Valentin Ahrens, Thomas Becher, Matthias Neubert, Li Lin Yang
We use renormalization-group methods in effective field theory to improve the theoretical prediction for the cross section for Higgs-boson production at hadron colliders. In addition to soft-gluon resummation at NNNLL, we also resum enhanced contributions of the form (C_Aπα_s)^n, which arise in the analytic continuation of the gluon form factor to time-like momentum transfer. This resummation is achieved by evaluating the matching corrections arising at the Higgs-boson mass scale at a time-like renormalization point μ^2<0, followed by renormalization-group evolution to μ^2>0. We match our resummed result to NNLO fixed-order perturbation theory and give numerical predictions for the total production cross section as a function of the Higgs-boson mass. Resummation effects are significant even at NNLO, where our improved predictions for the cross sections at the Tevatron and the LHC exceed the fixed-order predictions by about 13% and 8%, respectively, for m_H=120 GeV. We also discuss the application of our technique to other time-like processes such as Drell-Yan production, e^+ e^- --> hadrons, and hadronic decays of the Higgs boson.
Marcela Carena, Sandro Casagrande, Florian Goertz, Ulrich Haisch, Matthias Neubert
Measurements of the Higgs-boson production cross section at the LHC are an important tool for studying electroweak symmetry breaking at the quantum level, since the main production mechanism gg-->h is loop-suppressed in the Standard Model (SM). Higgs production in extra-dimensional extensions of the SM is sensitive to the Kaluza-Klein (KK) excitations of the quarks, which can be exchanged as virtual particles in the loop. In the context of the minimal Randall-Sundrum (RS) model with bulk fields and a brane-localized Higgs sector, we derive closed analytical expressions for the gluon-gluon fusion process, finding that the effect of the infinite tower of virtual KK states can be described in terms of a simple function of the fundamental (5D) Yukawa matrices. Given a specific RS model, this will allow one to easily constrain the parameter space, once a Higgs signal has been established. We explain that discrepancies between existing calculations of Higgs production in RS models are related to the non-commutativity of two limits: taking the number of KK states to infinity and removing the regulator on the Higgs-boson profile, which is required in an intermediate step to make the relevant overlap integrals well defined. Even though the one-loop gg-->h amplitude is finite in RS scenarios with a brane-localized Higgs sector, it is important to introduce a consistent ultraviolet regulator in order to obtain the correct result.
Michael Benzke, Seung J. Lee, Matthias Neubert, Gil Paz
We show that in the Standard Model the parametrically leading (by a factor 1/alpha_s) contribution to the inclusive CP asymmetry in B->X_{s,d}+gamma decays arises from a long-distance effect in the interference of the electromagnetic dipole amplitude with the amplitude for an up-quark penguin transition accompanied by soft gluon emission. This contribution is governed by a single hadronic parameter Lambda_{17}^u related to a matrix elements of a non-local operator. In view of current experimental data, a future precision measurement of the flavor-averaged CP asymmetry in B->X_s+gamma will signal the presence of new physics only if a value below -2% is found. A cleaner probe of new physics is offered by the difference of the CP asymmetries in charged versus neutral B-meson decays.
Valentin Ahrens, Andrea Ferroglia, Matthias Neubert, Ben D. Pecjak, Li Lin Yang
We make use of recent results in effective theory and higher-order perturbative calculations to improve the theoretical predictions of the top-quark pair production cross section at hadron colliders. In particular, we supplement the fixed-order NLO calculation with higher-order corrections from soft gluon resummation at NNLL accuracy. Uncertainties due to power corrections to the soft limit are estimated by combining results from single-particle inclusive and pair invariant-mass kinematics. We present our predictions as functions of the top-quark mass in both the pole scheme and the MS(bar) scheme. We also discuss the merits of using threshold masses as an alternative, and calculate the cross section with the top-quark mass defined in the 1S scheme as an illustrative example.
Anne Mareike Galda, Matthias Neubert
The $B$-meson light-cone distribution amplitude is a central quantity governing non-perturbative hadronic dynamics in exclusive $B$ decays. We show that the information needed to describe such processes at leading power in $Λ_{\rm QCD}/m_b$ is most directly contained in its Laplace transform $\tildeφ_+(η)$. We derive the renormalization-group (RG) equation satisfied by this function and present its exact solution. We express the RG-improved QCD factorization theorem for the decay $B^-\toγ\ell^-\barν$ in terms of $\tildeφ_+(η)$ and show that it is explicitly independent of the factorization scale. We propose an unbiased parameterization of $\tildeφ_+(η)$ in terms of a small set of uncorrelated hadronic parameters.
Martin Bauer, Matthias Neubert, Andrea Thamm
Scalar particles $S$ which are singlets under the Standard Model gauge group are generic features of many models of fundamental physics, in particular as possible mediators to a hidden sector. We show that the decay $S\to Zh$ provides a powerful probe of the CP nature of the scalar, because it is allowed only if $S$ has CP-odd interactions. We perform a model-independent analysis of this decay using an effective Lagrangian and compute the relevant Wilson coefficients arising from integrating out heavy fermions to one-loop order.
