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Jun Jiang
2015.1.10
Outline
 Background
 NLO Calculation
 Results &Discussion
 Summary
Background
 Bc Meson
Bc meson was discovered by CDF in 1998.
Phys. Rev. Lett. 81, 2432 (1998); Phys. Rev. D 58, 112004 (1998).
Mass & lifetime:
[PDG Collaboration], Chin. Phys. C 38, 090001 (2014).

M ( B c )  6.2756  0.0011G eV ,

 ( B c )  0.500  0.013 ps .
Excited states Bc(2S) was observed by ATLAS recently.
M ( B c (2 S ))  6842  4  5 M eV
Background
 Direct production
Various investigations by C. H. Chang, Y. Q. Chen, J. X. Wang,
C. F. Qiao, X. G. Wu, E. Braaten et al.
P-Wave
Phys. Rev. D 70, 114019 (2004).
Color-octet
Phys. Rev. D 71, 074012 (2005).
“Intrinsic heavy quark mechanism”
Phys. Rev. D 72, 114009 (2005).
Fragmentation
Phys. Rev. D 46, 3845 (1992) [Erratum-ibid. D 50, 6013 (1994)];
Phys. Rev. D 48, 5049 (1993).
BCVEGPY
Comput. Phys. Commun. 159, 192 (2004).
Background
 Indirect production
Top decays
Leading order(LO):
C. F. Qiao, C. S. Li and K. T. Chao, Phys. Rev. D 54, 5606 (1996);
C. H. Chang, J. X. Wang and X. G. Wu, Phys. Rev. D 77, 014022 (2008);
X. G. Wu, Phys. Lett. B 671, 318 (2009).
Next-to-leading order(NLO):
P. Sun, L. P. Sun and C. F. Qiao, Phys. Rev. D 81, 114035 (2010).
W decays
LO:
Z0 decays
C. F. Qiao et al. Eur. Phys. J. C 71, 1766 (2011);
X. G. Wu, Phys. Rev. D 85, 014032 (2012).
LO calculation by C. H. Chang etc., V. V. Kiselev etc.
NLO, Bc[1S0]: C. F. Qiao, L. P. Sun and R. L. Zhu, JHEP 1108, 131 (2011).
NLO, Bc *[3S1]: J. Jiang, L. B. Chen and C. F. Qiao,
arXiv: 1501.00338, submitting to PRD.
Background
 Motivation
Z0 platform
LHC
 ( Z )  34 nb
0
 ( Z )  30 nb
0
ILC at GigaZ mode
L
34
Phys. Rev. Lett. 112, 191802 (2014).
2
10 cm s
1
 10 nb
8
1
Phys. Lett. B 486, 125 (2000).

9
10 Z
Large correction
Z  Bc [ S 0 ]  c  b
0
1
  2mb , K 
 NLO
 LO
 1.08,
  m Z / 2, K  1.59,
0
events .
NLO Calculation
 Divergences
Z  Bc [ S1 ]  X
0
UV
Counter
terms
*
3
IR
Coulomb
One-Loop
Diagrams
Threshold
expansion
technique
M. Beneke and V. A. Smirnov,
Nucl. Phys. B 522, 321 (1998).
Counter
terms
Real
Correction
NLO Calculation
 IR in one-loop diagrams
IR finite
+
+
+
+
NLO Calculation
 IR in real correction
B. W. Harris and J. F. Owens,
Phys. Rev. D 65, 094032 (2002).
NLO Calculation
 Axial-vector current
J. G. Korner, D. Kreimer and K. Schilcher,
Z. Phys. C 54, 503 (1992).
No contribution.
No contribution.
Results & Discussion
 Decay width versus μ
Results & Discussion
 K-factor
 With μ increasing, K-factor grows, yet it grows slower at high μ region.
 With μ increasing, Γ(μ) decreases, yet it decreases slower at high μ region.
 Γ(μ) is much more sensitive to mc than mb.
Results & Discussion
 Uncertainties
Results & Discussion
 Production rate
At μ=2mb,
Total production rate,
K total  1.22.
At μ=mZ/2,
K total  1.67.
Summary
 In arXiv:1501.00338, we calculate the QCD NLO
Corrections to inclusive Bc* production in Z0 decays.
 When μ running from 2mb to mZ/2, K-factor gro
-ws from 1.33 to 1.73.
 Parameter of mc has a quite large influence on Γ.
2015.1.10