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Register a new userProbing QCD perturbation theory at high energies with continuum extrapolated lattice data
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Stefan Sint
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Precision tests of QCD perturbation theory are not readily available from experimental data. The main reasons are systematic uncertainties due to the confinement of quarks and gluons, as well as kinematical constraints which limit the accessible energy scales. We here show how continuum extrapolated lattice data may overcome such problems and provide excellent probes of renormalized perturbation theory. This work corresponds to an essential step in the ALPHA collaborations project to determine the $Lambda$-parameter in 3-flavour QCD. I explain the basic techniques used in the high energy regime, namely the use of mass-independent renormalization schemes for the QCD coupling constant in a finite Euclidean space time volume. When combined with finite size techniques this allows one to iteratively step up the energy scale by factors of 2, thereby quickly covering two orders of magnitude in scale. We may then compare perturbation theory (with $beta$-functions available up to 3-loop order) to our non-perturbative data for a 1-parameter family of running couplings. We conclude that a target precision of 3 percent for the $Lambda$-parameter requires non-perturbative data up to scales where $alpha_sapprox 0.1$, whereas the apparent precision obtained from applying perturbation theory around $alpha_s approx 0.2$ can be misleading. This should be taken as a general warning to practitioners of QCD perturbation theory.
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QCD thermodynamics is considered using Wilson fermions in the fixed scale approach. The temperature dependence of the renormalized chiral condensate, quark number susceptibility and Polyakov loop is measured at four lattice spacings allowing for a controlled continuum limit. The light quark masses are fixed to heavier than physical values in this first study. Finite volume effects are ensured to be negligible by using approriately large box sizes. The final continuum results are compared with staggered fermion simulations performed in the fixed N_t approach. The same continuum renormalization conditions are used in both approaches and the final results agree perfectly.
We present continuum extrapolated lattice results for the higher order fluctuations of conserved charges in high temperature Quantum Chromodynamics. Through the matching of the grand canonical ensemble on the lattice to the net charge and net baryon distribution realized in heavy ion experiments the temperature and the chemical potential may be estimated at the time of chemical freeze-out
We perform a detailed, fully-correlated study of the chiral behavior of the pion mass and decay constant, based on 2+1 flavor lattice QCD simulations. These calculations are implemented using tree-level, O(a)-improved Wilson fermions, at four values of the lattice spacing down to 0.054 fm and all the way down to below the physical value of the pion mass. They allow a sharp comparison with the predictions of SU(2) chiral perturbation theory (chi PT) and a determination of some of its low energy constants. In particular, we systematically explore the range of applicability of NLO SU(2) chi PT in two different expansions: the first in quark mass (x-expansion), and the second in pion mass (xi-expansion). We find that these expansions begin showing signs of failure around M_pi=300 MeV for the typical percent-level precision of our N_f=2+1 lattice results. We further determine the LO low energy constants (LECs), F=88.0 pm 1.3pm 0.3 and B^msbar(2 GeV)=2.58 pm 0.07 pm 0.02 GeV, and the related quark condensate, Sigma^msbar(2 GeV)=(271pm 4pm 1 MeV)^3, as well as the NLO ones, l_3=2.5 pm 0.5 pm 0.4 and l_4=3.8 pm 0.4 pm 0.2, with fully controlled uncertainties. We also explore the NNLO expansions and the values of NNLO LECs. In addition, we show that the lattice results favor the presence of chiral logarithms. We further demonstrate how the absence of lattice results with pion masses below 200 MeV can lead to misleading results and conclusions. Our calculations allow a fully controlled, ab initio determination of the pion decay constant with a total 1% error, which is in excellent agreement with experiment.
We continue our investigation of 2+1 flavor QCD thermodynamics using dynamical Wilson fermions in the fixed scale approach. Two additional pion masses, approximately 440 MeV and 285 MeV, are added to our previous work at 545 MeV. The simulations were performed at 3 or 4 lattice spacings at each pion mass. The renormalized chiral condensate, strange quark number susceptibility and Polyakov loop is obtained as a function of the temperature and we observe a decrease in the light chiral pseudo-critical temperature as the pion mass is lowered while the pseudo-critical temperature associated with the strange quark number susceptibility or the Polyakov loop is only mildly sensitive to the pion mass. These findings are in agreement with previous continuum results obtained in the staggered formulation.
We study the finite temperature transition in QCD with two flavors of dynamical fermions at a pseudoscalar pion mass of about 350 MeV. We use lattices with temporal extent of $N_t$=8, 10 and 12. For the first time in the literature a continuum limit is carried out for several observables with dynamical overlap fermions. These findings are compared with results obtained within the staggered fermion formalism at the same pion masses and extrapolated to the continuum limit. The presented results correspond to fixed topology and its effect is studied in the staggered case. Nice agreement is found between the overlap and staggered results.
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