NLO修正下的Wino潜力与Sommerfeld效应分析

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"NLO的Wino潜力和Sommerfeld效应" 这篇研究文章发表在Physics Letters B800(2020)135112中，主要探讨了标准模型中SU（2）×U（1）弱电势对铁离子三重态的影响，特别是在非相对论情况下的单环顺序（NLO）计算。该研究由Martin Beneke、Robert Szafron和Kai Urban共同完成，他们隶属于德国慕尼黑技术大学的物理系。文章的核心在于分析Wino（或Wino-like）暗物质粒子χ0的特性。Wino是一种超对称理论中的粒子，是弱相互作用超伙伴（WIMP）的一种，可能构成宇宙中暗物质的一部分。Sommerfeld效应是指在非相对论性系统中，由于交换虚光子或其他媒介粒子，使得相互作用粒子的有效势能增加，从而影响其湮灭过程。在暗物质的研究中，Sommerfeld效应可以显著地改变湮灭截面，特别是对于χ0这样的粒子。在NLO级别，研究人员计算了一环校正，这是非相对论修正的重要组成部分，能够解释在Wino粒子χ0湮灭过程中出现的大型Sommerfeld效应。通过这项计算，他们发现χ0χ0的湮灭截面发生了显著的改变，这意味着Wino粒子间的相互作用比预想的更为复杂。此外，研究还揭示了由于Wino势能的循环校正导致的共振位置的偏移，这一发现对于理解和预测暗物质的行为至关重要。该研究的重要性在于它提供了对Wino粒子性质的更精确理解，这对于暗物质研究和宇宙学模型的构建具有深远影响。通过考虑这些非相对论修正，科学家们能够更准确地预测暗物质粒子的湮灭行为，进而可能揭示宇宙中暗物质的性质和分布。同时，这些结果也对粒子物理学实验，如大型强子对撞机（LHC）的探测策略和暗物质直接探测实验的设计提供了重要的理论依据。这篇开放访问的文章通过深入研究Wino的Sommerfeld效应，不仅深化了我们对暗物质粒子相互作用的理解，也为未来实验寻找和研究暗物质粒子提供了理论指导。这一工作强调了高精度计算在解决宇宙学难题中的关键角色，并展示了理论物理与天体物理学交叉领域的合作成果。

Physics Letters B 800 (2020) 135112

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Wino potential and Sommerfeld effect at NLO

Martin Beneke, Robert Szafron

∗

, Kai Urban

Physik Department T31, James-Franck-Straße 1, Technische Universität München, D–85748 Garching, Germany

a r t i c l e i n f o a b s t r a c t

Article history:

Received

13 September 2019

Received

in revised form 19 November 2019

Accepted

20 November 2019

Available

online 28 November 2019

Editor:

J. Hisano

We calculate the SU(2)×U(1) electroweak static potential between a fermionic triplet in the broken phase

of the Standard Model in the one-loop order (NLO). The one-loop correction provides the leading non-

relativistic

correction to the large Sommerfeld effect in the annihilation of wino or wino-like dark matter

particles χ

. We ﬁnd sizeable modiﬁcations of the χ

annihilation cross section and determine the

shifts of the resonance locations due to the loop correction to the wino potential.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

It is by now well-known that the Sommerfeld effect due to the

electroweak Yukawa force [1–3]can lead to a dramatic enhance-

ment

of the annihilation cross section of two dark matter (DM)

particles if their mass is in the TeV range. Contrary to the classic

Sommerfeld effect for massless gauge boson exchange in QED and

QCD, which rises as 1/v as the relative velocity of the annihilat-

ing

particles decreases, the enhancement due to the Yukawa force

saturates at small velocities, except near isolated resonances. These

occur at dark matter mass values, when a zero-energy bound-state

develops in the spectrum. The phenomenon is quite general and

also appears for lighter DM, if there is a force carrier with even

smaller mass [4]. Furthermore, if the DM particle is part of a mul-

tiplet

with a small mass splitting, the effect depends sensitively on

the mass difference [5].

Its

main interest is nevertheless due to the fact that it is a

generic feature of the classic WIMP DM particle, where it arises

from the well-established Standard Model (SM) interactions. Thus,

it appears in the so-called minimal models [6] and for TeV scale

MSSM WIMPs (see, for example, [7–9]). The Sommerfeld effect is

particularly important for the annihilation rates and relic density

of the pure wino, an electroweak triplet of fermions of which the

electrically neutral member is the DM particle [2,3,6,10–12], or a

mixed but dominantly wino state [13,14]. The pure wino (“wino”

in the following) model has become a test case for the quantitative

understanding of large electroweak corrections in the annihilation

of TeV scale DM particles. In view of the possible detection or ex-

Corresponding author.

E-mail

address: robert.szafron@cern.ch (R. Szafron).

clusion of the wino particle through measurements of high-energy

cosmic rays, the wino annihilation rate into photons is of partic-

ular

interest. Here electroweak perturbation theory breaks down

due to electroweak Sudakov logarithms, which must be summed

in addition to the Sommerfeld corrections. Recent work on ex-

clusive

and semi-inclusive photon yields has shown that Sudakov

logarithms can be controlled with 1% accuracy with NLL’ resum-

mation

[15–17]. At this level of precision, the treatment of the

Sommerfeld effect should be revisited, since, up to the present, all

calculations have been done with the tree-level exchange poten-

tial,

which corresponds to the leading-order (LO) approximation in

non-relativistic effective ﬁeld theory (EFT) for the DM particle [8,

18,19].

this paper we compute the one-loop corrections to the wino

potential and discuss its effect on the wino pair annihilation cross

section to photons, χ

→ γ + X. We recall [1–3] that the LO

potential is given by the matrix

(r) =

⎛

⎜

⎝

0 −

√

2 α

−m

−

√

2 α

−m

−

−α

−m

⎞

⎟

⎠

(1)

The IJ entry refers to the non-relativistic scattering of wino two-

particle

states I → J with I, J = 1, 2 referring to χ

and χ

−

respectively. The above matrix describes the scattering of electri-

cally

neutral two-particle states in a

spin-angular-momentum

conﬁguration, since the spin-1 conﬁguration is forbidden due to

the Majorana nature of the χ

. One might expect the one-loop

correction to the potential to be small due to the smallness of the

SU(2)×U(1) couplings. However, we shall see that over most of the

interesting wino mass range from 1 to 10 TeV, the effect on the an-

https://doi.org/10.1016/j.physletb.2019.135112

0370-2693/

SCOAP

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