Soft-collinear Effective Theory Research Articles

All order factorization for virtual Compton scattering at next-to-leading power

We discuss all-order factorization for the virtual Compton process at next-to-leading power (NLP) in the ΛQCD/Q and −t\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{-t} $$\\end{document}/Q expansion (twist-3), both in the double-deeply-virtual case and the single-deeply-virtual case. We use the soft-collinear effective theory (SCET) as the main theoretical tool. We conclude that collinear factorization holds in the double-deeply virtual case, where both photons are far off-shell. The agreement is found with the known results for the hard matching coefficients at leading order αs0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\alpha}_s^0 $$\\end{document}, and we can therefore connect the traditional approach with SCET. In the single-deeply-virtual case, commonly called deeply virtual Compton scattering (DVCS), the contribution of non-target collinear regions complicates the factorization. These include momentum modes collinear to the real photon and (ultra)soft interactions between the photon-collinear and target-collinear modes. However, such contributions appear only for the transversely polarized virtual photon at the NLP accuracy and in fact it is the only NLP ~ (ΛQCD/Q)1 ~ (−t\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{-t} $$\\end{document}/Q)1 contribution in that case. We therefore conclude that the DVCS amplitude for a longitudinally polarized virtual photon, where the leading power ~ (ΛQCD/Q)0 ~ (−t\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{-t} $$\\end{document}/Q)0 contribution vanishes, is free of non-target collinear contributions and the collinear factorization in terms of twist-3 GPDs holds in that case as well.

QT spectrum for Higgs boson production via heavy quark annihilation at N3LL′+aN3LO

We study the transverse momentum (qT) spectrum of the Higgs boson produced via the annihilation of massive quarks (s, c, b) in proton-proton collisions. Using soft-collinear effective theory (SCET) and working in the five-flavor scheme, we provide predictions at three-loop order in resummed perturbation theory (N3LL′). We match the resummed calculation to full fixed-order results at next-to-next-to-leading order (NNLO), and introduce a decorrelation method to enable a consistent matching to an approximate N3LO (aN3LO) result. Since the b-quark initiated process exhibits large nonsingular corrections, it requires special care in the matching procedure and estimation of associated theoretical uncertainties, which we discuss in detail. Our results constitute the most accurate predictions to date for these processes in the small qT region and could be used to improve the determination of Higgs Yukawa couplings from the shape of the measured Higgs qT spectrum. Published by the American Physical Society 2024

Factorization of photon induced processes in ultra-peripheral heavy ion collisions

In this study, we investigate photon-photon scattering in ultra-peripheral heavy ion collisions (UPCs). We start by deriving an effective Lagrangian from first principles and then apply factorization techniques from Soft-Collinear effective theory (SCET). This approach allows us to decompose the photon-photon scattering cross-section into two primary factors: the generalized transverse momentum distributions (GTMDs) and the hard scattering amplitude. We further analyze the emission of soft photons by final state leptons, incorporating a soft function into the cross section through an evolution method. Our analysis yields detailed predictions for observable angular correlations among the final state leptons. Specifically, we calculate the angular correlations characterized by the azimuthal parameters 〈cos⁡2ϕ〉 and 〈cos⁡4ϕ〉, highlighting the influence of initial photons polarization and recoil effects from final state soft photons.

Heavy-to-light form factors to three loops

We compute three-loop corrections of O(αs3) to form factors with one massive and one massless quark coupling to an external vector, axialvector, scalar, pseudoscalar, or tensor current. We obtain analytic results for the color-planar contributions, for the contributions of light-quark loops, and the contributions with two heavy-quark loops. For the computation of the remaining master integrals we use the “expand and match” approach which leads to semianalytic results for the form factors. We implement our results in a and a ortran code which allows for fast and precise numerical evaluations in the physically relevant phase space. The form factors are used to compute the hard matching coefficients in Soft-Collinear Effective Theory for all currents. The tensor coefficients at lightlike momentum transfer are used to extract the hard function in B¯→Xsγ to three loops. Published by the American Physical Society 2024

Measurement of groomed event shape observables in deep-inelastic electron-proton scattering at HERA

