过汤川耦合,费米子也可以因为自发对称性破缺而获得质量。希子性质稍微复杂一点,但更实际一点,在最小标准模型(minimal standard model)里,希格斯场是复值二重态,是由两个复值标量场,或四个实值标量场组成,其中,两个带有电荷,两个是中性。在这模型里,还有四个零质量规范玻色子,都是横场,如同光子一样,具有两个自由度。总合起来,一共有十二个自由度。自发对称性破缺之后,一共有三个规范玻色子会获得质量、同时各自添加一个纵场,总共有九个自由度,另外还有一个具有两个自由度的零质量规范玻色子,剩下的一个自由度是带质量的希子。三个带质量规范玻色子分别是W、W和Z玻色子。零质量规范玻色子是光子。由于希格斯场是标量场(不会因洛伦兹变换而改变),希子不具有自旋。希子不带电荷,是自己的反粒子,具有CP-偶性。标准模型并没有预测希子的质量。假若质量在115和180 GeV之间,则能量尺度直到普朗克尺度(10GeV)上限,标准模型都有效。基于标准模型的一些不令人满意的性质,许多理论学者认为后标准模型的新物理会出现于TeV能量尺度。希子(或其他的电弱对称性破缺机制)能够具有的质量的尺度上限是1.4 TeV;超过此上限,标准模型变得不相容,因为对于某些散射过程违反了幺正性。现今,学术界有超过一百种不同关于希格斯质量的理论预测。理论而言,希子的质量或许可以间接估计。在标准模型里,希子会造成一些间接效应。最值得注意的是,希格斯回路会造成W玻色子质量和Z玻色子质量的小额度修正。通过整体拟合从各个对撞机获得的精密电弱数据。希子可能会与前面提到的标准模型粒子相互作用,但也可能会与诡秘的大质量弱相互作用粒子相互作用,形成暗物质,这在近期天文物理学研究领域里,是很重要的论题。希子制备粒子对撞机尝试通过碰撞两束高能量粒子的方式来制备希子。实际物理反应依使用的粒子与碰撞能量而定。最常发生的反应为胶子融合:胶子是负责传递强相互作用的玻色子。它们把重子内部的夸克捆绑在一起。假若碰撞粒子为重子,例如,在兆电子伏特加速器里的质子与反质子,或在大型强子对撞机里的质子,则最有可能发生两个胶子(g )碰撞在一起。制备希子最简单的方法就是两个胶子碰撞后,经过虚夸克圈而形成希子。由于希子与粒子的耦合跟粒子的质量成正比,粒子质量越大,聚变反应越容易发生。实际而言,只需要考虑虚顶夸克(t)与虚底夸克(b)的贡献,它们是质量最大的两种夸克。在兆电子伏特加速器、大型强子对撞机里,这是主要反应,比任何其它反应的发生次数多十倍以上。希子轫致辐射:假若基本费米子(f)与其反费米子相碰撞,例如夸克与反夸克相碰撞,或电子与正电子相碰撞,则会形成一个虚W玻色子或虚Z玻色子,假若带有足够能量,则可能会发射出希子。在大型正负电子对撞机里,这是主要反应,电子与正电子相碰撞形成虚Z玻色子。在兆电子伏特加速器里,这是第二主要反应。在大型强子对撞机里,这是第三主要反应,因为是两束质子相碰撞,与兆电子伏特加速器相比,大型强子对撞机比较不容易制备夸克与反夸克相碰撞。矢量玻色子融合:两个夸克分别发射一个W玻色子或Z玻色子,然后以W+W-或 ZZ 方式合并形成一个中性希子。在大型正负电子对撞机、大型强子对撞机里,这是第二主要反应。例如,上夸克与下夸克分别发射W+与W-,然后以W+W-方式合并形成一个中性希子。顶夸克融合:两个胶子(g)分别衰变为两个顶夸克( t )反顶夸克粒子对,然后 t与反顶夸克粒子对合并形成一个中性希子。这反应的发生次数很少(低过两个数量级)。希子衰变标准模型所预测的希子衰变宽度与质量有关。标准模型所预测的希子的几种不同衰变模式的分支比与质量有关。在量子力学里,假若粒子有可能衰变成一组质量较轻的粒子,则这粒子必会如此衰变。衰变发生的概率与几种因素有关:质量差值、耦合强度等等。标准模型已将大多数这些因素设定,希子质量是一个例外。假设希子质量为126GeV,则标准模型预测平均寿命(mean lifetime)大约为1.56x10⁻²²秒。由于希子会与每一种“已知”带质量基本粒子相互作用,希子有很多种不同的衰变道。每种衰变道都有其发生的概率,称为分支比(branching ratio),定义为这种衰变道发生的次数除以总次数。展示出,标准模型预测的几种不同衰变模式的分支比与质量之间的关系。在这几种希子衰变道之中,有一种衰变道是分裂为费米子反费米子对。对于希子衰变,产物质量越大,则耦合强度越大(呈线性或平方关系)。因此,希子比较可能衰变为较重的费米子,希子应该最常衰变为顶夸克反顶夸克对。但是,这种衰变必须遵守运动学约束,即希子质量必须大于346GeV,顶夸克质量的两倍。假设希子质量为126GeV,则标准模型预测最常发生的衰变为底夸克反底夸克对,概率为56.1%。第二常发生的衰变是τ子反τ子对,概率为6%。希子也有可能分裂为一对带质量规范玻色子。对于这模式,希子最有可能衰变为一对W玻色子,假设希子质量为126GeV,则概率为23.1%。在这之后,W玻色子可以衰变为夸克与反夸克,或者,衰变为轻子与中微子。这最后一种模式不能被重建,因为无法探测到中微子。希子衰变为一对Z玻色子会给出较干净的讯号,若果Z玻色子会继续衰变为易探测的带电荷轻子反轻子对(电子或μ子)。假设希子质量为126GeV,则概率为2.9%。希子还可能衰变为零质量胶子,但是中间需要经过夸克圈。对于这模式,最常会经过顶夸克圈,因为顶夸克最重,也因为如此,虽然这是个单圈图(one-loop diagram),而不是树图(tree-level diagram),它发生的衰变概率仍旧可观,不容忽略。假设希子质量为126GeV,则概率为8.5%。比较稀有的是希子衰变为零质量光子,概率为0.2%,这过程中间需要经过费米子圈或W玻色子圈。由于光子的能量与动量可以非常准确地测量,衰变粒子的质量可以准确重建出来。所以,在探索低质量希子的实验中,这过程非常重要。另类模型所有应用希格斯机制来解释质量问题的模型中,最小标准模型只设定了一个复值二重态希格斯场,是最简单的标准模型。其它模型的希格斯场可能会被延伸成具有更多二重态或三重态。双希格斯二重态模型(two-Higgs-doublet models, 2HDM)设定了两个复值二重态希格斯场,是在所有其它种模型中比较受到认可的模型,主要原因为1.在所有其它种模型中,它是最小、最简单的模型。2.它能够添加更多物理现象,例如,带电荷的希子。3.它遵守标准模型的主要理论约束。4.低能量超对称模型必须具有这种结构。双希格斯二重态模型预言五重态标量粒子的存在:两个CP-偶性的中性希子 h、H,一个CP-奇性的中性希子 A,和两个带电荷希子 H、H。不同版本的2HDM与最小标准模型的分辨方法主要建立于它们的耦合常数与希格斯衰变的分支比都不相同。在模型I里,一个二重态能与所有种类的夸克耦合,另一个二重态则不能与任何夸克耦合。在模型II里,一个二重态能与上型夸克(up-type quark)耦合,另一个二重态则与下型夸克(down-type quark)耦合。超对称模型(SUSY)是标准模型的一种延伸,属于2HDM模型II。在超对称模型中,最小超对称模型(MSSM)的希格斯机制产生的希子数量最少。在最小标准模型里,希子质量基本而言是一个自由参数,只要小于TeV能量尺度就行。在MSSM里,最轻的CP-偶性的中性希子h的质量上限大约为110-135GeV。假若希子质量在125GeV左右,则MSSM的模型参数会被强列约束。在艺彩理论(technicolor theory)里,两个强烈束缚的费米子所形成的粒子对扮演了希格斯场的角色。顶夸克凝聚理论(top quark condensate theory)提出希格斯场被顶夸克与反顶夸克共同组成的复合场替代的概念。有些模型完全不提供希格斯场,电弱对称性破缺是倚赖额外维度来达成。实验探索播报编辑为了要制成希子,在粒子对撞机里,两道粒子束被加速到非常高能量,然后在粒子探测器里相互碰撞,有时候,异乎寻常地,会因此生成产物希子。但是希子会在生成后会在非常短暂时间内发生衰变,无法直接被探测到,探测器只能记录其所有衰变产物(“衰变特征”),从这些实验数据,重建衰变过程,假若符合希子的某种衰变道,则归类为希子可能被生成事件。实际而言,很多种过程都会出现类似的衰变特征。很庆幸地是,标准模型精确地预言所有可能衰变模式与对应的或然率,假若探测到更多能够匹配希子衰变特征的事件,而不是更多不同于希子衰变特征的事件,则这应该是希子存在的强烈证据。在大型强子对撞机里,由于粒子碰撞生成希子的事件概率非常稀有,大约为百亿分之一,很多其它种碰撞事件具有类似的衰变特征,物理学者必须搜集与分析几百万亿个碰撞事件,只有显示出与希子相同衰变特征的事件才可被视为是可能的希子衰变事件。在确认发现新粒子之前,两个独立的粒子探测器(ATLAS与CMS)所观测到的衰变特征出自于背景随机标准模型的事件概率,都必须低于百万分之一,也就是说,观测到的事件数量比没有新粒子的事件数量,两者之间相异的程度为5个标准差。更多碰撞数据能够让物理学者更为正确地辨认新粒子的物理性质,从而决定新粒子是否为标准模型所描述的希子,还是其它种假想粒子。低能量实验设施可能无法找到希子,必须建造一座高能量粒子对撞机,这对撞机还需要具有高亮度来确保搜集到足够的碰撞数据。另外,还需要高功能电脑设施来有序处理大量碰撞数据(大约25petabyte每年)。至2012年为止,它的附属电脑设施,全球大型强子对撞机计算网格(Worldwide LHC Computing Grid)已处理了超过三百万亿(3×10)个碰撞事件。这是全球最大的计算网格,隶属于它的170个电算设施,散布在36国家,是以分布式计算的模式连结在一起。