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This paper presents a double spatio-temporal localized Dirac-delta solution for the linear wave equation. The solution arises from the interference of sinusoidal waves with frequencies that vary as a function of the time of emission. It is shown that the time-dependent frequency function required to produce a localized Dirac-delta wave is exclusively determined by the dispersion relation of the medium in which the wave is traveling. Both numerical and exact analytical solutions for a typical physical scenario are obtained and displayed. The application of this result to possible practical uses is discussed., Comment: 12 pages, 5 figures

The objective of this paper is to provide a pedagogical framework for the phenomenon of orbital decay of satellites in low Earth orbit. The dynamics of orbital decay are derived considering atmospheric drag as the only dissipative mechanism and using an educational approach suitable for undergraduate calculus-based physics and engineering courses. The resulting non-linear first order differential equation for the altitude as a function of time is solved numerically for the isothermal-barotropic atmospheric model with a {fixed} scale height. The model is validated using the uncontrolled reentry data of the Chinese space station Tiangong-1., Comment: 6 pages, 3 figures

We present the first calculation of the complete set of NNLO QED corrections for muon-electron scattering. This includes leptonic, non-perturbative hadronic, and photonic contributions. All fermionic corrections as well as the photonic subset that only corrects the electron or the muon line are included with full mass dependence. The genuine four-point two-loop topologies are computed as an expansion in the small electron mass, taking into account both, logarithmically enhanced as well as constant mass effects using massification. A fast and stable implementation of the numerically delicate real-virtual contribution is achieved by combining OpenLoops with next-to-soft stabilisation. All matrix elements are implemented in the McMule framework, which allows for the fully-differential calculation of any infrared-safe observable. This calculation is to be viewed in the context of the MUonE experiment requiring a background prediction at the level of 10 ppm. Our results thus represent a major milestone towards this ambitious precision goal., Comment: 31 pages, 6 figures, 3 tables

The objective of this paper is to study the tidally locked 3:2 spin-orbit resonance of Mercury around the Sun. In order to achieve this goal, the effective potential energy that determines the spinning motion of an ellipsoidal planet around its axis is considered. By studying the rotational potential energy of an ellipsoidal planet orbiting a spherical star on an elliptic orbit with fixed eccentricity and semi-major axis, it is shown that the system presents an infinite number of metastable equilibrium configurations. These states correspond to local minima of the rotational potential energy averaged over an orbit, where the ratio between the rotational period of the planet around its axis and the revolution period around the star is fixed. The configurations in which this ratio is an integer or an half integer are of particular interest. Among these configurations, the deepest minimum in the average potential energy corresponds to a situation where the rotational and orbital motion of the planet are synchronous, and the system is tidally locked. The next-to-the deepest minimum corresponds to the case in which the planet rotates three times around its axis in the time that it needs to complete two orbits around the Sun. The latter is indeed the case that describes Mercury's motion. The method discussed in this work allows one to identify the integer and half-integer ratios that correspond to spin-orbit resonances and to describe the motion of the planet in the resonant orbit., Comment: 10 pages, 5 figures

We present the analytic evaluation of the two-loop corrections to the amplitude for the scattering of four fermions in Quantum Electrodynamics, $f^- + f^+ + F^- + F^+ \to 0$, with $f$ and $F$ representing a massless and a massive lepton, respectively. Dimensional regularization is employed to evaluate the loop integrals. Ultraviolet divergences are removed by renormalizing the coupling constant in the ${\overline{\text{MS}}}$-scheme, and the lepton mass as well as the external fields in the on-shell scheme. The analytic result for the renormalized amplitude is expressed as Laurent series around $d=4$ space-time dimensions, and contains Generalized Polylogarithms with up to weight four. The structure of the residual infrared divergences of the virtual amplitude is in agreement with the prediction of the Soft Collinear Effective Theory. Our analytic results are an essential ingredient for the computation of the scattering cross section for massive fermion-pair production in massless fermion-pair annihilation, i.e. $f^- f^+ \to F^- F^+$, and crossing related processes such as the elastic scattering $f F \to f F$, with up to Next-to-Next to Leading Order accuracy., Comment: 5 pages, 2 figures, 1 table + supplemental material. v2: references added; plots added; Table 1: finite part of A(2) fixed; matches published version

