******************************************************************************************************
* Two-Loop helicity amplitudes for H+jet production to higher orders in the dimensional regulator    *
* Thomas Gehrmann, Petr Jakubčík, Cesare Carlo Mella, Nikolaos Syrrakos, Lorenzo Tancredi            *
******************************************************************************************************

In the tree of this folder are all the ancillary files to the article. They include:
- canonical bases definitions;
- solutions for the master integrals;
- all amplitudes as described in the main text.

The files are in Mathematica-readable format. 


****** Master integrals
The integral measure is defined as in eq. (4.1).

The auxiliary topology of the 1L integrals is
{k1^2, (k1 - p1)^2, (k1 - p1 - p2)^2, (k1 - p1 - p2 - p3)^2}
The 2L auxiliary topologies are defined in Table 1.

 1) The subdirectory 1L includes the definition of the canonical basis as described 
 in Appendix B, and the solutions for the integrals I[1],..., I[4] expanded in 
 epsilon up to weight 6.

 2) The subdirectory 2L includes the definition of the canonical basis for the family PL
 denoted INT["PL"][1], ..., INT["PL"][18], and for the family NPL denoted 
 INT["NPL"][1], ..., INT["NPL"][36] as described in Section 4. This subdirectory also
 contains the combined canonical basis denoted INT["COMBINED"][1], ..., INT["COMBINED"][89]
 necessary for the reduction of all integrals in the amplitude. We give the solutions for
 the integrals in the combined basis up to weight 6.



****** Amplitudes

  Amplitude are decomposed in color layers according to section 5.4 from the article:
  One-Loop has color layers --- A1, B1, C1
  Two-Loop has color layers --- A2, B2, C2, D2, E2, F2
  
  Each file contains one single amplitude written as a set of substitution rules:
  {{A1 -> (...), B1 -> (...), C1 -> (...)}, {A2 -> (...), ..., F2 -> (...)}}
   
   
- Kinematics as in the article:

  y = s13/M_H^2, z = s23/M_H^2

  
  For production solutions, definition for (u,v) is

  y = 1/v    z = -u/v



1) RenormalizedCoefficients contains renormalized helicity amplitudes 
   for the decay processes to higher order in epsilon
   
   - Folder Hggg:
     alpha_renormalized.m		H -> g_+(p1) g_+(p2) g_+(p3)
     beta_renormalized.m		H -> g_+(p1) g_+(p2) g_-(p3)
     
   - Folder Hqqbg:
     gamma1a_renormalized.m	H -> q_L(p1) qb_R(p2) g_+(p3)
   


2) FiniteRemainder contains the finite remainders in the SCET subtraction
   scheme for the decay and production processes
   
   - Folder Hggg:
     alpha.m				H -> g_+(p1) g_+(p2) g_+(p3)
     beta.m				H -> g_+(p1) g_+(p2) g_-(p3)
     ggHg_HA1.m				g_-(p1) g_-(p3) -> H g_+(p2)
     ggHg_HA2.m				g_-(p1) g_+(p3) -> H g_+(p2)
     ggHg_HA2.m				g_-(p1) g_-(p3) -> H g_-(p2)
     
   - Folder Hqqbg:
     gamma.m				H -> q_L(p1) qb_R(p2) g_+(p3)
     qgHq.m				q_R(p1) + g_-(p3) -> H + q_R(p2)
     qbgHqb.m				qb_L(p1) + g_-(p3) -> H + qb_L(p2)
     qqbHg.m				q_R(p1) + qb_L(p3) -> H + g_+(p2)