Deceased.
We present lattice QCD results for mesonic screening masses in the temperature range
At high temperatures the properties of strong-interaction matter change from being controlled by hadronic degrees of freedom to deconfined quarks and gluons. While the thermodynamics in the low temperature phase of QCD resembles many features of a hadron resonance gas, with hadrons keeping their vacuum masses, this quickly changes at temperatures close to and above the crossover transition to the high temperature phase. In fact, the zero temperature hadronic degrees of freedom seem to provide a quite satisfactory description of thermal conditions close to the transition to the high temperature phase
The chiral crossover separating the low and high temperature regimes for nonvanishing quark masses is characterized by a smooth but rapid change of the chiral condensate around
Despite a small explicit breaking of the chiral symmetry by the residual light quark masses, the chiral symmetry, which is spontaneously broken in the hadronic phase, gets effectively restored above
Calculations with staggered fermions
Several recent lattice QCD calculations performed in 2 and (
One of the motivations of this study is to also determine the extent to which
This paper is organized as follows: In the next section, we briefly review properties of spatial meson correlation functions and their evaluation using the staggered fermion discretization scheme. We describe the staggered fermion setup for our calculations in Sec.
Properties of the hadron spectrum at zero and nonzero temperature are commonly determined from an analysis of two-point correlation functions
In QCD, the finite temperature meson screening correlators, projected onto zero transverse momentum (
On the lattice, the continuum Dirac action must be replaced by a suitable discrete variant. Staggered fermions, which we use in this work, are described by one-component spinors rather than the usual four-component spinors. Because of this, they are relatively inexpensive to simulate. However the price to be paid is that the relation to the continuum theory is subtle. The continuum limit of the theory is the Dirac theory of four fermions rather than one. As a result, each meson too comes in sixteen degenerate copies, which are known as tastes, and the corresponding operators are of the form
In this work, we only consider
The list of local meson operators studied in this work. States associated with the nonoscillating and the oscillating part of the screening correlators are designated by the identifiers NO and O, respectively. Particle assignments of the corresponding states are given only for the
A typical staggered meson correlator, for a fixed separation (in lattice unit) between source and sink, is an oscillating correlator that simultaneously couples to two sets of mesons with the same spin but with opposite parities,
We calculated the six distinct mesonic correlators, constructed from local staggered fermion operators introduced in the previous subsection, numerically using (
All the above-mentioned gauge configurations used in this analysis have been generated with a strange quark mass tuned to its physical value by tuning the mass of the
The conversion of hadron masses, calculated in lattice units, into physical units as well as the determination of our temperature scale requires the calculation of one physical observable that is used for the scale setting. For this purpose we use the kaon decay constant,
The purpose of the new calibration of the parametrization of
A general meson correlator
We generally had to retain up to 2 to 3 states in Eq. At a small fit interval Assuming similar size of the nonoscillating and oscillating mass, the fit parameters for the combined fit may be estimated with Using the parameters from step 2 as an initial guess, perform a full one state fit with an oscillating and nonoscillating part. Increase the fit interval. Guess the mass of the next excited state of either the even or the odd part (we used Perform a full fit with higher states. Use the parameters from steps 3 and 4 as an initial guess. Repeat steps 4 to 5 until the desired number of states is reached.
Having developed a method to perform automated multiple state fits, we still have to find which set of fit parameters is the most reasonable one for a given fit interval. For that purpose we have used the corrected AICc
Screening masses for in the vector channel with a different number of states varying the fit interval for
We calculated screening correlation functions using point as well as corner wall sources. The point source is the simplest type of source that one can use to calculate mesonic screening functions and we have used one source for each color. However it does not suppress the excited states; therefore, isolating the ground state can be difficult unless the states are well separated or the lattice extent is large. The use of extended (smeared) sources can often help to suppress excited state contributions, allowing to extract the ground state mass and amplitude even on smaller lattices. Here we have used a corner wall source, which means putting a unit source at the origin of each
Comparison of point versus corner wall sources for (top) the scalar (
As the scale setting calculations as well as the determination of the line of constant physics was performed prior to our current screening mass analysis we tried to reconfirm the scales used in our calculation through additional zero temperature calculations performed on lattices of size
Although use of staggered quarks leads to taste splitting in every hadronic channels, its effects are particularly severe in the pseudoscalar sector (
Masses of the different taste partners of the pseudoscalar mesons, labeled by different
One can define the root mean square (RMS) pion mass
The
We now present our results for screening masses calculated in a range of temperatures going from just below the chiral crossover temperature,
Using the fitting procedure described in Sec.