The purpose of this work is to study the phenomenon of tidal locking in a pedagogical framework by analyzing the effective gravitational potential of a two-body system with two spinning objects. It is shown that the effective potential of such a system is an example of a fold catastrophe. In fact, the existence of a local minimum and saddle point, corresponding to tidally-locked circular orbits, is regulated by a single dimensionless control parameter which depends on the properties of the two bodies and on the total angular momentum of the system. The method described in this work results in compact expressions for the radius of the circular orbit and the tidally-locked spin/orbital frequency. The limiting case in which one of the two orbiting objects is point-like is studied in detail. An analysis of the effective potential, which in this limit depends on only two parameters, allows one to clearly visualize the properties of the system. The notorious case of the Mars' moon Phobos is presented as an example of a satellite that is past the no return point and, therefore, will not reach a stable or unstable tidally-locked orbit., Comment: 13 pages, 5 figures

A factorization formalism for jet processes involving massive colored particles such as the top quark is developed, extending earlier results for the massless case. The factorization of soft emissions from the underlying hard process is implemented in an effective field theory framework, which forms the basis for the resummation of large logarithms. The renormalization group evolution giving rise to non-global logarithms is implemented into a parton shower code in the large-$N_c$ limit. After a comparison of the massive and massless radiations patterns, the cross section for $t\bar{t}$ production with a veto on additional central jet activity is computed, taking into account radiation both from the production and the decay of the top quarks. The resummation of the leading logarithms leads to an improved description of ATLAS measurements at $\sqrt{s}=7\,{\rm TeV}$., Comment: 40 pages, 10 figures

We present the analytic computation of the master integrals associated to certain two-loop non-planar topologies, which are needed to complete the evaluation of the last two color coefficients for the top-pair production in the quark-annihilation channel, which are not yet known analytically. The master integrals have been computed exploiting the differential equations method in canonical form. The solution is given as a series expansion in the dimensional regularization parameter through to weight four, the expansion coefficients are given in terms of multiple polylogarithms., Comment: 11 pages, 2 figures, talk given at RADCOR2019, based on arXiv:1904.10834

This paper studies new possibilities to directly measure a hypothetical $CP$-odd (pseudoscalar) component in the top-quark Yukawa coupling. In particular, the role of the $t{\bar t} h$ center-of-mass rest frame in the associated production of a top pair and a $h$ boson at the LHC is explored. The $h$ boson is assumed to have both a $CP$-even (scalar) and a $CP$-odd coupling to the top quark. The relative strength of the scalar and pseudoscalar components is regulated by an angle $\alpha$. Observables sensitive to the nature of the top-quark Yukawa coupling are proposed. These observables are defined in terms of the transverse and longitudinal projections of $t$, $\bar{t}$ and $h$ momenta with respect to the beam axis in the $t{\bar t} h$ rest frame. Distributions differential with respect to those observables are evaluated up to NLO in QCD. These distributions are found to be sensitive to the $CP$ nature of the coupling. Dileptonic final states of the $t{\bar t} h$ system (with $h\rightarrow b\bar b$) are used, after fast DELPHES detector simulation and full event reconstruction through a kinematic fit, as a case study to test the observables' sensitivity to the $CP$ nature of the coupling. Confidence levels are presented as a function of the total integrated LHC luminosity for the case of exclusion of a pure $CP$-odd coupling against the Standard Model $CP$-even hypothesis. By using observables evaluated in the $t{\bar t} h$ system, the luminosity needed to directly probe the $CP$ properties of the top-quark Yukawa coupling at the High-Luminosity run of the LHC can be decreased by a few hundred inverse femtobarns, when compared to analyses that use observables in the laboratory rest frame. In addition, transverse momentum distributions of the $h$ boson and top quarks are found to provide no more discriminant power than a counting experiment., Comment: 15 pages, 14 figures

This work studies the associated production of a top-quark pair with a $W$, $Z$, or Higgs boson at the LHC. Predictions for the total cross sections as well as for several differential distributions of the massive particles in the final state are provided. These predictions, valid for the LHC operating at $13$ TeV, include without any approximation all the NLO electroweak and QCD contributions of $\mathcal{O}(\alpha_s^{i} \alpha^{j+1})$ with $i+j=2,3$. In addition, the predictions presented here improve upon the NLO QCD results by adding the effects of soft gluon emission corrections resummed to next-to-next-to-leading logarithmic accuracy. The residual dependence of the predictions on scale and PDF choices is analyzed., Comment: 44 pages, 8 figures

