Inclusive B->X_s gamma decay spectra by Dressed Gluon Exponentiation

Last modified: 21.10.2008
This page describes the programme used for the calculations presented in:
Jeppe R. Andersen, Einan Gardi,
Radiative B decay spectrum: DGE at NNLO
Cavendish-HEP-06-23
[hep-ph/0609250]
JHEP01(2007)029

See also:
TAMING THE ANTI-B ---> X(S) GAMMA SPECTRUM BY DRESSED GLUON EXPONENTIATION.
CAVENDISH-HEP-05-05 (Feb 2005) 50p.
[HEP-PH 0502159]
JHEP06(2005)030

How to obtain the program

[download]
These instructions refer to version 2.2 released 21.10.2008
Version 2.2 differs from Version 2.1 by two technical differences: (1) the way the CERNLIB functions are used (thus removing previous sensitivity to compler flags in gcc4) and (2) an added fixed-order option in Mode 18.
Previous Versions:
Version 2.1 released 03.03.2007
Version 2.1 differs from Veraion 2.0 only in what concerns par6: now, when it is varried the renormalization scale of the operators is fixed: \mu=m_b in Eq. 3.5 in [hep-ph/0609250].
Version 2.0 was released 25.09.2006 together with hep-ph/0609250

The C++ program calculating the spectrum according to the theoretical prediction of the above mentioned reference can be obtained here. The tar.gz file should be untarred and gunzip'ed:
tar xzvf package.tar.gz
The program B2XsgSpectrum can then be compiled by issuing the commands

cd package
make
The programme requires access to the CERN libraries, and assumes these are installed in the directory
/cern/pro/lib
If your libraries are installed in another directory, please change line 16 in the Makefile accordingly. Also, the Makefile is setup to run with gcc4. If you are using a different compiler, please change the Makefile as described within. After compilation the program can be run by the command
./B2XsgSpectrum 
which will result in the following output:
# B2XsgSpectrum ver. 2.0
Usage:
B2XsgSpectrum par1 par2 par3 par4 par5 par6 par7 par8 par9 par10 [par11]
with:
par1: alpha_s(Mz)
par2: m_b^MSbar(m_b^MSbar) [GeV]
par3: m_c^MSbar(m_c^MSbar) [GeV]
par4: Number of light flavours: Nf
par5: 3/2 Renormalon Residue
par6: Ren Scale in Matching Coefficients (factor*m_b)
par7: Ren Scale in Total BF (factor*m_b)
par8: f^{pv}
par9: Mode
Mode 1 : Calculates the normalised photon spectrum 1/Gamma(E>mb/20) dGamma/dE [GeV^-1]
Mode 2 : Calculates BR(E_gamma>E_0)/BR(E_gamma>E_1)
         Mode Par1: E0 [GeV]
         Mode Par2: E1 [GeV]
Mode 3 : Calculates the first 3 central moments with cut on photon energy
         Mode Par: E0 [GeV]
The meaning of and suitable values for the parameters are described in the paper mentioned above.

