Study of chemical potential effects on hadron mass by lattice Q C D

1. Hadron Physics & Lattice QCD, Japan 2004 Study of chemical potential effects on hadron mass by lattice QCD Pushkina Irina* Three main points • What do we know from first principles? • Why is QCD at finite density difficult? • What can we do in practice? *) School of Biosphere Science, Hiroshima University, Japan

2. HP&LQCD Japan 2004 Experimental data regarding in-medium hadrons • CERES: Observation of the large low mass e+e- pair enhancement in CERN SPS in Pb+Au collisions at 158 AGeV/c and 40 AGeV/c (nucl-ex/0212015). The data may only be reproduced if the properties of the intermediate r in the hot and dense medium are modified. • KEK: at KEK, invariant mass spectra of electron-positron pairs were measured in the region below thewmeson mass for the p+C and p+Cu collisions (nucl-ex/0011013). The possible signature of the r/w modification at a normal nuclear-matter density. • STAR: The invariant mass ofrmeson decays in Star experiment at Au+Au collisions at RHIC shows 60-70 MeV downward shift of the peak from the vacuum value (nucl-ex/0211001). The modification of the spectral function at finite T and m.

3. HP&LQCD Japan 2004 Introduction of chemical potential A thermodynamical system is described by the partition function For staggered fermions, the fermion determinant • Gavai considered more general form than (Phys.Rev.D32 (1985) 519) • Creutz discussed how the chemical potential appears in lattice fermion formulation (hep-lat/9905024) • Hasenfratz and Karsch have shown that such formula avoids nonphysical divergence of the free energy of quarks (Phys.Lett.125B (1983) 308) The chemical potential is introduced as,

4. HP&LQCD Japan 2004 Introduction of chemical potential The property of fermion determinant • Due to the complex nature of the fermion determinant, the standard Monte Carlo simulation is very difficult to obtain physical quantities. • Quench approximation of lattice QCD is not appropriate for finite density system.

5. HP&LQCD Japan 2004 Response of observables with respect to m Many challenging efforts… • The singlet and non-singlet quark number susceptibilities (S.Gottlieb et al., Phys.Rev.D55 (1997) 6852) • The susceptibilities for quenched and 2 flavors QCD (Phys.Rev.D65 (2002) 054506). The susceptibilities for 3 flavors with improved staggered fermions (MILC, hep-lat/0209079). • The responses of meson screening masses and the quark condensation with respect to the chemical potential at m=0 (QCD-TARO Collaboration, Phys.Rev.D65 (2002) 054501). Direct simulations are very hard! QCD-TARO Collaboration: • A. Nakamura • Ph. de Forcrand • M. Garcia Perez • H. Matsufuru • I.-O. Stamatescu • T. Takaishi • T. Umeda

6. HP&LQCD Japan 2004 A schematic representation of possible QCD phase diagram Response of hadron masses with respect to m Our strategy is to expand the hadronic quantities in the vicinity of zero m at finite temperature, and explore their changes through the response to the chemical potential at m = 0. T range of our work Tc QGP phase hadron phase 2CSC 3CSC 0 m mc The hadron correlator Here, and

7. HP&LQCD Japan 2004 Lattice simulations Problem: how to get the derivative of the correlator from lattice simulations? p+-meson the fermion determinant the meson propagator part the Dirac matrix for pseudoscalar meson for vector meson the quark propagator

8. HP&LQCD Japan 2004 Lattice simulations Crucial fact: the derivatives are taken before doing the integration numerically !

9. HP&LQCD Japan 2004 Lattice simulations Lattice size: 122×24×6 Polyakov line susceptibility Quark mass: amq = 0.100 The R-algorithm is used to generate 1000 configurations. The mesonic correlator and its derivatives were calculated every 25 sweeps with molecular dynamics step d = 0.2 and trajectory length of 50 steps in this run. The fitting range is z = 1-23 for pseudoscalar meson and z = 4-20 for vector meson. Z2 noise method with 200 noise vectors is used for the calculation of fermionic operators. , xa are L vectors of complex Gaussian random numbers, a = 1, … , L

10. HP&LQCD Japan 2004 Mesonic correlator The mesonic correlator:

11. HP&LQCD Japan 2004 First order responses Isoscalar chemical potential Isovector chemical potential The first order responses are equal to 0!

12. HP&LQCD Japan 2004 Second order responses Second order response of r-meson Second order response of p-meson • In the confinement phase the second order response is not changed much with increasing temperature • In the deconfinement phase the behavior of the second order response of both pseudoscalar and vector mesons is quite similar

13. HP&LQCD Japan 2004 Conclusion & Outlook • The behavior of hadrons can be investigated at finite m! • The extension of investigation to the chiral limit • The influence of the vector chemical potential on the screening mass of pseudoscalar meson in the deconfinement phase • The possibility to check the various scenarios concerning the nature of vector mesons (Harada & Sasaki, hep-ph/0109034) • The investigation of baryons at finite quark number chemical potential is in progress!