We present the analytic calculation of the Master Integrals for the two-loop, non-planar topologies that enter the calculation of the amplitude for top-quark pair hadroproduction in the quark-annihilation channel. Using the method of differential equations, we expand the integrals in powers of the dimensional regulator $\epsilon$ and determine the expansion coefficients in terms of generalized harmonic polylogarithms of two dimensionless variables through to weight four., Comment: 28 pages, 2 figures, ancillary files included

The successful operation of the Large Hadron Collider (LHC) and the excellent performance of the ATLAS, CMS, LHCb and ALICE detectors in Run-1 and Run-2 with $pp$ collisions at center-of-mass energies of 7, 8 and 13 TeV as well as the giant leap in precision calculations and modeling of fundamental interactions at hadron colliders have allowed an extraordinary breadth of physics studies including precision measurements of a variety physics processes. The LHC results have so far confirmed the validity of the Standard Model of particle physics up to unprecedented energy scales and with great precision in the sectors of strong and electroweak interactions as well as flavour physics, for instance in top quark physics. The upgrade of the LHC to a High Luminosity phase (HL-LHC) at 14 TeV center-of-mass energy with 3 ab$^{-1}$ of integrated luminosity will probe the Standard Model with even greater precision and will extend the sensitivity to possible anomalies in the Standard Model, thanks to a ten-fold larger data set, upgraded detectors and expected improvements in the theoretical understanding. This document summarises the physics reach of the HL-LHC in the realm of strong and electroweak interactions and top quark physics, and provides a glimpse of the potential of a possible further upgrade of the LHC to a 27 TeV $pp$ collider, the High-Energy LHC (HE-LHC), assumed to accumulate an integrated luminosity of 15 ab$^{-1}$., Comment: Report from Working Group 1 on the Physics of the HL-LHC, and Perspectives at the HE-LHC

A new algorithm is presented to perform the full kinematic reconstruction of top quark pair events produced at future electron-positron colliders in the case of dilepton decays of the $W$ bosons to electrons or muons. The momentum components of the undetected neutrino and anti-neutrino in the event are reconstructed by employing several kinematic conditions comprising a non-linear system of six equations. This system is solved numerically using two independent methods and the selection of the best candidate real solution for each event is determined by a likelihood discriminant. Results are presented for several reconstructed kinematic properties of the $W^\pm$ bosons, top (and anti-top) quarks using generator level information produced at leading order., Comment: 8 pages, 7 figures

The discovery of the Higgs boson in 2012, by the ATLAS and CMS experiments, was a success achieved with only a percent of the entire dataset foreseen for the LHC. It opened a landscape of possibilities in the study of Higgs boson properties, Electroweak Symmetry breaking and the Standard Model in general, as well as new avenues in probing new physics beyond the Standard Model. Six years after the discovery, with a conspicuously larger dataset collected during LHC Run 2 at a 13 TeV centre-of-mass energy, the theory and experimental particle physics communities have started a meticulous exploration of the potential for precision measurements of its properties. This includes studies of Higgs boson production and decays processes, the search for rare decays and production modes, high energy observables, and searches for an extended electroweak symmetry breaking sector. This report summarises the potential reach and opportunities in Higgs physics during the High Luminosity phase of the LHC, with an expected dataset of pp collisions at 14 TeV, corresponding to an integrated luminosity of 3 ab$^{-1}$. These studies are performed in light of the most recent analyses from LHC collaborations and the latest theoretical developments. The potential of an LHC upgrade, colliding protons at a centre-of-mass energy of 27 TeV and producing a dataset corresponding to an integrated luminosity of 15 ab$^{-1}$, is also discussed., Comment: Report from Working Group 2 on the Physics of the HL-LHC, and Perspectives at the HE-LHC, 364 pages

We describe predictions for top-quark pair differential distributions at hadron colliders, which combine state-of-the-art NNLO QCD calculations and NLO electroweak corrections together with double resummation at NNLL$'$ accuracy of threshold logarithms and small-mass logarithms. This is the first time that such a combination has appeared in the literature. Numerical results are presented for the invariant-mass distribution, the transverse-momentum distribution as well as rapidity distributions., Comment: Contribution to the proceedings of the 11th International Workshop on Top Quark Physics (TOP2018); v3: significantly modified version with more numeric results

