Abstract
Determining the type of excitations that can exist in a thermal medium is key to understanding how hadronic matter behaves at extreme temperatures. In this work we study this question for pseudo-scalar mesons comprised of light-strange and strange-strange quarks, analysing how their low-energy spectral properties are modified as one passes through the high-temperature chiral crossover region between T = 145.6 MeV and 172.3 MeV. We utilise the non-perturbative constraints satisfied by correlation functions at finite temperature in order to extract the low-energy meson spectral function contributions from spatial correlator lattice data in Nf = 2 + 1 flavour QCD. The robustness of these contributions are tested by comparing their predictions with data for the corresponding temporal correlator at different momentum values. We find that around the pseudo-critical temperature Tpc the data in both the light-strange and strange-strange channels is consistent with the presence of a distinct stable particle-like ground state component, a so-called thermoparticle excitation. As the temperature increases this excitation undergoes collisional broadening, and this is qualitatively the same in both channels. These findings suggest that pseudo-scalar mesons in QCD have a bound-state-like structure at low energies within the chiral crossover region which is still strongly influenced by the vacuum states of the theory.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C.E. Detar and J.B. Kogut, The Hadronic Spectrum of the Quark Plasma, Phys. Rev. Lett. 59 (1987) 399 [INSPIRE].
MT(c) collaboration, Hadronic correlation functions in the QCD plasma phase, Phys. Rev. Lett. 67 (1991) 302 [INSPIRE].
W. Florkowski and B.L. Friman, Spatial dependence of the finite temperature meson correlation function, Z. Phys. A 347 (1994) 271 [INSPIRE].
J.B. Kogut, J.F. Lagae and D.K. Sinclair, Topology, fermionic zero modes and flavor singlet correlators in finite temperature QCD, Phys. Rev. D 58 (1998) 054504 [hep-lat/9801020] [INSPIRE].
G. Aarts and J.M. Martinez Resco, Continuum and lattice meson spectral functions at nonzero momentum and high temperature, Nucl. Phys. B 726 (2005) 93 [hep-lat/0507004] [INSPIRE].
I. Wetzorke, F. Karsch, E. Laermann, P. Petreczky and S. Stickan, Meson spectral functions at finite temperature, Nucl. Phys. B Proc. Suppl. 106 (2002) 510 [hep-lat/0110132] [INSPIRE].
F. Karsch and E. Laermann, Thermodynamics and in medium hadron properties from lattice QCD, hep-lat/0305025 [INSPIRE].
P. Petreczky, Lattice calculations of meson correlators and spectral functions at finite temperature, J. Phys. G 30 (2004) S431 [hep-ph/0305189] [INSPIRE].
M. Asakawa and T. Hatsuda, J/ψ and ηc in the deconfined plasma from lattice QCD, Phys. Rev. Lett. 92 (2004) 012001 [hep-lat/0308034] [INSPIRE].
UKQCD collaboration, Meson spectral functions with chirally symmetric lattice fermions, JHEP 02 (2007) 062 [hep-lat/0612007] [INSPIRE].
H.T. Ding, A. Francis, O. Kaczmarek, F. Karsch, H. Satz and W. Soeldner, Charmonium properties in hot quenched lattice QCD, Phys. Rev. D 86 (2012) 014509 [arXiv:1204.4945] [INSPIRE].
Y. Burnier, O. Kaczmarek and A. Rothkopf, Quarkonium at finite temperature: Towards realistic phenomenology from first principles, JHEP 12 (2015) 101 [arXiv:1509.07366] [INSPIRE].
S. Mukherjee, P. Petreczky and S. Sharma, Charm degrees of freedom in the quark gluon plasma, Phys. Rev. D 93 (2016) 014502 [arXiv:1509.08887] [INSPIRE].
