We present the status of runs performed in the twisted mass formalism with
$N_{\rm f}=2+1+1$ flavours of dynamical fermions: a degenerate light doublet
and a mass split heavy doublet. The procedure for tuning to maximal twist will
be described as well as the current status of the runs using both thin and
stout links. Preliminary results for a few observables obtained on ensembles at
maximal twist will be given. Finally, a reweighting procedure to tune to
maximal twist will be described.Comment: 7 pages, 4 figures, talk presented at the XXVI International
  Symposium on Lattice Field Theory, July 14-19, 2008, Williamsburg, Virginia,
  US

Baron, Rémi

Boucaud, Philippe

Deuzeman, Albert

Drach, Vincent

Farchioni, Federico

Gimenez, Vicent

Herdoiza, Gregorio

Jansen, Karl

Montvay, István

Palao, David

Pallante, Elisabetta

Pène, Olivier

Reker, Siebren

Scholz, Enno E.

Urbach, Carsten

Wagner, Marc

Wenger, Urs

English

arXiv

Montvayh, István

Bern Open Repository and Information System (BORIS)

PoS(LATTICE 2008)094Status of ETMC simulations with Nf = 2+1+1twisted mass fermionsRUG-CTN 358, DESY 08-137, HU-EP-08/49, MS-TP-08-26Rémi Barona, Philippe Boucaudb, Albert Deuzemanc, Vincent Drachd ,Federico Farchionie, Vicent Gimenez f , Gregorio Herdoizag, Karl Janseng,István Montvayh, David Palao f , Elisabetta Pallantec, Olivier Pèneb, Siebren Reker∗†c‡,Enno E. Scholzi, Carsten Urbach j, Marc Wagner j and Urs WengerkaCEA, Centre de Saclay, IRFU/Service de Physique Nucléaire, F-91191 Gif-sur-Yvette, FrancebLaboratoire de Physique Théorique (Bât. 210), Université de Paris XI, Centre d’Orsay, 91405Orsay-Cedex, FrancecCentre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen, theNetherlandsdLaboratoire de Physique Subatomique et Cosmologie, 53 avenue des Martyrs, 38026 Grenoble,FranceeUniversität Münster, Institut für Theoretische Physik, Wilhelm-Klemm-Straße 9, D-48149Münster, GermanyfDep. de Física Teòrica and IFIC, Universitat de València-CSIC, Dr.Moliner 50, E-46100Burjassot, SpaingDESY, Platanenallee 6, D-15738 Zeuthen, GermanyhDeutsches Elektronen-Synchrotron DESY, Notkestr. 85, D-22603 Hamburg, GermanyiPhysics Department, Brookhaven National Laboratory, Upton, NY 11973, USAjHumboldt-Universität zu Berlin, Institut für Physik, Newtonstraße 15, D-12489 Berlin, GermanykInstitute for Theoretical Physics, University of Bern, Sidlerstr. 5, CH-3012 Bern, SwitzerlandWe present the status of runs performed in the twisted mass formalism with Nf = 2+1+1 flavoursof dynamical fermions: a degenerate light doublet and a mass split heavy doublet. The procedurefor tuning to maximal twist will be described as well as the current status of the runs using boththin and stout links. Preliminary results for a few observables obtained on ensembles at maximaltwist will be given. Finally, a reweighting procedure to tune to maximal twist will be described.The XXVI International Symposium on Lattice Field TheoryJuly 14-19 2008Williamsburg, Virginia, USA∗Speaker.†For the ETM Collaboration‡Email: s.f.reker@rug.nlc© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(LATTICE 2008)094Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren Reker1. IntroductionThe twisted mass formulation of Lattice QCD (see for example references [1, 2]) is beingstudied extensively with Nf = 2 dynamical flavours by the European Twisted Mass (ETM) collab-oration [3 – 7]. In the twisted mass formulation of QCD, the Wilson term is chirally rotated withina doublet. For the 2-flavour case, this amounts to a mass degenerate (u,d) quark doublet. In recentstudies, a partially quenched setup [8] was used to add the strange quark to this formulation. Oneway to include a dynamical strange quark is to add in addition to the strange quark a charm quark ina heavier and mass-split doublet. This formulation was introduced in [9] and first explored in [10].We will use that formulation and report on the current status of runs with Nf = 2+ 1+ 1 twistedmass quarks conducted by the ETM collaboration. In section 2 we will detail the lattice action andthe simulation algorithm, while in section 3 we describe our procedure for tuning to maximal twist.In section 3.3 we discuss a reweighting procedure allowing to speed up and improve the accuracyof tuning to maximal twist. In section 4 we show a set of preliminary results. Finally in section 5we describe first results from one level of stout smearing [11].2. Lattice action and simulation algorithmIn the gauge sector we use the Iwasaki [12] gauge action (with β = 1.9 in the ensembles weare discussing here). With this gauge action we observe a smooth dependence of phase sensitivequantities on the hopping parameter κ around its critical value (κcrit). The fermionic action for thelight doublet is given by:Sl = a4∑x{χ¯l(x) [DW [U ]+m0,l+ iµlγ5τ3]χl(x)} (2.1)[2], where m0,l is the untwisted bare quark mass tuned to its critical value mcrit, µl is the bare twistedquark mass for the light doublet, τ3 is the third Pauli matrix acting in flavour space and DW [U ] isthe Wilson-Dirac operator. The quark doublet fields that are proportional to the renormalized u andd doublet fields in the physical basis are given by:ψ physl = ei2ωlγ5τ3χl, ψ¯physl = χ¯lei2ωlγ5τ3 . (2.2)The light doublet twisting angle ωl takes the value ωl →±pi2 as m0,l −mcrit →±0. In the heavysector, as has been shown by Frezzotti and Rossi in [9], a real quark determinant with a mass-splitdoublet can be obtained if the mass splitting is taken to be orthogonal in isospin space to the twistdirection. The mass term in the heavy sector then becomes:Sh = a4∑x{χ¯h(x) [m0,h+ iµσ γ5τ1+µδ τ3]χh(x)} . (2.3)This time the mass splitting is in the τ3 direction and the twist in the τ1 direction, which yields asimilar rotation relation to the physical quark basis:ψ physh = ei2ωhγ5τ1χh, ψ¯physh = χ¯hei2ωhγ5τ1 . (2.4)At maximal twist (|ωl|= |ωh|= pi2 ) physical observables are automatically O(a) improved withoutthe need to determine any action or operator specific improvement coefficients. The gauge config-urations are generated with two different algorithms, depending on whether thin or stout links are2PoS(LATTICE 2008)094Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren Rekerbeing used. For thin links a Polynomial Hybrid Monte Carlo (PHMC) updating algorithm [13, 14],while for stout links the PHMC setup described in [15] is used.1 All ensembles described in thispaper correspond to lattices with spatial extension L/a = 24 and temporal extension T = 2L. Ourlightest twisted mass quark value (aµl = 0.004) corresponds to a pion mass of around 300 MeVand a value of mpiL around 3.5.3. Tuning action parameters3.1 ProcedureTuning to maximal twist requires to set m0,l and m0,h equal to some proper estimate of thecritical mass mcrit = mcrit(β ) [9]. Here we set m0,l = m0,h ≡ 1/(2κ)− 4 and, at fixed µσ and µδ ,for each value of µl , we tune κ so as to obtain amPCAC,l = 0 (see also eq. (3.1)). Note that theuntwisted PCAC mass arising from the heavy sector is O(a) and ωh is automatically very closeto pi2 [10]. Our way of implementing maximal twist can be viewed as the extension to the theorywith 2+1+1 dynamical quarks of the optimal critical mass method of Refs. [16]. In this way weexpect [17] the (absolute) magnitude of lattice artifacts to remain roughly constant as µl → 0. ThePCAC mass in the light sector is defined in the following way:mPCAC,l =∑x〈∂0Aa0,l(x, t)Pal (0)〉2∑x〈Pal (x, t)Pal (0)〉 , (3.1)where the axial and pseudoscalar bilinears Aµ,l and Pl areAaµ,l ≡ χ¯lγµγ5τa2χl and Pal = χ¯lγ5τa2χl. (3.2)The numerical precision at which the condition mPCAC,l = 0 is fulfilled in order to avoid residualO(a2) effects when the pion mass is decreased is, for the present range of lattice spacings, |ε/µl|.0.1, where ε is the small deviation of mPCAC,l from zero [4, 18]. Note that typically a good statisticalprecision on the estimate of mPCAC,l is required to satisfy this condition. This computationallydisadvantageous situation can be remedied through the use of reweighting, as described in section3.3.The heavy doublet mass parameters µσ and µδ should be adjusted in order to reproduce thephenomenological values of the renormalized s and c quark masses. The latter are related to µσand µδ via [9]:(ms,c)R =1ZP(µσ ∓ ZPZS µδ ) (3.3)where the − sign corresponds to the strange and the + sign to the charm. In practice we fix thevalues µσ and µδ by requiring the kaon mass to take its physical value and (mc)R & 10(ms)R(through an estimate of ZP/ZS).1Note that in the Monte Carlo simulation we monitor that the minimal eigenvalue of the Dirac operator of the heavydoublet always remains positive.3PoS(LATTICE 2008)094Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren Reker3.2 StatusThe tuning status of our ensembles is summarized in table 1 and illustrated in figure 1. Theensembles considered here have the following parameters: β = 1.9, aµσ = 0.15 and aµδ = 0.19,with lattice volumes of 243×48.aµl 0.004 0.006 0.008 0.01κcrit 0.163270 0.163265 0.163260 0.163255Table 1: Summary of tuning to maximal twist.3.0624 3.0625 3.0626 3.0627-0.4-0.20.00.20.41/(2k)mPCAC,l /m lFigure 1: Tuned runs at β = 1.9, with a box size of243×48, with aµσ = 0.15 and aµδ = 0.19. From leftto right the points correspond to aµl = 0.004 (red),aµl = 0.006 (green), aµl = 0.008 (blue) and aµl =0.01 (yellow). For all ensembles, mPCAC,l/µl is withinthe 10% level (see text).0.00 0.02 0.04 0.060.000.050.10(a mp)2a f pFigure 2: a fpi as a function of (ampi)2 for the fourensembles described above. All of these are at β =1.9, L/a = 24 and T/a = 48. Error bars are plotted,but they fall within the size of the dots.Tuning to κcrit was performed independently for each µl value. From table 1 we observe thatthe estimate of κcrit depends weakly on µl . Figure 1 shows that for all µl values the condition|ε/µl|. 0.1 has been fulfilled.3.3 ReweightingReweighting towards the chiral limit for (untwisted) Wilson fermions has been recently ex-plored in reference [19] (and see also the conference contribution [20] with further references). Fortwisted Wilson fermions one can use reweighting near maximal twist for tuning the last digits ofthe hopping parameter κ . Once the update is close to κcrit (in the present case for ∆κ = |κ−κcrit|=O(10−5)) the situation is rather advantageous for an effective reweighting because the gauge fieldconfiguration is fluctuating between positive and negative values of mPCAC,l. Thus, in order to com-plete the tuning one has to just reweight the ensemble to a close-by value of κ at which mPCAC,l = 0is realized.For calculating the ratio of determinants one could use the methods developed in reference[19], but we applied a simple and fast method based on least-square optimized polynomial approx-4PoS(LATTICE 2008)094Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren Rekerimations introduced in [21]. In the case of Nf flavours, these polynomials satisfylimn→∞P(1)n (x) = x−Nf/2, limn→∞P(2)n (x) =1√P(1)n1 (x), x ∈ [ε,λ ] (3.4)where the interval [ε,λ ] covers the spectrum of Q†(κ)Q(κ), with Q the fermion matrix and n1(ni)the actual value of n used in the case of the polynomial P(1)(P(i)). With these polynomials thereweighting factor for κ1 → κ2 is 1/det[P(2)n2 (κ1)P(1)n1 (κ2)P(2)n2 (κ1)]. A stochastic estimator of thereweighting factor can be obtained from a random Gaussian vector asexp{−η†(Ω−1)η}, with Ω≡ P(2)n2 (κ1)P(1)n1 (κ2)P(2)n2 (κ1) . (3.5)We showed in test runs that with a few stochastic estimators an effective reweighting can beachieved for ∆κ ' 10−5. We actually applied determinant break-up by a factor of 2, that is, weconsidered two copies of half doublets, both for light and heavy doublets. With this method thenumber of long tuning runs for maximal