We evaluate analytically the master integrals for double real radiation emission in the b --> u W* decay, where b and u are a massive and massless quark, respectively, while W* is an off-shell charged weak boson. Since the W boson can subsequently decay in a lepton anti-neutrino pair, the results of the present paper constitute a further step toward a fully analytic computation of differential distributions for the semileptonic decay of a b quark at NNLO in QCD. The latter partonic process plays a crucial role in the study of inclusive semileptonic charmless decays of B mesons. Our results are expressed in terms of multiple polylogarithms of maximum weight four., Comment: 21 pages, 6 figures, 2 tables

We construct predictions for top quark pair differential distributions at hadron colliders that combine state-of-the-art NNLO QCD calculations with double resummation at NNLL' accuracy of threshold logarithms arising from soft gluon emissions and of small mass logarithms. This is the first time a resummed calculation at full NNLO+NNLL' accuracy in QCD for a process with non-trivial color structure has been completed at the differential level. Of main interest to us is the stability of the M_{tt} and top-quark p_T distributions in the boosted regime where fixed order calculations may become strongly dependent on the choice of dynamic scales. With the help of numeric and analytic arguments we confirm that the choice for the factorization and renormalization scales advocated recently by some of the authors is indeed optimal. We further derive a set of optimized kinematics-dependent scales for the matching functions which appear in the resummed calculations. Our NNLO+NNLL' prediction for the top-pair invariant mass is significantly less sensitive to the choice of factorization scale than the fixed order prediction, even at NNLO. Notably, the resummed and fixed order calculations are in nearly perfect agreement with each other in the full M_{tt} range when the optimal dynamic scale is used. For the top-quark p_T distribution the resummation performed here has less of an impact and instead we find that upgrading the matching with fixed-order from NLO+NNLL' to NNLO+NNLL' to be an important effect, a point to be kept in mind when using NLO-based Monte Carlo event generators to calculate this distribution., Comment: 45 pages, 12 figures, 2 tables. Updated formatting and included a new appendix. Matches journal version

In this presentation, we will focus on a recent applications of the GoSam 2.0 automated framework which goes beyond the official scope of this code, originally designed for one-loop fixed order calculations. In particular, we describe a customized version of GoSam that has been recently employed to study the production of a top-antitop pair in association with a vector boson or with the Higgs boson to next-to-next-to-leading logarithmic accuracy. In the context of these calculations, the modified version of GoSam was used to evaluate the NLO hard functions which are needed to carry out the resummation of soft gluon emission effects. We also briefly comment on the ongoing efforts to generalize integrand reduction and unitarity for higher order calculation, towards the goal of developing efficient alternative computational techniques for the evaluation of scattering amplitudes beyond one loop., Comment: 10 pages, 1 figure, to appear in the proceedings of The European Physical Society Conference on High Energy Physics, 5-12 July 2017, Venice, Italy

We study the production of a Higgs boson in association to a top-antitop pair at the Large Hadron Collider. We show how precise predictions for the differential distributions with respect to the transverse momentum of the Higgs boson, to the invariant mass of the top-antitop-Higgs system and to the invariant mass of the top-antitop pair can provide useful information on the possible presence of a pseudoscalar component in the coupling of the top quark with the Higgs boson. We evaluate the production of a top-antitop pair and a Higgs boson to next-to-leading order in fixed order perturbation theory and we carry out the resummation of soft emission corrections to next-to-leading-logarithmic accuracy for the LHC operating at a center of mass energy of $13$ TeV. We discuss how the shape of these distributions can be employed experimentally, making a physics case for the kinematic reconstruction of dilepton channels., Comment: 13 pages, 9 figures

We study the resummation of soft gluon emission corrections to the production of a top-antitop pair in association with a Z boson at the Large Hadron Collider to next-to-next-to-leading logarithmic accuracy. By means of an in-house parton level Monte Carlo code we evaluate the resummation formula for the total cross section and several differential distributions at a center-of-mass energy of 13 TeV, and we match these calculations to next-to-leading order results., Comment: 21 pages, 7 figures. arXiv admin note: text overlap with arXiv:1611.00049

