三环模型：带p夸克三重态标量解释B→Kμ+μ-与暗物质

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本文探讨了一个新颖的三环中微子模型，其核心特征是引入了几种SU(2)_L三重态的瘦夸克标量(leptoquark scalars)。这些粒子在理论物理学中扮演着关键角色，因为它们能够在高阶量子效应下贡献中微子质量，同时解决了一些实验观测上的谜团。首先，模型关注的是B→K*(*)μ+μ-的异常衰变，这是标准模型预测与实验结果之间存在的一个显著偏差。通过三环机制，模型能够提供额外的贡献，可能有助于解释这种 Flavor Changing Neutral Current (FCNC)过程中的观测数据，从而对粒子物理的标准模型进行扩展。其次，模型还涉及到μ子g-2的观测值，即μ子磁矩的偏离，这是当前粒子物理学的一个热点问题。由于标准模型预测与实验测量之间的差异，可能存在新物理效应，而三重态leptoquarks的引入可以作为潜在的解释机制。此外，模型还提出了一种玻色子暗物质(bosonic dark matter)的候选者。在当前宇宙学研究中，暗物质的存在是支撑宇宙结构形成的重要假设。通过设计合理的模型参数，可以使得这种leptoquark标量粒子成为暗物质的合适候选，满足暗物质的稳定性和宇宙背景观测的要求。为了验证这个模型的有效性，作者进行了全球数值分析。他们对模型中的参数进行了细致的扫描，包括暗物质候选物的质量以及Yukawa耦合的各个组成部分，以确保模型不仅在理论上自洽，而且在实验约束下仍然可行。这一步骤对于建立一个实证支持的理论至关重要，因为它排除了不合适的参数组合，提高了模型预测的可信度。这篇《Physics Letters B》的文章提出了一种具有吸引力的理论框架，它结合了多个重要的物理现象，如中微子质量、B-meson异常衰变、μ子磁矩异常和暗物质。通过严格的数值分析，作者展示了模型在满足实验观测和限制的前提下，是如何解释这些现象并提供新的物理见解的。这一工作的发表对于进一步探索高能物理学的前沿领域具有重要意义。

Physics Letters B 768 (2017) 359–364

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

A three-loop neutrino model with leptoquark triplet scalars

Kingman Cheung

a,b,c

, Takaaki Nomura

, Hiroshi Okada

a,∗

Physics Division, National Center for Theoretical Sciences, Hsinchu 300, Taiwan

Department of Physics, National Tsing Hua University, Hsinchu 300, Taiwan

Division of Quantum Phases and Devices, School of Physics, Konkuk University, Seoul 143-701, Republic of Korea

School of Physics, KIAS, Seoul 130-722, Republic of Korea

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

Article history:

Received

10 January 2017

Received

in revised form 17 February 2017

Accepted

11 March 2017

Available

online 16 March 2017

Editor: M.

Trodden

We propose a three-loop neutrino mass model with a few leptoquark scalars in SU(2)

-triplet form,

through which we can explain the anomaly of B → K

(∗)

−

, a sizable muon g −2and a bosonic dark

matter candidate, and at the same time satisfying all the constraints from lepton ﬂavor violations. We

perform global numerical analyses and show the allowed regions, in which we ﬁnd somewhat restricted

parameter space, such as the mass of dark matter candidate and various components of the Yukawa

couplings in the model.

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

1. Introduction

Recently, there was an 2.6σ anomaly in lepton-universality vio-

lation

in the ratio R

≡ B(B → K μμ)/B(B → Kee) =0.745

+0.090

−0.074

0.036 by the LHCb Collaboration [1]. In addition, sizable deviations

were observed in angular distributions of B → K

∗

μμ [2]. The re-

sults

can be interpreted by a large negative contribution to the

Wilson coeﬃcient C

of the semileptonic operator O

, and also

contributions to other Wilson coeﬃcients, in particular to C



[3–6].

The

discrepancy between the theoretical prediction and exper-

imental

value on the muon anomalous magnetic dipole moment

has been a long-standing problem, which stands at 3.6σ level with

the deviation from the SM prediction at [7].

a

exp

−a

= 288(63)(49) × 10

−11

If one insists on fulﬁlling the muon g −2within 1σ −2σ of the ex-

perimental

value in any models, it puts a strong constraint on the

parameter space. For example, it requires a relatively light spec-

trum

in the supersymmetric particles in the MSSM in order to

bring the prediction to be within 1σ − 2σ of the experimental

value. A number of leptoquark models have been proposed to solve

the B → K

(∗)

μμ anomaly, but however it is very hard to satisfy si-

multaneously

the muon g −2: see for example Ref. [8].

this work, we propose a three-loop neutrino mass model

with a few leptoquark scalars in SU(2)

-triplet form. We attempt

Corresponding author.

E-mail

addresses: cheung@phys.nthu.edu.tw (K. Cheung), nomura@kias.re.kr

(T. Nomura),

macokada3hiroshi@cts.nthu.edu.tw (H. Okada).

to use the model to explain the anomaly of B

(∗)

→ K μ

−

, to

achieve a sizable muon g −2, and to provide a bosonic dark matter

candidate, and at the same time satisfying all the constraints from

lepton ﬂavor violations. The concrete model is based on the SM

symmetry and a Z

symmetry as SU(3)

× SU(2)

× U(1)

× Z

The model consists of the SM ﬁelds, 3 additional leptoquark triplet

ﬁelds 

,2,3

, and one colorless doublet scalar ﬁeld η. These ﬁelds

are assigned different Z

parities and hypercharges in such a way

that each of the Yukawa-type couplings contributes to either neu-

trino

mass, B → K

(∗)

μμ anomaly, muon g − 2, or the dark matter

interactions. In this way, although the model contains more param-

eter,

it can however explain all the above anomalies. The achieve-

ments

of the model can be summarized in the following.

1. The

neutrino mass pattern and oscillation can be accommo-

dated

with the Yukawa coupling terms f , g, h in three-loop

diagrams.

2. The Yukawa coupling term f can give useful contributions to

the Wilson coeﬃcients C

9,10

in such a way that it can explain

successfully the B → K

(∗)

μμ anomaly.

3. The

muon g −2 receives a large contribution from the Yukawa

coupling term r. With some adjustment of the parameters a

level of 10

−9

is possible.

4. It

provides a dark matter (DM) candidate η

, the real part of

the neutral component of the η ﬁeld with correct relic density.

See refs. [9–11] for representative three loop neutrino mass models.

http://dx.doi.org/10.1016/j.physletb.2017.03.021

0370-2693/

SCOAP

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