NNLO QCD下S→QQ¯X过程的实虚天线函数解析与RQ比值研究

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本文主要探讨了在量子色动力学（Quantum Chromodynamics, QCD）的下一个-to-leading-order (NNLO) 计算中，无色初始状态（如光子或Z玻色子）转化为一个大质量夸克对（QQbar）以及额外辐射X的实虚天线函数。在处理高阶QCD中的红外（infrared, IR）散度问题时，天线减法方法是一个关键工具，它允许将复杂的计算分解为可管理的部分，以便于单独处理。作者们在"Physics Letters B"杂志的738卷中详细分析了这一过程，特别关注的是实数发射（real emission）与虚拟修正（virtual corrections）的结合。他们利用先进的分析技术，如（环）谐波多对数（harmonic polylogarithms, HPLs），来计算了这些天线函数。这种分析不仅考虑了Leading Color（主导色）效应，还包括了Subleading Color（次要色）的影响，以提供更全面的理论预测。作为一项额外的验证，作者们计算了比值RQ，即电子-正电子对撞中产生γ⁎（虚拟光子）并进一步衰变为QQbar对与μ+μ-对的相对率。通过比较RQ的计算结果与已有的理论值，研究者们确认了其在αs²（强相互作用耦合常数的平方）精度下的准确性，这表明他们的方法具有高度的精确性和可靠性。这篇论文对理解和控制高能物理实验中的NNLO QCD过程至关重要，因为它不仅提供了关键的计算技术，而且对于校准实验数据和检验标准模型的预测有着实际意义。同时，它也为未来更高阶QCD计算的进展奠定了基础，尤其是在处理复杂多喷射事件时。

Physics Letters B 738 (2014) 325–333

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

The real–virtual antenna functions for S → Q

QXat NNLO QCD

Oliver Dekkers

, Werner Bernreuther

b,∗

PRISMA Cluster of Excellence and Institut für Physik, Johannes Gutenberg-Universität, D-55099 Mainz, Germany

Institut für Theoretische Physik, RWTH Aachen University, 52056 Aachen, Germany

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

Article history:

Received

13 September 2014

Accepted

29 September 2014

Available

online 2 October 2014

Editor:

A. Ringwald

Keywords:

QCD

NNLO

computations

Subtraction

methods

We determine, in the antenna subtraction framework for handling infrared divergences in higher order

QCD calculations, the real–virtual antenna functions for processes involving the production of a pair

of massive quarks by an uncolored initial state at NNLO QCD. The integrated leading and subleading

color real–virtual antenna functions are computed analytically in terms of (cyclotomic) harmonic

polylogarithms. As a by-product and check we compute R

= σ (e

−

→ γ

∗

→ Q

QX)/σ (e

−

→ γ

∗

→

−

) and compare with existing results. Our result for R

is exact to order α

(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP

1. Introduction

In this letter we report, within the antenna subtraction frame-

work

[1–4], on the calculation of the real–virtual antenna functions

for processes involving the production of a pair of massive quarks

by an uncolored initial state S at next-to–next-to leading order

(NNLO) QCD,

S → Q

Q + X, (1)

where S denotes, for example, an e

−

pair or an uncolored bo-

son.

Antenna subtraction is a method for handling infrared (IR),

i.e., soft and collinear divergences in higher order QCD calculations.

The general features of the method at NNLO QCD were presented

in [3]. Applications at NNLO QCD involving massless partons in-

clude

−

→ 2jets, 3jets[5–8] and pp → di-jets [9]. For QCD

processes involving massive quarks the method was worked out

to NLO in [10,11]. Partial results exist for NNLO QCD processes

with colored initial states and massive quarks in the ﬁnal state

[12–14]. For processes of the type (1) the un-integrated and inte-

grated

NNLO real radiation subtraction terms for the Q

q and

Qgg ﬁnal states were determined in [15] and in [16], respec-

tively.

The NNLO real–virtual antenna functions for (1), which were

missing so far, are the subject of this letter.

this point it seems appropriate to recall that other NNLO

subtraction techniques exist and have been successfully applied.

Corresponding author.

E-mail

addresses: dekkers@uni-mainz.de (O. Dekkers),

breuther@physik.rwth-aachen.de (W. Bernreuther).

Amethod was presented in [17–19] which can be used for mass-

less

and massive partons and was applied in the computation

of the total hadronic t

t cross section to order α

[20,21]. Other

techniques for handling the IR divergences of the individual con-

tributions

to partonic processes at NNLO QCD include the sec-

tor

decomposition algorithm [22–26] and the subtraction methods

[27–32]. Very recently, a NNLO QCD generalization of the phase–

space

slicing method has been presented by [33,34] for e

−

→

∗

→ Q

QX.

Coming

back to the issue of this letter, we outline in the next

section the construction of separately infrared (IR) ﬁnite contri-

butions

to the NNLO differential cross section of (1) from the

four-parton, three-parton, and two-parton ﬁnal states within the

antenna subtraction method. In Section 3 we describe our com-

putation

of the integrated massive real–virtual antenna functions.

As a ﬁrst application and check of our antenna subtraction terms

we compute in Section 4 the contribution of order α

to the ratio

for inclusive massive quark-pair production by e

−

annihila-

tion

via a virtual photon and compare with existing results in the

literature. We conclude in Section 5.

2. The real–virtual subtraction term for reactions (1)

The order α

term dσ

NNLO

in the strong-coupling expansion of

the differential cross section of (1), dσ = dσ

+ dσ

NLO

+ dσ

NNLO

receives the following contributions: i) the double virtual correc-

tion

dσ

NNLO

associated with the second-order matrix element of

S → Q

Q (i.e., 2-loop times Born and 1-loop squared), ii) the

real–virtual cross section dσ

NNLO

associated with the second-order

matrix element of S → Q

Qg (1-loop times Born), iii) the double

http://dx.doi.org/10.1016/j.physletb.2014.09.060

0370-2693/

SCOAP

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