We study the resummation of soft gluon emission corrections to the production of a top-antitop pair in association with a Higgs boson at the Large Hadron Collider. Starting from a soft-gluon resummation formula derived in previous work, we develop a bespoke parton-level Monte Carlo program which can be used to calculate the total cross section along with differential distributions. We use this tool to study the phenomenological impact of the resummation to next-to-next-to-leading logarithmic (NNLL) accuracy, finding that these corrections increase the total cross section and the differential distributions with respect to NLO calculations of the same observables., Comment: 26 pages, 9 figures. A few typos and an incorrect reference were fixed

This Report summarizes the results of the activities of the LHC Higgs Cross Section Working Group in the period 2014-2016. The main goal of the working group was to present the state-of-the-art of Higgs physics at the LHC, integrating all new results that have appeared in the last few years. The first part compiles the most up-to-date predictions of Higgs boson production cross sections and decay branching ratios, parton distribution functions, and off-shell Higgs boson production and interference effects. The second part discusses the recent progress in Higgs effective field theory predictions, followed by the third part on pseudo-observables, simplified template cross section and fiducial cross section measurements, which give the baseline framework for Higgs boson property measurements. The fourth part deals with the beyond the Standard Model predictions of various benchmark scenarios of Minimal Supersymmetric Standard Model, extended scalar sector, Next-to-Minimal Supersymmetric Standard Model and exotic Higgs boson decays. This report follows three previous working-group reports: Handbook of LHC Higgs Cross Sections: 1. Inclusive Observables (CERN-2011-002), Handbook of LHC Higgs Cross Sections: 2. Differential Distributions (CERN-2012-002), and Handbook of LHC Higgs Cross Sections: 3. Higgs properties (CERN-2013-004). The current report serves as the baseline reference for Higgs physics in LHC Run 2 and beyond., Comment: 869 pages, 295 figures, 248 tables and 1645 citations. Working Group web page: https://twiki.cern.ch/twiki/bin/view/LHCPhysics/LHCHXSWG

We consider soft gluon emission corrections to the production of a top-antitop pair in association with a W boson at the Large Hadron Collider. We obtain a soft-gluon resummation formula for this production process which is valid up to next-to-next-to-leading logarithmic accuracy. We evaluate the soft gluon resummation formula in Mellin space by means of an in-house parton level Monte Carlo code which allows us to obtain predictions for the total cross section as well as for several differential distributions. We study the impact of the soft-gluon resummation corrections in comparison to fixed order calculations., Comment: 31 pages, 8 figures and 5 tables

We present new results for QCD corrections to the top-pair invariant mass and top-quark $p_T$ distributions in boosted top-quark pair production at hadron colliders. They are derived from a formalism which allows the joint resummation of soft and small-mass logarithms at NNLL$'$ order, thus taking into account all potentially large corrections in the boosted regime, where the partonic center-of-mass energy is parameterically much larger than the mass of the top quark. We match these results with those from standard soft-gluon resummation away from the small-mass limit to NNLL order and also with NLO fixed-order calculations, so that our results are valid in the maximum possible range of phase space. The resummation effects on the $p_T$ and top-pair invariant mass distributions are significant, bringing theory predictions into better agreement with experimental data compared to pure NLO calculations., Comment: 7 pages, 1 figure, Talk given at TOP 2015, 8th International Workshop on Top Quark Physics, 14-18 September 2015, Ischia, Italy

We consider soft gluon emission corrections to the production of a top-antitop pair in association with a Higgs boson at hadron colliders. In particular, we present a soft-gluon resummation formula for this production process and gather all elements needed to evaluate it at next-to-next-to-leading logarithmic order. We employ these results to obtain approximate next-to-next-to-leading order (NNLO) formulas, and implement them in a bespoke parton-level Monte Carlo program which can be used to calculate the total cross section along with arbitrary differential distributions. We use this tool to study the phenomenological impact of the approximate NNLO corrections, finding that they increase the total cross section and the differential distributions which we evaluated in this work., Comment: 35 pages, 5 tables and 12 figures. Version published in JHEP 1603 (2016) 124

