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Register a new userThe Infrared Structure of QCD Amplitudes and $Hto g g$ in FDH and DRED
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We consider variants of dimensional regularization, including the four-dimensional helicity scheme (FDH) and dimensional reduction (DRED), and present the gluon and quark form factors in the FDH scheme at next-to-next-to-leading order. We also discuss the generalization of the infrared factorization formula to FDH and DRED. This allows us to extract the cusp anomalous dimension as well as the quark and gluon anomalous dimensions at next-to-next-to-leading order in the FDH and DRED scheme, using $overline{text{MS}}$ and $overline{text{DR}}$ renormalization. To obtain these results we also present the renormalization procedure in these schemes.
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The $Hto gg$ amplitude relevant for Higgs production via gluon fusion is computed in the four-dimensional helicity scheme (FDH) and in dimensional reduction (DRED) at the two-loop level. The required renormalization is developed and described in detail, including the treatment of evanescent $epsilon$-scalar contributions. In FDH and DRED there are additional dimension-5 operators generating the $H g g$ vertices, where $g$ can either be a gluon or an $epsilon$-scalar. An appropriate operator basis is given and the operator mixing through renormalization is described. The results of the present paper provide building blocks for further computations, and they allow to complete the study of the infrared divergence structure of two-loop amplitudes in FDH and DRED.
Using a careful choice of infrared (IR) subtraction scheme, we demonstrate the cancellation of all terms with transcendental weights 0,1,2 from the finite part of the full-color two-loop four-gluon $mathcal{N}=2$ supersymmetric QCD amplitude, with $N_f$ massless supersymmetric quarks. This generalizes the previously observed cancellation of weight-2 terms in the superconformal theory, where $N_f=2N_c$ for gauge group SU$(N_c)$. The subtraction scheme follows naturally both from general IR factorization principles and from an integrand-level analysis of divergences in this amplitude. The divergences are written in terms of scalar triangle integrals whose expressions are known to all orders in the dimensional regulator $epsilon=(4-D)/2$. We also present integrated expressions for the full-color two-loop four-point amplitudes with both matter and vectors on external legs in which lower-weight terms also cancel using an appropriate IR scheme. This provides us with values for the two-loop cusp, gluonic, and quark anomalous dimensions in $mathcal{N}=2$ supersymmetric QCD, which are cross-checked between the three different amplitudes.
The mixing of new vectorlike leptons with leptons in the standard model can generate flavor violating couplings of $h$, $W$ and $Z$ between heavy and light leptons. Focusing on the couplings of the muon, the partial decay width of $hto e_4^pm mu^mp$, where $e_4$ is the new lepton, can be significant when this process is kinematically allowed. Subsequent decays $e_4^pm to Zmu^pm$ and $e_4^pm to W^pm u$ lead to the same final states as $h to ZZ^* to Z mu^+mu^-$ and $h to WW^* to W mu u$, thus possibly affecting measurements of these processes. We calculate $hto e_4 ell_i to Zell_iell_j$, where $ell_{i,j}$ are standard model leptons, including the possibility of off-shell decays, interference with $hto ZZ^* to Z ell_i ell_i$, and the mass effect of $ell_{i,j}$ which are important when the mass of $e_4$ is close to the mass of the Higgs boson. We derive constraints on masses and couplings of the heavy lepton from the measurement of $hto 4ell$. We focus on the couplings of the muon and discuss possible effects on $hto ZZ^*$ from the region of parameters that can explain the anomaly in the measurement of the muon g-2.
With the long-standing tension between experiment and Standard-Model (SM) prediction in the anomalous magnetic moment of the muon $a_mu$ recently reaffirmed by the Fermilab experiment, the crucial question becomes which other observables could be sensitive to the underlying physics beyond the SM to which $a_mu$ may be pointing. While from the effective field theory (EFT) point of view no direct correlations exist, this changes in specific new physics models. In particular, in the case of explanations involving heavy new particles above the electroweak (EW) scale with chiral enhancement, which are preferred to evade exclusion limits from direct searches, correlations with other observables sensitive to EW symmetry breaking are expected. Such scenarios can be classified according to the $SU(2)_L$ representations and the hypercharges of the new particles. We match the resulting class of models with heavy new scalars and fermions onto SMEFT and study the resulting correlations with $htomumu$ and $Ztomumu$ decays, where, via $SU(2)_L$ symmetry, the latter process is related to $Zto u u$ and modified $W$-$mu$-$ u$ couplings.
We measure the hadronic contribution to the vacuum polarisation tensor, and use it to estimate the hadronic contribution to (g-2)_mu, the muon anomalous magnetic moment.
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