Session MJ: Ultrarelativistic Heavy Ions - Theory II

Analysis of forward hadron spectra within DHJ + Lund model

Models based on the Color Glass Condensate (CGC) framework have been successful in explaining many experimental data from RHIC and LHC. However, applicability of these models are limited to a high transverse momentum region or one relies on the assumption of hadron-parton duality to compute multiplicity of the produced hadrons, because there are always non-perturbative effects in the process of hadronic interactions. In this talk, we will present a newly developed Monte-Carlo event generator based on the CGC framework. Specifically, we generate partons based on the DHJ formula which includes initial and final state radiations. Strings are formed by those produced partons and remnants which are fragment into hadrons by the Lund string fragmentation model. We will show the comparison of our results to the forward hadron spectra at RHIC and LHCf, and discuss mechanism of the particle production.   

Finite pulse effects on fermion pair creation from strong electric fields

In the early stage of heavy ion collisions, there appear extraordinarily strong (color) EM fields. In the presence of such strong fields, we encounter essentially new phenomena that are not observed in the vacuum: Among those is fermion pair creation from the vacuum. In this talk, we consider fermion pair creation from the vacuum in a strong electric field with finite duration. Employing the Sauter-type pulsed electric field with height $E_0$ and width $\tau$, we demonstrate explicitly the interplay between the non-perturbative and perturbative aspects of the pair creation in a strong field with finite duration. We identify that two dimensionless parameters $\nu=|gE_0| \tau^2$ and $\gamma=|gE_0|\tau/m$ characterize the importance of multiple interactions with the field and the transition from the perturbative to the non-perturbative regime. We also show that the pair creation is enhanced compared to Schwinger's formula when the field strength is relativity weak $|gE_0|/m^2 < 1$ and the pulse duration is relatively short $m\tau < 1$, and reveal that the enhancement is predominantly described by the lowest order perturbation with a single photon. We also discuss some recent developments and applications. Ref: H. Taya et al., arXiv:1405.6182, to appear in PRD.   

Heavy quark master equations in the Lindblad form

Understanding the quantum dynamics of quarkonia is essential in the description of bottomonia and charmonia in the quark-gluon plasma. So far, it has been quite naively assumed that their dynamics can be described by the Schr\"odinger equation with in-medium, screened potential. Such a na\"ive approach is incomplete, especially when one studies the time-evolution of quarkonia. After the discovery of imaginary part in the real-time in-medium potential, it is recognized that quarkoia should be viewed as open quantum systems in the environment of quark-gluon plasma. In the open quantum system, master equation, instead of the Schr\"odinger equation, describes the quantum dynamics of quarkonia. Open quantum system techniques, such as influence functional approach, have been applied to quarkonia. In this presentation, I will summarize developments in this approach and show how to obtain the Lindblad-form master equation, which preserves the complete positivity of the density matrix of the system.   

Analysis of quarkonia at finite temperature from complex Borel sum rules

Recently, we proposed a new type of QCD sum rules i.e. the complex Borel sum rules (CBSR) [1]. It has been found that the CBSR is superior to the conventional QCD sum rules from the point of view of the maximum entropy method (MEM) analysis. Specifically, we have demonstrated that our novel method can be used to study the excited states of hadrons. The suppression of quarkonium states (e.g. J/psi and upsilon) is an important signature of the hot matter produced in relativistic heavy-ion collisions at RHIC and LHC. Recently, the behavior of the excited states at finite temperature, which can be different from the ground state, has attracted much attention. The suppression of the charmonium and bottomonium ground states has already been analyzed by conventional QCD sum rules with MEM [2,3]. In this talk, we report on the results of a reanalysis by CBSR with MEM to investigate the thermal behavior of the quarkonium excited states. \\[4pt] [1] K.-J. Araki, K. Ohtani, P. Gubler, and M. Oka, arXiv:1403.6299 (published in PTEP).\\[0pt] [2] P. Gubler, K. Morita, and M. Oka, Phys. Rev. Lett. 107, 092003 (2011).\\[0pt] [3] K. Suzuki, P. Gubler, K. Morita, and M. Oka, Nucl. Phys. A 897, 28 (2013).   