The H1 Collaboration at HERA reports the first measurement of groomed event shape observables in deep inelastic electron-proton scattering (DIS) at s=319\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s} =319~$$\\end{document}GeV, using data recorded between the years 2003 and 2007 with an integrated luminosity of 351 pb-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{pb}^{-1}$$\\end{document}. Event shapes provide incisive probes of perturbative and non-perturbative QCD. Grooming techniques have been used for jet measurements in hadronic collisions; this paper presents the first application of grooming to DIS data. The analysis is carried out in the Breit frame, utilizing the novel Centauro jet clustering algorithm that is designed for DIS event topologies. Events are required to have squared momentum-transfer Q2>150\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q^2 > 150$$\\end{document} GeV2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^2$$\\end{document} and inelasticity 0.2<y<0.7\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 0.2< y < 0.7$$\\end{document}. We report measurements of the production cross section of groomed event 1-jettiness and groomed invariant mass for several choices of grooming parameter. Monte Carlo model calculations and analytic calculations based on Soft Collinear Effective Theory are compared to the measurements.

The 1 → 3 massive splitting functions from QCD factorization and SCET

Splitting functions are universal functions describing the collinear dynamics of gauge theories, and as such are crucial ingredients for a wide variety of calculations in perturbative QCD. We present analytic results for the triple collinear splitting functions in QCD with a single massive parton. We derive the splitting functions using two distinct methods; first by expanding the squared matrix elements in the collinear limit, and secondly by using soft-collinear effective theory with massive quarks. We find agreement between these two approaches, providing a strong check of our results. Additionally, we also check all iterated and soft limits of our results, finding agreement with predictions from factorization. Our results provide an important ingredient for higher order perturbative calculations involving massive partons, and for the description of the collinear dynamics of heavy flavor jets.

Automated resummation of electroweak Sudakov logarithms in diboson production at future colliders

At energies that are large with respect to the electroweak scale, the electroweak corrections to scattering processes involve large logarithms that have to be resummed to obtain decent predictions. Soft-collinear effective theory (SCET) has been proposed as a suitable framework to allow for this resummation, while retaining non-logarithmic corrections in a consistent way. In this paper, we investigate the approximations needed to use this approach for the calculation of electroweak corrections to off-shell diboson production at high-energy colliders. Upon implementing the method into a Monte-Carlo integration code, we provide resummed predictions for cross sections and distributions at a 3TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3\\,\ ext {TeV} $$\\end{document} lepton collider and a 100TeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$100\\,\ ext {TeV} $$\\end{document} proton collider.

Precision three-dimensional imaging of nuclei using recoil-free jets

In this study, we explore the azimuthal angle decorrelation of lepton-jet pairs in e-p and e-A collisions as a means for precision measurements of the three-dimensional structure of bound and free nucleons. Utilizing soft-collinear effective theory, we perform the first-ever resummation of this process in e-p collisions at NNLL accuracy using a recoil-free jet axis. Our results are validated against Pythia simulations. In e-A collisions, we address the complex interplay between three characteristic length scales: the medium length L, the mean free path of the energetic parton in the medium λ, and the hadronization length Lh. We demonstrate that in the thin-dilute limit, where L ≪ Lh and L ~ λ, this process can serve as a robust probe of the three-dimensional structure for bound nucleons. We conclude by offering predictions for future experiments at the Electron-Ion Collider within this limit.

Effects of renormalon scheme and perturbative scale choices on determinations of the strong coupling from e+e− event shapes

We study the role of renormalon cancellation schemes and perturbative scale choices in extractions of the strong coupling constant αs(mZ) and the leading nonperturbative shift parameter Ω1 from resummed predictions of the e+e− event shape thrust. We calculate the thrust distribution to NL3L′ resummed accuracy in soft-collinear effective theory (SCET) matched to the fixed-order O(αs2) prediction, and perform a new high-statistics computation of the O(αs3) matching in , although we do not include the latter in our final αs fits due to some observed systematics that require further investigation. We are primarily interested in testing the phenomenological impact sourced from varying amongst three renormalon cancellation schemes and two sets of perturbative scale profile choices. We then perform a global fit to available data spanning center-of-mass energies between 35–207 GeV in each scenario. Relevant subsets of our results are consistent with prior SCET-based extractions of αs(mZ), but we are also led to a number of novel observations. Notably, we find that the combined effect of altering the renormalon cancellation scheme and profile parameters can lead to few-percent-level impacts on the extracted values in the αs−Ω1 plane, indicating a potentially important systematic theory uncertainty that should be accounted for. We also observe that fits performed over windows dominated by dijet events are typically of a higher quality than those that extend into the far tails of the distributions, possibly motivating future fits focused more heavily in this region. Finally, we discuss how different estimates of the three-loop soft matching coefficient cS˜3 can also lead to measurable changes in the fitted {αs,Ω1} values. Published by the American Physical Society 2024

