Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://qfthep.sinp.msu.ru/talks2011/talkinSOCHI.pdf Äàòà èçìåíåíèÿ: Wed Oct 5 00:05:16 2011 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 19:42:53 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: local bubble

Dilepton excess from local parity breaking in baryon matter Xumeu Planells
With: A. A. Andrianov

,

, V. A. Andrianov



and D. Espriu





Universitat de Barcelona, Spain

Saint-Petersburg State University, Russia

XXth International Workshop in High Energy Physics and Quantum Field Theory Sochi, September 25, 2011

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Outline
Motivation of local parity breaking (LPB) Axial baryon charge and chiral chemical potential Vector Meson Dominance (VMD) approach to LPB Manifestation of LPB in heavy ion collisions (HIC) Numerical results for dilepton excess Conclusions

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Motivation of local parity breaking
P-breaking

Parity: well established global symmetry of strong interactions. Reasons to believe it may be broken in a nite volume. Recent investigations: Chiral Magnetic Eect (CME): quantum uctuation of parameter (P -odd bubbles) [D. E. Kharzeev, L. D. McLerran & H. J. Warringa, Nucl. Phys. A803, 227 (2008)]

New QCD phase characterised by a local parity breaking due to pseudoscalar background [A. A. Andrianov, V. A. Andrianov & D. Espriu, Phys. Lett. B 678, 416 (2009)]
LPB background
hot dense nuclear reball in HIC

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Motivation of local parity breaking
PHENIX anomaly: abnormal

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excess in central HIC at low

pt

Hint to LPB?

[A. Adare et al. [PHENIX collaboration], Phys. Rev. C81, 034911 (2010)]
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Axial baryon charge and chiral chemical potential
Topological charge T5 may arise due to quantum uctuations in hot medium due to sphaleron transitions [Manton, McLerran, Rubakov, Shaposhnikov]. PCAC leads

q Q5 =
vol.

¯ d 3 x q 0 5 q , T5 =

8

1

2

vol.

d 3 x jkl Tr G j k G l - i G j G k G

2 3

l

d Q q - 2Nf T5 dt 5

0, mq

0 = µq Q q
5 5

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Axial baryon charge and chiral chemical potential

Lattice simulation of topological charge in QCD vacuum [Leinweber]
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Axial baryon charge and chiral chemical potential
LPB investigated in e.m. interactions of leptons and photons with hot/dense nuclear matter via heavy ion collisions. e.m. interaction implies Q q Q = Q q + Q New µ conjugated to Q Bosonization of Q q following VMD prescription Extra term in Lagrangian
5 5 5 em 5 5 5 5

L -
0

1 4

µ

^ Tr µ V V



,

^ ^ with µ = µ due to spatially homogeneous and isotropic background ( ^ isospin content) and µ - 1 MeV
5 1

T

5


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Vector Meson Dominance approach to LPB
L
int

¯^ = q µ V µ q ;

^ Vµ -eAµ Q + g µ Ins + g 0 3 + g µ Is , µ

(Vµ,a ) Aµ , µ , 0 , µ , µ L
kin

1 2

g



g g

1 2

6


= - (Fµ F

1 4

µ

^ m

2

3ge - 2 mV -3eg g
4

+ µ 2

µ

e

2

2

eg g2

^ + µ µ + µ µ )+ Vµ,a (m2 ) 2 2eg e - 3eg -g g2 1 0 0 0 1 0 2

a,b Vbµ

0

0

2

g g2

= mixing of , , ,

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Vector Meson Dominance approach to LPB
P -odd interaction

1 1 ^^^ Lmix Tr jkl Vj k Vl = jkl Vj ,a Nab k V 2 2


l ,b

f , non-negligible L-R oscillations due to s -quark mass term = Q s 0 (3 2 avors)
5

1 ^ = a 0 0


0 1 0

0 1 0 +b 0 0 0


0 -1 0

0 0 0


[A. A. Andrianov, V. A. Andrianov, D. Espriu and X. Planells, (2010)]

Abnormal dilepton yield from local parity breaking in heavy-ion collisions, arXiv:1010.4688 [hep-ph]; PoS, QFTHEP2010, 053
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Vector Meson Dominance approach to LPB
Mixing matrix N : Isosinglet pseudoscalar background (T

(Nab )

1

- -

3

10 9 10

g ge e

-

9

10

0

g g 22e e
3 10 2

-
9

9

0
10

10

g e

µ) [RHIC, LHC] , det N


g 22 e

=0

9g |k | = | | 10e Pion-like condensate (not considered) (µ T ) [FAIR, NICA]
2 2 mV , = mV - 2


(Nab )

1

- -

3

2 2

g ge e

-
3

3

0
2

2

g e

-
3 2

g e

2 2

0

g 2 g 2e e
2

, det (N ) = 0

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Vector Meson Dominance approach to LPB
Mixing matrix N : Isosinglet pseudoscalar background (T

(Nab )

1

- -

3

10 9 10

g ge e

-

9

10

0

g g 22e e
3 10 2

-
9

9

0
10

10

g e

µ) [RHIC, LHC] , det N


g 22 e

=0

9g |k | = | | 10e Pion-like condensate (not considered) (µ T ) [FAIR, NICA]
2 2 mV , = mV - 2


(Nab )

1

- -

3

2 2

g ge e

-
3

3

0
2

2

g e

-
3 2

g e

2 2

0

g 2 g 2e e
2

, det (N ) = 0

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Manifestation of LPB in heavy ion collisions
Co cktail of hadron decays

Cocktail of hadron decays: 0 e +e - e +e - e +e - e +e - e +e - 0e +e - ¯ background c c

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Manifestation of LPB in heavy ion collisions
Acceptance

Experimental detector cuts: |pt | > 200 MeV, |y | < 0.35

Invariant mass smearing: gaussian with width 10 MeV

Acceptance correction breaks Lorentz invariance. Phase space calculation becomes a non-trivial task = VEGAS
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Manifestation of LPB in heavy ion collisions
Enhanced dilepton pro duction

L, ± contribution for vector mesons before acceptance corrections: dNee d 4 xdM
â

cV


2 2 V mV 3 2 g 2 M 2 2 k0 - M

2 2 M 2 - nV m 2 2 2 mV - nV m 2

32

/

M

dk0

e

k0 /T

-1
2

4 mV

,
2 4 + mV

M 2 - mV
2 2

,
2

,

m

2 V

,

V

2

where nV = 2, 0; |k | = k - M and M > nV m . cV absorbs combinatorial factors dierent for and , µV , nite volume suppression. Empirically for = 0 the ratio c /c 10 holds.
2 0 2

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Numerical results for dilepton excess

sp ectral function

Polarization splitting in spectral function for LPB = 2 MeV.
POLARIZATION ASYMMETRY!!
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Numerical results for dilepton excess

sp ectral function

Polarization splitting in spectral function for LPB = 2 MeV.
POLARIZATION ASYMMETRY!!
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Numerical results for dilepton excess

sp ectral function

Comparison spectral function in vacuum and for LPB = 2 MeV. In-medium calculation is pushed up by factor 1.8 due to recombination into
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Numerical results for dilepton excess
PHENIX anomaly

and contributions to dilepton yield for LPB = 2 MeV.
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Numerical results for dilepton excess
PHENIX anomaly

+ contributions in vacuum and for LPB = 2 MeV (normalization given by the peak).
ENHANCEMENT OF DILEPTON YIELD!!
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Numerical results for dilepton excess
PHENIX anomaly

+ contributions in vacuum and for LPB = 2 MeV (normalization given by the peak).
ENHANCEMENT OF DILEPTON YIELD!!
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Numerical results for dilepton excess
PHENIX anomaly

Comparison of PHENIX cocktail with modied cocktail using + contributions for LPB with =1, 2 MeV.
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Conclusions
LPB not forbidden by any physical principle in QCD at nite temperature/density The eect leads to unexpected modications of the in-medium properties of vector mesons and photons LPB seems capable of explaining in a natural way the PHENIX 'anomaly'
Event-by-event measurements of the lepton polarization

asymmetry may reveal in an unambiguous way the existence of LPB Dalitz and decays and in isotriplet condensate could be the main responsibles of the enhancement at 300 < M < 700 [work on progress]
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Thank you for your attention!

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Backup I
Explicit formula for the simulation with acceptance correction:
dN = d 4 xdM
â
acc.

~ dM

~ 1 (M - M ) exp - 2 2 1 kt dkt dyd pt
2 2

2

cV P

2 ~ 24 M ~ M 2g

1- V ~ M
µ

2 n2 m 2

32

/

~ |Ek p - k Ep | e Mt
4 mV

/

T

µ

-1

+ 4pµ p

â
2

,
2 4 + mV

~ M 2 - mV

,

,

m

2 V
2

V

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Backup II

Typical evolution of baryon density in a HIC (similar to temperature). should show the same behavior.
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Backup III

and contributions to dilepton yield in vacuum.
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