LHC中的3HDM暗物质信号探索

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"3HDM在LHC处发出暗物质信号" 在本文中，研究者们探讨了3-Higgs Doublet模型（3HDM）在大型强子对撞机（LHC）上产生暗物质（DM）信号的可能性。3HDM是一种扩展标准模型的理论框架，其中包含三个Higgs二重态，而不仅仅是一个。在这种特定的3HDM配置中，只有一对二重态获得真空期望值（VEV），而其他两个是惰性的，不参与VEV生成，这就保持了一个由Z 2对称性控制的暗标量扇区。在这个模型中，最轻的CP即使标量H1被假定为暗物质的候选粒子。由于Z 2对称性，暗物质粒子H1与其他粒子的相互作用受到严格限制，主要通过一个中间的CP奇偶标量H2和带电标量进行。这些中间态允许H2衰变为H1以及标准模型（SM）粒子对，例如夸克（u, d, c, s, b）和轻子（e, μ, τ）。这种双峰衰变机制是3HDM的一个独特标志，因为它在只有两个惰性二重体的2HDM中是不允许的。在LHC的实际环境中，这种暗物质信号可能会在类似SM的希格斯玻色子h的级联衰变中显现出来，即h→H1H2→H1H1ff。这里的h是由胶子-胶子融合（ggF）或矢量玻色子融合（VBF）产生的，随后H2衰变为两个H1和一对SM粒子。这个过程将导致四暗物质粒子的最终状态，同时伴随着双瘦子/双喷嘴的产生。然而，这个信号也会与树级通道qq¯→H1H1Z *发生竞争，后者也产生暗物质对和Z玻色子。研究者还强调，当H2和H1的质量接近时，这种衰变过程特别显著，因为此时H2可以更有效地衰变为H1。文章中提到的研究团队包括来自墨西哥、芬兰、英国和波兰的物理学家，他们在2018年5月发布了这一研究成果。通过这样的分析，科学家们不仅在理论层面深化了对3HDM的理解，也在实验层面上为LHC探测暗物质信号提供了新的视角。这种研究对于理解宇宙中的暗物质成分及其可能的相互作用方式具有重要意义，有助于未来LHC实验的策略制定和暗物质探测技术的发展。

JHEP05(2018)030

resulting in

= nΛ

, Λ

= nΛ

, Λ

= nΛ

, (2.14)

without introducing any new symmetry to the potential. The motivation for this simpliﬁed

scenario is that in the n = 0 limit the model reduces to the well-known I(1+1)HDM. We

assume no speciﬁc relation among the other parameters of the potential. It is important to

note that the remaining quartic parameters, (λ

1,11,22,12

, λ

), do not inﬂuence the discussed

DM phenomenology of the model and thus their values have been ﬁxed in agreement with

the constraints discussed in section 2.4 and compliant with the results on unitarity obtained

in [14].

With this simpliﬁcation, it is possible to obtain analytical formulae for the parameters

of the potential in terms of chosen physical parameters. In this study, we choose the

set (m

, m

, g

, θ

, n) as the input parameters where g

is the Higgs-DM

coupling. The meaningful parameters of the model are then deﬁned as follows:

= Λ

−

+ m

1 + n

, (2.15)

− m

)

− (−1 + n)

(Λ

− µ

)

, (2.16)

(Λ

− Λ

), (2.17)

, (2.18)

(Λ

+ Λ

− 2Λ

), (2.19)

4(sin

+ n cos

)

, (2.20)

2µ

(1 − n) tan 2θ

, (2.21)

2µ

(1 − n) tan 2θ

. (2.22)

The mixing angle in the CP-even sector, θ

, is given by the masses of H

and H

and the

dark hierarchy parameter n:

tan

− nm

− m

. (2.23)

Notice that we restore the n = 1 limit of dark democracy discussed in [10–12] with

= π/4. For the correct deﬁnition of tan

, the following two relations need to be

satisﬁed: m

< nm

and m

. Without loss of generality, we can limit our-

selves to n < 1, which will correspond to tan 2θ > 0 for θ

< π/4. Reaching other values

of n is a matter of reparametrisation of the potential.

2.4 Theoretical and experimental constraints

As discussed in [10–12], the I(2+1)HDM is subject to various theoretical and experimental

constraints.

– 6 –

JHEP05(2018)030

In [10], we have studied in detail the theoretical constraints, namely the positivity of the

mass eigenstates, boundedness of the potential and positive-deﬁniteness of the Hessian. Our

parameter choice is also compliant with the EW Precision Test (EWPT) bounds [10, 11].

These limits have been taken into account in the present paper. The second set of experi-

mental constraints comes from the relic abundance of DM as well as dedicated direct and

indirect searches for DM particles. The Planck experiment provides a DM relic density

limit of [15]:

Ω

= 0.1197 ± 0.0022. (2.24)

In this work, we do not focus on the details of DM annihilation (for detailed discussions see

refs. [10–12]). However, we require that the DM candidate of the I(2+1)HDM is in agree-

ment with the upper limit from Planck (2.24) for all considered points. If relation (2.24)

is exactly satisﬁed, then H

provides 100% of the DM in the Universe. This is a case in

benchmark scenario A50 discussed in later sections [10, 11]. We also consider cases where

has a subdominant contribution and the missing relic density is to be provided by an

extension of the model. This usually happens where mass splittings between H

and other

inert particles are small, i.e., in the forthcoming benchmarks I5 and I10. In these two cases,

the coannihilation channels of H

→ Z → ff

are strong and reduce DM relic density

to values below the Planck value, even for very small values of Higgs-DM coupling.

Benchmark scenario A50 (for 53 GeV . m

. 73 GeV) is in agreement with the

most recent direct [16] and indirect [17] detection limits. However, for completeness, we

show a larger mass region (40 GeV . m

. 90 GeV) in our cross section plots, and

highlight the surviving regions.

For benchmarks I5 and I10, which — as mentioned — correspond to relic density

below the Planck value, detection limits should be rescaled, leading to the (relic density

dependent) limit of:

σ(m

) < σ

LUX

)

Ω

Planck

Ω

. (2.25)

We ensure this limit is satisﬁed for all studied points. The detailed analysis of astrophysical

signals in benchmarks I5 and I10 is beyond the scope of this paper. However, for all

masses in these benchmarks, relic density is within 10%–90% of the observed relic density.

The missing relic density can be easily augmented by late-stage decays of an additional

particle. The natural candidate here for the completion of the model would be a heavy

right handed neutrino in the same vein as the scotogenic model [5], which would decay into

DM after the thermal freeze-out of DM and bring back the under-abundant DM relic into

the observed range.

Finally, we take into account collider data from LEP and the LHC (including the Higgs

total decay width [18], Higgs invisible decays [19], direct searches for additional scalars and

the Branching Ratio (BR) for h → γ γ [19]), as discussed in [10–12]. In all cases, the mass

splittings are large enough not to inﬂuence the decay widths of the weak gauge bosons,

forbidding the on-shell decays Z → H

1,2

and W

→ H

1,2

If the Higgs-DM coupling is small enough, i.e., g

. 0.02, then both the Higgs

invisible decay BR and Higgs total decay width are in agreement with measured values.

– 7 –

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