arXiv subjects
Publications and source records attributed to Martin Beneke.
We complete the calculation of the QCD penguin amplitude at next-to-next-to-leading order in the QCD factorization approach to non-leptonic B-meson decays. This provides the last missing piece in the computation of the QCD correction to direct CP asymmetries at leading power in the heavy-quark expansion.
We report on the calculation of the two-loop penguin amplitudes in non-leptonic B decays in the framework of QCD factorization. We discuss the computation of this genuine two-loop, two-scale problem and provide details on the matching from QCD onto SCET, the evaluation of the master integrals, and the convolution of the hard scattering kernels with the light-cone distribution amplitude of the light meson. Preliminary results on the size of the two-loop correction are given.
We sum the leading logarithms $α_s^n \ln^{2 n-1}(1-z)$, n=1,2,... near the kinematic threshold $z=m_H^2/\hat{s}\to 1$ at next-to-leading power in the expansion in (1-z) for Higgs production in gluon fusion. We highlight the new contributions compared to Drell-Yan production in quark-antiquark annihilation and show that the final result can be obtained to all orders by the substitution of the colour factor $C_F\to C_A$, confirming previous fixed-order results and conjectures. We also provide a numerical analysis of the next-to-leading power leading logarithms, which indicates that they are numerically relevant.
We calculate the SU(2)$\times$U(1) electroweak static potential between a fermionic triplet in the broken phase of the Standard Model in the one-loop order (NLO). The one-loop correction provides the leading non-relativistic correction to the large Sommerfeld effect in the annihilation of wino or wino-like dark matter particles $χ^0$. We find sizeable modifications of the $χ^0χ^0$ annihilation cross section and determine the shifts of the resonance locations due to the loop correction to the wino potential.
A classic result, originally due to Kluberg-Stern and Zuber, states that operators that vanish by the classical equation of motion (eom) do not mix into "physical" operators. Here we show that and explain why this result does not hold in soft-collinear effective theory (SCET) for the renormalization of power-suppressed operators. We calculate the non-vanishing mixing of eom operators for the simplest case of $N$-jet operators with a single collinear field in every direction. The result implies that---for the computation of the anomalous dimension but not for on-shell matrix elements---there exists a preferred set of fields that must be used to reproduce the infrared singularities of QCD scattering amplitudes. We identify these fields and explain their relation to the gauge-invariant SCET Lagrangian. Further checks reveal another generic property of SCET beyond leading power, which will be relevant to resummation at the next-to-leading logarithmic level, the divergence of convolution integrals with the hard matching coefficients. We propose an operator solution that allows to consistently renormalize such divergences.
We resum the leading logarithms $α_s^n \ln^{2 n-1}(1-z)$, $n=1,2,\ldots$ near the kinematic threshold $z=Q^2/\hat{s}\to 1$ of the Drell-Yan process at next-to-leading power in the expansion in $(1-z)$. The derivation of this result employs soft-collinear effective theory in position space and the anomalous dimensions of subleading-power soft functions, which are computed. Expansion of the resummed result leads to the leading logarithms at fixed loop order, in agreement with exact results at NLO and NNLO and predictions from the physical evolution kernel at N$^3$LO and N$^4$LO, and to new results at the five-loop order and beyond.
We continue the investigation of the anomalous dimension of subleading-power $N$-jet operators. In this paper, we focus on the operators with fermion number one in each collinear direction, corresponding to quark (antiquark) initiated jets in QCD. We investigate the renormalization effects induced by the soft loop and compute the one-loop mixing of time-ordered products involving power-suppressed SCET Lagrangian insertions into $N$-jet currents through soft loops. We discuss fermion number conservation in collinear directions and provide explicit results for the collinear anomalous dimension matrix of the currents. The Feynman rules for the power-suppressed SCET interactions in the position-space formalism are collected in an appendix.
We determine the NNLO electroweak correction to the $e^+ e^-\to b\bar{b}W^+W^- X$ production cross section near the top-pair production threshold. The calculation includes non-resonant production of the final state as well as electroweak effects in resonant top anti-top pair production with non-relativistic resummation, and elevates the theoretical prediction to NNNLO QCD plus NNLO electroweak accuracy. We then study the impact of the new contributions on the top-pair threshold scan at a future lepton collider.
We construct a complete and minimal basis of subleading-power N-jet operators in position-space soft-collinear effective theory (SCET) and discuss how the Low-Burnett-Kroll amplitude is recovered in this framework. We begin a systematic investigation of the anomalous dimension of next-to-leading power N-jet operators in view of resummation of logarithmically enhanced terms in partonic cross sections and discuss the explicit result at the one-loop order for fermion-number two N-jet operators at the second order in the power expansion parameter of SCET.
We begin a systematic investigation of the anomalous dimension of subleading power N-jet operators in view of resummation of logarithmically enhanced terms in partonic cross sections beyond leading power. We provide an explicit result at the one-loop order for fermion-number two N-jet operators at the second order in the power expansion parameter of soft-collinear effective theory.
The top-quark mass can be determined with very high precision from a scan of the total $e^+e^-\to b\bar{b}W^+W^-X$ cross section near the top-pair production threshold. We present the full calculation of electroweak and non-resonant corrections to this process at NNLO. We discuss the size of the new contributions and estimate the theory uncertainty on the top-quark mass in the PS mass scheme.