2012年7月4日以前的探索最早大规模搜寻希子的实验设施是欧洲核子研究组织的大型正负电子对撞机,它在1990年代开始运作,直到2000年为止,但它并没有找到希子的确切存在证据,这是因为它的专长是精密测量粒子的性质。根据大型正负电子对撞机所收集到的数据,标准模型希子的质量下限被设定为114.4 GeV,置信水平95%。这意味着假若希子存在,则它应该会重于114.4GeV/c。费米实验室的兆电子伏特加速器继承了先前搜寻希子的任务。1995年,它发现了顶夸克。为了搜寻希子,设施的功能被大大提升,但这并不能保证兆电子伏特加速器会发现希子。在那时期,它是唯一正在运作中的超级对撞机,大型强子对撞机正在建造,超导超大型加速器计划已于1993年取消。历经多年运作,兆电子伏特加速器只能对于更进一步排除希子质量值域做出贡献,由于能量与亮度无法与建成的大型强子对撞机竞争,于2011年9月30日除役。从分析获得的实验数据,兆电子伏特加速器团队排除希子的质量在100-103GeV、147-180GeV以内,置信水平95%。在能量115–140GeV之间区域,超额事件的统计显著性为2.5个标准差,这对应于在550次事件中,有一次事件是归咎于统计涨落。这结果仍旧未能达到5个标准差,因此不能够作定论。欧洲核子研究组织的大型强子对撞机(LHC)的设计目标之一为能够确认或排除希子的存在。在瑞士日内瓦附近乡村的地底下,圆周为27km的坑道里,两个质子束相撞在一起,最初以3.5TeV每质子束(总共7TeV),大约为兆电子伏特加速器的3.6倍,未来还可提升至2 × 7 TeV(总共14TeV)。根据标准模型,假若希子存在,则这么高能量的碰撞应该能够将它揭露出来。这是史上最复杂的科学设施之一。在开启测试后仅仅九天,由于磁铁与磁铁之间电接连缺陷,发生磁体失超事件,造成50多个超导磁铁被毁坏、真空系统被污染,整个运作被迫延迟了14个月,直到2009年11月才再度重新运作 。2010年3月,LHC开始紧锣密鼓地进行数据搜集与分析。2011年12月,LHC的两个主要粒子探测器,超环面仪器(ATLAS)和紧凑μ子线圈(CMS)的实验团队,已将希子的可能质量值域缩小至115-130 GeV(ATLAS)与117-127 GeV (CMS)。另外,ATLAS在质量范围125-126GeV探测到超额事件,统计显著性为3.6个标准差,CMS在质量范围124GeV探测到超额事件,统计显著性为2.6个标准差。由于统计显著性并不够大,尚无法做结论或甚至正式当作一个观察事件。但是,两个探测器都独立地在同样质量附近检测出超额事件,这事实使得粒子物理社团极其振奋,期望能够在检验完毕2012年的碰撞数据之后,于明年年底排除或确认标准模型希子的存在。CMS团队发言人吉多·桐迺立(Guido Tonelli)表示:“统计显著性不够大,无法做定论。直到今天为止,我们所看到的与背景涨落或与玻色子存在相符合。更仔细的分析与这精心打造的巨环在2012年所贡献出的更多数据必定会给出一个答案。”发现新玻色子2012年6月22日,欧洲核子研究组织发表声明,将要召开专题讨论会与新闻发布会,报告关于寻找希子的最新研究结果。不消一刻,谣言传遍了新闻媒体,记者们与一些物理学者纷纷猜测欧洲核子研究组织是否会正式宣布证实希子存在。7月4日,欧洲核子研究组织举行专题讨论会与新闻发布会宣布,紧凑μ子线圈发现质量为125.3±0.6GeV的新玻色子,标准差为4.9;超环面仪器发现质量为126.5GeV的新玻色子标准差为4.6。物理学者认为这两个粒子可能就是希子。欧洲核子研究组织的所长说:“从一个外行人的角度来说,我们已经发现希子了;但从一个内行人的角度来说,我们还需要更多的数据。”一旦将其它种类的紧凑μ子线圈相互作用纳入计算,这两个实验达到局部统计显著性5个标准差──错误概率低于百万分之一。在新闻发布之前很长一段时间,两个团队彼此之间不能互通讯息,这样才能确保每一个团队得到的结果不会受到另一个团队的影响而发生任何偏差,这也可以让两个团队各自独立得到的研究结果可以彼此相互核对。如此规格的证据,通过两个被隔离团队与实验的独立确定,已达到确定发现所需要的正式标准。欧洲核子研究组织的治学态度非常严谨,不愿意引人非议;欧洲核子研究组织表明,新发现的粒子与希子相符,但是物理学者尚未明确地认定这粒子就是希子,仍旧需要更进一步搜集与分析数据才能够做定论。换句话说,从实验观测显示,新发现的玻色子可能是希子,很多物理学者都认为非常可能是希子,现在已经证实有一个新粒子存在,但仍旧需要更进一步研究这粒子,必需排除这粒子或许不是希子的任何可疑之处。7月31日,欧洲核子研究组织的紧凑μ子线圈小组和超环面仪器小组分别提交了新的探测结果的论文,将这种疑似希子的粒子的质量确定为紧凑μ子线圈的125.3 GeV(统计误差:±0.4、系统误差:±0.5、统计显著性:5.8个标准差)和超环面仪器的126.0 GeV(统计误差:±0.4、系统误差:±0.4、统计显著性:5.9个标准差)。2013年3月14日,欧洲核子研究组织发布新闻稿表示,先前探测到的新粒子是希子。确认希子在超环面仪器里,4-μ子候选事件示意图。在紧凑μ子线圈探测器里,从质心能量为8 TeV的质子-质子碰撞事件记录数据制作出的三维绘景图。2013年3月14日,欧洲核子研究组织公开确认:"紧凑μ子线圈小组与超环面仪器小组已对这粒子所拥有的自旋、宇称可能会产生的状况仔细分析比较,这些都指向零自旋与偶宇称(符合标准模型的两个对于希子的基要判据)。这事实,再加上测量到的新粒子与其它粒子彼此之间的相互作用,强烈显示这就是希子。这也是第一个被发现的基本标量粒子。以下列出几个检试这125GeV粒子是否为希子的实验项目:玻色子:只有玻色子才能够衰变为两个光子。从实验已观察到这125GeV粒子能够衰变为两个光子,因此,这粒子是玻色子。零自旋:这可以从检验衰变模式证实。在初始发现之时,观察到125GeV粒子衰变为两个光子,根据对称性定律,可以排除自旋为1,剩下两个候选自旋为0或2。这决定于衰变产物的运动轨道是否有嗜好方向,假若没有,则自旋为0,否则,自旋为2。2013年3月,125GeV粒子的自旋正式确认为0。偶宇称(正宇称):从研究衰变产物运动轨道的角度,可以查得到底是偶宇称还是奇宇称。有些理论主张,可能存在有膺标量(pseudoscalar )希子,这种粒子拥有奇宇称。2013年3月,125GeV粒子的宇称暂时确认为正宇称。排除零自旋奇宇称假说,置信水平超过99.9%。衰变道:标准模型已对希子的衰变模式给出详细预测,证实希格斯场可以与费米子相互作用。这意味着希子不只是衰变至传递作用力的玻色子,它还衰变至组成物质的费米子。对于这些模式,实验初始得到的分支比(branching ratio)或衰变率结果稍微高过预期值,意味着这粒子的物理行为可能更为怪异,但是,CMS团队领导约瑟·英侃德拉(Joseph Incandela)认为,这分歧并不严峻。与质量相耦合:希子必须能够通过希格斯场与质量相耦合,也就是说,与W玻色子、Z玻色子相耦合。对于标准模型希子而言,所涉及的耦合常数 cV=1 。从分析LHC实验得到的数据,CV在标准模型数值的 15%内,置信水平95%。高能量碰撞结果仍旧与先前一致:在大型强子对撞机2015年重新开启之后,碰撞能量将达到设计的13 – 14 TeV,未来实验将专注于寻找其它种类的希子(如同某些理论预测)与检试其它版本的粒子理论,实验获得的高能量结果必须与希格斯理论一致。2023年,欧洲核子研究中心(CERN)的超环面仪器实验(ATLAS)和紧凑缪子线圈实验(CMS)实验团队携手发布报告称,他们找到了希格斯玻色子衰变为Z玻色子和光子的首个证据,这种衰变有望提供间接证据,证明存在超出粒子物理学标准模型预测的新粒子。 [6]上帝粒子播报编辑美国物理学家、1988年诺贝尔物理学奖获得者利昂·莱德曼曾著有粒子物理方面的科普书籍《上帝粒子:如果宇宙是答案,那么问题是什么?》,后来媒体也沿用了这一称呼,常常将希子称作是“上帝粒子”(The God Particle)。这一称呼激起了公众媒体对于希子的关注和兴趣。莱德曼说他以“上帝粒子”为这粒子命名是因为这粒子“在当今物理学中处于极为中心的位置,对我们理解物质的结构极为关键、也极为难以捉摸”。不过他也开玩笑地补充说另一个原因是“图书出版商不让他把这粒子称作‘该死的粒子(Goddamn Particle)’,尽管这别称可能更恰当地表达了希子杳无踪迹的性质以及人们为之所付出的代价与遭受到的挫折感。”然而,许多科学家却不喜欢这一称呼,因为它过分强调了这粒子的重要性和太宗教化。而且即使这粒子被发现,物理学者仍旧无法回答一些关于强相互作用、电弱相互作用、引力相互作用的统一化问题,以及宇宙的起源问题;希格斯本人是无神论学者。2009年,英国的《卫报》展开了一次重命希子的竞赛,并最终从提交的命名中选择了“香槟酒瓶玻色子”(champagne bottle boson)作为最佳命名。“香槟酒瓶的瓶底正好是希格斯势的形状,而且它常常在物理讲座中被用来作为图解。因此它绝非胡乱编造的名字,而是便于记忆、与物理实际相关的名字。”精确测量播报编辑2022年10月,希格斯玻色子的质量分布测量结果为:3.2兆电子伏特。 [5]2023年7月22日,欧洲核子研究中心(CERN)超环面仪器实验(ATLAS)合作组报告了迄今最精确希格斯玻色子质量:125.11吉电子伏特,新结果达到了前所未有的0.09%的精度。 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希格斯玻色子是什么?为什么被称为「上帝粒子」呢? - 知乎

