Burger F, Kirchner M, Müller-Preußker M, et al. Thermal transition temperature from twisted mass QCD. Presented at the The XXVIII. International Symposium on Lattice Field Theory, Villasimius, Sardinia Italy

Burger, Florian

Ilgenfritz, Ernst-Michael

Kirchner, Malik

Lombardo, Maria Paola

Müller-Preußker, Michael

Philipsen, Owe

Urbach, Carsten

Zeidlewicz, Lars

arXiv

We present the current status of lattice simulations with Nf = 2 maximally twisted mass Wilson fermions at finite temperature. In particular, the determination of the thermal transition temperature is discussed

Müller-Preussker, Michael

Hochschulschriftenserver - Universität Frankfurt am Main

PoS(Lattice 2010)220Thermal transition temperature from twisted massQCDtmfT collaboration:Florian Burger, Malik Kirchner, Michael Müller-PreusskerHumboldt-Universität zu Berlin, Institut für Physik, 12489 Berlin, GermanyE-mail: burger@physik.hu-berlin.deE-mail: malik@physik.hu-berlin.deE-mail: mmp@physik.hu-berlin.deErnst-Michael IlgenfritzUniversität Bielefeld, Fakultät für Physik, 33615 Bielefeld, GermanyHumboldt-Universität zu Berlin, Institut für Physik, 12489 Berlin, GermanyE-mail: ilgenfri@physik.hu-berlin.deMaria Paola LombardoLaboratori Nazionali di Frascati, INFN, 100044 Frascati, Roma, ItalyE-mail: mariapaola.lombardo@lnf.infn.itOwe Philipsen, Lars ZeidlewiczGoethe-Universität Frankfurt, Insitut für Theoretische Physik, 60438 Frankfurt am Main,GermanyE-mail: philipsen@th.physik.uni-frankfurt.deE-mail: zeidlewicz@th.physik.uni-frankfurt.deCarsten UrbachUniversität Bonn, HISKP and Bethe Center for Theoretical Physics, 53115 Bonn, GermanyE-mail: urbach@hiskp.uni-bonn.deWe present the current status of lattice simulations with Nf = 2 maximally twisted mass Wilsonfermions at ﬁnite temperature. In particular, the determination of the thermal transition tempera-ture is discussed.The XXVIII International Symposium on Lattice Filed TheoryJune 14-19,2010Villasimius, Sardinia ItalySpeaker.c  Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(Lattice 2010)220Thermal transition temperature from twisted mass QCD Lars Zeidlewicz1. IntroductionOne of the main aspects to be studied in thermal quantum chromodynamics (QCD) is thetransition – or smooth crossover – from a chirally symmetric and deconﬁned region of phase spaceto a hadronic phase with broken chiral symmetry. This transition has occurred in the cooling of theearly universe and is hoped to be reproduced in heavy ion collision experiments.A lot of effort has been put into lattice studies of this transition, see e.g. [1] and the most recentoverview by K.Kanaya [2]. Hybrid Monte-Carlo simulations are restricted to vanishing or at mostsmall chemical potential due to the sign problem that otherwise prohibits importance sampling.In case of zero chemical potential and physical quark masses, it has been demonstrated that thethermal transition is no true phase transition but really a smooth crossover [3]. The current knowl-edge about the nature of the phase transition for different quark masses is shown in Figure 1. Thisdependence is particularly important for lattice simulations with Wilson-type fermions, for whichphysical quark masses have not been feasible so far and extrapolations are necessary. Furthermore,by knowing the qualitative properties of this plot, some constraints on the enlarged phase diagramincluding a non-vanishing chemical potential can be anticipated.mudms1st1stpuregaugeN f = 3Nf = 2 + 1phys. pt.Z(2)Z(2) crossoverNf = 2mtricsNf=1O(4)?Figure 1: Nature of the thermal transition in the quark mass plane.The critical temperature for a true phase transition is uniquely determined by non-analyticitiesin the partition function. For a crossover there are only pseudo-critical temperatures which dependon the observable. Here we use the Polyakov loop and its susceptibility and compare to the pionnorm and the screening mass in the pseudo-scalar channel.The aforementioned lattice results have been obtained from simulations in which predomi-nantly staggered fermions have been applied. However, the question to what extent this type offermions is reliable has still not been completely settled. The main problem is the so-called rootingprocedure, i.e. the need to take the fourth root of the staggered fermion determinant in order todescribe a single ﬂavour of quarks, see e.g. [4]. Therefore, it