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Register a new userConsistent higher order $sigma(mathcal{G} ,mathcal{G}rightarrow h)$, $Gamma(h rightarrow mathcal{G} ,mathcal{G})$ and $Gamma(h rightarrow gamma gamma)$ in geoSMEFT
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We report consistent results for $Gamma(h rightarrow gamma gamma)$, $sigma(mathcal{G} ,mathcal{G}rightarrow h)$ and $Gamma(h rightarrow mathcal{G} ,mathcal{G})$ in the Standard Model Effective Field Theory (SMEFT) perturbing the SM by corrections $mathcal{O}(bar{v}_T^2/16 pi^2 Lambda^2)$ in the Background Field Method (BFM) approach to gauge fixing, and to $mathcal{O}(bar{v}_T^4/Lambda^4)$ using the geometric formulation of the SMEFT. We combine and modify recent results in the literature into a complete set of consistent results, uniforming conventions, and simultaneously complete the one loop results for these processes in the BFM. We emphasise calculational scheme dependence present across these processes, and how the operator and loop expansions are not independent beyond leading order. We illustrate several cross checks of consistency in the results.
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A large set of techniques needed to compute decay rates at the two-loop level are derived and systematized. The main emphasis of the paper is on the two Standard Model decays H -> gamma gamma and H -> g g. The techniques, however, have a much wider range of application: they give practical examples of general rules for two-loop renormalization; they introduce simple recipes for handling internal unstable particles in two-loop processes; they illustrate simple procedures for the extraction of collinear logarithms from the amplitude. The latter is particularly relevant to show cancellations, e.g. cancellation of collinear divergencies. Furthermore, the paper deals with the proper treatment of non-enhanced two-loop QCD and electroweak contributions to different physical (pseudo-)observables, showing how they can be transformed in a way that allows for a stable numerical integration. Numerical results for the two-loop percentage corrections to H -> gamma gamma, g g are presented and discussed. When applied to the process pp -> gg + X -> H + X, the results show that the electroweak scaling factor for the cross section is between -4 % and + 6 % in the range 100 GeV < Mh < 500 GeV, without incongruent large effects around the physical electroweak thresholds, thereby showing that only a complete implementation of the computational scheme keeps two-loop corrections under control.
We compute the two-loop massless QCD corrections to the four-point amplitude $g+g rightarrow H+H$ resulting from effective operator insertions that describe the interaction of a Higgs boson with gluons in the infinite top quark mass limit. This amplitude is an essential ingredient to the third-order QCD corrections to Higgs boson pair production. We have implemented our results in a numerical code that can be used for further phenomenological studies.
Inspired by the recent work Sahin and Agha gave recursion formulas for $mathcal{G}_{1}$ and $mathcal{G}_{2}$ Horn hypergeometric functions cite{saa}. The object of work is to establish several new recursion relations, relevant differential recursion formulas, new integral operators, infinite summations and interesting results for Horns hypergeometric functions $mathcal{G}_{1}$, $mathcal{G}_{2}$ and $mathcal{G}_{3}$.
We study the loop-induced decays $h^0 to gamma , gamma$ and $h^0 to g , g$ in the Minimal Supersymmetric Standard Model (MSSM) with quark flavour violation (QFV), identifying $h^0$ with the Higgs boson with a mass of 125 GeV, where $gamma$ and $g$ are photon and gluon, respectively. We perform a MSSM parameter scan and a detailed analysis around a fixed reference point respecting theoretical constraints from vacuum stability conditions and experimental constraints, such as those from B meson data and electroweak precision data, as well as recent limits on supersymmetric (SUSY) particle masses from LHC experiments. We find that (i) the relative deviation of the decay width $Gamma(h^0 to g , g)$ from the Standard Model value, $DEV(g)$, can be large and negative, $lesssim - 15%$, (ii) the analogous deviation of $Gamma(h^0 to gamma , gamma)$ is strongly correlated, $DEV(gamma) simeq -1/4,DEV(g)$ for $DEV(g) lesssim - 4%$, (iii) the relative deviation of the width ratio $Gamma(h^0 to gamma , gamma)/Gamma(h^0 to g , g)$ from the SM value, $DEV(gamma/g)$, can be large (up to $sim$ 20%), (iv) the deviations can be large due to the up-type squark loop contributions, (v) the SUSY QFV parameters can have a significant effect on these deviations. Such large deviations can be observed at a future $e^+e^-$ collider like ILC. Observation of the deviation patterns as shown in this study would favour the MSSM with flavour-violating squark mixings and encourage to perform further studies in this model.
We show some of the conjectures of Pappas and Rapoport concerning the moduli stack of $mathcal{G}$-torsors on a curve C, where $mathcal{G}$ is a semisimple Bruhat-Tits group scheme on C. In particular we prove the analog of the uniformization theorem of Drinfeld-Simpson in this setting. Furthermore we apply this to compute the connected components of these moduli stacks and to calculate the Picard group of the stack of torsors in case $mathcal{G}$ is simply connected.
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