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Abstract
Fluctuations of conserved charges such as baryon number, electric charge and strangeness may provide a test for completeness of states in lattice QCD for three light flavors. We elaborate on the idea that the corresponding susceptibilities can be saturated with excited baryonic states with an underlying quark-diquark structure with a linearly confining interaction. Using Polyakov-loop correlators we show that in the static limit, the quark-diquark potential coincides with the quark-antiquark potential in marked agreement with recent lattice studies. We thus study in a quark-diquark model the baryonic fluctuations of electric charge, baryon number and strangeness: $\chi_{BQ}$, $\chi_{BB}$ and $\chi_{BS}$; by considering a realization of the hadron resonance gas model in the light flavor sector of QCD. These results have been obtained by using the baryon spectrum computed within a relativistic quark-diquark model, leading to an overall good agreement with the spectrum obtained with other quark models and with lattice data for the fluctuations.
Highlights
Quantum chromodynamics (QCD) is the fundamental non-Abelian gauge theory of strong interactions in terms of 2NcNf quarks and antiquarks and 2ðN2c − 1Þ gluons with Nc 1⁄4 3 the number of colors and Nf 1⁄4 6 the number of flavor species u, d, s, c, b, t
II, we review the relevant aspects of the hadron resonance gas (HRG) model from the point of view of the equation of state and the trace anomaly as compared to lattice QCD
The missing resonance problem, i.e., the apparent overcounting of excited baryonic states by the quark model compared to the experimentally found resonances, has been a long-standing puzzle which has motivated a wealth of theoretical analysis and experimental work, mainly grounded in the individual identification of resonance states in the production process
Summary
Quantum chromodynamics (QCD) is the fundamental non-Abelian gauge theory of strong interactions in terms of 2NcNf quarks and antiquarks and 2ðN2c − 1Þ gluons with Nc 1⁄4 3 the number of colors and Nf 1⁄4 6 the number of flavor species u, d, s, c, b, t. Finite width effects on the PDG (PDGΓ) naturally provide a shift towards lower masses [10,11] as a consequence of the mass spectrum spread weighted by the exponentially decreasing Boltzmann factor This remarkable agreement becomes significantly spoiled when susceptibilities involving conserved charges such as the baryon number, the electric charge, and the strangeness are considered [13,14]. We profit from the new perspective provided by lattice QCD at finite temperature based on separation of quantum numbers with the study of susceptibilities of conserved charges, where a combination of degeneracy and level density is involved. IV the quark-diquark potential obtained as a correlation function involving Polyakov loops This allows us to define our model and compute the spectrum by diagonalization in Sec. V where the susceptibilities are analyzed in terms of the free parameters of the theory. In the Appendices, we provide details on the semiclassical determination of the spectrum and prove a theorem on the sign of susceptibilities which is verified by lattice calculations
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