The classification of two-loop integrand basis in pure four-dimension

TY - JOUR

T1 - The classification of two-loop integrand basis in pure four-dimension

AU - Feng, Bo

AU - Huang, Rijun

PY - 2013/2/1

Y1 - 2013/2/1

N2 - In this paper, we have made the attempt to classify the integrand basis of all two-loop diagrams in pure four-dimensional space-time. The first step of our classification is to determine all different topologies of two-loop diagrams, i.e., the structure of denominators. The second step is to determine the set of independent numerators for each topology using Gröbner basis method. For the second step, varieties defined by putting all propagators on-shell has played an important role. We discuss the structures of varieties and how they split to various irreducible branches under specific kinematic configurations of external momenta. The structures of varieties are crucial to determine coefficients of integrand basis in reduction both numerically or analytically.

AB - In this paper, we have made the attempt to classify the integrand basis of all two-loop diagrams in pure four-dimensional space-time. The first step of our classification is to determine all different topologies of two-loop diagrams, i.e., the structure of denominators. The second step is to determine the set of independent numerators for each topology using Gröbner basis method. For the second step, varieties defined by putting all propagators on-shell has played an important role. We discuss the structures of varieties and how they split to various irreducible branches under specific kinematic configurations of external momenta. The structures of varieties are crucial to determine coefficients of integrand basis in reduction both numerically or analytically.

U2 - 10.1007/jhep02(2013)117

DO - 10.1007/jhep02(2013)117

M3 - Journal article

SN - 1126-6708

VL - 2013

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

IS - 2

M1 - 117

ER -