Michael Trott

Renormalization group evolution of the Standard Model dimension six operators III: gauge coupling dependence and phenomenology

A bstractWe calculate the gauge terms of the one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory (SM EFT). Combining these results with our previous results for the λ and Yukawa coupling terms completes the calculation of the one-loop anomalous dimension matrix for the dimension-six operators. There are 1350 CP -even and 1149 CP -odd parameters in the dimension-six Lagrangian for 3 generations, and our results give the entire 2499 × 2499 anomalous dimension matrix. We discuss how the renormalization of the dimension-six operators, and the additional renormalization of the dimension d ≤ 4 terms of the SM Lagrangian due to dimension-six operators, lays the groundwork for future precision studies of the SM EFT aimed at constraining the effects of new physics through precision measurements at the electroweak scale. As some sample applications, we discuss some aspects of the full RGE improved result for essential processes such as gg → h, h → γγ and h → Zγ, for Higgs couplings to fermions, for the precision electroweak parameters S and T, and for the operators that modify important processes in precision electroweak phenomenology, such as the three-body Higgs boson decay h → Z ℓ+ℓ− and triple gauge boson couplings. We discuss how the renormalization group improved results can be used to study the flavor problem in the SM EFT, and to test the minimal flavor violation (MFV) hypothesis. We briefly discuss the renormalization effects on the dipole coefficient Ceγ which contributes to μ → eγ and to the muon and electron magnetic and electric dipole moments.

Power-counting and the Validity of the Classical Approximation During Inflation

We use the power-counting formalism of effective field theory to study the size of loop corrections in theories of slow-roll inflation, with the aim of more precisely identifying the limits of validity of the usual classical inflationary treatments. We keep our analysis as general as possible in order to systematically identify the most important corrections to the classical inflaton dynamics. Although most slow-roll models lie within the semiclassical domain, we find the consistency of the Higgs-Inflaton scenario to be more delicate due to the proximity between the Hubble scale during inflation and the upper bound allowed by unitarity on the new-physics scale associated with the breakdown of the semiclassical approximation within the effective theory. Similar remarks apply to curvature-squared inflationary models.

First Glimpses at Higgs’ face

A bstractThe 8 TeV LHC Higgs search data just released indicates the existence of a scalar resonance with mass ~ 125 GeV. We examine the implications of the data reported by ATLAS, CMS and the Tevatron collaborations on understanding the properties of this scalar by performing joint fits on its couplings to other Standard Model (SM) particles. We discuss and characterize to what degree this resonance has the properties of the SM Higgs, and consider what implications can be extracted for New Physics in a (mostly) model-independent fashion. We find that, if the Higgs couplings to fermions and weak vector bosons are allowed to differ from their standard values, the SM is ~ 2σ from the best fit point to the current data. Fitting to a possible invisible decay branching ratio, we find BRinv ≃ 0.05 ± 0.32 (95% C.L.). We also discuss and develop some ways of using the data in order to bound or rule out models which modify significantly the properties of this scalar resonance, and apply these techniques to the current global dataset.

Renormalization group evolution of the standard model dimension six operators. I: formalism and λ dependence

A bstractWe calculate the order λ, λ2 and λy2 terms of the 59 × 59 one-loop anomalous dimension matrix of dimension-six operators, where λ and y are the Standard Model Higgs self-coupling and a generic Yukawa coupling, respectively. The dimension-six operators modify the running of the Standard Model parameters themselves, and we compute the complete one-loop result for this. We discuss how there is mixing between operators for which no direct one-particle-irreducible diagram exists, due to operator replacements by the equations of motion.

Renormalization group evolution of the Standard Model dimension six operators II: Yukawa dependence

A bstractWe calculate the complete order y2 and y4 terms of the 59 × 59 one-loop anomalous dimension matrix for the dimension-six operators of the Standard Model effective field theory, where y is a generic Yukawa coupling. These terms, together with the terms of order λ, λ2 and λy2 depending on the Standard Model Higgs self-coupling λ which were calculated in a previous work, yield the complete one-loop anomalous dimension matrix in the limit of vanishing gauge couplings. The Yukawa contributions result in non-trivial flavor mixing in the various operator sectors of the Standard Model effective theory.

