/
xscnnlo.cc
159 lines (150 loc) · 6.75 KB
/
xscnnlo.cc
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/*-----------------------------------------------------------------------------
xscnnlo.cc
Lisong Chen (lic114@pitt.edu), Ayres Freitas (afreitas@pitt.edu)
last revision: 14 Sep 2022
-------------------------------------------------------------------------------
matrix element class needed for description of cross-section at NNLO
precision near Z pole and NLO away from Z pole
-----------------------------------------------------------------------------*/
#include "xscnnlo.h"
#include "ff0.h"
#include "ff.h"
Cplx mat_SMNNLO::coeffR(void) const
{
double mz = ival->get(MZ),
gz = ival->get(GamZ);
double QWe, QWf, IVe, IVf, rIAA, xI,
zie0 = z0(it,iff,*ival), zjf0 = z0(ot,off,*ival),
iszp1 = isz1fp(*ival)+isz1bp(*ival),
iszpp1 = isz1fpp(*ival)+isz1bpp(*ival);
switch(iff)
{
case VEC: QWe = 1.-4*fabs(Qf[it])*realreg(SWi->result());
IVe = (az0(it,*ival)*(iz1f(it,VEC,*ival)+iz1b(it,VEC,*ival))
- vz0(it,*ival)*(iz1f(it,AXV,*ival)+iz1b(it,AXV,*ival)))
/sqr(az0(it,*ival));
break;
case AXV: QWe = 1; IVe = 0;
break;
}
switch(off)
{
case VEC: QWf = 1.-4*fabs(Qf[ot])*realreg(SWo->result());
IVf = (az0(ot,*ival)*(iz1f(ot,VEC,*ival)+iz1b(ot,VEC,*ival))
- vz0(ot,*ival)*(iz1f(ot,AXV,*ival)+iz1b(ot,AXV,*ival)))
/sqr(az0(ot,*ival));
break;
case AXV: QWf = 1; IVf = 0;
break;
}
rIAA = (iz1f(it,AXV,*ival)+iz1b(it,AXV,*ival))/az0(it,*ival)
+ (iz1f(ot,AXV,*ival)+iz1b(ot,AXV,*ival))/az0(ot,*ival)
- iszp1;
xI = (iz1fp(it,iff,*ival)+iz1bp(it,iff,*ival))/zie0
+ (iz1fp(ot,off,*ival)+iz1bp(ot,off,*ival))/zjf0 - iszpp1/2;
return(4*I3f[it]*I3f[ot]*sqrt(FAi->result()*FAo->result()) *
(QWe*QWf*(Cplx(1 - rIAA*rIAA/2, rIAA) - iszp1*iszp1/2
+ bRaz1(it,ot,cost,*ival))
+ (QWe*IVf + QWf*IVe)*Cplx(-rIAA,1) - IVe*IVf)
+ mz*gz*zie0*zjf0*xI);
}
Cplx mat_SMNNLO::coeffS1f(void) const
{
double mz = ival->get(MZ),
gz = ival->get(GamZ);
double gie0 = g0(it,iff,*ival), gjf0 = g0(ot,off,*ival),
zie0 = z0(it,iff,*ival), zjf0 = z0(ot,off,*ival);
Cplx zpie1 = Cplx(rz1fp(it,iff,*ival), iz1fp(it,iff,*ival)),
zpjf1 = Cplx(rz1fp(ot,off,*ival), iz1fp(ot,off,*ival)),
gie1 = Cplx(rg1f(it,iff,*ival), ig1f(it,iff,*ival)),
gjf1 = Cplx(rg1f(ot,off,*ival), ig1f(ot,off,*ival)),
szpp1 = Cplx(rsz1fpp(*ival), isz1fpp(*ival)),
sa1 = Cplx(rsg1f(*ival), isg1f(*ival));
return(zie0*zpjf1 + zpie1*zjf0 - zie0*zjf0*szpp1/2
+ (gie0*gjf1 + gie1*gjf0 + gie0*gjf0*(/*I*gz/mz*/ - sa1/(mz*mz)))/(mz*mz));
// the gz/mz term is already in coeffS = S_SMLO ^^^^^
}
Cplx mat_SMNNLO::coeffS1b(void) const
{
double mz = ival->get(MZ),
gz = ival->get(GamZ);
double gie0 = g0(it,iff,*ival), gjf0 = g0(ot,off,*ival),
zie0 = z0(it,iff,*ival), zjf0 = z0(ot,off,*ival);
Cplx zpie1 = Cplx(rz1bp(it,iff,*ival), iz1bp(it,iff,*ival)),
zpjf1 = Cplx(rz1bp(ot,off,*ival), iz1bp(ot,off,*ival)),
gie1 = Cplx(rg1b(it,iff,*ival), ig1b(it,iff,*ival)),
gjf1 = Cplx(rg1b(ot,off,*ival), ig1b(ot,off,*ival)),
szpp1 = Cplx(rsz1bpp(*ival), isz1bpp(*ival)),
sa1 = Cplx(rsg1b(*ival), isg1b(*ival));
return(zie0*zpjf1 + zpie1*zjf0 - zie0*zjf0*szpp1/2
+ (gie0*gjf1 + gie1*gjf0 + gie0*gjf0*(/*I*gz/mz*/ - sa1/(mz*mz)))/(mz*mz)
