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F1F2IN21.f
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CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCC CCC
CCC F1F220 version 0.995 - February 20, 2021 CCC
CCC Collection of subroutines to calculate inclusive cross sections CCC
CCC for range of nuclei. For A > 2 the parameterization is based on CCC
CCC by M. E. Christy, T. Gautam, and A Bodek to 12C, 27Al, 56Fe and CCC
CCC 64Cu. However, the fit scales relatively well with 'A' and CCC
CCC should be good for all nuclei with 10 < A < 80. CCC
CCC Also included is the proton cross section fit and a preliminary CCC
CCC deuteron/neutron fit by M. E. Christy, N. Kalantarians, J. Either CCC
CCC and W. Melnitchouk (to be published) based on both inclusive CCC
CCC deuteron and tagged deuteron data on n/d from BONuS. CCC
CCC Range of validity is W^2 < 32, Q^2 < 32.0 CCC
CCC New data included in deuteron fit, including photoproduction at CCC
CCC Q^2 = 0. CCC
CCC CCC
CCC CCC
CCC A > 2 nuclei fit are 4He, 12C, 27Al, and 56Fe. More nuclei CCC
CCC will be fit in the next version. CCC
CCC CCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
SUBROUTINE F1F2IN21(Z, A, QSQ, WSQ, F1, F2)
!--------------------------------------------------------------------
! Fit to inelastic cross sections for A(e,e')X
! valid for all W^<20 GeV2 and all Q2<30 GeV2
!
! Inputs: Z, A (real*8) are Z and A of nucleus
! (use Z=0., A=1. to get free neutron)
c Qsq (real*8) is 4-vector momentum transfer squared (positive in
c chosen metric)
c Wsq (real*8) is invarinat mass squared of final state calculated
c assuming electron scattered from a free proton
c
c Outputs: F1, F2 (real*8) are structure functions per nucleus
! Version of 02/20/2021 E. Christy
! Made to be consistent with calling F1F2IN09 from P. Bosted
! with much code borrowed.
!--------------------------------------------------------------------
implicit none
real*8 Z,A,QSQ,WSQ
real*8 avgn,F1,F2,FL,F1p,F1n,F2p,F2n,FLp,FLn
real*8 sigm,sigl,sigt,eps
integer IA,IZ,wfn,opt
logical off,doqe/.false./
off = .true.
IA = int(A)
IZ = int(Z)
avgN = A-z
if(IA.LT.2) then
call sf(WSQ,QSQ,F1p,FLp,F2p,F1n,FLn,F2n)
if(IZ.LT.1) then !!! Neutron
F1 = F1n
F2 = F2n
else !!! Proton
F1 = F1p
F2 = F2p
endif
elseif(IA.EQ.2) then !!! Deuteron
eps = 0.5 !!! pass 0 < eps < 1
wfn = 2 !!! CD-Bonn, default
doqe = .false. !!! don't include QE !!!
call rescsd(WSQ,QSQ,eps,doqe,F1,F2,FL,wfn,sigm)
call smearsub(WSQ,QSQ,wfn,off,F2,F1,FL)
c write(6,*) "in f1f2in21: ", wsq,qsq,eps,wfn,f1,f2
elseif(IA.GT.2) then !!! A>2 nuclei
opt = 3 !!! inelastic + MEC
call SFCROSS(WSQ,QSQ,A,Z,opt,sigt,sigl,F1,F2,FL)
endif
return
end
CCC-----------------
SUBROUTINE F1F2QE21(Z, A, QSQ, WSQ, F1qe, F2qe)
!--------------------------------------------------------------------
! Fit to QE cross sections for A(e,e')X
! valid for all W^<30 GeV2 and all Q2<30 GeV2
!
! Inputs: Z, A (real*8) are Z and A of nucleus
! (use Z=0., A=1. to get free neutron)
c Qsq (real*8) is 4-vector momentum transfer squared (positive in
c chosen metric)
c Wsq (real*8) is invarinat mass squared of final state calculated
c assuming electron scattered from a free proton
c
c Outputs: F1, F2 (real*8) are structure functions per nucleus
! Version of 02/20/2021 E. Christy
!
! Note: This is a calling routine in order to be consistent with
! calling of F1F2QE09 from P. Bosted. For the deuteron the
! QE distribution is calculated by smearing with a realistic
! wavefunction in the weak-binding approximation. For A>2
! a superscaling model is used for the fit.