Thomas Becher, Matthias Neubert
The complete two-loop expression for the jet function J(p^2,mu) of soft-collinear effective theory is presented, including non-logarithmic terms. Combined with our previous calculation of the soft function S(omega,mu), this result provides the basis for a calculation of the effect of a photon-energy cut in the measurement of the B-->X_s+gamma decay rate at next-to-next-to-leading order in renormalization-group improved perturbation theory. The jet function is also relevant to the resummation of Sudakov logarithms in other hard QCD processes.
Thomas Becher, Richard J. Hill, Matthias Neubert
The factorization properties of the radiative decays B->V gamma are analyzed at leading order in 1/m_b using the soft-collinear effective theory. It is shown that the decay amplitudes can be expressed in terms of a B->V form factor evaluated at q^2=0, light-cone distribution amplitudes of the B and V mesons, and calculable hard-scattering kernels. The renormalization-group equations in the effective theory are solved to resum perturbative logarithms of the different scales in the decay process. Phenomenological implications for the B->K* gamma branching ratio, isospin asymmetry, and CP asymmetries are discussed, with particular emphasis on possible effects from physics beyond the Standard Model.
Bjorn O. Lange, Matthias Neubert, Gil Paz
We present ``state-of-the-art'' theoretical expressions for the triple differential B->X_u l^- nu decay rate and for the B->X_s gamma photon spectrum, which incorporate all known contributions and smoothly interpolate between the ``shape-function region'' of large hadronic energy and small invariant mass, and the ``OPE region'' in which all hadronic kinematical variables scale with M_B. The differential rates are given in a form which has no explicit reference to the mass of the b quark, avoiding the associated uncertainties. Dependence on m_b enters indirectly through the properties of the leading shape function, which can be determined by fitting the B->X_s gamma photon spectrum. This eliminates the dominant theoretical uncertainties from predictions for B->X_u l^- nu decay distributions, allowing for a precise determination of |V_{ub}|. In the shape-function region, short-distance and long-distance contributions are factorized at next-to-leading order in renormalization-group improved perturbation theory. Higher-order power corrections include effects from subleading shape functions where they are known. When integrated over sufficiently large portions in phase space, our results reduce to standard OPE expressions up to yet unknown O(alpha_s^2) terms. Predictions are presented for partial B->X_u l^- nu decay rates with various experimental cuts. An elaborate error analysis is performed that contains all significant theoretical uncertainties, including weak annihilation effects. We suggest that the latter can be eliminated by imposing a cut on high lepton invariant mass.
Matthias Neubert
The study of charmless two-body decays of B mesons is currently one of the hottest topics in B physics. QCD factorization provides the theoretical framework for a systematic analysis of such decays. A global fit to B->pi K,pi pi branching fractions, combined with knowledge on |V(ub)|, establishes the existence of a CP-violating phase in the bottom sector of the CKM matrix and tends to favor values of gamma near 90 degrees, somewhat larger than those suggested by the standard analysis of the unitarity triangle. A novel construction of the unitarity triangle is presented, which is independent of B-B(bar) and K-K(bar) mixing. It can provide stringent tests of the Standard Model with small theoretical uncertainties.
Matthias Neubert
We review recent advances in the theory of strong-interaction effects and final-state interactions in hadronic weak decays of heavy mesons. In the heavy-quark limit, the amplitudes for most nonleptonic, two-body B decays can be calculated from first principles and expressed in terms of semileptonic form factors and light-cone distribution amplitudes. We summarize the main features of this novel QCD factorization and discuss its phenomenological applications to B->D^(*)+L decays (with L a light meson), and to the rare charmless decays B->pi+K and B->pi+pi.
Matthias Neubert
The element |V_{ub}| of the quark mixing matrix can be extracted with small theoretical uncertainties by combining weighted integrals over the endpoint regions of the lepton spectrum in B -> X_u l nu decays and the photon spectrum in B -> X_s gamma decays. The perturbative corrections to this determination are computed at next-to-leading order including operator mixing, which has an important impact. The effect of Sudakov resummation is shown to be numerically insignificant.
Matthias Neubert, Thomas Becher
We reduce the perturbative uncertainty in the determination of |V_{ub}| from inclusive semileptonic B decays by calculating the rate of B -> X_u l nu events with dilepton invariant mass q^2>(M_B-M_D)^2 at subleading order in the hybrid expansion, and to next-to-leading order in renormalization-group improved perturbation theory. We also resum logarithmic corrections to the leading power-suppressed contributions. Studying the effect of different b-quark mass definitions we find that the branching ratio after the cut is Br(B -> X_u l nu)=(20.9+-4.0)|V_{ub}|^2, where the dominant error is due to the uncertainty in the b-quark mass. This implies that |V_{ub}| can be determined with a precision of about 10%.
