METOOLS/Loops/PV_Integrals.H

0001 #ifndef METOOLS_Loops_PV_Integrals_H
0002 #define METOOLS_Loops_PV_Integrals_H
0003
0004 #include "ATOOLS/Math/MyComplex.H"
0005 #include "METOOLS/Loops/Divergence_Array.H"
0006 #include "METOOLS/Loops/Master_Integrals.H"
0007
0008 namespace METOOLS {
0009
0010   /*! Convention on input:
0011       - \f$ p_i^2 \f$ labels the squared outer momenta
0012       - \f$ m_i^2 \f$ labels the masses of the internal lines
0013       - \f$ s_{ij}=(p_i + p_j)^2 \f$
0014       - \f$ \mu^2 \f$ labels the renormalisation scale
0015       Convention on output:
0016       - array with the following entries
0017         [0] - \f$ \sim \frac{1}{\epsilon_{UV}} \f$
0018         [1] - \f$ \sim \frac{1}{\epsilon_{IR}} \f$
0019         [2] - \f$ \sim \frac{1}{\epsilon_{IR}^2} \f$
0020         [3] - \f$ \sim 1 \f$
0021         [4] - \f$ \sim \epsilon \f$
0022         [5] - \f$ \sim \epsilon^2 \f$
0023       All terms \f$ \sim \epsilon \f$ are currently not calculated.
0024       This is suitable for 1-loop integrals, but nothing beyond.
0025    */
0026   /*! This file declares the scalar parts of higher order tensor
0027       integrals in the Passarino-Veltman reduction scheme.
0028    */
0029
0030
0031   //! A_munu = g_munu A_2
0032   //!   A_2(m2;mu2)
0033   DivArrC
0034   PV_Tadpole_2(const Complex&,
0035                double);
0036
0037
0038   //! B_mu = p_mu B_1
0039   //!   B_1(s12;m02,m12;mu2)
0040   DivArrC
0041   PV_Bubble_1(const double&,
0042               const Complex&, const Complex&,
0043               double);
0044   //! B_munu = p_mu p_nu B_21 + g_munu B_22
0045   //!   B_21(s12;m02,m12;mu2)
0046   DivArrC
0047   PV_Bubble_21(const double&,
0048                const Complex&, const Complex&,
0049                double);
0050   //!   B_22(s12;m02,m12;mu2)
0051   DivArrC
0052   PV_Bubble_22(const double&,
0053                const Complex&, const Complex&,
0054                double);
0055   //! B_munurho = p_mu p_nu p_rho B_31 + {g,p}_munurho B_32
0056   //!   B_31(s12;m02,m12;mu2)
0057   DivArrC
0058   PV_Bubble_31(const double&,
0059                const Complex&, const Complex&,
0060                double);
0061   //!   B_32(s12;m02,m12;mu2)
0062   DivArrC
0063   PV_Bubble_32(const double&,
0064                const Complex&, const Complex&,
0065                double);
0066
0067
0068   //! C_mu = p_mu C_10
0069   //!   C_10(p2,p2,0;m02,m12,m22;mu2)
0070   DivArrC
0071   PV_Triangle_10(const double&,  const double&,  const double&,
0072                  const Complex&, const Complex&, const Complex&,
0073                  double);
0074   //! C_mu = p_1,mu C_11 + p_2,nu C_12
0075   //!   C_11(p12,p22,s12;m02,m12,m22;mu2)
0076   DivArrC
0077   PV_Triangle_11(const double&,  const double&,  const double&,
0078                  const Complex&, const Complex&, const Complex&,
0079                  double);
0080   //!   C_12(p12,p22,s12;m02,m12,m22;mu2)
0081   DivArrC
0082   PV_Triangle_12(const double&,  const double&,  const double&,
0083                  const Complex&, const Complex&, const Complex&,
0084                  double);
0085   //! C_munu = p_mu p_nu C_20 + g_munu C_24
0086   //!   C_20(p12,p22,s12;m02,m12,m22;mu2)
0087   DivArrC
0088   PV_Triangle_20(const double&,  const double&,  const double&,