Predictions for the normalised photon spectrum can be obtained by entering suitable values for the parameters, e.g.
./B2XsgSpectrum .1176 4.2 1.08 4 1 1 1 0 1
# B2XsgSpectrum ver. 2.0
#Arguments are:
#j: 3
#alpha_s(MZ)=0.1176
#m_b^MSbar=4.2
#m_c^MSbar=1.08
#NF=4
#3/2 Renormalon Residue=1
#Matching scale=1
#Ren scale in Total BF=1
#f^{pv} =0
#Mode = 1
#ModePar 1: 0
#From these we derived:
#alpha_s(m_b^MSbar)=0.22178
#m_b^Pole=4.87657
#\bar\Lambda=0.402429
#alpha_s(MatchScale*mb_pole)=0.212446
#alpha_s(MatchScale*mb_pole)/Pi=0.0676236
#mbmsbar(mbpolePV)=4.09184
#Lambda_QCD^2=0.112599 (GeV^2)
#Lambda_QCD=0.335558 (GeV)
#Calculated from Lambda_QCD and T(u): alpha_s(mb_pole) = 0.212446
#m_b^2(pole)=23.7809 (GeV^2)
#m_b(pole)=4.87657 (GeV)
#eta=0.564245
#z=0.0490477
#sqrt(z)=0.221467
#w1,w2 : 1.64736,-4.03216
#M=5.279
#angle : 1.5708
# Calculates the differential and integrated spectrum
# E0 [GeV] dG/dE(E0) [10^{-6} GeV^(-1)] G(E< E0) [10^{-6}]
1.5 14.0558 344.988
1.51 14.4696 344.845
1.52 14.902 344.699
1.53 15.354 344.547
1.54 15.8268 344.391
1.55 16.3217 344.231
1.56 16.8399 344.065
1.57 17.3828 343.894
1.58 17.9519 343.717
1.59 18.5491 343.535
Ratios of branching fractions can be calculated with the following parameters:
./B2XsgSpectrum .1176 4.2 1.08 4 1 1 1 0 2 1.8 1.6
# B2XsgSpectrum ver. 2.0
#Arguments are:
#j: 3
#alpha_s(MZ)=0.1176
#m_b^MSbar=4.2
#m_c^MSbar=1.08
#NF=4
#3/2 Renormalon Residue=1
#Matching scale=1
#Ren scale in Total BF=1
#f^{pv} =0
#Mode = 2
#ModePar 1: 1.8
#From these we derived:
#alpha_s(m_b^MSbar)=0.22178
#m_b^Pole=4.87657
#\bar\Lambda=0.402429
#alpha_s(MatchScale*mb_pole)=0.212446
#alpha_s(MatchScale*mb_pole)/Pi=0.0676236
#mbmsbar(mbpolePV)=4.09184
#Lambda_QCD^2=0.112599 (GeV^2)
#Lambda_QCD=0.335558 (GeV)
#Calculated from Lambda_QCD and T(u): alpha_s(mb_pole) = 0.212446
#m_b^2(pole)=23.7809 (GeV^2)
#m_b(pole)=4.87657 (GeV)
#eta=0.564245
#z=0.0490477
#sqrt(z)=0.221467
#w1,w2 : 1.64736,-4.03216
#M=5.279
#angle : 1.5708
# Calculates BR(E_gamma>E_0)/BR(E_gamma>E_1)
# E0 : 1.8 GeV
# E1 : 1.6 GeV
0.983393
Finally, the average photon energy, the variance, and 3rd higher central moments can be calculated in Mode 3:
./B2XsgSpectrum .1176 4.2 1.08 4 1 1 1 0 3 1.8
# B2XsgSpectrum ver. 2.0
#Arguments are:
#j: 3
#alpha_s(MZ)=0.1176
#m_b^MSbar=4.2
#m_c^MSbar=1.08
#NF=4
#3/2 Renormalon Residue=1
#Matching scale=1
#Ren scale in Total BF=1
#f^{pv} =0
#Mode = 3
#ModePar 1: 1.8
#From these we derived:
#alpha_s(m_b^MSbar)=0.22178
#m_b^Pole=4.87657
#\bar\Lambda=0.402429
#alpha_s(MatchScale*mb_pole)=0.212446
#alpha_s(MatchScale*mb_pole)/Pi=0.0676236
#mbmsbar(mbpolePV)=4.09184
#Lambda_QCD^2=0.112599 (GeV^2)
#Lambda_QCD=0.335558 (GeV)
#Calculated from Lambda_QCD and T(u): alpha_s(mb_pole) = 0.212446
#m_b^2(pole)=23.7809 (GeV^2)
#m_b(pole)=4.87657 (GeV)
#eta=0.564245
#z=0.0490477
#sqrt(z)=0.221467
#w1,w2 : 1.64736,-4.03216
#M=5.279
#angle : 1.5708
# Calculates the first 3 central moments with cut on photon energy:
# E0 : 1.8 GeV
# Output : N Moment Moment^(1/N)
1 2.31977 2.31977
2 0.0230341 0.15177
3 0.00273415 0.139832