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! $Id: qcd.f90,v 1.13 2004/09/18 14:39:29 salam Exp $
module qcd
use types; use consts_dp
integer, parameter :: nf_def = 5
real(dp), parameter :: ca_def = 3, cf_def = four/three, tr_def = half
real(dp), parameter :: tf_def = tr_def * nf_def
!-- the following are all modifiable, but have default values
real(dp), public :: ca = ca_def
real(dp), public :: cf = cf_def
real(dp), public :: tr = tr_def
integer, public :: nf_int = nf_def
integer, public :: nf_u = nf_def/2
integer, public :: nf_d = (nf_def+1)/2
real(dp), public :: nf = nf_def, tf = tf_def
! HACK TO GET GLUON + SINGLET EVOLUTION in 0 & 1
! For it to work, quark component in 2 must be zero.
!integer, parameter, public :: nf_u = nf_def, nf_d = 0
! beta2 is from Tarasov JINR P2-82-900 (Dubna 1982)
! Larin & Vermaseren NIKHEF-H/92-17 hep-ph/9302208
real(dp), public :: beta0 = (11*ca_def - four*tf_def)/(12*pi)
real(dp), public :: twopi_beta0 = (11*ca_def - four*tf_def)/6.0_dp
real(dp), public :: beta1 = (17*ca_def**2 - tf_def*(10*ca_def + 6*cf_def))&
& / (24*pisq)
real(dp), public :: beta2 = (2857*ca_def**3 &
& + (54*cf_def**2-615*cf_def*ca_def-1415*ca_def**2)*two*tf_def&
& + (66*cf_def + 79*ca_def)*(two*tf_def)**2)/(3456*pi**3)
!--- nomenclature is:
! alpha_s(nf+1,mu) = alpha_s(nf,mu) +
! sum_{mn} alphastep_mn * (alphas)^(m+1) ln^n(mu^2/m(mu^2)^2)
!
! taken from hep-ph/9411260; should also refer to
! Bernreuther, Wetzel, NPB197 (1982) 228
! Bernreuther, Annals of Phys. 151 (1983) 127
!
! Only use this if (mass_steps_on)?
logical, public :: mass_steps_on = .true.
!logical, public, parameter :: mass_steps_on = .false.
!---- the following is for the MSbar mass
! taken from hep-ph/9411260; should also refer to
! Bernreuther, Wetzel, NPB197 (1982) 228
! Bernreuther, Annals of Phys. 151 (1983) 127
real(dp), public :: alphastep11 = four*tr_def/(12*pi)
real(dp), public :: alphastep22 = (four*tr_def/(12*pi))**2
real(dp), public :: alphastep21 = tr_def*(10*ca_def + 6*cf_def)/(24*pisq)
real(dp), public :: alphastep20_msbar=&
&(13.0_dp/48.0_dp*cf_def-two/9.0_dp*ca_def) *tr_def/pisq
!-- for the pole mass, take this from hep-ph/9706430
! (Chetyrkin, Kniehl and Steinhauser), PRL 79 (1997) 2184
! though it is not the original referece, just a "container"
!-- expression not known for variable colour factors?
! NB: they express nf-1 in terms of nf...
real(dp), public :: alphastep20_pole = &
&(15.0_dp/16.0_dp*cf_def-two/9.0_dp*ca_def) * tr_def/pisq
real(dp), public :: cmw_K = ca_def*(67.0_dp/18.0_dp - pisq/6.0_dp) &
& - tf_def * 10.0_dp/9.0_dp
!!!! Taken from Moch, Vermaseren & Vogt: NB TR dependence not in...
real(dp), parameter :: cmw_K2_def = &
& ca_def**2 * ( 245._dp/24._dp - 67._dp/9._dp*zeta2 &
& + 11.0_dp/6._dp * zeta3 + 11.0_dp/5._dp * zeta2**2)&
&+ two*cf_def*tf_def * (-55._dp/24._dp + 2*zeta3)&
&+ two*ca_def*tf_def * (-209._dp/108._dp + 10._dp/9._dp*zeta2 &
& - 7._dp/3._dp * zeta3)&
&- four*tf_def**2 /27._dp
real(dp), public :: cmw_K2 = cmw_K2_def
real(dp), public :: mvv_A3 = 16*cf_def*cmw_K2_def
real(dp), public :: mvv_A3G = 16*ca_def*cmw_K2_def
!--- is it useful to have a fake upper entry?
! put charm quark mass just above sqrt(2)
real(dp), public, parameter :: &
& quark_masses_def(6) = (/1e-10_dp,1e-10_dp,0.15_dp,&
& 1.414213563_dp, 4.5_dp, 175.0_dp/)
public :: qcd_SetNf, qcd_SetGroup!, qcd_SetVogtImod
contains
!----------------------------------------------------------------------
subroutine qcd_SetNf(nf_in)
integer :: nf_in
nf_int = nf_in
nf = nf_int
nf_u = nf_int/2
nf_d = (nf_int+1)/2
tf = tr * nf
call qcd_set_beta0
end subroutine qcd_SetNf
!----------------------------------------------------------------------
subroutine qcd_SetGroup(ca_in,cf_in,tr_in)
real(dp), intent(in) :: ca_in,cf_in,tr_in
ca = ca_in
cf = cf_in
tr = tr_in
tf = nf * tr
call qcd_set_beta0
end subroutine qcd_SetGroup
!----------------------------------------------------------------------
subroutine qcd_set_beta0
beta0 = (11*ca - four*tf)/(12*pi)
twopi_beta0 = twopi * beta0
beta1 = (17*ca**2 - tf*(10*ca + 6*cf)) / (24*pisq)
beta2 = (2857*ca**3 + (54*cf**2-615*CF*CA-1415*ca**2)*two*tf&
& + (66*cf + 79*ca)*(two*tf)**2)/(3456*pi**3)
!-- matching thresholds -----------------
alphastep11 = four*tr/(12*pi)
alphastep22 = (four*tr/(12*pi))**2
alphastep21 = tr*(10*ca + 6*cf)/(24*pisq)
alphastep20_msbar = (13.0_dp/48.0_dp*cf-two/9.0_dp*ca)*tr/pisq
! -11.0_dp/72.0_dp/pisq
!-- expression not know for variable colour factors
!alphastep20_pole = 7.0_dp/24.0_dp/pisq
alphastep20_pole = (15.0_dp/16.0_dp*cf-two/9.0_dp*ca)*tr/pisq
cmw_K = ca*(67.0_dp/18.0_dp - pisq/6.0_dp) - tf*10.0_dp/9.0_dp
cmw_K2 = &
& ca**2 * ( 245._dp/24._dp - 67._dp/9._dp*zeta2 &
& + 11.0_dp/6._dp * zeta3 + 11.0_dp/5._dp * zeta2**2)&
&+ two*cf*tf * (-55._dp/24._dp + 2*zeta3)&
&+ two*ca*tf * (-209._dp/108._dp + 10._dp/9._dp*zeta2 &
& - 7._dp/3._dp * zeta3)&
&- four*tf**2 /27._dp
mvv_A3 = 16*cf*cmw_K2
mvv_A3G = 16*ca*cmw_K2
end subroutine qcd_set_beta0
!!$ !-------- overkill ----------------------------------------
!!$ subroutine qcd_SetVogtImod(imod)
!!$ integer, intent(in) :: imod
!!$ vogt_imod = imod
!!$ end subroutine qcd_SetVogtImod
end module qcd

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