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Articles 181 - 210 of 332

Full-Text Articles in Quantum Physics

Finite Volume Matrix Elements Of Two-Body States, Alessandro Baroni, Raúl A. Briceño, Maxwell T. Hansen, Filipe G. Ortega-Gama Jan 2019

Finite Volume Matrix Elements Of Two-Body States, Alessandro Baroni, Raúl A. Briceño, Maxwell T. Hansen, Filipe G. Ortega-Gama

Physics Faculty Publications

In this talk, we present a framework for studying structural information of resonances and bound states coupling to two-hadron scattering states. This makes use of a recently proposed finite-volume formalism to determine a class of observables that are experimentally inaccessible but can be accessed via lattice QCD. In particular, we shown that finite-volume two-body matrix elements with one current insertion can be directly related to scattering amplitudes coupling to the external current. For two-hadron systems with resonances or bound states, one can extract the corresponding form factors of these from the energy-dependence of the amplitudes.

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Progress Report On The Relativistic Three-Particle Quantization Condition, Tyler D. Blanton, Raúl A. Briceño, Maxwell T. Hanson, Fernando Romero-Lopez, Stephen R. Sharpe Jan 2019

Progress Report On The Relativistic Three-Particle Quantization Condition, Tyler D. Blanton, Raúl A. Briceño, Maxwell T. Hanson, Fernando Romero-Lopez, Stephen R. Sharpe

Physics Faculty Publications

We describe recent work on the relativistic three-particle quantization condition, generalizing and applying the original formalism of Hansen and Sharpe, and of Briceño, Hansen and Sharpe. In particular, we sketch three recent developments: the generalization of the formalism to include K-matrix poles; the numerical implementation of the quantization condition in the isotropic approximation; and ongoing work extending the description of the three-particle divergence-free K matrix beyond the isotropic approximation.

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Pdfs In Small Boxes, Raúl A. Briceño, Juan V. Guerrero, Maxwell T. Hansen, Christopher J. Monahan Jan 2019

Pdfs In Small Boxes, Raúl A. Briceño, Juan V. Guerrero, Maxwell T. Hansen, Christopher J. Monahan

Physics Faculty Publications

PDFs can be studied directly using lattice QCD by evaluating matrix elements of non-local operators. A number of groups are pursuing numerical calculations and investigating possible systematic uncertainties. One systematic that has received less attention is the effect of calculating in a finite spacetime volume. Here we present first attempts to assess the role of the finite volume for spatially non-local operators. We find that these matrix elements may suffer from large finite-volume artifacts and more careful investigation is needed.

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Finite Volume Matrix Elements Of Two-Body States With One Current Insertion, Alessandro Baroni, Raúl Briceño, Maxwell Hansen, Felipe Ortega Jan 2019

Finite Volume Matrix Elements Of Two-Body States With One Current Insertion, Alessandro Baroni, Raúl Briceño, Maxwell Hansen, Felipe Ortega

Physics Faculty Publications

No abstract provided.

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The Us Electron Ion Collider Accelerator Designs, A. Seryi, S.V. Benson, S.A. Bogacz, P.D. Brindza, M.W. Brucker, A. Camsonne, E. Daly, P.V. Degtiarenko, Y.S. Derbenev, M. Diefenthaler, J. Dolbeck, R. Ent, R. Fair, D. Fazenbaker, Y. Furletova, B.R. Gamage, D. Gaskell, R.L. Geng, P. Ghoshal, R.C. York, Et Al. Jan 2019

The Us Electron Ion Collider Accelerator Designs, A. Seryi, S.V. Benson, S.A. Bogacz, P.D. Brindza, M.W. Brucker, A. Camsonne, E. Daly, P.V. Degtiarenko, Y.S. Derbenev, M. Diefenthaler, J. Dolbeck, R. Ent, R. Fair, D. Fazenbaker, Y. Furletova, B.R. Gamage, D. Gaskell, R.L. Geng, P. Ghoshal, R.C. York, Et Al.

Physics Faculty Publications

With the completion of the National Academies of Sciences Assessment of a US Electron-Ion Collider, the prospects for construction of such a facility have taken a step forward. This paper provides an overview of the two site-specific EIC designs: JLEIC (Jefferson Lab) and eRHIC (BNL) as well as brief overview of ongoing EIC R&D.