H. Meyer, Lattice QCD, Spectral Functions and Transport Coefficients, PoS INPC2016 (2017) 364 [INSPIRE].
A. Rothkopf, Heavy Quarkonium in Extreme Conditions, Phys. Rep. 858 (2020) 1 [arXiv:1912.02253] [INSPIRE].
J.I. Kapusta and C. Gale, Finite-temperature field theory: Principles and applications, Cambridge University Press (2011) [https://doi.org/10.1017/CBO9780511535130] [INSPIRE].
M.L. Bellac, Thermal Field Theory, in Cambridge Monographs on Mathematical Physics, Cambridge University Press (2011).
M. Asakawa, T. Hatsuda and Y. Nakahara, Maximum entropy analysis of the spectral functions in lattice QCD, Prog. Part. Nucl. Phys. 46 (2001) 459 [hep-lat/0011040] [INSPIRE].
H.B. Meyer, Transport Properties of the Quark-Gluon Plasma: A Lattice QCD Perspective, Eur. Phys. J. A 47 (2011) 86 [arXiv:1104.3708] [INSPIRE].
E. Laermann and P. Schmidt, Meson screening masses at high temperature in quenched QCD with improved Wilson quarks, Eur. Phys. J. C 20 (2001) 541 [hep-lat/0103037] [INSPIRE].
S. Wissel, E. Laermann, S. Shcheredin, S. Datta and F. Karsch, Meson correlation functions at high temperatures, PoS LAT2005 (2006) 164 [hep-lat/0510031] [INSPIRE].
M. Cheng et al., Meson screening masses from lattice QCD with two light and the strange quark, Eur. Phys. J. C 71 (2011) 1564 [arXiv:1010.1216] [INSPIRE].
D. Banerjee, R.V. Gavai and S. Gupta, Quasi-static probes of the QCD plasma, Phys. Rev. D 83 (2011) 074510 [arXiv:1102.4465] [INSPIRE].
F. Karsch, E. Laermann, S. Mukherjee and P. Petreczky, Signatures of charmonium modification in spatial correlation functions, Phys. Rev. D 85 (2012) 114501 [arXiv:1203.3770] [INSPIRE].
B.B. Brandt, A. Francis, M. Laine and H.B. Meyer, A relation between screening masses and real-time rates, JHEP 05 (2014) 117 [arXiv:1404.2404] [INSPIRE].
A. Bazavov, F. Karsch, Y. Maezawa, S. Mukherjee and P. Petreczky, In-medium modifications of open and hidden strange-charm mesons from spatial correlation functions, Phys. Rev. D 91 (2015) 054503 [arXiv:1411.3018] [INSPIRE].
A. Bazavov et al., Meson screening masses in (2 + 1)-flavor QCD, Phys. Rev. D 100 (2019) 094510 [arXiv:1908.09552] [INSPIRE].
M. Dalla Brida, L. Giusti, T. Harris, D. Laudicina and M. Pepe, Non-perturbative thermal QCD at all temperatures: the case of mesonic screening masses, JHEP 04 (2022) 034 [arXiv:2112.05427] [INSPIRE].
P. Lowdon and O. Philipsen, Pion spectral properties above the chiral crossover of QCD, JHEP 10 (2022) 161 [arXiv:2207.14718] [INSPIRE].
J. Bros and D. Buchholz, Particles and propagators in relativistic thermo field theory, Z. Phys. C 55 (1992) 509 [INSPIRE].
D. Buchholz, On the manifestations of particles, in the proceedings of the International Conference on Mathematical Physics Towards the 21st Century, Negev, Israel, 14 April–19 March 1993, hep-th/9511023 [INSPIRE].
J. Bros and D. Buchholz, Relativistic KMS condition and Kallen-Lehmann type representations of thermal propagators, in the proceedings of the 4th Workshop on Thermal Field Theories and Their Applications, Dalian, China, 7–12 August 1995, pp. 103–110 [hep-th/9511022] [INSPIRE].
J. Bros and D. Buchholz, Axiomatic analyticity properties and representations of particles in thermal quantum field theory, Ann. Inst. Henri Poincaré Phys. Theor. 64 (1996) 495 [hep-th/9606046] [INSPIRE].
