轻前夸克模型中双虚拟π0，η，η'→γ*γ*转换形状因子研究

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"这篇研究论文探讨了光前夸克模型中的双虚（π0，η，η'）→γ*γ*过渡形状因子，这是粒子物理学中的一个重要概念，特别是在理解弱电相互作用和强相互作用的接口处。作者通过使用光前夸克模型（LFQM）来研究这些双虚拟过渡形式因子，该模型是一种理论工具，用于描述夸克在高能物理过程中的行为。" 在论文中，研究人员首次展示了在完全可求解的明显协变量贝特-沙拉珀（BS）模型中进行的LF计算，他们选择q1+ = 0框架进行分析，并发现LF和明显协变量计算对于FPγ*(Q12, Q22)的结果是一致的，这排除了双重虚拟TFF中存在LF零模式的可能性。LFQM是基于量子场论的一种方法，它允许在相对论不变性框架下研究夸克和胶子的动力学。接下来，研究团队将这个协变BS模型映射到标准LFQM，利用了由LFQM分析介子质量谱得到的现象学上更容易获取的高斯波函数。他们对FPγ*(Q12, Q22)进行了数值分析，并将LFQM的结果与实验数据、微扰量子色动力学（pQCD）预测以及矢量介子优势（VMD）模型进行了比较。当动量平方（Q12, Q22）趋向无穷大时，LFQM的结果与pQCD的预测一致，即FPγ*(Q12, Q22) ∼ 1/(Q12 + Q22)，而与VMD模型的FPγ* VMD(Q12, Q22) ∼ 1/(Q12Q22)表现不同。对于Fη'γ*(Q12, Q22)的LFQM预测，研究发现其与BABAR合作组最近在2 < (Q12, Q22) < 60 GeV2范围内获得的数据有显著差异，这可能为进一步理解η'介子的性质和强相互作用提供新的洞察。这项工作突出了LFQM在处理高能物理过程中复杂问题的有效性，同时也强调了理论模型与实验数据之间的比较对于验证和改进模型的重要性。开放获取的标签意味着这篇论文对所有感兴趣的研究人员都是可访问的，从而促进学术界更广泛地讨论和应用这些研究成果。

Doubly virtual (π

;η;η

) → γ



transition form factors

in the light-front quark model

Ho-Meoyng Choi

Department of Physics, Teachers College, Kyungpook National University, Daegu 41566, Korea

Hui-Young Ryu

Department of Physics, Pusan National University, Pusan 46241, Korea

Chueng-Ryong Ji

Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA

(Received 5 March 2019; published 19 April 2019)

We report our investigation on the doubly virtual transition form factors (TFFs) F

Pγ



ðQ

Þ for the

P → γ



ðq

Þγ



ðq

ÞðP ¼ π

; η; η

Þ transitions using the light-front quark model (LFQM). Performing a LF

calculation in the exactly solvable manifestly covariant Bethe-Salpeter (BS) model as the first illustration,

we use the q

¼ 0 frame and find that both LF and manifestly covariant calculations produce exactly the

same results for F

Pγ



ðQ

Þ. This confirms the absence of the LF zero mode in the doubly virtual TFFs.

We then map this covariant BS model to the standard LFQM using the more phenomenologically

accessible Gaussian wave function provided by the LFQM analysis of meson mass spectra. For the

numerical analyses of F

Pγ



ðQ

Þ, we compare our LFQM results with the available experimental data

and the perturbative QCD (pQCD) and vector meson dominance (VMD) model predictions. As

ðQ

Þ → ∞ , our LFQM result for doubly virtual TFF is consistent with the pQCD prediction, i.e.,

Pγ



ðQ

Þ ∼ 1=ðQ

þ Q

Þ, while it differs greatly from the result of the VMD model, which behaves

as F

VMD

Pγ



ðQ

Þ ∼ 1=ðQ

Þ. Our LFQM prediction for F



ðQ

Þ shows an agreement with the

very recent experimental data obtained from the BABAR Collaboration for the ranges of

2 < ðQ

Þ < 60 GeV

DOI: 10.1103/PhysRevD.99.076012

I. INTRODUCTION

The meson-photon transitions such as P → γ

ðÞ

ðP ¼

; η; η

Þ with one or two virtual photons have been of

interest to both theoretical and experimental physics

communities since they are the simplest possible bound

state processes in quantum chromodynamics (QCD) and

they play a significant role in allowing both the low- and

high-energy precision tests of the standard model.

In particular, both singly virtual and doubly virtual

transition form factors (TFFs) are required to estimate

the hadronic light-by-light (HLbL) scattering contri-

bution to the muon anomalous magnetic moment

ðg − 2Þ

. The HLbL contribution is in principle obtained

by integrating some weighting functions times the product

of a single-virtual and a double-virtual TFF for spacelike

momentum [1–3]. The single-virtual TFFs have been

measured either from the spacelike e

−

→ e

−

P process

in the single tag mode [4–6] or from the timelike Dalitz

decays P →

llγ [7–12], where ð2m

≤ q

≤ m

. The

timelike region beyond the single Dalitz decays may be

accessed through the e

−

→ Pγ annihilation processes,

and the BABAR Collaboration [13] measured the timelike

ð0Þ

TFFs from the reaction e

−

→ η

ð0Þ

γ at an average

−

center of mass energy of

ﬃﬃﬃ

¼ 10.58 GeV.

Very recently, the BABAR Collaboration [14] measured

for the first time the double-virtual γ



ðq

Þγ



ðq

Þ → η

TFF



ðQ

Þ in the spacelike (i.e., Q

1ð2Þ

¼ −q

1ð2Þ

> 0)

kinematic region of 2 < ðQ

Þ < 60 GeV

by using the

−

→ e

−

process in the double-tag mode as shown

in Fig. 1. It is very interesting to note that the measurement

of F

Pγ



ðQ

Þ at large Q

and Q

distinguishes the

predictions of the model inspired by perturbative QCD

(pQCD) [15,16], F

pQCD

Pγ



ðQ

Þ∼ 1=ðQ

þQ

Þ,fromthose

of the vector meson dominance (VMD) model [17–19],

Published by the American Physical Society under the terms of

the Creative Commons Attribution 4.0 International license.

Further distribution of this work must maintain attribution to

the author(s) and the published article’s title, journal citation,

and DOI. Funded by SCOAP

PHYSICAL REVIEW D 99, 076012 (2019)

2470-0010=2019=99(7)=076012(8) 076012-1 Published by the American Physical Society

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