Thomas Becher, Stephan Braig, Matthias Neubert, Alexander L. Kagan
The presence of a light b-squark (with mass about 4 GeV) and gluino (with mass about 15 GeV) might explain the observed excess in b-quark production at the Tevatron. Though provocative, this model is not excluded by present data. The light supersymmetric particles can induce large flavor-changing effects in radiative decays of B mesons. We analyse the decays B->X_s gamma and B->X_{sg} in this scenario and derive restrictive bounds on the flavor-changing quark-squark-gluino couplings.
Thomas Becher, Matthias Neubert, Alexey A. Petrov
We present exact results, at next-to-leading order in renormalization-group improved perturbation theory, for the Wilson coefficients appearing at order 1/m_Q in the heavy-quark expansion of heavy-light current operators. To this end, we complete the calculation of the corresponding two-loop anomalous dimension matrix. Our results are important for determinations of |V_{ub}| using exclusive and inclusive semileptonic B decays. They are also relevant to computations of the decay constant f_B based on a heavy-quark expansion.
Matthias Neubert
These notes provide a pedagogical introduction to the theory of non-leptonic heavy-meson decays recently proposed by Beneke, Buchalla, Sachrajda and myself. We provide a rigorous basis for factorization for a large class of non-leptonic two-body B-meson decays in the heavy-quark limit. The resulting factorization formula incorporates elements of the naive factorization approach and the hard-scattering approach, and allows us to compute systematically radiative (``non-factorizable'') corrections to naive factorization for decays such as B->D+pi and B->pi+pi.
Matthias Neubert
Precision tests of the Standard Model and searches for New Physics in the quark flavor sector depend on accurate theoretical calculations of decay rates and spectra for rare, flavor-changing processes. The theoretical status and recent developments of techniques allowing such calculations are reviewed. Special attention is paid to the calculation of the B->Xs+gamma branching ratio, the extraction of the b-quark mass from a fit to B->Xc+l+nu moments, and the determination of |V(ub)| from spectra in the inclusive decay B->Xu+l+nu. From a reanalysis of different inclusive distributions the updated average value |V(ub)|=(3.98+-0.15+-0.30)*10^{-3} is derived. Using only the theoretically cleanest channels, we obtain |V(ub)|=(3.70+-0.15+-0.28)*10^{-3}.
Martin Bauer, Matthias Neubert, Andrea Thamm
Scalar particles $S$ which are gauge singlets under the Standard Model are generic features of many models of fundamental physics, in particular as possible mediators to a hidden or dark sector. We show that the decay $S\to Zh$ provides a powerful probe of the CP nature of the scalar, because it is allowed only if $S$ has CP-odd interactions. We perform a model-independent analysis of this decay in the context of an effective Lagrangian and compute the relevant Wilson coefficients arising from integrating out heavy fermions to one-loop order. We illustrate our findings with the example of the 750 GeV diphoton resonance seen by ATLAS and CMS and show that the $S\to Zh$ decay rate could naturally be of similar magnitude or larger than the diphoton rate.
Ze Long Liu, Matthias Neubert
The rare radiative $B$-meson decay $B^-\toγ\ell^-\barν$ and the radiative Higgs-boson decay $h\toγγ$ mediated by light-quark loops both receive large logarithmic corrections in QCD, which can be resummed using factorization theorems derived in soft-collinear effective theory. In these factorization theorems the same radiative jet function appears, which is a central object in the study of factorization beyond the leading order in scale ratios. We calculate this function at two-loop order both in momentum space and in a dual space, where its renormalization-group evolution takes on a simpler form. We also derive the two-loop anomalous dimension of the jet function and present the exact solution to its evolution equation at two-loop order. Another important outcome of our analysis is the explicit form of the two-loop anomalous dimension of the $B$-meson light-cone distribution amplitude in momentum space.
Ze Long Liu, Matthias Neubert
It is by now well known that, at subleading power in scale ratios, factorization theorems for high-energy cross sections and decay amplitudes contain endpoint-divergent convolution integrals. The presence of these divergences hints at a violation of simple scale separation, as a result of the so-called collinear anomaly. At the technical level, endpoint divergences indicate an unexpected failure of dimensional regularization and the $\bar{\rm MS}$ subtraction scheme. In this paper we start a comprehensive discussion of factorization at subleading power within the framework of soft-collinear effective theory. As a concrete example, we factorize the decay amplitude for the radiative Higgs-boson decay $h\to γγ$ mediated by a $b$-quark loop, for which endpoint-divergent convolution integrals require both dimensional and rapidity regulators. We derive a factorization theorem for the decay amplitude in terms of bare Wilson coefficients and operator matrix elements. We show that endpoint divergences caused by rapidity divergences cancel to all orders in perturbation theory, while endpoint divergences that are regularized dimensionally can be removed by rearranging the terms in the factorization theorem. We use our result to resum the leading double-logarithmic corrections of order $α_s^n\ln^{2n+2}(-M_h^2/m_b^2)$ to all orders of perturbation theory.