Photoproduction of ee- in peripheral isobar collisions

2025-05-02 0 0 844.54KB 17 页 10玖币

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Photoproduction of e+e−in peripheral isobar collisions

Shuo Lin,1, ∗Ren-Jie Wang,1, †Jian-Fei Wang,1, ‡

Hao-Jie Xu,2, §Shi Pu,1, ¶and Qun Wang1, ∗∗

1Department of Modern Physics, University of Science

and Technology of China, Anhui 230026, China

2School of Science, Huzhou University, Huzhou, Zhejiang, 313000, China

Abstract

We investigate the photoproduction of di-electrons in peripheral collisions of 96

44Ru +96

44 Ru and

40Zr +96

40 Zr at 200 GeV. With the charge and mass density distributions given by the calculation

of the density functional theory, we calculate the spectra of transverse momentum, invariant mass

and azimuthal angle for di-electrons at 40-80% centrality. The ratios of these spectra in Ru+Ru

collisions over to Zr+Zr collisions are shown to be smaller than (44/40)4(the ratio of Z4for Ru and

Zr) at low transverse momentum. The deviation arises from the diﬀerent mass and charge density

distributions in Ru and Zr. So the photoproduction of di-leptons in isobar collisions may provide a

new way to probe the nuclear structure.

∗linshuo@mail.ustc.edu.cn

†wrjn@mail.ustc.edu.cn

‡wjf1996@mail.ustc.edu.cn

§haojiexu@zjhu.edu.cn

¶shipu@ustc.edu.cn

∗∗ qunwang@ustc.edu.cn

arXiv:2210.05106v1 [hep-ph] 11 Oct 2022

I. INTRODUCTION

In ultra-relativistic heavy ion collisions, extremely strong electromagnetic ﬁelds (of order

1015 Tesla) are generated when two colliding nuclei pass through each other [1–5]. Such

strong electromagnetic ﬁelds provide an experimental platform for the study of novel quan-

tum transport phenomena under extreme conditions, such as the chiral magnetic and sep-

aration eﬀects [6,7], the chiral electric separation eﬀect [8,9], and other nonlinear eﬀects

[10–12]. These chiral transport phenomena can be described by microscopic quantum ki-

netic theories [12–49] and macroscopic magnetohydrodynamics [5,50–54], see, e.g., Refs.

[45,55–62] for recent reviews. On the other hand, it is also possible to study nonlinear

eﬀects of quantum electrodynamics (QED) in ultra-relativistic heavy ion collisions, such

as light-by-light scatterings [63], matter generation directly from photons [64,65], vacuum

birefringence [64,66–70] and Schwinger mechanism [71–74].

In recent years, the lepton pair photoproduction in peripheral and ultra-peripheral colli-

sions has been extensively studied in both experiments and theories. To give a better un-

derstanding of experimental data [64,75–77], besides the equivalent photon approximation

(EPA) by STARlight [78], several theoretical methods have been developed, such as QED

models with generalized EPA in the background ﬁeld approach [65,79–86], the method

based on the factorization theorem [87–90] and the QED model with the wave-packet de-

scription of nuclei [91,92]. Furthermore, it has been shown in Ref. [85,89] that linearly

polarized photons, similar to linearly polarized gluons [93–97], can generate the azimuthal

angle modulation measured by the STAR collaboration [64]. A similar azimuthal angle

asymmetry in diﬀractive production of pions related to elliptic gluon Wigner distribution in

ultra-peripheral collisions is proposed in Ref. [98]. So the photonuclear reaction can be used

to probe the properties of initial gluons [98–102].

The isobar collisions of 96

44Ru+96

44Ru and 96

40Zr+96

40Zr at the top collision energy of RHIC were

originally proposed to search for the chiral magnetic eﬀect (CME) [103]. Since Ru and Zr are

isobars (with the same nucleon number but diﬀerent proton numbers), the electromagnetic

ﬁelds and thus the chiral magnetic eﬀect should be diﬀerent in isobar collisions at the same

centrality, while the backgrounds related to collision geometry, such as the elliptic ﬂow v2

and charged hadron multiplicity Nch, are expected to be the same. However, according

to the calculation based on the energy density functional theory (DFT), there are sizable

diﬀerences in nuclear density distributions for CME backgrounds which ruin the initial

premise of isobar collisions for the CME search [104,105]. This has recently been conﬁrmed

by the isobar data of STAR collaboration [106], indicating that the structure of isobar nuclei

is crucial to the baseline for the CME signal. The lepton pair photoproduction depends on

the charge distributions of colliding nuclei, which may provide a further constraint on the

nuclear structure parameters in isobar collisions.

