Estimation of uncertainties from missing higher orders in perturbative calculations

In this proceeding we present the results of our recent study (hep-ph/1409.5036) of the statistical performances of two different approaches, Scale Variation (SV) and the Bayesian model of Cacciari and Houdeau (CH)(hep-ph/1105.5152) (which we also extend to observables with initial state hadrons), to the estimation of Missing Higher-Order Uncertainties (MHOUs)(hep-ph/1307.1843) in perturbation theory. The behavior of the models is determined by analyzing, on a wide set of observables, how the MHOU intervals they produce are successful in predicting the next orders. We observe that the Bayesian model behaves consistently, producing intervals at $68\%$ Degree of Belief (DoB) comparable with the scale variation intervals with a rescaling factor $r$ larger than $2$ and closer to $4$. Concerning SV, our analysis allows the derivation of a heuristic Confidence Level (CL) for the intervals. We find that assigning a CL of $68\%$ to the intervals obtained with the conventional choice of varying the scales within a factor of two with respect to the central scale could potentially lead to an underestimation of the uncertainties in the case of observables with initial state hadrons.Comment: 4 pages, 4 figures, contribution to the proceedings of the 50th Rencontres de Moriond, QCD session, March 21-28, 2015, La Thuile, Italy. Version 2: added missing reference to hep-ph/1307.184

The Higgs transverse momentum distribution in gluon fusion as a multiscale problem

We consider Higgs production in gluon fusion and in particular the prediction of the Higgs transverse momentum distribution. We discuss the ambiguities affecting the matching procedure between fixed order matrix elements and the resummation to all orders of the terms enhanced by $\log(p_T^H/m_H)$ factors. Following a recent proposal (Grazzini et al., hep-ph/1306.4581), we argue that the gluon fusion process, computed considering two active quark flavors, is a multiscale problem from the point of view of the resummation of the collinear singular terms. We perform an analysis at parton level of the collinear behavior of the $\mathcal{O}(\alpha_s)$ real emission amplitudes; relying on the collinear singularities structure of the latter, we derive an upper limit to the range of transverse momenta where the collinear approximation is valid. This scale is then used as the value of the resummation scale in the analytic resummation framework or as the value of the $h$ parameter in the POWHEG-BOX code. A variation of this scale can be used to generate an uncertainty band associated to the matching procedure. Finally, we provide a phenomenological analysis in the Standard Model, in the Two Higgs Doublet Model and in the Minimal Supersymmetric Standard Model. In the two latter cases, we provide an ansatz for the central value of the matching parameters not only for a Standard Model-like Higgs boson, but also for heavy scalars and in scenarios where the bottom quark may play the dominant role.Comment: 33 pages, 13 figures; v2 matches version published in JHE

Improved determination of the Higgs mass in the MSSM with heavy superpartners

We present several advances in the effective field theory calculation of the Higgs mass in MSSM scenarios with heavy superparticles. In particular, we compute the dominant two-loop threshold corrections to the quartic Higgs coupling for generic values of the relevant SUSY-breaking parameters, including all contributions controlled by the strong gauge coupling and by the third-family Yukawa couplings. We also study the effects of a representative subset of dimension-six operators in the effective theory valid below the SUSY scale. Our results will allow for an improved determination of the Higgs mass and of the associated theoretical uncertainty.Comment: 33 pages, 7 PDF figure

An extensive survey of the estimation of uncertainties from missing higher orders in perturbative calculations

We consider two approaches to estimate and characterise the theoretical uncertainties stemming from the missing higher orders in perturbative calculations in Quantum Chromodynamics: the traditional one based on renormalisation and factorisation scale variation, and the Bayesian framework proposed by Cacciari and Houdeau. We estimate uncertainties with these two methods for a comprehensive set of more than thirty different observables computed in perturbative Quantum Chromodynamics, and we discuss their performance in properly estimating the size of the higher order terms that are known. We find that scale variation with the conventional choice of varying scales within a factor of two of a central scale gives uncertainty intervals that tend to be somewhat too small to be interpretable as 68% confidence-level-heuristic ones. We propose a modified version of the Bayesian approach of Cacciari and Houdeau which performs well for non-hadronic observables and, after an appropriate choice of the relevant expansion parameter for the perturbative series, for hadronic ones too.Comment: 34 pages, 24 figure

Higgs Mass and Unnatural Supersymmetry

Assuming that supersymmetry exists well above the weak scale, we derive the full one-loop matching conditions between the SM and the supersymmetric theory, allowing for the possibility of an intermediate Split-SUSY scale. We also compute two-loop QCD corrections to the matching condition of the Higgs quartic coupling. These results are used to improve the calculation of the Higgs mass in models with high-scale supersymmetry or split supersymmetry, reducing the theoretical uncertainty. We explore the phenomenology of a mini-split scenario with gaugino masses determined by anomaly mediation. Depending on the value of the higgsino mass, the theory predicts a variety of novel possibilities for the dark-matter particle.Comment: 36 pages, 13 pdf figures; v2: matches version published in JHE