Weak radiative decays of the B mesons belong to the most important flavor changing processes that provide constraints on physics at the TeV scale. In the derivation of such constraints, accurate standard model predictions for the inclusive branching ratios play a crucial role. In the current Letter we present an update of these predictions, incorporating all our results for the O(alpha_s^2) and lower-order perturbative corrections that have been calculated after 2006. New estimates of nonperturbative effects are taken into account, too. For the CP- and isospin-averaged branching ratios, we find B_{s gamma} = (3.36 +_ 0.23) * 10^-4 and B_{d gamma} = 1.73^{+0.12}_{-0.22} * 10^-5, for E_gamma > 1.6GeV. Both results remain in agreement with the current experimental averages. Normalizing their sum to the inclusive semileptonic branching ratio, we obtain R_gamma = ( B_{s gamma} + B_{d gamma})/B_{c l nu} = (3.31 +_ 0.22) * 10^-3. A new bound from B_{s gamma} on the charged Higgs boson mass in the two-Higgs-doublet-model II reads M_{H^+} > 480 GeV at 95%C.L., Comment: journal version, 5 pages, no figures

These lectures provide an introduction to Soft-Collinear Effective Theory. After discussing the expansion of Feynman diagrams around the high-energy limit, the effective Lagrangian is constructed, first for a scalar theory, then for QCD. The underlying concepts are illustrated with the Sudakov form factor, i.e. the quark vector form factor at large momentum transfer. We then apply the formalism in two examples: We perform soft gluon resummation as well as transverse-momentum resummation for the Drell-Yan process using renormalization group evolution in SCET, and we derive the infrared structure of n-point gauge theory amplitudes by relating them to effective theory operators. We conclude with an overview of the different applications of the effective theory., Comment: 172 pages, 28 figures, 1 table. v3: corrected typos found by readers over the years

We derive the hard functions for all 2->2 processes in massless QCD up to next-to-next-to-leading order (NNLO) in the strong coupling constant. By employing the known one- and two-loop helicity amplitudes for these processes, we obtain analytic expressions for the ultraviolet and infrared finite, minimally subtracted hard functions, which are matrices in color space. These hard functions will be useful in carrying out higher-order resummations in processes such as dijet and highly energetic top-quark pair production by means of soft-collinear effective theory methods., Comment: 20 pages

We review a Soft Collinear Effective Theory approach to the study of factorization and resummation of QCD effects in top-quark pair production. In particular, we consider differential cross sections such as the top-quark pair invariant mass distribution and the top-quark transverse momentum and rapidity distributions. Furthermore, we focus our attention on the large invariant mass and large transverse momentum kinematic regions, characteristic of boosted top quarks. We discuss the factorization of the differential cross section in the double soft gluon emission and small top-quark mass limit, both in Pair Invariant Mass (PIM) and One Particle Inclusive (1PI) kinematics. The factorization formulas can be employed in order to implement the simultaneous resummation of soft emission and small mass effects up to next-to-next-to-leading logarithmic accuracy. The results are also used to construct improved next-to-next-to-leading order approximations for the differential cross sections., Comment: 6 pages. Proceedings of the Second Annual Conference on Large Hadron Collider Physics (LHCP 2014), Columbia University, New York, June 2-7, 2014

If supersymmetry near the TeV scale is realized in Nature, the pair production of scalar top squarks is expected to be observable at the Large Hadron Collider. Recently, effective field-theory methods were employed to obtain approximate predictions for the cross section for this process, which include soft-gluon emission effects up to next-to-next-to-leading order (NNLO) in perturbation theory. In this work we employ the same techniques to resum soft-gluon emission effects to all orders in perturbation theory and with next-to-next-to-logarithmic (NNLL) accuracy. We analyze the effects of NNLL resummation on the stop-pair production cross section by obtaining NLO+NNLL predictions in pair invariant mass and one-particle inclusive kinematics. We compare the results of these calculations to the approximate NNLO predictions for the cross sections., Comment: 25 pages, 6 figures

This report summarizes the work of the Energy Frontier Top Quark working group of the 2013 Community Summer Study (Snowmass).