is highly desirable to use differentfermion formulations so that the possible caveats are under better mutual control. Wilson-typefermions have very different systematic effects from the staggered formulation. In particular, theydo not suffer from the so-called taste-breaking that needs to be controlled in staggered simulations,see [5]. The major problems of Wilson-type fermions are of course the explicit chiral symmetrybreaking and the introduction of O(a) effects.2PoS(Lattice 2010)220Thermal transition temperature from twisted mass QCD Lars ZeidlewiczIn this contribution we report on our ongoing investigation of the thermal transition of QCDapplying so-called maximally twisted-mass fermions. These Wilson-type fermions offer automaticO(a) improvement. The quark mass is determined by the multiplicatively renormalisable twistedmass parameter m. For an introduction, see [6].We use one doublet of degenerate fermions for the twisted mass action. Thus, in terms ofFig. 1, we are restricted to the upper boundary where the strange quark is inﬁnitely heavy. Herethe situation may well be different from that at the physical point. However, the Nf = 2 setup issomewhat natural to start from with our action as the twisting always acts on fermion doublets.Furthermore, there remains the question whether the thermal transition in the two-ﬂavour chirallimit is really of second order in the O(4) universality class. Therefore, the chosen setup is verywell suited to establish further information about the quark mass dependence of the QCD transition.Besides our approach relying on the twisted mass formulation, also clover-improved Wilsonfermions are currently used for ﬁnite temperature studies [7, 8], see also [9, 10] in these proceed-ings. As compared to our previous work [11, 12], we now report on simulations with light quarkmasses & 300MeV that will give information on the quark mass and lattice spacing dependence ofthe critical temperature.In the following section, we present the maximally twisted mass lattice formulation as usedfor our simulations. Furthermore, we describe the non-trivial (k;b;m) phase diagram and explainour realisation of scans in b. Section 3 gives a summary of our results obtained so far. We showthe Polyakov loop and the ﬂavour non-singlet pseudo-scalar screening mass as examples for theobserved signals and collect the transition temperatures available from our data. This also allowsfor a discussion of cutoff effects. Finally, in Section 4 we conclude and describe our plans for thecontinuation of this work.2. Lattice actionFor our simulations we rely on zero temperature information by the European Twisted MassCollaboration (ETMC) [13, 14]. The gauge action is chosen to be tree-level Symanzik improved.The maximally twisted fermion matrix takes the formMmtm = 1 kcDWilson+2ikcamg5t3 (2.1)and acts on one fermion doublet. The Pauli matrix t3 acts in ﬂavour space and kc is the hoppingparameter at its critical value. For m =0 the action has its standard Wilson form. In the continuum,the new term iamg5t3 can be obtained by a non-anomalous chiral-ﬂavour rotation. However, thisrotational symmetry is broken by the Wilson-term so that one has different cutoff effects for eachvalue of this so-called twist-angle. For maximal twist, i.e. if k = kc, it has been shown that non-vanishing physical observables are automatically O(a) improved (see [6] and references therein).We have checked that this remains true at ﬁnite temperature by means of a quenched analysis [11]and a perturbative calculation [15].Wilson-type fermions suffer from unphysical phases in their bare parameter phase space. Forstandard Wilson fermions the Aoki phase at strong coupling is well known [16, 17]. For the en-larged (k;b;m) space of twisted mass fermions an additional phase transition plane has been foundthat incorporates the line of critical hopping parameters kc(b;m = 0) [18, 19, 20].3PoS(Lattice 2010)220Thermal transition temperature from twisted mass QCD Lars Zeidlewiczthermal transition/crossoversurface∞∞κβκc(β,T = 0)deconﬁnement0 βcusp βququenched limit Aoki phaseµbulk transitionconﬁnementconﬁnementDoubler region? 0.154 0.156 0.158 0.16 0.162 0.164 0.166 3.75 3.8 3.85 3.9 3.95  4  4.05 4.1 4.15 4.2κcβETMCPadeFigure 2: Left: Phase diagram in (k;b;m)-space for twisted mass lattice fermions at ﬁnite temperature.Right: Interpolation of kc(b) from ETMC results. 