未来电子对撞机探测顶夸克CP违反：理论与实验工具

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"这篇研究论文探讨了未来线性电子正电子(e + e-)对撞机在探测顶夸克（top quark）CP违反（Charge Parity violation）方面的潜力。研究指出，标准模型的某些扩展，如双希格斯双重峰模型（2HDM），可能导致显著的异常顶夸克偶极矩，这种现象可以通过精确测量顶夸克对的产生率来检测。作者进行了详细的蒙特卡洛模拟研究，涵盖了500GeV的国际直线对撞机(ILC)和380GeV的紧凑型线性对撞机(CLIC)，并使用了部分级仿真来评估高能运行的可能性。他们发现，通过精确测量e + e-→tt过程中的顶夸克对产生以及后续的轻子加喷流最终状态的衰变，可以在可行的双希格斯模型中检测到由希格斯玻色子引起的CP违反。线性对撞机对违反夸克CP的电弱偶极子形状因子的探测能力比高亮度大型强子对撞机(HL-LHC)的预期高出一个数量级。" 文章发表于"Eur.Phys.J.C (2018) 78:155"，并且是开放访问的。作者包括来自德国亚琛工业大学、西班牙瓦伦西亚的Instituto de Física Corpuscular (IFIC)、法国Orsay的Laboratoire de l'Accelerateur Linéaire (LAL)以及德国马克斯普朗克物理研究所和瑞士CERN的研究人员。文章于2017年10月24日提交，2018年2月9日接受，作者保留2018年的开放访问发布权。本文的核心知识点包括： 1. **CP对称性违反**：在粒子物理学中，CP对称性违反是指粒子与它们的镜像反粒子的行为不完全相同，这是一个关键的物理现象，因为它在宇宙中物质-反物质不对称性的解释中起着关键作用。 2. **顶夸克**：顶夸克是已知最重的基本粒子，它在标准模型中扮演着重要角色，因为它的特性允许科学家们探索可能超出标准模型的新物理现象。 3. **双希格斯双重峰模型(2HDM)**：这是标准模型的一个扩展，包含两个希格斯玻色子双胞胎，可以导致新的物理效应，如CP违反的顶夸克偶极矩。 4. **异常顶夸克偶极矩**：如果存在，这将表示顶夸克与希格斯场之间的非标准相互作用，可能是新物理现象的信号。 5. **线性对撞机**：ILC和CLIC是两种设计用于高精度研究的电子正电子对撞机，它们的高能量和精确度使其能够探测到标准模型难以观测的现象。 6. **蒙特卡洛模拟**：这是一种统计方法，用于预测粒子碰撞事件的结果，以理解实验数据并评估对撞机的探测能力。 7. **部分级仿真**：在高能物理实验中，部分级仿真用于模拟粒子间的相互作用和衰变，以预测在特定对撞机条件下可能观察到的物理现象。 8. **探测能力比较**：文章指出线性对撞机的探测能力在CP违反方面远超HL-LHC，表明未来对撞机项目对于探索CP违反和新物理具有巨大潜力。通过这些研究，科学家们希望深化对基本粒子相互作用的理解，特别是关于CP对称性违反的机制，这可能揭示宇宙大爆炸后物质过剩之谜的线索。

Eur. Phys. J. C (2018) 78:155 Page 5 of 21 155

0.005

0.01

0.015

0.02

0.025

350 400 450 500 550 600

Re F

[GeV]

0.002

0.004

0.006

0.008

0.01

0.012

0.014

350 400 450 500 550 600

Im F

[GeV]

Fig. 1 Left panel: the real part of the top-quark EDF F

(solid, black)

and WDF F

(dashed, blue), evaluated with the couplings of Table 1

and neutral Higgs-bosonmasses m

= 125 GeV, m

= 1200 GeV, and

= 600 GeV, as a function of the c.m. energy. Right panel: the same

for the imaginary part of the top-quark EDF and WDF

Table 2 Values of the real and

imaginary parts of the top-quark

EDFandWDFfortwoc.m.

energies. Input parameters are as

in Fig. 1

√

s (GeV) Re F

Re F

Im F

380 8.1 ×10

−3

2.9 ×10

−3

1.3 ×10

−2

3.8 ×10

−3

500 −0.6 ×10

−3

0.7 ×10

−6

7.8 ×10

−3

2.2 ×10

−3

factors are listed in Table 2 for two c.m. energies that are

chosen for the simulations in Sects. 5–7.

In the kinematic range that we are interested in (

√

s  500

GeV) the imaginary parts of the EDF and WDF are rather

insensitive to the values of the heavy Higgs-boson masses,

as long as m

2,3

> 500 GeV. This is also the case for the

real parts of the form factors close to the t

t threshold that are

dominated by the contribution from h

exchange. This term

falls off strongly with increasing c.m. energy. Moreover, at

c.m. energies

√

s  500 GeV the contributions from h

, h

the real parts of the form factors may no longer be negligible.

We ﬁnd that the real parts of the EDF and WDF at

√

s = 500

GeV depend, for ﬁxed Higgs-boson couplings, sensitively on

the masses of h

, h

, but do not exceed 10

−3

in magnitude

for the couplings of Table 1.

As mentioned above, the formulae of [22] apply to any

type of 2HDM where tree-level FCNC are absent. In fact,

the results shown in Fig. 1 and given in Table 2 apply also to

other types of 2HDM in the low tan β region; for instance,

to the type-I model where all right-chiral quarks and charged

leptons are coupled to the Higgs doublet Φ

only, or to

the so-called lepton speciﬁc model where the right-chiral

quarks (right-chiral charged leptons) are coupled to Φ

(Φ

)

only.

In summary, within the 2HDM the real (imaginary) part of

the top-quark electric dipole form factor F

can be as large

as ∼ 0.02 (∼ 0.01) in magnitude near the t

t production

threshold, taking into account the present constraints from

LHC data.

3.2 The minimal supersymmetric SM extension

The Higgs sector of the MSSM corresponds to a type-II

2HDM. Supersymmetry (SUSY) forces the tree-level Higgs

potential V (Φ

,Φ

) of the MSSM to conserve CP. Nev-

ertheless, the MSSM contains in its general form many

CP-violating phases besides the KM phase, especially in

the supersymmetry-breaking terms of the model, including

phases of the complex Majorana mass terms of the neu-

tral gauginos and of the complex chargino and sfermion

mass matrices. Motivated by assumptions as regards SUSY

breaking at very high energies, one often puts constraints on

the SUSY-breaking terms, in particular on the CP-violating

phases, in order to restrict the number of unknown param-

eters of the model. Nevertheless, generic features of SUSY

CP violation remain. Unlike the case of Higgs-boson induced

one-loop EDMs, fermion EDMs generated at one-loop can

be large, also for u, d quarks and the electron. The exper-

imental upper bounds on the EDM of the neutron and of

atoms/molecules strongly constrain in particular the CP-

phases associated with the sfermion mass matrices of the

ﬁrst and second generation, barring ﬁne-tuned cancellations.

See, for instance, Ref. [41] for a review. However, the phases

of the sfermion mass matrices need not be ﬂavour-universal.

For the top ﬂavour the associated phase ϕ

can still be of

order one. Often a common phase of the gaugino masses

is assumed. Using phase redeﬁnitions of the ﬁelds in the

MSSM Lagrangian, one can choose for the parametriza-

tion of MSSM CP violation in the top-quark sector [42,43]

the phase ϕ

, the corresponding b-ﬂavour phase ϕ

, and the

123

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