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What Does Kinematical Target Mass Sensitivity In Dis Reveal About Hadron Structure?, E. Moffat, T. C. Rogers, W. Melnitchouk, N. Sato, F. Steffans Jan 2019

What Does Kinematical Target Mass Sensitivity In Dis Reveal About Hadron Structure?, E. Moffat, T. C. Rogers, W. Melnitchouk, N. Sato, F. Steffans

Physics Faculty Publications

We study the role of purely external kinematical approximations in inclusive deep-inelastic lepton–hadron scattering within QCD factorization, and consider factorization with an exact treatment of the target hadron mass. We discuss how an observed phenomenological improvement obtained by accounting for target mass kinematics could be interpreted in terms of general properties of target structure, and argue that such an improvement implies a hierarchy of nonperturbative scales within the hadron.

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Current-Driven Production Of Vortex-Antivortex Pairs In Planar Josephson Junction Arrays And Phase Cracks In Long-Range Order, Francisco Estellés-Duart, Miguel Ortuño, Andrés M. Somoza, Valerii M. Vinokur, Alex Gurevich Oct 2018

Current-Driven Production Of Vortex-Antivortex Pairs In Planar Josephson Junction Arrays And Phase Cracks In Long-Range Order, Francisco Estellés-Duart, Miguel Ortuño, Andrés M. Somoza, Valerii M. Vinokur, Alex Gurevich

Physics Faculty Publications

Proliferation of topological defects like vortices and dislocations plays a key role in the physics of systems with long-range order, particularly, superconductivity and superfluidity in thin films, plasticity of solids, and melting of atomic monolayers. Topological defects are characterized by their topological charge reflecting fundamental symmetries and conservation laws of the system. Conservation of topological charge manifests itself in extreme stability of static topological defects because destruction of a single defect requires overcoming a huge energy barrier proportional to the system size. However, the stability of driven topological defects remains largely unexplored. Here we address this issue and investigate numerically …

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Catalysis Of Stark-Tuned Interactions Between Ultracold Rydberg Atoms, A. L. Win, W. D. Williams, T. J. Carroll, C. I. Sukenik Sep 2018

Catalysis Of Stark-Tuned Interactions Between Ultracold Rydberg Atoms, A. L. Win, W. D. Williams, T. J. Carroll, C. I. Sukenik

Physics Faculty Publications

We have experimentally investigated a catalysis effect in the resonant energy transfer between ultracold 85Rb Rydberg atoms. We studied the time dependence of the process, 34p + 34p → 34s + 35s, and observed an enhancement of 34s state population when 34d state atoms are added. We have also performed numerical model simulations, which are in qualitative agreement with experiment and indicate that the enhancement arises from a redistribution of p-state atoms due to the presence of the d-state atoms.

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Effect Of Self-Bias On Cylindrical Capacitive Discharge For Processing Of Inner Walls Of Tubular Structures-Case Of Srf Cavities, J. Upadhyay, J. Peshl, S. Popović, A.-M. Valente-Feliciano, L. Vušković Aug 2018

Effect Of Self-Bias On Cylindrical Capacitive Discharge For Processing Of Inner Walls Of Tubular Structures-Case Of Srf Cavities, J. Upadhyay, J. Peshl, S. Popović, A.-M. Valente-Feliciano, L. Vušković

Physics Faculty Publications

Cylindrical capacitive discharge is a convenient medium for generating reactive ions to process inner walls superconductive radio-frequency (SRF) cavities. These cavities, used in particle accelerators, presents a three-dimensional structure made of bulk Niobium, with axial cylindrical symmetry. Manufactured cavity walls are covered with Niobium oxides and scattered particulates, which must be removed for desired SRF performance. Cylindrical capacitive discharge in a mixture of Ar and Cl2 is a sole and natural non-wet acid choice to purify the inner surfaces of SRF cavities by reactive ion etching. Coaxial cylindrical discharge is generated between a powered inner electrode and the grounded …

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Electron- And Positron-Impact Ionization Of Inert Gases, R. I. Campeanu, H. R. J. Walters, Colm T. Whelan Jun 2018

Electron- And Positron-Impact Ionization Of Inert Gases, R. I. Campeanu, H. R. J. Walters, Colm T. Whelan

