Perturbative Color Correlations in Double Parton Scattering.

2025-05-02 0 0 929.75KB 60 页 10玖币

侵权投诉

B. Blok∗and J. Mehl†

Department of Physics, Technion – Israel Institute of Technology, Haifa, Israel

We study the contribution of color correlations to Double Parton Scattering (DPS). We

show that there is a speciﬁc class of Feynman diagrams related to so called 1 →2 processes

when the contribution of these color correlations is not Sudakov suppressed with the trans-

verse scales. The eﬀective absence of Sudakov suppression gives hope that although they are

small relative to color singlet correlations, they eventually can be observed.

∗blok@physics.technion.ac.il

†yonatanm@campus.technion.ac.il

arXiv:2210.13282v2 [hep-ph] 11 May 2024

CONTENTS

I. Introduction 3

II. pQCD Formalism 7

A. Color Non-Singlet DGLAP equation 7

B. Generalized Parton Distribution 12

C. 1→2for Color Non-Singlet Channels 14

Self Consistency of the α

[1]DAB

hNormalization 18

D. Regularization of zi→1Singularity 20

III. Numerics 22

IV. Conclusion 25

Acknowledgments 26

A. Color Kernels 26

1. Color Factor for the 8aRepresentation 27

a. CG

G28

b. CG

F29

c. CF

F30

d. CF

G30

2. Color Factor for the 8sRepresentation 31

a. CG

G31

b. CG

F32

c. CF

F33

d. CF

G33

3. Normalization of CG

Fand CF

G34

a. 8a35

b. 8s35

B. Formal Derivation of the Non-Singlet DGLAP Equation 36

C. e

Aat the Limit x→138

D. Regularizing Divergent Integrals 44

E. Rules for Color Projectors 46

1. Exact Form of Projectors 46

2. Properties 47

a. Projectors 47

b. Symmetries 47

c. Change in Basis 48

d. Interaction Force 50

e. Dimensions of the Representation 50

f. Completeness Relation 51

3. Proof of Incoming-Outgoing Symmetry 51

F. Comments on Diﬀerent Formalisms 51

1. The Sudakov Suppression Factor. 51

a. Proof of the Singlet Case 52

b. The non-Singlet Case. 53

c. Diﬀerent Sudakov Factors 55

2. Regularization of z→1divergence 56

References 59

I. INTRODUCTION

The theory of double parton scattering (DPS) in QCD was the subject of intensive development

in recent years. The ﬁrst work on DPS was done in the early 80s [1, 2], and the ﬁrst detailed

experimental observations of DPS were done in Tevatron. Recently new detailed experimental

studies of DPS were carried out at LHC while a new theoretical formalism based on pQCD was

developed [3–11]. In these works, the fundamental role of parton correlations in DPS scattering

was realized and estimated and new physical objects to study these correlations - two particle

generalized parton distribution (2GP D ) were introduced. However, most of this work was devoted

to the study of color singlet correlations in DPS processes.

Recently, a lot of interest was attended to color non-singlet correlations in proton-proton colli-

sions. The possibility of such correlations was already discussed in the 80s [12, 13]. However, it was

shown that such correlations are strongly Sudakov suppressed due to a need to change color quan-

tum numbers between the amplitude and the complex conjugate [12, 13]. The color correlations





``>>OOOO

OOOO

(a) (b)

Figure 1. The diﬀerent diagrams contributing to double parton scattering (DPS) (a)the two possible 1+2

processes and (b)a2+2 process. As explained in the text there is no “1+1” contribution. the =line

represents the hadrons

were shown to be suppressed as

exp −αslog2 Q2

Λ2

QCD !! (1)

where Qis the transverse momenta. As a result, such correlations are negligible, at least in

conventional hard processes, and rapidly decrease with hard scale. Such correlations were ﬁrst

considered in [12, 13] for conventional hard processes, and for the so-called 2→2processes in the

DPS (see ﬁgure 1 (b)).

More recently it was realized that the color correlations can occur also in the so-called 1→2

processes and they were studied in [8, 11, 14–16]. In recent work [17] it was noted that the two

particle 2GP D that described color non-singlet correlations can be negative.

Still, there remains a problem to ﬁnd the contribution of color correlations in DPS processes.

Indeed, the contribution of color correlations is Sudakov suppressed, so the appearance of color

ladders in the scattering amplitudes is negligible for transverse momenta where one can expect to

observe the DPS processes. On the other hand, the analysis of singlet correlations in DPS processes

shows that a signiﬁcant part of the contribution to 2GP D comes from the processes where the ladder

splits into two short ladders, corresponding to the fundamental solutions of DGLAP equations for

x∼1, leading to two hard processes. In these ladders, the transverse momenta evolve not from

0∼0.5GeV 2to Q2, but from kto Q2Where Q0≪k≪Qof some indeterminate perturbative

scale where the split occurred.

For such processes, one can consider the 1→2processes depicted in ﬁgure 2 (a). Indeed the two

ladders coming from below in ﬁgure 1 (a), and the ladder that splits are not suppressed. Only two

ladders that go to hard processes after the split are colored and will be suppressed, but Sudakov



singlet e

OOΛ2

QCD



rep. Q2



yy''

77eek2



a a b b Q2

1, Q2

2asinglet a b singlet b

rep. αrep. αrep. rep.

(a) (b)

Figure 2. (a)The 1→2process diagram and its complex conjugate with the DGLAP ladders presented

explicitly. Both parton pairs a, a and b, b are in some nonsinglet representation αwhile e, e are in a singlet

state. (b)the 2→2diagram and its complex conjugate, now a, a and b, b are in a singlet representation

because other representations are Sudakov suppressed. The scales of the ladder evolution are shown in

middle.

suppression may be much smaller

∼exp −αslog2Q2

k2.(2)

In this paper we shall calculate 2GP D corresponding to such processes, and ﬁnd that such

2GP D may be indeed large - up to 5-10% relative to singlet 2GP D, extensively studied before

[9, 18]. Moreover, this contribution does not decrease with Q2and slowly increases relative to mean

ﬁeld contribution to 2GP D like for color singlet 1→2processes, thus being present at Tevatron

and LHC. We shall see that these contributions can be both positive and negative, depending on

the representation of color SU (3).

We shall see that the characteristic scale where the singlet ladder in 1→2is increasing with

the hard scale Q of the process. This is contrary to singlet split scale, which does not depend on

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：

PerturbativeColorCorrelationsinDoublePartonScattering.B.Blok∗andJ.Mehl†DepartmentofPhysics,Technion–IsraelInstituteofTechnology,Haifa,IsraelWestudythecontributionofcolorcorrelationstoDoublePartonScattering(DPS).WeshowthatthereisaspecificclassofFeynmandiagramsrelatedtosocalled1→2processeswhenthecontr...

展开>> 收起<<

Perturbative Color Correlations in Double Parton Scattering..pdf

共60页,预览5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！

Perturbative Color Correlations in Double Parton Scattering.

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: