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Taste symmetry breaking at finite temperature

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Abstract

The breaking of the taste symmetry is studied in the temperature range between 140 MeV to 550 MeV. In order to investigate this violation we have calculated the screening masses of the various taste states fitting the exponential decay of the spatial correlators. The computation has been performed using dynamical N f =2+1 gauge field configurations generated with the p4 staggered action along the Line of Constant Physics (LCP) defined by a pion mass m π of approximately 220 MeV and the kaon mass m K equals 500 MeV. For temperatures below the transition an agreement with the predictions of the staggered chiral perturbation theory has been found and no temperature effect can be observed on the taste violation. Above the transition the taste splitting still shows an \(\mathcal{O}(a^{2})\) behavior but with a temperature-dependent slope. In addition to the analysis done for the pion multiplet we have performed an analogous computation for the light–strange and strange mesons and also looked at the scalar, vector and axial-vector channels to understand how the multiplets split at finite temperature. Finally the temperature dependence of the pion decay constant f π is investigated to get further information regarding the chiral symmetry restoration.

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Notes

  1. In the spinor-taste basis we will indicate with γ and ξ the spin and the taste gamma matrices, respectively.

  2. This subgroup should not be confused with the anomalous U(1) A of continuum QCD.

  3. The rest frame group is the invariance group of the transfer matrix.

  4. The symmetry group of the dimensionally reduced theory \(C_{v}^{4} \simeq D_{4}\) is the group of the isometries of a square.

  5. \(\hat{i}\ \mbox{and}\ \hat{j} \in \{\hat{x},\hat{y},\hat{\tau}\}\).

  6. Note that both amplitudes are positive [31], A NO,A O≥0.

  7. ξ μ are the Dirac gamma matrices and \(\xi_{I}= \mathbb{I}_{4\times4}\).

  8. Simulations in which disconnected contributions are not taken into account describe only non-diagonal flavor states π ±,K ±….

  9. Through this paper we use for the transition temperature T c ≃196 MeV (191 MeV) that is the chiral crossover temperature obtained form the peak of the chiral susceptibility for 243×6 (323×8) lattice with m π ≃220 MeV and m K ≃500 MeV.

  10. The amplitude A PS is related to A NO(O) (8) through the relation \(A_{\mathrm{NO}(\mathrm{O})} = 2 A_{PS} e^{-m_{\pi} N_{s} /2} \).

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Acknowledgements

This work is supported by the Research Executive Agency (REA) of the European Union under Grant Agreement PITNGA- 2009-238353 (ITN STRONGnet). F.P. would like to thank the hospitality of the G. Galilei Institute for Theoretical Physics, Florence. The numerical computations have been carried out on the apeNEXT at Bielefeld University.

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Correspondence to Fabrizio Pucci.

Appendix

Appendix

In Tables 3 and 4

Table 3 Screening masses for some taste states in the pion multiplet from N τ =8 lattices
Table 4 Screening masses for some taste states in the pion multiplet from N τ =6 lattices

we have summarized the pion screening masses for different taste states. The screening masses are given in lattice units and the data can be easily converted to either temperature or vacuum (r 0) units by means of the included zero temperature results for r 0/a from [35].

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Laermann, E., Pucci, F. Taste symmetry breaking at finite temperature. Eur. Phys. J. C 72, 2200 (2012). https://doi.org/10.1140/epjc/s10052-012-2200-1

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