We present integrated subtraction terms and finite remainders for arbitrary processes with massless partons at hadron and lepton colliders in the context of the nested soft-collinear subtraction scheme. These results provide the very last ingredients needed to make this scheme a fully local, analytic and process-independent framework for treating infrared singularities at next-to-next-to-leading order in perturbative QCD. The explicit infrared finiteness of all required contributions, as well as their process-independence, puts these results on par with subtraction schemes developed for next-to-leading order computations and opens up a clear path towards the automation of next-to-next-to-leading order computations in QCD.

Nearly thirty years ago, Bern, Dixon and Kosower computed all helicity amplitudes for the annihilation of an electron-positron pair into four QCD partons through an electroweak vector boson. More recently, the leading-color two-loop amplitudes for the same process were obtained. When such amplitudes are expressed in the massless spinor-helicity formalism, they effectively correspond to the decay of a transversely polarized vector boson. However, for several reasons, it is highly desirable to extend these calculations to the case where the polarization of the vector boson is longitudinal. Due to the complexity of such computations, repeating them to obtain the result for the ”missing” polarization of the electroweak boson is a significant undertaking even at one loop. Besides, when attempting new higher-loop computations, it is beneficial to identify the minimal set of quantities (e.g. form factors) that must be determined to obtain the full amount of physically-relevant information. In this paper, we show that amplitudes involving vector-boson decays to massless leptons-although they appear to project onto the transverse polarization-still encode the full information about all polarization states of the vector boson, including the longitudinal one. This follows from the little-group (spin) covariance of the amplitude, which allows us-largely through simple replacement rules-to rewrite the helicity amplitudes as a matrix with open SU(2) spin indices in the massive spinor-helicity (or spin-spinor) formalism. Therefore, knowledge of an amplitude for any polarization component suffices to reconstruct the full covariant matrix.

A bstract We present a new method to compute the soft function for the N -Jettiness variable for arbitrary N at high perturbative orders in QCD. It is based on the observation that the most singular part of the soft function, the dipole contribution, can be represented by a sum of an analytically calculable inclusive soft function and a remainder. The latter is absent at NLO, is immediately finite at NNLO, and we expect that can be made finite with the help of simple NLO-like infrared subtractions at N 3 LO. As a byproduct of this approach, we derive a very simple formula for the tripole contribution to the N -Jettiness NNLO soft function, which results in a fast numerical evaluation. We apply this method to compute the N -Jettiness soft function at NNLO, and report numerical results for up to five jets for the hadron-collider soft function. We finally outline the prospects for applications at N 3 LO.

Understanding the infrared sensitivity of perturbative predictions in QCD is important for assessing the magnitude of possible non-perturbative power corrections to processes with large momentum transfer. In renormalon models, this sensitivity can be related to computable dependences of perturbative quantities on a small gluon mass. However, this procedure cannot be applied to collider processes with gluons at the Born level. To address this problem, we promote the gluon mass to a parameter of a consistent non-Abelian quantum field theory where the gauge symmetry is spontaneously broken through the Higgs mechanism. Working in the limit in which the gluon mass m_g is the smallest dimensionful parameter, we compute through two loops the 𝒪(m_g) contributions to the relation between the pole and MS masses of a heavy quark and to the relation between corresponding field counterterms. We expect that the proposed framework will provide a useful laboratory for probing linear infrared sensitivity of collider observables in QCD.

We compute the next-to-leading-power corrections in the N-jettiness variable to the production of a prompt photon and a jet at next-to-leading order in perturbative QCD in the qq annihilation channel. We employ the k⊥ jet algorithm and assume that the N-jettiness value divided by the jet transverse momentum is the smallest parameter in the problem; in particular it should be small compared to the jet radius R.

We estimate the magnitude of the leading non-perturbative QCD corrections to the decays of the Higgs boson to the γZ and γγ final states. These corrections originate from the light-quark contributions to such decays. We show that the non-perturbative effects are suppressed by the small Yukawa couplings of light quarks, but that there is no further quark-mass suppression. This is at variance with what is found in the standard perturbative calculations of the light-quark contributions. We demonstrate that the non-perturbative corrections modify the H → γZ and H → γγ decay rates by 𝒪(10^-5) , well below the expected precision with which such decays can be studied both at the high-luminosity LHC and at future colliders.

