New estimate of the chromomagnetic dipole moment of quarks in the standard model

A. I. Hernández-Juárez; A. Moyotl; G. Tavares-Velasco

doi:10.1140/epjp/s13360-021-01239-9

2024 Impact factor 2.9

EPJ PLUS - Condensed Matter and Complex Systems

Eur. Phys. J. Plus (2021) 136: 262
https://doi.org/10.1140/epjp/s13360-021-01239-9

Regular Article

New estimate of the chromomagnetic dipole moment of quarks in the standard model

A. I. Hernández-Juárez¹^a, A. Moyotl² and G. Tavares-Velasco¹

¹ Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, C.P. 72570, Puebla, Puebla, Mexico
² Ingeniería en Mecatrónica, Universidad Politécnica de Puebla, Tercer Carril del Ejido Serrano s/n, San Mateo Cuanalá, Juan C. Bonilla, Puebla, Puebla, Mexico

^a alaban7_3@hotmail.com

Received: 24 September 2020
Accepted: 16 February 2021
Published online: 26 February 2021

Abstract

A new estimate of the one loop contributions of the standard model to the chromomagnetic dipole moment (CMDM) ${\hat{μ}}_{q} (q^{2})$ $\hat{\mu }_q(q^2)$ of quarks is presented with the aim to address a few disagreements arising in previous calculations. The most general case with arbitrary $q^{2}$ $$q^2$$ is considered and analytical results are obtained in terms of Feynman parameter integrals and Passarino-Veltman scalar functions, which are then expressed in terms of closed form functions when possible. It is found that while the QCD contribution to the static CMDM ( $q^{2} = 0$ $$q^2=0$$ ) is infrared divergent, which agrees with previous evaluations and stems from the fact that this quantity has no sense in perturbative QCD, the off-shell CMDM ( $q^{2} \neq 0$ $q^2\ne 0$ ) is finite and gauge independent, which is verified by performing the calculation for arbitrary gauge parameter $ξ$ $\xi$ via both a renormalizable linear $R_{ξ}$ $R_\xi$ gauge and the background field method. It is thus argued that the off-shell ${\hat{μ}}_{q} (q^{2})$ $\hat{\mu }_q(q^2)$ can represent a valid observable quantity. For the numerical analysis we consider the region 30 GeV $< ‖ q ‖ <$ $<\Vert q\Vert<$ 1000 GeV and analyze the behavior of ${\hat{μ}}_{q} (q^{2})$ $\hat{\mu }_q(q^2)$ for all the standard model quarks. It is found that the CMDM of light quarks is considerably smaller than that of the top quark as it is directly proportional to the quark mass. In the considered energy interval, both the real and imaginary parts of ${\hat{μ}}_{t} (q^{2})$ $\hat{\mu }_t(q^2)$ are of the order of $10^{- 2} - 10^{- 3}$ $10^{-2}-10^{-3}$ , with the largest contribution arising from the QCD induced diagrams, though around the threshold $q^{2} = 4 m_{t}^{2}$ $$q^2=4m_t^2$$ there are also important contributions from diagrams with Z gauge boson and Higgs boson exchange.