#include "METOOLS/Loops/Master_Integrals.H"
#include "METOOLS/Loops/PV_Integrals.H"
#include "ATOOLS/Math/MathTools.H"
#include "ATOOLS/Org/Message.H"
#include "ATOOLS/Org/Exception.H"
using namespace std;
using namespace ATOOLS;
using namespace METOOLS;
//! C_10(p12,p22,s12;m02,m12,m22)
//! C_11(p12,p22,s12;m02,m12,m22)
//! C_12(p12,p22,s12;m02,m12,m22)
//! C_20(p2,p2,0;m02,m2,m2)
//! C_21(p12,p22,s12;m02,m12,m22)
//! C_22(p12,p22,s12;m02,m12,m22)
//! C_23(p12,p22,s12;m02,m12,m22)
//! C_24(p2,p2,0;m02,m2,m2)
//! C_24(p12,p22,s12;m02,m12,m22)
//! C_30(p2,p2,0;m02,m2,m2)
//! C_38(p2,p2,0;m02,m2,m2)
/*! all momenta incoming
p2
-----|\ p1 + p2 + p3 = 0
| \ m0
| \ s12 = p3^2 = (-p1-p2)^2 = (p1+p2)^2
| \ p3
m2 | |-----
| /
| / s12 > 0 s-channel
| / m1 s12 < 0 t-channel
-----|/ s12 = 0 in wave-function corrections
p1
*/
METOOLS::DivArrC
METOOLS::PV_Triangle_10(const double& p12, const double& p22, const double& s12,
const Complex& m02, const Complex& m12, const Complex& m22,
double mu2=0.) {
if (mu2 == 0.) mu2 = GLOBAL_RENORMALISATION_SCALE;
if (!IsZero(s12) || !IsEqual(p12,p22) || !IsEqual(m12,m22)) {
THROW(fatal_error,"call in ill-defined situation");
}
else {
double p2(0.5*(p12+p22));
Complex m2(0.5*(m12+m22));
if (IsZero(p2)) {
//! C_10(0,0,0;m02,m2,m2) = ?
msg_Out()<<"not implemented yet\n";
return DivArrC(0.,0.,0.,0.,0.,0.);
}
else {
//! C_10(p2,p2,0;m02,m2,m2) = 1/(2*p2) * ( B_0(p2;m12,m2) - B_0(0;m2,m2)
//! + fC C_0(p2,p2,0;m02,m2,m2) )
Complex fC(-p2+m2-m02);
return 0.5/p2*(Master_Bubble(p2,m02,m2,mu2)
-Master_Bubble(0.,m2,m2,mu2)
+(!IsZero(fC)?fC*Master_Triangle(p2,p2,0.,m02,m2,m2,mu2)
:DivArrC(0.,0.,0.,0.,0.,0.)));
}
}
return DivArrC(0.,0.,0.,0.,0.,0.);
}
METOOLS::DivArrC
METOOLS::PV_Triangle_11(const double& p12, const double& p22, const double& s12,
const Complex& m02, const Complex& m12, const Complex& m22,
double mu2=0.) {
if (mu2 == 0.) mu2 = GLOBAL_RENORMALISATION_SCALE;
if (IsZero(s12)) {
//! s12 = 0 ==> p1 = p2
//! ==> C_11(p12,p22,0;m02,m12,m22) = C_10(p2,p2,0;m02,m12,m22)
return PV_Triangle_10(p12,p22,s12,m02,m12,m22,mu2);
}
else {
//! C_11(p12,p22,s12;m02,m12,m22)
//! = 1/2 * 1/(p12p22-(p1p2)^2)
//! * ( p22 ( B_0(p22;m02,m22) - B_0(s12;m12,m22)
//! + f1C C_0(p12,p22,s12;m02,m12,m22) )
//! - (p1p2) ( B_0(p12;m02,m12) - B_0(s;m12,m22)
//! + f2C C_0(p12,p22,s12;m02,m12,m22) ) )
double p1p2(0.5*(s12-p12-p22));
Complex f1C(-p12+m12-m02), f2C(-p22+m22-m02);
if (IsZero(p12*p22-sqr(p1p2))) {
msg_Out()<<"not implemented yet\n";
return DivArrC(0.,0.,0.,0.,0.,0.);
}
else {
DivArrC C0(((!IsZero(f1C)) || (!IsZero(f2C)))?
Master_Triangle(p12,p22,s12,m02,m12,m22,mu2):
DivArrC(0.,0.,0.,0.,0.,0.));
return 0.5/(p12*p22-sqr(p1p2))
* ((!IsZero(p22)?p22*(Master_Bubble(p22,m02,m22,mu2)
-Master_Bubble(s12,m12,m22,mu2)
+f1C*C0)
:DivArrC(0.,0.,0.,0.,0.,0.))
