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This article reviews the discovery of the Higgs boson, discusses the studies of its properties, and introduces the physical prospects of the future Higgs factories. The greatest goal of particle physics is to understand the fundamental particles of the universe and how they interact with each other (or more generally, how the universe operates). In the Standard Model of particle phyiscs, the Higgs mechanism is proposed to explain the origin of elementary particle mass and predict the existence of the Higgs boson. Higgs physics is one of the most important research areas in particle physics. The Large Hadron Collider (LHC) at CERN (Geneva, Switzerland) accelerates proton beams to collide at center-of-mass energy of 13 TeV, thus defining the world's energy frontier. The ATLAS and CMS detectors are two general-purpose detectors at the LHC for studying the debris from the collisions. The Higgs boson was discovered in the ATLAS and CMS experiments in 2012. This discovery completed the fundamental particle spectrum of the Standard Model and was an important milestone for particle physics. Since then, many studies have been conducted on the properties of Higgs boson, including spin, mass and couplings, to deepen our understanding of the Higgs mechanism. In particular, the Higgs bosons coupling to fermions and to themselves present new kinds of fundamental interactions with paramount significance, which have not been fully confirmed. Additionally, the Higgs bosons have become an important tool to search for dark matter, heavy resonance, and other new physical phenomena. So far, there has been no deviation from the predictions of the Standard Model. Looking forward to the future, it is proposed to use the electron-positron collisions to study the Higgs boson in more depth. Physics studies have shown that these Higgs factories can significantly improve the accuracy of many properties of the Higgs boson, including width and couplings, and provide great physics prospects. -
Keywords:
- standard model /
- electroweak symmetry breaking /
- Higgs boson
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图 6 希格斯玻色子胶子胶子融合产生机制以及希格斯衰变为光子对的费曼图
Figure 6. The Feynman diagram of ggF and Higgs decay into a pair of photons
图 7 希格斯玻色子伴随一对顶夸克对产生模式的费曼图
Figure 7. The Feynman diagram of $ {\rm{t}}{\bar {\rm{t}}}{\rm{H}} $ production model
图 8 ATLAS实验组获得的$ {\rm{t}}{\bar {\rm{t}}}{\rm{H}} $产生过程候选事例三维展示图, 在事例中, 探测器下部有两个孤立的光子(绿色), 共产生六个喷注(黄色锥形), 包括一个B-标记喷柱(蓝色锥形)[19]
Figure 8. This figure shows 3D display of a candidate event of $ {\rm{t}}{\bar {\rm{t}}}{\rm{H}} $ production mode from ATLAS. The event has the two isolated photons (green line below the detector) and six jets (yellow cone), including one B-tagged jet (blue cone).
图 10 如图表示标准模型中, 发生自发性破缺前的希格斯势场的示意图, 形状酷似“墨西哥帽”. 可以从图中看出, 势能的最低点并不处于原点
Figure 10. The figure shows the diagram of the Higgs potential field before spontaneous breaking in the standard model(SM), shaped like a “Mexican hat”. As you can see from the diagram, the lowest point of the potential energy is not at the origin.
图 11 如图为希格斯玻色子对和三希格斯玻色子末态的费曼图, 左图为希格斯玻色子对过程, 蓝色圈代表三希格斯玻色子自耦合顶点$ \lambda_3 $, 右图为三希格斯玻色子产生过程, 红色圈代表四希格斯玻色子自耦合顶点$ \lambda_4 $
Figure 11. The figure shows the Feynman diagram of the Higgs boson pair and triple Higgs final state, the left picture is the Higgs boson pair process, the blue circle represents the three Higgs Boson self-coupling vertex $ \lambda_3 $, the right picture is the triple Higgs boson production process, the red circle represents the quartic Higgs Boson self-coupling vertex $ \lambda_4 $.
图 14 希格斯玻色子的矢量玻色子融合产生(左)和矢量玻色子伴随产生(右)两种模式的领头阶费曼图
Figure 14. Leading-order Feynman diagrams for Higgs boson production via vector boson fusion (left) and vector boson associated production (right) modes.
图 18 二期运行期间ATLAS和CMS组统计合并测量希格斯玻色子衰变到Z玻色子和一个光子的信号强度结果[33]
Figure 18. Combined measurement of the signal strength for Higgs boson decay into a Z boson and a photon by the ATLAS and CMS collaborations during Run II upciteaad 2024 evidence.
图 20 一期运行多个衰变道数据合并中, 标准模型与$ 2^+ $的自旋假设的比较: 上图: CMS实验结果[17], 下图: ATLAS实验结果[18]
Figure 20. Comparison of the Standard Model with the $ 2^+ $ spin assumption with the combination of multiple decay channels in Run I: top: results from the ATLAS experiment[17], bottom: results from the CMS experiment[18].
图 21 LHC实验对暗物质粒子的探测示意图[46], 暗物质对探测器不可见, LHC实验通过计算所有可见物质的横向动量和来推算缺失动量, 从而搜寻潜在的暗物质信号
Figure 21. An illustration of the LHC experiment's search for dark matter particles[46], which are invisible to the detector. The search for potential dark matter signals is conducted by calculating the transverse momentum of all visible matter and inferring the missing transverse momentum.
