Programme

P.35 -- Poster, NCTP-43

Date: Tuesday, 31 July 2018

Time: 08:30 - 10:00

One-loop Feynman integrals with complex internal-masses, general space-time dimension and higher-power $\epsilon$-expansion

K. H. Phan and T. N. H. Pham

VNUHCM-University of Science, 227 Nguyen Van Cu St., Ward 4, District 5, Ho Chi Minh City, Vietnam

In this talk, we study systematically scalar one-loop two-, three-, and four-point Feynman integrals with the following aspects: (i) The first aspect is to regularize Landau singularities and solve Inverse Gram determinant appear in computing one-loop corrections to processes of interest at future colliders. We consider the calculation for one-loop integrals with complex internal masses in order to regularize Landau singularity. Furthermore, unlike the traditional approach proposed by G.~~'t Hooft and M. Veltman, the method used in our work can also extend to evaluate directly tensor one-loop integrals. Thus, this may open a new approach to solve the Inverse Gram determinant problem analytically. (ii) The second aspect is to obtain higher-power $\epsilon$-expansion terms for one-loop integrals. This plays a important role as building blocks in general higher-loop or multi-leg processes. We develop a new method for evaluating one-loop integrals. The results are presented in terms of generalized hypergeometric series such as Gauss, Appell $F_1$ functions, etc. We also perform the numerical checks for the analytical expressions in this work by comparing with LoopTools and AMBRE/MB. We find that the numerical results from this work are in good agreement with LoopTools at $\epsilon^0$-terms and AMBRE/MB at higher-order of $\epsilon$-expansions, at higher d-dimension. Additionally, this work is applied for evaluating scalar one-loop Feynman integrals developed leading Landau singularities which may appear in real scattering processes at future colliders.

Presenter: Phan Hong Khiem