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.
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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
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
Compatible with both broadening and dropping-mass scenarios
Broadening favored, dropping mass
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
Urban, Buballa, Rapp,Wambach ‘98
Experiments not fully compatible:
KEK-E325 (C,Fe-Ti): a = 0.0920.002
Jlab-CLAS (C,Cu): a = 0.020.02
ppproduction in Nuclear Matter:
threshold enhancement in the s(I=J=0) channel
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
(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
pp scattering amplitude and ppg form factors in T > 0 SU(2)
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.
Weinberg’s chiral power counting:
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):
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).
(2nd Riemann sheet)
Thermal phase space
enhancement + Increase of effective rpp vertex, small mass reduction up to Tc.
(for a narrow Breit-Wigner resonance)
compatible with dilepton data and VMD analysis:
However, the pole remains wide even for M~2 mp
(spectral function not peaked around the mass for broad resonances)
(2nd Riemann sheet)
Strong pole mass reduction (chiral restoration) means phase space squeezing, which overcomes low-T thermal enhancement
Phase space squeezing
(R “particle” at rest)
r(s) strongly peaked around
r(s) broadly distributed
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
for wide enough r(s) !
Narrow vs Broad Resonances
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
No additional poles for T0 with the
Does not behave as a (thermal) state, not even near the chiral limit
Consistent with not- scalar nonet
THE NATURE OF THERMAL RESONANCES: f0(600)/s
Brown&Rho ‘05 the chiral limit
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 ( the chiral limitr0,T=0)
Non chiral-restoring many-body effects not included (p-h, p-wave p self-energy, …)
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
pp the chiral limitbound state
“non-molecular” ( ) the chiral limit
Compatible with BR-like scaling
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.
Full finite-density analysis, SU(3) extension (f-,K*,a0,…)