希格斯玻色子是什么?为什么被称为「上帝粒子」呢? - 知乎首页知乎知学堂发现等你来答​切换模式登录/注册物理学理论物理量子物理粒子物理学希格斯玻色子是什么?为什么被称为「上帝粒子」呢?关注者403被浏览594,047关注问题​写回答​邀请回答​好问题 15​3 条评论​分享​18 个回答默认排序知乎用户“希格斯粒子”(Higgs particle)与空间中的物体的质量的形成有关。有了质量,粒子才会结合为原子,有了原子,才会有分子,有了分子,才能有物体。因此,“希格斯粒子”被认为是一种形塑了世界万物的粒子,没有它,就没有人们所见的世界,可能这就是为什么它会被赞誉为“上帝粒子”(God particle)的原因。上个世纪六十年代,英国物理学家彼得·希格斯(Peter Higgs)开始尝试研究物质拥有质量的根本原因。需要知道的是,“质量”不只简单地代表物体所含的物质的量,它的另一个意义在于物体获得加速度的难度。举个例子,一辆较重的大卡车要刹车或加速,肯定会比一辆较轻的小轿车困难得多,用的时间长,需要的能量也大。加速的难度越大,质量越大。据说,希格斯在一次野外散步的时候突发奇想,认为空间就像水,水中的物体在运动时会遇到阻力,让运动变得困难,相应地,粒子穿行于空间中,也应该承受某种“阻碍”,使其需要有所付出才能获得加速度,在宏观世界中体现为“质量”。空间中的这种使物质获得质量的机制,被称作“希格斯场”(Higgs field)。理论物理学家布莱恩·葛林(Brian Greene)曾经提到过一个很有意思的比喻:可以把“希格斯场”想象成“狗仔队”,把空间中的各种物质看作“明星”。“狗仔队”看见明星就会一拥上前,将其团团围住,而明星则必须要使劲往前挤才能逃走;明星挤得越费劲,与狗仔队的互动越多,受到的阻碍越大,当然也从侧面说明,他的“名气”越大。演员们的名气,就等价于物质的“质量”。由于演员们的名气有大有小,相应地,不同物质(基本粒子)的质量也各不相同。比如,光子的(静止)质量是零,因此光能以理论上空间中的最快速度运动。后来,欧洲核子研究组织(CERN)在日内瓦建造了一座“大型强子对撞机”(LHC),科学家们开始尝试把粒子加速到接近光速的速度,希望能从空间中找到“希格斯场”中的粒子,也就是“希格斯粒子”,以此验证希格斯的理论。2013年,通过对撞机实验,初步确认已经发现了“希格斯粒子”,定名为“希格斯玻色子”(Higgs Boson,粒子分为“玻色子”和“费米子”两类,它们的自旋特性不同),证明了“希格斯场”的存在,希格斯本人也因此荣获诺贝尔奖。* “希格斯玻色子”仅仅是基本粒子,比如电子等的质量的来源,虽然世界万物都由基本粒子构成,然而它却并不完全是物质的全部的质量的给予者。物体的绝大部分质量来自于胶子场中的能量。根据公式 E=mc^2,能量与质量是等价的。计算机模拟的“希格斯玻色子”的运作模型。图片来源:Youtube 视频截图视频地址:https://www.youtube.com/watch?v=1Yt-1IKoZTE“希格斯粒子”的发现,应该算是人类探究空间的一个重大里程碑,因为它不仅证明了“真空不空”,而且还说明,“空间”不是一种虚无的东西,它拥有自己与生俱来的固定的特性;“希格斯粒子”被认为普遍存在于空间中,作用就是给运动的物质施加质量(加速的难度)。这同时也说明了,即使是人们一般认为的“绝对真空”,也能够对物质造成实在的影响。可以参考这里:Higgs boson(Wikipedia 上关于希格斯玻色子的详细解释)。Peter Higgs interview: 'I have this kind of underlying incompetence'(Peter Higgs 的访谈)。还有,PBS NOVA 的纪录片《The Fabric of the Cosmos: What Is Space?》。编辑于 2019-07-05 12:08​赞同 881​​78 条评论​分享​收藏​喜欢收起​探索之子​灵遁者:更在于探索。灵遁者代表作品:科普四部曲,国学三部曲。​ 关注 在标准模型里,W玻色子与Z玻色子借着应用希格斯机制于希格斯场而获得质量,费米子借着应用希格斯机制于希格斯场与费米子场的汤川耦合而获得质量。 只有希格斯玻色子不倚赖希格斯机制获得质量。不过尽管希格斯机制已被证实,它仍旧不能给出所有质量,而只能将质量赋予某些基本粒子。例如,像质子、中子一类复合粒子的质量,只有约1%是归因于将质量赋予夸克的希格斯机制,剩余约99%是夸克的动能与强相互作用的零质量胶子的能量。 希格斯场的存在会促使自发对称性破缺,从而造成不同粒子、不同作用力彼此之间的差异。例如,在电弱理论里,从希格斯场的理论物理秉性,可以解释为什么当温度降低到某程度,电磁相互作用与弱相互作用的性质迥然不同,答案是对称性已被打破。 在标准模型里,希格斯机制是基本粒子获得质量的物理机制。1964年,分别有三组研究小组几乎同时地独立延伸发展出希格斯机制,其中,一组为弗朗索瓦·恩格勒和罗伯特·布绕特,另一组为彼得·希格斯,第三组为杰拉德·古拉尼、卡尔·哈庚和汤姆·基博尔。他们的论文表明,假若将局域规范不变性与自发对称性破缺的概念以某种特别方式连结在一起,则规范玻色子必然会获得质量。 于1967年,史蒂文·温伯格与阿卜杜勒·萨拉姆分别应用希格斯机制来打破电弱对称性,并且表述希格斯机制怎样能够并入稍后成为标准模型一部分的谢尔登·格拉肖的电弱理论。 应用希格斯机制,温伯格与萨拉姆分别发现传递弱作用力的W及Z玻色子具有质量,而传递电磁作用力的光子不具有质量。质量的起源或质量的创始时常被归功于希格斯机制。 但是,对于质量的秉性,物理学者疑问希格斯机制是否给出了足够解释。如同物理学者马克斯·杰莫(Max Jammer)所说,“假若某过程生成质量,则一个合理要求为,它也应该给出一些关于它生成的到底是什么的资料。”但是,希格斯机制不是使用一种奇迹式的“无中生有”(creatio ex nihilo)方法来生成粒子质量,而是从以能量形式储存质量的希格斯场将质量转传给粒子,因此,“希格斯机制与其相关理论并没有贡献出对于质量秉性的了解。” 希格斯机制假定存在着一种称为希格斯场的标量场遍布于宇宙。借着与希格斯场耦合,某些原本没有质量的粒子可以获得能量,根据质能关系式,这就等于获得质量。粒子与希格斯场耦合越强,则粒子的质量越大。 希格斯场可以比拟为一池黏的蜜糖,黏着于某种尚未带有质量的基本粒子。当这种粒子通过希格斯场的时候,会变成带质量粒子。这比拟并不完全。 第一、有些种类的粒子(例如光子、胶子)不会被蜜糖沾黏,这些粒子的质量为零。希格斯场与不同种类的粒子,两者之间的耦合不同。第二、蜜糖施加于被沾黏物体的作用力为阻力,不论物体的速度为何,都会感受到这阻力,而质量是与物体的加速度运动有关,物体质量越大,必须施加越大的作用力才能给出同样的加速度。 更精致地,可以将希格斯场比拟为在物理学术大会里均匀分布的学者。无名人士可以轻松地穿过会场,没有人会注意到他的存在,就如同希格斯场与零质量光子之间的相互作用。假若物理大师进入会场,大家会被大师的魅力吸引,在大师四周挤成一团。因此,他会获得很多质量。若以同样速度穿过会场,他所具有的动量当然会比较大,改变他的移动速度也比较不容易,必须施加更大的作用力,就如同希格斯场赋予W玻色子或Z玻色子质量后的物理效应。这点子源自凝聚体物理学。在晶体里,带正电原子的晶格排列具有周期性,当电子移动穿过晶格时,带正电原子会施加库伦力于这电子,使这电子的有效质量大大增加。 我们还需要了解自发性对称破缺,量子力学的真空与一般认知的真空不同。在量子力学里,真空并不是全无一物的空间,虚粒子会持续地随机生成或湮灭于空间的任意位置,这会造成奥妙的量子效应。将这些量子效应纳入考量之后,空间的最低能量态,是在所有能量态之中,能量最低的能量态,不具有额外能量来制造粒子,又称为基态或“真空态”。最低能量态的空间才是量子力学的真空。 设想某种对称群变换,只能将最低能量态变换为自己,则称最低能量态对于这种变换具有“不变性”,即最低能量态具有这种对称性。尽管一个物理系统的拉格朗日量对于某种对称群变换具有不变性,并不意味着它的最低能量态对于这种对称群变换也具有不变性。假若拉格朗日量与最低能量态都具有同样的不变性,则称这物理系统对于这种变换具有“外显的对称性”;假若只有拉格朗日量具有不变性,而最低能量态不具有不变性,则称这物理系统的对称性被自发打破,或者称这物理系统的对称性被隐藏,这现象称为“自发对称性破缺”。 如右图所示,假设在墨西哥帽(sombrero)的帽顶有一个圆球。这个圆球是处于旋转对称性状态,对于绕着帽子中心轴的旋转,圆球的位置不变。这圆球也处于局部最大引力势的状态,极不稳定,稍加摄动,就可以促使圆球滚落至帽子谷底的任意位置,因此降低至最小引力势位置,使得旋转对称性被打破。 尽管这圆球在帽子谷底的所有可能位置因旋转对称性而相互关联,圆球实际实现的帽子谷底位置不具有旋转对称性──对于绕着帽子中心轴的旋转,圆球的位置会改变。 在帽子谷底有无穷多个不同、简并的最低能量态,都具有同样的最低能量。对于绕着帽子中心轴的旋转,会将圆球所处的最低能量态变换至另一个不同的最低能量态,除非旋转角度为360°的整数倍数,所以,圆球的最低能量态对于旋转变换不具有不变性,即不具有旋转对称性。总结,这物理系统的拉格朗日量具有旋转对称性,但最低能量态不具有旋转对称性,因此出现自发对称性破缺现象。 有数学能力强的同学,可以看一下数学表述。 假若希格斯场不存在,则夸克、W玻色子、Z玻色子的质量都会变为零。由于像质子、中子一类复合粒子的质量,只有约1%是归因于其所含有的夸克,它们的性质只会有些小改变。τ子、μ子的质量也会变为零,但是它们与现实生活没什么关系。只有电子的质量变为零会对世界带来很大影响。电子质量越小,原子的尺寸越大。当电子质量变为零之时,超特大尺寸的原子会因相互碰撞,将整个原子拆散,所有原子核与电子会混合在一起,原子无法单独存在,也不会有水、空气与人类所生存的世界。 希格斯场能够打破对称性。假若没有希格斯场,则所有带电荷轻子,即电子、τ子、μ子,都会变得一样,因为它们原本相互区分的质量都变为零了。类似地,带电荷为+2/3的夸克,即上夸克、奇夸克、顶夸克都会变得一样;而带电荷为-1/3的夸克,即下夸克、粲夸克、底夸克也都变得一样。 有些宇宙学者认为希格斯场是真空能量的起源。在宇宙的最初时刻,温度特高,希格斯场的对称性毫无任何特征,宇宙能量也同样的没有些微区别。由于宇宙温度的降低,在之后接连发生的几次相变所造成的对称性破缺给出了千变万化的宇宙。 最后一个相变所造成的对称性破缺打破了电弱力,使得弱作用力与电磁作用力被分离。现在,物理学者已有能力做出达到这相变所需条件的实验,但是分离电弱作用力与强作用力的相变所需条件仍旧远不可及。不论如何,被公认为静质量起源的希格斯场也是研究强作用力的关键。 根据大统一理论,当温度高过大统一温度时(1029K,对应于平均热能为1016GeV的温度,注意到太阳中心温度仅为107K),由于希格斯场可以拥有更多的能量,它的能量密度也随着增加,开始剧烈震动,它的位置不再局限于墨西哥帽的谷底,它的平均位置是在帽子中心,希格斯场的对称性又恢复如前。这时,电弱作用力与强作用力会统一为电核作用力(electronuclear force),传递电弱作用力的玻色子(光子)与传递强作用力的玻色子(胶子)的任何特征性质也都烟消云散,它们的物理行为完全一样。 大统一理论假定有很多种不同强度的希格斯场(注意到最小标准模型(minimal standard model)只假定有一个希格斯场)。假设温度低于大统一温度,则希格斯场可以发挥作用。不同的粒子与不同的希格斯场相互作用,而粒子的质量就是由这相互作用决定,这样,电子、W玻色子、Z玻色子、夸克等等分别获得其特定的质量,而光子、胶子也因此不拥有质量。由于W玻色子、Z玻色子特别沉重,质量分别为80GeV、91GeV,弱相对作用的距离极短,而电磁相对作用的距离几乎为无穷远。 近期,从各方面独立观测得到的结果,包括宇宙微波背景辐射、宇宙的大尺度结构等等,证实了宇宙正在加速膨胀,天文学者认为解释宇宙加速膨胀的模型可能是某种形式的暗能量,而这暗能量可能是源自希格斯场的真空能量。 我在《变化》中就真空不空,也提出过这样的观点。在我们对宇宙根本的法则不知情的情况下,任何关于暗能量,暗物质的理论只是限于我们的认知。其实他们可能就是真空能量,而不是我们现在口中所说的暗能量的概念。 在这里还要跟大家强调一点,那就是希格斯机制和希格斯场是两回事。就好比希格斯机制是方法,希格斯场是平台,用这样的方法,在这个平台上给粒子赋予质量。这就是希格斯机制和希格斯场的作用。 所以下面再为大家介绍一下希格斯机制。很明显,希格斯机制(英语:Higgs mechanism)是一种生成质量的机制,能够使基本粒子获得质量。 为什么费米子、W玻色子、Z玻色子具有质量,而光子、胶子的质量为零?希格斯机制可以解释这问题。希格斯机制应用自发对称性破缺来赋予规范玻色子质量。在所有可以赋予规范玻色子质量,而同时又遵守规范理论的可能机制中,这是最简单的机制。根据希格斯机制,希格斯场遍布于宇宙,有些基本粒子因为与希格斯场之间相互作用而获得质量。 更仔细地解释,在规范场论里,为了满足定域规范不变性,必须设定规范玻色子的质量为零。由于希格斯场的真空期望值不等于零,造成自发对称性破缺,因此规范玻色子会获得质量,同时生成一种零质量玻色子,称为戈德斯通玻色子,而希格斯玻色子则是伴随着希格斯场的粒子,是希格斯场的振动。通过选择适当的规范,戈德斯通玻色子会被抵销,只存留带质量希格斯玻色子与带质量规范矢量场。 费米子也是因为与希格斯场相互作用而获得质量,但它们获得质量的方式不同于W玻色子、Z玻色子的方式。在规范场论里,为了满足定域规范不变性,必须设定费米子的质量为零。通过汤川耦合,费米子也可以因为自发对称性破缺而获得质量。这个上面已经表述过。 需要相关数学描述的,可以参考下面截图文献资料【来源于维基百科】,可以作为图片放大看: 数学描述仅限于高等物理学生参考,普通科普学习者,可以略过。但要理解和认识希格斯机制和希格斯场。知道在我们生活的宇宙中,有这一法则,就已经是领略了一种美。 我自己就属于后者,这样数学描述,我看了也头疼。但我依然喜欢去知道一些我不知道,我不了解的东西。我希望你们也喜欢知道一些不为大众所熟知的东西。 因为有些东西,一定要有一些人知道,才能传承,才能发展。 摘自独立学者,诗人,作家,国学起名师灵遁者量子力学书籍《见微知著》编辑于 2018-09-17 16:23​赞同 124​​4 条评论​分享​收藏​喜欢