We investigate electromagnetic corrections to the rare $B$-meson leptonic decay $B_{s,d} \to μ^+μ^-$ from scales below the bottom-quark mass $m_b$. Contrary to QCD effects, which are entirely contained in the $B$-meson decay constant, we find that virtual photon exchange can probe the $B$-meson structure, resulting in a "non-local annihilation" effect. We find that this effect gives rise to a dynamical enhancement by a power of $m_b/Λ_{\rm QCD}$ and by large logarithms. The impact of this novel effect on the branching ratio of $B_{s,d}\toμ^+μ^-$ is about $1\%$, of the order of the previously estimated non-parametric theoretical uncertainty, and four times the size of previous estimates of next-to-leading order QED effects due to residual scale dependence. We update the Standard Model prediction to $\overline{\cal B}(B_s \to μ^+μ^-)_{\rm SM} = (3.57 \pm 0.17) \cdot 10^{-9}$.
Kinematic edges of cascade decays of new particles produced in high-energy collisions may provide important constraints on the involved particles' masses. For the exemplary case of gluino decay $\tilde{g}\to q\bar q \tildeχ$ into a pair of quarks and a neutralino through a squark resonance, we study the hadronic invariant mass distribution in the vicinity of the kinematic edge. We perform a next-to-leading order calculation in the strong coupling $α_s$ and the ratio of squark width and squark mass $Γ_\tilde{q}/m_\tilde{q}$, based on a systematic expansion in $Γ_\tilde{q}/m_\tilde{q}$. The separation into hard, collinear and soft contributions elucidates the process dependent and universal features of distributions in the edge region, represented by on-shell decay matrix elements, universal jet functions and a soft function that depends on the resonance propagator and soft Wilson lines.
We delineate the allowed parameter and mass range for a wino-like dark matter particle containing some Higgsino admixture in the MSSM by analysing the constraints from diffuse gamma-rays from the dwarf spheroidal galaxies, galactic cosmic rays, direct detection and cosmic microwave background anisotropies. A complete calculation of the Sommerfeld effect for the mixed-neutralino case is performed. We find that the combination of direct and indirect searches poses significant restrictions on the thermally produced wino-Higgsino dark matter with correct relic density. For $μ>0$ nearly the entire parameter space considered is excluded, while for $μ<0$ a substantial region is still allowed, provided conservative assumptions on astrophysical uncertainties are adopted.
We present predictions for the total cross sections for pair production of squarks and gluinos at the LHC including a combined NNLL resummation of soft and Coulomb gluon effects. We derive all terms in the NNLO cross section that are enhanced near the production threshold, which include contributions from spin-dependent potentials and so-called annihilation corrections. The NNLL corrections at $\sqrt{s}=13$ TeV range from up to $20\%$ for squark-squark production to $90\%$ for gluino pair production relative to the NLO results and reduce the theoretical uncertainties of the perturbative calculation to the $10\%$ level. Grid files with our numerical results are publicly available.
There is an increasing interest in accurate dark matter relic density predictions, which requires next-to-leading order (NLO) calculations. The method applied up to now uses zero-temperature NLO calculations of annihilation cross sections in the standard Boltzmann equation for freeze-out, and is conceptually problematic, since it ignores the finite-temperature infrared (IR) divergences from soft and collinear radiation and virtual effects. We address this problem systematically by starting from non-equilibrium quantum field theory, and demonstrate on a realistic model that soft and collinear temperature-dependent divergences cancel in the collision term. Our analysis provides justification for the use of the freeze-out equation in its conventional form and determines the leading finite-temperature correction to the annihilation cross section. This turns out to have a remarkably simple structure.
We apply the operator product expansion (OPE) technique to the decay and annihilation of heavy particles in a thermal medium with temperature below the heavy particle mass, m_chi. This allows us to explain two interesting observations made before: a) that the leading thermal correction to the decay width of a charged particle is the same multiplicative factor of the zero-temperature width for a two-body decay and muon decay, and b) that the leading thermal correction to fermionic dark matter annihilation arises only at order T^4/m_chi^4. The OPE further considerably simplifies the computation and factorizes it into model-independent matrix elements in the thermal background, and short-distance coefficients to be computed in zero-temperature field theory.
We show how to correctly treat threshold singularities in fixed-order perturbative calculations of the electron anomalous magnetic moment and hadronic pair production processes such as top pair production. With respect to the former, we demonstrate the equivalence of the "non-perturbative", resummed treatment of the vacuum polarization contribution, whose spectral function exhibits bound state poles, with the fixed-order calculation by identifying a threshold localized term in the four-loop spectral function. In general, we find that a modification of the dispersion relation by threshold subtractions is required to make fixed-order calculations well-defined and provide the subtraction term. We then solve the apparent problem of a divergent convolution of the partonic cross section with the parton luminosity in the computation of the top pair production cross section starting from the fourth-order correction. We find that when the computation is performed in the usual way as an integral of real and virtual corrections over phase space at a given order in the expansion in the strong coupling, an additional contribution has to be added at N3LO.