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 220  225  230  235  240  245  250  255  260T (MeV)Real(L)Nτ=10Nτ=12 0.05 0.055 0.06 0.065 0.07 0.075 0.08 0.085 0.09 220  225  230  235  240  245  250  255  260T (MeV)χ(Real(L))Nτ=10Nτ=12Figure 3: Real part of the Polyakov loop (left) and its susceptibility (right) from the two available latticespacings at mp  380MeV. The vertical line indicates the value of Tc.It is of course very important to make sure that the ﬁnite temperature simulations are notaffected by these unphysical phases. In Fig. 2, left, our ﬁndings are summarised [12]. The thermaltransition can be found as a surface that winds around the line of critical hopping parameters. Thisbehaviour can be understood as a remnant of the continuum symmetry under twist rotations [21].In conclusion, it is possible to perform physical simulations towards the continuum limit that arenot affected by unphysical bulk behaviour.Our simulation strategy is to perform scans in the lattice coupling b while keeping maximaltwist in order to be O(a) improved. The knowledge of kc(b) as well as the lattice spacing and pionmasses can be obtained from ETMC data [13, 14]. The interpolation of kc(b) is shown in Fig. 2,right. It is also possible to keep a ﬁxed pion mass by adjusting m(b;mp).3. Thermal signalsSince the expected behaviour is that of a continuous crossover, it is very important to studythe temperature dependence of several observables. In our study, we look at the real part of the4PoS(Lattice 2010)220Thermal transition temperature from twisted mass QCD Lars Zeidlewicz 2.2 2.4 2.6 2.8 3 3.2 3.4 220  225  230  235  240  245  250  255Mscr/TT (MeV)Nτ=10Nτ=12 0 100 200 300 400 500 600 700 800 900 1000 220  225  230  235  240  245  250  255  260σ2|π|2T (MeV)Nτ=10Nτ=12Figure 4: Left: Flavour non-singlet pseudo-scalar screening mass from the two available lattice spacingsat mp  380MeV. Right: Variance of pion norm at mp  380MeV. The vertical line marks Tc from thePolyakov loop susceptibility.Polyakov loop, the chiral condensate, the pion norm (pseudo-scalar susceptibility), the plaquetteand screening masses.In this contribution we present plots for the Polyakov loop, Fig. 3, the pseudo-scalar ﬂavournon-singlet screening mass and the variance of the pion norm, Fig. 4, at mp  380MeV. The peakposition of the susceptibility of the Polyakov loop is used to deﬁne Tc. For mp  380MeV, weobtain Tc(Nt = 10) = 243(10)MeV and Tc(Nt = 12) = 243(8)MeV from the respective maximalvalues.These crossover temperatures are consistent with the pseudo-scalar ﬂavour non-singlet screen-ing mass, presented in Fig. 4, left. This screening mass shows a qualitative change in behaviour atthe onset of the transition region, i.e. just left to the corresponding value of Tc. A combined anal-ysis of this screening mass and the corresponding scalar one will give information on the splittingintroduced by the UA(1)-anomaly. If the anomaly is still sufﬁciently strong near Tc, the transitionin the chiral limit is expected to be in the O(4) universality class, although a ﬁrst order scenariois not excluded [22, 23]. The size of this splitting is thus an indicator for the order of the Nf = 2transition in the chiral limit.The variance of the pion norm normalised to the spatial volumes2jpj2 = N3sD jpj22E Djpj2E2(3.1)isshowninFig.4, right. Forthisobservableapeakcanbefoundatapproximatelythesamepositionat which the Polyakov susceptibility peaks.In Fig. 5, left, Tc for the two lattice spacings at mp  380MeV is plotted. The Nt = 12 resultcan possibly be further reﬁned and at least a third lattice spacing is needed for a ﬁnal statement.However, the cutoff dependence appears to be rather small.In addtion to the points for mp  380MeV we currently simulate at Nt = 12 with mp 300MeV and 460MeV. For mp  300MeV, a ﬁrst value of Tc  225(11)MeV is available. Fig. 5,right, shows our results compared to those of [7]. It seems that our points tend to be at somewhathigher temperatures. A small shift in our results due to the scale set by the new ETMC data mightoccur, but we expect this to be at the percent level.5PoS(Lattice 2010)220Thermal transition temperature from twisted mass QCD Lars Zeidlewicz 220 230 240 250 260 270 0  0.002  0.004  0.006  0.008Tc (MeV)a2 (fm2)Nτ=10Nτ=12 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0  