We study the free energies of heavy quarks calculated from Polyakov loop
correlation functions in full 2-flavour QCD using the p4-improved staggered
fermion action. A small but finite Baryon number density is included via Taylor
expansion of the fermion determinant in the Baryo-chemical potential mu. For
temperatures above Tc we extract Debye screening masses from the large distance
behaviour of the free energies and compare their mu-dependence to perturbative
results.Comment: 6 pages, Presented at 23rd International Symposium on Lattice Field
  Theory (Lattice 2005), Trinity College, Dublin, Ireland, 25-30 Jul 200

Doring, M.

Ejiri, S.

Kaczmarek, O.

Karsch, F.

Laermann, E.

English

arXiv

The XXIIIrd Internaitonal Symposium on Lattice Field Theory 25-30 July 2005 Trinity College, Dublin, IrelandWe study the free energies of heavy quarks calculated from Polyakov loop correlation functions in full 2-flavour QCD using the p4-improved staggered fermion action. A small but finite baryon number density is included via Taylor expansion of the fermion determinant in the baryo-chemical potential m. For temperatures above Tc we extract Debye screening masses from the large distance behaviour of the free energies and compare their m-dependence to perturbative results

Doring, Matthias

Name not available

Heavy quark free energies and screening at finite temperature and density

We study the free energies of heavy quarks calculated from Polyakov loop correlation functions in full 2-flavour QCD using the p4-improved staggered fermion action. A small but finite baryon number density is included via Taylor expansion of the fermion determinant in the baryo-chemical potential {mu}. For temperatures above T{sub c} we extract Debye screening masses from the large distance behavior of the free energies and compare their {mu}-dependence to perturbative results