J. Bros and D. Buchholz, Asymptotic dynamics of thermal quantum fields, Nucl. Phys. B 627 (2002) 289 [hep-ph/0109136] [INSPIRE].
J. Bros and D. Buchholz, Towards a relativistic KMS condition, Nucl. Phys. B 429 (1994) 291 [hep-th/9807099] [INSPIRE].
R.F. Streater and A.S. Wightman, PCT, spin and statistics, and all that, Addison-Wesley, Redwood City, CA, U.S.A. (1989) [INSPIRE].
R. Haag, Local quantum physics: Fields, particles, algebras, Springer, Berlin, Germany (1992) [INSPIRE].
N.N. Bogolyubov, A.A. Logunov, A.I. Oksak and I.T. Todorov, General Principles of Quantum Field Theory, Kluwer Academic Publishers, Dordrecht, The Netherlands (1990).
G. Källén, On the definition of the Renormalization Constants in Quantum Electrodynamics, Helv. Phys. Acta 25 (1952) 417 [INSPIRE].
H. Lehmann, On the Properties of propagation functions and renormalization contants of quantized fields, Nuovo Cim. 11 (1954) 342 [INSPIRE].
P. Lowdon, Euclidean thermal correlation functions in local QFT, Phys. Rev. D 106 (2022) 045028 [arXiv:2201.12180] [INSPIRE].
P. Lowdon and O. Philipsen, Non-perturbative insights into the spectral properties of QCD at finite temperature, Eur. Phys. J. Web Conf. 274 (2022) 05013 [arXiv:2211.12073] [INSPIRE].
P. Lowdon, R.-A. Tripolt, J.M. Pawlowski and D.H. Rischke, Spectral representation of the shear viscosity for local scalar QFTs at finite temperature, Phys. Rev. D 104 (2021) 065010 [arXiv:2104.13413] [INSPIRE].
P. Lowdon and R.-A. Tripolt, Real-time observables from Euclidean thermal correlation functions, Phys. Rev. D 106 (2022) 056006 [arXiv:2202.09142] [INSPIRE].
HotQCD collaboration, Chiral crossover in QCD at zero and non-zero chemical potentials, Phys. Lett. B 795 (2019) 15 [arXiv:1812.08235] [INSPIRE].
R.C. Brower, H. Neff and K. Orginos, The Möbius domain wall fermion algorithm, Comput. Phys. Commun. 220 (2017) 1 [arXiv:1206.5214] [INSPIRE].
Particle Data collaboration, Review of Particle Physics, PTEP 2022 (2022) 083C01 [INSPIRE].
LHCb collaboration, Studies of the resonance structure in D0 → K∓π±π±π∓ decays, Eur. Phys. J. C 78 (2018) 443 [arXiv:1712.08609] [INSPIRE].
P.A. Henning, E. Polyachenko and T. Schilling, Approximate spectral functions in thermal field theory, Phys. Rev. D 54 (1996) 5239 [hep-ph/9510322] [INSPIRE].
C. Rohrhofer et al., Symmetries of spatial meson correlators in high temperature QCD, Phys. Rev. D 100 (2019) 014502 [arXiv:1902.03191] [INSPIRE].
C. Rohrhofer, Y. Aoki, L.Y. Glozman and S. Hashimoto, Chiral-spin symmetry of the meson spectral function above Tc, Phys. Lett. B 802 (2020) 135245 [arXiv:1909.00927] [INSPIRE].
L.Y. Glozman, O. Philipsen and R.D. Pisarski, Chiral spin symmetry and the QCD phase diagram, Eur. Phys. J. A 58 (2022) 247 [arXiv:2204.05083] [INSPIRE].
D. Alvarez, JUWELS Cluster and Booster: Exascale Pathfinder with Modular Supercomputing Architecture at Juelich Supercomputing Centre, JLSRF 7 (2021) A183.
