We show that the fluctuations in the wounded-nucleon model of the initial stage of relativistic heavy-ion collisions, together with the natural assumption that the forward- (backward-) moving wounded nucleons emit particles preferably in the forward (backward) direction, lead to an event-by-event torqued fireball. The principal axes associated with the transverse shape are rotated in the forward region in the opposite direction than in the backward region. On the average, the standard deviation of the relative torque angle between the forward and backward rapidity regions is ~20\ifmmode^\circ\else\textdegree\fi{} for the central and 10\ifmmode^\circ\else\textdegree\fi{} for the midperipheral collisions. The hydrodynamic expansion of a torqued fireball leads to a torqued collective flow, yielding, in turn, torqued principal axes of the transverse-momentum distributions at different rapidities. We propose experimental measures, based on cumulants involving particles in different rapidity regions, which should allow for a quantitative determination of the effect from the data. To estimate the nonflow contributions from resonance decays we run Monte Carlo simulations with therminator, a thermal heavy-ion generator. If the event-by-event torque effect is found in the data, it will support the assumptions concerning the fluctuations in the early stage of the fireball formation, as well as the hypothesis of the asymmetric rapidity shape of the emission functions of the moving sources in the nucleus-nucleus collisions.

The effect of a strong magnetic field on the location of the critical end point (CEP) in the QCD phase diagram is discussed under different scenarios. In particular, we consider the contribution of the vector interaction and take into account the inverse magnetic catalysis obtained in lattice QCD calculations at zero chemical potential. The discussion is realized within the ($2+1$) Polyakov–Nambu–Jona-Lasinio model. It is shown that the vector interaction and the magnetic field have opposite competing effects, and that the winning effect depends strongly on the intensity of the magnetic field. The inverse magnetic catalysis at zero chemical potential has two distinct effects for magnetic fields above $\gtrsim 0.3{\mathrm{GeV}}^2$: it shifts the CEP to lower chemical potentials, hinders the increase of the CEP temperature and prevents a too large increase of the baryonic density at the CEP. For fields $eB<0.1{\mathrm{GeV}}^2$ the competing effects between the vector contribution and the magnetic field can move the CEP to regions of temperature and density in the phase diagram that could be more easily accessible to experiments.

It is shown that the end point of the first-order transition line, which merges into a crossover regime in the phase diagram of the Nambu–Jona-Lasinio model, extended to include the six-quark ’t Hooft and eight-quark interaction Lagrangians, is pushed toward vanishing chemical potential and higher temperatures with increasing strength of the Okubo-Zweig-Iizuka–violating eight-quark interactions. We clarify the connection between the location of the end point in the phase diagram and the mechanism of chiral symmetry breaking at the quark level. We show how the $8q$ interactions affect the number of effective quark degrees of freedom. We are able to obtain the correct asymptotics for this number at large temperatures by using the Pauli-Villars regularization. DOI: http://dx.doi.org/10.1103/PhysRevD.81.116005 © 2010 The American Physical Society

It is shown that eight-quark interactions, which are needed to stabilize the ground state of the combined three flavor Nambu–Jona-Lasinio and 't Hooft Lagrangians, play also an important role in determining the critical temperature at which transitions occur from the dynamically broken chiral phase to the symmetric phase.