γγ∗→ππ过程的分散分析研究

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过程的分散分析在粒子物理学中，过程的分散分析是研究γγ∗→ππ过程的重要方法。该过程是研究强子物理和量子场论的重要实验平台。γγ∗→ππ过程是指γγ∗粒子衰变成ππ粒子的过程，其中γγ∗是γγ∗粒子，π是π介子。在γγ∗→ππ过程中，存在多种衰变通道，例如γγ∗→π+π−、γγ∗→π0π0等。这些衰变通道的研究对于理解强子物理和量子场论的机理具有重要意义。在本文中，我们将讨论γγ∗→ππ过程的理论研究。我们采用Omnès representation来描述ππ不变质量的散射振幅。同时，我们还实现了coupled-channel unitarity来描述f0(980) resonance的性质。我们的研究结果为当前实验two-photon fusion program at BESIII提供了重要的输入。同时，这些结果也可以作为hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment的重要输入。在γγ∗→ππ过程中，存在多种强子的交换过程。这些强子交换过程对γγ∗→ππ过程的影响非常重要。我们可以使用 dispersion relations 来研究这些强子交换过程对γγ∗→ππ过程的影响。 Dispersion relations是研究强子物理和量子场论的重要工具。它可以用来研究强子交换过程对散射振幅的影响。我们可以使用 dispersion relations 来研究γγ∗→ππ过程中的强子交换过程，从而获得更加准确的理论结果。在γγ∗→ππ过程中，我们还可以研究ππ不变质量的散射振幅。我们可以使用 Omnès representation 来描述ππ不变质量的散射振幅。这将有助于我们更好地理解γγ∗→ππ过程的机理。 γγ∗→ππ过程的理论研究对于理解强子物理和量子场论的机理具有重要意义。我们的研究结果为当前实验two-photon fusion program at BESIII提供了重要的输入，同时这些结果也可以作为hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment的重要输入。在未来，我们将继续研究γγ∗→ππ过程中的强子交换过程和ππ不变质量的散射振幅。这将有助于我们更好地理解γγ∗→ππ过程的机理，并为当前实验two-photon fusion program at BESIII提供更加准确的理论结果。

Physics Letters B 789 (2019) 366–372

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Dispersive analysis of the γγ

∗

→ ππ process

Igor Danilkin

∗

, Marc Vanderhaeghen

Institut für Kernphysik & PRISMA Cluster of Excellence, Johannes Gutenberg Universität, D-55099 Mainz, Germany

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

Article history:

Received

10 October 2018

Received

in revised form 4 December 2018

Accepted

20 December 2018

Available

online 21 December 2018

Editor:

J.-P. Blaizot

We present a theoretical study of the γγ

∗

→ π

−

, π

processes from the threshold through the

(1270) region in the ππ invariant mass. We adopt the Omnès representation in order to account for

rescattering effects in both s- and d-partial waves. For the description of the f

(980) resonance, we

implement a coupled-channel unitarity. The constructed amplitudes serve as an essential framework to

interpret the current experimental two-photon fusion program at BESIII. They also provide an important

input for the dispersive analyses of the hadronic light-by-light scattering contribution to the muon’s

anomalous magnetic moment.

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

1. Introduction

The two-photon fusion reaction is a prime example where us-

ing

S-matrix constraints, such as analyticity and unitarity one can

make predictions, which serve as direct input into the Standard

Model calculation of the hadronic light-by-light (HLbL) scattering

contribution to the muon’s anomalous magnetic moment a

. The

HLbL contribution is currently the largest source of uncertainty in

this precision quantity, which at present shows a 3–4 σ deviation

between theory and experiment [1,2]. Ongoing experimental pro-

grams

at FERMILAB [3] and J-PARC [4]aim to reach a fourfold in-

crease

in precision in the direct measurement of a

. This prospect

calls to reduce the theory uncertainty accordingly, which in turn

critically entails to reduce the error on the HLbL contribution by a

concerted theoretical and experimental effort. Experimentally, two-

photon

fusion reactions are studied at e

−

colliders. When both

leptons in the process e

−

→ e

−

X are detected in the ﬁnal

state, this reaction allows to access the two-photon fusion process

∗

→ X , where both photons have a spacelike virtuality. The

dominant HLbL contributions to a

are coming from the produc-

tion

of the lightest pseudoscalar mesons X = π

, η, η



. The next

important contribution comes from pion pairs, which we consider

in this paper. The ﬁrst measurement of the γγ

∗

→ π

process

has been reported recently by the Belle Collaboration [5]for Q

the region from 3.5–30 GeV

. At small momentum transfers, the

Corresponding author.

E-mail

address: danilkin@uni-mainz.de (I. Danilkin).

BESIII Collaboration is currently analyzing both π

−

and π

production in the 0.2GeV

 Q

 2GeV

range [6], correspond-

ing

with the most relevant kinematical region for quantifying the

HLbL contribution to a

Very

close to threshold, the γγ → ππ process has been stud-

ied

in χ PT up to two-loop accuracy [7,8]as a tool to access pion

polarizabilities. Such approaches fail however to describe the res-

onance

region, which require resummation techniques to comply

with exact unitarity [9–13]. Among those, the most established

ones respect analyticity properties of the S-matrix [11–14]. The

energy range of applicability of such dispersive techniques is typi-

cally

limited by the inelastic contributions and inclusion of higher

partial waves. Extending such dispersive techniques to the par-

tial

wave helicity amplitudes of the single virtual γγ

∗

→ ππ

process is not straightforward, as in addition to the well-known

low-energy constraints, partial-wave amplitudes exhibit kinematic

constraints. Therefore, so far, the dispersive analyses of γγ

∗

→ ππ

have been limited to the s-wave and single-channel description

[15,16] which only covers the f

(500) resonance region. The aim

of this work is to extend the dispersive approach to the coupled-

channel

case by including K

K intermediate states and to include

for the ﬁrst time the d-wave contribution, which allows for a full

dispersive formalism through the prominent f

(1270) tensor me-

son

region. This will allow for a validation of such approach by

forthcoming BESIII data for the γγ

∗

→ ππ reaction, which is a

prerequisite for a data-driven approach in quantifying the uncer-

tainty

of the HLbL contribution to a

https://doi.org/10.1016/j.physletb.2018.12.047

0370-2693/

SCOAP

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