In this paper, we employ the theoretical method developed in previous studies [91,92] by

some of us to investigate the lepton pair photoproduction in isobar collisions. The method

is based on QED in a classical ﬁeld approximation with the wave-packet description of

colliding nuclei encoding the information of the polarization and transverse momentum (or

impact parameter) dependence of photons in the diﬀerential cross section. It can describe

the photoproduction data of lepton pairs in peripheral and ultra-peripheral collisions [64,

76,107].

We will calculate the transverse momentum, invariant mass and azimuthal angle distribu-

tions for e+e−pairs at √sNN = 200 GeV in Ru+Ru and Zr+Zr collisions. The Woods-Saxon

parameters for isobar nuclei are obtained by the state-of-art DFT calculation through nuclear

charge and mass density distributions [108]. Since the nuclear mass and charge density dis-

tributions give sizable diﬀerence in multiplicity distributions in isobar collisions, the lepton

pair photoproduction is calculated with the charge density distribution, while the centrality

is deﬁned from the Glauber model with the nuclear mass density. The centrality determined

from the charge density distribution will also be computed as a control. This study provides

a new way of probing the nuclear structure through photoproduction of lepton pairs in isobar

collisions.

The paper is organized as follows. In Sec. II, we brieﬂy review the theoretical method

[91] and introduce the parameters in the numerical calculation. In Sec. III, we present

the transverse momentum, invariant mass and azimuthal angle distributions for e+e−at

√sNN =200 GeV in Ru+Ru and Zr+Zr collisions. We study the charge and centrality

dependence of the cross section in Sec. IV. We make a summary of the main result in

Sec. V.

Notational convention. We use Pee

T=k1T +k2T for the transverse momentum of the

electron pair and Kee

T=1

2(k2T −k1T)for the diﬀerence in transverse momentum between

the electron and positron. We use Mee for the invariant mass of the electron pair and φfor

the angle between Pee

Tand Kee

T. We also use Pee

T=|Pee

T|and Kee

T=|Kee

T|for the lengths of

two vectors.

II. THEORETICAL METHOD AND SETUP

We will use in our calculation the method developed by some of us for lepton pair pho-

toproduction in the classical ﬁeld approximation with the wave packet description of nuclei

[91,92]. Suppose two identical nuclei A1and A2move in ±zdirection with the velocity

uµ

1,2=γ(1,0,0,±v)[γ= 1/√1−v2is the Lorentz factor] respectively. Two photons from

colliding nuclei produce a lepton pair as γ(p1) + γ(p2)→l(k1) + l(k2), where pµ

1and pµ

are four-momenta of photons (photons are not exactly on-shell), and kµ

1= (Ek1,k1)and

kµ

2= (Ek2,k2)are on-shell four-momenta leptons. The Born-level total cross section can be

written into a compact form,

σ=Z4e4

2γ4v3ˆd2bTd2b1Td2b2Tˆdω1d2p1T

(2π)3

dω2d2p2T

(2π)3

×ˆd2p0

(2π)2e−ib1T·(p0

1T−p1T)F∗(−p02

−p02

F(−p2

−p2

×ˆd2p0

(2π)2e−ib2T·(p0

2T−p2T)F∗(−p02

−p02

F(−p2

−p2

×ˆd3k1

(2π)32Ek1

d3k2

(2π)32Ek2

(2π)4δ(4) (p1+p2−k1−k2)δ(2) (bT−b1T+b2T)

×X

spin of l,l

[u1µu2νLµν (p1, p2;k1, k2)] [u1σu2ρLσρ∗(p0

1, p0

2;k1, k2)] ,(1)

where Zis the proton number of the nuclei, biT is the transverse position of the photon

emission in the nucleus Ai,bTis the impact parameter of colliding nuclei, piand p0

iare

photon momenta in the classical ﬁeld approximation and deﬁned as (i= 1,2)

pµ

i=ωi,piT ,(−1)i+1 ωi

v, p0µ

i=ωi,p0

iT ,(−1)i+1 ωi

v,(2)

satisfying pi·ui=p0

i·ui= 0, the lepton tensor Lµν is given by

Lµν (p1, p2;k1, k2) = −ie2u(k1)"γµγ·(k1−p1) + m

(k1−p1)2−m2+iεγν

+γνγ·(p1−k2) + m

(p1−k2)2−m2+iεγµ#v(k2),(3)

and F(−p2)is the nuclear charge form factor, Fourier transform of the nuclear charge density

distribution.

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摘要：

Photoproductionofe+einperipheralisobarcollisionsShuoLin,1,Ren-JieWang,1,yJian-FeiWang,1,zHao-JieXu,2,xShiPu,1,{andQunWang1,1DepartmentofModernPhysics,UniversityofScienceandTechnologyofChina,Anhui230026,China2SchoolofScience,HuzhouUniversity,Huzhou,Zhejiang,313000,ChinaAbstractWeinvestigatethephot...

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