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陈龙斌中国科学院大学导师 : 乔从丰教授时间 : 2015-01-11

Bc 纯轻衰变的两圈 QCD 修正

2015 强子物理与核物理前沿研讨会

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Background

Leptonic Decay of Bc:

Chao-Hsi chang, Cai-Dian Lu, Guo-Li Wang, Hong-Shi ZongPhys.Rev.D. 60.(1999) 114013.

One-loop QCD corrections:E. Braaten, S. Fleming Phys. Rev. D 52 (1995)181

LogarithmExpress the decay constant f_Bc in terms of NRQCD matrix elements

Background:M. Beneke, A. Singer, and V.A. Smirnov, Phys. Rev. Lett. 80,2535(1998)A. Czarnecki and K. Melnikov, Phys. Rev. Lett. 80, 2531(1998)

M. Beneke, Y. Kiyo, P. Marquard, A. Penin, J. Piclum, D. Seidel and M. Steinhauser,

Phys. Rev. Lett. 112, 151801 (2014). 3loop

A.Czarnecki and K. Melnikov, Phys. Lett. B 519, 212(2001)

Andrei I. Onishchenko and Oleg L. Veretin, Eur. Phys. J. C50, 801(2007).

Ο(mc/mb)^2

Harmonic Polylogarithms:

Ref. arXiv:hep-ph/9905237

Numerical Evaluation:arXiv: hep-ph/0107173 hep-ph/0111255

Multiple polylogarithms:aXiv:1105.2076 [math.AG] 1007.1891 [hep-ph]

Diagram generating and Amplitude Manipulation:FeynCalc;Fire;

Master Integrals Calculation:Ambre;MB;HPL;FIESTA;

Calculation programs:

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Two-Loop QCD correction Diagrams

FeynArts, FeynCalc, FIRE, $Apart

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Reduction to Master Integrals:

MB, AMBRE,HPL-- packages

O(ϵ^2)

1/(D-4)^2-Appear

Represent:

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Differential-Equation Method

找一组恰当的主积分 g(ϵ,x), 使微分方程形式化为：

微分方程的求解大为化简，可按 ϵ 一阶一阶递归求解

已知函数

Johannes M.Henn, Phys. Rev. Lett. 110, 251601(2013).

g(ϵ,x), Ф(ϵ,x):Array A(x): Matrix

mb

mcx

Base

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Analytical Results - Harmonic PolyLogarithms

Check with FIESTA

对积分 10,11 用类似的方法解得

积分 10 与 :M.Argeri, P. Mastolia and E. Remiddi, Nucl. Phys. B 631, 388(2002) 对比，发现其结果错误。

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Two-Loop Renormalization

Mass-renormalization counter-diagrams

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Analytical Results

A.I. Onishchenko O.L. Veretin, Eur. Phys. J. C 50 (2007) 801.

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Numerical Results

Note: 用我们这套技术方法，得到的 J/psie+e- 两圈修正解析结果与：

完全一致

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谢谢 !

博学笃志 格物明德

To Be Continued…