A development of an accelerator board dedicated for multi-precision arithmetic operations and its application to Feynman loop integrals

S Motoki,N Nakasato,A Kawai,T Fukushige,T Ishikawa,F Yuasa,J Makino,H Daisaka

doi:10.1088/1742-6596/608/1/012011

Abstract

Higher order corrections in perturbative quantum field theory are required for precise theoretical analysis to investigate new physics beyond the Standard Model. This indicates that we need to evaluate Feynman loop diagrams with multi-loop integrals which may require multi-precision calculation. We developed a dedicated accelerator system for multiprecision calculations (GRAPE9-MPX). We present performance results of our system for the case of Feynman two-loop box and three-loop selfenergy diagrams with multi-precision.

Highlights

With the discovery of Higgs particle at the CERN Large Hadron Collider, precision measurements are expected at a future International Linear Collider to explore new physics beyond the Standard Model
The numerical results in quadruple precision obtained by GRAPE9-MPX in the maximum problem size are I2loop = 0.008536 and I3loop = 0.279609, which are within the relative errors of 10−3 for the two-loop crossed box and 10−5 for the three-loop selfenergy compared to the previous works [12, 13]
Summary We have developed GRAPE9-MPX system, an accelerator system for multi-precision arithmetic operations which can accelerate the calculation of Feynman loop integrals

Summary

Introduction

With the discovery of Higgs particle at the CERN Large Hadron Collider, precision measurements are expected at a future International Linear Collider to explore new physics beyond the Standard Model. This indicates that we can accelerate the calculation of Feynman loop integrals effectively by using GRAPE9-MPX. 3. Feynman loop integrals Figure 3 shows the two-loop crossed box diagram and the three-loop selfenergy diagram used for the performance measurement.

Results

Conclusion