双峰与三峰LQ模型：μg-2，RK(*)和RD(*)的解析

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本研究探讨了在瘦夸克模型（leptoquark model）中，μg-2、RK(*)和RD(*)这三个物理量的异常行为。模型中包含一个双峰态、一个三重峰态和一个单峰态的标量夸克（scalar leptoquarks，简称LQ）。LQ在粒子物理学中是一种假设的粒子，它能够同时携带电荷和弱相互作用，从而可能解释某些超出标准模型的现象。作者们分析了一个具体模型，该模型中的LQ与μ介子（muon）相关的磁矩（muon g-2），以及B meson的两种衰变过程，即B到μμ（B_s→μ+μ-）和B+到K+反中微子（B+→K+νν̄）的实验结果。这些过程对LQ的性质有着严格的限制，因为它们的观测值与理论预期之间存在显著的不一致性，也就是所谓的"anomalies"。当严格考虑这些限制时，发现单个标量LQ难以同时解释所有的异常，因为它们之间存在强烈的关联性。为了克服这个难题，研究者在分析中忽略了部分约束和较小的耦合。结果显示，μg-2的异常可以通过双峰态LQ得到一定程度的解释，因为其在模型中的存在能够提升mt（top quark mass）的影响。然而，对于较小的RK(*)，则需要双峰态和三重峰态LQ的联合效应。这表明在特定的模型配置下，不同类型的LQ组合能够提供更全面的解决方案。至于RD(*)和RD(*)*的过量，则主要依赖于单线态LQ的标量和张量类型相互作用。这些发现揭示了LQ模型在解释精细物理测量时的复杂性，以及多峰态LQ在满足实验数据和理论预测之间的微妙平衡中的角色。总结来说，这项研究深入探讨了在特定的LQ模型框架内，如何通过多重态LQ的组合来解释μg-2和B meson衰变的异常，并展示了这种模型在解释物理现象时的灵活性和限制。这对于理解基础粒子物理学的潜在新物理现象以及标准模型的扩展具有重要意义。

Physics Letters B 774 (2017) 456–464

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Excesses of muon g −2, R

(∗)

, and R

(∗)

in a leptoquark model

Chuan-Hung Chen

, Takaaki Nomura

b,∗

, Hiroshi Okada

Department of Physics, National Cheng-Kung University, Tainan 70101, Taiwan

School of Physics, KIAS, Seoul 02455, Republic of Korea

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

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

Article history:

Received

22 March 2017

Received

in revised form 27 September

2017

Accepted

1 October 2017

Available

online 4 October 2017

Editor: B. Grinstein

In this study, we investigate muon g −2, R

(∗)

, and R

(∗)

anomalies in a speciﬁc model with one doublet,

one triplet, and one singlet scalar leptoquark (LQ). When the strict limits from the 



→ γ , B = 2,

→ μ

−

, and B

→ K

ν processes are considered, it is diﬃcult to use one scalar LQ to explain

all of the anomalies due to the strong correlations among the constraints and observables. After ignoring

the constraints and small couplings, the muon g − 2can be explained by the doublet LQ alone due to

the m

enhancement, whereas the measured and unexpected smaller R

(∗)

requires the combined effects

of the doublet and triplet LQs, and the R

and R

∗

excesses depend on the singlet LQ through scalar-

and

tensor-type interactions.

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

1. Introduction

Several interesting excesses in semileptonic B decays have been

determined in experiments such as: (i) the angular observable P



of B → K

∗

−

[1], where a 3.4σ deviation due to the integrated

luminosity of 3.0fb

−1

was found at the LHCb [2,3], and the same

measurement with a 2.6σ deviation was also reported by Belle [4];

and (ii) the branching fraction ratios R

D,D

∗

, which are deﬁned and

measured as [5–10]:

B → Dτν

B → Dν



0.375 ±0.064 ± 0.026 Belle [5] ,

0.440 ±0.058 ± 0.042 BaBar [6,7] ,

∗

B → D

∗

τν

B → D

∗

ν

⎧

⎪

⎨

⎪

⎩

0.302 ±0.030 ± 0.011 Belle [8] ,

0.270 ±0.035±

+0.028

−0.025

Belle [9] ,

0.332 ±0.024 ± 0.018 BaBar [6,7] ,

0.336 ±0.027 ± 0.030 LHCb [10] ,

(1)

where  = (e, μ), and these measurements can test the viola-

tion

of lepton-ﬂavor universality. The averaged results from the

heavy ﬂavor averaging group are R

= 0.403 ± 0.040 ± 0.024 and

∗

= 0.310 ± 0.015 ± 0.008 [11], and the standard model (SM)

predictions are around R

≈ 0.3 [12,13] and R

∗

≈ 0.25, respec-

tively.

Corresponding author.

E-mail

addresses: physchen@mail.ncku.edu.tw (C.-H. Chen), nomura@kias.re.kr

(T. Nomura),

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

Further tests of lepton-ﬂavor universality can be made us-

ing

the branching fraction ratios R

(∗)

= BR(B → K

(∗)

−

BR(B → K

(∗)

−

). The current LHCb measurements are R

0.745

+0.090

−0.074

± 0.036 [14] and R

∗

= 0.69

+0.11

−0.07

± 0.05 [15], which

indicate a more than 2.5σ deviation from the SM results. In ad-

dition,

a known anomaly is the muon anomalous magnetic dipole

moment (muon g − 2), where its latest measurement is a

exp

− a

= (28.8 ± 8.0) × 10

−10

[16]. If we assume that these

results are correct, we need to extend the SM to explain these

excesses. Inspired by these experimental observations, various so-

lutions

to the anomalies have been proposed [17–78].

the SM, the b → c







decays (



= e, μ, τ ) arise from the

W -mediated tree diagram, whereas the b → s

+



−

decays are

generated by W -mediated box and Z -mediated penguin diagrams.

In the present study, based on our earlier study of muon g −2 and

anomalies [73], we attempt to establish a speciﬁc model that

simultaneously explains the muon g −2, R

(∗)

, and R

(∗)

anomalies

when the experimental bounds involved are satisﬁed. The serious

constraints include 

→ 

γ , F = 2, B

→ μ

−

, B → K ν

ν, etc.

To clarify the effects introduced, we do not scan all of the param-

eters

involved, but instead we retain the relevant couplings that

can satisfy or escape from the experimental bounds, whereas we

directly neglect the constrained and smaller couplings.

obtain the non-universal lepton-ﬂavor effects, we consider

the extension of the SM by including scalar leptoquarks (LQs),

where the LQs are colored scalar particles that are coupled to a

lepton and a quark at the same vertex, and the couplings to the

quarks and leptons are ﬂavor-dependent free parameters. LQs can

https://doi.org/10.1016/j.physletb.2017.10.005

0370-2693/

SCOAP

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