希格斯轻子风味违反：HL-LHC与ILC的探测前景

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本文主要探讨了在高能粒子物理领域中的一个重要发现，即在欧洲核子研究组织（CERN）的大型强子对撞机（LHC）第一期运行（Run-I）期间，由CMS合作组观察到希格斯玻色子（Higgs boson）可能存在轻子风味（lepton flavor）违反的现象，具体表现在h→μτ（希格斯衰变为μ子和τ子）的衰变通道中，该效应具有局部显著性高达2.4σ。这一结果可能标志着希格斯粒子与标准模型预言不符的首次信号，暗示着新物理的存在或对现有理论的修正。作者们回顾了当前对希格斯粒子的轻子风味违反Yukawa耦合（控制基本粒子之间相互作用的强度）的限制，这些限制来自于直接搜索、低能量测量以及未来实验的预期成果。他们特别关注了两个关键的实验设施：即将来临的高能大型强子对撞机（HL-LHC）和国际直线加速器（International Linear Collider, ILC），这两种设备在探测这种违反现象方面具有独特的能力。对于HL-LHC，预期在下一个运行阶段，其能够限制希格斯衰变为μ子和τ子的分支比（branching ratio, BR）分别为BR(h→μτ) ≲ O(0.5%)和BR(h→eτ) ≲ O(0.5%)，以及BR(h→eμ) ≲ O(0.02%)。这意味着即使在大规模的数据收集和更精细的分析下，希格斯的轻子风味违反可能仍然保持在非常低的水平，但其测量精度将进一步提高。相比之下，ILC作为一台能量更高的对撞机，计划运行时中心能量达到1 TeV，预计可以达到更高的灵敏度。对于ILC，预期能够测量到BR(h→eτ)和BR(h→μτ)到O(0.2%)的水平，这将提供更精确的测试和可能的突破性发现。这篇文章不仅探讨了现有的实验数据和理论限制，还对未来在HL-LHC和ILC上对希格斯轻子风味违反的进一步探索进行了展望。任何证实或排除这些违反行为的观测都将对标准模型的基本假设产生深远影响，并推动理论物理学的发展，尤其是在粒子味的守恒定律和希格斯机制的理解上。

JHEP07(2016)059

2.1.2 Limits from low-energy measurements

We motivate below the diﬀerent bounds on these Yukawa couplings that emerge from the

low energy ﬂavour violating processes and summarise these limits in table 1.

• Y

µτ

is constrained by the non-observation of processes like τ → µγ and τ → 3µ. The

branching ratio of the process τ → µγ is bounded by BR(τ → µγ) < 4.4 × 10

−8

90% C.L. [70, 71]. Assuming the low energy dynamics to be governed by the two

ﬂavour violating couplings Y

µτ

and Y

τµ

, the decay width of this process reads as [27]

Γ(τ → µγ) =

αm

64π

(|c

+ |c

), (2.10)

where the Wilson coeﬃcients, c

and c

at one loop are given by

L(R)

∼

ττ

τµ



−1 +

log



. (2.11)

In the above expression, for simplicity, we assume that Y

τµ

= Y

µτ

. Higher-order

corrections to c

L/R

receive contributions from the top Yukawa coupling and hence

can be large [27]. For example, including two-loop contributions, c

L/R

increases by a

factor O(4). For a full discussion on the dependence of Y

we refer to ref. [27]. Hence

by assuming Y

τµ

= Y

µτ

and also a SM-like Y

ττ

, we obtain Y

µτ

. 0.011.

In presence of ﬂavour violating Yukawa interactions, the process τ → 3µ has a decay

width of

Γ(τ → 3µ) =

6(2π)

(|c

+ |c

). (2.12)

Taking into account the one-loop contribution, the constraint on the Yukawa coupling

is, Y

µτ

< 0.177. Similar to the previous limit, this also depends on the couplings

ττ

, Y

µµ

and Y

and their SM values have been assumed in deriving the limit on Y

µτ

This limit is weaker than τ → µγ due to an additional factor of α (where α is the

ﬁne-structure constant).

• The coupling Y

τe

is also constrained from similar low energy ﬂavour violating pro-

cesses, such as, τ → eγ and τ → 3e. The decay width for τ → eγ has a similar

expression as given in eq. (2.10), where µ has to be replaced by e [27]. Under sim-

ilar assumptions, one obtains Y

τe

. 0.01 from τ → eγ, while from τ → 3e, this is

relaxed owing to the extra α factor. Assuming Y

τe

= Y

eτ

, we show the bounds on

the Yukawas in table. 1.

• The Yukawa coupling Y

µe

is severely constrained by the µ → eγ limit from MEG [72].

The Wilson coeﬃcients have similar expression as given in eq. (2.10), with {τ, µ} →

{µ, e}. The two loop contribution proportional to the top Yukawa coupling can be

large [27]. The updated limit on the branching ratio, viz., BR(µ → eγ) < 5.7 ×

−13

[70] imposes a tight constraint on the Yukawa

µe

+ |Y

eµ

. 1.75 ×10

−6

Assuming, Y

µe

= Y

eµ

this constrains Y

µe

. 1.24 × 10

−6

. The other LFV process,i.e,

µ → 3e constrains Y

µe

. 2.19 × 10

−5

– 5 –

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