We plot the screening masses for
Examples for the continuum extrapolations for the pseudoscalar (top), scalar (bottom) screening masses in a reduced temperature range. The data for different
(Left to right) Results for all four screening masses for the
Continuum bands for screening masses of all four types of mesons for
For
The situation is far more complicated in the
As the crossover temperature is approached, the vector and axial vector screening masses should become equal due to effective restoration of chiral symmetry. At
In Fig.
Despite the above argument, we may nevertheless try and estimate the effective
We plot our results, along with the continuum extrapolations, for the difference of the scalar and pseudoscalar susceptibilities for the
Difference between the pseudoscalar and scalar susceptibilities as a function of the temperature. The difference is multiplied by
Before moving on, we note that the behavior of the screening masses and susceptibilities in the
In the previous subsection we have seen that the temperature dependence of the screening masses at
Although attempts have been made
Screening masses divided by the temperature, for temperatures
The behavior of the screening masses in the weak coupling picture beyond the free theory limit can be understood in terms of dimensionally reduced effective field theory, called electrostatic QCD (EQCD)
In EQCD the correction to the free theory value for the screening masses is obtained by solving the Schrödinger equation in two spatial dimensions with appropriately defined potential
We have performed an in-depth analysis of mesonic screening masses in (
At high temperatures the screening masses overshoot the free theory expectations in qualitative agreement with the weak coupling calculations at
This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics in the following ways: (i) Through Contract No. DE-SC0012704, (ii) within the framework of the Beam Energy Scan Theory (BEST) Topical Collaboration, and (iii) through the Scientific Discovery through Advanced Computing (SciDAC) award Computing the Properties of Matter with Leadership Computing Resources.
This research also was funded by the following: (i) the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Grant No. CRC-TR 211 “Strong-interaction matter under extreme conditions”—project number 315477589—TRR 211; (ii) Grant No. 05P18PBCA1 of the German Bundesministerium für Bildung und Forschung; (iii) Grant No. 283286 of the European Union; (iv) the U.S. National Science Foundation under Grant No. PHY-1812332; (v) The Early Career Research Award of the Science and Engineering Research Board of the Government of India; (vi) the Ramanujan Fellowship of the Department of Science and Technology, Government of India; and (vii) the National Natural Science Foundation of China under Grants No. 11775096 and No. 11535012.
This research used awards of computer time provided by the following: (i) the INCITE and ALCC programs Oak Ridge Leadership Computing Facility, a DOE Office of Science User Facility operated under Contract No. DE-AC05-00OR22725; (ii) the ALCC program at National Energy Research Scientific Computing Center, a U.S. Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-05CH11231; (iii) the INCITE program at Argonne Leadership Computing Facility, a U.S. Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-06CH11357; and (iv) the USQCD consortium at its Jefferson Laboratory and Fermilab computing facilities. This research would like to acknowledge the following for computing resources: (i) The GPU supercomputing cluster of Bielefeld University, (ii) PRACE for awarding us access to Piz Daint at CSCS, Switzerland, and Marconi at CINECA, Italy, and (iii) JUWELS at NIC Juelich, Germany.
For the scale setting in this project we used the kaon decay constant, i.e.,
Comparison of updated
In Fig.
Here we summarize our data sets and the number of configurations on which point and wall source correlators have been calculated are given in the last two columns of the tables, which are labeled point and wall, respectively.
Summary of statistics for
Summary of statistics for
Summary of statistics for
Summary of statistics for
Summary of statistics for
Summary of statistics for
Summary of statistics for
Summary of statistics for
Here we have tabulated the continuum extrapolated screening masses of
Continuum-extrapolated values of the light-light screening masses.
Continuum-extrapolated values of the strange-light screening masses.
Continuum-extrapolated values of the strange-strange screening masses.