-(!IsZero(p1p2)?p1p2*(Master_Bubble(p12,m02,m12,mu2)
-Master_Bubble(s12,m12,m22,mu2)
+f2C*C0)
:DivArrC(0.,0.,0.,0.,0.,0.)));
}
}
return DivArrC(0.,0.,0.,0.,0.,0.);
}
METOOLS::DivArrC
METOOLS::PV_Triangle_12(const double& p12, const double& p22, const double& s12,
const Complex& m02, const Complex& m12, const Complex& m22,
double mu2=0.) {
//! C_12(p12,p22,s12;m02,m12,m22) = C_11(p22,p12,s12;m02,m22,m12)
return PV_Triangle_11(p22,p12,s12,m02,m22,m12,mu2);
}
METOOLS::DivArrC
METOOLS::PV_Triangle_20(const double& p12, const double& p22, const double& s12,
const Complex& m02, const Complex& m12, const Complex& m22,
double mu2=0.) {
if (mu2 == 0.) mu2 = GLOBAL_RENORMALISATION_SCALE;
if (!IsZero(s12) || !IsEqual(p12,p22) || !IsEqual(m12,m22)) {
THROW(fatal_error,"call in ill-defined situation");
}
else {
double p2(0.5*(p12+p22));
if (IsZero(p2)) {
msg_Out()<<"not implemented yet\n";
return DivArrC(0.,0.,0.,0.,0.,0.);
}
else {
Complex m2(0.5*(m12+m22));
Complex fC(-p2+m2-m02);
//! C_20(p2,p2,0;m02,m2,m2)
//! = 1/2 * 1/(p4(D-1))
//! * ( D/2 (p2 B_1(p2;m02,m2) + p2 B_0(0;m2,m2)
//! + fC p2 C_10(p2,p2,0;m02,m2,m2) )
//! - p2 ( B_0(0;m2,m2)
//! + m02 C_0(p2,p2,0;m02,m2,m2)))
return 0.5/(p2*(D-1.))
*(0.5*D*(PV_Bubble_1(p2,m02,m2,mu2)
+Master_Bubble(0.,m2,m2,mu2)
+(!IsZero(fC)?fC*PV_Triangle_10(p2,p2,0.,m02,m2,m2,mu2)
:DivArrC(0.,0.,0.,0.,0.,0.)))
- (Master_Bubble(0,m2,m2,mu2)
+(!IsZero(m02)?m02*Master_Triangle(p2,p2,0,m02,m2,m2,mu2)
:DivArrC(0.,0.,0.,0.,0.,0.))));
}
}
return DivArrC(0.,0.,0.,0.,0.,0.);
}
METOOLS::DivArrC
METOOLS::PV_Triangle_21(const double& p12, const double& p22, const double& s12,
const Complex& m02, const Complex& m12, const Complex& m22,
double mu2=0.) {
if (mu2 == 0.) mu2 = GLOBAL_RENORMALISATION_SCALE;
//! C_21(p12,p22,s12;m02,m12,m22)
//! = 1/2 * 1/(p12p22-(p1p2)^2)
//! * ( p22 ( B_1(s12;m12,m22) - B_0(s12;m12,m22)
//! + f1C C_11(p12,p22,s12;m02,m12,m22)
//! - 2 C_24(p12,p22,s12;m02,m12,m22) )
//! - (p1p2) ( B_1(p12;m02,m12) - B_1(s12;m22,m12)
//! + f2C C_12(p12,p22,s12;m02,m12,m22) ) )
double p1p2(0.5*(s12-p12-p22));
if (IsZero(p12*p22-sqr(p1p2))) {
msg_Out()<<"not implemented yet\n";
return DivArrC(0.,0.,0.,0.,0.,0.);
}
else {
Complex f1C(-p12+m12-m02), f2C(-p22+m22-m02);
DivArrC C11(((!IsZero(f1C)) || (!IsZero(f2C)))?
PV_Triangle_24(p12,p22,s12,m02,m12,m22,mu2):
DivArrC(0.,0.,0.,0.,0.,0.));
return 0.5/(p12*p22-sqr(p1p2))
*((!IsZero(p22)?p22*(PV_Bubble_1(s12,m12,m22,mu2)
-Master_Bubble(s12,m12,m22,mu2)
+f1C*C11
-2.*PV_Triangle_24(p12,p22,s12,m02,m12,m22,mu2))
:DivArrC(0.,0.,0.,0.,0.,0.))