0.5  1  1.5  2  2.5  3  3.5r0Tcr0mπQCDSF/DIKNτ=8Nτ=10Nτ=12Figure 5: Left: Lattice spacing dependence for Tc as detemined by the Polyakov loop for mp  380MeV.Right: Values of Tc(mp) from the Polyakov loop susceptibility for different lattice spacings. The values ofQCDSF/DIK from [7] are shown for comparison.4. Conclusions and outlookWe have presented results of our study of the thermal transition of QCD applying maximallytwisted mass fermions. Relying on the ETMC data at zero temperature, we can investigate a massrange mp & 300MeV. Our current simulations will soon provide enough input to perform a chi-ral and continuum extrapolation of the critical temperature. So far we have concentrated on thePolyakov loop to deﬁne this temperature. Screening masses supplement our set of observables.Their splittings can give insights into the Nf = 2 chiral transition.AcknowledgmentsO.P. and L.Z. acknowledge support by the Deutsche Forschungsgemeinschaft, grant PH 158/3-1. F.B. and M. M.-P. acknowledge ﬁnancial support by DFG (GK 1504 and SFB/TR 9). We thankfor the generous support with supercomputing power by the HLRN Berlin and Hannover. Some ofthe computations have been performed on the apeNEXT in Rome. We thank the apeNEXT stafffor continual support.References[1] C. E. DeTar, “Recent Progress in Lattice QCD Thermodynamics,” PoS LATTICE2008 (2008) 001[arXiv:0811.2429 [hep-lat]].[2] K. Kanaya, these proceedings.[3] Y. Aoki, G. Endrodi, Z. Fodor, S. D. Katz and K. K. Szabo, “The order of the quantumchromodynamics transition predicted by the standard model of particle physics,” Nature 443 (2006)675 [arXiv:hep-lat/0611014].[4] M. Creutz, “Comments on staggered fermions / Panel discussion,” PoS CONFINEMENT8 (2008)016 [arXiv:0810.4526 [hep-lat]].[5] A. Bazavov, these proceedings.6PoS(Lattice 2010)220Thermal transition temperature from twisted mass QCD Lars Zeidlewicz[6] A. Shindler, “Twisted mass lattice QCD,” Phys. Rept. 461 (2008) 37 [arXiv:0707.4093 [hep-lat]].[7] V. G. Bornyakov et al., “Probing the ﬁnite temperature phase transition with Nf=2 nonperturbativelyimproved Wilson fermions,” arXiv:0910.2392 [hep-lat].[8] S. Ejiri et al. [WHOT-QCD Collaboration], “Equation of State and Heavy-Quark Free Energy atFinite Temperature and Density in Two Flavor Lattice QCD with Wilson Quark Action,” Phys. Rev. D82 (2010) 014508 [arXiv:0909.2121 [hep-lat]].[9] V. G. Bornyakov, these proceedings.[10] B. Brandt, these proceedings.[11] E.-M. Ilgenfritz, K. Jansen, M. Kirchner, M. P. Lombardo, M. Müller-Preussker, M. Petschlies,O. Philipsen, D. Schulze, L. Zeidlewicz and C. Urbach, “On the phase structure of lattice QCD withtwisted-mass Wilson fermions at non-zero temperature,” PoS(Lat2009)266 [arXiv:0912.0919[hep-lat]].[12] E.-M. Ilgenfritz, K. Jansen, M. P. Lombardo, M. Müller-Preussker, M. Petschlies, O. Philipsen andL. Zeidlewicz, “Phase structure of thermal lattice QCD with Nf = 2 twisted mass Wilson fermions,”Phys. Rev. D 80 (2009) 094502 [arXiv:0905.3112 [hep-lat]].[13] R. Baron et al. [ETM Collaboration], “Light Meson Physics from Maximally Twisted Mass LatticeQCD,” arXiv:0911.5061 [hep-lat].[14] ETMC, personal communication with K.Jansen.[15] O. Philipsen and L. Zeidlewicz, “Cutoff effects of Wilson fermions on the QCD equation of state toO(g2),” Phys. Rev. D 81 (2010) 077501 [arXiv:0812.1177 [hep-lat]].[16] S. Aoki, “New phase structure for lattice QCD with Wilson fermions,” Phys. Rev. D 30 (1984)2653-2663.[17] S. Aoki, “Solution to the U(1) problem on a lattice,” Phys. Rev. Lett. 57 (1986) 3136-3139.[18] S. R. Sharpe and J. M. S. Wu, “The phase diagram of twisted mass lattice QCD,” Phys. Rev. D 70(2004) 094029 [arXiv:hep-lat/0407025].[19] F. Farchioni et al., “Twisted mass quarks and the phase structure of lattice QCD,” Eur. Phys. J. C 39(2005) 421 [arXiv:hep-lat/0406039].[20] F. Farchioni et al., “Dynamical twisted mass fermions,” PoS LAT2005 (2006) 072[arXiv:hep-lat/0509131].[21] M. Creutz, “Effective potentials, thermodynamics, and twisted mass quarks,” Phys. Rev. D 76 (2007)054501 [arXiv:0706.1207 [hep-lat]].[22] R. D. Pisarski and F. Wilczek, “Remarks On The Chiral Phase Transition In Chromodynamics,” Phys.Rev. D 29 (1984) 338.[23] F. Parisen Toldin, A. Pelissetto and E. Vicari, “The 3-D O(4) universality class and the phasetransition in two-ﬂavor QCD,” JHEP 0307 (2003) 029 [arXiv:hep-ph/0305264].7