Polarized fragmenting jet functions in inclusive and exclusive jet production

In this work, we present a complete theoretical framework for analyzing the distribution of polarized hadrons within jets, with and without measuring the transverse momentum relative to the standard jet axis. Using soft-collinear effective theory (SCET), we derive the factorization and provide the theoretical calculation of both semi-inclusive and exclusive fragmenting jet functions (FJFs) under longitudinal and transverse polarization. With the polarized FJFs, one gains access to a variety of new observables that can be used for extracting both collinear and transverse momentum dependent parton distribution functions (PDFs) and fragmentation functions (FFs). As examples, we provide numerical results for the spin asymmetry ATU,TcosϕS−ϕ̂Sh\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {A}_{TU,T}^{\\cos \\left({\\phi}_S-{\\hat{\\phi}}_{S_h}\\right)} $$\\end{document} from polarized semi-inclusive hadron-in-jet production in polarized pp collisions at RHIC kinematics, where a transversely polarized quark would lead to the transverse spin of the final-state hadron inside the jet and is thus sensitive to the transversity fragmentation functions. Similarly, another spin asymmetry, ATU,Lcosϕq−ϕS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {A}_{TU,L}^{\\cos \\left({\\phi}_q-{\\phi}_S\\right)} $$\\end{document} from polarized exclusive hadron-in-jet production in polarized ep collisions at EIC kinematics would allow us to access the helicity fragmentation functions. These observables demonstrate promising potential in investigating transverse momentum dependent PDFs and FFs and are worthwhile for further measurements.

Probing light quark Yukawa couplings through angularity distributions in Higgs boson decay

We propose to utilize angularity distributions in Higgs boson decay to probe light quark Yukawa couplings at e+e− colliders. Angularities τa are a class of 2-jet event shapes with variable and tunable sensitivity to the distribution of radiation in hadronic jets in the final state. Using soft-collinear effective theory (SCET), we present a prediction of angularity distributions from Higgs decaying to quark and gluon states at e+e− colliders to NNLL + \U0001d4aa(αs) accuracy. Due to the different color structures in quark and gluon jets, the angularity distributions from H → \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q\\overline{q }$$\\end{document} and H → gg show different behaviors and can be used to constrain the light quark Yukawa couplings. We show that the upper limit of light quark Yukawa couplings could be probed to the level of ~ 15% of the bottom quark Yukawa coupling in the Standard Model in a conservative analysis window far away from nonperturbative effects and other uncertainties; the limit can be pushed to ≲ 7 – 9% with better control of the nonperturbative effects especially on gluon angularity distributions and/or with multiple angularities.

Initial-state and final-state effects on hadron production in small collision systems

Heavy meson production in reactions with nuclei is an active new frontier to understand QCD dynamics and the process of hadronization in nuclear matter. Measurements in various colliding systems at RHIC and LHC, including Pb-Pb, Xe-Xe, O-O, p-Pb, and p-O, enable precision tests of the medium-size, temperature, and mass dependencies of the in-medium parton propagation and shower formation. We employ a coupled DGLAP evolution framework that takes advantage of splitting functions recently obtained in softcollinear effective theory with Glauber gluons (SCETG) and hard thermal loop (HTL) motivated collisional energy loss effects. With jet quenching effects constrained to the nuclear modification factor of charged hadrons in Pb-Pb collisions at 5.02 TeV, we present predictions for light and heavy-meson in Xe-Xe, O-O and p-Pb collisions at the LHC.We find that the nuclear modification scales non-trivially with the quark mass and medium properties. In particular, there can be sizeable collision-induced attenuation of heavy mesons in small systems such as oxygen-oxygen and high-multiplicity p-Pb events. Finally, we analyze the impact of different models of initial-state parton dynamics on the search for QGP signatures in small colliding systems.

