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Understanding the QGP through Spectral Functions and Euclidean Correlators BNL April 2008

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Angel Gómez Nicola

Universidad Complutense

Madrid

IN MEDIUM LIGHT MESON RESONANCES AND CHIRAL SYMMETRY RESTORATION

Understanding the QGP through Spectral Functions and Euclidean Correlators

BNL April 2008

r→ dilepton spectrum (CERES,NA60) and nuclear matter

Broadening vs Mass shift (scaling?)

f0 (600)/s→ vacuum quantum numbers, chiral symmetry restoration

Observed in nuclear matter experiments (CHAOS, …) through

threshold enhancement?

Any chance for Heavy Ions (finite T)?

What can medium effects tell about the nature of these states?

Spectral properties of light meson resonances in

hot and dense matter: Motivation

Rapp-WambachBrown/Rho

meson cocktail

2000 data

DILEPTONS

NA60 (m+m-)

NA45/CERES (e+e-)

Compatible with both broadening and dropping-mass scenarios

Broadening favored, dropping mass

almost excluded

normal nuclear matter density

r→ e+e- IN NUCLEAR MATTER

Signals free of T≠0 complications

Linear decrease of vector meson masses from scaling&QCD sum rules:

Brown, Rho ‘91

Hatsuda, Lee ‘92

Other many-body approaches give negligible mass shift

Chanfray,Schuck ‘98

Urban, Buballa, Rapp,Wambach ‘98

Cabrera,Oset,Vicente-Vacas ‘02

Experiments not fully compatible:

KEK-E325 (C,Fe-Ti): a = 0.0920.002

Jlab-CLAS (C,Cu): a = 0.020.02

Crystal Ball

CHAOS

MAMI-B

ppproduction in Nuclear Matter:

threshold enhancement in the s(I=J=0) channel

pA→ ppA’

gA→ p0p0A’

Ms <s> decreases, so that when Ms 2mp , phase space

is squeezed Gs 0 and the s pole reaches the real axis

Hatsuda, Kunihiro ‘85

Narrow resonance argument !

O(N) modelsat finite Tshow that the s remains broad when Ms 2mp

Further in-medium strength causes 2nd-sheet pole to move into

1st sheet pp bound state.

Patkos et al ‘02

Hidaka et al ‘04

Finite density analysis compatible with threshold enhancement

of pp cross section

Davesne, Zhang, Chanfray ‘00

Roca et al ‘02

Threshold enhancement as a signal of chiral

symmetry restoration:

Inverse Amplitude Method

“Thermal” poles

Dynamically generated

(no explicit resonance fields)

OUR APPROACH: UNITARIZED CHIRAL PERTURBATION THEORY

AGN, F.J.Llanes-Estrada, J.R.Peláez PLB550, 55 (2002), PLB606:351-360,2005

A.Dobado, AGN, F.J.Llanes-Estrada, J.R.Peláez, PRC66, 055201 (2002)

D.Fernández-Fraile,AGN, E.Tomás-Herruzo, PRD76:085020,2007

+

CHIRAL SYMMETRY

UNITARITY

pp scattering amplitude and ppg form factors in T > 0 SU(2)

one-loop ChPT

Chiral Perturbation Theory:

Relevant for low and moderate temperatures below Chiral SSB

Most general derivative and mass expansion of NGB mesons compatible with the SSB pattern of QCDmodel-independentlow-energy predictions.

NLSM

Weinberg’s chiral power counting:

Two-pion thermal phase space

enhancement

Enhancement Absorption

Unitarization: The Inverse Amplitude Method

ChPT does not reproduce resonances due to the lack of exact unitarity (resonances saturate unitarity bounds).

In the two-pion c.om. frame: (static resonaces):

Perturbative Unitarity

*

+

Exact unitarity

ChPT matching at low energies

Thermal s and r poles

(2nd Riemann sheet)

Very sucessful at T=0 for scattering data up to 1 GeV

and low-lying resonance multiplets, also for SU(3)

Dobado, Peláez, Oset, Oller, AGN.

