The charmonium dissociation in an “anomalous wind”

Published for SISSA by Springer Received: November 3, 2015 Accepted: December 27, 2015 Published: January 11, 2016 The charmonium dissociation in an “anomalous wind” a Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139 U.S.A. b ITEP, B. Cheremushkinskaya 25, Moscow, 117218 Russia c Physics Department, Brookhaven National Laboratory, Upton, NY, 11973 U.S.A. E-mail: , Abstract: We study the charmonium dissociation in a strongly coupled chiral plasma in the presence of magnetic field and axial charge imbalance. This type of plasma carries “anomalous flow” induced by the chiral anomaly and exhibits novel transport phenomena such as chiral magnetic effect. We found that the “anomalous flow” would modify the charmonium color screening length by using the gauge/gravity correspondence. We derive an analytical expression quantifying the “anomalous flow” experienced by a charmonium for a large class of chiral plasma with a gravity dual. We elaborate on the similarity and qualitative difference between anomalous effects on the charmonium color screening length which are model-dependent and those on the heavy quark drag force which are fixed by the second law of thermodynamics. We speculate on the possible charmonium dissociation induced by the chiral anomaly in heavy ion collisions. Keywords: Quark-Gluon Plasma, Holography and quark-gluon plasmas, Anomalies in Field and String Theories ArXiv ePrint: 1510.06760 Open Access, c The Authors. Article funded by SCOAP3 . doi:10.1007/JHEP01(2016)052 JHEP01(2016)052 Andrey V. Sadofyeva,b and Yi Yinc Contents 1 2 The holographic setup 3 3 The screening length ls in the anomalous flow 3.1 String stretched by “anomalous flow” 5 8 4 Representative results for N = 4 SYM chiral plasma 9 5 Discussion and phenomenological consequences 5.1 Comparison with anomalous contribution to heavy quark drag force 5.2 Phenomenological implications 11 11 12 A Derivation of (3.10) 13 1 Introduction and summary The work of Matsui and Satz [1] introduced the idea of using a quarkonium to probe quark gluon plasma (QGP). In a deconfined QGP, quarkonium bound states such as charmonium cc̄ will dissociate because of color screening and thereby exhibit a suppression relative to the confined phase. Due to its importance, the problem of charmonium dissociation in QGP has been a focus of many recent studies (see refs. [2, 3] for reviews and references). In this paper, we consider the problem of charomium dissociation in a chiral (parityviolating) plasma with a finite chiral (axial) charge density1 and in the presence of an external magnetic field. This environment is pertinent to the QGP, which is approximately chiral, created in heavy-ion collisions. First, a very strong magnetic field is generated from the incoming nuclei that are positively charged and move at nearly the speed of light. Such magnetic field has a magnitude of the order of eB ∼ m2π and its lifetime can be significant when medium’s effect is taken into consideration [5, 6]. Meanwhile, QCD as a non-Abelian gauge theory has topologically nontrivial gluonic configurations such as instantons and sphalerons. These configurations couple to quarks through the chiral anomaly and translate topological fluctuations into the chiral imbalance for quarks. The focus of our study is on the effects of the chiral anomaly on the color screening length ls , which is an important parameter quantifying charmonium dissociation. In heavyion collisions, the produced charmonium is moving relative to QGP and the relative velocity v (or rapidity η = tanh−1 (v)) can be significant. We therefore also take dependence of ls on rapidity η into consideration. 1 For a recent discussion of lattice QCD with chiral chemical potential see e.g. [4]. –1– JHEP01(2016)052 1 Introduction and summary Anomaly-induced effects in a chiral medium has attracted much interests recently (see refs. [7–10] for reviews). One familiar example is the chiral magnetic effect (CME) [11–16], the generation of a vector current jV along an external magnetic field B. In particular and closely related to the current work, those anomalous effects modify hydrodynamics of chiral fluids [17] (see also refs. [18–20]). For such fluid in the frame that energy density is at rest (i.e. in the Landau frame), the entropy density is not at rest and is moving opposite to the direction of chiral magnetic current jCME = CA µA B: sanom = svanom B̂ , vanom ≡ − CA = Nc , 2π 2 (1.1) where , s, p, µ (µA ) denotes the energy density, entropy density, pressure and vector (axial) chemical potential respectively and the coefficient CA is fixed by the chiral anomaly.2 In this work, we will use charmonium (or in general quarkonium) to probe such an anomalous chiral fluid and ask how its screening length ls (η; vanom ) would be influenced by the presence of the “anomalous flow” vanom . To compute the rapidity-dependent color screening length ls (η; vanom ), we will use the gauge/gravity correspondence following the general formalism of ref. [21]. Previously, ls (η) and the dissociation of a moving charmonium has been studied in the framework of holographic correspondence from both top-down [21, 22] and bottom-up [23] approaches. Quarkonia dissociation in the presence of magnetic field has also been addressed previously (see for example refs. [24–28]). To the extent of our knowledge, the effects of the chiral anomaly on the charmonium dissociation have not been reported in literature before. The main finding of this paper is that the charmonium color screening length ls (η; vanom ) receives contributions from the chiral anomaly: a charmonium finds itself in a wind induced by anomalous flow (1.1). Let us quantify the “anomalous flow” felt by a charmonium introducing ηanom with following properties: ls (η; vanom ) = ls (η + ηanom ; vanom = 0) . (1.2) In other words, the color screening length of a charmonium moving at rapidity η in the presence of the anomalous flow vanom equals to that of a charmonium moving at rapidity η + ηanom in the absence of the anomalous flow. For small vanom  1, we obtain an analytical expression within the current holographic model at linear order in vanom for ηanom . We observe that the magnitude of ηanom is proportional to vanom . However, its value is model-dependent. Very recently, anomalous contributions to the heavy quark drag force were studied for a holographic chiral fluids [29]. Our study here provides further insights on the “anomalous flow” felt by heavy probes of the chiral plasma. This paper is organized as follows. In section 2, we describe our holographic set-up. In section 3, we derive the analytic formula which determines the anomalous contribution to the color screening length ls (η; ηanom ). At this point, our results are valid for a large class of holographic chiral fluids. In section 4, we take N = 4 SYM theory as an example and present ηanom as well as anomalous co (...truncated)