FERMILAB-PUB-22-762-TIPPP2272 Transverse momentum resummation at N3LLNNLO for diboson processes John M. Campbell1 R. Keith Ellis2 Tobias Neumann3 and Satyajit Seth4

2025-05-06 0 0 695.87KB 12 页 10玖币

侵权投诉

FERMILAB-PUB-22-762-T,IPPP/22/72

Transverse momentum resummation at N3LL+NNLO for diboson processes

John M. Campbell1, R. Keith Ellis2, Tobias Neumann3, and Satyajit Seth4

1Fermilab, PO Box 500, Batavia IL 60510-5011, USA

2Institute for Particle Physics Phenomenology, Durham University, Durham, DH1 3LE, UK

3Department of Physics, Brookhaven National Laboratory, Upton, New York 11973, USA

4Physical Research Laboratory, Navrangpura, Ahmedabad - 380009, India,

Abstract

Diboson processes are one of the most accessible and stringent probes of the Standard Model’s electroweak gauge

structure at the

LHC

. They will be probed at the percent level at the high-luminosity

LHC

, challenging current

theory predictions. We present transverse momentum resummed calculations at

N3LL+NNLO

for the processes

W Z

W H

and

, compare our predictions with most recent

LHC

data and present predictions at

13.6 TeV

including theory uncertainty estimates. For

W+W−

production we further present jet-veto resummed results at

N3LLp+NNLO

. Our calculations will be made publicly available in the upcoming

MCFM

release and allow future

analyses to take advantage of improved predictions.

Contents

1 Introduction 1

2 Phenomenology 3

2.1 ZZ production .............................................. 3

2.1.1 ZZ production at √s= 13.6 TeV ................................ 3

2.1.2 Comparison with CMS measurements.............................. 4

2.1.3 Comparison with ATLAS measurements ............................ 5

2.2 W±Zproduction............................................. 6

2.2.1 W Z production at √s= 13.6 TeV ............................... 6

2.2.2 Comparison with CMS measurements.............................. 6

2.3 W+W−production............................................ 7

2.4 W H and ZH production ........................................ 8

3 Conclusions 8

1 Introduction

Large experimental eﬀorts at the

LHC

are dedicated

to the analysis of Standard Model (

) electroweak

gauge bosons. The production of

γ, W, Z

and

are

typically considered either alone or in pairs, see table 1

for analyses of diboson processes at

13 TeV

. Recent de-

velopments include evidence for the triboson processes

[

–

]. The standard treatment of all these processes

exploits the collinear factorization theorem to combine

parton distribution functions (

PDF

s) and a hard scatter-

ing cross-section evaluated at a scale close to

to derive

a prediction. The scale

is the invariant mass of the

produced colorless ﬁnal state. These collinear factoriza-

tion predictions are not appropriate at small transverse

momentum

, where predictions at a ﬁxed order of

αs

contain powers of

log

(

Q2/q2

). In addition, for the

same reason, collinear factorization predictions are not

suitable for cross-sections where jet activity is vetoed. In

the region of small transverse momentum the ﬁxed-order

predictions need to be enhanced with resummation of

these logarithms to all orders in

αs

. This necessitates

an improved power counting where

log

(

Q2/q2

)

∼

/αs

and exploits a factorization theorem at small

, valid

up to terms suppressed by some power of qT/Q.

Since the dominant fraction of cross-section resides at

low transverse momentum, accurate theoretical con-

arXiv:2210.10724v1 [hep-ph] 19 Oct 2022

1 INTRODUCTION

trol of this region is important. In addition, precise

resummed predictions are necessary to validate the

transverse-momentum spectra obtained from parton

shower event generators operating at a lower logarith-

mic accuracy. Compared to single boson production,

resummation eﬀects for boson pair processes are ex-

pected to be even more important at the same value of

qTbecause the value of Qis much larger.

Of all massive diboson processes, the production of

W+W−

has received most theoretical and phenomeno-

logical attention. This is because of its sizable cross-

section and its role as a background to top-quark pro-

duction and to Higgs-boson production. Transverse

momentum resummation in

W+W−

processes has been

considered in refs. [

–

]. In particular ref. [

] discusses

the resummation of transverse momentum logarithms at

N2LL

NNLO

. The important topic of the resummation

of jet veto logarithms in

W+W−

processes has been

considered in refs. [7–10].

