Vorticity in Heavy Ion
Collisions and its
manifestations
NICA/JINR-FAIR Bilateral
Workshop,
FIAS, April 4 2012
Oleg Teryaev
JINR
Outline
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Rotating QCD matter
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Spin@NICA/MPD - search for signs of global rotation
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Chiral Vortical Effect & neutron asymmetries @ NICA
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Background: Dilepton angular distributions in heavy
ion collisions
Hyperon polarizations
How fast is the rotation in
HIC?
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Magnetic field – highest possible ever =
CME
Rotation – another pseudovector –
angular velocity
Also highest possible! - velocities ~ c at
the distances ~ Compton length
Is it observable?!
Anomaly in medium – new
external lines in VVA graph
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Gauge field -> velocity
CME -> CVE
Kharzeev,
Zhitnitsky (07) –
EM current
Straightforward
generalization:
any (e.g. baryonic)
current – neutron asymmeries@NICA Rogachevsky, Sorin, OT - PRC82:054910,2010.
Сomments on anomaly in
medium
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Quarks or hadrons?
The same – t’Hooft principle
Real photons-massless modes (like pion)
Used also for media
Virtual – collective effect
(Klopot,Oganesian,OT)
T or chemical potential – like virtuality?
Anomaly = averaged quark diagram
Quark diagram – only an estimate
Baryon charge with neutrons –
(Generalized) Chiral Vortical Effect
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Coupling:
Current:
- Uniform chemical potentials:
- Rapidly (and similarly) changing
chemical potentials:
Comparing CME and CVE
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Orbital Angular Momentum and
magnetic moment are proportional –
Larmor theorem
No antibaryons – no mirror correlations
CME for 3 flavours – no baryon charge
separation (2/3-1/3-1/3=0!) (Kharzeev,
Son) - but strange mass!
Same scale as magnetic field
Studying vorticity
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Vorticity for uniform rotation –
proportional to OAM
Tests are required
Natural object – hydrodynamical helicity
(= v rot v)-related to chaos
Model calculations: JINR(DSM: Baznat,
Gudima, Sorin,OT)+FIAS(UrQMD:
Bleicher, Steinheimer, Stoecker)
Relativistic Vorticity and
Lagrangian Chaos
(A.S.Sorin, OT, in progress)
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“Maximal” vorticity/helicity Beltrami flows
For ideal fluid – Bernoulli condition in
the 3D region ~ chaos (normally only
along streamlines ~ integrability)
Relativistic generalization for isentropic
“steady”(
)flows
Relativistic Bernoulli condition in 4D region
Causality: account for
compressiibility required (in progress)
Hydrodynamical Helicity
separation (DCM)
Hydrodynamical Helicity
separation (UrQMD)
Observation of GCVE
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Sign of topological field fluctuations
unknown – need quadratic (in induced
current) effects
CME – like-sign and opposite-sign
correlations – S. Voloshin
No antineutrons, but like-sign baryonic
charge correlations possible
Look for neutron pairs correlations!
MPD may be well suited for neutrons!
Estimates of statistical accuracy
at NICA MPD (months of running)
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UrQMD model :
2-particles -> 3-particles correlations
no necessity to fix
the event plane
2 neutrons from
mid-rapidity
+1 from ZDC
Other sources of quadratic
effects
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Quadratic effect of induced currents –
not necessary involve (C)P-violation
May emerge also as C&P even quantity
Complementary probes of two-current
correlators desirable
Natural probe – dilepton angular
distributions
Observational effects of
current correlators in medium
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McLerran Toimela’85
Dileptons production rate
Structures –similar to DIS F1, F2
(p ->v)
Tensor polarization of in-medium
vector mesons (Bratkovskaya,
Toneev, OT’95)
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Hadronic in-medium
tensor – analogs of
spin-averaged
structure functions:
p -> v
Only polar angle
dependence
Tests for production
mechanisms
Dilepton anisotropies vs
(CME)2 correlations
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Small correlations -> small anisotropies?
Dileptons -> EM currents
Vector currents correlator for hadrons
production – quark hadron duality
How it works in medium?!
Hagedorn spectrum – small coupling of
currents to higher states – suppression of
anisotropies present in correlator
P-odd effects from W3 type
function
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For dilepton productions – due to
interference with Z0 exchange
Suppressed as Q2/MZ2 ~10-6
Leads to energy disbalance between
positively and negatively charges
leptons
Also for hadrons?!
General hadronic tensor and
dilepton angular distribution
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Angular distribution
Positivity of the matrix (= hadronic
tensor in dilepton rest frame)
+ cubic – det M> 0
1st line – Lam&Tung by SF method
Magnetic field conductivity
and asymmetries
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zz-component of conductivity
(~hadronic) tensor dominates
λ =-1
Longitudinal polarization with respect to
magnetic field axis
Extra dileptons hidden in the reaction
plane
Azimuthal asymmetries suppressed by
positivity
Other signals of rotation
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Hyperons (in particular, Λ) polarization
(self-analyzing in weak decay)
Searched at RHIC (S. Voloshin et al.) –
oriented plane (slow neutrons) - no
signal observed
No tensor polarizations as well
Why rotation is not seen?
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Possible origin – distributed orbital angular
momentum and local spin-orbit coupling
Only small amount of collective OAM is
coupled to polarization
The same should affect lepton polarization
Global (pions) momenta correlations
(handedness)
New source of Λ polarization
coupling to vorticity
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Bilinear effect of vorticity – generates
quark axial current (Son, Surowka)
Strange quarks - should lead to Λ
polarization
Simulations -> ~ 1 unit of chirality
(helicity) per event -> ~ % polarization
Proportional to chemical potential –
small at RHIC – may be probed at
FAIR & NICA
Induced current (UrQMD)
Another description of spin-rotation
coupling – gravitomagnetic effects
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Rotation +Equivalence Principle =
gravitomagnetic field
Coupled to Gravitational Formfactors
Analogous to EM ones – related to
Generalized Parton Distributions and
angular momenta of quarks and gluons
Dirac equation in (strong) gravitational
fields – Obukhov, Silenko, OT
HIC applications in progress
Induced current for (heavy - with
respect to magnetic field strength)
strange quarks
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Effective Lagrangian
~
~
4
4
L  c( FF )(GG) / m  d ( FF)(GG) / m
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Current and charge density from c (~7/45) –
~
~ 

j

2
c
F

(
G
G
) / m4
term
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
 ~ H 
(multiscale medium!)
~
~
 ~ (GG ) / m 4   d 4 xGG
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Light quarks -> matching with D. Kharzeev et al’ ->
correlation of density of electric charge with a
gradient of topological one (Lattice ?)
Properties of perturbative
charge separation
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Current carriers are obvious - strange quarks -> matching ->
light quarks?
NO obvious relation to chirality – contribution to axial current
starts from pentagon (!) diagram
No relation to topollogy (also pure QED effect exists)
Effect for strange quarks is of the same order as for the light
ones if topological charge is localized on the distances ~ 1/ms ,
strongly (4th power!) depends on the numerical factor : Ratio of
strange/light – sensitive probe of correlation length
Universality of strange and charm quarks separation - charm
separation suppressed as (ms /mc)4 ~ 0.0001
Charm production is also suppressed – relative effects may be
comparable at moderate energies (NICA?) – but low statistics
Comparing CME to
strangeness polarization
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Strangeness polarization – correlation of
(singlet) quark current
(chromo)magnetic field
(nucleon) helicity
Chiral Magnetic Effect - correlation of
(electromagnetic) quark current
(electro)magnetic field
(Chirality flipping) Topological charge
gradient
Local symmetry violation
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CME – assumed to be the sign of local
P(C) violation
BUT Matrix elements of topological
charge, its density and gradient are
zero
Signs of real C(P) violation – forbidden
processes
Forbidden decays in vacuum –
allowed in medium
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C-violation by chemical potential ->
 


e
e
(Weldon ’92)
  
(OT’96; Radzhabov, Volkov,
Yudichev ’05,06 - NJL)
 


e
e
New (?) option:
in magnetic

H
~
field 
m
Polarization (angular distribution in c.m.
2
~
1

cos
 (with
frame ) of dilepton
respect to field direction!)
 e e
 

2
4

Approximation: EM part – vacuum
value Two-stage forbidden decays - I
 
  
Two-stage forbidden decays II
 
  e e
Relating forbidden and
allowed decays
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In the case of complete mass
degeneracy (OT’05, unpublished):
 e e
 
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9  e e

4  
Tests and corrections – in progress
Conclusions
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Chiral Vortical Effect may be probed in the neutron
asymmetries at NICA
Bilinear current correlator may be probed in dilepton
asymmetries
CME/CVE for (heavy) strange quarks is similar to
their polarization in a nucleon
Various medium-induced decays may be related to
each other