Cold nuclear matter effects on azimuthal decorrelation in heavy-ion collisions

Published for SISSA by Springer Received: August 5, Revised: September 23, Accepted: September 27, Published: November 13, 2024 2024 2024 2024 Néstor Armesto , Florian Cougoulic and Bin Wu Instituto Galego de Física de Altas Enerxías IGFAE, Universidade de Santiago de Compostela, E-15782 Galicia, Spain E-mail: , , Abstract: The assumption of factorization lies at the core of calculations of medium effects on observables computable in perturbative Quantum Chromodynamics. In this work we examine this assumption, for which we propose a setup to study hard processes and bulk nuclear matter in heavy-ion collisions on the same footing using the Glauber modelling of heavy nuclei. To exemplify this approach, we calculate the leading-order corrections to azimuthal decorrelation in Drell-Yan and boson-jet processes due to cold nuclear matter effects, not considering radiation. At leading order in both the hard momentum scale and the nuclear size, the impact-parameter dependent cross section is found to factorize for both processes. The factorization formula involves a convolution of the hard cross section with the medium-modified parton distributions, and, for boson-jet production, the medium-modified jet function. Keywords: Deep Inelastic Scattering or Small-x Physics, Quark-Gluon Plasma ArXiv ePrint: 2407.19243 Open Access, © The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP11(2024)081 JHEP11(2024)081 Cold nuclear matter effects on azimuthal decorrelation in heavy-ion collisions Contents 1 Introduction 1 2 A unified description of hard processes and bulk matter 2.1 The impact-parameter dependent cross section in heavy-ion collisions 2.2 The observable: azimuthal decorrelation 2.3 Perturbative description of hard processes and bulk matter 2 2 5 6 8 8 11 4 Cold nuclear effects on spatial parton distributions 4.1 Initial-state single scattering 4.2 Multiple scattering for the Drell-Yan process in large nuclei 13 13 18 5 Cold nuclear effects on jets 5.1 The coordinates for jet production 5.2 Single scattering of a jet in QCD medium 5.3 The boson-jet azimuthal decorrelation in large nuclei 5.4 Discussion about factorization 19 19 20 23 24 6 Summary and outlook 25 1 Introduction Factorization in Quantum Chromodynamics [1–4] plays a central role in hadron collider physics. While it has been proved in l+ l− collisions and Deep Inelastic Scattering (DIS), in hadron-hadron collisions it has only been vetted for processes where the final state consists of colorless particles. Besides, situations are known where factorization fails, see e.g. [5–7] and references therein. Factorization is also widely assumed for hard processes in heavy-ion collisions, but it has been analyzed more rarely that in nucleon-nucleon scattering and most often discussed in the context of DIS and photoproduction, see, e.g., [8, 9] and refs. therein. In spite of this, its application lies at the core of studies dedicated to the extraction of properties of the bulk matter or medium produced in such collisions using hard probes like jet or large transverse momentum hadron production. Checks of the (lack of) validity of factorization in collisions involving nuclei require the description of both hard processes and bulk matter in a theoretically well-grounded, unified framework. This central issue remains, despite many efforts, an open question. Parton saturation, also known as the Color Glass Condensate (CGC), provides a promising description of bulk matter (soft and semihard partons) in the early stages of heavy-ion collisions [10]. In this framework, the production of these partons has been conventionally –1– JHEP11(2024)081 3 Expansion of Feynman diagrams at high Q 3.1 Expansion in momentum space 3.2 Expansion in coordinate space 2 A unified description of hard processes and bulk matter In this section, we present the main formula to calculate the impact-parameter dependent cross section for hard processes in heavy-ion collisions. The constituent nucleons of the colliding nuclei are taken to be uncorrelated, following the perturbative approach to parton saturation in refs. [13, 15] and the Glauber model [16]. 2.1 The impact-parameter dependent cross section in heavy-ion collisions In quantum theory, the impact-parameter dependent cross section for any observable O in the collision of two ultra-relativistic particles can be generically defined as [22] dσ = 2 d bdO Z Yh = Z Yh i dΓpf δ(O − O({pf })⟨ϕ1 ϕ2 |Ŝ † |{pf }⟩⟨{pf }|Ŝ|ϕ1 ϕ2 ⟩ f i dΓpf δ(O − O({pf })Tr Ŝ † |{pf }⟩⟨{pf }|Ŝ|ϕ1 ϕ2 ⟩⟨ϕ1 ϕ2 | ,  f –2–  (2.1) JHEP11(2024)081 calculated using classical color sources, as originally proposed in the McLerran-Venugopalan (MV) model [11, 12]. Alternatively, parton saturation has also been studied by treating heavy-nucleus states as uncorrelated nucleon states [13–15]. The latter approach shares some modeling characteristics with the Glauber model [16]. The production of soft gluons at fixed order in the strong coupling αs has been carried out in refs. [17, 18], revealing qualitative differences from kinetic theory in the coupling expansion within ϕ4 theory [19]. Recently, the broadening of high-energy partons in the early-stage color fields have been studied in refs. [20, 21]. In this work, we investigate whether and how one may formulate hard processes and bulk matter on the same footing by modelling heavy-nuclei as uncorrelated nucleons. The focus will be on whether the impact-parameter dependent cross section, defined in ref. [22], factorizes at fixed order in αs as well as at leading order in both the hard momentum scale and the nuclear size. Instead of treating bulk matter and jets differently like in the previous studies, we carry out a detailed calculation of azimuthal decorrelation of the Drell-Yan (DY) and boson-jet processes in heavy-ion collisions. Such an observable has been extensively studied in proton-proton [23–30] and high-energy nuclear collisions [31–38]. We consider the rescattering of the partons entering and leaving the hard scattering with partons from different nucleon-nucleon collisions. We do not include radiation. The manuscript is organized as follows: in section 2 we define the collision parameterdependent cross section in heavy ion collisions, the associated observable of interest in this study, namely the azimuthal decorrelation of the final state pair, which is either a Drell-Yan pair or a photon-jet pair. In section 3 we define the Feynman rules used in momentum space and in coordinate space. In section 4 we implement the cold nuclear effects in our observables and discuss their impact on the initial state distributions. These are all the modifications necessary to discuss the Drell-Yan pair azimuthal decorrelation. In section 5 we implement the cold nuclear effects for the hadronic final states, which are necessary to complete the discussion of the photon-jet azimuthal decorrelation. Finally, we discuss the form of t (...truncated)