玻色-爱因斯坦分布(Boson-Einstein Distribution)、光子气体、黑体辐射 - 知乎

玻色-爱因斯坦分布(Boson-Einstein Distribution)、光子气体、黑体辐射 - 知乎切换模式写文章登录/注册玻色-爱因斯坦分布(Boson-Einstein Distribution)、光子气体、黑体辐射Ang5.0USTC量子物理/地理区划迷/非典型直男在近代物理学发展的过程中,黑体辐射(Blackbody radiation)起到了举足轻重的作用。可以说,对于黑体辐射的研究和现象解释,直接导致了近代物理学史无前例的一场革命——开启了量子物理的新纪元。最近我个人在研究关于黑体辐射的有关话题,发现黑体辐射这一模块跟许多物理学分支都有所关联——几乎把四大力学的各种知识都运用上了(至于量子力学则只是一个开端)。对于黑体辐射的终极公式——普朗克公式,也可以通过许多角度来进行推导,但是最终我们都绕不开统计物理的相关内容。我本人也是对统计物理这一领域比较感兴趣,正好能够借此机会整理一下相关的知识。首先,我们要明白黑体辐射本质上是一种热辐射,就是由于物理具有温度而辐射电磁波的现象。当然这个定义是基于波的观点来定义的。根据波粒二象性,既然能够运用波的观点来解释热辐射现象,也一定可以利用与之等效的粒子观点来进行解释。而与热辐射对应的“粒子”实际上就是我们平常说的“光子”,也就是“光量子”。这时候,我们就可以说热辐射就是指物体以往外发射光子的形式放出能量。我们要通过粒子的角度研究黑体辐射(源于量子化假设),首先就要研究光子在不同能级上的分布(也即“光子气体”)。·我们首先注意到光子自旋量子数为1,说明光子是一种玻色子(自旋量子数是整数的粒子)。常见的粒子分布有3种——一是玻尔兹曼分布(适用于满足经典极限的粒子);二是玻色——爱因斯坦分布(适用于玻色子);三是费米——狄拉克分布(适用于费米子)。为了简便,我们首先来研究全同(具有完全相同的内禀属性,例如质量、电荷、自旋等)、近独立(粒子之间相互作用很弱,因而满足能量可加性)的例子。对于更普遍的情形,我将会用系综理论来再次进行更加严格的推导。研究粒子的分布,对于可分辨的粒子而言,关键是要确定每一个粒子的量子态(一般来讲,一个系统有多个能级,一个能级又有多个量子态);而对于不可分辨的粒子而言,则主要是确定每个量子态上的粒子数。由经典粒子组成的系统称为玻尔兹曼系统,它是由可分辨的全同近独立粒子构成,且处于每个量子态上的粒子数不受限制(玻尔兹曼最早的假设,建立时间远早于量子力学)。由玻色子组成的系统叫做玻色系统,认为粒子是不可分辨的,每一个量子态容纳的粒子不受限制。由费米子组成的系统叫费米系统,费米分布中粒子同样是不可分辨的,但是根据泡利不相容原理,在含有多个全同近独立粒子的费米子系统中,一个个体量子态最多只能容纳一个费米子。因此,对于三种分布而言,计算微观态可能数目的公式也是不同的。接下来我们将建立三种分布的微观态计算公式。首先假设一个系统,由大量全同近独立粒子组成,具有确定的粒子数 N ,能量 E 和体积 V ,以 \epsilon_{l}(l=1,2,3,...) 代表粒子的能级, \omega_{l} 代表能级 \epsilon_{l} 的简并度, a_l 代表能级\epsilon_{l}上的粒子数。为了方便起见,我们用数列 \left\{ a_l \right\} 来表示粒子的分布。对于具有确定N、E、V的分布,需要满足以下约束条件:\sum_{l}{a_l}=N \sum_{l}{a_{l}\epsilon_l}=E 才可以实现。接下来其实就是数学上的排列组合问题了,这里我不在详细介绍了,直接给出最终表达式:对于玻尔兹曼系统:\Omega_{M.B.}=\frac{N!}{\prod_{l}a_l}\prod_{l}\omega_l^{a_l} 对于玻色系统:\Omega _{B.E.}=\prod_{l}\frac{(\omega_l+a_l-1)!}{a_l!(\omega_l-1)!} 对于费米系统:\Omega_{F.D.}=\frac{\omega_l!}{a_l!(\omega_l-a_l)!} 我们注意到在条件 \frac{a_l}{\omega_l}<<1 (对所有的 l)下(即经典极限条件或非简并性条件),有下面表达式成立:\Omega_{B.E.}\approx\Omega_{F.D.}\approx\frac{\Omega_{M.B.}}{N!} 经典极限条件表明,在所有的能级,粒子数都远远小于量子态数。也就是说,平均而言每一个量子态上的粒子数远远小于1.这时候玻色系统、费米系统跟玻尔兹曼系统的差距就体现在因子 \frac{1}{N!} 上(相当于经典系统)。我们重点关注玻色系统。采用热力学中处理的方法,即采用拉格朗日乘子法,解决条件极值问题。首先我们对玻色系统的微观态取对数,得到:ln \Omega=\Sigma_{l}[ln (\omega_l+a_l-1)!-lna_l!-ln(\omega_l-1)!] 假设 a_l>>1 , \omega_l>>1 ,因此 \omega_l+a_l-1\approx\omega_l+a_l , \omega_l-1\approx\omega_l ,同时采用近似式lnm! \approx m(lnm-1) 我们有 ln\Omega=\sum_{a}[{(\omega_l+a_l)ln(\omega_l+a_l)-a_llna_l-\omega_lln\omega_l}] 取变分:\delta ln \Omega=\sum_{l}[{ln(\omega_l+a_l)-lna_l]\delta a_l} 但是每个 \delta a_l 不是完全独立的,必须满足条件:\delta N=\sum_{l}{\delta a_l}=0 \delta E=\sum_{l}{\epsilon_l\delta a_l}=0 根据拉格朗日乘子法原理,上式中每一个\delta a_l的系数都必须为0:ln (\omega_l+a_l)-ln a_l-\alpha-\beta \epsilon_l=0 即a_l=\frac{\omega_l}{e^{\alpha+\beta\epsilon_l}-1} 其中,系数 \alpha 和 \beta 由约束条件确定。实际上我们可以根据热力学公式得到表达式:\alpha=-\frac{\mu}{kT} , \beta=\frac{1}{kT} 这时经典极限条件可以写为: e^\alpha>>1 至此,我们成功地推出了玻色-爱因斯坦分布的表达式。但是,我们推导以上公式的时候,为了简便计算,采用了条件a_l>>1 , \omega_l>>1,这个条件是不满足一般性的。我们将采用巨正则系综的方法重新推导这一分布。“系综”这个统计学概念,是指在一定的宏观条件下,由大量性质和结构完全相同的、处于各种运动状态的、各自独立的系统组成的集合。至于巨正则系综,指的是具有确定 \mu 、 V 、 T 的系统组成的系综,相当于一个与热源和粒子源接触形成的系统。由于系统和源可以交换粒子和能量,在系统可能的微观状态下,其粒子和能量值是不确定的(但是化学势是确定的)。这时就有疑问了:在之前推导玻色分布的过程中,总能量跟粒子总数不是确定的吗?这里实际上是把每个能级的能量和粒子数进行求和的,也就是说,每个能级看成了一个系统,不同能级组成了一个系综。由于不同能级之间的能量值是不确定的,因此可以利用巨正则系综来进行求解。巨正则分布为:\rho_{Ns}=\frac{1}{\Xi}e^{-\alpha N-\beta E_s} 其中 \Xi 是巨配分函数\Xi=\sum_{N}\sum_{s}{e^{-\alpha N-\beta E_s}} 考虑粒子的简并性,下面来推导近独立粒子的平均分布。用 \epsilon_l (l=1,2,3...) 表示粒子的能级, \omega_l 表示能级\epsilon_l的简并度。在给定粒各能级的分布 \left\{ a_l \right\} 后,系统的粒子数 N 和能量 E 为N=\sum_{l}{a_l} , E=\sum_{l}{\epsilon_l a_l} 上面推得玻色系统可能微观状态数:\Omega=\prod_{l}\Omega_l=\prod_{l}\frac{(\omega_l+a_l-1)!}{a_l!(\omega_l-1)!} 为求巨配分函数,当将对系统所有可能的粒子数 N 和状态 S 求和变换为对可能的分布 \left\{ a_l \right\} 求和时,必须乘上一个分布所对应的系统的微观状态数 \Omega 。因此\Xi=\sum_{N}\sum_{s}{e^{-\alpha N-\beta E_s}} =\sum_{\left\{ a_l \right\}}{\Omega e^{-\sum_{l}{(\alpha+\beta \epsilon_l)a_l}}} =\sum_{\left\{ a_l \right\}}{\prod_{l}\Omega_le^{-(\alpha+\beta \epsilon_l)a_l}} =\prod_{l}\sum_{ a_l }{\Omega_le^{(-\alpha+\beta \epsilon_l)a_l}} =\prod_{l}\Xi_l 其中, \Xi_l=\sum_{a_l}{\Omega_le^{-(\alpha+\beta \epsilon_l)a_l}} 对于玻色粒子,我们有\Xi_l=\sum_{a_l=0}^{\infty}{C_{\omega_l+a_l-1}^{a_l}}e^{-(\alpha+\beta \epsilon_l)a_l} =[1-e^{-(\alpha+\beta \epsilon_l)}]^{-\omega_l} (广义二项式定理)ln \Xi_l=-\omega_lln[1-e^{-(\alpha+\beta \epsilon_l)}] 每个能级的平均粒子数为:\bar{a_l}=-\frac{\partial}{\partial \alpha}ln\Xi_l=\frac{\omega_l}{e^{\alpha+\beta \epsilon_l}-1} 得出的方法与用热力学公式相同,且在计算过程中没有经过近似处理。到此为止,我们成功地得到了玻色-爱因斯坦分布的表达式。然后回归我们最初的问题——黑体辐射问题。根据粒子的观点,我们可以把空腔内的辐射场看做光子气体。当然,我们也有对应的波动处理方法——将辐射场看做无穷多个平面波的叠加。当然,这两种表述是等价的。根据波粒二象性的相关公式,我们可以得到光子的能量——动量关系\varepsilon=cp 由于光子是玻色子,达到平衡之后遵从玻色分布。由于窖壁不断发射和吸收光子,光子气体中光子数是不守恒的(这也是跟之前推导玻色分布的一个很大的不同所在)。因此我们只需要引入一个拉格朗日乘子 \beta ,同时取平衡时的化学势为0,即 \alpha=0 ,此时光子气体的分布为: a_l=\frac{\omega_l}{e^{\beta \epsilon_l}-1} 利用经典的瑞利——金斯的方法可得在体积为 V 的空窖内,在 \omega\sim\omega+d\omega 的圆频率范围内,光子的量子态数为:\frac{V}{\pi^2c^3}\omega^2d\omega 利用刚才所得分布可以求出辐射场的内能:U(\omega,T)d\omega=\frac{V}{\pi^2c^3}\frac{h\omega^3}{2\pi( e^{h\omega/2\pi kT}-1)}d\omega 此式符合普朗克公式的结论。总结一下整个推导过程,我首先通过玻色子的性质出发,利用热力学方法推导出玻色-爱因斯坦分布,然后通过系综理论严格证明了分布表达式,最后应用在黑体辐射中普朗克公式的表达当中。我通过写这篇文章,算是重新温习了热统的一些内容,并且把跟明天(不对,今天晚上)就要做的黑体辐射报告完美地结合起来。在这里祝福自己的报告能够顺利完成。发布于 2019-04-25 01:19物理学​赞同 80​​4 条评论​分享​喜欢​收藏​申请

Boson | Elementary, Force Carrier & Quantum | Britannica

Boson | Elementary, Force Carrier & Quantum | Britannica

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Also known as: vector gauge boson

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Science & Tech

Key People:

Peter Higgs

François Englert

Satyendra Nath Bose

(Show more)

Related Topics:

photon

gluon

graviton

intermediate vector boson

photino

(Show more)

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boson, subatomic particle with integral spin (i.e., angular momentum in quantum-mechanical units of 0, 1, etc.) that is governed by the Bose-Einstein statistics (q.v.). Bosons include mesons (e.g., pions and kaons), nuclei of even mass number (e.g., helium-4), and the particles required to embody the fields of quantum field theory (e.g., photons and gluons). Bosons differ significantly from a group of subatomic particles known as fermions in that there is no limit to the number that can occupy the same quantum state. This behaviour gives rise, for example, to the remarkable properties of helium-4 when it is cooled to become a superfluid.