twist can be reduced.4. ResultsIn this section we present preliminary results for the light quark mass dependence of the piondecay constant and the pion, kaon and nucleon masses (figures 2,3 and 4). The pion masses inthese ensembles are in the range from 300 to 500 MeV, corresponding to β = 1.9 and aµl = 0.004to 0.01 (see section 3.2).0.000 0.003 0.006 0.009 0.012 0.0150.000.020.040.060.080.10a ml(amK/ p)2Figure 3: The kaon (blue) and pion (red) squaredlattice masses are plotted versus the bare quark massaµl .0.00 0.02 0.04 0.060.000.250.500.75(a mp)2a mNFigure 4: The nucleon mass (amN) as a function of(ampi)2 for the four ensembles described above. Asubset of the available statistics has been used here.We measured r0/a and performed its chiral extrapolation. The results are compared to thoseof our Nf = 2 runs with β = 3.9 at the same lattice volume in table 2. The vicinity of the twovalues is very encouraging, since it might allow to perform a direct comparison between these twoensembles and identify possible effects due to the dynamical strange and charm quarks.5PoS(LATTICE 2008)094Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren RekerSGauge β r0/a in chiral limitNf = 2 tl-Sym 3.9 5.22(2)Nf = 2+1+1 Iwasaki 1.9 5.18(5)Table 2: Comparison of r0/a in the chiral limit between the Nf = 2 and Nf = 2+1+1 runs5. Stout smearingWe separately tested the effectiveness and impact on observables of one level of stout smearing[11] with ρ = 0.15 (in every direction). In order to perform this comparison, we tuned a run withstout smearing at aµl = 0.004 to maximal twist. The parameters of this run are compared withthe one with thin links in table 3. For the simulation with stout smearing the values of the heavyρ traj κcrit aµl aµσ aµδ0 ∼ 5000 0.16327 0.004 0.15 0.190.15 ∼ 2500 0.14552 0.004 0.17 0.185Table 3: Comparison of the ensembles with aµl = 0.004, with (ρ = 0.15) and without (ρ = 0) stout smear-ing.doublet mass parameters µσ and µδ were chosen according to the same criterion as described insection 3.1. The difference in the values for µσ and µδ reported in Table 3 is likely due to the factthat the ratio of the renormalization factors ZP/ZS increases when replacing thin links with stoutlinks. Although the statistics are somewhat different between the two runs we can still make a fewconclusive comparisons. We observe that our estimate of κcrit decreases with stout links. In table 4we show a weak dependence of r0/a on aµl for simulations with stout links. Finally we observe thatat fixed bare quark mass aµl the pion mass (in physical units) from stout link simulations decreaseswith respect to that from thin link simulations. This finding can be ascribed to an increase ofthe value of the renormalization constant ZP (implying a decrease of the renormalized light quarkmass).aµl 0.004 0.006 0.008r0/a 4.97(8) 4.90(8) 4.99(8)Table 4: Comparison of r0/a values for various ensembles with stout smearing at different light twistedquark mass value aµl .6. ConclusionsWe have presented preliminary results for a set of simple observables obtained from ensembleswith Nf = 2+1+1 dynamical flavours of maximally twisted Wilson fermions. We have tuned tomaximal twist at four values of µl on 243×48 lattices at β = 1.9. A detailed analysis of the dataas well as a systematic control of finite size and discretization effects is in progress.6PoS(LATTICE 2008)094Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren RekerAcknowledgmentsWe thank Roberto Frezzotti for useful discussions and comments on this write-up. We wouldalso like to thank the computer centres of Barcelona, Groningen, Paris (IDRIS), Jülich, Munichand Rome (apeNEXT) for providing us with the necessary technical help and computer resourcesto enable us to perform this work.References[1] ALPHA Collaboration, R. Frezzotti, P. A. Grassi, S. Sint and P. Weisz, JHEP 0108, 058 (2001)[arXiv:hep-lat/0101001].[2] R. Frezzotti and G.C. Rossi, JHEP 0408 (2004) 007, K. Jansen et al. Phys. Lett. B. 619 (2005) 184;F. Farchioni et al. Eur. Phys. J. C39 (2005) 421; F. Farchioni et al., Eur. Phys. J. C47 (2006) 453;[3] ETM Collaboration, Ph. Boucaud et al., Phys. Lett. B. 650 (2007) 304[arXiv:hep-lat/0701012].[4] ETM Collaboration, Ph. Boucaud et al., [arXiv:0803.0224 [hep-lat]].[5] ETM Collaboration, C. Urbach, PoS LAT2007 (2007) 022 [arXiv:0710.1517 [hep-lat]].[6] ETM Collaboration, C. Alexandrou et al., PoS LAT2007 (2007) 087 [arXiv:0710.1173[hep-lat]].[7] ETM Collaboration, C. Alexandrou et al., Phys. Rev. D78 (2008) [arXiv:0803.3190[hep-lat]].[8] ETM Collaboration, B. Blossier et al., JHEP 0804, 020 (2008), [arXiv:0709.4574[hep-lat]].[9] R. Frezzotti and G. C. Rossi, Nucl. Phys. Proc. Suppl. 128 (2004)[arXiv:hep-lat/0311008v2].[10] T. Chiarappa et al, Eur. Phys. J. C50 (373) [arXiv:hep-lat/0606011].[11] C. Morningstar and M. J. Peardon, Phys. Rev. D69 (2004) [arXiv:hep-lat/0311018].[12] Y. Iwasaki, Nucl. Phys. B 258 (1985) 141.[13] T. Chiarappa, R. Frezzotti and C. Urbach, PoS LAT2005 (2006) 103 [arXiv:hep-lat/0509154][14] C. Urbach, K. Jansen, A. Shindler and U. Wenger, Comput. Phys. Commun. 174, 87 (2006)[arXiv:hep-lat/0506011][15] I. Montvay and E. Scholz, Phys. Lett. B. 623 (2005) [arXiv:hep-lat/0506006v3].[16] S. Aoki and O. Bär, Phys.Rev. D70 (2004) 116011; S.R. Sharpe and J.M.S. Wu, Phys. Rev. D71(2005) 074501; R. Frezzotti, G. Martinelli, M. Papinutto and G.C. Rossi, JHEP 0604 (2006) 038.[17] R. Frezzotti and G.C. Rossi, internal note for the ETM Collaboration[18] ETM Collaboration, P. Dimopoulos, R. Frezzotti, G. Herdoiza, C. Urbach and U. Wenger, PoSLAT2007, 102 (2007) [arXiv:0710.2498 [hep-lat]].[19] A. Hasenfratz, R. Hoffmann and S. Schaefer, Phys. Rev. D78 (2008) 014515 [arXiv:0805.2369[hep-lat]].[20] M. Luscher and F. Palombi, [arXiv:0810.0946 [hep-lat]].[21] I. Montvay, Nucl. Phys. B 466 (1996) 259 [arXiv:hep-lat/9510042].7