Physics Faculty Publications

Triple-differential cross sections (TDCS) are presented for the electron and positron impact ionization of inert gas atoms in a range of geometries where a number of significant few body effects compete to define the shape of the TDCS. Using both positrons and electrons as projectiles has opened up the possibility of performing complementary studies which could effectively isolate competing interactions which cannot be separately detected in an experiment with a single projectile. A comparison is presented between theory and the recent experiments of [Gavin, deLucio, and DuBois, Phys. Rev. A95, 062703 (2017)] for e± and contrasted with the …

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Power Corrections To Tmd Factorization For Z-Boson Production, I. Balitsky, A. Tatasov May 2018

Power Corrections To Tmd Factorization For Z-Boson Production, I. Balitsky, A. Tatasov

Physics Faculty Publications

A typical factorization formula for production of a particle with a small transverse momentum in hadron-hadron collisions is given by a convolution of two TMD parton densities with cross section of production of the final particle by the two partons. For practical applications at a given transverse momentum, though, one should estimate at what momenta the power corrections to the TMD factorization formula become essential. In this paper we calculate the first power corrections to TMD factorization formula for Z-boson production and Drell-Yan process in high-energy hadron-hadron collisions. At the leading order in Nc power corrections are expressed in …

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Light-Nuclei Spectra From Chiral Dynamics, M. Piarulli, A. Baroni, L. Girlanda, A. Kievsky, A. Lovato, Ewing Lusk, L. E. Marcucci, Steven C. Pieper, R. Schiavilla, M, Viviani, R. B. Wiringa Feb 2018

Light-Nuclei Spectra From Chiral Dynamics, M. Piarulli, A. Baroni, L. Girlanda, A. Kievsky, A. Lovato, Ewing Lusk, L. E. Marcucci, Steven C. Pieper, R. Schiavilla, M, Viviani, R. B. Wiringa

Physics Faculty Publications

In recent years local chiral interactions have been derived and implemented in quantum Monte Carlo methods in order to test to what extent the chiral effective field theory framework impacts our knowledge of few- and many-body systems. In this Letter, we present Green's function Monte Carlo calculations of light nuclei based on the family of local two-body interactions presented by our group in a previous paper in conjunction with chiral three-body interactions fitted to bound- and scattering-state observables in the three-nucleon sector. These interactions include Δ intermediate states in their two-pion-exchange components. We obtain predictions for the energy levels and …

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Isoscalar Ππ; Kk; Ηη Scattering And The Σ; F0; F2 Mesons From Qcd, Raul A. Briceño, Jozef J. Dudek, Robert G. Edwards, David J. Wilson Jan 2018

Isoscalar Ππ; Kk; Ηη Scattering And The Σ; F0; F2 Mesons From Qcd, Raul A. Briceño, Jozef J. Dudek, Robert G. Edwards, David J. Wilson

Physics Faculty Publications

We present the first lattice QCD study of coupled isoscalar ππ;K ¯K; ηη S- and D-wave scattering extracted from discrete finite-volume spectra computed on lattices which have a value of the light quark mass corresponding to mπ ∼ 391 MeV. In the JP = 0+ sector we find analogues of the experimental σ and f0 (980) states, where the σ appears as a stable bound-state below ππ threshold, and, similar to what is seen in experiment, the f0 (980) manifests itself as a dip in the ππ cross section in the vicinity of the …

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Resonances From Lattice Qcd, Raúl A. Briceño Jan 2018

Resonances From Lattice Qcd, Raúl A. Briceño

Physics Faculty Publications

The spectrum of hadron is mainly composed as shortly-lived states (resonance) that decay onto two or more hadrons. These resonances play an important role in a variety of phenomenologically significant processes. In this talk, I give an overview on the present status of a rigorous program for studying of resonances and their properties using lattice QCD. I explain the formalism needed for extracting resonant amplitudes from the finite-volume spectra. From these one can extract the masses and widths of resonances. I present some recent examples that illustrate the power of these ideas. I then explain similar formalism that allows for …

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Scattering Processes And Resonances From Lattice Qcd, Raúl A. Briceño, Jozef J. Dudek, Ross D. Young Jan 2018

Scattering Processes And Resonances From Lattice Qcd, Raúl A. Briceño, Jozef J. Dudek, Ross D. Young

