750GeV共振与暗物质：LHC双光子信号下的新物理与希格斯膨胀

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本文主要探讨了利用大型强子对撞机（LHC）在Run-2阶段观测到的750GeV附近的新双光子信号，该信号可能暗示着超出了标准模型（SM）的新型物理学。研究者提出了一种最小化的理论扩展，即引入一个单重态标量粒子S和一对双态矢量状夸克，以解释这一现象。 S标量粒子的实部被设计为新的750GeV共振，负责解释LHC Run-2中观察到的双光子过量事件。这一模型中的CP对称性使得其中的CP奇数虚分量χ成为自然暗物质（DM）的潜在候选者。暗物质的部分湮灭过程通过S粒子的不可见衰变为χχ，这可能导致单喷射信号，研究人员已经对这一信号进行了探讨，以期在LHC上进行进一步验证。模型还涉及对希格斯场稳定性的影响，S新标量自由度有助于维持希格斯真空的稳定性，并且在理论框架内，它能够支持在大统一理论（GUT）能量尺度上的希格斯膨胀，这种膨胀现象与当前宇宙学观测相吻合。文章展示了模型的两个示例——样本A和B，详细地研究了这些模型如何满足实验数据，并探讨了它们对暗物质剩余密度的贡献，以及直接和间接暗物质探测实验的限制。这篇研究论文将LHC的最新发现与暗物质和希格斯膨胀的理论结合，提供了一个有前景的框架来解释这些未解的物理现象，同时对实验结果和理论约束进行了深入分析，为未来的粒子物理学研究提供了重要的线索和方向。

482 S.-F. Ge et al. / Physics Letters B 757 (2016) 480–492

The observed sizable di-photon rate at M

γγ

≈ 750 GeV and the

absence of dijet excess in the same mass region so far suggests that

the new resonance S

should have enhanced decay rate into di-

photons.

This indicates that the heavy quarks may have larger elec-

tric

charges and thus enhanced couplings with di-photons. For this,

we introduce a weak doublet of vector-like quarks, T = (T



, T )

with hypercharge Y =

and thus the electric charges





where the heavy quark T shares the same electric charge with

the SM up-type quarks.

According to the model construction in Table 1, we write down

the relevant Yukawa interactions including the Yukawa interaction

between the vector-like quark doublet T and singlet scalar S , as

well as the Yukawa interactions between T and light SM up-type

quarks,

=−y



−

TT +h.c., (2.3)

where



H = iτ

∗

, and i, j =1, 2 stand for ﬂavor indices of the ﬁrst

and second family fermions. We see that T does not mix with third

family top quark due to Z

symmetry. The Yukawa coupling

Eq. (2.3) is real, since the singlet S interactions conserve CP. Be-

sides,

all interactions respect Z

symmetry, and the only possible

soft breaking term of Z

is the bare mass term (M

) of vector-like

quark doublet T. Eq. (2.3) gives the following mixing mass matrix

for u

( j = 1, 2) and T ,

√

⎧

⎪

⎩

v 0

u +

√

⎫

⎪

⎭

(2.4)

where the (3, 3)-component contains both the VEV contribution

term

√

2[from the third term of Eq. (2.3)] and the bare mass

term M

[from the fourth term of Eq. (2.3)]. For our purpose, we

consider the parameter space of

v 

u +

√

. Taking the

small non-diagonal couplings

1,2

being comparable, we estimate

the small mixing of T and u

, θ

≈ y

u +

√

)

for

the left-handed quarks, and θ

≈

v/(

u +

√

) for the right-

handed

quarks. Thus, we have nearly degenerate heavy quarks,



≈ M

≈

√

u + M

. (2.5)

The small mixing couplings

will induce T and T



decays.

The heavy quark T has two main decay channels, T → u

h and

T → d

, while T



dominantly decays via T



→ u

. We

ﬁnd that for channels T → d

, u

Z and T



→ u

, the de-

cay

amplitudes are dominated by the ﬁnal state with longitudinal

polarization W

. Since M

 M

, we can apply equivalence the-

orem [15] to

compute the corresponding Goldstone amplitudes

with W

replaced by π

. Thus, we estimate the leading decay

width for each channel as follows,

We also note that the small quark mixings between the light families and

the third family can arise from dimension-5 effective operators involving singlet

scalar, (y

/)S



and (y

/)S

, where i = 1, 2and  is the cut-

off.

Such effective operators will induce the desired small CKM mixings. They may

result from integrating out a heavy Higgs doublet H



which is Z

odd and can re-

alize

dimension-4 Yukawa terms between the light families and the third family,







and y



. Adding this heavy Higgs doublet H



will increase the

scalar degrees of freedom and make vacuum stability much easier, but does not

change the main physics picture. For the current purpose of accommodating the

diphoton excess, we focus on the minimal setup for simplicity.

Table 2

Coupling

ratios ξ

hXY

and ξ

SXY

of the Higgs bosons h and S, relative to the SM

counterparts, where V = W , Z , and the SM Yukawa coupling is y

/v.

XY f

fVVTT

hXY

(

)

SXY

−s

(

)

[T →u

h]≈

16π

,[T →d

, u

Z]≈

32π

[



→u

]≈

32π



. (2.6)

It is clear that T → u

h is the dominant decay mode for T . For

later analysis, we will consider the parameter range, 10

−5



−3

. This is suﬃcient to evade the ﬂavor constraints involving

the ﬁrst two family quarks, and the tiny mixing coupling

negligible in our later analysis of renormalization group running

and collider studies. Furthermore, this ensures that the lifetimes

of T and T



are much smaller than 10

−13

s. So they are short-

lived

and will have prompt decays inside the detector [16]. The

searches of heavy vector-like quarks via prompt decays put non-

trivial

constraints on the new quark masses. The limits on their

decays into a light quark are weaker than that into top or bot-

tom.

For T



→ u

, the limit is M



 690 GeV, while the decay

channel T → u

h is much less constrained [17].

3. New particle decays and production

In the physical vacuum, the Higgs doublet H and singlet S ac-

quire

nonzero VEVs, as shown in (2.1). This spontaneously breaks

SU(2)

⊗U(1)

⊗Z

down to U(1)

, while the CP symmetry is re-

tained.

The CP-even states (h

, S

) can mix with each other via h =

+ s

and S = c

− s

, where (c

, s

) ≡ (cos α, sin α).

The mixing angle α is determined by diagonalizing the mass ma-

trix,

⎧

⎪

⎩

2λ

vu 2λ

⎫

⎪

⎭

, =⇒ (M

)

diag

⎧

⎪

⎩

0 M

⎫

⎪

⎭

(3.1)

with

tan 2α =

−λ

. (3.2)

Alternatively, we may resolve the 3 involved scalar couplings

(λ

, λ

) in terms of the measured mass-eigenvalues (M

, M

) 

(

125, 750) GeV, the known light Higgs VEV v  246 GeV, and the

Higgs mixing angle α (which is taken as an input parameter, but

will be constrained by the LHC data). Thus, we have,

,λ

−M

)

. (3.3)

Although the singlet scalar S does not couple to the SM fermions

and gauge bosons, the mixing between the two CP-even compo-

nents

and h

will induce these couplings suppressed by sin α.

Table 2 summarizes the coupling ratios ξ

hXY

and ξ

SXY

relative to

the SM counterparts, for the mass-eigenstates h and S.

Inspecting

the cubic scalar coupling of Shh vertex and using

Eq. (3.3), we derive its compact form as follows,

Shh

(uc

− vs

)

+2M

). (3.4)

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