Status of ETMC simulations with Nf=2+1+1 twisted mass fermions

We present the status of runs performed in the twisted mass formalism with Nf =2+1+1 flavours of dynamical fermions: a degenerate light doublet and a mass split heavy doublet. The procedure for tuning to maximal twist will be described as well as the current status of the runs using both thin and stout links. Preliminary results for a few observables obtained on ensembles at maximal twist will be given. Finally, a reweighting procedure to tune to maximal twist will be described

Hochschulschriftenserver - Universität Frankfurt am Main

PoS(LATTICE 2008)094Status of ETMC simulations with Nf = 2+1+1twisted mass fermionsRUG-CTN 358, DESY 08-137, HU-EP-08/49, MS-TP-08-26Rémi Barona, Philippe Boucaudb, Albert Deuzemanc, Vincent Drachd,Federico Farchionie, Vicent Gimenezf, Gregorio Herdoizag, Karl Janseng,István Montvayh, David Palaof, Elisabetta Pallantec, Olivier Pèneb, Siebren Reker†c‡ ,Enno E. Scholzi, Carsten Urbachj, Marc Wagnerj and Urs WengerkaCEA, Centre de Saclay, IRFU/Service de Physique Nucléaire, F-91191 Gif-sur-Yvette, FrancebLaboratoire de Physique Théorique (Bât. 210), Université de Paris XI, Centre d’Orsay, 91405Orsay-Cedex, FrancecCentre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen, theNetherlandsdLaboratoire de Physique Subatomique et Cosmologie, 53 avenue des Martyrs, 38026 Grenoble,FranceeUniversität Münster, Institut für Theoretische Physik, Wilhelm-Klemm-Straße 9, D-48149Münster, GermanyfDep. de Física Teòrica and IFIC, Universitat de València-CSIC, Dr.Moliner 50, E-46100Burjassot, SpaingDESY, Platanenallee 6, D-15738 Zeuthen, GermanyhDeutsches Elektronen-Synchrotron DESY, Notkestr. 85, D-22603 Hamburg, GermanyiPhysics Department, Brookhaven National Laboratory, Upton, NY 11973, USAjHumboldt-Universität zu Berlin, Institut für Physik, Newtonstraße 15, D-12489 Berlin, GermanykInstitute for Theoretical Physics, University of Bern, Sidlerstr. 5, CH-3012 Bern, SwitzerlandWe present the status of runs performed in the twisted mass formalism with Nf =2+1+1 ﬂavoursof dynamical fermions: a degenerate light doublet and a mass split heavy doublet. The procedurefor tuning to maximal twist will be described as well as the current status of the runs using boththin and stout links. Preliminary results for a few observables obtained on ensembles at maximaltwist will be given. Finally, a reweighting procedure to tune to maximal twist will be described.The XXVI International Symposium on Lattice Field TheoryJuly 14-19 2008Williamsburg, Virginia, USASpeaker.†For the ETM Collaboration‡Email: s.f.reker@rug.nlc  Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/PoS(LATTICE 2008)094Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren Reker1. IntroductionThe twisted mass formulation of Lattice QCD (see for example references [1, 2]) is beingstudied extensively with Nf = 2 dynamical ﬂavours by the European Twisted Mass (ETM) collab-oration [3–7]. In the twisted mass formulation of QCD, the Wilson term is chirally rotated withina doublet. For the 2-ﬂavour case, this amounts to a mass degenerate (u;d) quark doublet. In recentstudies, a partially quenched setup [8] was used to add the strange quark to this formulation. Oneway to include a dynamical strange quark is to add in addition to the strange quark a charm quark ina heavier and mass-split doublet. This formulation was introduced in [9] and ﬁrst explored in [10].We will use that formulation and report on the current status of runs with Nf = 2+1+1 twistedmass quarks conducted by the ETM collaboration. In section 2 we will detail the lattice action andthe simulation algorithm, while in section 3 we describe our procedure for tuning to maximal twist.In section 3.3 we discuss a reweighting procedure allowing to speed up and improve the accuracyof tuning to maximal twist. In section 4 we show a set of preliminary results. Finally in section 5we describe ﬁrst results from one level of stout smearing [11].2. Lattice action and simulation algorithmIn the gauge sector we use the Iwasaki [12] gauge action (with b = 1:9 in the ensembles weare discussing here). With this gauge action we observe a smooth dependence of phase sensitivequantities on the hopping parameter k around its critical value (kcrit). The fermionic action for thelight doublet is given by:Sl = a4åxf ¯ cl(x)[DW[U]+m0;l +imlg5t3]cl(x)g (2.1)[2], where m0;l is the untwisted bare quark mass tuned to its critical value mcrit, ml is the bare twistedquark mass for the light doublet, t3 is the third Pauli matrix acting in ﬂavour space and DW[U] isthe Wilson-Dirac operator. The quark doublet ﬁelds that are proportional to the renormalized u andd doublet ﬁelds in the physical basis are given by:yphysl = ei2wlg5t3cl; ¯ yphysl = ¯ clei2wlg5t3: (2.2)The light doublet twisting angle wl takes the value wl ! p2 as m0;l  mcrit ! 