Extraction of Pion Transverse Momentum Distributions from Drell-Yan data TheMAP Collaboration Matteo Cerutti1 2yLorenzo Rossi1 2zSimone Venturini1 2xAlessandro

2025-04-27 0 0 599KB 9 页 10玖币

侵权投诉

Extraction of Pion Transverse Momentum Distributions from Drell-Yan data

The MAP Collaboration∗

Matteo Cerutti,1, 2, †Lorenzo Rossi,1, 2, ‡Simone Venturini,1, 2, §Alessandro

Bacchetta,1, 2, ¶Valerio Bertone,3, ∗∗ Chiara Bissolotti,4, †† and Marco Radici2, ‡‡

1Dipartimento di Fisica, Universit`a di Pavia, via Bassi 6, I-27100 Pavia, Italy

2INFN - Sezione di Pavia, via Bassi 6, I-27100 Pavia, Italy

3IRFU, CEA, Universit´e Paris-Saclay, F-91191 Gif-sur-Yvette, France

4HEP Division, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, IL, 60439 USA

We map the distribution of unpolarized quarks inside a unpolarized pion as a function of

the quark’s transverse momentum, encoded in unpolarized Transverse Momentum Distributions

(TMDs). We extract the pion TMDs from available data of unpolarized pion-nucleus Drell–Yan

processes, where the cross section is diﬀerential in the lepton-pair transverse momentum. In the

cross section, pion TMDs are convoluted with nucleon TMDs that we consistently take from our

previous studies. We obtain a fairly good agreement with data. We present also predictions for

pion-nucleus scattering that is being measured by the COMPASS Collaboration.

I. INTRODUCTION

The pion is the simplest of all hadrons and together with the nucleon constitutes one of the most fundamental

entities in the visible Universe. In the Standard Model, both particles are built as bound states of the quark and

gluon degrees of freedom of Quantum ChromoDynamics (QCD). However, in this context the pion plays a unique

role since it is the Goldstone boson of chiral symmetry breaking. Therefore, it is extremely important to investigate

its internal structure and understand how the latter is responsible of the macroscopic diﬀerences between the bound

state of a pion and of a nucleon (see, e.g., Ref. [1] for a review).

The internal structure of the pion can be described in terms of Parton Distribution Functions (PDFs). Starting

from the 1990s, PDFs have been extracted from data in various papers [2–12]. In spite of this extensive literature,

the structure of the pion is known to a much less extent than that of the proton, due to the scarcity of data on

high-energy scattering processes involving pions.

While PDFs describe the distribution of quarks and gluons as a function of only their momentum component

longitudinal to the parent hadron, Transverse Momentum Distributions (TMDs) describe the distribution in three-

dimensional momentum space. If the knowledge of the one-dimensional structure of the pion is limited, almost

nothing is known about its three-dimensional structure. Model calculations of pion TMDs have been discussed in

Refs. [13–20].

The extraction of TMDs from data is based on TMD factorization theorems and is more challenging than that

of collinear PDFs. For proton TMDs, factorization theorems have been proven for Semi-Inclusive Deep-Inelastic

Scattering (SIDIS), for Drell-Yan (DY) lepton-pair production in hadronic collisions, and for semi-inclusive electron-

positron annihilations (see Ref. [21] and references therein). Recently, very accurate studies of proton unpolarized

TMDs have been released [22–28], some of which are based on a global analysis of such processes. For pion TMDs,

data are available only for the DY process and only two analyses have been published [29, 30].

In this paper, we present an extraction of unpolarized pion quark TMDs by analyzing for the ﬁrst time the whole

set of available data for the DY lepton-pair production in π−-nucleus collisions, obtained from the E615 [31] and

∗The MAP acronym stands for “Multi-dimensional Analyses of Partonic distributions”. It refers to a collaboration aimed

at studying the three-dimensional structure of hadrons. The public codes released by the collaboration are available at

https://github.com/MapCollaboration.

†Electronic address: matteo.cerutti@pv.infn.it – ORCID: 0000-0001-7238-5657

‡Electronic address: lorenzo.rossi@pv.infn.it – ORCID: 0000-0002-8326-3118

§Electronic address: simone.venturini01@universitadipavia.it – ORCID: 0000-0002-4105-7930

¶Electronic address: alessandro.bacchetta@unipv.it – ORCID: 0000-0002-8824-8355

∗∗Electronic address: valerio.bertone@cea.fr – ORCID: 0000-0003-0148-0272

††Electronic address: cbissolotti@anl.gov – ORCID: 0000-0003-3061-0144

‡‡Electronic address: marco.radici@pv.infn.it – ORCID: 0000-0002-4542-9797

arXiv:2210.01733v1 [hep-ph] 4 Oct 2022

E537 [32] experiments. The cross section diﬀerential in the lepton-pair transverse momentum can be written as a

convolution of a unpolarized proton TMD and a unpolarized pion TMD. For the proton TMD, we use the result

recently obtained by the MAP collaboration [28] and we extract the pion TMD from data using the same formalism.