0089                  const Complex&, const Complex&, const Complex&,
0090                  double);
0091   //! C_munu = p_1,mu p_1.nu C_21 + p_2,mu p_2.nu C_22
0092   //!          + {p_1,p_2}_munu C_23 + g_munu C_24
0093   //!   C_21(p12,p22,s12;m02,m12,m22;mu2)
0094   DivArrC
0095   PV_Triangle_21(const double&,  const double&,  const double&,
0096                  const Complex&, const Complex&, const Complex&,
0097                  double);
0098   //!   C_22(p12,p22,s12;m02,m12,m22;mu2)
0099   DivArrC
0100   PV_Triangle_22(const double&,  const double&,  const double&,
0101                  const Complex&, const Complex&, const Complex&,
0102                  double);
0103   //!   C_23(p12,p22,s12;m02,m12,m22;mu2)
0104   DivArrC
0105   PV_Triangle_23(const double&,  const double&,  const double&,
0106                  const Complex&, const Complex&, const Complex&,
0107                  double);
0108   //!   C_24(p12,p22,s12;m02,m12,m22;mu2)
0109   DivArrC
0110   PV_Triangle_24(const double&,  const double&,  const double&,
0111                  const Complex&, const Complex&, const Complex&,
0112                  double);
0113   //! C_munurho = p_mu p_nu p_rho C_30 + {g,p}_munurho C_38
0114   //!   C_30(p12,p22,s12;m02,m12,m22;mu2)
0115   DivArrC
0116   PV_Triangle_30(const double&,  const double&,  const double&,
0117                  const Complex&, const Complex&, const Complex&,
0118                  double);
0119   //!   C_38(p12,p22,s12;m02,m12,m22;mu2)
0120   DivArrC
0121   PV_Triangle_38(const double&,  const double&,  const double&,
0122                  const Complex&, const Complex&, const Complex&,
0123                  double);
0124   //! C_munu = p_1,mu p_1,nu p_1,rho C_31 + {p_1,p_1,p_2}_munurho C_32
0125   //!           + {p_1,p_2,p_2}_munurho C_33 + p_2,mu p_2.nu p_1,rho C_34
0126   //!           + {g,p_1}_munurho C_35 + {g,p_2}_munurho C_36
0127   //!   C_31(p12,p22,s12;m02,m12,m22;mu2)
0128   DivArrC
0129   PV_Triangle_31(const double&,  const double&,  const double&,
0130                  const Complex&, const Complex&, const Complex&,
0131                  double);
0132   //!   C_32(p12,p22,s12;m02,m12,m22;mu2)
0133   DivArrC
0134   PV_Triangle_32(const double&,  const double&,  const double&,
0135                  const Complex&, const Complex&, const Complex&,
0136                  double);
0137   //!   C_33(p12,p22,s12;m02,m12,m22;mu2)
0138   DivArrC
0139   PV_Triangle_33(const double&,  const double&,  const double&,
0140                  const Complex&, const Complex&, const Complex&,
0141                  double);
0142   //!   C_34(p12,p22,s12;m02,m12,m22;mu2)
0143   DivArrC
0144   PV_Triangle_34(const double&,  const double&,  const double&,
0145                  const Complex&, const Complex&, const Complex&,
0146                  double);
0147   //!   C_35(p12,p22,s12;m02,m12,m22;mu2)
0148   DivArrC
0149   PV_Triangle_35(const double&,  const double&,  const double&,
0150                  const Complex&, const Complex&, const Complex&,
0151                  double);
0152   //!   C_36(p12,p22,s12;m02,m12,m22;mu2)
0153   DivArrC
0154   PV_Triangle_36(const double&,  const double&,  const double&,
0155                  const Complex&, const Complex&, const Complex&,
0156                  double);
0157
0158
0159 }
0160
0161 #endif