propagation of spectral functions and dilepton production

B. Kampfer I Institute of Radiation Physics I www.hzdr.deMember of the Helmholtz Associationpage 1

B. Kampfer I Institute of Radiation Physics I www.hzdr.de

Propagation of Spectral Functions and Dilepton Production (Imprints of Chiral Restoration on Dielectron Spectra)

B. Kämpfer

Helmholtz-Zentrum Dresden-Rossendorf Technische Universität Dresden

Changes of hadron properties in mediumcarry signals of the way in whichthe vacuum changes in a nuclear environment W. Weise, NPA 574 (1994) 347c

- the hydro picture: local equilibrium- kinetic approach: BRoBUU- rho meson: VOC- AdS/QCD: emissivities and spectral fncts- theory: making particles, e.g. e+ e-


The Hydro Picture

- ignore pre-equilibrium- sum contributions over space + time till f.o.*)- add free decays after f.o. (hadronic cocktail)

*) only local equilibrium emissivities are needed

Wightman fnct

ret. Green fnct

schematic hydro: T(t), n(t)


Old DreamGMOR ora la BR or Joffe

fireball evolutionfor SIS18

Eur.Phys.J. A17 (2003) 83-87 caveat:riding on a steep bckgdisappearence of the signal

f.o.


Kinetic Approaches: Transport Models

- evolve distribution functions in space + time- species are coupled via coll. terms + decays (problems: detailed balance, cross sections)- mean field(s) included - propagate spectral functions

many realizations are at our disposal (Frankfurt, Giessen, Tubingen, ...)

here: BRoBUU = derivate of Giessen evolved by Barz, Wolf, Zetenyi, Schade „much room for improvements“


BUU Transport Codepropagation of broad resonances

Kadanoff-Baym Cassing-Juchem, Leupold (2000)test particles

ansatz


The Open Nuclear & Particle Physics Journal 3 (2010) 1,arXiv 0910.1541, nucl-th/0605036, Barz et al.

Spectral Functions: extreme mass shifts


Mass Evolution toward Freeze Out red: time instant of disappearence


tiny in-medium effects (even with extreme paramerters)


Prediction: Au + Au

postdictions: C+C (1.04 AGeV - DLS, 1 AGeV – HADES)


QCD Sum Rules: Predictions of Medium Modifications?

(i) as solution of integral eq. (Fredholm 1): too scarce information on OBE side

(ii) MEM:

(iii) moments: mean (= center of gravity) – OK variance (= width) skewness (= deformation) kurtosis (= up/down shot)

too large gapin powers of M

(iv) insert hadronic model

(v) pole + continuum ansatz

truncate: i < 6 (8, 12)

Titov, BK, PRC (2007)

Kwon, Weise, PRC (2010):another hierarchy+chiral gap

Gubler, Morita, Oka, PRL (2011)


QCD sum rules: hadron spectral moments QCD condensates (n,T), Landau

Kwon, Procura, Weise PRC (2008):

num. irrelevant

Hatsuda, Lee PRC (1992):

center of gravity

maximum flatness in Borel window


chiraltransformations

VOC: keep even conds., but set odd conds. to zero

Bordes, Dominguez, Pennarrocha, Schilcher JHEP (2006):

reconstruct from QCD sum rule

Hilger, Thomas, BK, Leupold PLB (2012)


rho Meson and a Schematic VOC Scenario(vanishing of chirally odd condenstates: VOCOC = V(OC) VOC)

chiral restoration: <q q> 0 (large density/temperature)

vac

VOC

2

spec

tral

mom

ent


vacuum: parameterize the spectral function

consistent QCD sum rule result

data: ALEPH (2005),


VOC

vackeep width

keeppeak

improvement of Leupold, Peters, Mosel NPA (1998)


VOC: minimum scenario of chiral restoration broadening as signal of chiral restoration

disclaimer: at chiral restoration more can happen

VOC

much less influence of VOC

NA60


Chiral Partners

chiraltransf.

with open charm

Hilger, BK, Leupold PRC (2011)chiral QCD sum rules

splitting of spectral densities between chiral partnersmust be driven by order parameters of spontaneouschiral symmetry breaking only

Wigner‘s nondegeneracy

Hohler, Rapp, Nucl.Phys. A892 (2012) 58


the case of V-A

in contrast to Weinberg‘s sum rules: no Goldstone propertieson r.h.s. (qQ currents are not conserved)

heavy quark symmetry: degeneracy of V – P, A - S

vacuum: Hayashigaki, Terasaki 0411285Reinders, Rubinstein, Yazaki PR (1985)

r.h.s.: „order parameters“ of chiral symm. breaking

Hilger, Buchheim, BK, Leupold PPNP(2012):


AdS/QCD

5D Riemann: x,z 4D Minkowski: x

semi-class. gravity strongly coupled gauge theo.

X(x, z) gauge-inv. Operators (x)

asymp. AdS black brane: T (Hawking) s (Bekenstein)

semi-class. functional correlation functions breaking conf. sym. by mass scale, e.g. dilation + potential


Example 1: only dilaton medium

bottom-up approach: EoS (lattice QCD) dilaton potential

ansatz: Gubser type pot. + polynom. distortions


lattice QCD, SU(3) gauge theory, Borsanyi et al., 1204.6184


benefit: w/o further input spectral functions transport coefficients

not universal (as, e.g. sheary viscosity/entropy)but sensitive dependence on pot. parameters


AdS/QCD, soft-wall model, Cui. Takeuchi, Wu, 1112.5923(T in GeV)

JHEP 1204 (2012) 144

Example 2: meson in vector channel

Abelian field strength of Vsoft-wall model:

mass shift


AdS/QCD, soft-wall model, Colangelo, Giannuzzi, Nicotri, 1201.1564, JHEP 1205 (2012) 076

Schwarzschild BH Reissner-Nordstrom BH: chem. pot.

vision: beyond soft-wall ansatz dilaton consistent with EoSproblem: missing unique QCD results with quarks

mass shift + broadening


e+ e- Production: Theory

coupling to an external field/environment particle production- gravitation: cosmic expansion (Basler, BK 1990)- homog. E(t) field: dyn. Schwinger effect- E = const field: Schwinger effect- m(t) due to chiral restoration (Greiner et al. 1995, 1996, 2012)

mimicks E(t), looks like dyn. Schwinger effect,non-Markovian process

problem: what are particles, quasi-particles, out-states?


q qbar production by chiral mass shift m(t)

Michler et al., arXiv:1208.6565


Blaschke, BK, Schmidt, Panferov, Prozorkevich,

Smolyansky. arXiv:1301.1640 E(t) = E0 sin (νt) exp (−t^2/tG^2 )

tG = 10

Dynamical Schwinger Effect


Summary

Medium changes of condensates (should) drive medium modifications of hadrons

difficult to identify rho, omega mass shifts (if there are any)in AA via inv. e+e- mass spectra (BRoBUU)

QCD sum rules: no direct link to shape of hadron spect. fncts. Landau term vs. density effects in condensates omega: significant density dependence of 4q conds. needed to balance Landau damping term Thomas, Hilger, BK PRL 2005

chiral sum rules most favorable

dream:AdS/CFT correspondence AdS/QCD: EoS, transport coeff. + hadrons


BUU

Width of Strangeoniump

proposed by Hernandez, Oset, ZPA (1992)

PLB (2011)


in Valencia – Paryev models:

analog in omega and phi photo-production

CLAS, PRL (2011)

CLAS PRL (2010)

CBELSA-TAPSPRL (2008)

prediction of broadening:Klingl, Wass, Weise, PLB (1998)

Spr

ing-

8: Is

hika

wa

et a

l., P

LB (

2005

)

V e+e-

Oset, Cabrera,...


ANKE data:Phys.Rev. C85 (2012) 035206

BRoBUU: H. Schade


ANKE PRC (2012)

BUU: H. Schade

mystery: phi phase space

stopping power of nuclear matter

p Acms(pN)

y


Hot/Dense Medium in AdS/CFT1998:Maldacena,Gubser, Klebanov, PolyakovWitten

class. gravity in 5D

asymptotically AdS + black brane thermo field theory: hQCD

5D gravity setting: Riemann-Hilbert + scalar field

graviton dilaton

decoupled in strong-coupling limit


condensate = vacuum + density dep. part

q density

sigma term

QCD trace anomaly

GORlattice

charmoniumscalar

twist-2 DIS pdf

DIS pdf

DIS pdf

GLS SR

fac. hyp.

twist-3 pdf

fac. hyp.

>Narison

if real condensate:couples to gravity


OBE sides: medium effects

significant medium effects

Kapusta, Shuryak PRD (1994)

elaboration of hadronic sides for light-light mesons

vac

med.

vac

med.

Hohler, Rapp, Nucl.Phys. A892 (2012) 58


AdS/CFT Emissivities

Baier,Stricker, Taanila, Vuorinen, Phys.Rev. D86 (2012) 081901, JHEP 1207 (2012) 094

at T > 200 MeV, one obtains the thermalization time scale ~ 0.1 fm/c, which one might compare with the typical production time of dileptons with mass/energy larger than 5 GeV, tau_p < 0.04 fm/c. It appears that dilepton pairs produced early on have a reasonable chance to escape the system while it is still out of thermal equilibrium.

problem of particle production in dynamical systems

propagation of spectral functions and dilepton production

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