We study single-particle inclusive (1PI) distributions in top-quark pair production at hadron colliders, working in the highly boosted regime where the top-quark p_T is much larger than its mass. In particular, we derive a novel factorization formula valid in the small-mass and soft limits of the differential partonic cross section. This provides a framework for the simultaneous resummation of soft gluon corrections and small-mass logarithms, and also an efficient means of obtaining higher-order corrections to the differential cross section in this limit. The result involves five distinct one-scale functions, three of which arise through the subfactorization of soft real radiation in the small-mass limit. We list the NNLO corrections to each of these functions, building on results in the literature by performing a new calculation of a soft function involving four light-like Wilson lines to this order. We thus obtain a nearly complete description of the small-mass limit of the differential partonic cross section at NNLO near threshold, missing only terms involving closed top-quark loops in the virtual corrections., Comment: 36 pages

We calculate the two-loop corrections to heavy-quark pair production in the gluon fusion channel which arise from diagrams involving a closed light-quark loop. The calculation is carried out by keeping the exact dependence on the heavy-quark mass. The analytic results are written in terms of logarithms, classical polylogarithms Li_n (n=2,3,4), and genuine multiple polylogarithms Li_{2,2}. The functional arguments are rational expressions of two independent external invariants and they are chosen in such a way that the functions are real in all the physical phase-space points. Through systematic changes in the functional basis, we obtain expansions of the results in both the production threshold and small mass limits., Comment: 25 pages, 3 figures, ancillary files with results

We derive closed expressions and useful expansions for the contributions of the tree-level W-boson propagator to the the muon and tau leptonic decay rates. Calling M and m the masses of the initial and final charged leptons, our results in the limit m=0 are valid to all orders in M^2/M_W^2. In the terms of O(m_j^2/M_W^2) (m_j=M,m), our leading corrections, of O(M^2/M_W^2), agree with the canonical value (3/5) M^2/M_W^2, while the coefficient of our subleading contributions, of O(m^2/M_W^2), differs from that reported in the recent literature. A possible explanation of the discrepancy is presented. The numerical effect of the O(m_j^2/M_W^2) corrections is briefly discussed. A general expression, valid for arbitrary values of M_W, M and m in the range M_W>M>m, is given in the Appendix. The paper also contains a review of the traditional definition and evaluation of the Fermi constant., Comment: 5 pages

We obtain a soft plus virtual approximation to the NNLO QCD contributions to the top-pair invariant mass distribution at hadron colliders. It is valid up to corrections of order m_t^2/M^2, with M the pair invariant mass. This is currently the most complete QCD calculation for a differential cross section in top-quark pair production, and is useful for describing the high invariant mass region characteristic of boosted top quarks. We use our results to construct an improved NNLO approximation for the pair invariant mass distribution and compare it with previous, less complete approximations based on logarithmic terms from NNLL soft-gluon resummation alone. We find that the new NNLO approximation produces moderate enhancements of the differential cross section compared to previous ones, the effect being slightly more important at low values of invariant mass than at high ones. On the other hand, at high values of invariant mass the new NNLO corrections are dominated by even higher-order effects included in NNLL soft-gluon resummation, reaffirming the need for resummation in describing the highly boosted regime., Comment: 23 pages, 5 tables, 1 figure; version published in JHEP

If the minimal supersymmetric standard model at scales of around 1 TeV is realized in nature, the total top-squark pair production cross section should be measurable at the CERN Large Hadron Collider. In this work we present precise predictions for this observable, which are based upon approximate NNLO formulas obtained using soft-collinear effective theory methods., Comment: 36 pages, 7 figures and 11 tables. Version published in JHEP 1307 (2013) 042

This talk reviews the Standard Model predictions for the top-quark forward backward and charge asymmetries measured at the Tevatron and at the LHC., Comment: 8 pages, 2 figures. Proceedings of CKM 2012, the 7th International Workshop on the CKM Unitarity Triangle, University of Cincinnati, USA, 28 September - 2 October 2012

Assuming that the recently discovered particle at LHC is the Standard Theory (ST) Higgs Boson, we compare the ST predictions of M_W and Sin^2 theta^lept_eff with the experimental values of these basic observables. While the Sin^2 theta^lept_eff prediction is in excellent agreement with its experimental value, that of M_W shows a 1.33 sigma deviation. Implications of these comparisons for possible future developments at LHC and a future GigaZ linear collider are briefly discussed. It is also pointed out that these comparisons are consistent with the conjecture that the newly discovered particle is indeed the ST Higgs boson., Comment: 2 pages