Transverse-momentum-dependent (TMD) factorization in reactions with nuclei: From Drell-Yan to hadron production

We study cold nuclear matter effects on Drell-Yan production at small and moderate pT in proton/pion-nucleus collisions using a new transversemomentum dependent (TMD) factorization framework. Both collisional broadening and medium-induced radiative corrections in the initial state are considered in the soft-collinear effective theory with Glauber gluons (SCETG) approach. We demonstrate that in-medium bremsstrahlung exhibits rapidity divergences as x → 1 and collinear divergences at the endpoints x = 0, 1 of the medium-induced emission spectra. We further show that the rapidity divergences lead to the Balitsky-Fadin-Kuraev-Lipatov (BFKL) evolution of the collision kernel and can be resummed into the transverse momentum broadening of particle production. In turn, the endpoints divergences of in-medium radiation can be resummed through the collinear evolution of parton densities in nuclear matter. The TMD factorization framework is applied to understand the transverse-momentum spectra of Drell-Yan pair production in pA and πA collisions and provides calculations with improved accuracy for hadron production in cold QCD processes at RHIC and LHC.

Factorization of non-global LHC observables and resummation of super-leading logarithms

We present a systematic formalism based on a factorization theorem in soft-collinear effective theory to describe non-global observables at hadron colliders, such as gap-between-jets cross sections. The cross sections are factorized into convolutions of hard functions, capturing the dependence on the partonic center-of-mass energy ŝ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{\\hat{s}} $$\\end{document}, and low-energy matrix elements, which are sensitive to the low scale Q0 ≪ ŝ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{\\hat{s}} $$\\end{document} characteristic of the veto imposed on energetic emissions into the gap between the jets. The scale evolution of both objects is governed by a renormalization-group equation, which we derive at one-loop order. By solving the evolution equation for the hard functions for arbitrary 2 → M jet processes in the leading logarithmic approximation, we accomplish for the first time the all-order resummation of the so-called “super-leading logarithms” discovered in 2006, thereby solving an old problem of quantum field theory. We study the numerical size of the corresponding effects for different partonic scattering processes and explain why they are sizable for pp → 2 jets processes, but suppressed in H/Z and H/Z + jet production. The super-leading logarithms are given by an alternating series, whose individual terms can be much larger than the resummed result, even in very high orders of the loop expansion. Resummation is therefore essential to control these effects. We find that the asymptotic fall-off of the resummed series is much weaker than for standard Sudakov form factors.

NNLO+PS W+W− production using jet veto resummation at NNLL′

We construct a novel event generator for the process pp→ℓ−ν¯ℓℓ′+νℓ′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ pp\ o {\\ell}^{-}{\\overline{\ u}}_{\\ell }{\\ell^{\\prime}}^{+}{\ u}_{\\ell^{\\prime }} $$\\end{document}, which matches fixed-order predictions at next-to-next-to-leading order in the strong coupling to a parton shower program. The matching is achieved using the Geneva method, in this case exploiting a resummed calculation for the hardest jet transverse momentum at next-to-next-to-leading logarithmic accuracy obtained via soft-collinear effective theory and implemented in the C++ library SCETlib. This choice of resolution variable ensures that the introduction of a jet veto, commonly used by experimental analyses to reject multi-jet background events, does not result in the appearance of unmitigated large logarithms for low veto scales before showering. After validating our partonic results against publicly available fixed order and resummed calculations, we compare our predictions to measurements taken at the ATLAS and CMS experiments, finding good agreement. This is the first NNLO+PS accurate event generator to use the hardest jet transverse momentum as a resolution variable.

Top quark mass calibration for Monte Carlo event generators — an update

We generalize and update our former top quark mass calibration framework for Monte Carlo (MC) event generators based on the e+e− hadron-level 2-jettiness τ2 distribution in the resonance region for boosted tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document} production, that was used to relate the Pythia 8.205 top mass parameter mtMC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {m}_t^{\ extrm{MC}} $$\\end{document} to the MSR mass mtMSRR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {m}_t^{\ extrm{MSR}}(R) $$\\end{document} and the pole mass mtpole\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {m}_t^{\ extrm{pole}} $$\\end{document}. The current most precise direct top mass measurements specifically determine mtMC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {m}_t^{\ extrm{MC}} $$\\end{document}. The updated framework includes the addition of the shape variables sum of jet masses τs and modified jet mass τm, and the treatment of two more gap subtraction schemes to remove the O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(ΛQCD) renormalon related to large-angle soft radiation. These generalizations entail implementing a more versatile shape-function fit procedure and accounting for a certain type of (mt/Q)2 power corrections to achieve gap-scheme and observable independent results. The theoretical description employs boosted heavy-quark effective theory (bHQET) at next-to-next-to-logarithmic order (N2LL), matched to soft-collinear effective theory (SCET) at N2LL and full QCD at next-to-leading order (NLO), and includes the dominant top width effects. Furthermore, the software framework has been modernized to use standard file and event record formats. We update the top mass calibration results by applying the new framework to Pythia 8.305, Herwig 7.2 and Sherpa 2.2.11. Even though the hadron-level resonance positions produced by the three generators differ significantly for the same top mass parameter mtMC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {m}_t^{\ extrm{MC}} $$\\end{document} value, the calibration shows that these differences arise from the hadronization modeling. Indeed, we find that mtMC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {m}_t^{\ extrm{MC}} $$\\end{document} agrees with mtMSR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {m}_t^{\ extrm{MSR}} $$\\end{document}(1 GeV) within 200 MeV for the three generators and differs from the pole mass by 350 to 600 MeV.