Physics Faculty Publications

The vast majority of hadrons observed in nature are not stable under the strong interaction; rather they are resonances whose existence is deduced from enhancements in the energy dependence of scattering amplitudes. The study of hadron resonances offers a window into the workings of quantum chromodynamics (QCD) in the low-energy nonperturbative region, and in addition many probes of the limits of the electroweak sector of the standard model consider processes which feature hadron resonances. From a theoretical standpoint, this is a challenging field: the same dynamics that binds quarks and gluons into hadron resonances also controls their decay into lighter …

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Pion Distribution Amplitude And Quasidistributions, A. V. Radyushkin Mar 2017

Pion Distribution Amplitude And Quasidistributions, A. V. Radyushkin

Physics Faculty Publications

We extend our analysis of quasidistributions onto the pion distribution amplitude. Using the formalism of parton virtuality distribution amplitudes, we establish a connection between the pion transverse momentum dependent distribution amplitude Ψ(x, k2⊥) and the pion quasidistribution amplitude (QDA) Qπ(y, p3). We build models for the QDAs from the virtuality-distribution-amplitude-based models for soft transverse momentum dependent distribution amplitudes, and analyze the p3 dependence of the resulting QDAs. As there are many models claimed to describe the primordial shape of the pion distribution amplitude, we present the p3-evolution …

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Exomol Line List – Xxi. Nitric Oxide (No), Andy Wong, Sergei N. Yurchenko, Peter Bernath, Holger S.P. Müller, Stephanie Mcconkey, Jonathan Tennyson Jan 2017

Exomol Line List – Xxi. Nitric Oxide (No), Andy Wong, Sergei N. Yurchenko, Peter Bernath, Holger S.P. Müller, Stephanie Mcconkey, Jonathan Tennyson

Chemistry & Biochemistry Faculty Publications

Line lists for the X 2Pi electronic ground state for the parent isotopologue of nitric oxide (14N16O) and five other major isotopologues (14N17O, 14N18O, 15N16O, 15N17O and 15N18O) are presented. The line lists are constructed using empirical energy levels (and line positions) and high-level ab initio intensities. The energy levels were obtained using a combination of two approaches, from an effective Hamiltonian and from solving the rovibronic Schrödinger equation variationally. The effective Hamiltonian model was obtained through a fit …

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Unification Of Gravity And Quantum Theory, Adam Daniels Jan 2017

Unification Of Gravity And Quantum Theory, Adam Daniels

Faculty-Sponsored Student Research & Capstones

An overview of the four fundamental forces of physics as described by the Standard Model (SM) and prevalent unifying theories beyond it is provided. Background knowledge of the particles governing the fundamental forces is provided, as it will be useful in understanding the way in which the unification efforts of particle physics has evolved, either from the SM, or apart from it. It is shown that efforts to provide a quantum theory of gravity have allowed supersymmetry (SUSY) and M-Theory to become two of the prevailing theories for unifying gravity with the remaining non-gravitational forces.

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Quasi-Parton Distribution Fuctions, Momentum Distributions, And Pseudo-Parton Distribution Functions, A. V. Radyushkin Jan 2017

Quasi-Parton Distribution Fuctions, Momentum Distributions, And Pseudo-Parton Distribution Functions, A. V. Radyushkin

Physics Faculty Publications

We show that quasi-parton distribution functions (quasi-PDFs) may be treated as hybrids of PDFs and primordial rest-frame momentum distributions of partons. This results in a complicated convolution nature of quasi-PDFs that necessitates using large p3 ≳ 3 GeV momenta to get reasonably close to the PDF limit. As an alternative approach, we propose using pseudo-PDFs P(x, z²3) that generalize the light-front PDFs onto spacelike intervals and are related to Ioffe-time distributions M(v, z²3), the functions of the Ioffe time v = p3z3 and the distance parameter z²3 with respect to which it …

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Isoscalar 𝜋𝜋 Scattering And The Σ Meson Resonance From Qcd, Raúl A. Briceño, Jozef J. Dudek, Robert G. Edwards, David J. Wilson Jan 2017

Isoscalar 𝜋𝜋 Scattering And The Σ Meson Resonance From Qcd, Raúl A. Briceño, Jozef J. Dudek, Robert G. Edwards, David J. Wilson