0. In the heavysector, as has been shown by Frezzotti and Rossi in [9], a real quark determinant with a mass-splitdoublet can be obtained if the mass splitting is taken to be orthogonal in isospin space to the twistdirection. The mass term in the heavy sector then becomes:Sh = a4åxf¯ ch(x)[m0;h+imsg5t1+mdt3]ch(x)g: (2.3)This time the mass splitting is in the t3 direction and the twist in the t1 direction, which yields asimilar rotation relation to the physical quark basis:yphysh = ei2whg5t1ch; ¯ yphysh = ¯ chei2whg5t1: (2.4)At maximal twist (jwlj = jwhj = p2) physical observables are automatically O(a) improved withoutthe need to determine any action or operator speciﬁc improvement coefﬁcients. The gauge conﬁg-urations are generated with two different algorithms, depending on whether thin or stout links are2PoS(LATTICE 2008)094Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren Rekerbeing used. For thin links a Polynomial Hybrid Monte Carlo (PHMC) updating algorithm [13, 14],while for stout links the PHMC setup described in [15] is used.1 All ensembles described in thispaper correspond to lattices with spatial extension L=a = 24 and temporal extension T = 2L. Ourlightest twisted mass quark value (aml = 0:004) corresponds to a pion mass of around 300 MeVand a value of mpL around 3:5.3. Tuning action parameters3.1 ProcedureTuning to maximal twist requires to set m0;l and m0;h equal to some proper estimate of thecritical mass mcrit = mcrit(b) [9]. Here we set m0;l = m0;h  1=(2k) 4 and, at ﬁxed ms and md,for each value of ml, we tune k so as to obtain amPCAC;l = 0 (see also eq. (3.1)). Note that theuntwisted PCAC mass arising from the heavy sector is O(a) and wh is automatically very closeto p2 [10]. Our way of implementing maximal twist can be viewed as the extension to the theorywith 2+1+1 dynamical quarks of the optimal critical mass method of Refs. [16]. In this way weexpect [17] the (absolute) magnitude of lattice artifacts to remain roughly constant as ml ! 0. ThePCAC mass in the light sector is deﬁned in the following way:mPCAC;l =åxD¶0Aa0;l(x;t)Pal (0)E2åxPal (x;t)Pal (0) ; (3.1)where the axial and pseudoscalar bilinears Am;l and Pl areAam;l  ¯ clgmg5ta2cl and Pal = ¯ clg5ta2cl: (3.2)The numerical precision at which the condition mPCAC;l = 0 is fulﬁlled in order to avoid residualO(a2) effects when the pion mass is decreased is, for the present range of lattice spacings, je=mlj.0:1, wheree isthesmalldeviationofmPCAC;l fromzero[4,18]. Notethattypicallyagoodstatisticalprecision on the estimate of mPCAC;l is required to satisfy this condition. This computationallydisadvantageous situation can be remedied through the use of reweighting, as described in section3.3.The heavy doublet mass parameters ms and md should be adjusted in order to reproduce thephenomenological values of the renormalized s and c quark masses. The latter are related to msand md via [9]:(ms;c)R =1ZP(ms ZPZSmd) (3.3)where the   sign corresponds to the strange and the + sign to the charm. In practice we ﬁx thevalues ms and md by requiring the kaon mass to take its physical value and (mc)R & 10(ms)R(through an estimate of ZP=ZS).1Note that in the Monte Carlo simulation we monitor that the minimal eigenvalue of the Dirac operator of the heavydoublet always remains positive.3PoS(LATTICE 2008)094Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren Reker3.2 StatusThe tuning status of our ensembles is summarized in table 1 and illustrated in ﬁgure 1. Theensembles considered here have the following parameters: b = 1:9, ams = 0:15 and amd = 0:19,with lattice volumes of 24348.aml 0:004 0:006 0:008 0:01kcrit 0:163270 0:163265 0:163260 0:163255Table 1: Summary of tuning to maximal twist.3.0624 3.0625 3.0626 3.0627-0.4-0.20.00.20.41/(2k)mPCAC,l /mlFigure 1: Tuned runs at b = 1:9, with a box size of24348, with ams = 0:15 and amd = 0:19. From leftto right the points correspond to aml = 0:004 (red),aml = 0:006 (green), aml = 0:008 (blue) and aml =0:01(yellow). Forallensembles, mPCAC;l=ml iswithinthe 10% level (see text).0.00 0.02 0.04 0.060.000.050.10(a mp)2a fpFigure 2: afp as a function of (amp)2 for the fourensembles described above. All of these are at b =1:9, L=a = 24 and T=a = 48. Error bars are plotted,but they fall within the size of the dots.Tuning to kcrit was performed independently for each ml value. From table 1 we observe thatthe estimate of kcrit depends weakly on ml. Figure 1 shows that for all ml values the conditionje=mlj . 0:1 has been fulﬁlled.3.3 ReweightingReweighting towards the chiral limit for (untwisted) Wilson fermions has been recently ex-plored in reference [19] (and see also the conference contribution [20] with further references). Fortwisted Wilson fermions one can use reweighting near maximal twist for tuning the last digits ofthe hopping parameter k. Once the update is close to kcrit (in the present case for Dk =jk kcritj=O(10 5)) the situation is rather advantageous for an effective reweighting because the gauge ﬁeldconﬁguration is ﬂuctuating between positive and negative values of mPCAC;l. Thus, in order to com-plete the tuning one has to just reweight the ensemble to a close-by value of k at which mPCAC;l =0is realized.For calculating the ratio of determinants one could use the methods developed in reference[19], but we applied a simple and fast method based on least-square optimized polynomial approx-4PoS(LATTICE 2008)094Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren Rekerimations introduced in [21]. In the case of Nf ﬂavours, these polynomials satisfylimn!¥P(1)n (x) = x Nf=2; limn!¥P(2)n (x) =1qP(1)n1 (x); x 2 [e;l] (3.4)where the interval [e;l] covers the spectrum of Q†(k)Q(k), with Q the fermion matrix and n1(ni)the actual value of n used in the case of the polynomial P(1)(P(i)). With these polynomials thereweighting factor for k1 ! k2 is 1=det[P(2)n2 (k1)P(1)n1 (k2)P(2)n2 (k1)]. A stochastic estimator of thereweighting factor can be obtained from a random Gaussian vector asexpf h†(W 1)hg; with W  P(2)n2 (k1)P(1)n1 (k2)P(2)n2 (k1) : (3.5)We showed in test runs that with a few stochastic estimators an effective reweighting can beachieved for Dk ' 10 5. We actually applied determinant break-up by a factor of 2, that is, weconsidered two copies of half doublets, both for light and heavy doublets. With this method thenumber of long tuning runs for maximal twist can be reduced.4. ResultsIn this section we present preliminary results for the light quark mass dependence of the piondecay constant and