Magneto-vortical evolution of QGP in heavy ion collisions

Abstract

The interplay of magnetic field and thermal vorticity in a relativistic ideal fluid might generate fluid vorticity during the fluid evolution provided the flow fields and the entropy density of the fluid is inhomogeneous [1]. Exploiting this fact and assuming large magnetic Reynolds number we study the evolution of generalised magnetic field (B) which is defined as a combination of the usual magnetic field ( B) and relativistic thermal vorticity (ω µν ), in a 2(space)+1(time) dimensional isentropic evolution of Quark Gluon Plasma (QGP) with longitudinal boost invariance. The temporal evolution ofB is found to be different than B , and theB evolution also depends on the position of the fluid along the beam direction (taken along the z axis) with respect to the mid-plane z = 0. Further it is observed that the transverse components (Bx,By) evolve differently around the mid-plane. PACS numbers: 12.38.Mh, 25.75.Ag

One particle distribution function and shear viscosity in magnetic field: A relaxation time approach

“…The relationships can be found by noting that η 1 , η 3 are the viscosity coefficients for which the corresponding shear-stress tensor satisfy the following relationship: b i S ij = b j S ij = 0 and for η 2 , η 4 the corresponding relationship is: b i b j S ij = 0, where S ij 's are defined in Eqs. (9)(10)(11)(12)(13). Similar calculation can also be found in [43].…”

“…For example, the phenomena of chiral magnetic effect (CME), chiral magnetic wave, and change in the photon and dilepton productions to name a few [4,[8][9][10][11][12]. Some other theoretical developments related to the magnetic field in heavy ion collisions includes magnetovortical evolution [13][14][15], calculation of Wigner functions for fermions in strong magnetic fields [17], shear viscosity in an anisotropic unitary Fermi gas [16], the shear and bulk viscosity of Quark-Gluon-Plasma (QGP) in strong magnetic fields [18][19][20] etc. On the other hand, several model studies in the last decade show that the QGP created in high energy heavy ion collisions possesses a very small value of shear viscosity to entropy density ratio.…”

How does the Quark-Gluon Plasma know the collision energy?

“…There is, however, another, closely related difference between the two cases: in the peripheral case only, huge values of the vorticity are produced, an effect long predicted (see for example [58,4,[59][60][61][62]) and recently observed, by the STAR collaboration [63], in the form of global Λ hyperon polarization [64]. This could be relevant to the questions raised in this work, either directly or through the subtle interactions of vorticity with magnetic fields [30,65]. It remains to be seen whether including this effect can improve the holographic predictions, particularly since the attenuation effect considered here does not apply to that case.…”

“…This uncertainty as to the value of the magnetic field at relevant times is one of the most pressing problems for the entire subject: for example, it obviously affects the many investigations regarding the chiral magnetic effect [24]. The most elementary observation, that the field must decrease simply due to the departure of the spectator nucleons, has to be tempered by subtle effects connected with the conductivity of the system formed by the collision, penetration depth effects, the interaction of the magnetic field with the associated vorticity, corrections required by event-by-event analyses [25], and so on: see [26][27][28][29][30][31][32] for balanced discussions of these rather formidable complexities, and the relevant references.…”

“…In view of these uncertainties, we will proceed cautiously. Guided by the discussions in [26][27][28][29][30][31][32], we will consider three scenarios: one in which we directly use the values given in [21], then one in which those values are decreased, due to the time evolution of the magnetic field, by a factor of 10, and finally one in which the attenuation factor is 100. Note that, even in this last ("most pessimistic") case, the magnetic fields involved are still enormous (on the order of 10 18 gauss), so it is far from obvious that there will be no effect even in this case.…”