Fingerprinting Higgs suspects at the LHC

A bstractWe outline a method for characterizing deviations from the properties of a Standard Model (SM) Higgs boson. We apply it to current data in order to characterize up to which degree the SM Higgs boson interpretation is consistent with experiment. We find that the SM Higgs boson is consistent with the current data set at the 82 % confidence level, based on data of excess events reported by CMS and ATLAS, which are interpreted to be related to the mass scale mh ∼ 124 − 126 GeV, and on published CLs exclusion regions. We perform a global fit in terms of two parameters characterizing the deviation from the SM value in the gauge and fermion couplings of a Higgs boson. We find two minima in the global fit and identify observables that can remove this degeneracy. An update for Moriond 2012 data is included in the appendix, which finds that the SM Higgs boson is now consistent with the current data set at only the 89 % confidence level (which corresponds to ∼ 2 σ tension compared to the best fit point).

On Higgs inflation and naturalness

We reexamine recent claims that Einstein-frame scattering in the Higgs inflation model is unitary above the cut-off energy Λ ≃ Mp/ξ. We show explicitly how unitarity problems arise in both the Einstein and Jordan frames of the theory. In a covariant gauge they arise from non-minimal Higgs self-couplings, which cannot be removed by field redefinitions because the target space is not flat. In unitary gauge, where there is only a single scalar which can be redefined to achieve canonical kinetic terms, the unitarity problems arise through non-minimal Higgs-gauge couplings.

Global analysis of inclusive B decays

In light of the large amount of new experimental data, we revisit the determination of |V{sub cb}| and m{sub b} from inclusive semileptonic and radiative B decays. We study shape variables to order {Lambda}{sub QCD}{sup 3}/m{sub b}{sup 3} and {alpha}{sub s}{sup 2}{beta}{sub 0}, and include the order {alpha}{sub s} {Lambda}{sub QCD}/m{sub b} correction to the hadron mass spectrum in semileptonic decay, which improves the agreement with the data. We focus on the 1S and kinetic mass schemes for the b quark, with and without expanding m{sub b}-m{sub c} in HQET. We perform fits to all available data from BABAR, BELLE, CDF, CLEO, and DELPHI, discuss the theoretical uncertainties, and compare with earlier results. We find |V{sub cb}| = (41.9 {+-} 0.6 {+-} 0.1{sub {tau}{sub B}}) x 10{sup -3} and m{sub b}{sup 1S} = 4.68 {+-} 0.04GeV, including our estimate of the theoretical uncertainty in the fit.

Renormalization group scaling of Higgs operators and h → γγ decay

A bstractWe compute the renormalization of dimension six Higgs-gauge boson operators that can modify the h → γγ rate at tree-level. Operator mixing is shown to lead to an important modification of new physics effects which has been neglected in past calculations. We also find that the usual formula for the S oblique parameter contribution of these Higgs-gauge boson operators needs additional terms to be consistent with renormalization group evolution. We study the implications of our results for Higgs phenomenology and for new physics models which attempt to explain a deviation in the h → γγ rate. We derive a new relation between the S parameter and the h → γγ and h → Zγ decay rates.

Probing for invisible Higgs decays with global fits

A bstractWe demonstrate by performing a global fit on Higgs signal strength data that large invisible branching ratios (Brinv) for a Standard Model (SM) Higgs particle are currently consistent with the experimental hints of a scalar resonance with mass mh ~ 124 GeV. For this mass, we find Brinv< 0.64 (95% CL) from a global fit to individual channel signal strengths supplied by ATLAS, CMS and the Tevatron collaborations. Novel tests that can be used to improve the prospects of experimentally discovering the existence of a Brinv with future data are proposed. These tests are based on the combination of all visible channel Higgs signal strengths, and allow us to examine the required reduction in experimental and theoretical errors in this data that would allow a more significantly bounded invisible branching ratio to be experimentally supported. We examine in some detail how our conclusions and method are affected when a scalar resonance at this mass scale has couplings deviating from the SM ones.