the pion, kaon and nucleon masses (ﬁgures 2,3 and 4). The pion masses inthese ensembles are in the range from 300 to 500 MeV, corresponding to b = 1:9 and aml = 0:004to 0:01 (see section 3.2).0.000 0.003 0.006 0.009 0.012 0.0150.000.020.040.060.080.10a ml(amK/p)2Figure 3: The kaon (blue) and pion (red) squaredlattice masses are plotted versus the bare quark massaml.0.00 0.02 0.04 0.060.000.250.500.75(a mp)2a mNFigure 4: The nucleon mass (amN) as a function of(amp)2 for the four ensembles described above. Asubset of the available statistics has been used here.We measured r0=a and performed its chiral extrapolation. The results are compared to thoseof our Nf = 2 runs with b = 3:9 at the same lattice volume in table 2. The vicinity of the twovalues is very encouraging, since it might allow to perform a direct comparison between these twoensembles and identify possible effects due to the dynamical strange and charm quarks.5PoS(LATTICE 2008)094Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren RekerSGauge b r0=a in chiral limitNf = 2 tl-Sym 3:9 5:22(2)Nf = 2+1+1 Iwasaki 1:9 5:18(5)Table 2: Comparison of r0=a in the chiral limit between the Nf = 2 and Nf = 2+1+1 runs5. Stout smearingWe separately tested the effectiveness and impact on observables of one level of stout smearing[11] with r = 0:15 (in every direction). In order to perform this comparison, we tuned a run withstout smearing at aml = 0:004 to maximal twist. The parameters of this run are compared withthe one with thin links in table 3. For the simulation with stout smearing the values of the heavyr traj kcrit aml ams amd0  5000 0:16327 0:004 0:15 0:190:15  2500 0:14552 0:004 0:17 0:185Table 3: Comparison of the ensembles with aml = 0:004, with (r = 0:15) and without (r = 0) stout smear-ing.doublet mass parameters ms and md were chosen according to the same criterion as described insection 3.1. The difference in the values for ms and md reported in Table 3 is likely due to the factthat the ratio of the renormalization factors ZP=ZS increases when replacing thin links with stoutlinks. Although the statistics are somewhat different between the two runs we can still make a fewconclusive comparisons. We observe that our estimate of kcrit decreases with stout links. In table 4weshowaweakdependenceofr0=aonaml forsimulationswithstoutlinks. Finallyweobservethatat ﬁxed bare quark mass aml the pion mass (in physical units) from stout link simulations decreaseswith respect to that from thin link simulations. This ﬁnding can be ascribed to an increase ofthe value of the renormalization constant ZP (implying a decrease of the renormalized light quarkmass).aml 0:004 0:006 0:008r0=a 4:97(8) 4:90(8) 4:99(8)Table 4: Comparison of r0=a values for various ensembles with stout smearing at different light twistedquark mass value aml.6. ConclusionsWe have presented preliminary results for a set of simple observables obtained from ensembleswith Nf = 2+1+1 dynamical ﬂavours of maximally twisted Wilson fermions. We have tuned tomaximal twist at four values of ml on 24348 lattices at b = 1:9. A detailed analysis of the dataas well as a systematic control of ﬁnite size and discretization effects is in progress.6PoS(LATTICE 2008)094Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren RekerAcknowledgmentsWe thank Roberto Frezzotti for useful discussions and comments on this write-up. We wouldalso like to thank the computer centres of Barcelona, Groningen, Paris (IDRIS), Jülich, Munichand Rome (apeNEXT) for providing us with the necessary technical help and computer resourcesto enable us to perform this work.References[1] ALPHA Collaboration, R. Frezzotti, P. A. Grassi, S. Sint and P. Weisz, JHEP 0108, 058 (2001)[arXiv:hep-lat/0101001].[2] R. Frezzotti and G.C. Rossi, JHEP 0408 (2004) 007, K. Jansen et al. Phys. Lett. B. 619 (2005) 184;F. Farchioni et al. Eur. Phys. J. C39 (2005) 421; F. Farchioni et al., Eur. Phys. J. C47 (2006) 453;[3] ETM Collaboration, Ph. Boucaud et al., Phys. Lett. B. 650 (2007) 304[arXiv:hep-lat/0701012].[4] ETM Collaboration, Ph. Boucaud et al., [arXiv:0803.0224 [hep-lat]].[5] ETM Collaboration, C. Urbach, PoS LAT2007 (2007) 022 [arXiv:0710.1517 [hep-lat]].[6] ETM Collaboration, C. Alexandrou et al., PoS LAT2007 (2007) 087 [arXiv:0710.1173[hep-lat]].[7] ETM Collaboration, C. Alexandrou et al., Phys. Rev. D78 (2008) [arXiv:0803.3190[hep-lat]].[8] ETM Collaboration, B. Blossier et al., JHEP 0804, 020 (2008), [arXiv:0709.4574[hep-lat]].[9] R. Frezzotti and G. C. Rossi, Nucl. Phys. Proc. Suppl. 128 (2004)[arXiv:hep-lat/0311008v2].[10] T. Chiarappa et al, Eur. Phys. J. C50 (373) [arXiv:hep-lat/0606011].[11] C. Morningstar and M. J. Peardon, Phys. Rev. D69 (2004) [arXiv:hep-lat/0311018].[12] Y. Iwasaki, Nucl. Phys. B 258 (1985) 141.[13] T. Chiarappa, R. Frezzotti and C. Urbach, PoS LAT2005 (2006) 103 [arXiv:hep-lat/0509154][14] C. Urbach, K. Jansen, A. Shindler and U. Wenger, Comput. Phys. Commun. 174, 87 (2006)[arXiv:hep-lat/0506011][15] I. Montvay and E. Scholz, Phys. Lett. B. 623 (2005) [arXiv:hep-lat/0506006v3].[16] S. Aoki and O. Bär, Phys.Rev. D70 (2004) 116011; S.R. Sharpe and J.M.S. Wu, Phys. Rev. D71(2005) 074501; R. Frezzotti, G. Martinelli, M. Papinutto and G.C. Rossi, JHEP 0604 (2006) 038.[17] R. Frezzotti and G.C. Rossi, internal note for the ETM Collaboration[18] ETM Collaboration, P. Dimopoulos, R. Frezzotti, G. Herdoiza, C. Urbach and U. Wenger, PoSLAT2007, 102 (2007) [arXiv:0710.2498 [hep-lat]].[19] A. Hasenfratz, R. Hoffmann and S. Schaefer, Phys. Rev. D78 (2008) 014515 [arXiv:0805.2369[hep-lat]].[20] M. Luscher and F. Palombi, [arXiv:0810.0946 [hep-lat]].[21] I. Montvay, Nucl. Phys. B 466 (1996) 259 [arXiv:hep-lat/9510042].7

