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Density Dependence of Condensates (Medium Modifications of Hadrons)

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Density Dependence of Condensates (Medium Modifications of Hadrons)

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Density Dependence of Condensates

(Medium Modifications of Hadrons)

B. Kämpfer

Research Center Dresden-Rossendorf

Technical University Dresden

* in preparation

with R. Thomas, Th. Hilger

Hadrons = Excitations of QCD Ground State

QCD ground state (vacuum)

n,T

UniversalMaterial Constants of Vacuum?

dil. symm. break.

symm. break. (spont.), o.p.

Condensates,

Monopoles,

Instantons,

Vortices, ...

vacuum

=

Medium in

Dilute Gas Approx.

Expansion not à la Taylor but Wilson: OPE

Wilson coeff.

quark& gluon

operators

Observables:

QCD Sum Rules à la Borel

condensates

Landau damp.

pert. term

Borel

4-quark condensates

(factorization fails)

CB-TAPS:

Trnka et al. ´05

Zschocke, Pavlenko, BK PLB ´03

also dim-8

contributions

norm. moment

Thomas/Zschocke/BK

PRL ´05

strong density dependence of combined 4-quark conds.:

chirally invariant

otherwise: Landau damping term would push up the mass

Book Keeping of 4-Quark Condensates

a la Klingl & Weise

1. flavor-pure

NPA 2007

by Fierz:

w/o color (1 ... 10)

w/ color

nucleon:

no inverse

pure flavor conds.:

(1‘ ... 10‘)

componets

not indep.

relations exist between 4-q conds.

(not accurately fulfilled in models)

Tuebingen chiral quark model : approx. fulfilled

2. flavor mix

NPA 2007

all together:

vacuum: 2•5 +10 = 20

medium: 2•10+24 = 44

flavor symmetry: 10 (20)

4-q cond. = order parameter of chiral symmetry?

4-q conds. for nucleon 4-q conds. for V

interpolating current:

Fierz

Joffe: t = -1

4-q cond. = order parameter of chiral symmetry?

example: nucleon in vacuum

chirally invariant:

chirally non-invariant:

vacuum: Jido ´96

Ansatz:

l.h.s=

3 indep. sets of combinations

of 4-q conds. enter

phenomenological

point of view

Scheinast et al.

PRL 2006

magnifier

2000

2001

D in medium: Weise/Morath, Hayashigaki

expected pattern:

hadron scenario

Lutz, Korpa 2005:

w/o inel.

w/ inel.

hadron properties

QCD

basic features (Weise,Morath 2001):

Pole + Continuum Ansatz

w/o change of continuum

Weise/Morath ... ´99: tiny in-medium effects

Generalis/Broadhurst ´84:

medium resistent

OPE: operator mixing

CB-TAPS & Borel QSR:

1.

Conclusions

strong in-medium change of 4q cond.

4q cond. = new order parameter?

2. N: 4q conds. vs. phenomenlogy

3. D:

Sensors for

QCD vaccum

Quantify change of QCD vacuum:

nB, T dependence of material constants

hadron masses condensates

back up slides

Limitations of usual QCDSR

even/odd parts:

isolating lowest states

neg. energy

Tlab = 25 AGeV

Chem. Freeze-Out

Cleymans-Redlich-Wheaton param.

Fuchs et al.: T > 100 MeV meson effects

Leupold: 4-q cond. vs. nB, T

Spec. Function [GeV^-2]

E [GeV]

1.6

2.0

= center of gravity of

pole ansatz is not appropriate:

D+

Lutz, Korpa

pole

+ continuum

ansatz

How to Measure Med.-Mod. of D Mesons?

K-

FAIR: CBM

PANDA

D0

pi+

lesson from K: measure multiplicity of D

Tsushima, Sibirtsev, Friman, Lee,...

Mystery of Mass

sensitive to medium modifications

3. ss sector:

?

strangeness in nucleon?

OZI rule

Case of Strangeness: K

2.5 GeV

Au (1 AGeV) + Au

BUU

Uhlig et al. (KaoS) PRL 2005

Scheinast at al. (KaoS) PRL 2006

Case of Di-Electrons

A

QCD sum rules

CB-TAPS

Rossendorf

BUU model

e+

e-

Understanding Hadron Masses

Stark

Zeeman

nuclear matter = external field

Brown & Rho (1991):

search by HADES ...

sensors for QCD vacuum?

e+

e-

Nucleus as Laboratory

HADES

KEK

CLAS

no FSI: direct probes

V. Metag & U. Mosel

CB-TAPS

@ ELSA

FSI