1. 2015强子物理与核物理前沿研讨会 Bc纯轻衰变的两圈QCD修正 陈龙斌 中国科学院大学 导师: 乔从丰教授 时间: 2015-01-11
时间: 1 1

2. Background Leptonic Decay of Bc:
Chao-Hsi chang, Cai-Dian Lu, Guo-Li Wang, Hong-Shi Zong
Phys.Rev.D. 60.(1999) 2

3. One-loop QCD corrections:
E. Braaten, S. Fleming Phys. Rev. D 52 (1995)181
Logarithm
Express the decay constant f_Bc in terms of NRQCD matrix elements

4. Background: Ο(mc/mb)^2
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, (2014) loop
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

5. Harmonic Polylogarithms:
Ref. arXiv:hep-ph/

6. Numerical Evaluation:
arXiv: hep-ph/
hep-ph/
Multiple polylogarithms:
aXiv: [math.AG]
[hep-ph]

7. Calculation programs:
Diagram generating and Amplitude Manipulation:
FeynCalc;
Fire;
Master Integrals Calculation:
Ambre;
MB;
HPL;
FIESTA;

8. Two-Loop QCD correction Diagrams
FeynArts, FeynCalc, FIRE, $Apart 8

9. Reduction to Master Integrals:
1/(D-4)^2-Appear
MB, AMBRE,HPL-- packages 9

10. Represent:

11. Differential-Equation Method
Johannes M.Henn, Phys. Rev. Lett. 110, (2013).
找一组恰当的主积分g(ϵ,x),使微分方程形式化为：
g(ϵ,x), Ф(ϵ,x):Array
A(x): Matrix
已知函数
微分方程的求解大为化简，可按ϵ一阶一阶递归求解 11

12. Base

13. Analytical Results - Harmonic PolyLogarithms
Check with FIESTA 13

14. 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。

15. Two-Loop Renormalization15

16. Mass-renormalization counter-diagrams

17. Analytical Results 17

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

19. Note:用我们这套技术方法，得到的J/psie+e-两圈修正解析结果与：
Numerical Results
Note:用我们这套技术方法，得到的J/psie+e-两圈修正解析结果与：
完全一致 19

20. 博学笃志 格物明德
To Be Continued…
谢谢! 20