We present a semi-analytic calculation of the integrated double-emission eikonal function of two massive emitters whose momenta are at an arbitrary angle to each other. This result is needed for extending the nested soft-collinear subtraction scheme [Eur. Phys. J. C 77 (2017) 248] to processes with massive partons.

Reconstruction of one-dimensional kinematic distributions from calculations based on high-dimensional Monte-Carlo integration is a standard problem in high-energy physics. Traditionally, this is done by collecting randomly-generated events in histograms. In this article, we explore an alternative approach, whose main idea is to approximate the target distribution by a weighted sum of orthogonal basis functions whose coefficients are calculated using the Monte-Carlo integration. This method has the advantage of directly yielding smooth approximations to target distributions. Furthermore, in the context of high-order perturbative calculations with local subtractions, it eliminates the so-called bin-to-bin fluctuations, which often severely affect the quality of conventional histograms. We also demonstrate that the availability of a high-quality approximation to the target distribution, for example the leading-order result in the perturbative expansion, can be exploited to construct an optimized orthonormal basis. We compare the performance of this method to conventional histograms in both toy-model and real Monte-Carlo settings, applying it to Higgs boson production in weak boson fusion as an example.

I review the status of QCD predictions for Standard Model processes at the LHC and emphasize the need for further improvements in the theoretical description of hard hadron collisions.

Recently, we have presented the result for the zero-jettiness soft function at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD [1], without providing technical details of the calculation. The goal of this paper is to describe the most important element of that computation, the triple real-emission contribution. We present a detailed discussion of the many technical aspects of the calculation, for which a number of methodological innovations was required. Although some elements of the calculation were discussed earlier [2–6], this paper is intended to provide a complete summary of the methods used in the computation of the triple real-emission contribution to the soft function.

We derive the neutrino oscillation probability in vacuum using scattering theory methods developed earlier in the context of collider physics [1–3]. It is computed from Feynman diagrams that combine neutrino production and detection processes into a single quantum amplitude. Initial-state particles in the neutrino source and the detector are treated as wave packets. In contrast to many other approaches, we work with transition probabilities, rather than the amplitude itself, and do not specify the form of the wave packets to arrive at the neutrino oscillation formula. Our approach offers a simple and transparent framework to discuss decoherence effects in neutrino oscillations, as well as the effects of the finite lifetime of the neutrino source. The latter are particularly relevant for oscillation experiments using neutrinos from pion decays in flight.

We compute next-to-leading power corrections in the zero-jettiness variable for the production of colorless final states at hadron colliders at next-to-leading order in QCD. To assess if the process-independence of leading power contributions can be extended, we attempt to construct generic expansions of phase spaces and matrix elements squared through next-to-leading power in the zero-jettiness. We highlight challenges associated with the collinear limit, where universality no longer holds at the subleading power, making the result process-dependent. We show that quantities that need to be calculated in the collinear limit can be obtained using Berends-Giele currents, enabling computation of power corrections to high-multiplicity final states. As a concrete example, we apply our method to compute power corrections in the zero-jettiness for lepton pair as well as multi-photon production in qq collisions.

We study the impact of the pointlike qq'WH interactions originating from a subset of dimension-six operators of the Standard Model effective field theory (SMEFT) on the Higgs boson associated production pp -> W+H at the LHC. For consistency, we also take into account the corresponding qq'W vertices implied by these operators. We compute the next-to-next-to-leading order quantum chromodynamics (QCD) corrections to this process and compare these corrections in the Standard Model and SMEFT production mechanisms.

We present an analytic calculation of the integrated double-emission eikonal function of a massive and a massless emitter whose momenta are at an arbitrary angle to each other. This quantity provides one of the required ingredients for extending the nested soft-collinear subtraction scheme to processes with massive final-state particles. To calculate it, we use the standard methodology involving reverse unitarity and its extension to cases with Heaviside functions, integration-by-parts technology and reduction to master integrals, and differential equations. In addition, we also describe a semi-numerical method based on the subtraction of infra-red and collinear singularities from the eikonal function, allowing us to extract divergences of the integrated eikonal function analytically, and to derive a simple integral representation for the finite remainder.

Recently, it was observed that an aggressive cut on the b jets' transverse momenta applied to Higgs boson production in weak-boson fusion followed by the decay H-* bb & strns; leads to very large QCD corrections to the fiducial cross section. In this paper, we show that these corrections are caused by soft and collinear QCD radiation and, therefore, can be efficiently treated by a parton shower. We combine the parton-shower description of the decay H-* bb & strns; with next-to-next-to-leading order QCD corrections to Higgs production in weak-boson fusion and its subsequent decay and demonstrate that the quality of the theoretical prediction is markedly improved even if b jets with rather high transverse momenta are selected. The remaining uncertainty of the theoretical prediction, mainly driven by imprecise modeling of H-* bb & strns; decay, is estimated to be of the order of O(5-7%).

We describe the calculation of integrated subtraction terms in the nested soft-collinear subtraction scheme for hadron collider processes with quarks and gluons, thereby extending the results presented in Ref.[1]. Although this extension eventually proves to be straightforward, it requires a more careful treatment of certain collinear limits to achieve a compact and physically-transparent final result. We also show that the cancellation of infrared divergences can be organized in such a way that, once soft contributions are removed, it occurs independently for each of the external partons. We consider these results to be important stepping stones on the way to deriving finite remainders of the integrated subtraction terms for fully-general hadron collider processes in the context of the nested soft-collinear subtraction scheme.

We present the high-precision result for the zero-jettiness soft function at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. At this perturbative order, the soft function is the last missing ingredient required for the computation of a hadronic color singlet production or a color singlet decay into two jets using the zero-jettiness variable as the slicing parameter. Furthermore, the knowledge of the N3LO soft function enables the resummed description of the thrust distribution in the process e^{+}e^{-}→hadrons through next-to-next-to-next-to-leading logarithmic order, which is important for the extraction of the strong coupling constant using this shape variable. On the methodological side, the complexity of the zero-jettiness variable forced us to develop a new semi-analytic method for phase-space integration in the presence of constraints parameterized through Heaviside functions which, hopefully, will be useful for further development of the N-jettiness slicing scheme.

We study QCD corrections to the process where a Higgs boson is produced in weak boson fusion and then decays into a pair of massive b quarks. We find that typical experimental criteria used to identify b jets in this process affect QCD corrections to the decay, making it necessary to account for them in the proper description of this process. Indeed, if corrections to the production and decay are combined, the fiducial cross section of the weak boson fusion process pp -> H(-> bb)jj is reduced by about 40% relative to leading-order predictions, compared to just about 8% if only corrections to the production process are considered. We investigate the origin of these large corrections through next-to-next-to-leading order and conclude that they appear because a number of independent moderately large effects conspire to significantly reduce the fiducial cross section for this process.

We present an analytic calculation of the one-loop correction to the double-real emission contribution to the zero-jettiness soft function at N3LO in QCD, accounting for both gluon-gluon and quark-antiquark soft final-state partons. We explain all the relevant steps of the computation including the reduction of phase-space integrals to master integrals in the presence of Heaviside functions, and the methods we employed to compute them.

We compute, in the framework of renormalon calculus, the 𝒪(Λ_QCD) corrections to the production of tt pairs in hadron collisions under the assumption that qq→ tt is the dominant partonic channel. This assumption is not applicable to top quark pair production at the LHC but it is valid for the Tevatron where collisions of protons and anti-protons were studied. We show that the linear power correction to the total tt production cross section vanishes provided one uses a short-distance scheme for the top quark mass. We also derive relatively simple formulas for the power corrections to top quark kinematic distributions. Although small numerically, these power corrections exhibit interesting dependencies on top quark kinematics.