!--------------------------------------------------------------------
IMPLICIT none
real*8 wsq,qsq,A,Z,sigt,sigl,F1qe,F2qe,FLqe
integer opt/1/
integer wfn/2/
logical first/.false./
if(A.EQ.2.0) then
call SQESUB(wsq,qsq,wfn,f2qe,f1qe,fLqe,first)
elseif(A.GT.2.0) then
call sfcross(wsq,qsq,A,Z,opt,sigt,sigl,F1qe,F2qe,FLqe)
endif
c write(6,*) wsq,qsq,a,z,f1qe,f2qe,fLqe
end
CCC-----------------
C=======================================================================
Subroutine FORMFACTS(q2,gmp,gep,gmn,gen)
CCC Returns proton and neutron form factors based on new proton fit CCC
CCC by M.E. Christy including GMp12 data. Neutron starts with CCC
CCC Kelly fit, but includes correction factors extracted from fit to CCC
CCC inclusive deuteron data. Version from July 22, 2020 CCC
!--------------------------------------------------------------------
IMPLICIT NONE
REAL*8 q2,tau,gd,gmp,gep,gmn,gen,mcor,ecor
REAL*8 mu_p/ 2.792782/ ,mu_n/ -1.913148 /
REAL*8 mp/ 0.9382727 /, mp2
mp2 = mp*mp
tau = q2 / 4.0 / mp2
CCC 2021 Christy fit to GMp and GEp including GMp12 data CCC
GMP = mu_p*(1.+0.099481*tau)/
& (1.0+11.089*tau+19.374*tau*tau+5.7798*tau**3)
GEP = (1.+0.24482*tau**2)/
& (1.0+11.715*tau+11.964*tau*tau+27.407*tau**3)
GD = (1./(1 + q2/0.71))**2
CCC 2021 fit to deuteron inclusive data CCC
GMn = mu_n*(1.0+0.12417E-04*tau)/
& (1.000+11.404*tau+17.014*tau*tau+31.219*tau**3)
GEn = (1.5972*tau / (1.0+0.19655*tau)) * GD
return
end
SUBROUTINE RESCSP(w2,q2,sigtp,siglp)
CCCC Returns proton transverse and longitudinal cross sections CCCC
CCCC February 4, 2021 CCCC
IMPLICIT none
real*8 w2,q2,sigtp,siglp
real*8 xvalp(100),xval1(50),xvalL(50)
Integer i
real*8 sigtdis,sigLdis,w2max,w2min
data xvalp /
& 0.12287E+01,0.15196E+01,0.15044E+01,0.17009E+01,0.16765E+01,
& 0.14455E+01,0.12472E+00,0.23000E+00,0.91162E-01,0.88525E-01,
& 0.80876E-01,0.37521E+00,0.76849E+01,0.45411E+01,0.42458E+01,
& 0.18299E+01,0.68593E+01,0.13435E-01,0.17015E+04,0.45076E+01,
& 0.59724E+00,0.18944E+02,0.54924E-01,0.24830E+01,0.30381E+00,
& 0.19419E+02,0.13587E+00,0.20332E+01,0.24378E+01,0.48652E+01,
& 0.30850E+01,0.26876E+01,0.10685E-02,0.97878E+04,0.14193E+00,
& 0.21888E+01,0.25592E+00,0.73812E+00,0.20187E+01,0.93656E-01,
& 0.12867E-01,0.39477E+00,0.19371E+01,0.46900E+01,0.12106E-01,
& 0.17154E+00,0.19929E+01,0.55000E+00,0.42980E+01,0.41895E+00,
& 0.99122E+00,0.99085E+00,0.99798E+00,0.10028E+01,0.98145E+00,
& 0.10163E+01,0.10226E+01,0.10165E+01,0.00000E+00,0.00000E+00,
& 0.00000E+00,0.00000E+00,0.11353E-05,0.10605E+02,0.19705E+01,
& 0.00000E+00,0.19429E-09,0.75543E+02,0.60997E+01,0.00000E+00,
& 0.73839E+01,0.59820E-05,0.19247E+01,0.00000E+00,0.23239E+01,
& 0.16384E+01,0.14220E+01,0.00000E+00,0.10015E-03,0.57993E+00,
& 0.64963E+00,0.00000E+00,0.10093E-03,0.41844E+00,0.42011E+00,
& 0.00000E+00,0.39842E+00,0.86421E+01,0.10000E+00,0.10000E+01,
& -.82435E+01,0.48718E+02,0.51146E+02,0.29711E+01,0.11295E-02,
& 0.47865E+00,0.00000E+00,0.00000E+00,0.00000E+00,0.18935E+02 /
do i=1,50
xval1(i) = xvalp(i)
xvalL(i) = xvalp(50+i)
if(i.LE.12) xvalL(i) = xval1(i)
if(i.EQ.47.OR.i.EQ.48) xvalL(i) = xval1(i)
enddo
w2max = 34.0 !!! max for resonance fit
w2min = 36.0 !!! min for dis fit
call resmodp(1,w2,q2,xval1,sigTp)
call resmodp(2,w2,q2,xvalL,sigLp)
c if(w2.GT.w2min) then
c call disp(w2,q2,sigTdis,sigLdis)
c if(w2.LE.w2max) then
c sigTp = (w2max-w2)*sigTp+(w2-w2min)*sigTdis
c sigLp = (w2max-w2)*sigLp+(w2-w2min)*sigLdis
c sigTp = sigTp/2.0
c sigLp = sigLp/2.0
c else
c sigTp = sigTdis
c sigLp = sigLdis
c endif
c endif
return
end
SUBROUTINE RESCSD(w2,q2,eps,doqe,f1dqe,f2dqe,fLdqe,wfn,sigm)
CCCC Calcultes deuteron cross sections from smeared p+n. CCCC
CCCC Requires SQESUB be called first to read in smearing functions. CCCC
CCCC This should be one at the lowest level to keep from reading CCCC
CCCC multiple times.
IMPLICIT none
real*8 w2,q2,q2t,eps,t1,x,gamma2,q2min
real*8 sigtp,sigtn,siglp,sigln,sigt,sigl,sigm,m
real*8 m2,pi2,alpha,f1d,f2d,fLd,f1dqe,f2dqe,fLdqe
real*8 xvaln(100),off_mKP_fit,delta,xfr,xfl
integer i,j,k,ntssot,wfn,drn
logical doqe,off
c INCLUDE 'parm.cmn'
external off_mKP_fit
off = .false. !! off-shell corrections
c off = .true.
q2min = 4.0E-5
q2t = q2
if(q2.LT.q2min) q2t = q2min
drn = 5
xfr = 0.95
xfl = 1.0E-3
alpha = 1./137.036
m = (0.938272+0.939565)/2.0d0 !!! average p,n
m2 = m*m
pi2 = 3.14158*3.14159
c if(q2.LT.q2min) q2 = q2min !!! Hack to fix photoproduction
x = q2/(w2-m2+q2)
gamma2 = 1.+4.*m2*x*x/q2
t1 = gamma2*f2dqe-2.*x*f1dqe
if(f2dqe.LT.0.0.OR.f1dqe.LT.0.0.OR.fLdqe.LT.0.0)
& write(34,*) w2,q2,f2dqe,f1dqe,fLdqe
call SMEARSUB(w2,q2t,wfn,off,f2d,f1d,fLd)
if(doqe) then
f1d = f1d+f1dqe
f2d = f2d+f2dqe
fLd = fLd+fLdqe
endif
sigt = 0.3894e3*f1d*pi2*alpha*8.0/abs(w2-m2)
sigl = 0.3894e3*fLd*pi2*alpha*8.0/abs(w2-m2)/2.*abs(w2-m2+q2)/q2
sigm = sigt+eps*sigl
return
end
SUBROUTINE RESCSN(w2,q2,sigtn,sigln)
IMPLICIT none
real*8 w2,q2,sigtn,sigln
real*8 xval1(50),xvalL(50)
integer i
real*8 xvaln(100)/
& 0.12287E+01,0.15195E+01,0.15042E+01,0.17062E+01,0.16787E+01,
& 0.14474E+01,0.12502E+00,0.23000E+00,0.90468E-01,0.86480E-01,
& 0.75000E-01,0.38012E+00,0.71001E+01,0.32634E+01,0.10730E+01,
& 0.22650E+01,0.23212E+01,0.18872E+01,0.37882E+01,0.12554E+01,
& 0.29554E+01,0.95547E+01,0.12848E+02,0.27110E+01,0.97586E+03,
& 0.46182E+03,0.25324E+02,0.47504E+05,0.27562E+00,0.20067E+02,
& 0.23779E+00,0.23150E+01,0.28648E+01,0.12912E+04,0.63948E+01,
& 0.61034E+02,0.33488E+00,0.16043E+01,0.24234E+02,0.12297E+00,
& 0.10214E+00,0.52532E+00,0.22671E+01,0.48200E+01,-.77397E-01,
& 0.15751E-01,0.19872E+01,0.54078E+00,0.24385E+01,0.18916E-01,
& 0.10198E+01,0.97431E+00,0.99305E+00,0.98196E+00,0.10425E+01,
& 0.10123E+01,0.98465E+00,0.98416E+00,0.10284E+01,0.98698E+00,
& 0.10162E+01,0.10125E+01,0.11713E+02,0.94676E+02,0.60923E+01,
& 0.46433E-03,0.29789E-01,0.21407E+02,0.29234E+01,0.11574E+02,
& 0.52793E+00,0.41040E+01,0.16980E+01,0.16856E+02,0.35216E+01,
& 0.10865E+02,0.29016E+01,0.31103E+02,0.11927E+02,0.26535E+02,
& 0.81055E+01,0.16015E+01,0.28755E-01,0.24493E+01,0.83532E+00,
& 0.19400E+00,0.15667E+00,0.33667E+01,0.21528E+01,0.10000E+01,
& 0.29325E+02,0.56383E+01,0.73032E+01,0.72695E+01,0.18496E+00,
& 0.78960E+00,0.19850E+01,0.44998E+00,0.10037E+01,0.28875E+01 /
do i=1,50
xval1(i) = xvaln(i)
xvalL(i) = xvaln(50+i)
if(i.LE.12) xvalL(i) = xval1(i) !!! use same masses for L as T !!!
if(i.EQ.47.OR.i.EQ.48) xvalL(i) = xval1(i)
enddo
call resmodn(1,w2,q2,xval1,sigtn)
call resmodn(2,w2,q2,xvalL,sigLn)
return
end
SUBROUTINE RESMODP(sf,w2,q2,xval,sig)
CCC Returns proton transverse (sf=1) and longitudinal (sf=2 Cross sections CCC
CCC Version from February 21, 2021 - Author: M.E. Christy CCC
CCC This routine returns proton photo-absorbtion cross sections CCC
CCC for either transverse or longitudinal photons in units of ub/Sr/Gev. CCC
CCC CCC
CCC Fit form is empirical. Interpret physics from it at your own risk. CCC
CCC replaced 2-pi threshold with eta CCC
IMPLICIT NONE
REAL*8 W,w2,q2,mp,mp2,mpi2,xb,sig,xval(50),mass(7),width(7)
REAL*8 height(7),rescoef(6,4)
REAL*8 nr_coef(3,4),sigr(7),wdif(2),sig_nr,pi2,alpha
REAL*8 mpi,meta,intwidth(7),k,kcm,kr(7),kcmr(7),ppicm,ppi2cm
REAL*8 petacm,ppicmr(7),ppi2cmr(7),petacmr(7),epicmr(7),epi2cmr(7)
REAL*8 eetacmr(7),epicm,epi2cm,eetacm,br(7,3),ang(7)
REAL*8 pgam(7),pwid(7,3),x0(7),dip,mon,q20,A0
REAL*8 sig_res,xpr(2),t1,t2
INTEGER i,j,num,sf
mp = 0.9382727
mpi = 0.134977
mpi2 = mpi*mpi
meta = 0.547862
mp2 = mp*mp
alpha = 1./137.036
W = sqrt(w2)
wdif(1) = w - (mp + mpi)
wdif(2) = w - (mp + meta)
q20 = 0.05
q20= xval(50)
CCCC single pion branching ratios CCCC
br(1,1) = 1.00 !!! P33(1232)
br(2,1) = 0.45 !!! S11(1535)
br(3,1) = 0.60 !!! D13(1520)
br(4,1) = 0.65 !!! F15(1680)
br(5,1) = 0.60 !!! S11(1650)
br(6,1) = 0.65 !!! P11(1440) roper
br(7,1) = 0.60 !!! F37(1950)
CCCC eta branching ratios CCCC
br(1,3) = 0.0 !!! P33(1232)
br(2,3) = 0.40 !!! S11(1535)
br(3,3) = 0.08 !!! D13(1520)
br(4,3) = 0.0 !!! F15(1680)
br(5,3) = 0.20 !!! S11(1650)
br(6,3) = 0.0 !!! P11(1440) roper
br(7,3) = 0.0 !!! F37(1950)
CCCC 2-pion branching ratios CCCC
do i=1,7
br(i,2) = 1.-br(i,1)-br(i,3)
enddo
CCCC Meson angular momentum CCCC
ang(1) = 1. !!! P33(1232)
ang(2) = 0. !!! S11(1535)
ang(3) = 2. !!! D13(1520)
ang(4) = 3. !!! F15(1680)
ang(5) = 0. !!! S15(1650)
ang(6) = 1. !!! P11(1440) roper
ang(7) = 3. !!! F37(1950)
do i=1,7 !!! resonance damping parameter !!!
x0(i) = 0.178 !!!
enddo
c x0(1) = 0.125
x0(1) = 0.142
do i=1,7
br(i,2) = 1.-br(i,1)-br(i,3)
enddo
dip = 1./(1.+q2/1.05)**2. !!! Dipole parameterization !!!
mon = 1./(1.+q2/1.05)**1.
xb = q2/(q2+w2-mp2)
xpr(1) = 1.+(w2-(mp+mpi)**2)/(q2+q20)
xpr(1) = 1./xpr(1)
xpr(2) = 1.+(w2-(mp+meta)**2)/(q2+q20)
xpr(2) = 1./xpr(2)
if(w.LE.(mp+mpi)) xpr(1) = 1.0
if(w.LE.(mp+meta)) xpr(2) = 1.0
CCC Calculate kinematics needed for threshold Relativistic B-W CCC
k = (w2 - mp2)/2./mp
kcm = (w2-mp2)/2./w
epicm = (W2 + mpi**2 -mp2 )/2./w
ppicm = SQRT(MAX(0.0,(epicm**2 - mpi**2)))
epi2cm = (W2 + (2.*mpi)**2 -mp2 )/2./w
ppi2cm = SQRT(MAX(0.0,(epi2cm**2 - (2.*mpi)**2)))
eetacm = (W2 + meta*meta -mp2 )/2./w
petacm = SQRT(MAX(0.0,(eetacm**2 - meta**2)))
num = 0
do i=1,6 !!! Read in resonance masses !!!
num = num + 1
mass(i) = xval(i)
enddo
do i=1,6 !!! Read in resonance widths !!!
num = num + 1
intwidth(i) = xval(num)
width(i) = intwidth(i)
enddo
mass(7) = xval(47)
intwidth(7) = xval(48)
width(7) = intwidth(7)
do i=1,7
kr(i) = (mass(i)**2-mp2)/2./mp
kcmr(i) = (mass(i)**2.-mp2)/2./mass(i)
epicmr(i) = (mass(i)**2 + mpi**2 -mp2 )/2./mass(i)
ppicmr(i) = SQRT(MAX(0.0,(epicmr(i)**2 - mpi**2)))
epi2cmr(i) = (mass(i)**2 + (2.*mpi)**2 -mp2 )/2./mass(i)
ppi2cmr(i) = SQRT(MAX(0.0,(epi2cmr(i)**2 - (2.*mpi)**2)))
eetacmr(i) = (mass(i)**2 + meta*meta -mp2 )/2./mass(i)
petacmr(i) = SQRT(MAX(0.0,(eetacmr(i)**2 - meta**2)))
CCC Calculate partial widths CCC
pwid(i,1) = intwidth(i)*(ppicm/ppicmr(i))**(2.*ang(i)+1.)
& *((ppicmr(i)**2+x0(i)**2)/(ppicm**2+x0(i)**2))**ang(i)
c !!! 1-pion decay mode
pwid(i,2) = intwidth(i)*(ppi2cm/ppi2cmr(i))**(2.*ang(i)+4.)
& *((ppi2cmr(i)**2+x0(i)**2)/(ppi2cm**2+x0(i)**2))
& **(ang(i)+2) !!! 2-pion decay mode
pwid(i,2) = W/mass(i)*pwid(i,2)
pwid(i,3) = 0. !!! eta decay mode
if(i.EQ.2.OR.i.EQ.5) then
pwid(i,3) = intwidth(i)*(petacm/petacmr(i))**(2.*ang(i)+1.)
& *((petacmr(i)**2+x0(i)**2)/(petacm**2+x0(i)**2))**ang(i)
c !!! eta decay only for S11's
endif
pgam(i) = (kcm/kcmr(i))**2*
& (kcmr(i)**2+x0(i)**2)/(kcm**2+x0(i)**2)
pgam(i) = intwidth(i)*pgam(i)
width(i) = br(i,1)*pwid(i,1)+br(i,2)*pwid(i,2)+br(i,3)*pwid(i,3)
enddo
CCC End resonance kinematics and Widths calculations CCC
CCC Begin resonance Q^2 dependence calculations CCC
do i=1,6
do j=1,4
num = num + 1
rescoef(i,j)=xval(num)
enddo
if(sf.EQ.1) then
height(i) = rescoef(i,1)*
& (1.+rescoef(i,2)*q2/(1.+rescoef(i,3)*q2))*
& mon**rescoef(i,4)
else
height(i) = (rescoef(i,1)+rescoef(i,2)*q2)
& *exp(-1.*rescoef(i,3)*q2)
endif
height(i) = height(i)*height(i)
enddo
if(sf.EQ.2) then !!! 4th resonance region !!!
height(7) = (xval(44)+xval(45)*q2)*exp(-1.0*xval(46)*q2)
else
height(7) = xval(49)*mon
endif
height(7) = height(7)*height(7)
CCC End resonance Q^2 dependence calculations CCC
do i=1,3 !!! Non-Res coefficients !!!
do j=1,4
num = num + 1
nr_coef(i,j)=xval(num)
enddo
enddo
CCC Calculate Breit-Wigners for all resonances CCC
sig_res = 0.0
do i=1,7
sigr(i) = width(i)*pgam(i)/((W2 - mass(i)**2.)**2.
& + (mass(i)*width(i))**2.)
sigr(i) = height(i)*kr(i)/k*kcmr(i)/kcm*sigr(i)/intwidth(i)
sig_res = sig_res + sigr(i)
enddo
sig_res = sig_res*w
if(sf.EQ.2) sig_res = sig_res*q2
CCC Finish resonances / start non-res background calculation CCC
sig_nr = 0.
if(sf.EQ.1.and.xpr(1).LT.1.0) then
A0 = (1.0+xval(44)*q2)/(1.+q2/xval(42))**xval(43) !!! overall amplitude
t1 = xval(38)*log(2.0+q2/xval(39)) !!! exponent of (1-xpr)
t2 = xval(40)*log(2.0+q2/xval(41))+xval(45) !!! exponent of xpr
if(xpr(1).LE.1.0) then !!! 1-pi threshold
sig_nr = xval(37)*389.4*A0*(1.-xpr(1))**t1*xpr(1)**t2
endif
if(xpr(2).LE.1.0) then !!! eta threshold
sig_nr = sig_nr+xval(46)*389.4*A0*(1.-xpr(2))**t1*xpr(2)**t2
endif
elseif(sf.EQ.2.and.xpr(1).LT.1.0) then
t1 = xval(38)*log(1.001+q2/q20) !!! exponent of (1-xpr)
t2 = xval(41)/(1.001+q2/xval(42))**xval(43) !!! exponent of xpr
if(xpr(1).LE.1.0) then
sig_nr = sig_nr + xval(37)*389.4*
& xb*(1.-xpr(1))**t1*xpr(1)**t2
endif
sig_nr =sig_nr/log(1.001+q2/xval(39))
endif
sig = sig_res + sig_nr
if((w-mp).LT.wdif(1)) sig = 0.0
1000 format(8f12.5)
1001 format(7f12.3)
RETURN
END
SUBROUTINE RESMODN(sf,w2,q2,xval,sig)
CCC Returns proton transverse (sf=1) and longitudinal (sf=2 Cross sections CCC
CCC Version from February 21, 2021 - Author: M.E. Christy CCC
CCC This routine returns proton photo-absorbtion cross sections CCC
CCC for either transverse or longitudinal photons in units of ub/Sr/Gev. CCC
CCC CCC
CCC Fit form is empirical. Interpret physics from it at your own risk. CCC
CCC replaced 2-pi threshold with eta CCC
IMPLICIT NONE
REAL*8 W,w2,q2,mp,mp2,mpi2,xb,sig,xval(50),mass(7),width(7)
REAL*8 height(7),rescoef(6,4)
REAL*8 nr_coef(3,4),sigr(7),wdif(2),sig_nr,pi2,alpha
REAL*8 mpi,meta,intwidth(7),k,kcm,kr(7),kcmr(7),ppicm,ppi2cm
REAL*8 petacm,ppicmr(7),ppi2cmr(7),petacmr(7),epicmr(7),epi2cmr(7)
REAL*8 eetacmr(7),epicm,epi2cm,eetacm,br(7,3),ang(7)
REAL*8 pgam(7),pwid(7,3),x0(7),dip,mon,q20,A0
REAL*8 sig_res,xpr(2),t1,t2
INTEGER i,j,num,sf
mp = 0.939565
mpi = 0.134977
mpi2 = mpi*mpi
meta = 0.547862
mp2 = mp*mp
alpha = 1./137.036
W = sqrt(w2)
wdif(1) = w - (mp + mpi)
wdif(2) = w - (mp + meta)
q20 = 0.05
q20= xval(50)
CCCC single pion branching ratios CCCC
br(1,1) = 1.00 !!! P33(1232)
br(2,1) = 0.45 !!! S11(1535)
br(3,1) = 0.60 !!! D13(1520)
br(4,1) = 0.65 !!! F15(1680)
br(5,1) = 0.60 !!! S11(1650)
br(6,1) = 0.65 !!! P11(1440) roper
br(7,1) = 0.60 !!! F37(1950)
CCCC eta branching ratios CCCC
br(1,3) = 0.0 !!! P33(1232)
br(2,3) = 0.40 !!! S11(1535)
br(3,3) = 0.08 !!! D13(1520)
br(4,3) = 0.0 !!! F15(1680)
br(5,3) = 0.20 !!! S11(1650)
br(6,3) = 0.0 !!! P11(1440) roper
br(7,3) = 0.0 !!! F37(1950)
CCCC 2-pion branching ratios CCCC
do i=1,7
br(i,2) = 1.-br(i,1)-br(i,3)
enddo
CCCC Meson angular momentum CCCC
ang(1) = 1. !!! P33(1232)
ang(2) = 0. !!! S11(1535)
ang(3) = 2. !!! D13(1520)
ang(4) = 3. !!! F15(1680)
ang(5) = 0. !!! S15(1650)
ang(6) = 1. !!! P11(1440) roper
ang(7) = 3. !!! F37(1950)
do i=1,7 !!! resonance damping parameter !!!
x0(i) = 0.178 !!!
enddo
c x0(1) = 0.125
x0(1) = 0.142
do i=1,7
br(i,2) = 1.-br(i,1)-br(i,3)
enddo
dip = 1./(1.+q2/1.05)**2. !!! Dipole parameterization !!!
mon = 1./(1.+q2/1.1)**1.
xb = q2/(q2+w2-mp2)
xpr(1) = 1.+(w2-(mp+mpi)**2)/(q2+q20)
xpr(1) = 1./xpr(1)
xpr(2) = 1.+(w2-(mp+meta)**2)/(q2+q20)
xpr(2) = 1./xpr(2)
if(w.LE.(mp+mpi)) xpr(1) = 1.0
if(w.LE.(mp+meta)) xpr(2) = 1.0
CCC Calculate kinematics needed for threshold Relativistic B-W CCC
k = (w2 - mp2)/2./mp
kcm = (w2-mp2)/2./w
epicm = (W2 + mpi**2 -mp2 )/2./w
ppicm = SQRT(MAX(0.0,(epicm**2 - mpi**2)))
epi2cm = (W2 + (2.*mpi)**2 -mp2 )/2./w
ppi2cm = SQRT(MAX(0.0,(epi2cm**2 - (2.*mpi)**2)))
eetacm = (W2 + meta*meta -mp2 )/2./w
petacm = SQRT(MAX(0.0,(eetacm**2 - meta**2)))
num = 0
do i=1,6 !!! Read in resonance masses !!!
num = num + 1
mass(i) = xval(i)
enddo
do i=1,6 !!! Read in resonance widths !!!
num = num + 1
intwidth(i) = xval(num)
width(i) = intwidth(i)
enddo
mass(7) = xval(47)
intwidth(7) = xval(48)
width(7) = intwidth(7)
do i=1,7
kr(i) = (mass(i)**2-mp2)/2./mp
kcmr(i) = (mass(i)**2.-mp2)/2./mass(i)
epicmr(i) = (mass(i)**2 + mpi**2 -mp2 )/2./mass(i)
ppicmr(i) = SQRT(MAX(0.0,(epicmr(i)**2 - mpi**2)))
epi2cmr(i) = (mass(i)**2 + (2.*mpi)**2 -mp2 )/2./mass(i)
ppi2cmr(i) = SQRT(MAX(0.0,(epi2cmr(i)**2 - (2.*mpi)**2)))
eetacmr(i) = (mass(i)**2 + meta*meta -mp2 )/2./mass(i)
petacmr(i) = SQRT(MAX(0.0,(eetacmr(i)**2 - meta**2)))
CCC Calculate partial widths CCC
pwid(i,1) = intwidth(i)*(ppicm/ppicmr(i))**(2.*ang(i)+1.)
& *((ppicmr(i)**2+x0(i)**2)/(ppicm**2+x0(i)**2))**ang(i)
c !!! 1-pion decay mode
pwid(i,2) = intwidth(i)*(ppi2cm/ppi2cmr(i))**(2.*ang(i)+4.)
& *((ppi2cmr(i)**2+x0(i)**2)/(ppi2cm**2+x0(i)**2))
& **(ang(i)+2) !!! 2-pion decay mode
pwid(i,2) = W/mass(i)*pwid(i,2)
pwid(i,3) = 0. !!! eta decay mode
if(i.EQ.2.OR.i.EQ.5) then
pwid(i,3) = intwidth(i)*(petacm/petacmr(i))**(2.*ang(i)+1.)
& *((petacmr(i)**2+x0(i)**2)/(petacm**2+x0(i)**2))**ang(i)
c !!! eta decay only for S11's
endif
pgam(i) = (kcm/kcmr(i))**2*
& (kcmr(i)**2+x0(i)**2)/(kcm**2+x0(i)**2)
pgam(i) = intwidth(i)*pgam(i)
width(i) = br(i,1)*pwid(i,1)+br(i,2)*pwid(i,2)+br(i,3)*pwid(i,3)
enddo
CCC End resonance kinematics and Widths calculations CCC
CCC Begin resonance Q^2 dependence calculations CCC
do i=1,6
do j=1,4
num = num + 1
rescoef(i,j)=xval(num)
enddo
if(sf.EQ.1) then
height(i) = rescoef(i,1)*
& (1.+rescoef(i,2)*q2/(1.+rescoef(i,3)*q2))*
& mon**rescoef(i,4)
else
height(i) = (rescoef(i,1)+rescoef(i,2)*q2)
& *exp(-1.*rescoef(i,3)*q2)
endif
height(i) = height(i)*height(i)
enddo
if(sf.EQ.2) then !!! 4th resonance region !!!
height(7) = (xval(44)+xval(45)*q2)*exp(-1.0*xval(46)*q2)
else
height(7) = xval(49)*mon
endif
height(7) = height(7)*height(7)
CCC End resonance Q^2 dependence calculations CCC
do i=1,3 !!! Non-Res coefficients !!!
do j=1,4
num = num + 1
nr_coef(i,j)=xval(num)
enddo
enddo
CCC Calculate Breit-Wigners for all resonances CCC
sig_res = 0.0
do i=1,7
sigr(i) = width(i)*pgam(i)/((W2 - mass(i)**2.)**2.
