Strong-Coupling Constant at Three Loops in Momentum Subtraction Scheme

In this paper we compute the three-loop corrections to the $\beta$ function in a momentum subtraction (MOM) scheme with a massive quark. The calculation is performed in the background field formalism applying asymptotic expansions for small and large momenta. Special emphasis is devoted to the relation between the coupling constant in the MOM and $\overline{\rm{MS}}$ schemes as well as their ability to describe the phenomenon of decoupling. It is demonstrated by an explicit comparison that the $\overline{\rm{MS}}$ scheme can be consistently used to relate the values of the MOM-scheme strong-coupling constant in the energy regions higher and lower than the massive-quark production threshold. This procedure obviates the necessity to know the full mass dependence of the MOM $\beta$ function and clearly demonstrates the equivalence of both schemes for the description of physics outside the threshold region.Comment: 17 pages, 5 figure

Scale setting for alpha_s beyond leading order

We present a general procedure for incorporating higher-order information into the scale-setting prescription of Brodsky, Lepage and Mackenzie. In particular, we show how to apply this prescription when the leading coefficient or coefficients in a series in the strong coupling alpha_s are anomalously small and the original prescription can give an unphysical scale. We give a general method for computing an optimum scale numerically, within dimensional regularization, and in cases when the coefficients of a series are known. We apply it to the heavy quark mass and energy renormalization in lattice NRQCD, and to a variety of known series. Among the latter, we find significant corrections to the scales for the ratio of e+e- to hadrons over muons, the ratio of the quark pole to MSbar mass, the semi-leptonic B-meson decay width, and the top decay width. Scales for the latter two decay widths, expressed in terms of MSbar masses, increase by factors of five and thirteen, respectively, substantially reducing the size of radiative corrections.Comment: 39 pages, 15 figures, 5 tables, LaTeX2

Effective QCD Interactions of CP-odd Higgs Bosons at Three Loops

In the virtual presence of a heavy quark t, the interactions of a CP-odd scalar boson A, with mass M_A << 2M_t, with gluons and light quarks can be described by an effective Lagrangian. We analytically derive the coefficient functions of the respective physical operators to three loops in quantum chromodynamics (QCD), adopting the modified minimal-subtraction (MS-bar) scheme of dimensional regularization. Special attention is paid to the proper treatment of the gamma_5 matrix and the Levi-Civita epsilon tensor in D dimensions. In the case of the effective ggA coupling, we find agreement with an all-order prediction based on a low-energy theorem in connection with the Adler-Bardeen non-renormalization theorem. This effective Lagrangian allows us to analytically evaluate the next-to-leading QCD correction to the A -> gg partial decay width by considering massless diagrams. For M_A = 100GeV, the resulting correction factor reads 1+(221/12)alpha_s^(5)(M_A)/pi +165.9(alpha_s^(5)(M_A)/pi)^2 approx 1+0.68+0.23. We compare this result with predictions based on various scale-optimization methods.Comment: 17 pages (Latex), 2 figures (Postscript

Higgs Decay into Gluons up to O(\alpha_s^3 G_F m_t^2)

The decay of the Standard Model Higgs boson in the intermediate-mass range into gluons is considered where special emphasis is put on the influence of the leading electroweak corrections proportional to G_F m_t^2. An effective Lagrangian approach is used where the top quark is integrated out. The evaluation of the coefficient function is performed using two different methods. The first one is concerned with the direct evaluation of the vertex diagrams and the second method is based on a low-energy theorem. In a first step the tools needed for the computation are provided namely the renormalization constants of the QCD Lagrangian are computed up to O(\alpha_s^2 G_F m_t^2). Also the decoupling constants for the strong coupling constant \alpha_s and the light quark masses relating the quantities of the full theory to the corresponding quantities of the effective one are evaluated up to order \alpha_s^2 G_F m_t^2.Comment: 20 pages (revtex), 3 figure

Beautiful Mirrors and Precision Electroweak Data

The Standard Model (SM) with a light Higgs boson provides a very good description of the precision electroweak observable data coming from the LEP, SLD and Tevatron experiments. Most of the observables, with the notable exception of the forward-backward asymmetry of the bottom quark, point towards a Higgs mass far below its current experimental bound. The disagreement, within the SM, between the values for the weak mixing angle as obtained from the measurement of the leptonic and hadronic asymmetries at lepton colliders, may be taken to indicate new physics contributions to the precision electroweak observables. In this article we investigate the possibility that the inclusion of additional bottom-like quarks could help resolve this discrepancy. Two inequivalent assignments for these new quarks are analysed. The resultant fits to the electroweak data show a significant improvement when compared to that obtained in the SM. While in one of the examples analyzed, the exotic quarks are predicted to be light, with masses below 300 GeV, and the Higgs tends to be heavy, in the second one the Higgs is predicted to be light, with a mass below 250 GeV, while the quarks tend to be heavy, with masses of about 800 GeV. The collider signatures associated with the new exotic quarks, as well as the question of unification of couplings within these models and a possible cosmological implication of the new physical degrees of freedom at the weak scale are also discussed.Comment: 21 pages, 4 embedded postscript figures, LaTeX. Two minor corrections performe

