弦论景观下的LHC SUSY与WIMP暗物质搜寻：125 GeV Higgs与未发现的新线索

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本文主要探讨了在高能物理领域，特别是在LHC（大型强子对撞机）和暗物质搜索背景下，弦论理论的真空解对超对称(SUSY)和弱相互作用粒子(WIMP)暗物质模型的影响。弦论景观，即多元宇宙理论中无数可能的真空态，提供了一种统计性的框架来理解物理常数，包括宇宙常数，这与宇宙的观察特性紧密相关。在超对称粒子模型中，SUSY的软破缺项（即超对称粒子的质量差异）的大小受到了弦论统计的启发。理论上，统计趋势倾向于较大的软项，但必须与观测到的弱尺度（约100 GeV）相协调，以满足人类存在条件下的宇宙。特别是当考虑n=1的单个F项导致的SUSY破缺时，轻希格斯粒子的质量（即Higgs boson）更倾向于125 GeV，这正是LHC发现的标准模型Higgs粒子的质量范围。然而，这一理论预测并未在LHC的实验数据中找到其他超对称粒子或WIMP暗物质的信号。文章着重讨论了LHC在软对称符号多电子多喷注+未观测到的不寻常能量轨迹（MET）通道中寻找SUSY的可能，这是n=1理论地形的典型信号。同时，它也指出大规模液态WIMP探测器在全面探索n=1理论参数空间方面的重要性，因为它们可能揭示更多关于SUSY的信息。尽管LHC的实验结果并未发现预期的SUSY或WIMP信号，但这些研究继续推动理论物理的边界，提示我们可能需要在理论层面上重新审视SUSY模型的某些假设，或者探索弦论景观中的其他可能性。这篇文章将理论物理的前沿进展与实际观测结果相结合，展现了理论与实验之间的对话和挑战。

JHEP04(2019)043

where m

hidden

is a mass scale associated with the hidden sector

(and usually in SUGRA-mediated models it is assumed m

hidden

∼ 10

GeV such that the

gravitino gets a mass m

3/2

∼ m

hidden

According to Douglas et al. [14] from investigations of ﬂux compactiﬁcations in IIB

string theory, the distribution of vacua ought to have the form

vac

hidden

, m

weak

, Λ] = f

SUSY

hidden

) · f

EWFT

· f

· dm

hidden

(2.4)

where we deﬁne the weak scale m

weak

' m

W,Z,h

' 100 GeV and where m

hidden

sets the scale

for SUSY breaking with m

hidden

for a (in general) more complicated

SUSY breaking sector containing multiple sources of SUSY breaking, as may be expected

to occur in string theory.

The function f

SUSY

contains the expected statistical distribution of SUSY breaking

scales. This is related to the mass scale of MSSM soft terms as m

soft

' m

hidden

. If the

sources of SUSY breaking have uniformly distributed vacuum expectation values (vevs),

then it is surmised that

SUSY

hidden

) ∼ (m

hidden

)

−1

(2.5)

where n

is the number of F-breaking ﬁelds and n

is the number of D-term breaking

ﬁelds in the hidden sector [11–14]. We will denote the collective exponent in f

SUSY

n ≡ 2n

+ n

− 1. Since the F terms are complex-valued but the modulus |F | sets the

scale of SUSY breaking, then they contribute as (m

hidden

)

whereas the real valued D

terms contribute as (m

hidden

)

. In terms of MSSM soft SUSY breaking parameters, one

would expect a statistically uniform distribution of soft terms m

soft

only for a single D-

term breaking ﬁeld so that n

= 1. A single F -term breaking ﬁeld leads to f

SUSY

∼ m

soft

so that there is a linearly increasing preference for large soft terms. For more complex

conﬁgurations with larger number of n

and n

, then there is an even greater statistical

preference for large soft terms which could lead to a preference for models with high scale

SUSY breaking.

Regarding the role of the cosmological constant in determining the SUSY breaking

scale, a key observation of Denef and Douglas [13, 14] and Susskind [12] was that W

at the minima is distributed uniformly as a complex variable, and the distribution of

K/m

|W |

is not correlated with the distributions of F

and D

. Setting the cosmo-

logical constant to nearly zero, then, has no eﬀect on the distribution of supersymmetry

breaking scales. Physically, this can be understood by the fact that the superpotential

receives contributions from many sectors of the theory, supersymmetric as well as non-

supersymmetric. The cosmological ﬁne-tuning penalty is f

∼ Λ/m

where the above

discussion leads to m

∼ m

string

rather than m

∼ m

hidden

, rendering this term inconse-

quential for determining the number of vacua with a given SUSY breaking scale.

The ﬁnal term f

EWFT

merits some discussion. Following ref. [21], an initial guess [12,

14, 16, 17] for f

EWFT

was that f

EWFT

∼ m

weak

soft

which may be interpretted as con-

ventional naturalness in that the larger the Little Hierarchy between m

weak

and m

soft

, then

the greater is the ﬁne-tuning penalty. As pointed out in ref. [22], there are several problems

with this ansatz.

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