Directed flow as an effect of the transient state rotation in hadron and nucleus collisions S.M. Troshin, N.E. Tyurin IHEP, Protvino

Directed flow introduced for description of nucleus collisions can be extended to hadronic reactions. Role of rotation of the transient matter. Motivation

Directed flow Several experimental probes of collective dynamics in AA interactions: momentum anisotropies defined by means of the Fourier expansion of the secondary particle distribution over the momentum azimuthal angle. The azimuthal angle is the angle of the detected particle with respect to the reaction plane, (spanned by the collision axis z and the impact parameter vector b directed along the x axis).

Recent experimental results (RHIC) Incidend-energy scaling: in the projectile frame directed flow does not depend on the incident energy. Directed flow is vanishing in central collisions and increases with centrality. It has the same values for Cu-Cu and Au-Au collisions. Our goal is to treat hadron-hadron collisions and confront predictions for hh collisions with experimental results for AA- collisions keeping in mind similarity of hh and AA The geometrical picture of hadron collision has an apparent analogy with collisions of nuclei and determination of the reaction plane in the non-central hadronic collisions could be experimentally realizable with the utilization of the standard procedure.

Measurements of the characteristics of multiparticle production processes in hadronic collisions at fixed impact parameter should be performed with selection of the specific events sensitive to the value and direction of impact parameter. The relationship of the impact parameter with the final state multiplicity. Chou-Yang approach: one can restore the values of impact parameter from the charged particle multiplicity. W. Broniowski, W. Florkowski, Phys. Rev. C 65 (2002) Centrality and impact parameter c(N) is the centrality of the events with multiplicity larger than N and b(N) is the impact parameter where mean multiplicity is equal to N.

Inclusive cross-section integrated over impact does not depend on azimuthal angle (for unpolarized particles) unitarity Inclusive cross-section

S-matrix representation One-to-one transform 0 1

Fixed impact parameter b 

Transient state Transient state generation time Quark-Pion Liquid

Overlap region x y

Rotation of transient matter (quark-pion liquid) Coherent rotation with the same angular velocity (minimal value of kinetic energy for the given value of the orbital angular momentum L) Such coherent rotation is absent in the parton picture. The parton interaction was assumed to be a driving force of the orbital angular momentum conversion to the global system polarization (due to spin-orbital coupling), which, however, has not been detected experimentally. Z.-T. Liang, X.-N. Wang, Phys. Rev. Lett. 94 (2005) , ibid. 96 (2006) B.I. Abelev et al, (STAR Collaboration), arXiv:

Rotation as an origin of directed flow Assumed particle production mechanism at moderate transverse momenta is an excitation of a part of the rotating transient state of massive constituent quarks (interacting by pion exchanges) by the one of the valence constituent quarks with subsequent hadronization of the quark-pion liquid droplets. Q

Incident-energy independence  Effect of rotation is most significant in the peripheral part of the rotating quark- pion liquid and weaker in less peripheral regions, i.e. the directed flow depends on the depth where the excitation of the quark-pion liquid takes place Depth should be proportional to the energy loss of constituent valence quark in the medium prior an excitation occurs, i.e. should be proportional to the rapidity difference between the rapidity of the final particle and the rapidity of the projectile particle.

Experimental data (STAR Collaboration: nucl-ex/ v2)

Transverse momentum dependence of directed flow Size of the region where the virtual massive quarkcomes from the quark-pion liquid is determined by its transverse momentum, i.e. It is evident that R should not be larger than the interaction radius of the valence constituent quark (interacting with the quarks and pions from the transient liquid state). The production processes with high transverse momentum such that R is much less than the geometrical size of the valence constituent quark resolve its internal structure as a cluster of the non-interacting partons.

Transverse momentum dependence (STAR)

Conclusion  Qualitative features of the transient state in hh and AA collsions and role of rotating quark-pion liquid in the directed flow formation.  Effect of rotation is maximal for peripheral collisions.  Vanishing directed flow can serve as a signal of a genuine QGP formation.  If QGP is formed, OAM can be converted to the global polarization of the secondary particles.  LHC studies of anisotropic flows. As it was predicted by Z.-T. Liang and X.-N. Wang