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This White Paper presents the community inputs and scientific conclusions from the Hot and Cold QCD Town Meeting that took place September 23-25, 2022 at MIT, as part of the Nuclear Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of 424 physicists registered for the meeting. The meeting highlighted progress in Quantum Chromodynamics (QCD) nuclear physics since the 2015 LRP (LRP15) and identified key questions and plausible paths to obtaining answers to those questions, defining priorities for our research over the coming decade. In defining the priority of outstanding physics opportunities for the future, both prospects for the short (~ 5 years) and longer term (5-10 years and beyond) are identified together with the facilities, personnel and other resources needed to maximize the discovery potential and maintain United States leadership in QCD physics worldwide. This White Paper is organized as follows: In the Executive Summary, we detail the Recommendations and Initiatives that were presented and discussed at the Town Meeting, and their supporting rationales. Section 2 highlights major progress and accomplishments of the past seven years. It is followed, in Section 3, by an overview of the physics opportunities for the immediate future, and in relation with the next QCD frontier: the EIC. Section 4 provides an overview of the physics motivations and goals associated with the EIC. Section 5 is devoted to the workforce development and support of diversity, equity and inclusion. This is followed by a dedicated section on computing in Section 6. Section 7 describes the national need for nuclear data science and the relevance to QCD research., Comment: QCD Town Meeting White Paper, as submitted to 2023 NSAC LRP committee on Feb. 28, 2023

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. [Submitted to the US Community Study on the Future of Particle Physics (Snowmass 2021).], Comment: 83 pages, 27 figures, contribution to Snowmass 2021; v.3: journal version

We use the spinor helicity formalism to calculate the cross section for production of three partons of a given polarization in Deep Inelastic Scattering (DIS) off proton and nucleus targets at small Bjorken x. The target proton or nucleus is treated as a classical color field (shock wave) from which the produced partons scatter multiple times. We reported our result for the final expression for the production cross section and studied the azimuthal angular correlations of the produced partons in [1]. Here we provide the full details of the calculation of the production cross section using the spinor helicity methods., Comment: 26 pages, 24 figures

Azimuthal angular correlations between produced hadrons/jets in high energy collisions are a sensitive probe of the dynamics of QCD at small x. Here we derive the triple differential cross section for inclusive production of 3 polarized partons in DIS at small x using the spinor helicity formalism. The target proton or nucleus is described using the Color Glass Condensate (CGC) formalism. The resulting expressions are used to study azimuthal angular correlations between produced partons in order to probe the gluon structure of the target hadron or nucleus. Our analytic expressions can also be used to calculate the real part of the Next to Leading Order (NLO) corrections to di-hadron production in DIS by integrating out one of the three final state partons., Comment: 5 pages, 6 figures; version accepted for publication in Physics Letters B

This White Paper presents the science case of an Electron-Ion Collider (EIC), focused on the structure and interactions of gluon-dominated matter, with the intent to articulate it to the broader nuclear science community. It was commissioned by the managements of Brookhaven National Laboratory (BNL) and Thomas Jefferson National Accelerator Facility (JLab) with the objective of presenting a summary of scientific opportunities and goals of the EIC as a follow-up to the 2007 NSAC Long Range plan. This document is a culmination of a community-wide effort in nuclear science following a series of workshops on EIC physics and, in particular, the focused ten-week program on "Gluons and quark sea at high energies" at the Institute for Nuclear Theory in Fall 2010. It contains a brief description of a few golden physics measurements along with accelerator and detector concepts required to achieve them, and it benefited from inputs from the users' communities of BNL and JLab. This White Paper offers the promise to propel the QCD science program in the U.S., established with the CEBAF accelerator at JLab and the RHIC collider at BNL, to the next QCD frontier., Comment: The Second Edition, 164 pages

We provide a broad overview of the theoretical status and phenomenological applications of the Color Glass Condensate effective field theory describing universal properties of saturated gluons in hadron wavefunctions that are extracted from deeply inelastic scattering and hadron-hadron collision experiments at high energies., Comment: 41 pages, 18 figures, submitted to the Annual Review of Nuclear and Particle Sciences

This writeup is a compilation of the predictions for the forthcoming Heavy Ion Program at the Large Hadron Collider, as presented at the CERN Theory Institute 'Heavy Ion Collisions at the LHC - Last Call for Predictions', held from May 14th to June 10th 2007., Comment: LaTeX, 185 pages, uses iop styles; writeup of the CERN Theory Institute 'Heavy Ion Collisions at the LHC - Last Call for Predictions', held from May 14th to June 10th 2007

We present results for prompt photon and inclusive $\pi^0$ production in p-p and A-A collisions at RHIC and LHC energies. We include the full next-to-leading order radiative corrections and nuclear effects, such as nuclear shadowing and parton energy loss. We find the next-to-leading order corrections to be large and $p_T$ dependent. We show how measurements of $\pi^0$ production at RHIC and LHC, at large $p_T$, can provide valuable information about the nature of parton energy loss. We calculate the ratio of prompt photons to neutral pions and show that at RHIC energies this ratio increases with $p_T$ approaching one at $p_T \sim 10$ GeV, due to the large suppression of $\pi^0$ production. We show that at the LHC, this ratio has steep $p_T$ dependence and approaches 10% effect at $p_T \sim 20$ GeV., Comment: Talk presented by I. Sarcevic, to appear in the Proceedings of Quark Matter 2002; 4 pages including 4 color figures