二次量子化算符表达式推导:Boson - 知乎

二次量子化算符表达式推导:Boson - 知乎切换模式写文章登录/注册二次量子化算符表达式推导:Boson毛咕咕每天玩苹果手机,博士学位远离你鉴于许多教科书对于二次量子化构造语焉不详,给初学者带来一定困难。本文从波函数对称/反称化出发给出物理量算符在二次量子化后的表达形式。朗道量子力学一书曾指出二次量子化以及其算符表达式是多粒子体系波函数对称/反称化的直接结果,然而并未给出详细推导过程。该推导过程较为繁琐却并不困难,在此我们给出这个过程的详细推导。对于多粒子体系 \varphi(x_1,...x_n) ,设 P_{12} 为粒子交换算符。由粒子全同性 P_{12}\varphi=\lambda\varphi ,且 P_{12}^2=1 。 因此 \lambda^2=1 。对于Boson子, \lambda=1 。因此可以取一组对称的体系波函数为基函数, \varphi(x_1,...x_n)=\sqrt{\frac{N_1!N_2!...N_s!}{N!}}\sum\varphi_{i_1}(x_1)\varphi_{i_2}(x_2)...\varphi_{i_n}(x_n)= 。 N_j 表示有 N_j 个单粒子波函数 \varphi_{i_k}(x_k) 处在第 E_j 个态。由排列组合基本原理, \sqrt{\frac{N_1!N_2!...N_s!}{N!}} 为归一化系数。因此二次量子化是以粒子数为表象的另一组基函数,可以更方便得表示对称化/反对称化后的波函数。利用单粒子波函数正交性易证明,当粒子数分布不一时, =0 。单粒子算符表达式接下来我们计算单粒子算符 \hat{F}^1=\hat{f}(x_1)+\hat{f}(x_2)+...\hat{f}(x_n) ,在二次量子化下的表达式。我们记 [i_1,i_2,...]=\varphi_{i_1}(x_1)\varphi_{i_2}(x_2)...\varphi_{i_n}(x_n) 。我们首先计算 I_1= , I_1=\sum_{\sigma}\sqrt{\frac{N_1!(N_2-1)!...N_s!}{N!}}\sqrt{\frac{(N_1-1)!N_2!...N_s!}{N!}}<[E_1,...]|f(x_1)|[E_2,...]> 对波函数的求和只剩下如上形式( x_1坐标的波函数只能在E_1/E_2态下 ),这是由于其他排列下由于粒子数不同, x_2-x_n的波函数积分全部为零 。对x_2-x_n的波函数积分求和得到 \frac{(N-1)!}{(N_1-1)!(N_2-1)!...N_s!} 。因此 I_1=\frac{\sqrt{N_1N_2}}{N}f^1_{12} ,对 I_k 求和可得 I=\sqrt{N_1N_2}f^1_{12} 。定义 a_i^{\dagger}|Ni-1> = \sqrt{N_i}|N_i> 以及 a_i^{}|N_i> = \sqrt{N_i}|N_i-1> 。因此 \hat{F}^1 = f_{ik}a_i^{\dagger}a_k 在 |N_1-1,N_2> (i=1,k=2)下满足。由形式对称性,其他态 (i\ne k )下该表达式也满足。此外易证, I_1==\frac{N_1}{N}f_{11}+\frac{N_2}{N}f_{22}+... 。因此 I=\sum N_if_{ii} ,故 \hat{F}^1 = f_{ik}a_i^{\dagger}a_k 也满足。至此,证明了单粒子算符在二次量子化下的算符表达形式 \hat{F}^1 = f_{ik}a_i^{\dagger}a_k 。双粒子算符表达式下面给出Boson子双粒子算符的表达式推导。双粒子算符常见于相互作用势能算符中,如电子两两相互作用等。\hat{F}^2=\sum_{aa^\dagger_ia^\dagger_ja_la_k 验证 \frac{1}{2}a^\dagger_ia^\dagger_ia_ja_j 项。I_1=\\ ~~~~=\frac{\sqrt{N_1!(N_2-2)!(N_1-2)!N_2!}}{N!}\sum_{\sigma}<[1,1,...]|\hat{f}(x_1,x_2)|[2,2,...]>类似上部分讨论,除了该表达式形式,其余组合均为零(第三项开始的粒子数不守恒且无相互作用函数,因此积分必为零)。对 \sigma 的求和得到系数 \frac{(N-2)!}{(N_1-2)!(N_2-2)!} ,(忽略 N_3,N_4,... 因为最终被约化)。由此得到,I_1=\frac{\sqrt{N_1(N_1-1)N_2(N_2-1)}}{N(N-1)}f_{1122}\Rightarrow \\I=\frac{1}{2}\sqrt{N_1(N_1-1)N_2(N_2-1)}f_{1122} 因此 \frac{1}{2}a^\dagger_ia^\dagger_ia_ja_j 项满足。2. 计算 I_1= (1) s\ne 1, 2 I_{11}=\sum_{s}\frac{\sqrt{(N_1-1)!N_2!N_1!(N_2-1)!}(N_s-1)!}{N!}\sum_{\sigma}<[1,s,...]|f(x_1,x_2)|[2,s,...]> ,其中对 \sigma 的求和代表[a,b,...]中"..."的所有组合的求和,积分求和后得到系数 \frac{(N-2)!}{(N_1-1)!(N_2-1)!(N_s-1)!} 。因此, I_{11}=\frac{\sqrt{N_1N_2}N_s}{N(N-1)}f_{1s2s} ,对 f(x_i,x_j)的任意两粒子求和得,I_1=\frac{\sqrt{N_1N_2}N_s}{2}f_{1s2s} 。因此 I_1=\frac{1}{2}<1s|\hat{F}^2|2s>a^\dagger_1a^\dagger_sa_2a_s 项满足。同理, I’_1=\frac{1}{2}a^\dagger_sa^\dagger_1a_sa_2 项也满足。(2) s=1 I_{21}=\frac{\sqrt{(N_1-1)!N_2!N_1!(N_2-1)!}}{N!}\sum_{\sigma}<[1,1,...]|f(x_1,x_2)|[2,1,...]> ,其中对 \sigma 的求和代表[a,b,...]中"..."的所有组合的求和,积分后得到系数 \frac{(N-2)!}{(N_1-2)!(N_2-1)!} 。因此, I_{21}=\frac{\sqrt{N_1N_2}(N_1-1)}{N(N-1)}f_{1121} ,对 f(x_i,x_j)的任意两粒子求和得,I_2=\frac{\sqrt{N_1N_2}(N_1-1)}{2}f_{1121} 。因此 I_2=\frac{1}{2}<11|\hat{F}^2|21>a^\dagger_1a^\dagger_1a_2a_1 项满足。同理, I’_2=\frac{1}{2}<11|\hat{F}^2|12>a^\dagger_1a^\dagger_1a_1a_2 项也满足。(3) s=2同理可得。因此,综合步骤(1),(2),(3)可得,I= 满足 \hat{F}^2=\sum_{i,j,k,l}\frac{1}{2}a^\dagger_ia^\dagger_ja_la_k 。3. I_1= ,需验证 <[k,k,...]|f(x_1,x_2)|[k,k,...]>,<[i,j,...]|f(x_1,x_2)|[i,j,...]>,<[i,j,...]|f(x_1,x_2)|[j,i,...]> 等项即可。编辑于 2022-10-29 12:18算符量子物理​赞同​​1 条评论​分享​喜欢​收藏​申请

The Z boson | CERN

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This image taken by the UA1 experiment on 30 April 1983 was the first detection of a Z0 particle.

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The Z boson

The Z boson is a neutral elementary particle that - along with its electrically charged cousin, the W boson - carries the weak force

Discovered in 1983 by physicists at the Super Proton Synchrotron (SPS) at CERN, the Z boson is a neutral elementary particle. Like its electrically charged cousin, the W boson, the Z boson carries the weak force.

The weak force is essentially as strong as the electromagnetic force, but it appears weak because its influence is limited by the large mass of the W and Z bosons. Their mass limits the range of the weak force to about 10-18 metres, and it vanishes altogether beyond the radius of a single proton.

Enrico Fermi was the first to put forth a theory of the weak force in 1933, but it was not until the 1960s that Sheldon Glashow, Abdus Salam and Steven Weinberg developed the theory in its present form, when they proposed that the weak and electromagnetic forces are actually different manifestations of one electroweak force. 

By emitting an electrically charged W boson, the weak force can cause a particle such as the proton to change its charge by changing the flavour of its quarks. In 1958, Sidney Bludman suggested that there might be another arm of the weak force, the so-called "weak neutral current," mediated by an uncharged partner of the W bosons, which later became known as the Z boson.

Physicists working with the Gargamelle bubble chamber experiment at CERN presented the first convincing evidence to support this idea in 1973. Neutrinos are particles that interact only via the weak interaction, and when the physicists examined collisions they were able to detect evidence of the weak neutral current, and hence indirect evidence for the Z boson.

At the end of the 1970s, physicists Carlo Rubbia, Peter McIntyre and David Cline suggested converting what was then CERN’s biggest accelerator, the Super Proton Synchrotron, to operate as a proton-antiproton collider, with the aim of producing W and Z bosons directly. Both types of particle were observed there for the first time in 1983 by the UA1 and UA2 experiments.

The bosons were then studied in more detail at CERN and at Fermi National Accelerator Laboratory in the US. In 1989, first physics results from the Large Electron-Positron collider at CERN measured the width of the Z boson and confirmed that there are only three neutrino types in Nature: electron, muon and tau. During the 1990s, LEP and the SLAC Linear Collider in the US produced millions of Z bosons for further study. These results culminated in the need to search for the final piece of the Standard Model – the Higgs boson, which was discovered in July 2012.

The discovery of W and Z bosons was an extraordinary technical triumph, confirming a critical aspect of the Standard Model. As a result, the 1984 Nobel prize in physics was awarded to Carlo Rubbia and Simon van der Meer.

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What are bosons? | Space

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The Universe

What are bosons?

References

By Robert Lea last updated 21 September 2022

Bosons are 'sociable' particle and the cosmos would be a dull place without them

An illustration of two bosons produced by two colliding protons.

(Image credit: Mark Garlick/Getty Images)

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Bosons: What makes a particle a boson?