-(!IsZero(p1p2)?p1p2*(PV_Bubble_1(p12,m02,m12,mu2)
-PV_Bubble_1(s12,m22,m12,mu2)
+f2C*C11)
:DivArrC(0.,0.,0.,0.,0.,0.)));
}
return DivArrC(0.,0.,0.,0.,0.,0.);
}
METOOLS::DivArrC
METOOLS::PV_Triangle_22(const double& p12, const double& p22, const double& s12,
const Complex& m02, const Complex& m12, const Complex& m22,
double mu2=0.) {
if (mu2 == 0.) mu2 = GLOBAL_RENORMALISATION_SCALE;
//! C_22(p12,p22,s12;m02,m12,m22) = C_21(p22,p12,s12;m02,m22,m12)
return PV_Triangle_21(p22,p12,s12,m02,m22,m12,mu2);
}
METOOLS::DivArrC
METOOLS::PV_Triangle_23(const double& p12, const double& p22, const double& s12,
const Complex& m02, const Complex& m12, const Complex& m22,
double mu2=0.) {
if (mu2 == 0.) mu2 = GLOBAL_RENORMALISATION_SCALE;
//! C_23(p12,p22,s12;m02,m12,m22)
//! = 1/2 * 1/(p12p22-(p1p2)^2)
//! * ( p12 ( B_1(p12;m02,m12) - B_1(s12;m22,m12)
//! + f2C C_12(p12,p22,s12;m02,m12,m22) )
//! - (p1p2) ( B_1(s12;m12,m12) + B_0(s12;m12,m22)
//! + f1C C_11(p12,p22,s12;m02,m12,m22)
//! - 2 C_24(p12,p22,s12;m02,m12,m22) ) )
double p1p2(0.5*(s12-p12-p22));
if (IsZero(p12*p22-sqr(p1p2))) {
msg_Out()<<"not implemented yet\n";
return DivArrC(0.,0.,0.,0.,0.,0.);
}
else {
Complex f1C(-p12+m12-m02), f2C(-p22+m22-m02);
DivArrC C11(((!IsZero(f1C)) || (!IsZero(f2C)))?
PV_Triangle_24(p12,p22,s12,m02,m12,m22,mu2):
DivArrC(0.,0.,0.,0.,0.,0.));
return 0.5/(p12*p22-sqr(p1p2))
*((!IsZero(p12)?p12*(PV_Bubble_1(p12,m02,m12,mu2)
-PV_Bubble_1(s12,m22,m12,mu2)
+f2C*C11)
:DivArrC(0.,0.,0.,0.,0.,0.))
-(!IsZero(p1p2)?p1p2*(PV_Bubble_1(s12,m12,m22,mu2)
-Master_Bubble(s12,m12,m22,mu2)
+f1C*C11
-2.*PV_Triangle_24(p12,p22,s12,m02,m12,m22,mu2))
:DivArrC(0.,0.,0.,0.,0.,0.)));
}
return DivArrC(0.,0.,0.,0.,0.,0.);
}
METOOLS::DivArrC
METOOLS::PV_Triangle_24(const double& p12, const double& p22, const double& s12,
const Complex& m02, const Complex& m12, const Complex& m22,
double mu2=0.) {
if (mu2 == 0.) mu2 = GLOBAL_RENORMALISATION_SCALE;
if (IsZero(s12) && IsEqual(p12,p22) && IsEqual(m12,m22)) {
//! C_24(p2,p2,0;m02,m2,m2)
//! = 1/(p4(D-1)) * ( p4 ( B_0(0;m2,m2) + m02 C_0(p2,p2,0;m02,m2,m2) )
//! - p2/2 ( p2 B_1(p2;m02,m2) + p2 B_0(0;m2,m2)
//! + fC p2 C_10(p2,p2,0;m02,m2,m2) ) )
double p2(0.5*(p12+p22));
Complex m2(0.5*(m12+m22));
Complex fC(-p2+m2-m02);
return 1./(D-1.)*(Master_Bubble(0.,m2,m2,mu2)
+(!IsZero(m02)?m02*Master_Triangle(p2,p2,0.,m02,m2,m2,mu2)
:DivArrC(0.,0.,0.,0.,0.,0.))
