Orbital Momentum Effects in Heavy Ion and Hadron

CollisionsSergey Troshin, IHEP, Protvino

Motivation – role of polarization measurements in search of quark-gluon plasma

Tool – stable pattern of hyperon polarization (lambda, in particular) observed in unpolarized hadron interactions: energy independence, linear rise with xF, 1 GeV/cPP

20-30%

p0Polarization is determined through weak (parity non-conserving) decay

Earlier (mid-eighties) prediction: isotropic distribution of the parton momenta in the plasma rest frame.

QGP does not remember the directions of the initial momenta. Vanishing polarization of hyperons relative to production plane (due to

parity conservation there could not be longitudinal polarization).

Papers: P. Hoyer, Phys. Lett. B, 187, 162, 1987; A.D. Panagiotou, Phys. Rev. C 33, 1999, 1986; R. Stock et al., Proc. of the Conference on Quark Matter Formation in

Heavy-Ion Collisions, Singapore 1982. Vanishing hyperon polarization w.r.t. production plane follows from various models also

0,0)( bbPP b - impact parameter

Peripheral collisions (b is different from 0)

b

)(2

),( bDs

bbsL C

b

L

0

5_

10)( RHICL

7_

10)( LHCL

1h

P. Carruthers, 1983: “Enormous angular momentum involved in a high energy nucleus-nucleus collisions”

Reaction plane

What are the observable effects of the large angular orbital momentum presented in the peripheral heavy-ion and hadron collisions?

Burst of polarized vector mesons (P. Carruthers, 1983)? Strong necessity for the spins of the outgoing particles to

line up parallel to each other in the transverse direction to the reaction plane (C.N. Yang and T.T. Chou, 1986)?

Reaction plane is the plane perpendicular to the orbital momentum

0)( 21 averageTT

due to a net deficiency of orbital angular momentum in the left and right-moving outgoing systems

Thus, in the process of high energy hadron or nuclear collisions large initial orbital angular momentum can, in principle, be converted into the spin angular momentum of final particles resulting in their polarization relative to the reaction plane. We would try to connect this possibility with the nature of transient strong interaction matter.

Experimental facts

Asymptotic freedom in QCD formation of QGP - gas of free quarks and gluons [J. C. Collins, M. J. Perry; Phys. Rev. Lett. 34, 1353 - 1356 (1975)]

Discovery of the deconfined state of matter has been announced by the four major experiments at RHICDespite the highest values of energy and density have been reached, a genuine quark-gluon plasma QGP was not found. The deconfined state reveals the properties of the perfect liquid, being strongly interacting collective state and therefore it was labelled as sQGP.

How can orbital momentum help in detecting nature and properties of transient quark-gluon matter produced in the non-central collisions?

Weakly-coupled matter (parton model with final state interactions) Z.-T. Liang, X.-N. Wang, Phys. Rev. Lett, 94, 102301, 2005: no collective rotation of the system, finite transverse gradient of the average longitudinal momentum per produced in the overlap region parton. It is claimed that relative OAM in collision of partons will lead to global quark polarization due to spin-orbital coupling.

Significant (order of tens %) polarization of hyperons relative to reaction plane was anticipated. Similar ideas were used for the hyperon polarization in hadron non-central collisions, S. Voloshin, 2004, nucl-th/0410089v1. To observe circularly polarized photons as a signalof quark polarization in the QGP was proposed in A. Ipp, A Di Piazza, J. Evers, C.H. Keitel, arXiv: 0710.5700v1. Also: B. Betz, M. Gyulassy, G. Torrieri, Phys. Rev. C 76, 044901, 2007

Typical values of global hyperon polarization relative to reaction plane were predicted to be

3.0 Rq

RH PP

The measurements of global polarization and were performed at RHIC (STAR Collaboration) and upper limit has been obtained

02.0|| , RP

AuAu

GeVsNN 200;4.62Global polarization measurements in Au+Au collisions, B.I. Abelev et al. Phys. Rev. C 76, 024915 (2007)

)sin(8 *

RPpH

RHP

No centrality (impact parameter) dependence was found for hyperon global polarization in Au+Au collisions at RHIC.

I. Selyuzhenkov (for the STAR Collaboration), J. Phys. G 34 (2007) S1099

Thus, at the moment no experimental evidence exists for conversion of the orbital angular momentum into the spin angular momentum in nuclear collisions and this conclusion is correlated but not necessarily follow from the result on the strongly interacting nature of transient matter observed at RHIC.

The question arise again: what are the experimental manifestations of the large orbital angular momentum could be in the case of strongly interacting transient matter ?

Global spin alignment for φ, K*0 and global polarization for Λ were not observed.

Ideal liquid low viscosity large interaction cross-section (order of 40 mb)

Large orbital angular momentum rotation of the transient deconfined matter in the overlap region as a whole, i.e. all parts have the same angular velocity and orbital angular momentum does not convert to spin angular momentum.

Experimental manifestations – directed flow v1

What is 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).

nv

S.M. Troshin, N.E. Tyurin, Int. J. Mod. Phys. E, 2008

nvn cos

ppv p /ˆcos)(1 pb

1

2

3

3

cos2121

nn

TT

nvdydppNd

pdNd

E

Provided impact parameter is fixed and known, the directed flow can be studied in nuclear as well as in hadronic collisions.

Asimuthal angle of RP is taken to be zero RP

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.

inel

NbNc

)(

)(2

W. Broniowski, W. Florkowski,Phys. Rev. C 65 (2002) 024905

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.

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 feasible with standard procedure.

Transient state in nuclei and hadron collisions

effQCD LL

CIeff LLLL

Transient state generation time

inttttsg

Quark-Meson LiquidQQ mR /

Overlap region

ch

ch

Q

Q DDm

skbsN 21

)1(),(~

x

y

Fixed impact parameter b

3n nII

10 ]cos),,,(21)[,,,(

21

),,,(n

n npybsvpybsIysI

pb

2|),(1|),,,(),,,( bsiUpybsvpybsv nn

Inclusive cross-section

02|),(1|

),,(8

bsiUbsI

bdbdd

unitarity

Rotation as an origin of directed flow

Assumed particle production mechanism at moderate transversemomenta 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

lv

1|| 1 yl || beamyyy

||1

|| 1beamyy

v

nv 1

Weakly increasing energy dependence of the directed flow (due to increase of elastic scattering cross section

P dependence of directed flowT

TpR /1

At high transverse momentum an internal structure of constituent quark is resolved – vanishing directed flow is expected

Directed flow in nuclear collisions

Au+Au and Cu+Cu at 62.4 and 200 GeV at RHIC (STAR preliminary data)

Other effects related to OAM

Contribution to elliptic flow

2222 /)(2cos)( ppppv yxp

S.M. Troshin, N.E. Tyurin, hep-ph/0609248

F. Becattini, F. Piccinini, J. Rizzo, Phys. Rev. C77: 024906, 2008. [arXiv: 0711.1253]

Conclusion: expectations for the LHC

What kind of the deconfined matter would be produced at the LHC energies?

Vanishing directed flow – weakly-coupled system, QGP.

What about global polarization? Is this a signal of QGP formation? Not necessarily, the reason is the reflective (antishadowing) scattering.

Spin correlations due to antishadowing. S.M. Troshin, Phys.Lett.B597:391,2004

22 |),(1|),(Im

41

),(bsiUbsU

dbd

bs inel

4/1 4/1 4/1

b b b

Black disk

LHC

Negative imbalance of the orbital momentum at the LHC energies 2

)()(2)(

2sxsnsRs

L L

)(sR

Qualitative features of the transient state in hh and AA collsions and role of rotating quark-meson liquid in the directed flow formation.

Effect of rotation is maximal for peripheral collisions – centrality dependence.

Vanishing directed flow can serve as a signal of a genuine QGP formation.

If genuine QGP is formed, OAM can be converted to the global polarization of the secondary particles.

LHC studies of anisotropic flows: global polarization can exists even when sQGP is formed, it is then results from reflective scattering.

Further studies (theoretical and experimental) are necessary in this field combining experience of spin studies with multiparticle production.