UNT (University of North Texas) Digital Library

BROOKHI EN NATI 0 N A L LAB 0 RATORY BNL-75085-2005-CP Heavy Quark Free Energies and Screening at Finite Temperature and Density Matthias Doring Universitat Bielefeld Fakultat fur Physik Universitatsstrsse 25 D-33615 Bielefeld, Germany F. Karsch, S. Ejiri, 0. Kaczmarek, E. Laermann Brookhaven National Laboratory, Upton, New York, 11973, USA Presented at the 23rd Znternational Symposium on Lattice Field Theory Dublin, Ireland July 25-30,2005 October 2005 Physics Department Brookhaven National Laboratory P.O. Box 5000 Upton, NY 1 1973-5000 www.bnl.gov Notice: This manuscript has been authored by employees of Brookhaven Science Associates, LLC under Contract No. DE-ACOZ 98CH10886 with the US. Department of Energy. The publisher by accepting the manuscript for publication acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or any third party's use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof or its contractors or subcontractors. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. , * .  “ “ . .  . .. . .  . , .  . .  . . . . . ... - . . . . . . -. . .. . . . . . . . . . . . . . . . - . Heavy quark free energies and screening at finite temperature and density Matthias Doring* Fakultiit f i r  Physik, Universitat Bielefeld, 0-3361 5 Bielefeld, Germany E-mail: doering@physik.uni-bielefeld.de S. Ejirib, 0. Kaczmareka, F. KarschaiC, E. Laermanna “Fakultatfur Physik, Universitat Bielefeld, 0-3361 5 Bielefeld, Germany bDepartnierit of Physics, The University of Tokyo, Tokyo 113-0033, Japan ‘Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA We study the free energies of heavy quarks calculated from Polyakov loop correlation functions in full 2-flavour QCD using the pCimproved staggered fermion action. A small but finite baryon number density is included via Taylor expansion of the fermion determinant in the baryo-chemical potential p. For temperatures above Tc we extract Debye screening masses from the large distance behaviour of the free energies and compare their p-dependence to perturbative results. BI-TP-2005-34 and TKYNT-05-23 and BNL-NT-05-29 PACS: 11.15.Ha, lZ.lO.Wx, 12.38Gc, 12.38.Mh XXIIIrd Interizational Syniposiimz on Lattice Field Theory Trinity College, Dublin, Ireland 25-30 Jdy  2005 *Speaker. @ Copyright owned by die author(s) under the terms of the Creative Commons Attribution-Noncommercial-ShareAlikeLicence. http://pos.sissa.it/ Heavy quarkpee energies and Debye screening masses atfinite temperature and density Matthias Doring 1. Introduction Lattice QCD has widely been used to get infoilnation about the properties of matter at high temperature and vanishing net baryon density pb [l]. These studies have been extended to non- vanishing baryon density. Le., the equation of state has been discussed using Taylor expansion [2], reweighting [3] or imaginary chemical potential techniques 1141. Furthermore the free energy of static quark anti-quark sources at pr, = 0 received much atten- tion [5]. We will now apply here the Taylor expansion approach in order to extend the results on this free energy to non-zero quark chemical potential. A first attempt to do this was discussed in [6]. Furthermore we will analyze the large distance behaviour of the free energy and determine the corresponding expansion coefficients of the screening mass, which can be compared to perturbative predictions. We will restrict the discussion of the expansion up to the 2nd order in pb here. Results up to the 6th order as well as furhter details on the simlulation and the Taylor expansion technique can be found in [7].  2. Taylor expansion method in QCD at finite density The staggered fermion partition function 2 p - s   D U A ( p ) e - ‘ ,  (2.1) where in our 2-flavour case A ( p )  is the square root of the fermion determinant, can be Taylor expanded in powers of the quark chemical potential p = yb/3 by inserting the expansion of A ( p )  in powers of p. The odd orders in the expansion of 2, are vanishing because D, is imaginary for odd and real for even n. The simulation can be done at p = 0, where the D,, are handled like observable quantities. This procedure can be extended easily to the p-dependent expectation value of an observable d that does not directly depend on p, We apply this scheme to the Polyakov loop correlation functions discussed in the next section. 3. Heavy quark free energies A heavy (static) quark Q at site x is represented by the Polyakov loop, N7 x4 = 1 L(X) = n U4(3C7x4) > 193 1 2  Heavy quark free energies arid Debye screening masses atJiiiite temperature and density Matthias Doring 0 1 2 3 4 5 6 0 1 2 3 4 5 6 (a> (b) Figure 1: The 0'" order coefficients fbQ,o and fav- for the singlet (a) and colour averaged (b) free energies. f & o  is matched to the T = 0 heavy quark potential at small distances (a). QQ,o which is an SU(3) matrix. A heavy anti-quark Q is described by the corresponding hermitian conjugate matrix. The colour averaged and singlet QQ-free energies F ~ ( P ,  T ,  p)  and F&(r, T ,  p)  can be calculated from the corresponding correlation functions ( P ) ,  FaVJ'(r,T,p)=-T QQ ~ n ( ~ a v ~ 1 ( P ) ) = f ~ ~ ~ ( P , T ) + f ~ ~ 2 ( P , T ) ( ~ ) ~ + @ ( ( ~ ) ~ )  , (3.2) where 1 1  @"(Y) = - - xTrL(x)TrLt(y) , Jy N,2 x,y 1 1  @' (Y) = - - TrL(x)L$ (y) . Jy Ne x,y (3.3) In Fig. 1 and 2 we show the results for the 0th and 2nd order expansion coefficients in p / T  for temperatures above and below T,. Because fzb:2(~, T )  is always negative, we find that for small p the free energy of a static quark anti-quark pair decreases in a medium with a net excess of quarks or anti-quarks. We determine the large distance value of these coefficients, shown in Fig. 3, by taking the weighted average of the values at the five largest distances. fa';' (m, T )  signs the transition tem- perature by showing a pronounced peak at T,. The coefficients of the colour averaged and singlet free energy are identical at infinite distance. Q Q J  4. Screening masses For temperatures above T, and large distances r the heavy quark free energies are expected to be screened, 193 I 3  Heavy qua y k  p e e  energies and Debye screening masses atjnite temperature arid deplsity Matthias Doring 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 -0.2 -0.4 -0.6 -0.8 -1 -1  7 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 _.