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Bosons are particles that carry energy and forces throughout the universe. The standard model of particle physics  —  the most robust theory we have of the sub-atomic world  —  divides every particle in the universe and even the larger composite particles fit into two broad categories; fermions and bosons. Fermions such as quarks, electrons, neutrinos, protons, and neutrons are the foundation of matter, while one category of bosons, the gauge bosons, are responsible for acting as the 'carriers' of at least three of the four fundamental forces  —  electromagnetism, the strong nuclear force, and the weak nuclear force. That means that fermions interact with each other via the exchange of gauge bosons.

There may also be a boson to carry the force of gravity, but that isn't currently certain. The gauge bosons are fundamental particles  —  meaning they're not comprised of smaller particles  —  but there are other bosons that are composed of smaller particles. Related: Higgs boson: The 'God Particle' explainedRobert LeaSocial Links NavigationScience journalistRobert Lea holds a bachelor of science degree in physics and astronomy from the U.K.'s Open University. Robert has contributed to Space.com for over a decade, and his work has appeared in Physics World, New Scientist, Astronomy Magazine, All About Space and more. Bosons: What makes a particle a boson?Bosons take their name from Indian physicist Satyendra Nath Bose who conducted important research in the 1920s regarding the behavior of the most famous boson  —  the photon.One of the key defining characteristics of bosons relates to a quantum mechanical quality called 'spin'  which can be thought of as the deflection a particle takes as it experiences a magnetic field imparting angular momentum.

Though similar, spin is more complex than angular momentum in the macroscopic world of classical physics, mainly because particles can have fractions of spin, meaning there is no real 'classical' way of describing spin.A fermion is a particle with 1/2 spin that can have plus or minus values. This means that fermions can have values such as 1/2, -1/2, 3/2, and -3/2. The plus or minus determines the direction of intrinsic angular momentum particle will take.Because bosons don't obey the Pauli exclusion principle they are free to occupy the same quantum numbers, unlike 'unsocial' fermions. The dashed red line represents the formation of Bose-Einstein condensates.  (Image credit: Robert Lea)Bosons, on the other hand, have whole integer spins including zero. This means the spin values these particles can take are 0, 1, -1, 2, -2, and so on.Mathematically adding two halves together makes a whole integer, and in a similar way, combining even numbers of fermions creates a larger particle that is a boson.These include mesons  —  which form when two quarks bond  —  and even atoms with even numbers of fermions. For example, helium-4 atoms are bosons because they consist of two protons, two neutrons, and two electrons. Helium-4 atoms will take a special relevance when thinking about the special and unique properties of bosons.What are the different bosons?Bosons can be divided up a few ways, but to introduce the different particles that make up this wing of the 'particle zoo' it's handy to sort them into two rough groupings  —  particles we have experimental evidence of, and those that are currently just theoretical. Discovered BosonsPhotonsEasily, the most famous gauge boson is the photon, the constituent particle of light and the mediator of the electromagnetic force. For photons  —  which have a spin of 1  —  spin is the quantum mechanical equivalent of polarization, or the direction in which a light wave is orientated. This means photon spins can be parallel or anti-parallel in orientation. Photons were the first gauge bosons to be discovered when at the turn of the 20th century Max Planck and Albert Einstein suggested light exists in packets of energy called 'quanta.' The name 'photon' was introduced for these quanta in 1928 by American chemist Gilbert Lewis. Related: The double-slit experiment: Is light a wave or a particle?The gauge bosons are responsible for carrying the fundamental forces of the universe.  (Image credit: Robert Lea)GluonsGluons, the second discovered gauge boson, are the bosons that carry the strong nuclear force. As a result, they are responsible for 'sticking' other particles together.

Specifically, gluons bind quarks together to create protons and neutrons. But gluons don't stop there: They also bind these composite particles  —  collectively called 'nucleons' — together in the atomic nucleus at the heart of all everyday matter.Gluons were discovered at the electron-positron collider PETRA of DESY, Germany, in 1979.The W and Z BosonsThe W and Z bosons are the gauge bosons responsible for carrying the weak nuclear force  —  stronger than gravity but only effective across incredibly short ranges. These spin 0 bosons are responsible for nuclear decay in which one element changes to another by helping protons change to neutrons and vice versa. One of the big problems with the W and Z bosons, which were found in 1983, was figuring out how they got their mass, as theories at the time suggested they should be massless like the photon.Higgs BosonsThe Higgs boson was first introduced into the standard model of particle physics to explain how the W and Z bosons got their mass, but its mass-granting role as the facilitator of the Higgs field was soon extended to almost all particles.The Higgs boson was discovered in 2012 emerging from high-energy proton-proton collisions at the Large Hadron Collider (LHC)  —  the world's most powerful particle accelerator. The Higgs boson has a proposed spin of 0 and its discovery is said to have completed the standard model, but there is still physics outside this model to discover. The exploration of physics beyond the standard model means there are other theoretical bosons to explore.Because bosons don't obey the Pauli exclusion principle they are free to occupy the same quantum numbers, unlike 'unsocial' fermions. The dashed red line represents the formation of Bose-Einstein condensates.  (Image credit: CERN)Theoretical BosonsGravitonsOne thing the framework of the standard model of particle physics can't describe is gravity. That's because quantum mechanics  —  the physics of the subatomic  —  and general relativity, Einstein's theory of gravity, don't mesh. The other fundamental forces get a gauge boson to carry them (and the weak force even gets two) so why shouldn't gravity? A gauge boson for gravity  —  the 'graviton'  —  has been theorized but has thus far failed to manifest experimentally. Because gravity is negligible at a sub-atomic level, missing gravitons and the lack of a 'quantum theory of gravity' hasn't hindered this model too much. Boson superpartnersOne potential model of physics beyond the standard model is 'supersymmetry.' This theory  —  proposed to 'fix' the mass of the Higgs boson  —  suggests that every fermion in the particle zoo has a bosonic partner.

The extra particles would help 'cancel out' some of the mass of the Higgs boson, explaining why it is relatively light.  Bosons: The 'sociable' particles Thanks to a phenomenon called the Pauli exclusion principle, half-integer spin fermions are incapable of possessing the same quantum numbers. This means that fermions are incapable of bunching together.Bosons, however, with their full integer spins, don't abide by the Pauli exclusion principle. This means they can closely group together giving rise to some unique physical properties. The most common example of 'social bosons' is laser light, which is comprised of photons with the same wavelength and frequency all moving in the same direction. Laser beams are composed of photons, a type of boson. (Image credit: Wladimir Bulgar/Getty Images)A more exotic example of bosons defying the Pauli exclusion principle was suggested in 1924. Albert Einstein and Bose determined that bosons should condense together in their ground state  —  the state of their lowest possible energy  —  leading to Bose-Einstein condensation, the creation of superfluidity in liquid helium cooled to 2.17 K and thus its lowest possible energy.Coupled electrons  —  called 'Cooper pairs'  — are classed as 'quasi-particles' and can be coerced into behaving like bosons, condensing into a state with zero electrical resistance. The creation of Bose-Einstein condensation in dilute gases of alkali atoms would win three researchers the Nobel Prize in Physics in 2001.Additional ReadingExplore the Higgs boson in more detail and discover why it's so special with CERN. Learn more about particle physics with this free course from The Open University. Bibliography"Fermions, Bosons." Hyperphysics (2022).

"The Standard Model." CERN (2022)."Meet a superpartner at the LHC." APS Physics (2010). "Supersymmetry." CERN (2022)."Discovery of the Gluon." Sau Lan Wu, University of Wisconsin-Madison/CERN,(2018). "This Month in Physics History." APS News (2012). Follow us on Twitter @Spacedotcom or on Facebook.  

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Robert LeaSocial Links NavigationContributing WriterRobert Lea is a science journalist in the U.K. whose articles have been published in Physics World, New Scientist, Astronomy Magazine, All About Space, Newsweek and ZME Science. He also writes about science communication for Elsevier and the European Journal of Physics. Rob holds a bachelor of science degree in physics and astronomy from the U.K.’s Open University. Follow him on Twitter @sciencef1rst.

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The basics of a boson | CERN

The basics of a boson | CERN

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(Video: TED-Ed/CERN)"The basics of a boson" – a lesson by Dave Barney of the CMS collaboration and Steven Goldfarb of the ATLAS collaboration. Animation by Jeanette Nørgaard for TED-Ed.

In 2012, physicists at CERN discovered evidence of the Higgs boson. The what? The Higgs boson is one of two types of fundamental particles, and it’s a particular game-changer in the field of particle physics, proving how particles gain mass. Using the Socratic method, CERN physicists Dave Barney and Steve Goldfarb explain the exciting implications of the Higgs boson.

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The Higgs boson turns ten | Nature

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The Higgs boson turns ten

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Published: 04 July 2022

The Higgs boson turns ten

Gavin P. Salam 

ORCID: orcid.org/0000-0002-2655-43731,2, Lian-Tao Wang3 & Giulia Zanderighi 

ORCID: orcid.org/0000-0001-6878-16494,5 

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volume 607, pages 41–47 (2022)Cite this article

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PhenomenologyTheoretical particle physics

AbstractThe discovery of the Higgs boson, ten years ago, was a milestone that opened the door to the study of a new sector of fundamental physical interactions. We review the role of the Higgs field in the Standard Model of particle physics and explain its impact on the world around us. We summarize the insights into Higgs physics revealed so far by ten years of work, discuss what remains to be determined and outline potential connections of the Higgs sector with unsolved mysteries of particle physics.

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A portrait of the Higgs boson by the CMS experiment ten years after the discovery

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MainTen years ago, on 4 July 2012, scientists and journalists gathered at CERN, and remotely around the world, for the announcement of the discovery of a new fundamental particle, the Higgs boson. The discovery, by the ATLAS1 and CMS2 collaborations at the Large Hadron Collider (LHC), came almost 50 years after theorists had postulated the existence of such a particle. The significance of the discovery was not only that a new, long-awaited particle had been found, but that the existence of this particle provides first direct evidence that surrounding us there is a new kind of fundamental ‘field’, known as the Higgs field.Fields in physics are familiar in everyday life, for example in the form of the earth’s magnetic field, and its impact on the needle of a compass. The most important difference between the Higgs field and a magnetic field is that if one removes the magnetic source, the magnetic field disappears. By contrast, the Higgs field is non-zero everywhere, all the time, independently of whether anything else is present in the Universe. In a way, it is reminiscent of the ancient Greek concept of Aether with the crucial difference that it is consistent with Einstein’s theory of special relativity.Physicists’ current theory of fundamental particles and forces is known as the Standard Model, a theoretical framework that provides a description of elementary particles and the forces that make them interact with one another, with the exception of gravity. Within the Standard Model, the Higgs field is essential to describe the world as we know it.As we shall see below, the strength of the interaction between any particle and the Higgs field directly affects a fundamental property of that particle: its mass. As such3, it ultimately determines the size of atoms, makes the proton stable and sets the timescale of radioactive (β) decays, which for example impact the lifetime of stars (Table 1). Yet, in everyday life, we do not notice that the Higgs field is all around us. The only way we have of revealing the Higgs field is to perturb it, a little like throwing a stone into water and seeing the ripples. The particle known as the Higgs boson is the manifestation of such a perturbation.Table 1 Ways in which the Higgs boson affects the world around usFull size tableThe significance of its discovery in 2012 was such that the Nobel prize was awarded one year later to François Englert and Peter Higgs who, with the late Robert Brout, were the first to discuss the potential importance of such a field for fundamental physics4,5,6. Since then, the Higgs boson has become a powerful tool to study the ways in which the underlying Higgs field affects the fundamental particles of the Standard Model. Furthermore, the ubiquity of the Higgs field means that the Higgs boson is, today, widely used in the search for signatures of particles or effects that are hitherto unknown and lie outside the Standard Model.The Higgs boson in the Standard ModelIn the Standard Model, aside from the Higgs boson, there are two kinds of particles. There are fermions, such as the up and down quarks and the electron, which make up ordinary matter. These specific particles (together with one of the three neutrinos) are called first-generation fermions. Two further sets of fermions (second and third generations) involve heavier particles, not normally present in the world around us. Additionally, there are the force carriers: the photon, the W and Z bosons and the gluon, collectively called vector bosons. When these are exchanged between two fermions, they create an attractive or repulsive force between those fermions: photons carry the electromagnetic force, W and Z bosons the weak force and gluons the strong force.In the 1960s, as physicists were taking the first steps towards assembling this picture, it remained unclear whether a self-consistent theory that included massive force carriers could be constructed. This question was being posed in the context of nuclear physics and also superconductivity in condensed matter physics. Researchers found that such a theory was ultimately possible if one introduced an interaction of the force carriers with a ‘Higgs’ field, and if one could also engineer a non-zero value for that field4,5,6,7,8,9.As the electroweak part of the Standard Model was being developed10,11,12, interactions of particles with a Higgs field were to become a central part of its formulation, especially in order to generate masses for the W and Z bosons, as required for consistency with experimental observations, while photons and gluons remain massless.Remarkably, interactions with the Higgs field also provided a consistent theoretical mechanism for producing fermion masses: each fermion interacts with the Higgs field with a different strength (or ‘coupling’), and the stronger the interaction, the larger the resulting mass for the particle. Within the Standard Model the interaction is known as a ‘Yukawa’ interaction13. Thus any question about the origin of the masses of fermions reduces to a question about the origin of the interactions of fermions with the Higgs field.Why is the Higgs field non-zero in the first place? According to the Standard Model there is a potential energy density associated with the value of the Higgs field and the lowest potential energy corresponds to a non-zero value of the Higgs field. The Standard Model potential has a form dictated by internal consistency conditions. With some simplifications, labelling the magnitude of the Higgs field as ϕ, the potential has the form$$V(\varphi )\propto -{\varphi }^{2}+\frac{1}{2}{\varphi }^{4}\,.$$