Physics Faculty Publications

We present for the first time a determination of the energy dependence of the isoscalar ππ elastic scattering phase shift within a first-principles numerical lattice approach to QCD. Hadronic correlation functions are computed including all required quark propagation diagrams, and from these the discrete spectrum of states in the finite volume defined by the lattice boundary is extracted. From the volume dependence of the spectrum, we obtain the S-wave phase shift up to the KK¯ threshold. Calculations are performed at two values of the u, d quark mass corresponding to mπ=236,391  MeV, and the resulting amplitudes …

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Role Of The Euclidean Signature In Lattice Calculations Of Quasidistributions And Other Nonlocal Matrix Elements, Raúl A. Briceño, Maxwell T. Hansen, Christopher J. Monahan Jan 2017

Role Of The Euclidean Signature In Lattice Calculations Of Quasidistributions And Other Nonlocal Matrix Elements, Raúl A. Briceño, Maxwell T. Hansen, Christopher J. Monahan

Physics Faculty Publications

Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for first-principles calculations of nucleon structure. However, for quantities such as light-front parton distribution functions (PDFs) and generalized parton distributions (GPDs), the restriction to Euclidean time prevents direct calculation of the desired observable. Recently, progress has been made in relating these quantities to matrix elements of spatially nonlocal, zero-time operators, referred to as quasidistributions. Still, even for these time-independent matrix elements, potential subtleties have been identified in the role of the Euclidean signature. In this work, we investigate the analytic behavior of spatially nonlocal correlation functions and demonstrate that …

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Relating The Finite-Volume Spectrum And The Two And Three-Particle S Matrix For Relativistic Systems Of Identical Scalar Particles, Raúl Briceño, Maxwell T. Hansen, Stephen R. Sharpe Jan 2017

Relating The Finite-Volume Spectrum And The Two And Three-Particle S Matrix For Relativistic Systems Of Identical Scalar Particles, Raúl Briceño, Maxwell T. Hansen, Stephen R. Sharpe

Physics Faculty Publications

Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicity L. This gives the relation between the finite-volume spectrum and the infinite-volume 2 → 2, 2 → 3, and 3 → 3 scattering amplitudes for such theories. The result holds for relativistic systems composed of scalar particles with nonzero mass m, whose center of mass energy lies below the four-particle threshold, and for which the two-particle K matrix has no singularities below the three-particle threshold. The quantization condition is exact …

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Rapidity Evolution Of Gluon Tmd From Low To Moderate X, Ian Balitsky Jan 2016

Rapidity Evolution Of Gluon Tmd From Low To Moderate X, Ian Balitsky

Physics Faculty Publications

I discuss how the rapidity evolution of gluon transverse momentum dependent distribution changes from nonlinear evolution at small x ≪ 1 to linear evolution at moderate x ~ 1.

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Structure Constant Of Twist-2 Light Ray Operators In The Regge Limit, Ian Balitsky, Vladimir Kazakov, Evgeny Sobko Jan 2016

Structure Constant Of Twist-2 Light Ray Operators In The Regge Limit, Ian Balitsky, Vladimir Kazakov, Evgeny Sobko

Physics Faculty Publications

We compute the normalized structure constant of three twist-2 operators in N =4 SYM in the leading Balitsky-Fadin-Kuraev-Lipatov (BFKL) approximation at any Nc . The result is applicable to other gauge theories including QCD.

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First Results Of Magnetic Field Penetration Measurements Of Multilayer Sis Structures, O. B. Malyshev, L. Gurran, R. Valizadeh, S. Pattalwar, N. Pattalwar, K. D. Dumbell, A. Gurevich Jan 2016

First Results Of Magnetic Field Penetration Measurements Of Multilayer Sis Structures, O. B. Malyshev, L. Gurran, R. Valizadeh, S. Pattalwar, N. Pattalwar, K. D. Dumbell, A. Gurevich

Physics Faculty Publications

The performance of superconducting RF cavities made of bulk Nb is limited by a breakdown field of Bp ≈200 mT, close to the superheating field for Nb. A potentially promising solution to enhance the breakdown field of the SRF cavities beyond the intrinsic limits of Nb is a multilayer coating suggested in [1]. In the simplest case, such a multilayer may be a superconductor-insulator-superconductor (S-I-S) coating, for example, bulk niobium (S) coated with a thin film of insulator (I) followed by a thin layer of another superconductor (S) which could be e.g. dirty niobium [2]. Here we report the …

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Rapidity Factorization And Evolution Of Gluon Tmds, Ian Balitsky Jan 2016

Rapidity Factorization And Evolution Of Gluon Tmds, Ian Balitsky

Physics Faculty Publications

I discuss how the rapidity evolution of gluon transverse momentum dependent distribution changes from nonlinear evolution at small x « 1 to linear evolution at moderate x ∼ 1.