As for the other processes, ref. [

] considers the

W±Z

and

processes (as well as

W+W−

) at

N2LL

NLO

Resummation in the

(and

W+W−

) processes has

been considered in ref. [

] at

N2LL

NNLO

. The inter-

face of RadISH resummation to the

MATRIX

program

allows for

N3LL

NNLO

resummation [

] of all dibo-

son processes but no phenomenological results for the

W±Z

and

processes at this level have been pub-

lished.

In this paper we present an upgrade of

CuTe-MCFM

[

] which implements the

SCET

-based

resummation

formalism of refs. [

–

]. We describe the

N3LL

resum-

mation matching to the remaining diboson processes

W W

and

W Z

that have been recently implemented

MCFM

at ﬁxed order

NNLO

[

]. Our goal is to show

these improvements and the phenomenological capabili-

ties of our code, especially since the diboson calculations

were previously only presented at a technical level in

MCFM

[

]. We present resummed results for the mas-

sive diboson processes

W+W−

W±Z

, and

W H

at the level of

N3LL+NNLO

, compare with data as far

as currently available, and provide predictions for the

current LHC energy of √s= 13.6 TeV.

In addition to

resummation, resummation eﬀects

become important when we veto against jet activity, for

example in

W+W−

production to reduce background

from

t¯

production. Although a discussion of jet-veto

Table 1:

Experimental publications for boson pair pro-

duction at 13 TeV.

Process ATLAS CMS

W Z [19] [20–22]

ZZ [23, 24] [25]

W W [26, 27] [21, 28]

W H/ZH [29, 30] [31]

results is not the principal aim of our study, in view of

its experimental importance we present the results of

jet-veto resummation for the case of

W+W−

production.

We leave a detailed analysis of jet-veto resummation of

this and other processes for a future study.

In this paper we use the

SCET

-based “collinear anomaly”

resummation formalism introduced in refs. [

–

Formulations of

resummation that are fully per-

formed in impact parameter space have the drawback

that the transformation from the impact parameter

space

back to

involve the running coupling at

scale

. Therefore, when performing the Fourier trans-

form over all values of the impact parameter, one is

forced to introduce a prescription to avoid the Landau

pole in the running coupling. In the formulation of

refs. [

–

] this issue is avoided, setting the scale di-

rectly in

space. The cross-section is obtained by

combining the contributions from the partonic channels

i, j ∈q, ¯q, g

. Up to terms suppressed by powers of

qT/Q

these channels exhibit a factorized form that is fully

diﬀerential in the momenta

{q}

of the colorless ﬁnal

state

dσij (p1, p2,{q}) =

dz1Z1

dz2dσ0

ij (z1p1, z2p2,{q})Hij (z1p1, z2p2,{q}, µ)

×1

4πZd2x⊥e−iq⊥x⊥x2

TQ2

0−Fij (x⊥,µ)

×Bi(z1, x⊥, µ)·Bj(z2, x⊥, µ),(1)

where

and

are the incoming hadron momenta.

The function d

σ0

denotes the diﬀerential cross-section

for the hard Born-level process and the hard-function

Hij

contains the associated virtual corrections. The

beam functions

and

include the eﬀects of soft and

2.1 ZZ production 2 PHENOMENOLOGY

collinear emissions at large transverse separation

x⊥

and the indices

and

and the momentum fractions

and

refer to the partons which enter the hard process

after these emissions. The collinear anomaly leads to the

-dependent factor within the Fourier-integral over the

transverse position

x⊥

. The perturbatively calculable

anomaly exponent

Fij

is also referred to as the rapidity

anomalous dimension in the framework of ref. [

]. We

further have

= 2

e−γE

, where

γE

is the Euler constant,

and x2

T=−x2

⊥.

This framework for

resummation has been imple-

mented at

N3LL

CuTe-MCFM

[

], see ref. [

]

for further details. Matching to large-

ﬁxed-order

predictions were previously performed at relative order

α2

for the processes

H, Z, W ±

[

W±H

and

[

γγ

[

Zγ

[

], as well as at N

LL+N

LO for

pro-

duction in ref. [

]. The code is fully diﬀerential in the

Born kinematics, including the decays of the bosons

and provides an eﬃcient way to estimate uncertainties

from ﬁxed-order truncation, resummation, and parton

distribution functions.