// the gz/mz term is already in coeffS = S_SMLO ^^^^^
+ B1(it,ot,iff,off,s,cost,*ival,1,1));
}
Cplx mat_SMNNLO::resoffZ1f(void) const
{
double mz = ival->get(MZ);
double gie0 = g0(it,iff,*ival), gjf0 = g0(ot,off,*ival),
zie0 = z0(it,iff,*ival), zjf0 = z0(ot,off,*ival);
Cplx zie1 = Cplx(rz1fs(it,iff,s,*ival), iz1fs(it,iff,s,*ival)),
zie1z = Cplx(rz1f(it,iff,*ival), iz1f(it,iff,*ival)),
zpie1z = Cplx(rz1fp(it,iff,*ival), iz1fp(it,iff,*ival)),
zjf1 = Cplx(rz1fs(ot,off,s,*ival), iz1fs(ot,off,s,*ival)),
zjf1z = Cplx(rz1f(ot,off,*ival), iz1f(ot,off,*ival)),
zpjf1z = Cplx(rz1fp(ot,off,*ival), iz1fp(ot,off,*ival)),
gie1 = Cplx(rg1fs(it,iff,s,*ival), ig1fs(it,iff,s,*ival)),
gie1z = Cplx(rg1f(it,iff,*ival), ig1f(it,iff,*ival)),
gjf1 = Cplx(rg1fs(ot,off,s,*ival), ig1fs(ot,off,s,*ival)),
gjf1z = Cplx(rg1f(ot,off,*ival), ig1f(ot,off,*ival)),
sz1 = Cplx(rsz1fs(s,*ival), isz1fs(s,*ival)),
sz1z = Cplx(rsz1f(*ival), isz1f(*ival)),
szp1z = Cplx(rsz1fp(*ival), isz1fp(*ival)),
szpp1z = Cplx(rsz1fpp(*ival), isz1fpp(*ival)),
sa1 = Cplx(rsg1fs(s,*ival), isg1fs(s,*ival)),
sa1z = Cplx(rsg1f(*ival), isg1f(*ival));
Cplx Rp = -zie0*zjf0*sz1z,
R = zie0*zjf1z + zie1z*zjf0 - zie0*zjf0*szp1z,
S = (zie0*zpjf1z + zpie1z*zjf0 - zie0*zjf0*szpp1z/2
+ (gie0*gjf1z + gie1z*gjf0 - gie0*gjf0*sa1z/(mz*mz))/(mz*mz)),
mats1 = ((zie0*zjf1 + zie1*zjf0 - zie0*zjf0*sz1/(s-mz*mz))/(s-mz*mz)
+ (gie0*gjf1 + gie1*gjf0 - gie0*gjf0*sa1/s)/s);
return(mats1 - ((R + Rp/(s-mz*mz))/(s-mz*mz) + S));
}
Cplx mat_SMNNLO::resoffZ1b(void) const
{
double mz = ival->get(MZ);
double gie0 = g0(it,iff,*ival), gjf0 = g0(ot,off,*ival),
zie0 = z0(it,iff,*ival), zjf0 = z0(ot,off,*ival);
Cplx zie1 = Cplx(rz1bs(it,iff,s,*ival), iz1bs(it,iff,s,*ival)),
zie1z = Cplx(rz1b(it,iff,*ival), iz1b(it,iff,*ival)),
zpie1z = Cplx(rz1bp(it,iff,*ival), iz1bp(it,iff,*ival)),
zjf1 = Cplx(rz1bs(ot,off,s,*ival), iz1bs(ot,off,s,*ival)),
zjf1z = Cplx(rz1b(ot,off,*ival), iz1b(ot,off,*ival)),
zpjf1z = Cplx(rz1bp(ot,off,*ival), iz1bp(ot,off,*ival)),
gie1 = Cplx(rg1bs(it,iff,s,*ival), ig1bs(it,iff,s,*ival)),
gie1z = Cplx(rg1b(it,iff,*ival), ig1b(it,iff,*ival)),
gjf1 = Cplx(rg1bs(ot,off,s,*ival), ig1bs(ot,off,s,*ival)),
gjf1z = Cplx(rg1b(ot,off,*ival), ig1b(ot,off,*ival)),
sz1 = Cplx(rsz1bs(s,*ival), isz1bs(s,*ival)),
sz1z = Cplx(rsz1b(*ival), isz1b(*ival)),
szp1z = Cplx(rsz1bp(*ival), isz1bp(*ival)),
szpp1z = Cplx(rsz1bpp(*ival), isz1bpp(*ival)),
sa1 = Cplx(rsg1bs(s,*ival), isg1bs(s,*ival)),
sa1z = Cplx(rsg1b(*ival), isg1b(*ival));
Cplx Rp = -zie0*zjf0*sz1z,
R = zie0*zjf1z + zie1z*zjf0 + zie0*zjf0*(-szp1z + bRaz1(it,ot,cost,*ival)),
S = (zie0*zpjf1z + zpie1z*zjf0 - zie0*zjf0*szpp1z/2
+ (gie0*gjf1z + gie1z*gjf0 - gie0*gjf0*sa1z/(mz*mz))/(mz*mz)
+ B1(it,ot,iff,off,s,cost,*ival,1,1,1e-12)),
mats1 = ((zie0*zjf1 + zie1*zjf0 - zie0*zjf0*sz1/(s-mz*mz))/(s-mz*mz)
+ (gie0*gjf1 + gie1*gjf0 - gie0*gjf0*sa1/s)/s
+ B1s(it,ot,iff,off,s,cost,*ival,1,1));
return(mats1 - ((R + Rp/(s-mz*mz))/(s-mz*mz) + S));
}
Cplx mat_SMNNLO::result(void) const
{
double mz = ival->get(MZ),
gz = ival->get(GamZ);
Cplx sminuss0(s - mz*mz, mz*gz);
return(coeffR()/sminuss0 + coeffS() + coeffSp()*sminuss0 + resoffZ());
}