Alexandrou et al.,

internal note for the ETM Collaboration

Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions

7 pages, 4 figures, talk presented at the XXVI International
  Symposium on Lattice Field Theory, July 14-19, 2008, Williamsburg, Virginia,
  USAWe present the status of runs performed in the twisted mass formalism with Nf = 2 + 1 + 1 flavours of dynamical fermions: a degenerate light doublet and a mass split heavy doublet. The procedure for tuning to maximal twist will be described as well as the current status of the runs using both thin and stout links. Preliminary results for a few observables obtained on ensembles at maximal twist will be given. Finally, a reweighting procedure to tune to maximal twist will be described

Reker, S

Baron, R

Boucaud, P

Deuzeman, A

Drach, V::0000-0001-8948-0220

Farchioni, F

Gimenez, V

Herdoiza, G

Jansen, K

Montvay, I

Palao, D

Pallante, E

Pene, O

Scholz, EE

Urbach, C

Wagner, M

Wenger, U

Plymouth Electronic Archive and Research Library

Status of ETMC simulations with Nf = 2+1+1twisted mass fermionsRUG-CTN 358, DESY 08-137, HU-EP-08/49Rémi Barona, Philippe Boucaudb, Albert Deuzemanc, Vincent Drachd ,Federico Farchionie, Vicent Gimenez f , Gregorio Herdoizag, Karl Janseng,István Montvayh, David Palao f , Elisabetta Pallantec, Olivier Pèneb, Siebren Reker∗†c‡,Enno E. Scholzi, Carsten Urbach j, Marc Wagner j and Urs WengerkaCEA, Centre de Saclay, IRFU/Service de Physique Nucléaire, F-91191 Gif-sur-Yvette, FrancebLaboratoire de Physique Théorique (Bât. 210), Université de Paris XI, Centre d’Orsay, 91405Orsay-Cedex, FrancecCentre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen, theNetherlandsdLaboratoire de Physique Subatomique et Cosmologie, 53 avenue des Martyrs, 38026 Grenoble,FranceeUniversität Münster, Institut für Theoretische Physik, Wilhelm-Klemm-Straße 9, D-48149Münster, Germanyf Dep. de Física Teòrica and IFIC, Universitat de València-CSIC, Dr.Moliner 50, E-46100Burjassot, SpaingDESY, Platanenallee 6, D-15738 Zeuthen, GermanyhDeutsches Elektronen-Synchrotron DESY, Notkestr. 85, D-22603 Hamburg, GermanyiPhysics Department, Brookhaven National Laboratory, Upton, NY 11973, USAjHumboldt-Universität zu Berlin, Institut für Physik, Newtonstraße 15, D-12489 Berlin, GermanykInstitute for Theoretical Physics, University of Bern, Sidlerstr. 5, CH-3012 Bern, SwitzerlandWe present the status of runs performed in the twisted mass formalism with Nf = 2+1+1 flavoursof dynamical fermions: a degenerate light doublet and a mass split heavy doublet. The procedurefor tuning to maximal twist will be described as well as the current status of the runs using boththin and stout links. Preliminary results for a few observables obtained on ensembles at maximaltwist will be given. Finally, a reweighting procedure to tune to maximal twist will be described.The XXVI International Symposium on Lattice Field TheoryJuly 14-19 2008Williamsburg, Virginia, USA∗Speaker.†For the ETM Collaboration‡Email: s.f.reker@rug.nlc© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/arXiv:0810.3807v1  [hep-lat]  21 Oct 2008Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren Reker1. IntroductionThe twisted mass formulation of Lattice QCD (see for example references [1, 2]) is beingstudied extensively with Nf = 2 dynamical flavours by the European Twisted Mass (ETM) collab-oration [3 – 7]. In the twisted mass formulation of QCD, the Wilson term is chirally rotated withina doublet. For the 2-flavour case, this amounts to a mass degenerate (u,d) quark doublet. In recentstudies, a partially quenched setup [8] was used to add the strange quark to this formulation. Oneway to include a dynamical strange quark is to add in addition to the strange quark a charm quark ina heavier and mass-split doublet. This formulation was introduced in [9] and first explored in [10].We will use that formulation and report on the current status of runs with Nf = 2 + 1 + 1 twistedmass quarks conducted by the ETM collaboration. In section 2 we will detail the lattice action andthe simulation algorithm, while in section 3 we describe our procedure for tuning to maximal twist.In section 3.3 we discuss a reweighting procedure allowing to speed up and improve the accuracyof tuning to maximal twist. In section 4 we show a set of preliminary results. Finally in section 5we describe first results from one level of stout smearing [11].2. Lattice action and simulation algorithmIn the gauge sector we use the Iwasaki [12] gauge action (with β = 1.9 in the ensembles weare discussing here). With this gauge action we observe a smooth dependence of phase sensitivequantities on the hopping parameter κ around its critical value (κcrit). The fermionic action for thelight doublet is given by:Sl = a4 ∑x{χ̄l(x) [DW [U ]+m0,l + iµlγ5τ3]χl(x)} (2.1)[2], where m0,l is the untwisted bare quark mass tuned to its critical value mcrit, µl is the bare twistedquark mass for the light doublet, τ3 is the third Pauli matrix acting in flavour space and DW [U ] isthe Wilson-Dirac operator. The quark doublet fields that are proportional to the renormalized u andd doublet fields in the physical basis are given by:ψphysl = ei2 ωlγ5τ3 χl, ψ̄physl = χ̄lei2 ωlγ5τ3 . (2.2)The light doublet twisting angle ωl takes the value ωl →±π2 as m0,l −mcrit →±0. In the heavysector, as has been shown by Frezzotti and Rossi in [9], a real quark determinant with a mass-splitdoublet can be obtained if the mass splitting is taken to be orthogonal in isospin space to the twistdirection. The mass term in the heavy sector then becomes:Sh = a4 ∑x{χ̄h(x) [m0,h + iµσ γ5τ1 + µδ τ3]χh(x)} . (2.3)This time the mass splitting is in the τ3 direction and the twist in the τ1 direction, which yields asimilar rotation relation to the physical quark basis:ψphysh = ei2 ωhγ5τ1 χh, ψ̄physh = χ̄hei2 ωhγ5τ1 . (2.4)At maximal twist (|ωl|= |ωh|= π2 ) physical observables are automatically O(a) improved withoutthe need to determine any action or operator specific improvement coefficients. The gauge config-urations are generated with two different algorithms, depending on whether thin or stout links are2Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren Rekerbeing used. For thin links a Polynomial Hybrid Monte Carlo (PHMC) updating algorithm [13, 14],while for stout links the PHMC setup described in [15] is used.1 All ensembles described in thispaper correspond to lattices with spatial extension L/a = 24 and temporal extension T = 2L. Ourlightest twisted mass quark value (aµl = 0.004) corresponds to a pion mass of around 300 MeVand a value of mπL around 3.5.3. Tuning action parameters3.1 ProcedureTuning to maximal twist requires to set m0,l and m0,h equal to some proper estimate of thecritical mass mcrit = mcrit(β ) [9]. Here we set m0,l = m0,h ≡ 1/(2κ)− 4 and, at fixed µσ and µδ ,for each value of µl , we tune κ so as to obtain amPCAC,l = 0 (see also eq. (3.1)). Note that theuntwisted PCAC mass arising from the heavy sector is O(a) and ωh is automatically very closeto π2 [10]. Our way of implementing maximal twist can be viewed as the extension to the theorywith 2+1+1 dynamical quarks of the optimal critical mass method of Refs. [16]. In this way weexpect [17] the (absolute) magnitude of lattice artifacts to remain roughly constant as µl → 0. ThePCAC mass in the light sector is defined in the following way:mPCAC,l =∑x〈∂0Aa0,l(x, t)Pal (0)〉2∑x〈Pal (x, t)Pal (0)〉 , (3.1)where the axial and pseudoscalar bilinears Aµ,l and Pl areAaµ,l ≡ χ̄lγµγ5τa2χl and Pal = χ̄lγ5τa2χl. (3.2)The numerical precision at which the condition mPCAC,l = 0 is fulfilled in order to avoid residualO(a2) effects when the pion mass is decreased is, for the present range of lattice spacings, |ε/µl|.0.1, where ε is the small deviation of mPCAC,l from zero [4, 18]. Note that typically a good statisticalprecision on the estimate of mPCAC,l is required to satisfy this condition. This computationallydisadvantageous situation can be remedied through the use of reweighting, as described in