We show that particle production in proton-nucleus (pA) collisions in the Color Glass Condensate model can be related to Deep Inelastic Scattering of leptons on protons/nuclei (DIS). The common building block is the quark antiquark (or gluon-gluon) dipole cross section which is present in both DIS and pA processes. This correspondence in a sense generalizes the standard leading twist approach to pA collisions based on collinear factorization and perturbative QCD, and allows one to express the pA cross sections in terms of a universal quantity (dipole cross section) which, in principle, can be measured in DIS or other processes. Therefore, using the parameterization of dipole cross section at HERA, one can calculate particle production cross sections in proton-nucleus collisions at high energies. Alternatively, one could use proton-nucleus experiments to further constrain models of the dipole cross-section. We show that the McLerran-Venugopalan model predicts enhancement of cross sections at large p_t (Cronin effect) and suppression of cross sections at low p_t. The cross over depends on rapidity and moves to higher p_t as one goes to more forward rapidities., Comment: 19 pages, 5 postscript figures

We present results for inclusive $\pi^0$ production in proton-proton and in Au-Au at RHIC energy $\sqrt s=200$ GeV. We use next-to-leading order perturbative QCD calculation and we include nuclear effects such as parton energy loss and nuclear shadowing. We consider the ratio of $\pi^0$ distribution in Au-Au and p-p collisions for $p_T > 3$ GeV for three cases of parton energy loss: 1) constant parton energy loss per parton scattering, $\epsilon^a_n=const$, 2) Landau-Pomeranchuk-Migdal energy-dependent energy loss, $\epsilon^a_n \sim \sqrt E^a_n$ and 3) Bethe-Heitler energy-dependent energy loss, $\epsilon^a_n \sim E^a_n$. We show that recently observed suppression of $\pi^0$ production in Au-Au collisions at RHIC, which is found to increase with $p_T$ increasing from 3GeV to 8GeV, can be reproduced by $\epsilon^a_n=0.06 E^a_n$. We show that the ratio of prompt photons to neutral pions produced in Au-Au collisions at RHIC has a strong $p_T$ dependence approaching one at $p_T\sim 10$GeV., Comment: minor corrections; version accepted for publication in Physics Letters B

We present results for the large-$p_T$ inclusive $\pi^0$ production in p-p and A-A collisions at RHIC and LHC energies. We include the full next-to-leading order radiative corrections, $O(\alpha_s^3)$, and nuclear effects such as parton energy loss and nuclear shadowing. We find the next-to-leading order corrections and the parton energy loss effect to be large and $p_T$ dependent, while the nuclear shadowing effects are small ($< 10%$). We calculate the ratio of prompt photons to neutral pions produced in heavy ion collisions and show that at RHIC energies this ratio increases with $p_T$ approaching one at $p_T \sim 8$ GeV, due to the large suppression of $\pi^0$ production. We show that at the LHC, this ratio has a steep $p_T$ dependence and approaches 25% effect at $p_T \sim 40$ GeV. We discuss theoretical uncertainties inherent in our calculation, such as choice of the renormalization, factorization and fragmentation scales and the K-factors which signify the size of higher-order corrections., Comment: minor corrections, version accepted for publication in Nuclear Physics A

In this summary of the considerations of the QCD working group at Snowmass 2001, the roles of quantum chromodynamics in the Standard Model and in the search for new physics are reviewed, with empahsis on frontier areas in the field. We discuss the importance of, and prospects for, precision QCD in perturbative and lattice calculations. We describe new ideas in the analysis of parton distribution functions and jet structure, and review progress in small-$x$ and in polarization., Comment: Snowmass 2001. Revtex4, 34 pages, 4 figures, revised to include additional references on jets and lattice QCD

We calculate the inclusive cross section for prompt photon production in heavy-ion collisions at RHIC energies ($\sqrt{s}=130$ GeV and $\sqrt{s}=200$ GeV) in the central rapidity region including next-to-leading order, $O(\alpha_{em}\alpha_s^2)$, radiative corrections, initial state nuclear shadowing and parton energy loss effects. We show that there is a significant suppression of the nuclear cross section, up to $\sim 30%$ at $\sqrt{s}=200$ GeV, due to shadowing and medium induced parton energy loss effects. We find that the next-to-leading order contributions are large and have a strong $p_t$ dependence., Comment: 9 pages, 5 figures, expanded discussion of the K factor

We show estimates for shadowing of gluons at small values of $x$, appropriate to RHIC and LHC experiments using a new evolution equation which takes into account the effects of gluon recombination to all orders in gluon density. We show that there is a significant depletion in the gluon density of large nuclei., Comment: 6 pages, 1 figure, Talk given at XXIX Int. Symp. on Multiparticle Dynamics (ISMD99), 9-13 August 1999, Providence, RI, USA

We consider production of dilepton pairs through coherent electro-magnetic radiation during nuclear collisions. We show that the number of pairs produced through bremsstrahlung is about two orders of magnitude smaller than the yield measured by the CERES collaboration. Therefore, coherent bremsstrahlung can be ruled out as an explanation for the observed enhancement of low mass dileptons in CERES and HELIOS., Comment: 9 pages, 2 figures

We investigate the temperature dependence of \eta and \eta^{\prime} masses due to scatterings from thermal pions in a heat bath using the non-linear sigma model. We show that mass shifts of \eta and \eta^{\prime} and the shift in the mixing angle are negligible., Comment: Latex, 11 pages, 2 eps figures included

We compute the quantum corrections to the gluon distribution function in the background of a non--Abelian Weizs\"acker--Williams field. These corrections are valid to all orders in the effective coupling $\alpha_s \mu$, where $\mu^2$ denotes the average valence quark color charge squared per unit area. We find $\ln(1/x)$ logarithmic corrections to the classical gluon distribution function. The one loop corrections to the classical Weizs\"acker-Williams field do not contribute to these singular terms in the distribution function. Their effect is to cause the running of $\alpha_s$., Comment: Latex, 40 pages, 4 figures available upon request to the authors as postscript files