Transverse momentum dependent distribution functions in the threshold limit

We apply the joint threshold and transverse momentum dependent (TMD) factorization theorem to introduce new threshold-TMD distribution functions, including threshold-TMD parton distribution functions (PDFs) and fragmentation functions (FFs). We apply Soft-Collinear Effective Theory and renormalization group methods to carry out QCD evolution for both threshold-TMD PDFs and FFs. We show the universality of threshold-TMD functions among three standard processes, i.e. the Drell-Yan production in pp collisions, semi-inclusive deep-inelastic scattering and back-to-back two hadron production in e+e− collisions. In the end, we present the numerical predictions for different threshold-TMD functions and also transverse momentum distributions at pp, ep, and e+e− collisions.

Complete analysis on QED corrections to Bq → τ+τ−

Motivated by a dynamical enhancement of the electromagnetic corrections by a power of ΛQCD/mb in Bd,s→ μ+μ− at next-to-leading order (NLO), we extend the QED factorization effects on the leptonic B meson decays with light muon leptons to tauonic final states, Bd,s→ τ+τ−, using soft-collinear effective theory (SCET). This extension is necessary owing to the appearance of the large τ mass, which will lead to different power counting in SCET and also different results. We provide a complete NLO electromagnetic corrections to Bd,s→ τ+τ−, which include hard functions and hard-collinear functions below the bottom quark mass scale μb. The power enhanced electromagnetic effects from hard-collinear contributions on Bd,s→ μ+μ− discussed before also exist in Bd,s→ τ+τ−. However the logarithm term arising from contributions of hard-collinear photon and lepton virtualities for Bd,s→ τ+τ− is not large as it is in muon case due to the hard-collinear scale of τ mass, which lead to only approximately 0.04% QED corrections to the branching fraction of Bd,s→ τ+τ− compared with overall reduction about 0.5% in Bd,s→ μ+μ−.

QCD resummation of dijet azimuthal decorrelations in pp and pA collisions

We study the azimuthal angular decorrelations of dijet production in both proton-proton (pp) and proton-nucleus (pA) collisions. By utilizing soft-collinear effective theory, we establish the factorization and resummation formalism at the next-to-leading logarithmic accuracy for the azimuthal angular decorrelations in the back-to-back limit in pp collisions. We propose an approach where the nuclear modifications to dijet production in pA collisions are accounted for in the nuclear modified transverse momentum dependent parton distribution functions (nTMDPDFs), which contain both collinear and transverse dynamics. This approach naturally generalizes the well-established formalism related to the nuclear modified collinear parton distribution functions (nPDFs). We demonstrate strong consistency between our methodology and the CMS measurements in both pp and pA collisions, and make predictions for dijet production in the forward rapidity region in pA collisions at LHC kinematics and for mid-rapidity kinematics at sPHENIX. Throughout this paper, we focus on the application of this formalism to a simultaneous fit to both collinear and transverse momentum dependent contributions to the transverse momentum dependent distributions.

Small-x factorization from effective field theory

We derive a factorization theorem that allows for resummation of small-x logarithms by exploiting Glauber operators in the soft collinear effective field theory. Our analysis is carried out for the hadronic tensor Wμν in deep inelastic scattering, and leads to the definition of a new gauge invariant soft function Sμν that describes quark and gluon emission in the central region. This soft function provides a new framework for extending resummed calculations for coefficient functions to higher logarithmic orders. Our factorization also defines impact factors by universal collinear functions that are process independent, for instance being identical in small-x DIS and Drell-Yan.