Download Local Parity Violation in Strong Interactions

Proc. 25th Winter Workshop on
Nuclear Dynamics (2009) 000–000
25th Winter Workshop
on Nuclear Dynamics
Big Sky, Montana, USA
February 1–8, 2009
Local Parity Violation in Strong Interactions
Dhevan Gangadharan1
1
UCLA,
Los Angeles, California
[email protected]
Abstract. Local parity violation of the strong interactions have been proposed
to occur in heavy-ion collisions at RHIC[1]. Parity-odd states are produced
locally in a heavy-ion collision by means of a vacuum transition via instantons
and sphalerons. Manifestation of the parity-odd state is made with the help
of a very large but brief magnetic field caused by the spectator nuclei of a
non-central collision. The experimental signature for a P-odd state has been
shown to be dynamical charge separation with respect to the reaction plane.
Recent experimental techniques used to look for parity violation with the STAR
detector at RHIC as well as estimates on background contamination to the
correlation function used are discussed here.
Keywords: local, parity, violation
PACS: 25.75.Ag
1. Theory Introduction
The hot and dense regions created in heavy-ion collisions at RHIC are predicted to
allow for certain non-trivial vacuum transitions. In general, all non-trivial vacuum
transitions can be classified by their winding number and all vacuum configurations can be classified by the Chern-Simons number, NC S[2]. It is pointed out by
Kharzeev et al.[1] that all non-zero NC S states lead to a non-conservation of the axial current which in turn leads to parity violation of the strong interactions. Positive
and negative NC S are equally probable though, and lead to opposite experimental signatures. Thus, taken together or looked at from a global perspective–large
distance scale where many independent vacuum transitions are summed together–
parity is still conserved. It is only at the local level–small distance scale–where
parity is violated. Parity violation of this sort is thus local in nature.
Realization of a P-odd state in a heavy-ion collision is made with the help of a
very large but brief magnetic field. The magnetic field can be understood as arising
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Dhevan Gangadharan
from the spectator nuclei in a non-central heavy-ion collision. The spectator protons
are charged and are moving relativistically and thus provide a magnetic field just by
ordinary electro-dynamics. It has been shown that the interaction of this magnetic
field with the P-odd state can further induce an electric field oriented parallel to the
magnetic field[1]. The sign of the orientation is linked with the sign of NC S and thus
fluctuates event-by-event. It is then clear that the resulting experimental observable
will be charge-separation relative to the reaction plane. This is the so-called Chiral
Magnetic Effect. Figure 1 illustrates this idea.
Fig. 1. The Chiral Magnetic Effect
2. Detector and Data Used
For a review of results using data from the STAR detector at RHIC the reader
is directed to Sergei Voloshin’s Quark Matter 2009 presentation[3]. Here, model
predictions and simulations are presented.
Various cuts were imposed on all data-sets. The location of the primary vertex
along the beam line was required to be within 30cm of the TPC center to ensure
good particle tracking. A lower pt cut of .15 GeV/c was imposed to remove tracks
which bend too much in STAR’s magnetic field and never leave the TPC. An upper
pt cut of 2 GeV/c was also applied since the Chiral Magnetic Effect is a low-pt
effect. An eta cut |η| < 1 was applied for similar reasons. Finally, at least 15 TPC
hit-points were required as well as the ratio of hit-points to maximum number of
hit-points > .52 for track quality assurance.
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3. Correlation function
A three particle correlation function has been proposed[4] to look for charge-separation
relative to the reaction plane:
< cos(φa + φb − 2φc ) >
(1)
< cos(φa + φb − 2φc + 2ΨRP − 2ΨRP ) >
(2)
which can be rewritten as
and under the assumption that particle c is only correlated with particles a and b
through the ΨRP equation 2 can further be written as
< cos(φa + φb − 2ΨRP ) > v2c
(3)
v2c
where
is the elliptic flow of particle c. Finally, with the help of a double-angle
trigonometric identity equation 3 can be rewritten as:
< cos(φa −ΨRP ) cos(φb −ΨRP )−sin(φa −ΨRP ) sin(φb −ΨRP ) > v2c = (v1a v1b −aa ab )v2c
(4)
where v1 =< cos(φ − ΨRP ) > and a =< sin(φ − ΨRP ) > are Fourier coefficients
of the azimuthal particle distribution. The first term is sensitive to directed flow of
particles a and b. However, with the symmetric η range chosen, the first term should
vanish. The second term is sensitive to the Chiral Magnetic Effect. Both terms are
sensitive to non-flow which cancels out in the subtraction. One should also notice
that this correlator is P-even since the Fourier coefficients v1 and a effectively appear
squared in equation 4. It is thus susceptible to P-even fluctuations in addition to
the P-odd fluctuations of the Chiral Magnetic Effect. The value of this correlator is
studied in the cases where particles a and b are of the same-charge and when they
are of unlike charge. If particles a and b are chosen to be of the same-charge and
both undergo the Chiral Magnetic Effect it is clear that the correlator will be driven
more negative. If they are chosen to be of opposite-charge then the correlator will
be driven more positive.
4. Results Obtained With Models
A theoretical prediction for the same-charge correlations in Au+Au 130 GeV collisions[5] is presented in figure 2. The y-axis shows the value of −(a+ a+ + a− a− )/2
which represents the same-charge contribution to equation 4 scaled by v2c and with
the first term vanishing. The x-axis shows the collision centrality. Although not
plotted, the opposite-charge correlations would indeed be positive instead of negative as it is for the same-charge correlations. We therefore take the simultaneous
feature of positive opposite-charge correlations and negative same-charge correlations increasing with centrality in the data as possible evidence for local strong
parity violation. It should also be noted that figure 2 represents only one of many
possible theoretical outcomes for this effect due to various theoretical uncertainties
such as the vacuum transition rates.
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Dhevan Gangadharan
〈-a+-a+-〉
A Theoretical Prediction
×10-3
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% Most Central
Fig. 2. A theoretical prediction
To access possible signal contamination from P-even sources like jets and resonances we also study the value of the correlator (Eq. 3) with an explicitly known
reaction plane in various Au+Au 200 GeV heavy-ion simulations are presented in
figure 3. None of these simulations incorporate P-odd transitions. As can be seen
below, in none of these simulations do we simultaneously observe positive oppositecharge correlations and negative same-charge correlations.
5. Conclusions
Local parity violation of the strong interactions has been predicted to occur in
heavy-ion collisions at RHIC. A correlation function directly sensitive to P-odd
fluctuations has been presented. A theoretical prediction for this correlator as
well as its value in various heavy-ion simulations have been presented as well. We
observe that the known P-even physical processes built into these simulations can
not reproduce the expected P-odd results.
Acknowledgments
I would like to thank Dmitri Kharzeev for many beneficial discussions on this subject.
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Fig. 3. Simulations
References
1. K. Fukushima, D. Kharzeev and H. Warringa, Phys. Rev. D 78 2008 074033.
2. D. Diakonov, Prog.Part.Nucl.Phys 51 2003 173-222.
3. S. Voloshin, Talk presented at Quark Matter 2009, Knoxville, TN. March 30th
– April 4th, 2009; to be published in the proceedings by Journal of Physics G.
4. S. Voloshin, Phys. Rev. C, 70 2004 057901.
5. D. Kharzeev, L. McLerran and H. Warringa, Nucl. Phys. A 803 2008 227.