An overwhelming number of theoretical predictions for hadron colliders require parton distribution functions (PDFs), which are an important ingredient of theory infrastructure for the next generation of high-energy experiments. This whitepaper summarizes the status and future prospects for determination of high-precision PDFs applicable in a wide range of energies and experiments, in particular in precision tests of the Standard Model and in new physics searches at the high-luminosity Large Hadron Collider and Electron–Ion Collider. We discuss the envisioned advancements in experimental measurements, QCD theory, global analysis methodology, and computing that are necessary to bring unpolarized PDFs in the nucleon to the N2LO and N3LO accuracy in the QCD coupling strength. Special attention is given to the new tasks that emerge in the era of the precision PDF analysis, such as those focusing on the robust control of systematic factors both in experimental measurements and theoretical computations. Various synergies between experimental and theoretical studies of the hadron structure are explored, including opportunities for studying PDFs for nuclear and meson targets, PDFs with electroweak contributions or dependence on the transverse momentum, for incisive comparisons between phenomenological models for the PDFs and computations on discrete lattice, and for cross-fertilization with machine learning/AI approaches.

Germany

S. Amoroso

United States

A. Apyan

Spain

N. Armesto

United Kingdom

R.D. Ball

France

V. Bertone

C. Bissolotti

J. Blümlein

R. Boughezal

Italy

G. Bozzi

D. Britzger

A. Buckley

A. Candido

S. Carrazza

F.G. Celiberto

Türkiye

S. Cerci

Portugal

G. Chachamis

A.M. Cooper-Sarkar

Mexico

A. Courtoy

T. Cridge

J.M. Cruz-Martinez

CERN

F. Giuli

M.G. Guzzi

C. Gwenlan

L.A. Harland-Lang

F. Hekhorn

M. Hentschinski

T.J. Hobbs

S. Hoeche

A. Huss

J. Huston

Poland

S. Jadach

J. Jalilian-Marian

M. Klein

G.K. Krintiras

H.-W. Lin

C. Loizides

Netherlands

G. Magni

B. Malaescu

B. Mistlberger

S. Moch

P.M. Nadolsky

E.R. Nocera

F.I. Olness

F. Petriello

J. Pires

K. Rabbertz

J. Rojo

C. Royon

G. Schnell

C. Schwan

A. Siódmok

D.E. Soper

M. Sutton

R.S. Thorne

M. Ubiali

G. Vita

J.H. Weber

J. Whitehead

K. Xie

C.-P. Yuan

B. Zhou

Snowmass 2021 Whitepaper: Proton Structure at the Precision Frontier

Motivated by the recent work of Brzemiński, Motyka, Sadzikowski and Stebel in [1], where forward Drell–Yan production is studied in proton–proton collisions at the LHC, we improve their calculation by introducing an unintegrated gluon density obtained in [2] from a fit to combined HERA data at small values of Bjorken x. This gluon density was calculated within the BFKL formalism at next-to-leading order with collinear corrections. We show that it generates a good description of the forward Drell–Yan cross section dependence on the invariant mass of the lepton pair both for LHCb and ATLAS data.

D. Gordo Gómez

A. Sabio Vera

Forward Drell–Yan production at the LHC in the BFKL formalism with collinear corrections

We study ratios of azimuthal-angle distributions in Mueller–Navelet jets after imposing a rapidity veto constraint: the minijet radiation activity is restricted to only allow final-state partons separated at least a distance in rapidity b. It is well-known that the asymptotic growth with the rapidity separation of the two tagged jets of the NLLA BFKL Green's function requires a value of <math><mi>b</mi><mo>≃</mo><mi>O</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> in order to avoid unphysical cross sections. We further investigate this point from a phenomenological point of view and work out those values of b which best fit angular distributions measured at the LHC in a realistic set-up where impact factors and parton distribution effects are also taken into account.

F. Caporale

Inclusive dijet hadroproduction with a rapidity veto constraint

We present our predictions for the inclusive production of two heavy quark–antiquark pairs, separated by a large rapidity interval, in the collision of (quasi-)real photons at the energies of LEP2 and of some future electron–positron colliders. We include in our calculation the full resummation of leading logarithms in the center-of-mass energy and a partial resummation of the next-to-leading logarithms, within the Balitsky–Fadin–Kuraev–Lipatov (BFKL) approach.

Russia

D.Yu. Ivanov

B. Murdaca

A. Papa

High-energy resummation in heavy-quark pair photoproduction

Recently, new observables in LHC inclusive events with three tagged jets were proposed. Here, we extend that proposal to events with four tagged jets. The events are characterized by one jet in the forward direction, one in the backward direction with a large rapidity distance Y from the first one and two more jets tagged in more central regions of the detector. In our setup, non-tagged associated mini-jet multiplicity is present and needs to be accounted for by the inclusion of BFKL gluon Green functions. The projection of the cross section on azimuthal-angle components opens up the opportunity for defining new ratios of correlation functions of the azimuthal-angle differences among the tagged jets that can be used as probes of the BFKL dynamics.

Inclusive four-jet production at 7 and 13 TeV: Azimuthal profile in multi-Regge kinematics

We propose the study of new observables in LHC inclusive events with three tagged jets, one in the forward direction, one in the backward direction and both well-separated in rapidity from the each other (Mueller–Navelet jets), together with a third jet tagged in central regions of rapidity. Since non-tagged associated mini-jet multiplicity is allowed, we argue that projecting the cross sections on azimuthal-angle components can provide several distinct tests of the BFKL dynamics. Realistic LHC kinematical cuts are introduced.

BFKL azimuthal imprints in inclusive three-jet production at 7 and 13 TeV

We study the production of MuellerâNavelet jets at 13Â TeV LHC, within collinear factorization and including the BFKL resummation of energy logarithms in the next-to-leading approximation. We calculate several azimuthal correlations for different values of the rapidity separation Y between the two jets and evaluate the effect of excluding those events where, for a given Y , one of the two jets is produced in the central region.

D. Yu. Ivanov

Mueller–Navelet jets at 13 TeV LHC: dependence on dynamic constraints in the central rapidity region

We evaluate differential cross sections for production of four jets in multi-Regge kinematics at a hadron collider. The main focus lies on the azimuthal angle dependences. As in previous studies, the ratios of correlation functions of products of cosines of azimuthal angle differences among the tagged jets offer us the cleanest quantities to compare with the experimental data. The calculations are based on the jet production from a single BFKL ladder with a convolution of three BFKL Green functions where we always have two forward/backward jets tagged in the final state. We also demand the tagging of two further jets in more central regions of the detectors with a relative separation in rapidity from each other, plus the inclusive production of an arbitrary number of mini-jets. We show that dependences on the transverse momenta and rapidity of the two central jets can be a distinct signal of the onset of BFKL dynamics.

Multi-Regge kinematics and azimuthal angle observables for inclusive four-jet production

The production of forward jets separated by a large rapidity gap at LHC, the so-called MuellerâNavelet jets, is a fundamental testfield for perturbative QCD in the high-energy limit. Several analyses have already provided us with evidence about the compatibility of theoretical predictions, based on collinear factorization and BFKL resummation of energy logarithms in the next-to-leading approximation, with the CMS experimental data at 7Â TeV of center-of-mass energy. However, the question if the same data can be described also by fixed-order perturbative approaches has not yet been fully answered. In this paper we provide numerical evidence that the mere use of partially asymmetric cuts in the transverse momenta of the detected jets allows for a clear separation between BFKL-resummed and fixed-order predictions in some observables related with the MuellerâNavelet jet production process.

Mueller–Navelet jets at LHC: BFKL versus high-energy DGLAP