With respect to Ref. [30], we use more data and diﬀerent prescriptions for the implementation of TMD evolution.

With respect to Ref. [29], we use more data, a higher theoretical accuracy, a up-to-date extraction of the proton

TMDs, and we consistently use the same Collins–Soper kernel for proton and pion TMDs.

II. FORMALISM

In the DY process

hA(PA) + hB(PB)→γ∗(q) + X→`+(l) + `−(l0) + X(1)

the collision between two hadrons hAand hBwith four-momenta PAand PB, respectively, and center-of-mass

energy squared s= (PA+PB)2, produces a neutral vector boson γ∗/Z with four-momentum qand large invariant

mass Q=pq2. The vector boson eventually decays into a lepton and an antilepton with four-momenta constrained

by momentum conservation, q=l+l0. The cross section of this process can be written in terms of two structure

functions F1

UU ,F2

UU . Being Mthe mass of the incoming hadrons and qTthe transverse component of the vector

boson momentum, in the kinematic region where M2Q2and q2

TQ2the structure function F2

UU is suppressed.

Therefore, the cross section can be expressed as

dσDY

d|qT|dydQ '16π2α2

9Q3|qT|F1

UU (xA, xB,qT, Q)

=16π2α2

9Q3|qT|xAxB

2πHDY (Q;µ)X

ca(Q2)ˆd|bT||bT|J0(|qT||bT|)ˆ

1(xA,b2

T;µ, ζA)ˆ

f¯a

1(xB,b2

T;µ, ζB),

(2)

where αis the electromagnetic coupling, yis the pseudorapidity of the vector boson, xA,B =Q

√se±y,HDY is the

hard factor and ˆ

1is the Fourier transform of the unpolarized TMD PDF for ﬂavor a,1which depends on the

renormalization and rapidity scales µand ζ, respectively. The summation over ain Eq. (2) runs over the active

quarks and antiquarks at the hard scale Q, with ca(Q2) the corresponding electroweak charges [28].

The dependence of ˆ

f1on the scales µand ζarises from the removal of the ultraviolet and rapidity divergences

in its operator deﬁnition. In the MS renormalization scheme, it turns out that the choice of the initial scale

µ0=√ζ0=µb(|bT|)=2e−γE/|bT|(with γEthe Euler constant) greatly simpliﬁes the expression of ˆ

f1[26].

However, in order to prevent µbfrom becoming larger than Qat small |bT|and/or hitting the Landau pole at large

|bT|it is necessary to introduce an ad-hoc prescription b∗(b2

T) to avoid these limits. Then, the TMD PDF can be

simply rewritten as [26]

f1(x, b2

T;µ, ζ) = "ˆ

f1(x, b2

T;µ, ζ)

f1(x, b∗(b2

T); µ, ζ)#ˆ

f1(x, b∗(b2

T); µ, ζ)

≡f1NP (x, b2

T;ζ)ˆ

f1(x, b∗(b2

T); µ, ζ),(3)

which eﬀectively deﬁnes the nonperturbative part f1NP of the TMD PDF.

For the collision of a pion and a nucleus (that in ﬁrst approximation is described as a collection of free nu-

cleons), the cross section of Eq. (2) involves the TMD PDFs ˆ

1pand ˆ

1πof a quark ain the proton and in the

pion, respectively. As for the proton, we use for ˆ

1pthe recent global extraction of the MAP Collaboration [28]

at next-to-next-to-next-leading-logarithm (N3LL) accuracy, adopting the same b∗(b2

T) prescription and the same

parametrization of the nonperturbative part fp

1NP . As for the pion, for ˆ

1πwe consistently retain the same b∗(b2

1For the deﬁnition of the Fourier transform see Ref. [28].

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

ExtractionofPionTransverseMomentumDistributionsfromDrell-YandataTheMAPCollaborationMatteoCerutti,1,2,yLorenzoRossi,1,2,zSimoneVenturini,1,2,xAlessandroBacchetta,1,2,{ValerioBertone,3,ChiaraBissolotti,4,yyandMarcoRadici2,zz1DipartimentodiFisica,UniversitadiPavia,viaBassi6,I-27100Pavia,Italy2INFN-...

展开>> 收起<<

Extraction of Pion Transverse Momentum Distributions from Drell-Yan data TheMAP Collaboration Matteo Cerutti1 2yLorenzo Rossi1 2zSimone Venturini1 2xAlessandro.pdf

共9页,预览2页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Extraction of Pion Transverse Momentum Distributions from Drell-Yan data TheMAP Collaboration Matteo Cerutti1 2yLorenzo Rossi1 2zSimone Venturini1 2xAlessandro

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: