Dilepton excess from local parity breaking in baryonic matter · Thus the generic situation in heavy ion collisions could be described by a combination of baryon and chiral chemical

Dilepton excess from local parity breaking inbaryonic matter

Domènec Espriu

Departament d’Estructura i Constituents de la Matèria &

Institut de Ciències del Cosmos,

Universitat de Barcelona

Brookhaven, 27 June 2012

With A. Andrianov, V. Andrianov and X. Planells

Domènec Espriu LPB in HI collisions 1

Outline

Introduction

Parity breaking at large densities

Parity breaking from topological fluctuations

Some consequences of LPB

How hadronic physics is modified by LPB

Can this possibility be tested in HIC?

The CERES/NA60/PHENIX/STAR ’anomaly’

Enhanced dilepton production explained?

Summary, conclusions and outlook


Introduction

Parity is one of the well established symmetries of stronginteractions. Yet there are reasons to believe that it may be brokenin some circumstances

The Vafa-Witten theorem does not apply at µ 6= 0. Nofundamental principle forbids spontaneus parity breaking

P-and CP-odd condensates = “pion” condensates

A Vilenkin, Phys. Rev. D22, 3080 (1980); A.B. Migdal, Zh.Eksp. Teor. Fiz. 61 (1971); T. D. Lee and G. C. Wick, Phys.Rev. D 9, 2291 (1974) (and many others); A.A.Andrianovand D.Espriu, Phys.Lett. B 663 (2008) 450; A.A.Andrianov,V.A.Andrianov and D.Espriu, Phys.Lett. B 678 (2009) 416


Introduction

Local large fluctuations in the topological charge probably exist ina hot environment.

For peripheral collisions they lead to the Chiral Magnetic Effect(CME): Large ~B ⇒ large ~E ⇒ charge separationFor central collisions (and light quarks) they correspond to anephemeral phase with chiral chemical potential µ5 6= 0

Topological fluctuations

D. Kharzeev, R. D. Pisarski and M. H. G. Tytgat, Phys. Rev.Lett. 81, 512 (1998); K. Buckley, T. Fugleberg, and A.Zhitnitsky, Phys. Rev. Lett. 84 (2000) 4814; D. E. Kharzeev,L. D. McLerran and H. J. Warringa, Nucl. Phys. A 803, 227(2008); A. Andrianov, V. Andrianov, D. Espriu, X. Planells,Phys. Lett. B 710 (2012) 230.


Introduction

Thus the generic situation in heavy ion collisions could be describedby a combination of baryon and chiral chemical potentials

µ ⇒ V0, µ5 ⇒ A0

Both A0 and V0 will be isosinglets but the latter may trigger apseudoscalar condensate in a non-singlet channel as we will seebelow.

We will present an effective meson theory description of bothphenomena.



Take a model with two scalar doublets Hj = σ̃j I+ i π̂j , j = 1, 2

Veff =1

2Tr{−

2∑

j ,k=1

H†j ∆jkHk+λ1(H

†1H1)

2+λ2(H†2H2)

2+λ3H†1H1H

†2H2

+1

2λ4(H

†1H2H

†1H2 + H

†2H1H

†2H1) +

1

2λ5(H

†1H2 + H

†2H1)H

†1H1

+1

2λ6(H

†1H2 + H

†2H1)H

†2H2} − q̄RH1qL + q̄LH

†1qR

The constants ∆ij , λi are constrained by QCD properties at lowenergies.

At least two scalar doublets are necessary to trigger a pseudoscalarcondensate.



This model provides a fairly accurate description of many aspectsof hadronic and nuclear physics: condensation point, absence ofchiral collapse, nuclear compressibility,...

The vacuum structure of this model is quite complex

It is a generic feature of the model that, after imposing all QCDconstraints, a phase with a pseudoscalar condesate appears

〈π̂2〉 = ρτ3 6= 0

The transition of is of second order (may be an artifact of theapproximation).



The transition is located at intermediate densities (from 3 to 6 ×ρN), where using several isomultiplets seems particularly justified


Some consequences of parity breaking

Some features:

Parity is no longer a good quantum number in stronginteractions: S ↔ PGenuine mass eigenstates do not posess a definite parity inthe decays

Isospin symmetry broken: SU(2) → U(1) if 〈π̂2〉 6= 0Two new Goldstone bosons may appear

Likely to influence the equation of state of neutron stars


Phenomenological consequences of SPB


Physical scenario

In a HIC the nuclear matter is first compressed and heated during< 0.5 fm, then cools down for 5-10 fm until freeze-out. We shallassume that a situation of quasi-equilibrium is established and thatthe fireball can be approximately described by a spatiallyhomogeneous but time dependent pseudoscalar background.

The scalar meson effective theory has already been shown (thepseudoscalar condensate will be time dependent: 〈π̂2〉 = ρ(t)τ3)In addition we get a new contribution via the anomaly

∆L ≃ εµνρσTr[

ζ̂µVνVρσ

]

with ζ̂µ ≃ (ζ̂ ,~0) for a homogenous fireball. ζ̂0 ∝ ∂0ρ(t) and itcould be either SU(3)f singlet or diagonal part of SU(3)f octet ora mixture of the two

This term influences the properties of vector mesons.


Parity breaking from topological fluctuations

During the compression and heating period a topological chargemay emerge. This can be treated by including a term

∆Ltop = µθ∆T5

Until freeze-out the topological charge is approximately conserved.

For light quarks the creation of topological charge leads to thegeneration of an axial charge (anomaly equation). The axial chargeis conserved too provided that the quark mass term remainssubdominant.

The characteristic oscillation time is governed by inverse quarkmasses. For u, d quarks 1/m̂q ∼ 1/5 MeV−1 ∼ 40 fm ≫ τfireballand the left-right quark mixing can be neglected. For strangequarks as 1/ms ∼ 1/200 MeV−1 ∼ 1 fm ≪ τfireball and the meanvalue of strange quark axial charge is around zero due to left-rightoscillations.


Effective description in terms of chiral charge

For u, d quarks QCD with a topological charge 〈∆T5〉 6= 0 can beequally described at the Lagrangian level by topological chemicalpotential µθ or by axial chemical potential µ5

〈∆T5〉 ≃1

2Nf〈Qq5 〉 ⇐⇒ µ5 ≃

1

2Nfµθ,

∆Ltop = µθ∆T5 ⇐⇒ ∆Lq = µ5Qq5We have to account for the photon contribution to the singlet axialanomaly

Qq5 → Q̃5 = Q

q5 − T em5 , T em5 =

Nc

8π2

∫

vol.

d3x εjkl Tr(

Âj∂k Âl)

.

The following term appears

∆L ≃ εµνρσTr[

ζ̂µVνVρσ

]

with ζ̂µ = ζ̂δµ0 for a spatially homogeneous fireball and ζ ∝ µ5Domènec Espriu LPB in HI collisions 15

Effective meson theory with chiral charge

The scalar part of the lagrangian can be estimated by using thespurion technique

Dν =⇒ Dν − i{µ5δ0ν , ·} = Dν − 2iµ5δ0ν

Two new processes are then likely to be most relevant inside thefireball thermodynamics: the decays η, η′ → ππ that are strictlyforbidden in QCD on parity grounds.

Dimension four terms in the chiral lagrangian lead to couplingssuch as

∼ 16µ5Fηf 2π

L ∂η ∂π∂π

A rough estimate of the partial width gives values comparable toΓρ→ππ: if ρ’s are in thermal equilibrium in the pion bath, so willthe η.


New eigenstates of strong interactions with LPB

Effective lagrangian:

L = 14Tr

(

DµHDµH†

)

+b

2Tr

[

M(H + H†)]

+M2

2Tr

(

HH†)

−λ12Tr

[

(HH†)2]

− λ24

[

Tr(

HH†)]2

+c

2(detH + detH†)

+d1

2Tr

[

M(HH†H + H†HH†)]

+d2

2Tr

[

M(H + H†)]

Tr(

HH†)

with

H = ξΣξ, ξ = exp

(

iΦ

2f

)

, Φ = λaφa, Σ = λbσb



Φ =

ηq + π0

√2π+ 0√

2π− ηq − π0 00 0

√2ηs

,Σ =

vu + σ + a00

√2a+0 0√

2a−0 vd + σ − a00 00 0 vs

(

ηqηs

)

=

(

cosψ sinψ− sinψ cosψ

)(

ηη′

)

For µ5 = 0, we assume vu = vd = vs = v0 ≡ fπ ≈ 93 MeV.For non-vanishing µ5 we assume isospin symmetry and thus, weimpose to our solutions to be vu = vd = vq 6= vs .The coupling constants are fitted to phenomenology (MeV):

b = −3510100,M2 = 1255600, c = 1252.2, d1 = −1051.7,

d2 = 523.21, λ1 = 67.007, λ2 = 9.3126



L = −12

(

σ ηq ηs)

−k2 + 2Σ iΘk0 0−iΘk0 −k2 + 2Qv gn

0 gn −k2 + 2S

σηqηs

+ interaction terms

Σ = −(M2 + 6d1mvq + 12d2mvq + cvs + 2d2msvs − 6v2qλ1− 6v2qλ2 − v2s λ2 + 2µ25)

Qv = bm/vq + d1mvq + 2d2mvq + 2cvs + d2mv2s /vq

S = bms/vs + cv2q/vs + 2d2msv

2q/vs + d1msvs + d2msvs

Θ = 4µ5, gn = 2√2cvq

After diagonalization new eigenstates are defined: σ̃, η̃ and η̃′.π and a0 are also included and lead to new states π̃ and ã0.


Masses

Mass dependence on µ5 for two values of the 3-momenta


Masses

The dependence of π̃ and ã0 masses on µ5 for ~k = 0


Widths

Widths depend strongly on µ5 and (unfortunately) on the detailsof the effective theory. η̃′ shows clear violations of unitarity ⇒more hadronic d.o.f. are needed


VMD and LPB

Lint = q̄γµV̂ µq; V̂µ ≡ −eAµQ +1

2gωωµI+ gρρµ

τ32

(Vµ,a) ≡ (Aµ, ωµ, ρµ ≡ (ρ0)µ) ,where Q = τ3

2+ 1

6; gω ≃ gρ ≡ g ≃ 6

Lkin = −1

4(FµνF

µν + ωµνωµν + ρµνρ

µν) +1

2Vµ,a(m̂

2)a,bVµb ,

(m̂2)a,b = m2V

10e2

9g2− e

3g− e

g

− e3g

1 0

− eg

0 1

, det

(

m̂2)

= 0.


VMD and SPB

The parity-odd interaction affecting vector mesons is given by theterm

Lmixing (k) = −1

4εµνρσ tr ζ̂µV̂ν(x)V̂ρσ(x) =

1

2ζǫjkl Vj ,aNab ∂kVl ,b

For isosinglet pseudoscalar background the mixing matrix is

(Nab) ≃

10e2

9g2− e

3g− e

g

− e3g

1 0

− eg

0 1

, det (N) = 0

For iso-triplet condensate (not considered in the following)

(Nab) ≃

2e2

3g2− e

g− e

3g

− eg

0 1

− e3g

1 0

, det (N) = 0


VMD and SPB

Physical states:

εµL =ζµk2 − kµ(ζ · k)

√

k2(

(ζ · k)2 − ζ2k2)

; εµ,LεµL = −1,

Kµνεν± =

(

k2I− m̂2 ±√

(ζ · k)2 − ζ2k2 N̂)

εµ±; ε− · ε+ = −1.

After the simultaneous diagonalization of matrices m̂2, N̂

N = diag

[

0, 1, 1 +10e2

9g2

]

≃ diag [0, 1, 1]

m̂2 = m2V diag

[

0, 1, 1 +10e2

9g2

]

≃ diag [0, 1, 1]


VMD and SPB

After diagonalization

m2V ,± ≡ m2V ± ζ|~k |

The photon itself is unaffected by a singlet ζ̂

The position of the poles for ± polarized mesons is moving withwave vector |~k |

Massive vector mesons split into three polarizations with massesm2V ,− < m

2V ,L < m

2V ,+.

This splitting unambiguously signifies LPB. Can it be measured?


Separation of helicities

Corresponds to µ5 = 290 MeV


Bouncing back to the medium

(A.Andrianov, S.Kolevatov, R.Soldati)

Mean free paths for vectormesons:

Lρ ∼ 0.8fm≪ Lfireball ∼ 5− 10fmLω ∼ 16fm ≫ LfireballLPB ”vacuum”6= empty vacuum= coherent stateof vacuum mesons

Mesons have different dispersion relations on both sides of thewall: continuity of the wave function implies that transmission willbe accompannied by reflection back to the medium.


Bouncing back to the medium

The reflection coefficient approaches 1 for large pT and close tothe vacuum on-shell condition. Many ω will decay inside thefirewall, in the LPB vacuum.

The ω much like the ρ will show a distorted shape.The emission of mesons at large pT should be suppressed.Can this be experimentally quantitatively verified?


Distorted spectral functions

Mixing of vector mesons with their axial counterparts has not beenconsidered. This mixing is however expected to be relatively smalldue to the relatively large mass differences and that mV ≫ µ5.


How to test these ideas?

Electromagnetic probes (electrons, positrons and photons, but alsomuons) are best suited to extract information about the possibleexistence of a LPB phase (and also other properties of hot/densenuclear matter)

Do we understand the electromagnetic properties of hot and densenuclear matter and/or the QGP?



This is an old puzzle...

Theoretical interpretations have so far failed...


Enhanced dilepton production

Theoretical calculation ’cocktail’ by Rapp and van Hees, Nucl.Phys. A806, 339 (2008)The contribution from hadron decays is independently normalizedbased on meson measurements.


Modified ρ+ ω contributionComparison with NA60 measurements (no acceptace correction)

A large value of µ5 required for best fit. µ5 is meant to be anaverage, experiment dependent quantity.LPB gives a good description for M2 > m2V but ’something ismissing’ for M2 < m2V .This region could receive additional contributions from the statesη̃, η̃′ in thermal equilibrium now as well as from ω Dalitz decay.


Modified Dalitz contribution

We only show the contribution of particles in thermal equilibrium.The ω Dalitz decay is not includedThe green line represents the new contribution due to µ5 6= 0On top of this one has to include the contribution from the directη η′ and ω decays


Conclusions and outlook

Local parity breaking is not forbidden by any physical principlein strong interactions at finite chemical potential

Topological fluctuations transmit their influence to hadronicphysics via a chiral chemical potential

LPB leads to unexpected modifications of the in-mediumproperties of scalar and vector mesons

Measurement event-by-event of the lepton polarization mayreveal in an unambiguous way the existence of parity violation

The ‘bouncing back effect’ may change the high pT spectrumand reinforce thermal equilibration

LPB may help explaining the observed lepton spectrum in theLMR of PHENIX and STAR

The possibility of breaking a fundamental symmetry is quiteopen!

Other implications?


Documents

Dilepton excess from local parity breaking in baryonic matter · Thus the generic situation in heavy ion collisions could be described by a combination of baryon and chiral chemical