English

[WHOT-QCD Collaboration], “Equation of State and Heavy-Quark Free Energy at Finite Temperature and Density in Two Flavor Lattice QCD with Wilson Quark Action,” Phys.

Comments on staggered fermions /

Cutoff effects of Wilson fermions on the QCD equation of state to O(g2),” Phys.

Effective potentials, thermodynamics, and twisted mass quarks,”

New phase structure for lattice QCD with Wilson fermions,”

On the phase structure of lattice QCD with twisted-mass Wilson fermions at non-zero temperature,”

personal communication with K.Jansen.

Probing the ﬁnite temperature phase transition with

Remarks On The Chiral Phase Transition In

Solution to the U(1) problem on a lattice,”

The 3-D O(4) universality class and the phase transition in two-ﬂavor

The order of the quantum chromodynamics transition predicted by the standard model of particle physics,”

The phase diagram of twisted mass lattice

these proceedings.

these proceedings. 6P o S ( L a t t i c e ) Thermal transition temperature from twisted mass QCD Lars Zeidlewicz

Twisted mass lattice QCD,” Phys.

Twisted mass quarks and the phase structure of lattice

Thermal transition temperature from twisted mass QCD

Publications at Bielefeld University

Thermal transition temperature from twisted mass QCD

Abstract

Similar works

Full text

Available Versions

Hochschulschriftenserver - Universität Frankfurt am Main

Publications at Bielefeld University