Page MenuHomeHEPForge
Files F8723601

No OneTemporary
Actions

View Options

diff --git a/resum/sudakov.f b/resum/sudakov.f
index 6d783f4..dd380df 100644
--- a/resum/sudakov.f
+++ b/resum/sudakov.f
@@ -1,254 +1,272 @@
function alphasl(nq2)
c.....reference scale is factorization scale: muf2=muf**2
implicit none
c implicit real*8(a-h,o-z)
double precision blim
integer xlp
double complex xlambda,aa1,all,alphasl,qq,t,xlt,bstar,b,blog
double complex log1xlambda
double complex nq2,aa2,aa3,aa4
include 'const.h'
include 'sudakov_inc.f'
include 'scales_inc.f'
c.....Here computes NLL expression for alphas
c here nq2=b0^2/b^2 and the result is now alpha(nq2)/alpha(Qres)
c To understand these formulas:
c nq2 = a*b0^2/b^2 = a*qb2
c Q2 = (m_ll/a)^2
c alphas(qb2) = alphas(Q2) / (1 - beta0 * alphas(mur2) * log (Q2/qb2)) (why there is a mismatch between Q2 and mur2?)
c with the changes:
c IR cut off: b=b0p/nq -> bstar = b/sqrt(1+(b**2)/(blim**2))
c modified sudakov: loq(Q2/qb2) -> loq(Q2/qb2 + 1)
c The result is actually alphas(qb2)/alphas(Q2), where Q2 is the resummation scale
c HERE CHANGE: order of alphas related to order of evolution
xlp=0
if(iord.ge.1) then
xlp=1
elseif(iord.eq.0) then
xlp=0
endif
b=sqrt((b0p**2/nq2))
blim=rblim
bstar=b
c.....choose bstar (b) for real axis (complex plane) integration
if (flagrealcomplex.eq.0) bstar=b/sqrt(1+(b**2)/(blim**2))
if (imod.eq.1) blog=log( (q*bstar/b0p)**2 + 1) !modified sudakov
if (imod.eq.0) blog= log( (q*bstar/b0p)**2 ) !normal sudakov
xlambda=beta0*aass*blog
c I think it would be more correct to calculate alphas at the resummation scale, rather than aass which is alphas at the renormalisation scale
c xlambda=beta0*dyalphas_lhapdf(q/a_param)/pi*blog
c --> Not really, the running of alphas in this function reflects the definition of lambda in Eq. 25 of hep-ph/0508068.
c print *,aass*pi,dyalphas_lhapdf(q),dyalphas_lhapdf(q/a_param),sqrt(nq2),xlambda
!c HERE now a dependence (without constant term)!
! log1xlambda=log(1-xlambda)
! aa1=log1xlambda+aass*xlp*
-! . (beta1/beta0*log1xlambda/(1-xlambda)
+! . (beta1/beta0*log1xlambda/(1-xlambda)
! . + beta0*xlambda/(1-xlambda)*rlogq2mur2
!c . + beta0*log(q2/muf2)
! . -2d0*beta0*xlambda*rloga/(1-xlambda) )
log1xlambda=log(1-xlambda)
aa1=log1xlambda
if (iord.ge.1) then
aa1 = aa1+aass*
- . beta1/beta0*log1xlambda/(1-xlambda)
+ . beta1/beta0*log1xlambda/(1-xlambda)
endif
if (iord.ge.2) then
aa1 = aa1+aass**2*
. ((beta1**2/beta0**2-beta2/beta0)*xlambda/(1d0-xlambda)**2
. +(beta1**2/beta0**2)*log1xlambda/(1d0-xlambda)**2
- . +(beta1**2/beta0**2)*log1xlambda**2/(2d0*(1d0-xlambda)**2))
+c . +(beta1**2/beta0**2)*log1xlambda**2/(2d0*(1d0-xlambda)**2))
+ . -(beta1**2/beta0**2)*log1xlambda**2/(2d0*(1d0-xlambda)**2))
endif
! Scale dependence
if (iord.ge.1) then
aa1 = aa1+aass*(rlogq2mur2-2d0*rloga)*
. beta0*xlambda/(1-xlambda)
endif
if (iord.ge.2) then
aa1 = aa1+aass**2*(rlogq2mur2-2d0*rloga)*
- . beta1*(xlambda/(1d0-xlambda)**2+log1xlambda/(1d0-xlambda)**2)
+c . beta1*(xlambda/(1d0-xlambda)**2+log1xlambda/(1d0-xlambda)**2)
+ . (beta1*(xlambda/(1d0-xlambda)**2
+ . -beta1*log1xlambda/(1d0-xlambda)**2))