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From Qcd To Physical Resonances, Daniel R. Bolton, Raúl A. Briceño, David J. Wilson Jan 2016

From Qcd To Physical Resonances, Daniel R. Bolton, Raúl A. Briceño, David J. Wilson

Physics Faculty Publications

In this talk, we present the first chiral extrapolation of a resonant scattering amplitude obtained from lattice QCD. Finite-volume spectra, determined by the Hadron Spectrum Collaboration at mπ = 236 MeV [1], for the isotriplet ππ channel are analyzed using the Lüscher method to determine the infinite-volume scattering amplitude. Unitarized Chiral Perturbation Theory is then used to extrapolate the scattering amplitude to the physical light quark masses. The viability of this procedure is demonstrated by its agreement with the experimentally determined scattering phase shift up to center-of-mass energies of 1.2 GeV. Finally, we analytically continue the amplitude to …

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𝜋𝜋 → 𝜋𝛾* Amplitude And The Resonant 𝜌 → 𝜋𝛾* Transition From Lattice Qcd, Raúl A. Briceño, Jozef J. Dudek, Robert G. Edwards, Christian J. Shultz, Christopher E. Thomas, David J. Wilson Jan 2016

𝜋𝜋 → 𝜋𝛾* Amplitude And The Resonant 𝜌 → 𝜋𝛾* Transition From Lattice Qcd, Raúl A. Briceño, Jozef J. Dudek, Robert G. Edwards, Christian J. Shultz, Christopher E. Thomas, David J. Wilson

Physics Faculty Publications

We present a determination of the P-wave 𝜋𝜋 → 𝜋𝛾⋆ transition amplitude from lattice quantum chromodynamics. Matrix elements of the vector current in a finite volume are extracted from three-point correlation functions, and from these we determine the infinite-volume amplitude using a generalization of the Lellouch-Lüscher formalism. We determine the amplitude for a range of discrete values of the 𝜋𝜋 energy and virtuality of the photon and observe the expected dynamical enhancement due to the ρ resonance. Describing the energy dependence of the amplitude, we are able to analytically continue into the complex energy plane and from the residue …

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Relativistic, Model-Independent, Multichannel 2 → 2 Transition Amplitudes In A Finite Volume, Raúl A. Briceño, Maxwell T. Hansen Jan 2016

Relativistic, Model-Independent, Multichannel 2 → 2 Transition Amplitudes In A Finite Volume, Raúl A. Briceño, Maxwell T. Hansen

Physics Faculty Publications

We derive formalism for determining 2+𝓙 → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or nonidentical and, in the latter case, can be either degenerate or nondegenerate. We further accommodate any number of strongly coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of the ρ-meson form factor, in which the unstable nature of …

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Relating Transverse-Momentum-Dependent And Collinear Factorization Theorems In A Generalized Formalism, J. Collins, L. Gamberg, A. Prokudin, T. C. Rogers, N. Sato, B. Wang Jan 2016

Relating Transverse-Momentum-Dependent And Collinear Factorization Theorems In A Generalized Formalism, J. Collins, L. Gamberg, A. Prokudin, T. C. Rogers, N. Sato, B. Wang

Physics Faculty Publications

We construct an improved implementation for combining transverse-momentum-dependent (TMD) factorization and collinear factorization. TMD factorization is suitable for low transverse momentum physics, while collinear factorization is suitable for high transverse momenta and for a cross section integrated over transverse momentum. The result is a modified version of the standard 𝑊 + 𝑌 prescription traditionally used in the Collins-Soper-Sterman (CSS) formalism and related approaches. We further argue that questions regarding the shape and 𝑄 dependence of the cross sections at lower 𝑄 are largely governed by the matching to the 𝑌 term.

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