section3.3.The heavy doublet mass parameters µσ and µδ should be adjusted in order to reproduce thephenomenological values of the renormalized s and c quark masses. The latter are related to µσand µδ via [9]:(ms,c)R =1ZP(µσ ∓ZPZSµδ ) (3.3)where the − sign corresponds to the strange and the + sign to the charm. In practice we fix thevalues µσ and µδ by requiring the kaon mass to take its physical value and (mc)R & 10(ms)R(through an estimate of ZP/ZS).1Note that in the Monte Carlo simulation we monitor that the minimal eigenvalue of the Dirac operator of the heavydoublet always remains positive.3Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren Reker3.2 StatusThe tuning status of our ensembles is summarized in table 1 and illustrated in figure 1. Theensembles considered here have the following parameters: β = 1.9, aµσ = 0.15 and aµδ = 0.19,with lattice volumes of 243×48.aµl 0.004 0.006 0.008 0.01κcrit 0.163270 0.163265 0.163260 0.163255Table 1: Summary of tuning to maximal twist.3.0624 3.0625 3.0626 3.0627-0.4-0.20.00.20.41/(2k)mPCAC,l /m lFigure 1: Tuned runs at β = 1.9, with a box size of243×48, with aµσ = 0.15 and aµδ = 0.19. From leftto right the points correspond to aµl = 0.004 (red),aµl = 0.006 (green), aµl = 0.008 (blue) and aµl =0.01 (yellow). For all ensembles, mPCAC,l/µl is withinthe 10% level (see text).0.00 0.02 0.04 0.060.000.050.10(a mp)2a f pFigure 2: a fπ as a function of (amπ)2 for the fourensembles described above. All of these are at β =1.9, L/a = 24 and T/a = 48. Error bars are plotted,but they fall within the size of the dots.Tuning to κcrit was performed independently for each µl value. From table 1 we observe thatthe estimate of κcrit depends weakly on µl . Figure 1 shows that for all µl values the condition|ε/µl|. 0.1 has been fulfilled.3.3 ReweightingReweighting towards the chiral limit for (untwisted) Wilson fermions has been recently ex-plored in reference [19] (and see also the conference contribution [20] with further references). Fortwisted Wilson fermions one can use reweighting near maximal twist for tuning the last digits ofthe hopping parameter κ . Once the update is close to κcrit (in the present case for ∆κ = |κ−κcrit|=O(10−5)) the situation is rather advantageous for an effective reweighting because the gauge fieldconfiguration is fluctuating between positive and negative values of mPCAC,l. Thus, in order to com-plete the tuning one has to just reweight the ensemble to a close-by value of κ at which mPCAC,l = 0is realized.For calculating the ratio of determinants one could use the methods developed in reference[19], but we applied a simple and fast method based on least-square optimized polynomial approx-4Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren Rekerimations introduced in [21]. In the case of Nf flavours, these polynomials satisfylimn→∞P(1)n (x) = x−Nf/2, limn→∞P(2)n (x) =1√P(1)n1 (x), x ∈ [ε,λ ] (3.4)where the interval [ε,λ ] covers the spectrum of Q†(κ)Q(κ), with Q the fermion matrix and n1(ni)the actual value of n used in the case of the polynomial P(1)(P(i)). With these polynomials thereweighting factor for κ1 → κ2 is 1/det[P(2)n2 (κ1)P(1)n1 (κ2)P(2)n2 (κ1)]. A stochastic estimator of thereweighting factor can be obtained from a random Gaussian vector asexp{−η†(Ω−1)η}, with Ω≡ P(2)n2 (κ1)P(1)n1 (κ2)P(2)n2 (κ1) . (3.5)We showed in test runs that with a few stochastic estimators an effective reweighting can beachieved for ∆κ ' 10−5. We actually applied determinant break-up by a factor of 2, that is, weconsidered two copies of half doublets, both for light and heavy doublets. With this method thenumber of long tuning runs for maximal twist can be reduced.4. ResultsIn this section we present preliminary results for the light quark mass dependence of the piondecay constant and the pion, kaon and nucleon masses (figures 2,3 and 4). The pion masses inthese ensembles are in the range from 300 to 500 MeV, corresponding to β = 1.9 and aµl = 0.004to 0.01 (see section 3.2).0.000 0.003 0.006 0.009 0.012 0.0150.000.020.040.060.080.10a ml(amK/ p)2Figure 3: The kaon (blue) and pion (red) squaredlattice masses are plotted versus the bare quark massaµl .0.00 0.02 0.04 0.060.000.250.500.75(a mp)2a mNFigure 4: The nucleon mass (amN) as a function of(amπ)2 for the four ensembles described above. Asubset of the available statistics has been used here.We measured r0/a and performed its chiral extrapolation. The results are compared to thoseof our Nf = 2 runs with β = 3.9 at the same lattice volume in table 2. The vicinity of the twovalues is very encouraging, since it might allow to perform a direct comparison between these twoensembles and identify possible effects due to the dynamical strange and charm quarks.5Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren RekerSGauge β r0/a in chiral limitNf = 2 tl-Sym 3.9 5.22(2)Nf = 2+1+1 Iwasaki 1.9 5.18(5)Table 2: Comparison of r0/a in the chiral limit between the Nf = 2 and Nf = 2+1+1 runs5. Stout smearingWe separately tested the effectiveness and impact on observables of one level of stout smearing[11] with ρ = 0.15 (in every direction). In order to perform this comparison, we tuned a run withstout smearing at aµl = 0.004 to maximal twist. The parameters of this run are compared withthe one with thin links in table 3. For the simulation with stout smearing the values of the heavyρ traj κcrit aµl aµσ aµδ0 ∼ 5000 0.16327 0.004 0.15 0.190.15 ∼ 2500 0.14552 0.004 0.17 0.185Table 3: Comparison of the ensembles with aµl = 0.004, with (ρ = 0.15) and without (ρ = 0) stout smear-ing.doublet mass parameters µσ and µδ were chosen according to the same criterion as described insection 3.1. The difference in the values for µσ and µδ reported in Table 3 is likely due to the factthat the ratio of the renormalization factors ZP/ZS increases when replacing thin links with stoutlinks. Although the statistics are somewhat different between the two runs we can still make a fewconclusive comparisons. We observe that our estimate of κcrit decreases with stout links. In table 4we show a weak dependence of r0/a on aµl for simulations with stout links. Finally we observe thatat fixed bare quark mass aµl the pion mass (in physical units) from stout link simulations decreaseswith respect to that from thin link simulations. This finding can be ascribed to an increase ofthe value of the renormalization constant ZP (implying a decrease of the renormalized light quarkmass).aµl 0.004 0.006 0.008r0/a 4.97(8) 4.90(8) 4.99(8)Table 4: Comparison of r0/a values for various ensembles with stout smearing at different light twistedquark mass value aµl .6. ConclusionsWe have presented preliminary results for a set of simple observables obtained from ensembleswith Nf = 2 + 1 + 1 dynamical flavours of maximally twisted Wilson fermions. We have tuned tomaximal twist at four values of µl on 243×48 lattices at β = 1.9. A detailed analysis of the dataas well as a systematic control of finite size and discretization effects is in progress.6Status of ETMC simulations with Nf = 2+1+1 twisted mass fermions Siebren RekerAcknowledgmentsWe thank Roberto Frezzotti for useful discussions and comments on this write-up. We wouldalso like to thank the computer centres of Barcelona, Groningen, Paris (IDRIS), Jülich, Munichand Rome (apeNEXT) for providing us with the necessary technical help and computer resourcesto enable us to perform this work.References[1] ALPHA Collaboration, R. Frezzotti, P. A. Grassi, S. Sint and P. Weisz, JHEP 0108, 058 (2001)[arXiv:hep-lat/0101001].[2] R. Frezzotti and G.C. Rossi, JHEP 0408 (2004) 007, K. Jansen et al. Phys. Lett. B. 619 (2005) 184;F. Farchioni et al. Eur. Phys. J. C39 (2005) 421; F. Farchioni et al., Eur. Phys. J. C47 (2006) 453;[3] ETM Collaboration, Ph. Boucaud et al., Phys. Lett. B. 650 (2007) 304[arXiv:hep-lat/0701012].[4] ETM Collaboration, Ph. 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Status of ETMC simulations with Nf=2+1+1 twisted mass fermions

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