endif
alphasl=Exp(-aa1)
! write(*,*) iord,alp,b,blim,flagrealcomplex,xlambda,as,a_param
! .,mur,blog,nq2,aa1,alphasl
c.....Now compute the factors
c.....needed to resum the logs which multiply the N-dependent part
c.....of the C coefficients
-! aa2= xlambda/(1- xlambda)
-! aexpB=Exp(aa2)
-!
-! aa3 = xlambda*(xlambda-2d0)/(1-xlambda)**2 ! --> should be xlambda*(xlambda-2d0)/(2*(1-xlambda)**2) ?
-! aexpC=Exp(aa3)
-!
-! aa4 = log1xlambda/(1-xlambda)**2 ! --> should be (xlambda*(2d0-xlambda)+2d0*log1xlambda)/(2d0*(1-xlambda)**2) ?
-! aexpD=Exp(aa4)
-
-
c the limit below implies xlambda<1/2 and then aa2<= 1
c blim=b0p*(1/q)*exp(1/(2*as*beta0))
c blim=b0p*(1/q)*exp(1/(4*as*beta0))
C Set a limit to avoid very large values of b (= very small scales ~1/b)
! blim=b0p*(1/q)*exp(1/(2*aass*beta0)) ! avoid Landau pole
! write(*,*) "blim",blim
! without this additional blim some scale variations will fail (when mures > muren)
blim=0.5d0 ! --> allow this to a separate blim in the settings, or set it using muren instead of mures
! blim=1.1229190d0
+! blim=3d0
if (flagrealcomplex.eq.0) bstar=b/sqrt(1+(b**2)/(blim**2))
if (imod.eq.1) blog=log( (q*bstar/b0p)**2 + 1) !modified sudakov
if (imod.eq.0) blog= log( (q*bstar/b0p)**2 ) !normal sudakov
xlambda=beta0*aass*blog
c HERE now a dependence (without constant term)!
+c log1xlambda=log(1-xlambda)
+c aa1=log1xlambda+aass*xlp*
+c . (beta1/beta0*log1xlambda/(1-xlambda)
+c . + beta0*xlambda/(1-xlambda)*rlogq2mur2
+c . -2d0*beta0*xlambda*rloga/(1-xlambda) )
+
log1xlambda=log(1-xlambda)
- aa1=log1xlambda+aass*xlp*
- . (beta1/beta0*log1xlambda/(1-xlambda)
- . + beta0*xlambda/(1-xlambda)*rlogq2mur2
- . -2d0*beta0*xlambda*rloga/(1-xlambda) )
+ aa1=log1xlambda
+ if (iord.ge.1) then
+ aa1 = aa1+aass*
+ . beta1/beta0*log1xlambda/(1-xlambda)
+ endif
+ if (iord.ge.2) then
+ aa1 = aa1+aass**2*
+ . ((beta1**2/beta0**2-beta2/beta0)*xlambda/(1d0-xlambda)**2
+ . +(beta1**2/beta0**2)*log1xlambda/(1d0-xlambda)**2
+ . -(beta1**2/beta0**2)*log1xlambda**2/(2d0*(1d0-xlambda)**2))
+ endif
+
+! Scale dependence
+ if (iord.ge.1) then
+ aa1 = aa1+aass*(rlogq2mur2-2d0*rloga)*
+ . beta0*xlambda/(1-xlambda)
+ endif
+ if (iord.ge.2) then
+ aa1 = aa1+aass**2*(rlogq2mur2-2d0*rloga)*
+ . (beta1*(xlambda/(1d0-xlambda)**2
+ . -beta1*log1xlambda/(1d0-xlambda)**2))
+ endif
+
aexp=Exp(-aa1)
- aa2= xlambda/(1- xlambda)
+ aa2= xlambda/(1d0-xlambda)
aexpB=Exp(aa2)
- aa3 = xlambda*(xlambda-2d0)/(1-xlambda)**2 ! --> should be xlambda*(xlambda-2d0)/(2*(1-xlambda)**2) ?
+ aa3 = xlambda*(xlambda-2d0)/(1d0-xlambda)**2
aexpC=Exp(aa3)
- aa4 = log1xlambda/(1-xlambda)**2 ! --> should be (xlambda*(2d0-xlambda)+2d0*log1xlambda)/(2d0*(1-xlambda)**2) ?
+ aa4 = log1xlambda/(1d0-xlambda)**2
aexpD=Exp(aa4)
-
return
end
c.....Sudakov form factor
function S(b)
implicit none
complex *16 S,f0,f1,f2,b,bstar,blim,blog
integer flag1
COMMON/flag1/flag1
real*8 g
common/NP/g
complex *16 y
include 'sudakov_inc.f'
include 'scales_inc.f'
include 'const.h'
! blim=(1/q)*exp(1/(2*aass*beta0))
c****************************
c mass dependence in blim
blim=cblim
