Abstract Four 3-loop two-point functions are studied analytically and numerically using a simplified sector decomposition method. The coefficients of the ultraviolet divergent part are determined analytically, and those of the finite part are computed numerically. The energy dependence of the integrals is shown explicitly, and a discussion of its behavior is presented.

United States

Elise de Doncker

Japan

Tadashi Ishikawa

Kiyoshi Kato

Fukuko Yuasa

Analytic and Numerical Approaches for Depictive 3-Loop Integrals Using Sector Decomposition

Numerical calculation of two-loop electroweak corrections to the muon anomalous magnetic moment (<math><mi>g</mi><mo>−</mo><mn>2</mn></math>) is done based on on shell renormalization scheme (OS) and free quark model (FQM). The GRACE-FORM system is used to generate Feynman diagrams and corresponding amplitudes. Total 1780 two-loop diagrams and 70 one-loop diagrams composed of counterterms are calculated to get the renormalized quantity. As for the numerical calculation, we adopt the trapezoidal rule with double exponential method (DE). Linear extrapolation method (LE) is introduced to regularize UV- and IR-divergences and to get finite values. The reliability of our result is guaranteed by several conditions. The sum of one and two loop electroweak corrections in this renormalization scheme becomes <math><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>EW</mi><mo>:</mo><mi>OS</mi></mrow></msubsup><mo>[</mo><mn>1</mn><mo>+</mo><mn>2</mn><mtext>−</mtext><mi>loop</mi><mo>]</mo><mo>=</mo><mn>151.2</mn><mo>(</mo><mo>±</mo><mn>1.0</mn><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>11</mn></mrow></msup></mrow></math>, where the error is due to the numerical integration and the uncertainty of input mass parameters and of the hadronic corrections to electroweak loops. By taking the hadronic corrections into account, we get <math><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>EW</mi></mrow></msubsup><mo>[</mo><mn>1</mn><mo>+</mo><mn>2</mn><mtext>−</mtext><mrow><mi>loop</mi></mrow><mo>]</mo><mo>=</mo><mn>152.9</mn><mo>(</mo><mo>±</mo><mn>1.0</mn><mo>)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>11</mn></mrow></msup></mrow></math>. It is in agreement with the previous works given in PDG [Phys. Rev. D 98, 030001 (2018)] within errors.

Nobuya Nakazawa

Yoshiaki Yasui

Numerical calculation of the full two-loop electroweak corrections to muon (<math><mi>g</mi><mo>−</mo><mn>2</mn></math>)

Abstract The one-loop effects of the Minimal Supersymmetric Standard Model (MSSM) at the International Linear Collider (ILC) are investigated through numerical analysis, studying the Higgs production processes  and  at the ILC. It is found that the magnitude of the MSSM contribution through the one-loop effects is sizable enough to be detected. In the study, three sets of MSSM parameters are proposed that are consistent with the observed Higgs mass, the muon -, the dark matter abundance, and the decay branching ratios of  mesons. In the  process, the one-loop effects of the MSSM are visible and distinction of the parameter sets is partially possible. For the study of , we used the equivalent -boson approximation in the evaluation of the one-loop cross section. While the one-loop effect of the MSSM is visible, distinction of the parameter sets might not be possible in this process under a realistic luminosity value at the ILC.

Yusaku Kouda

Tadashi Kon

Yoshimasa Kurihara

Masato Jimbo

Masaaki Kuroda

One-loop effects of Minimal Supersymmetric Standard Model particles in And at the International Linear Collider

Within the framework of the minimal supersymmetric (SUSY) standard model, we investigate the one-loop effects of supersymmetric particles on third-generation fermion-pair production at the International Linear Collider. Three sets of SUSY parameters are proposed that are consistent with the observed Higgs mass, the muon - , the dark matter abundance, and the decay branching ratios of the B meson. We discuss the possibility of discovering signals consistent with SUSY, as well as of experimentally distinguishing the proposed sets of SUSY parameters.

One loop effects of natural SUSY in third generation fermion production at the ILC