- 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 (c) -0.2 -0.4 -0.6 -0.8 -1 -1.2 r . .  I r*1/2 - 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 (b) .- ./ 0 0.5 I 1.5 2 2.5 3 3.5 4 4.5 ( 4  Figure 2: The 2"d order coefficients of the singlet (a,c) and colour averaged (b,d) free energies below (a,b) and above (c,d) T,. with IZ = 1,2 for the singlet and colour averaged free energies respectively. In the infinite distance limit we thus get, Expanding the logarithm in powers of p we see that only the even orders of the expansion coeffi- cients for the screening mass are non-zero, i.e. the second order coefficient can be written as where we write AfFbln for the expansion coefficients of AFZ'. We use this expression to determine the expansion coefficient of order 2 from the infinite distance limit. For the 0th order coefficient we refer to fits of the form of eq. 4.1. In fact the rational expression under the limit in eq. 4.3 shows 193 /4 Heavy quark free energies and Debye screening inasses atjnite temperature and density Matthias Doring 2.5 2 1.5 1 0.5 0 a .  ?a E C B a a E E e  ' e  yTc , 0.8 1 1.2 1.4 1.6 1.8 2 (a> -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1 0 T K  , 0.8 1 1.2 1.4 1.6 1.8 2 (b) Figure 3: The coefficients for the singlet and colour averaged free energies at infinite distance rT versus temperature. only little r-dependence and we see a wide plateau starting close to rT = 0. We therefore determine m:""(T) by fitting the ratio in eq. 4.3 to a constant in the plateau range. The resulting coefficient, shown in Fig. 4 (b) is always positive and leads to an eiihancment of the screening mass for small pb # 0. At high temperatures m;""(T) is in remarkable agreement with the LO high temperature perturbative prediction resulting from the p-expansion of the Debye mass mD(T,p) = g ( T ) T  (4.4) where we introduce an additional scale factor A via nzl ( T )  = A . mD(T),  which is determined from fitting mh(T). We find A = 1.397(18). Finally we see, that mi(T)  and m y ( T )  differ by a factor 1/2, which is expected at high temperature for all the coefficients but has not been observed for the 0th order so far. 5. Conclusions We analyzed Le dependence of heavy quark free energies and screening on the baryon- chemical potential. The free energies are decreasing to first order in p 2 ,  while the screening mass is increasing. This suggests that the screening length in a baryon or anti-baryon rich quark gluon plasma decreases with increasing value of the chemical potential, which is consistent with the ex- pectation that a non-zero p shifts the transition to lower temperatures. The screening behaviour is in good agreement with perturbation theory for T/Tc>,2. We observed that the p-dependent corrections of the colour averaged screening mass are twice as large as those of the colour singlet. This suggests that the contribution to the p-dependent corrections of the colour averaged screening mass is due to two-gluon exchange. 193 1 5  Heavy quark f iee energies and Debye screening inasses atJiiiite temperature and density Matthias Doring 2.5 2 -  1.5 1 -  0.5 0 3  3.::h ~ ~ - - - ?c , 2 1 .5 1 0.5 0 ?Tc , 1 1 1.5 2 2.5 3 3.5 4 (b) Figure 4: 0th and 2nd order expansion coefficients of the screening mass. The solid lines are connected to the LO perturbation theory. 6. Acknowledgments Our work has been supported partly through the DFG under grant KA 1198/6-4, the GSI col- laboration grant BI-KAR and a grant of the BMBF under contract no. 06BI106. MD is supported through a fellowship of the DFG funded graduate school GRK 881. The work of FK has been partly supported by a contract DE-AC02-98CH1-886 with the U.S. Department of Energy. References [l] E Karsch and E. Laermann, hep-lat/O305025. [2] C. R. Allton, S. Ejiri, S. J. Hands, 0. Kaczmarek, E Karsch, E. Laermann and C. Schmidt, Phys. Rev. D 68 (2003) 014507; C. R. Allton, M. Doring, S. Ejiri, S.J. Hands, 0. Kaczmarek, E Karsch, E. Laermann, K. Redlich, Phys. Rev D 71 (2005) 054508. [3] Z. Fodor, S. D. Katz and K. K. Szabo, Phys. Lett. B 568 (2003) 73; E Csikor, G. I. Egri, Z. Fodor, S .  D. Katz, K. K. Szabo and A. I. TBth, JHEP 0405 (2004) 046. [4] M. D’Elia and M. P. Lombardo, Phys. Rev. D 70 (2004) 074509. [5] 0. Kaczmarek, E Karsch, E Zantow, P. Petrecky, Phys.Rev. D 70 (2004) 074505. [6] Z. Fodor, S. D. Katz, K. K. Szabo and A. I. TBth, Nucl. Phys. B (Proc. Suppl.) 140 (2005) 508. [7] M. Doring, S. Ejiri, 0. Kaczmarek, E Karsch, E. Laermann, hep-lat/O509001. 193 I 6  

Heavy quark free energies and screening at finite temperature and density

Abstract

Similar works

Full text

Available Versions

Name not available

UNT (University of North Texas) Digital Library