Analytic Tadpole Coefficients of One-loop Integrals

Abstract

One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In this paper, we reconsider the problem by applying differential operators over an auxiliary vector $R$. Using differential operators, we establish the corresponding differential equations for tadpole coefficients at the first step. Then using the tensor structure of tadpole coefficients, we transform the differential equations to the recurrence relations for undetermined tensor coefficients. These recurrence relations can be solved easily by iteration, and we can obtain analytic expressions of tadpole coefficients for arbitrary one-loop integrals.

37 pages, 2 figures

References in corpus (13)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• Reduction schemes for one-loop tensor integrals
• Unifying Relations for Scattering Amplitudes
• Unitarity Cuts with Massive Propagators and Algebraic Expressions for Coefficients
• Integral Coefficients for One-Loop Amplitudes
• Closed-Form Decomposition of One-Loop Massive Amplitudes
• Single Cut Integration
• Solving for tadpole coefficients in one-loop amplitudes
• Expansion of Einstein-Yang-Mills theory by Differential Operators
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space

Cited by in corpus (10)

• Generation Function For One-loop Tensor Reduction
• One-loop Feynman Integral Reduction by Differential Operators
• PV-Reduction of Sunset Topology with Auxiliary Vector
• Reduction of General One-loop Integrals Using Auxiliary Vector
• Reduction with Degenerate Gram matrix for One-loop Integrals
• Module Intersection and Uniform Formula for Iterative Reduction of One-loop Integrals
• Universal Treatment of Reduction for One-Loop Integrals in Projective Space
• Nontrivial One-loop Recursive Reduction Relation
• Tensor Reduction for Feynman Integrals with Lorentz and Spinor Indices
• Integrands of Less-Supersymmetric Yang-Mills at One Loop