To provide phenomenologically meaningful results also

for

W+W−

production, we have implemented jet-veto

resummation at

N3LLp+NNLO

following the collinear

anomaly formalism of ref. [

]. Beam- and soft-functions

are taken from refs. [

] and the rapidity anoma-

lous dimension at the two-loop level is taken from

refs. [

]. The notation

N3LLp

indicates that full

N3LL

accuracy is not achieved since an approximate

form, valid at small jet-radii, for the three-loop term in

the collinear anomaly exponent is used [

]. A detailed

presentation of our implementation and its phenomenol-

ogy for various processes will be presented elsewhere

[44].

2 Phenomenology

In the following we ﬁrst present ﬁnely binned transverse

momentum spectra at

13.6 TeV

and compare ﬁxed-order

and resummation improved predictions for each diboson

process. These demonstrate the impact of the

N3LL

resummation for future analyses. In practice, in current

experimental analyses the binning is still large, so that

the impact of resummation is less apparent. We compare

with experimental measurements as far as available for

the 13 TeV LHC.

Table 2:

Fiducial volume of the

CMS ZZ

analysis pre-

sented in ref. [25].

lepton cuts ql1

T>20 GeV,ql2

T>10 GeV,

ql3,4

T>10 GeV,|ηl|<2.5

lepton pair mass 60 GeV < ml−l+<120 GeV

In section 2.1 we ﬁrst consider

production. For this

process the transverse momentum of the vector boson

pair system is directly measured, unlike for processes

with

bosons which have missing energy. We compare

with diﬀerential and total cross-section measurements

from both

CMS

and

ATLAS

. We then present results

for

W±Z

production in section 2.2 and compare with

ATLAS

data. Finally we present jet-veto resummed pre-

dictions for

W+W−

in section 2.3 and compare to

CMS

measurements. Finally, we show diﬀerential predictions

at 13.6 TeV for W±Hand ZH in section 2.4.

Input parameters.

Throughout this paper we use the

PDF

set

NNPDF31_nnlo_as_0118

which has ﬁve active

ﬂavors, except for the

W+W−

process where we use

the

PDF

set

NNPDF31_nnlo_as_0118_nf_4

with four

active ﬂavors [

]. We work in the electroweak

Gµ

scheme with

80.385 GeV

91.1876 GeV

Gµ

1.166 390 ×10−5GeV−2

and further have Γ

2.0854 GeV

,Γ

2.4952 GeV

125 GeV

173.3 GeV.

At ﬁxed order we set the default renormalization and

factorization scales to the invariant mass of the dibo-

son system. For the resummation-improved results we

vary hard scale, resummation scale and rapidity scale

following refs. [

]. We symmetrize resummation un-

certainty bands to account for a frozen out downwards

scale variation at small

that would otherwise evaluate

αs

in the non-perturbative regime. Since our resumma-

tion includes the matching through a transition function,

we vary this function to estimate a matching uncertainty

and include this in the uncertainty bands. For the de-

tailed procedure we refer the reader to ref. [13].

2.1 ZZ production

2.1.1 ZZ production at √s= 13.6 TeV

We ﬁrst present results for

production at

√s

13.6 TeV

using the

CMS

cuts in table 2 [

] to study

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：

FERMILAB-PUB-22-762-T,IPPP/22/72TransversemomentumresummationatN3LL+NNLOfordibosonprocessesJohnM.Campbell1,R.KeithEllis2,TobiasNeumann3,andSatyajitSeth41Fermilab,POBox500,BataviaIL60510-5011,USA2InstituteforParticlePhysicsPhenomenology,DurhamUniversity,Durham,DH13LE,UK3DepartmentofPhysics,Brookhaven...

展开>> 收起<<

FERMILAB-PUB-22-762-TIPPP2272 Transverse momentum resummation at N3LLNNLO for diboson processes John M. Campbell1 R. Keith Ellis2 Tobias Neumann3 and Satyajit Seth4.pdf

共12页,预览3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！

FERMILAB-PUB-22-762-TIPPP2272 Transverse momentum resummation at N3LLNNLO for diboson processes John M. Campbell1 R. Keith Ellis2 Tobias Neumann3 and Satyajit Seth4

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: