1. Study of chemical potential effects on hadron mass by lattice QCD Pushkina Irina* Hadron Physics & Lattice QCD, Japan 2004 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. 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  in the hot and dense medium are modified. KEK: at KEK, invariant mass spectra of electron-positron pairs were measured in the region below the  meson mass for the p+C and p+Cu collisions ( nucl-ex/0011013 ). The possible signature of the  modification at a normal nuclear-matter density. STAR: The invariant mass of  meson 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 . HP&LQCD Japan 2004

3. Introduction of chemical potential A thermodynamical system is described by the partition function For staggered fermions, the fermion determinant The chemical potential is introduced as, 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) HP&LQCD Japan 2004

4. Introduction of chemical potential 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. The property of fermion determinant HP&LQCD Japan 2004

5. Response of observables with respect to  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  =0 (QCD-TARO Collaboration, Phys.Rev.D65 (2002) 054501). Direct simulations are very hard! Many challenging efforts… QCD-TARO Collaboration: HP&LQCD Japan 2004 A. Nakamura Ph. de Forcrand M. Garcia Perez H. Matsufuru I.-O. Stamatescu T. Takaishi T. Umeda

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

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

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

9. Lattice size: 12 2 × 24 × 6Polyakov line susceptibility Lattice simulations Quark mass: am q = 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  = 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. Z 2 noise method with 200 noise vectors is used for the calculation of fermionic operators.   are L vectors of complex Gaussian random numbers, HP&LQCD Japan 2004  = 1, …, L

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

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

12. Second order responses Second order response of  -meson Second order response of  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 HP&LQCD Japan 2004

13. Conclusion & Outlook The behavior of hadrons can be investigated at finite  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! HP&LQCD Japan 2004