-0.5*(PV_Bubble_1(p2,m02,m2,mu2)
+Master_Bubble(0.,m2,m2,mu2)
+(!IsZero(fC)?fC*PV_Triangle_10(p2,p2,0.,m02,m2,m2,mu2)
:DivArrC(0.,0.,0.,0.,0.,0.))));
}
else {
//! C_24(p12,p22,s12;m02,m12,m22)
//! = 1/(D-2) * ( m02 C_0(p12,p22,s12;m02,m12,m22)
//! + 1/2 B_0(s12;m12,m22)
//! - f1C C_11(p12,p22,s12;m02,m12,m22)
//! - f2C C_12(p12,p22,s12;m02,m12,m22) )
Complex f1C(-p12+m12-m02), f2C(-p22+m22-m02);
return 1./(D-2.)*((!IsZero(m02)?m02*Master_Triangle(p12,p22,s12,m02,m12,m22,mu2)
:DivArrC(0.,0.,0.,0.,0.,0.))
+0.5*Master_Bubble(s12,m12,m22,mu2)
-(!IsZero(f1C)?f1C*PV_Triangle_11(p12,p22,s12,m02,m12,m22,mu2)
:DivArrC(0.,0.,0.,0.,0.,0.))
-(!IsZero(f2C)?f2C*PV_Triangle_12(p12,p22,s12,m02,m12,m22,mu2)
:DivArrC(0.,0.,0.,0.,0.,0.)));
}
return DivArrC(0.,0.,0.,0.,0.,0.);
}
METOOLS::DivArrC
METOOLS::PV_Triangle_30(const double& p12, const double& p22, const double& s12,
const Complex& m02, const Complex& m12, const Complex& m22,
double mu2=0.) {
if (mu2 == 0.) mu2 = GLOBAL_RENORMALISATION_SCALE;
if (!IsZero(s12) || !IsEqual(p12,p22) || !IsEqual(m12,m22)) {
THROW(fatal_error,"call in ill-defined situation");
}
else {
double p2(0.5*(p12+p22));
if (IsZero(p2)) {
msg_Out()<<"not implemented yet\n";
return DivArrC(0.,0.,0.,0.,0.,0.);
}
else {
//! C_30(p2,p2,0;m02,m2,m2)
//! = 1/(2p2) * ( B_21(p2;m02,m2) - B_21(0;m2,m2)
//! + fC C_20(p2,p2,0;m02,m2,m2) )
//! - 2/p2 C_38(p2,p2,0;m02,m2,m2)
//!
//! = 1/(2p2) * ( B_21(p2;m02,m2) - B_21(0;m2,m2)
//! + fC C_20(p2,p2,0;m02,m2,m2) )
//! - 1/p4 * ( B_22(p2;m02,m2) - B_22(0;m2,m2)
//! + fC C_24(p2,p2,0;m02,m2,m2) )
Complex m2(0.5*(m12+m22));
Complex fC(-p2+m2-m02);
return 0.5/p2*(PV_Bubble_21(p2,m02,m2,mu2)
-PV_Bubble_21(0.,m2,m2,mu2)
+(!IsZero(fC)?fC*PV_Triangle_20(p2,p2,0,m02,m2,m2,mu2)
:DivArrC(0.,0.,0.,0.,0.,0.)))
-1./sqr(p2)*(PV_Bubble_22(p2,m02,m2,mu2)
-PV_Bubble_22(0.,m2,m2,mu2)
+(!IsZero(fC)?fC*PV_Triangle_24(p2,p2,0,m02,m2,m2,mu2)
:DivArrC(0.,0.,0.,0.,0.,0.)));
}
}
return DivArrC(0.,0.,0.,0.,0.,0.);
}
METOOLS::DivArrC
METOOLS::PV_Triangle_38(const double& p12, const double& p22, const double& s12,
const Complex& m02, const Complex& m12, const Complex& m22,
double mu2=0.) {
if (mu2 == 0.) mu2 = GLOBAL_RENORMALISATION_SCALE;
if (!IsZero(s12) || !IsEqual(p12,p22) || !IsEqual(m12,m22)) {
THROW(fatal_error,"call in ill-defined situation");
}
else {
double p2(0.5*(p12+p22));
if (IsZero(p2)) {
msg_Out()<<"not implemented yet\n";
return DivArrC(0.,0.,0.,0.,0.,0.);
}
else {
//! C_38(p2,p2,0;m02,m2,m2)
//! = 1/(2p2) * ( B_22(p2;m02,m2) - B_22(0;m2,m2)
//! + fC C_24(p2,p2,0;m02,m2,m2) )
Complex m2(0.5*(m12+m22));
Complex fC(-p2+m2-m02);
return 0.5/sqr(p2)*(PV_Bubble_22(p2,m02,m2,mu2)
-PV_Bubble_22(0.,m2,m2,mu2)
+(!IsZero(fC)?fC*PV_Triangle_24(p2,p2,0,m02,m2,m2,mu2)
:DivArrC(0.,0.,0.,0.,0.,0.)));
}
}
return DivArrC(0.,0.,0.,0.,0.,0.);
}