c In reading these formulas, notice that blog is L = log(q*bstar/b0p) = log[(q/a_param)*bstar/b0] = log[Q * bstar/b0], according to Eq. (13) and (17) of hep-ph/0508068.
bstar=b
c.....choose bstar (b) for real axis (complex plane) integration
c mass dependence in bstar
if (flagrealcomplex.eq.0) bstar=b/sqrt(1+(b**2)/(blim**2))
c mass dependence in blog
if (imod.eq.1) blog=log( (q*bstar/b0p)**2+1) !modified sudakov
if (imod.eq.0) blog= log( (q*bstar/b0p)**2 ) !normal sudakov
c mass dependence in f0(y), f1(y), f2(y)
y = beta0*aass*blog
log1y=log(1-y)
if (flag1.eq.0) then
S=exp(blog*f0(y))
elseif (flag1.eq.1) then
S=exp(blog*f0(y)+f1(y))
elseif (flag1.eq.2) then
S=exp(blog*f0(y)+f1(y)+aass*f2(y))
endif
!
if ((flagrealcomplex.eq.0).and.(DBLE(S).gt.1d2)) then
write(*,*) "WARNING! LARGE SUDAKOV, S(b)=",S,"; for bstar=",bstar
S=cmplx(0d0,0d0)
endif
!
c S=S*exp(-g*b**2)
return
c****************************
end
c.....Soft-gluon-Resummation of LL (Eq.22 of arXiv:hep-ph/0508068)
function f0(y)
implicit none
complex *16 f0,y
include 'const.h'
include 'sudakov_inc.f'
f0=(A1q/beta0)*(y+log1y)/(y)
! f0 = 0d0
return
end
c.....Soft-gluon-Resummation of NLL (Eq.23 of arXiv:hep-ph/0508068)
c.....Now we have mu_r dependence!
function f1(y)
implicit none
complex *16 f1,y
include 'const.h'
include 'sudakov_inc.f'
f1=((A1q*beta1)/(beta0**3))*((1d0/2)*log1y*log1y +
\ (y)/(1-y)+log1y/(1-y)) -
\ (A2q/(beta0**2))*(log1y+(y)/(1-y)) +
\ (B1q/beta0)*log1y +
\ (A1q/beta0)*(y/(1-y)+log1y)*rlogq2mur2 !!! should be rlogq2mur2 -> log(mures^2/mur^2) = (logq2mur2-2.*loga) (is this a bug in DYRES?) (--> no see a dependence below)
c a dependence
f1=f1-2*rloga*A1q/beta0*y/(1-y) !!! (Here is missing the term log1y in (y/(1-y)+log1y) ???)
! \ (A1q/beta0)*(y/(1-y)+log1y)*(rlogq2mur2-2.*rloga)
! f1 = 0d0
return
end
c.....Soft-gluon-Resummation of NNLL (Eq.24 of arXiv:hep-ph/0508068)
c.....Now we have mu_r dependence!
function f2(y)
implicit none
complex *16 f2,y
include 'const.h'
include 'sudakov_inc.f'
f2=((A2q*beta1)/(beta0**3))*((y/2)*((3*y-2d0)/(1-y)**2)-
\ ((1-2*y)*log1y/(1-y)/(1-y))) -
\ (B2q/beta0)*((y)/(1-y))+
\ (B1q*beta1/beta0**2)*((y)/(1-y)+log1y/(1-y))-
\ (A3q/2/beta0**2)*(y)*(y)/(1-y)/(1-y) +
\ A1q*((beta1**2/2/beta0**4)*(1-2*y)/(1-y)
\ /(1-y)*log1y*log1y +
\ log1y*((beta0*beta2-beta1**2)/(beta0**4)+
\ beta1**2/beta0**4/(1-y)) +
c \ beta1**4/beta0**4/(1-y)) +
\ (y)/(2*beta0**4*(1-y)*(1-y))*
\ (beta0*beta2*(2d0-3*y)+beta1**2*y)) -
\ (A1q/2)*(y)*(y)/(1-y)/(1-y)*rlogq2mur2*rlogq2mur2 + !!! should be rlogq2mur2 -> log(mures^2/mur^2) = (logmur2q2-2.*loga) (is this a bug in DYRES?)
\ rlogq2mur2*(B1q*y/(1-y)+A2q/beta0*y*y/(1-y)/(1-y)+
\ A1q*beta1/beta0**2*(y/(1-y)+(1-2*y)/(1-y)/(1-y)*log1y))
\ +2d0*C1qqn*((y)/(1-y))
c a dependence (now without constant term)
f2=f2+2*A1q*y*(y-2)/(1-y)**2*rloga**2-rloga
\ *(2*B1q*y/(1-y)+2*y/beta0*A2q/(1-y)**2
\ -2*A1q*beta1/beta0**2*y*log1y/(1-y)**2)
!
\ + A1q*rloga*rlogq2mur2*y*2d0/(1-y)**2
! f2 = 0d0
return
end

File Metadata

Mime Type
text/x-diff
Expires
Mon, Jan 20, 8:52 PM (23 h, 58 s)
Storage Engine
blob
Storage Format
Raw Data
Storage Handle
4242343
Default Alt Text
(10 KB)

Event Timeline