Charmonium spectra and dispersion relations with maximum entropy method in extended vector space

We study charmonium properties at finite temperature and finite momentum in quenched lattice QCD with an extended maximum entropy method. We analyze the spectral functions and the dispersion relations of charmonia in an extended vector space, which is a product space of two different lattice correlators. We find that there is a mass shift of charmonium in pseudoscalar and vector channels at finite temperature. Our result shows that the dispersion relations are nevertheless consistent with Lorentz invariant form even near the dissociation temperature.   

Charmonium spectroscopy in strong magnetic fields by QCD sum rules

We address effects of strong magnetic fields on charmonium spectra by using QCD sum rules. To this end, we propose a general framework of QCD sum rules necessary for investigating any meson spectra in strong magnetic fields, that is, a consistent treatment of mixing effects in external magnetic fields. We then show charmonium spectra from QCD sum rules, and compare it with those from a hadronic effective theory.   

Gradient flow and energy-momentum tensor in lattice gauge theory

Defining the energy-momentum tensor (EMT) in lattice gauge theory is a nontrivial problem, because of the explicit breaking of the Poincare invariance in lattice regularization. Recently, on the basis of the Yang-Mills gradient flow a construction of the EMT on the lattice is proposed. We apply this EMT to the analysis of the bulk thermodynamics of the SU(3) gauge theory. It is shown that the energy density and pressure measured by taking the thermal expectation values of the EMT well agree with the previous results. Applications to the measurement of correlation functions will also be discussed.   

QCD effective potential with strong magnetic fields at zero and finite temperatures

In this contribution, we will discuss QCD vacuum in strong magnetic fields. As a first step towards understanding the effects of magnetic fields on QCD vacuum properties, we analytically derive the Euler-Heisenberg action for QCD $+$ QED at zero and finite temperatures. From the action, at zero temperature, we found that the chromo-magnetic field prefers to be parallel to the external magnetic field, and thus the QCD vacuum with strong magnetic fields is spatially anisotropic. This result is consistent with recent lattice data. Furthermore, the chromo-magnetic condensate increases with an increasing magnetic field, which supports the ``gluonic magnetic catalysis'' as observed in current lattice data. Next, we will discuss the effective potential with strong magnetic fields at finite temperatures. In particular, we focus on the influence of the magnetic field on the center symmetry in QCD. The pure Yang-Mills theory has the center symmetry (being spontaneously broken at high temperature), but dynamical quarks explicitly break it. We will show how the magnetic fields affect the explicit symmetry breaking, by using the effective potential for the Polyakov loop. We will also discuss the confinement-deconfinement phase transition in strong magnetic fields in terms of nonperturbative approaches such as functional renormalization group.   

Chiral phase transition with fluctuation and finite coupling effects at strong coupling

We investigate chiral phase transition including both fluctuation and finite coupling effects on QCD phase diagram in the strong coupling lattice QCD (SC-LQCD). The effective action is obtained in terms of hadronic degrees of freedom in SC-LQCD after analytic integration over link variables followed by Grassmann variables, and we expect weaker sign problem at finite density. Recently, we have evaluated fluctuation effects in the strong coupling limit in the auxiliary field Monte-Carlo (AFMC) method [1]. We found fluctuation effects modify the chiral phase transition boundary, as suggested by the monomer-dimer-polymer simulation [2]. Finite coupling effect [3] is another important ingredient to obtain insight into continuum QCD phase diagram. In the presentation, we give a brief explanation on how to include both fluctuation and finite coupling effects via sequential bosonization procedure in AFMC, and show what kind of plaquette configuration modifies the behavior of the chiral condensate. We also discuss the sign problem in AFMC and a probable way to weaken the sign problem.\\[4pt] [1] T. Ichihara, A. Ohnishi, T. Z. Nakano, arXiv:1401.4647.\\[0pt] [2] W. Unger, P. de Forcrand, J. Phys. G38 (2011) 124190.\\[0pt] [3] K. Miura, T. Z. Nakano, A. Ohnishi and N. Kawamoto, Phys. Rev. D 80, 074034 (2009)