JHEP01(2020)085
Further kinematic constraints are assumed to be implemented through the measurement
function. We write the single-particle phase-space measure for particle n + 1 as
dφ
1
≡ µ
4−d
d
d−1
k
1
(2π)
d−1
2k
0
1
=
µ
2
2(2π)
d−1
√
s
2
d−2
ξ
1−2
1
(1 − y
2
1
)
−
dξ
1
dy
1
dΩ
(d−2)
1
= dΥ
1
dξ
1
ξ
1−2
1
, (2.6)
where the d − 3 angular integrations dΩ
(d−2)
1
and trivial factors are collected in dΥ
1
.
Denoting by dΦ
n,1
the remainder of the (n+1)-parton phase space, i.e. dΦ
n+1
= dΦ
n,1
dφ
1
,
we write the real part of the NLO differential cross section as
dσ
(1)
r
= dΦ
n,1
dφ
1
M
(0)
n+1
= dΥ
1
dΦ
n,1
dξ
1
ξ
2
1
M
(0)
n+1
ξ
−1−2
1
. (2.7)
To isolate the soft singularities in the phase-space integration we use the identity
ξ
−1−2
= −
ξ
−2
c
2
δ(ξ) +
1
ξ
1+2
c
,
1
ξ
n
c
, f
=
Z
1
0
dξ
f(ξ) − f(0)θ(ξ
c
− ξ)
ξ
n
,
(2.8)
to expand ξ
−1−2
1
in terms of distributions. Here we have introduced an unphysical free
parameter ξ
c
that can be chosen arbitrarily [1, 2] as long as
0 < ξ
c
≤ ξ
max
.
The dependence of ξ
c
has to drop out exactly since no approximation was made. There-
fore, any fixed value could be chosen. However, keeping it variable is useful to test the
implementation of the scheme.
Using (2.8) we split the real cross section into a hard and a soft part
2
dσ
(1)
r
= dσ
(1)
s
(ξ
c
) + dσ
(1)
h
(ξ
c
) , (2.9a)
dσ
(1)
s
(ξ
c
) = −dΥ
1
dΦ
n,1
ξ
−2
c
2
δ(ξ
1
) dξ
1
ξ
2
1
M
(0)
n+1
, (2.9b)
dσ
(1)
h
(ξ
c
) = +dΥ
1
dΦ
n,1
1
ξ
1+2
1
c
dξ
1
ξ
2
1
M
(0)
n+1
. (2.9c)
In dσ
(1)
s
we can now (trivially) perform the ξ
1
integration. To do this systematically, we
define for photons the general soft limit S
i
of the i-th particle
S
i
M
(0)
m
≡ lim
ξ
i
→0
ξ
2
i
M
(0)
m
= E
i
M
(0)
m−1
with ξ
i
=
2E
i
√
s
,
2
In [1] the second term is called dσ
(ns)
for ‘non-soft’. We will label it h (for ‘hard’) instead to avoid
confusion when we need more than one such label later.
– 5 –
剩余27页未读，继续阅读
weixin_38744902
- 粉丝: 9
- 资源: 933
我的内容管理
展开
最新资源
- 解决Eclipse配置与导入Java工程常见问题
- 真空发生器：工作原理与抽吸性能分析
- 爱立信RBS6201开站流程详解
- 电脑开机声音解析：故障诊断指南
- JAVA实现贪吃蛇游戏
- 模糊神经网络实现与自学习能力探索
- PID型模糊神经网络控制器设计与学习算法
- 模糊神经网络在自适应PID控制器中的应用
- C++实现的学生成绩管理系统设计
- 802.1D STP 实现与优化：二层交换机中的生成树协议
- 解决Windows无法完成SD卡格式化的九种方法
- 软件测试方法：Beta与Alpha测试详解
- 软件测试周期详解：从需求分析到维护测试
- CMMI模型详解：软件企业能力提升的关键
- 移动Web开发框架选择：jQueryMobile、jQTouch、SenchaTouch对比
- Java程序设计试题与复习指南
资源上传下载、课程学习等过程中有任何疑问或建议，欢迎提出宝贵意见哦~我们会及时处理！
点击此处反馈