Vacuum stability and supersymmetry at high scales with two Higgs doublets

We investigate the stability of the electroweak vacuum for two-Higgs doublet models with a supersymmetric UV completion. The supersymmetry breaking scale is taken to be of the order of the grand unification scale. We first study the case where all superpartners decouple at this scale. We show that contrary to the Standard Model with one Higgs doublet, matching to the supersymmetric UV completion is possible if the low-scale model contains two Higgs doublets. In this case vacuum stability and experimental constraints point towards low values of tan(beta) < 2 and pseudoscalar masses of at least about a TeV. If the higgsino superpartners of the Higgs fields are also kept light, the conclusions are similar and essentially independent of the higgsino mass. Finally, if all gauginos are also given electroweak-scale masses (split supersymmetry with two Higgs doublets), the model cannot be matched to supersymmetry at very high scales when requiring a 125 GeV Higgs. Light neutral and charged higgsinos therefore emerge as a promising signature of a supersymmetric UV completion of the Standard Model at the grand unification scale.Comment: 27 pages, 4 figures; v2: minor changes in references and text, results unchange

Higgs boson pair production at NLO in the POWHEG approach and the top quark mass uncertainties

We present a new Monte Carlo code for Higgs boson pair production at next-to-leading order in the POWHEG-BOX Monte Carlo approach. The code is based on analytic results for the two loop virtual corrections which include the full top quark mass dependence. This feature allows to freely assign the value of all input parameters, including the trilinear Higgs boson self coupling, as well as to vary the renormalization scheme employed for the top quark mass. We study the uncertainties due to the top-mass renormalization scheme allowing the trilinear Higgs boson self coupling to vary around its Standard Model value including parton shower effects. Results are presented for both inclusive and differential observables.Comment: 21 pages, 7 figure

The rise and fall of light stops in the LHC top quark sample

We discuss the possibility that light new physics in the top quark sample at the LHC can be found by investigating with greater care well known kinematic distributions, such as the invariant mass $m_{b\ell}$ of the $b$-jet and the charged lepton in fully leptonic $t\bar{t}$ events. We demonstrate that new physics can be probed in the rising part of the already measured $m_{b\ell}$ distribution. To this end we analyze a concrete supersymmetric scenario with light right-handed stop quark, chargino and neutralino. The corresponding spectra are characterized by small mass differences, which make them not yet excluded by current LHC searches and give rise to a specific end-point in the shape of the $m_{b\ell}$ distribution. We argue that this sharp feature is general for models of light new physics that have so far escaped the LHC searches and can offer a precious handle for the implementation of robust searches that exploit, rather than suffer from, soft bottom quarks and leptons. Recasting public data on searches for new physics, we identify candidate models that are not yet excluded. For these models we study the $m_{b\ell}$ distribution and derive the expected signal yields, finding that there is untapped potential for discovery of new physics using the $m_{b\ell}$ distribution.Comment: 3 figures, 7 page

Lepton-pair production in association with a bbˉb\bar{b} pair and the determination of the WW boson mass

We perform a study of lepton-pair production in association with bottom quarks at the LHC based on the predictions obtained at next-to-leading order in QCD, both at fixed order and matched with a QCD parton shower. We consider a comprehensive set of observables and estimate the associated theoretical uncertainties by studying the dependence on the perturbative QCD scales (renormalisation, factorisation and shower) and by comparing different parton-shower models (Pythia8 and Herwig++) and matching schemes (MadGraph5_aMC@NLO and POWHEG). Based on these results, we propose a simple procedure to include bottom-quark effects in neutral-current Drell-Yan production, going beyond the standard massless approximation. Focusing on the inclusive lepton-pair transverse-momentum distribution $p_{\bot}^{l^+l^-}$, we quantify the impact of such effects on the tuning of the simulation of charged-current Drell-Yan observables and the $W$-boson mass determination.Comment: 47 pages, 29 figures, 1 tabl

Pseudoscalar MSSM Higgs Production at NLO SUSY-QCD

One of the most important mechanisms at the Large Hadron Collider (LHC) for the production of the pseudoscalar Higgs boson of the Minimal Supersymmetric Standard Model (MSSM) is the loop-induced gluon fusion process gg → A. The higher-order QCD corrections have been obtained a long time ago and turned out to be large. However, the genuine supersymmetric (SUSY–)QCD corrections have been obtained only in the limit of large SUSY particle masses so far. We describe our calculation of the next-to-leading-order (NLO) SUSY-QCD results with full mass dependence and present numerical results for a few representative benchmark points. We also address the treatment of the effective top and bottom Yukawa couplings, in the case of heavy SUSY particles, in terms of effective low-energy theories where the heavy degrees of freedom have been decoupled. Furthermore, we include a discussion of the relation between the SUSY-QCD corrections that we have computed and the Adler-Bardeen theorem for the axial anomaly. In addition, we apply our results to the gluonic and photonic pseudoscalar Higgs decays A → gg, γγ at NLO