(1)

This is illustrated by the red line in Fig. 1. The minimum of the potential, that is, the energetically most favourable choice for ϕ, lies at a value of ϕ that is non-zero, ϕ = 1. An important implication of the non-zero constant value of the Higgs field is the impossibility to carry angular momentum, or more technically having ‘spin 0’. A non-zero value for the spin would break at least one of the well-tested space–time symmetries. Hence, the excitation of the Higgs field, the Higgs boson, must be a spin-0 particle and it is in fact the only known fundamental particle with this property.Fig. 1: Higgs potential.The potential energy density \(V(\varphi )\) associated with the Higgs field ϕ, as a function of the value of ϕ. The red curve shows the potential within the Standard Model. The Higgs field has a value corresponding to a minimum of the potential and the region highlighted in black represents our current experimental knowledge of the potential. Alternative potentials that differ substantially from the Standard Model away from that minimum (for example, the blue curve) would be equally consistent with current data.Full size imageOne of the reasons for the central importance of the discovery of the Higgs boson was that it finally made it possible to start testing the remarkable theoretical picture outlined above. It is not possible to probe the interactions of a given particle with the Higgs field. However, one can instead measure a particle’s interaction with the excitations of the Higgs field, that is, with a Higgs boson. If the Standard Model provides the correct picture for the generation of mass, the strength of any particle’s interaction with the Higgs boson has to be directly related to that particle’s mass.Aside from providing a powerful way of testing the Higgs mechanism, the interaction of the Higgs boson with other particles is intriguing because it implies the existence of a ‘fifth force’, mediated by the exchange of Higgs bosons. The fact that such a force is stronger for heavier particles makes it qualitatively different from all other interactions in the Standard Model, whose interaction strengths come in multiples of some basic unit of charge, like the electron charge for the electric force. The pattern is, if anything, more reminiscent of gravity, but with important differences. One is that the force mediated by the Higgs boson is active only at very short distances, whereas Einstein’s gravity acts over all distance scales. Another is that the Higgs boson couples directly only to elementary Standard Model particles. By contrast, gravity couples to the total mass. In ordinary matter, that total mass is much larger than the sum of the elementary particle masses, because the strong force contributes substantially to the proton and neutron masses14.What we know so far and howThe Higgs mechanism provides the simplest model to explain particle masses in a way that is consistent with the electroweak interactions. As physicists we should seek to establish whether it is the model chosen by nature.Experimental studies of the Higgs boson take place at particle colliders. The likelihood of producing a Higgs boson in a collision becomes larger when the particles that collide interact strongly with the Higgs field, that is, when they are heavy. At the high centre-of-mass energies that are required, particle physicists know how to collide just two things: protons and electrons, as well as their antiparticles. That poses an issue, because electrons and the particles that make up protons are light, that is, they interact only very weakly with the Higgs boson.The approach of particle physicists is to exploit the occasional production of heavy particles in the high-energy collision of light particles, and to then have those heavy particles produce a Higgs boson. CERN’s LHC collides protons, which are mostly made of up and down quarks and gluons. The most frequent way of producing a Higgs boson is for a pair of gluons, one from each proton, to collide and create a top quark and a top anti-quark as a very short-lived quantum fluctuation. The top quark is the heaviest known particle (about 184 times the proton mass) and so the top and anti-top quarks interact strongly with the Higgs field, thereby occasionally producing a Higgs boson. A short while later (about 10−22 s), the Higgs boson decays. About 2.6% of decays are to a pair of Z bosons, which themselves also decay almost immediately, for example each to an electron–positron or muon–anti-muon pair (so-called charged leptons), which gives a distinctive experimental signature. This sequence is illustrated in Fig. 2a.Fig. 2: Higgs production at the LHC.a, Illustration of one process for the production and decay of a Higgs boson at the LHC. b, Total centre-of-mass energy of four leptons (4l; electrons and/or muons and their antiparticles) from the CMS experiment; the peak around 125 GeV corresponds to decays of Higgs bosons, whereas the peak near 91.2 GeV corresponds to decays of single Z bosons (not Higgs-induced), adapted from ref. 95. The decay to Z bosons was one of the channels used for the discovery of the Higgs boson, with the other important discovery channels being the decay to two W bosons and that to two photons (the latter proceeds through a quantum fluctuation with top quarks and W bosons).Full size imageThe ATLAS and CMS experiments at the LHC select events with four such leptons and record the total of the energy of the leptons (in their centre-of-mass frame). There are a variety of ways in which four leptons can be produced, but for those events in which they come from a Higgs-boson decay, the total energy is expected to cluster around the Higgs mass—the red peak in Fig. 2b. That red peak provides considerable information: (1) the existence of the peak near 125 GeV tells us that there is a new particle, the Higgs boson; (2) the position of the peak indicates the mass of the Higgs boson; (3) other features of the events in the peak, for example the relative angular distributions of the leptons (not shown in the figure), confirm that the Higgs boson carries no intrinsic angular momentum, that is, it is a spin-0 particle; (4) the number of events in the peak is sensitive to the interaction strength of the Higgs boson both with top quarks and with Z bosons. This last point is crucial because the Standard Model Higgs mechanism predicts a very specific interaction strength of each particle with the Higgs boson. Point (4) provides us with a first test of this hypothesis.There are several potential concerns about the robustness of these kinds of test. For instance, in the process shown in Fig. 2 there is an assumption that there was a quantum fluctuation producing a top–anti-top pair. Even if that assumption is correct, the number of events in the peak tells us about the product of the top and Z interactions, not the top and Z interactions separately. For this reason, the LHC experiments look for the Higgs boson in a multitude of production and decay processes, each one with complementary sensitivity. For example, it is possible to observe Higgs-boson decays in events in which top quarks are not simply an evanescent quantum fluctuation, but are instead produced as short-lived real particles that emerge in their own right from the collision together with the Higgs boson and can be experimentally detected. Doing so15,16, in 2018, was a major milestone in particle physics, as were the highly challenging observations of the Higgs boson decaying to bottom quarks17,18 and τ leptons19,20. Together, these measurements conclusively established that the Higgs mechanism is responsible for the mass of the full third generation of charged fermions.Overall, by assembling information from different production and decay channels, a picture has emerged of Higgs interactions for the heaviest particles—both vector bosons and fermions—that is consistent with the Standard Model hypothesis to within the current measurement accuracies that range from 5% to 20%, as summarized in Fig. 3. On the other hand, interactions with very light particles, such as the electron and up and down quarks of which we are made of, are too rare for current methods to observe.Fig. 3: Status of our knowledge of Higgs interactions with known particles.a, Summary of which Higgs interactions have been conclusively established and future prospects. Photons and gluons are omitted because they are massless and do not interact directly with the Higgs field. Neutrinos are also omitted: their masses are very small relative to those of the other leptons shown, and not individually known. b, Plot of measured strength of interaction of particles with the Higgs boson versus particle mass, as determined by the ATLAS Collaboration (adapted from ref. 96). The straight line shows the expected Standard Model behaviour, in which the interaction strength is proportional to the mass of the fermions (squared mass for W and Z bosons). The CMS Collaboration has similar results97.Full size imageAlthough the discovery of the Standard Model Higgs boson was highly anticipated at the LHC, the ability to explore so many of its features was a surprise. To have established even part of the broad picture of Higgs-boson interactions in just ten years is a major achievement, especially when one considers that, at the time when the LHC was being commissioned, many of the production and decay channels that are central to today’s measurements were believed to be beyond the reach of the LHC21,22.There are many reasons why this progress has been possible. One of them is that nature happens to have chosen a value for the Higgs mass that is particularly fortunate for experimental studies. Had the Higgs boson been 50 GeV heavier, it would have been almost impossible to detect more than just two basic decay channels (to a pair of W bosons or a pair of Z bosons). Had it been just 10 GeV lighter, the decays to W bosons and Z bosons would probably have been impossible to see so far. It was not just a question of good fortune, however.The excellent performance of the LHC accelerator and of the ATLAS and CMS detectors, each of them a highly complex system, has been crucial. Furthermore, in the past ten years, there have been major advances in techniques for analysing collider data. One facet has been to learn how to reliably extract information about individual proton–proton collisions when detectors contain not just one proton–proton collision at a time, but dozens filling the detector simultaneously, 40 million times per second23,24. Another reflects the fact that the beautifully clear peak in Fig. 2b is the exception rather than the rule: for most other Higgs-boson studies (for example, Higgs decay to two bottom quarks or two W bosons), experimenters and theorists have had to develop a wide range of technology for differentiating Higgs-boson signals from the many processes with signatures similar to that of a Higgs boson, but that do not involve a Higgs boson. These studies are increasingly benefiting from a combination of new ideas for how to perform the analyses (for example, ref. 25) and the power of machine learning26.The quantitative interpretation of observed signal rates in terms of Higgs interaction strengths would also not have been possible without several decades of progress in the prediction and modelling of the rich array of effects that occur when protons collide, often associated with the strong interaction. It is crucial, for example, to have excellent theoretical control over the rate of quark and gluon collisions given a certain number of proton collisions27,28. Another facet is that collisions often involve not just one quantum fluctuation, as in Fig. 2, but multiple additional quantum fluctuations, each one of which modifies the probability of Higgs-boson production. The greater the number of quantum fluctuations that one can account for in theoretical predictions (today up to three additional fluctuations29), the more accurately one can relate experimental observations to the Standard Model30,31. Finally, Fig. 2 is a vastly simplified picture and the experiments rely profoundly on accurate simulation32,33 of the full structure of proton–proton collisions, involving the production of hundreds of particles per collision.What is still to be established?In many respects, the experimental exploration of the Higgs sector is only in its infancy. There are two broad directions of ongoing investigation: obtaining higher precision in studies of interactions that have already been observed and detecting further kinds of interactions that are, so far, yet to be seen.We start with the question of precision. Examining Fig. 3b, one sees that the interactions of the Higgs boson with W and Z bosons and the third-generation charged leptons and quarks are currently known to a precision of about 5–20%. We would not consider the theory of electromagnetism established if we had only verified the strength of electromagnetic forces to within 10% accuracy.One of the reasons for aiming for higher precision is that even though the Standard Model Higgs mechanism outlined above is the simplest model that is consistent with data, it is far from being the only viable one. Indeed, as we shall elaborate on below, it is widely believed that the Standard Model as it stands cannot be a complete description of nature. For example, it is conceivable that the Higgs boson is not an elementary particle, but rather is composed of other, yet-to-be discovered particles. High-precision measurements of Higgs-related processes can be very sensitive to such extensions of the Standard Model. In particular, the rates of Higgs-related processes could be affected by quantum fluctuations involving any new particles. Such effects might be visible even in scenarios where the new particles are too heavy to be directly produced and observed at a given collider. In general, increasing the precision by a factor of four effectively doubles the mass scale that can be indirectly probed for those new particles.The path for improvement is conceptually straightforward: with 20 times more data to come in the next 15–20 years from the approved high-luminosity upgrade of the LHC, and foreseeable improvements in analysis techniques and theoretical calculations, the ATLAS and CMS experiments expect to determine the currently observed set of interactions to within a