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

Abstract

A new estimate of the one loop contributions of the standard model to the chromomagnetic dipole moment (CMDM) μq of quarks is presented with the aim to address a few disagreements arising in previous calculations. We consider the most general case with non-zero gluon transfer momentum q 2 and obtain analytical results 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 the QCD contribution from a three-gluon Feynman diagram diverges at q 2 = 0, which agrees with a previous evaluation and stems from the fact that the static CMDM [μ(0)] has no sense in perturbative QCD. For the numerical analysis we consider the region 30 GeV< q < 1000 GeV and analyze the behavior of μq (q 2 ) for all the SM 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 μt (q 2 ) are of the order of 10 −2 − 10 −3 , with the largest contribution arising from the QCD induced diagrams, though around the threshold q 2 = 4m 2 t there are also important contributions from diagrams with Z gauge boson and Higgs boson exchange.

The top quark chromomagnetic dipole moment in the SM from the four-body vertex

“…Regarding to the top quark CMDM, the experimental CMS Collaboration reported that μExp t = −0.024 +0.013 −0.009 (stat) +0.016 −0.011 (syst) [6], at 95% C. L., using proton-proton collisions at the centre-of-mass energy of 13 TeV with an integrated luminosity of 35.9 fb −1 . Within the SM context, the CMDM has been exhaustively studied from the three-body g tt coupling [1][2][3][4], at the one-loop level, where the most promising prediction establishes that Re μt (−m 2 Z ) = −0.0224 [2,3], which supports the solidity of the model. This last result was computed in the spacelike domain (s = −m 2 Z ), just as α s (m 2 Z ) is conventionally evaluated for high-energy physics [7][8][9][10][11], where the energy scale is fixed at the mass of the Z boson.…”

“…In the Standard Model (SM), the anomalous chromomagnetic dipole moment (CMDM) is induced at the oneloop level and receives contributions from quantum chromodynamics (QCD), electroweak (EW) and Yukawa (YK) sectors [1][2][3][4]. Moreover, it has already been established in the literature that the non-static CMDM (μ t (q 2 )) is consistent with the properties of an observable, since this one is gauge invariant, gauge independent, infrared (IR) finite and ultraviolet (UV) finite [3,4].…”

“…In the Standard Model (SM), the anomalous chromomagnetic dipole moment (CMDM) is induced at the oneloop level and receives contributions from quantum chromodynamics (QCD), electroweak (EW) and Yukawa (YK) sectors [1][2][3][4]. Moreover, it has already been established in the literature that the non-static CMDM (μ t (q 2 )) is consistent with the properties of an observable, since this one is gauge invariant, gauge independent, infrared (IR) finite and ultraviolet (UV) finite [3,4]. On the other hand, from the effective Lagrangian approach it is straightforward to appreciate that μq and the chromoelectric dipole moment (CEDM) dq are proportional to both the Abelian threebody g qq and to the non-Abelian four-body gg qq couplings [5].…”

A new evaluation of the $HZZ$ coupling: direct bounds on anomalous contributions and $CP$ violating effects via a new assymetry

“…Off-shell couplings have been of great interest in recent years [35][36][37] as they can develop an imaginary (absorptive) part due to the optical theorem, thereby giving rise to some effects on physical processes. Such a property has been studied for instance in the off-shell chromomagnetic and chromoeletric dipole moments of quarks [38,39], where the gluon is off-shell, and also in the trilinear neutral gauge boson couplings [40,41], which are non-vanishing when at least one of the three gauge bosons is off-shell [42,43]. Also, the phenomenological implications of the absorptive part of the off-shell Higgs boson couplings have been brought to attention by many authors [18,20,22,28], nonetheless, to our knowledge, a precise determination of the SM contribution has not been reported yet, which may stem from the fact that there has been some controversy on whether or not off-shell couplings represent valid observable quantities.…”

Chromomagnetic dipole moment of the top quark in the Bestest Little Higgs model

“…From the theoretical point of view, it is known that the CMDM of the SM quarks cannot be well defined in a static scenario, that is to say, when q 2 = 0; it can only be established an off-shell CMDM, which is consistent with an observable given that it is gauge invariant, gauge independent, infrared finite and ultraviolet finite [11,12,26,27]. Thus, we will present the evaluation of this observable considering an off-shell gluon (q 2 = 0) at large-momentum transfer.…”