Effects of a strong magnetic field on the QCD flux tube

Abstract

In this work we investigate the effect of an external magnetic field B on the shape of flux tubes in QCD by means of lattice simulations, performed with N f = 2 + 1 flavors of stout improved dynamical staggered quarks with physical masses. After having discussed some difficulties in the practical definition of the flux tube at B = 0, we show that these ambiguities do not affect the determination of the flux tube modifications induced by the magnetic field. Different results are obtained depending on the relative orientations of the flux tube and of the magnetic field: they confirm that the magnetic field acts as transverse confinement catalyser and longitudinal confinement inhibitor; moreover, the flux tube itself loses its axial symmetry when it is not directed along the magnetic background. * Electronic address: claudio.bonati@df.unipi.it † Electronic address: scali@uni-wuppertal.de ‡ Electronic address: massimo.delia@unipi.it § Electronic address: michele.mesiti@swansea.ac.uk ¶ Electronic address: fnegro@pi.infn.it * * Electronic address: andrea.rucci@pi.infn.it † † Electronic address: francesco.sanfilippo@roma3.infn.it

θ -dependence and center symmetry in Yang-Mills theories

“…It is therefore quite remarkable that, instead, lattice results obtained for SU (3), which have been reported for the first time in Ref. [63], show that one recovers exactly the same θ-dependence as in the confined phase (i.e. the same value, within errors, for both χ and b 2 ) as soon as the trace deformation is strong enough to inhibit the breaking of center symmetry.…”

“…However, the restoration of a global symmetry can also be induced by disorder, since order parameters are spatially averaged quantities, and this is what actually happens in many well known cases, just like ordinary Yang-Mills theory (see, e.g., the discussion on the adjoint Polyakov loop in Ref. [63]). This will be particularly important in the following, when we will present an analysis of the predicted phase diagram of the deformed SU (4) gauge theory based on the 1-loop effective potential of the Polyakov loop: this kind of analysis assumes a spatially uniform Polyakov loop, hence neglects the possibility of long-distance disorder.…”

“…The purpose of the present study is to make progress along this line of investigation, by extending the results of Ref. [63] to larger SU (N ) gauge groups, considering in particular the case N = 4. There are various reasons to expect that the study of SU (4) may lead to new non-trivial insights.…”

“…The disagreement with semiclassical predictions is not a surprise, since the values of the compactification radius L explored in Ref. [63] go up to L −1 ≡ T ≈ 500 MeV, while the condition for the validity of the semiclassical approximation is T ≫ N Λ where Λ is the non-perturbative scale of the theory, so that T ∼ 500 MeV is a scale where nonperturbative corrections can still be important. What is a surprise, claiming for further investigations, is the fact that such non-perturbative corrections are exactly the same as in the standard confined phase, leading to the same θ-dependence also from a quantitative point of view.…”

Fluctuating temperature and baryon chemical potential in heavy-ion collisions and the position of the critical end point in the effective QCD phase diagram

“…From the theoretical side, efforts to describe this diagram have been carried out employing a wide range of tools such as finite energy sum rules, Dyson-Schwinger equations, functional renormalization, holography and effective models . Lattice QCD (LQCD) calculations are also a useful technique [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40], although these cannot be used to access large values of µ B , given the severe sign problem [41].…”