& + (mass(i)*width(i))**2.)
sigr(i) = height(i)*kr(i)/k*kcmr(i)/kcm*sigr(i)/intwidth(i)
sig_res = sig_res + sigr(i)
enddo
sig_res = sig_res*w
if(sf.EQ.2) sig_res = sig_res*q2
CCC Finish resonances / start non-res background calculation CCC
sig_nr = 0.
if(sf.EQ.1.and.xpr(1).LT.1.0) then
A0 = (1.0+xval(44)*q2)/(1.+q2/xval(42))**xval(43) !!! overall amplitude
t1 = xval(38)*log(2.51+q2/xval(39)) !!! exponent of (1-xpr)
t2 = xval(40)*log(2.51+q2/xval(41))+xval(45) !!! exponent of xpr
if(xpr(1).LE.1.0) then !!! 1-pi threshold
sig_nr = xval(37)*389.4*A0*(1.-xpr(1))**t1*xpr(1)**t2
endif
if(xpr(2).LE.1.0) then !!! eta threshold
sig_nr = sig_nr+xval(46)*389.4*A0*(1.-xpr(2))**t1*xpr(2)**t2
endif
elseif(sf.EQ.2.and.xpr(1).LT.1.0) then
t1 = xval(38)*log(1.001+q2/q20) !!! exponent of (1-xpr)
t2 = xval(41)/(1.001+q2/xval(42))**xval(43) !!! exponent of xpr
if(xpr(1).LE.1.0) then
sig_nr = sig_nr + xval(37)*389.4*
& xb*(1.-xpr(1))**t1*xpr(1)**t2
endif
sig_nr =sig_nr/log(1.001+q2/xval(39))
endif
sig = sig_res + sig_nr
if((w-mp).LT.wdif(1)) sig = 0.0
1000 format(8f12.5)
1001 format(7f12.3)
RETURN
END
SUBROUTINE SMEARSUB(w2,q2,wfn,off,f2s,f1s,fLs)
CCCC Fermi smears structure functions. Requires subroutne GETFY CCCC
CCCC to be initialized first. CCCC
IMPLICIT none
real*8 w2,q2,mp,mp2,x,z,wwz,alpha,alpha2,gamma,gamma2
real*8 y,fy11,fy12,fy2,inc,f2s,f1s,fLs,f2pi,f2ni,xvaln(100)
real*8 sigtp,sigtn,siglp,sigln,f1pi,f1ni,fLpi,fLni
real*8 f1i(1000),f2i(1000),vfact1(1000),vfact2(1000)
real*8 vfact1off(1000),vfact2off(1000),fy11off,fy12off
real*8 fy2off,f1soff,f2soff,fLsoff
real*8 ymin,ymax,pi,pi2,epsd
real*8 c0,c1,c2,delta(1000)
integer i,j,nbins,wfn
c logical first/.true./
logical firsty/.false./
logical off
real*8 dsimps
external dsimps
C *****Off-shell parameters*****
if(wfn.eq.1) then
c0=-3.6735d0
c1=0.057717d0
c2=0.36419d0
elseif(wfn.eq.2) then
c0=-7.2061d0
c1=0.062022d0
c2=0.38018d0
elseif(wfn.eq.3) then
c0=1.7204d0
c1=0.050923d0
c2=0.34360d0
elseif(wfn.eq.4) then
c0=-1.7690d0
c1=0.058321d0
c2=0.36976d0
else
c0=0.d0
c1=0.d0
c2=0.d0
write(6,*) "Warning: wavefunction undefined"
endif
C ******************************
mp = (0.938272+0.939565)/2.0d0 !!! average of p, n
mp2 = mp*mp
alpha = 1/137.03599
alpha2 = alpha*alpha
pi = 3.14159
pi2 = pi*pi
epsd = -2.2E-03
x = q2/(w2-mp2+q2)
f2s = 0.0
f1s = 0.0
fLs = 0.0
if(x.LT.0.0D0) return
gamma2 = (1.+4.*mp2*x*x/q2)
gamma = sqrt(gamma2)
nbins = 60
if(w2.LT.1.6) nbins = 80
c nbins = 200 !!! adjust as needed
if(w2.GE.2.6.AND.Q2.GE.2.0) nbins = 46
CCC/// Fill array for Simpson's rule calculation ///CCC
c if(x.LT.1.0) then
c ymin = max(x*(1.0D0-2.0D0*epsd*mp/(w2-mp2)),x)
c else
c ymin = x
c endif
CCC Note problem if Q2 = 0 CCC
ymin = max(x*(1.0D0-2.0D0*epsd*mp/q2),x)
c ymin = min(ymin,2.0d0)
ymax = min(1.0d0+gamma2/2.0d0+epsd/mp,2.0d0)
c write(6,*) "W2, ymin, ymax: ",w2,ymin,ymax
if(ymin.GE.ymax) return
c ymax = 2.0d0
c write(6,*) off
if(ymin.EQ.0) write(6,*) "Error ymin = 0"
inc = (ymax-ymin)/float(nbins)
y = ymin-inc
!$OMP PARALLEL DO PRIVATE(i,y,z,wwz,F1pi,FLpi,f1ni,FLni,f2pi,f2ni,fy11,fy12,fy2)
do i=1,nbins+1 !!!! First calculate the cross smearing function for each y bin !!!!
y = y + inc
z = x/y