couple of percent34. Reaching beyond that requires a different kind of collider. An electron–positron collider with centre-of-mass energies of around 250 GeV (a ‘Higgs factory’)35,36,37,38,39 is widely considered to be a promising option (see the European Strategy for Particle Physics40). Advantages are that electrons and positrons, in contrast to protons, are simple fundamental particles, and that the main Higgs-boson production mechanisms at an electron–positron collider are largely free of complications associated with strong interactions. Such a collider could improve the precision of our knowledge of the Higgs interactions by a further factor of about ten41.Let us now turn to a discussion of interactions that are yet to be observed. Notwithstanding the good prospects for dramatically improving the precision of Higgs measurements connected with the vector bosons and third-generation (heaviest) quarks and leptons, recall that the relevance of the Higgs sector for our everyday life is that it is believed to generate masses for the first (lightest) generation of fundamental particles, the electron and up and down quarks. Even though experimentally testing our theoretical expectations for the interactions between first-generation fermions and the Higgs boson is highly challenging, there are prospects for the second generation, and in particular the interactions of the Higgs boson with the muon, which can be observed through the \(H\to {\mu }^{+}{\mu }^{-}\) decay. So far the data is suggestive of such decays42,43, and definitive observation of \(H\to {\mu }^{+}{\mu }^{-}\), if it occurs at a rate that is compatible with the Standard Model, is expected to come in the next decade. Measurements involving the rest of the second generation are more difficult.The LHC can exclude anomalously large interactions of the Higgs boson with charm quarks34 (for example, using ideas such as those in refs. 44,45). It has long been thought that to definitively observe \(H\to c\bar{c}\) decays would require a future \({e}^{+}{e}^{-}\) collider (or alternatively an electron–proton collider46). Significant recent improvements in sensitivity to this decay channel at the LHC47,48 raise the question of whether future developments can bring its observation within reach of the high-luminosity LHC. For other Yukawa interactions, the path is less clear.Investigations are ongoing to establish the potential sensitivity of a future \({e}^{+}{e}^{-}\) collider to electron and strange-quark Yukawa interactions (see, for example, ref. 49), although currently it seems that it will be challenging to obtain a statistically conclusive signal. For the coupling of up and down quarks to the Higgs boson, there are currently no concrete possibilities in sight unless those couplings are very strongly enhanced relative to the Standard Model expectation. There has been discussion of whether precise atomic physics measurements could be sensitive to the Higgs forces involving light quarks50; however, this seems challenging51.Central to all of Higgs physics is the Higgs potential. Recall that the Higgs field is non-zero everywhere in the Universe, and so produces non-zero masses for fermions and electroweak bosons, because the minimum of the Higgs potential, equation (1) and Fig. 1, lies at a non-zero value of the Higgs field ϕ. One of the most important open questions in Higgs physics is whether the potential written in that equation is the one chosen by nature. We cannot directly explore the potential across different values of the Higgs field. However, it turns out that the specific shape of the potential in the immediate vicinity of the minimum determines the probability of an important process—the splitting of a Higgs boson into two (or even three) Higgs bosons; this kind of process is referred to as a Higgs-boson self-interaction. Accurate observation of such a process is widely considered to be the best (but not the only52) way of experimentally establishing whether the world we live in is consistent with that simple potential. By the end of the high-luminosity LHC’s operation in 15–20 years, the ATLAS and CMS experiments are expected to see first indications of the simultaneous production of two Higgs bosons. However, gathering conclusive evidence for a contribution to Higgs-pair production from the splitting of a first Higgs boson almost certainly requires a more powerful collider and several options are under discussion36,53,54,55,56.These are but some of the questions that are being explored. Other important ones that the LHC experiments are starting to be sensitive to include the lifetime of the Higgs boson57,58,59,60 and the nature of Higgs interactions at energies well above the electroweak energy scale61,62.Higgs and major open questions of particle physics and cosmologyMany of the above measurements are of interest not just owing to the fundamental nature of the Higgs sector within the Standard Model, but because they are also sensitive to scenarios that extend the role of the Higgs sector beyond that in the Standard Model. Even though the Standard Model has successfully passed all the numerous experimental tests so far, it leaves open several major questions. To various degrees, the Higgs boson is tied to potential solutions to these puzzles.We close our discussion with an overview of some of these possible connections, illustrated in Fig. 4, as they play an important role in guiding ongoing experimental and theoretical research directions in particle physics. There is a lot of ground to cover, so we will begin with and give more emphasis to aspects closely related to the Higgs boson, and only briefly mention later some of the more speculative ideas.Fig. 4: Possible connections of Higgs physics with major open questions of particle physics and cosmology.There are several major open questions in particle physics that are motivated by experimental observations or theoretical arguments. The Higgs boson could be the key to unravelling some of these problems.Full size imageOne major puzzle is that the weak and Higgs interactions are much stronger, by a factor of about 1032, than the gravitational interaction. This is especially challenging if one harbours the hope—as do many physicists—that all the known interactions might come from a unifying and simpler framework. Over the past decades, the desire to explain the origin of this large difference, the so-called ‘hierarchy problem’, has motivated a range of theoretical proposals.One possibility is for the Higgs boson not to be an elementary particle, but rather a composite object made of other, as yet undiscovered particles63. Examples of other well studied proposals are new (approximate) space–time symmetries64,65,66 and new space dimensions67,68,69,70. More recently, some more speculative ideas suggested possible connections between the weak scale and cosmological evolution71,72,73 or the amount of dark energy in the Universe74,75.Without one of these proposals, or a new mechanism yet to be thought of, the hierarchy between the weak and the gravitational interaction can only arise if distinct parameters in some ultimate fundamental theory cancel to within 1 part in 1032. This is known as the fine-tuning problem of the Higgs sector.The discovery of the Higgs boson brought such questions unavoidably to the fore. The mere existence of the Higgs boson, and the (still approximate) picture of its properties, already exclude many theoretical ideas. In comparison with the decades before its discovery, we now have a much clearer target and sharper questions to answer with our theoretical models.Another important question is why there is more matter than antimatter in the Universe. This so-called baryonic asymmetry cannot be explained within the Standard Model. Such an asymmetry can be generated if a suitable set of conditions is met76. One promising avenue that is being explored follows the history of the Universe as it cooled down after the Big Bang.When the Universe was very hot, the minimum of the Higgs potential at a non-zero value of the Higgs field was largely irrelevant because temperature fluctuations were much larger than the depth of the potential. As the Universe cooled, the situation changed. Within the Standard Model that change is smooth. Other promising scenarios, which involve new particles interacting with the Higgs boson, would generate a sharper transition, which sets the stage for generating the observed baryon asymmetry77, although further ingredients are also needed.These scenarios involve more complex structures for the Higgs potential, and at least one new particle at the electroweak energy scale, which can be searched for at the LHC either through its direct production or through its indirect impact on the Higgs couplings, in particular the Higgs self-interaction. A measurement of the latter is therefore essential to shed light on this question. Early-Universe phase transitions could also produce gravitational signatures that can be detected by future gravitational wave experiments78,79.In addition to the questions directly related to the Higgs boson mentioned above, there are also other contexts in which the Higgs boson can play an important role. One example of this is the question of dark matter. Astrophysical and cosmological observations show that the majority of the matter in the Universe is dark and not made of any particle we know of. Such observations rely on the gravitational effects of the dark matter on ordinary, Standard Model matter. At the same time, we know very little about the non-gravitational properties of dark matter. New particles with masses around the electroweak and Higgs mass scales can be promising dark-matter candidates.As the Higgs mechanism is responsible for generating similar masses of the Standard Model particles, it is possible that it plays some role in generating the dark-matter mass as well80,81,82. There are also scenarios in which the dark-matter sector involves more than one kind of particle. Similar to particles in the Standard Model, they could have their own interactions, and a whole set of other closely related particles. In this case, the Higgs boson would provide a portal to a new ‘dark world’83.The origin of the pattern of masses and interactions among different generations of the Standard Model particles is an intriguing puzzle. For example, first-generation quarks are much lighter than third-generation quarks, which in the Standard Model needs to be arranged manually by setting correspondingly disparate values of the Yukawa couplings. Understanding the origin of this pattern has also been the focus of decades of efforts. As the Higgs sector is responsible for generating the masses of these particles, it is tempting to think that the actual Higgs sector may be structurally different from the Standard Model, in a way that causes the observed pattern to emerge naturally84,85,86.The models that explore such ideas often lead to predictions of modified interactions between the Higgs boson and the quarks (and/or leptons). One signature of such models is that the Higgs boson could decay into a pair of quarks or leptons with different flavour. Similarly, one may also ask whether the Higgs mechanism has a role in generating the extremely small masses for neutrinos and various models have been envisaged in this respect87.The questions above relate the Higgs boson with known or unknown elementary particles. However, there are also mysteries in fundamental physics that go beyond such types of questions and speculative, yet intriguing, links have been proposed with the Higgs sector. For example, it has been noted that the Standard Model self-interaction of the Higgs boson becomes very close to zero if it is measured88,89,90 at energies nine orders of magnitude beyond the Higgs mass91,92. A curious and connected fact is that it seems likely that the Standard Model Higgs sector has a ground state with lower energy than the state we live in. Hence, quantum mechanics would allow a ‘tunnelling’ process through which our whole Universe can decay, even though the probability of such an event happening within the 14-billion year age of the Universe is tiny. The final possibility that we mention for new dynamics of the Higgs field at high energies is a possible link to inflation, which is a period of exponential expansion in the early niverse that is essential to explain the striking long-distance uniformity of the cosmic microwave background. The Higgs boson, having spin 0, may be responsible for driving inflation93.The Higgs boson is an invaluable tool in the search for answers to several of the above questions. Many of the proposed solutions predict the existence of new particles that generally interact directly with the Higgs boson. These particles are actively searched for at high-energy colliders. Still, even if the direct production of these particles lies outside our reach, for instance because the LHC is not energetic enough, their involvement in quantum fluctuations may affect Higgs-boson production and decay, in the same way that top-quark quantum fluctuations mediate Higgs production in Fig. 2. The expected future advances in precision measurements of the Higgs boson, as mentioned above, will bring considerably improved sensitivity to such scenarios.ConclusionsThe discovery of the Higgs boson at the LHC marked the beginning of a new era of particle physics. In the ten years since, the exploration of the Higgs sector has progressed far beyond original expectations, owing to ingenious advances both experimental and theoretical. Every Higgs-related measurement so far has been consistent with the Standard Model, the simplest of all current models of particle physics: a remarkable win for Occam’s razor. Today, it is clear that the Higgs mechanism, first proposed in the 1960s, is responsible not only for the masses of the W and Z bosons and but also for those of the three heaviest fermions. This directly implies the existence of a fifth force, mediated by the Higgs boson. Still, much remains to be probed. Whatever is found in the coming decades, we will be wiser: either with solid evidence for parts of the Standard Model that remain crucially to be established, such as the nature of the Higgs potential, or by opening a window to new horizons and the major mysteries of the Universe.

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