P.A. Boyle, G. Cossu, A. Yamaguchi and A. Portelli, Grid: A next generation data parallel C++ QCD library, PoS LATTICE2015 (2016) 023 [arXiv:1512.03487] [INSPIRE].
A. Yamaguchi, P.A. Boyle, G. Cossu, G. Filaci, C. Lehner and A. Portelli, Grid: OneCode and FourAPIs, PoS LATTICE2021 (2022) 035 [arXiv:2203.06777] [INSPIRE].
C. Lehner et al., Grid Python Toolkit (GPT), https://github.com/lehner/gpt.
H.B. Nielsen and M. Ninomiya, No Go Theorem for Regularizing Chiral Fermions, Phys. Lett. B 105 (1981) 219 [INSPIRE].
H.B. Nielsen and M. Ninomiya, Absence of Neutrinos on a Lattice. Part 1. Proof by Homotopy Theory, Nucl. Phys. B 185 (1981) 20 [Erratum ibid. 195 (1982) 541] [INSPIRE].
H.B. Nielsen and M. Ninomiya, Absence of Neutrinos on a Lattice. Part 2. Intuitive Topological Proof, Nucl. Phys. B 193 (1981) 173 [INSPIRE].
HPQCD collaboration, Further improvements to staggered quarks, Nucl. Phys. B Proc. Suppl. 129 (2004) 447 [hep-lat/0311004] [INSPIRE].
HPQCD and UKQCD collaborations, Highly improved staggered quarks on the lattice, with applications to charm physics, Phys. Rev. D 75 (2007) 054502 [hep-lat/0610092] [INSPIRE].
D.B. Kaplan, A Method for simulating chiral fermions on the lattice, Phys. Lett. B 288 (1992) 342 [hep-lat/9206013] [INSPIRE].
D.B. Kaplan, Chiral Symmetry and Lattice Fermions, in the proceedings of the Les Houches Summer School: Session 93: Modern perspectives in lattice QCD: Quantum field theory and high performance computing, Les Houches, France, 3–28 August 2009, pp. 223–272 [arXiv:0912.2560] [INSPIRE].
O. Bar, C. Bernard, G. Rupak and N. Shoresh, Chiral perturbation theory for staggered sea quarks and Ginsparg-Wilson valence quarks, Phys. Rev. D 72 (2005) 054502 [hep-lat/0503009] [INSPIRE].
D. Bala, O. Kaczmarek, P. Lowdon, O. Philipsen and T. Ueding, Data Publication for “Pseudo-scalar meson spectral properties in the chiral crossover region of QCD”, Bielefeld University (2024) [https://doi.org/10.4119/unibi/2989968].
Acknowledgments
The authors acknowledge support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Collaborative Research Center CRC-TR 211 “Strong-interaction matter under extreme conditions” — Project No. 315477589-TRR 211. O.P. also acknowledges support by the State of Hesse within the Research Cluster ELEMENTS (Project ID 500/10.006). The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (https://www.gauss-centre.eu/) for funding this project by providing computing time through the John von Neumann Institute for Computing (NIC) on the GCS Supercomputer JUWELS [53] at the Jülich Supercomputing Centre (JSC). We also acknowledge the EuroHPC Joint Undertaking for awarding this project access to the EuroHPC supercomputer LUMI, hosted by CSC (Finland) and the LUMI consortium through a EuroHPC Extreme Scale Access call. For the calculations on these machines we were using Grid [54, 55] and the Grid Python Toolkit (GPT) [56]. Part of the analysis was performed on the GPU cluster at Bielefeld University. We thank the Bielefeld HPC.NRW team for their support.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2310.13476
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Bala, D., Kaczmarek, O., Lowdon, P. et al. Pseudo-scalar meson spectral properties in the chiral crossover region of QCD. J. High Energ. Phys. 2024, 332 (2024). https://doi.org/10.1007/JHEP05(2024)332
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2024)332