* At T>0, valid for dilute gas (only two-pion states).

= 20 MeV

THETHERMALrPOLE

(2nd Riemann sheet)

Thermal phase space

enhancement + Increase of effective rpp vertex, small mass reduction up to Tc.

(for a narrow Breit-Wigner resonance)

The unitarized EM pion form factor shows also broadening

compatible with dilepton data and VMD analysis:

= 20 MeV

T=100 MeV

However, the pole remains wide even for M~2 mp

(spectral function not peaked around the mass for broad resonances)

THETHERMALf0(600)/sPOLE

(2nd Riemann sheet)

Strong pole mass reduction (chiral restoration) means phase space squeezing, which overcomes low-T thermal enhancement

Narrow vs Broad Resonances

NARROW:

Phase space squeezing

Threshold enhancement

differential

decay rate

2-particle differential

phase space

(R “particle” at rest)

r(s) strongly peaked around

r(s) broadly distributed

BROAD:

s pole away from the real axis ChPT approach valid at threshold no enhancement

Generalized decay rate:

H.A.Weldon, Ann.Phys.228 (1993) 43

NO phase-squeezing

for wide enough r(s) !

Narrow vs Broad Resonances

Narrow vs Broad Resonances:

No problem for I=J=1

REAL AXIS POLES AND ADLER ZEROS

AGN,J.R.Peláez,G.Ríos PRD77, 056006 (2008)

Require extra terms in the IAM to account properly for Adler zeros t(sA)=0.

Otherwise, spurious real poles below threshold in the 1st,2nd Riemann sheets.

Preserving chiral symmetry+unitarity:

No difference away from sA

Alternatively derived with dispersion

relations.

No additional poles for T0 with the

redefined amplitudes.

Does not behave as a (thermal) state, not even near the chiral limit

Consistent with not- scalar nonet

(tetraquark,glueball,meson-meson…)

“molecule” picture

M.Alford,R.L.Jaffe ‘00

J.R.Peláez ‘04

THE NATURE OF THERMAL RESONANCES: f0(600)/s

Brown&Rho ‘05

Harada&Sasaki ‘06

THE NATURE OF THERMAL RESONANCES: r

No BR-like scaling with condensate.

Mass dropping only very near “critical” (too high) T0 , as in BR-HLS models

Nature of our thermal r dominated by non-restoring effects (broadening)

Justified by approximate validity of GOR (r0,T=0)

Non chiral-restoring many-body effects not included (p-h, p-wave p self-energy, …)

Cabrera,Oset,Vicente-Vacas ‘05

Chiral restoring expected to be important in the s-channel as densityapproachesthe transition . No broadening to compete with now !

NUCLEAR CHIRAL RESTORING EFFECTS

Chiral restoring effects at T=0 and finite nuclear density approx. encoded in fp

Thorsson,Wirzba ‘95

Meissner,Oller,Wirzba ‘02

ppbound state

(“molecule” behaviour)

r

=

r

1

.

9

0

s

“non-molecular” ( )

r

Compatible with BR-like scaling

Brown,Rho ‘04

No threshold enhancement for reasonably high densities.

Mass linear fits:

Compatible with some theoretical estimates and KEK experiment.

However, additional medium effects (important in this channel!) might lead to negligible mass shift

In-medium light meson resonances studied through scattering poles in Unitarized ChPT provide chiral symmetry predictions for their spectral properties and nature.

The f0(600)/sshows chiral symmetry restoration features but remains as a T0wide not- state no threshold enhancement at finite T.

The r finite-T behaviour is dominated by thermal broadening in qualitative agreement with dilepton data. Mass dropping does not scale with the condensate.

Nuclear density chiral-restoring effects encoded in fp (r) drive the poles to the real

axis giving threshold enhancement in the s-channel and BR-like scaling in the

r-channel. pp bound states of different nature formed near the transition.

CONCLUSIONS

Full finite-density analysis, SU(3) extension (f-,K*,a0,…)