Calculations of binding energies and masses of heavy quarkonia using renormalon cancellation

We use various methods of Borel integration to calculate the binding ground energies and masses of b-bbar and t-tbar quarkonia. The methods take into account the leading infrared renormalon structure of the hard+soft part of the binding energies E(s), and of the corresponding quark pole masses m_q, where the contributions of these singularities in M(s) = 2 m_q + E(s) cancel. Beforehand, we carry out the separation of the binding energy into its hard+soft and ultrasoft parts. The resummation formalisms are applied to expansions of m_q and E(s) in terms of quantities which do not involve renormalon ambiguity, such as MSbar quark mass, and alpha_s. The renormalization scales are different in calculations of m_q, E(s) and E(us). The MSbar mass of b quark is extracted, and the binding energies of t-tbar and the peak (resonance) energies for (t+tbar) production are obtained.Comment: 23 pages, 8 double figures, revtex4; the version to appear in Phys.Rev.D; extended discussion between Eqs.(25) and (26); the paragraph between Eqs.(32) and (33) is new and explains the numerical dependence of the residue parameter on the factorization scale; several new references were added; acknowledgments were modified; the numerical results are unchange

Standard Model Higgs-Boson Branching Ratios with Uncertainties

We present an update of the branching ratios for Higgs-boson decays in the Standard Model. We list results for all relevant branching ratios together with corresponding uncertainties resulting from input parameters and missing higher-order corrections. As sources of parametric uncertainties we include the masses of the charm, bottom, and top quarks as well as the QCD coupling constant. We compare our results with other predictions in the literature.Comment: 32 pages, 4 figures, contribution to LHC Higgs Cross Section Working Group https://twiki.cern.ch/twiki/bin/view/LHCPhysics/CrossSections, theoretical uncertainties for H->\mu\mu{} added, version to appear in European Physical Journal

Measurements of the Q2Q^2-Dependence of the Proton and Neutron Spin Structure Functions g1p and g1n

The structure functions g1p and g1n have been measured over the range 0.014 < x < 0.9 and 1 < Q2 < 40 GeV2 using deep-inelastic scattering of 48 GeV longitudinally polarized electrons from polarized protons and deuterons. We find that the Q2 dependence of g1p (g1n) at fixed x is very similar to that of the spin-averaged structure function F1p (F1n). From a NLO QCD fit to all available data we find $\Gamma_1^p - \Gamma_1^n =0.176 \pm 0.003 \pm 0.007$ at Q2=5 GeV2, in agreement with the Bjorken sum rule prediction of 0.182 \pm 0.005.Comment: 17 pages, 3 figures. Submitted to Physics Letters

Top-Quark Mediated Effects in Hadronic Higgs-Strahlung

Novel contributions to the total inclusive cross section for Higgs-Strahlung in the Standard Model at hadron colliders are evaluated. Although formally of order $\alpha_s^2$, they have not been taken into account in previous NNLO predictions. The terms under consideration are induced by Higgs radiation off top-quark loops and thus proportional to the top-quark Yukawa coupling. At the Tevatron, their effects to HW production are below 1% in the relevant Higgs mass range, while for HZ production, we find corrections between about 1% and 2%. At the LHC, the contribution of the newly evaluated terms to the cross section is typically of the order of 1%-3%. Based on these results, we provide updated predictions for the total inclusive Higgs-Strahlung cross section at the Tevatron and the LHC.Comment: 21 pages, 9 figures, 3 table

Three-Loop O(alpha_s^2 G_F M_t^2) Corrections to Hadronic Higgs Decays

We calculate the top-quark-induced three-loop corrections of O(alpha_s^2 G_F M_t^2) to the Yukawa couplings of the first five quark flavours in the framework of the minimal standard model with an intermediate-mass Higgs boson, with mass M_H << 2M_t. The calculation is performed using an effective-Lagrangian approach implemented with the hard-mass procedure. As an application, we derive the O(alpha_s^2 G_F M_t^2) corrections to the H -> q q-bar partial decay widths, including the case q=b. The couplings of the Higgs boson to pairs of leptons and intermediate bosons being known to O(alpha_s^2 G_F M_t^2), this completes the knowledge of such corrections in the Higgs sector. We express the results both in the MS-bar and on-shell schemes of mass renormalization. We recover the notion that the QCD perturbation expansions exhibit a worse convergence behaviour in the on-shell scheme than they do in the MS-bar scheme.Comment: 23 pages (Latex), 9 figures (Postscript), accepted for publication in Nuclear Physics