图 23 ATLAS合作组分析mono-Higgs信号得到的排除轮廓[48], 合并了$ {\rm{b}}\bar{\rm{b}} $和$ \gamma\gamma $希格斯玻色子衰变道的分析结果. 黑色虚线表示仅有标准模型背景假设下预期轮廓, 绿带为1σ误差范围, 黑色实线为观测轮廓. 灰色虚线为动力学限制, 即$ m_{Z'_B} = 2 m_{{\cal{X}}} $
Figure 23. Exclusion contours obtained by the ATLAS collaboration analyzing the mono-Higgs signal[48], combining results from the Higgs boson decay channels of $ {\rm{b}}\bar{\rm{b}} $ and $ \gamma\gamma $. The black dashed line represents the expected contour under the assumption of only the Standard Model background, with the green band indicating the 1σ error range, and the black solid line representing the observed contour. The grey dashed line represents a kinematic constraint, namely $ m_{Z'_B} = 2 m_{{\cal{X}}} $.
图 24 胶子融合产生希格斯玻色子对的领头阶费曼图[49]. 左图和中图: 非共振态粒子产生希格斯玻色子的三角图和盒形图, 其符合标准模型. 右图: 通过一个新共振粒子产生的希格斯玻色子费曼图, 其中新共振粒子用X表示
Figure 24. Leading order Feynman diagrams of Higgs boson pair production via gluon fusion[49]. Left and middle: the triangle and box diagrams, respectively for nonresonant H production, as expected from the SM. Right: a diagram for H boson production through a new resonance of labeled as X.
图 25 自旋为0的共振态粒子$ {\rm{X}}\rightarrow {\rm{HH}} $的产生截面与衰变分支比乘积$ {\sigma {\cal{B}}} $在95%置信水平下的上限结果[49]. 其中实线表示观察到的结果, 虚线表示的是期望结果
Figure 25. Search for $ {\rm{X}}\rightarrow {\rm{HH}} $: Observed and expected 95% CL upper limits on the product of the cross section for the production of a spin-0 resonance X and the branching fraction for the corresponding HH decay[49]. The observed limits are indicated by markers connected with solid lines and the expected limits by dashed lines.
图 26 hMSSM模型对$ {\rm{X}}\rightarrow {\rm{HH}} $的寻找结果的诠释[49]. 图中展示了在$ (m_{\rm{A}}, \, \tan\beta) $平面上, HH的联合分析在95%置信水平下观察到的和预期的排除区域, 并将其与hMSSM模型中重标量粒子衰变为$ \tau\tau $[64]、tt[65]和WW[66]的寻找结果进行了对比. 此外, 还给出了$ {\rm{A}}\rightarrow {\rm{ZH}} $的一个代表性寻找结果[67], 以及通过测量希格斯玻色子耦合强度给出的间接约束[68]
Figure 26. Interpretation of the results from the searches for the $ {\rm{X}}\rightarrow {\rm{HH}} $ decay, in the hMSSM model[49]. The observed and expected exclusion contours at 95% CL, in the $ (m_{\rm{A}}, \tan \beta) $ plane from the combined likelihood analysis of HH analyses are shown. A comparison of the region excluded by the combined likelihood analysis shown in this figure with selected results from other searches for the production of heavy scalar bosons in the hMSSM, in $ \tau\tau $[64], tt[65] and WW[66] decays is shown. Also shown, are the results from one representative search for A → ZH[67] and indirect constraints obtained from measurements of the coupling strength of the observed H boson[68].
图 32 用喷注本源鉴别算法得到的Higgs稀有衰变以及奇异衰变的分支比上限, 如绿色柱状图所示[76]. CEPC(蓝色柱状图)[75]和高亮度大型强子对撞机(橙色柱状图)[80]预期的Higgs耦合的相对不确定度
Figure 32. Expected upper limits on the branching ratios of rare Higgs boson decays (green bars)[76] and the relative uncertainties of Higgs couplings anticipated at CEPC (blue)[75] and HL-LHC (orange)[80].
图 29 经过CEPC基线探测器[73]模拟的对撞能量为$ 240\, $ GeV的$ { {\rm{e}}^+{\rm{e}}^-} \to\nu\bar{\nu} {{\rm{H}}} \to\nu\bar{\nu} {\rm{gg}} $事例样本[76]
Figure 29. Event display of an $ { {\rm{e}}^+{\rm{e}}^-} \to\nu\bar{\nu} {{\rm{H}}} \to\nu\bar{\nu} {\rm{gg}} $ ($ \sqrt{s} = $$ 240\; {\rm{GeV}} $) event[76] simulated and reconstructed with the CEPC baseline detector[73].
图 30 正负电子对撞能量为240 GeV时, 利用CEPC基线探测器全模拟的$ \nu\bar{\nu} {\rm{H}}, {\rm{H}}\to {\rm{jj}} $样本, 基于ParticleNet深度学习模型训练, 在测试数据上得到的喷注味道鉴别矩阵[76]
Figure 30. The confusion matrix $ M_{11} $ based on full simulated $ \nu\bar{\nu}{\rm{H}} $, $ {\rm{H}}\to {\rm{jj}} $ at 240 GeV center-of-mass energy at CEPC baseline detector[76].
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