NLO+NLL'精度下e+e-碰撞多喷嘴生产的Durham分辨率尺度预测

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本文档探讨了在电子正电子湮灭(e+e-)过程中，多喷嘴生产中的重要物理现象——达勒姆喷气分辨率尺度y_n, n+1的次高阶修正（NLO + NLL'）恢复预测。这是在著名的Sherpa计算框架内，通过Caesar形式主义方法实现的创新性工作。Sherpa是一个广泛使用的事件生成器，它结合了矩阵元素和部分喷射模拟，用于精确模拟高能物理实验中的粒子相互作用。作者们首次提供了对4、5和6个喷嘴分辨率尺度的全面分析，特别关注了次领域能量色贡献（subleading colour contributions）。这些次领域能量色效应在高多喷嘴事件中起着关键作用，它们相比于矩阵元素和parton-shower模型预测，能够提供更准确的理论描述。在高能物理研究中，对喷嘴分辨率尺度的精确预测有助于理解基本粒子相互作用过程中的细节，以及验证或改进现有理论计算。研究中，通过严谨的数值计算和理论分析，作者展示了如何将这些次领域能量色效应纳入到Sherpa的计算框架中，从而提高喷嘴分辨率尺度预测的准确性。这种技术的发展对于理解在e+e-碰撞实验中产生的复杂多喷嘴事件分布至关重要，因为它影响着对量子色动力学(QCD)和其他基本物理现象的解释。论文在2020年4月17日发表在《Journal of High Energy Physics》(JHEP)上，是开放获取的，反映了作者们对高能物理实验数据的细致解析和理论模型的不断精细化。他们的工作不仅提升了粒子物理研究的精度，也为未来类似实验的设计和数据分析提供了有力的理论支持。

JHEP04(2020)112

Dimension

Process e

−

→ q¯qg q¯qq¯q q¯qgg q¯qq¯qg q¯qggg

Colour Space 1 2 3 4 10

Trace Basis 1 2 3 4 11

Reduced Trace Basis 1 2 3 4 10

Table 1. Colour-space and corresponding bases dimensionalities for all relevant Born channels.

with the hard matrix H

αβ

= A

in terms of partial amplitudes A

. In this notation,

the soft function may be written as

S(t) =

−

†

−

Tr [cH]

, (2.8)

with

Γ = −2

i<j

+ iπ

ij=

II,F F

. (2.9)

Here, the ﬁrst sum runs over all colour dipoles ij, while the second one runs over those

consisting only of ﬁnal-ﬁnal or inital-initial conﬁgurations, corresponding to the exchange

of Coulomb gluons [36]. Explicit results for H, c, and Γ are known for up to four hard

(coloured) legs; the form of S and the structure of Γ, however, holds more generally [37].

We obtain the hard matrix H from the matrix-element generator C

OMIX

[32] that

is part of S

HERPA

. All calculations of colour correlators relevant here contain at least

one quark-antiquark pair and are performed in the trace basis. An all-orders trace basis is

obtained by connecting each quark with an antiquark in all possible ways and subsequently

attaching all gluons in all possible ways. Colour correlators are then evaluated by explicitly

employing SU(N

) identities. We note that this slightly diﬀers from the approach in the

OLOR

ULL

[38] package, which uses specialised replacements in the trace basis instead.

One problem arising in the context of trace bases is that these are generally over-

complete for n

q¯q

+ n

> N

, such that the metric deﬁned in eq. (2.6) does not possess a

unique inverse. Although this has generally been solved in ref. [28], within this study we

can circumvent it in an even simpler way. The only critical process is e

−

→ q ¯q + 3g (cf.

table 1), for which the dimensionality of the basis exceeds the dimensionality of the colour

space by one. Thus, we are able to deﬁne a basis with lower dimension by combining basis

vectors corresponding to the same partial amplitude, i.e.,



:= |b

1,2,...,m

i+(−1)

1,m,...,2

i≡Tr[T

···T

]+(−1)

Tr[T

···T

]. (2.10)

We refer to this as the “reduced trace basis”. In section 3.2, we report on the validation

of the colour correlators for the speciﬁc processes under investigation.

The multiple-emission function F . The component F of eq. (2.1) captures the eﬀect

of multiple emissions on the cumulative distribution Σ. Recursive infrared collinear safety

of the observable guarantees that one can treat emissions below a cutoﬀ  as unresolved,

– 5 –

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