The aim of this article is to review the very important role played by radiative corrections in precision electroweak physics, in the framework of both the Fermi Theory of Weak Interactions and the Standard Theory of Particle Physics. Important theoretical developments, closely connected with the study and applications of the radiative corrections, are also reviewed. The role of radiative corrections in the analysis of some important signals of new physics is also discussed., Comment: 47 pages, to be published in Reviews of Modern Physics

At high values of the pair invariant mass the differential cross section for top-quark pair production at hadron colliders factorizes into soft, hard, and fragmentation functions. In this paper we calculate the next-to-next-to-leading-order (NNLO) corrections to the soft function appearing in this factorization formula, thus providing the final piece needed to evaluate at NNLO the differential cross section in the virtual plus soft approximation in the large invariant-mass limit. Technically, this amounts to evaluating the vacuum expectation value of a soft Wilson loop operator built out of light-like Wilson lines for each of the four partons participating in the hard scattering process, with a certain constraint on the total energy of the soft radiation. Our result turns out to be surprisingly simple, because in the sum of all graphs the three and four parton contributions multiply color structures whose coefficients are governed by the non-abelian exponentiation theorem., Comment: 18 pages main text, 11 pages appendix

We investigate the production of highly energetic top-quark pairs at hadron colliders, focusing on the case where the invariant mass of the pair is much larger than the mass of the top quark. In particular, we set up a factorization formalism appropriate for describing the differential partonic cross section in the double soft and small-mass limit, and explain how to resum simultaneously logarithmic corrections arising from soft gluon emission and from the ratio of the pair-invariant mass to that of the top quark to next-to-next-to-leading logarithmic accuracy. We explore the implications of our results on approximate next-to-next-to-leading order formulas for the differential cross section in the soft limit, pointing out that they offer a simplified calculational procedure for determining the currently unknown delta-function terms in the limit of high invariant mass., Comment: 32 pages

The current theoretical predictions for the observables related to the top-quark pair and the single-top productions at hadron colliders are briefly reviewed. The theoretical predictions are compared to the experimental measurements carried out at the Tevatron and the LHC., Comment: To appear in the proceedings of the XXIst International Europhysics Conference on High Energy Physics, EPS-HEP2011. Extended version. 12 pages

We make use of recent results in effective theory and higher-order perturbative calculations to improve the theoretical predictions of the QCD contribution to the top-quark pair production forward-backward asymmetry at the Tevatron. In particular, we supplement the fixed-order NLO calculation with higher-order corrections from soft gluon resummation at NNLL accuracy performed in two different kinematic schemes, which allows us to make improved predictions for the asymmetry in the $p\bar p$ and $t\bar t$ rest frames as a function of the rapidity and invariant mass of the $t\bar t$ pair. Furthermore, we provide binned results which can be compared with the recent measurements of the forward-backward asymmetry in events with a large pair invariant mass or rapidity difference. Finally, we calculate at NLO+NNLL order the top-quark charge asymmetry at the LHC as a function of a lower rapidity cut-off for the top and antitop quarks., Comment: 12 pages, 6 figures, 4 tables

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., Comment: 9 pages

We use techniques from soft-collinear effective theory (SCET) to derive renormalization-group improved predictions for single-particle inclusive (1PI) observables in top-quark pair production at hadron colliders. In particular, we study the top-quark transverse-momentum and rapidity distributions, the forward-backward asymmetry at the Tevatron, and the total cross section at NLO+NNLL order in resummed perturbation theory and at approximate NNLO in fixed order. We also perform a detailed analysis of power corrections to the leading terms in the threshold expansion of the partonic hard-scattering kernels. We conclude that, although the threshold expansion in 1PI kinematics is susceptible to numerically significant power corrections, its predictions for the total cross section are in good agreement with those obtained by integrating the top-pair invariant-mass distribution in pair invariant-mass kinematics, as long as a certain set of subleading terms appearing naturally within the SCET formalism is included., Comment: 55 pages, 14 figures, 6 tables

The status of the theoretical predictions for the top-anti top production in hadronic collisions is shortly reviewed, paying a articular attention to the analytic calculation of the two-loop QCD corrections to the parton-level matrix elements., Comment: Talk presented at the 35th International Conference of High Energy Physics - ICHEP2010, July 22-28, 2010, Paris France