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Register a new userQuark Condensate from Renormalization Group Optimized Spectral Density
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Our renormalization group consistent variant of optimized perturbation, RGOPT, is used to calculate the nonperturbative QCD spectral density of the Dirac operator and the related chiral quark condensate $langle bar q q rangle$, for $n_f=2$ and $n_f=3$ massless quarks. Sequences of approximations at two-, three-, and four-loop orders are very stable and give $langle bar q q rangle^{1/3}_{n_f=2}(2, {rm GeV}) = -(0.833-0.845) barLambda_2 $, and $ langle bar q q rangle^{1/3}_{n_f=3}(2, {rm GeV}) = -(0.814-0.838) barLambda_3 $ where the range is our estimated theoretical error and $barLambda_{n_f}$ the basic QCD scale in the $rm bar{MS}$-scheme. We compare those results with other recent determinations (from lattice calculations and spectral sum rules).
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We reconsider our former determination of the chiral quark condensate $langle bar q q rangle$ from the related QCD spectral density of the Euclidean Dirac operator, using our Renormalization Group Optimized Perturbation (RGOPT) approach. Thanks to the recently available {em complete} five-loop QCD RG coefficients, and some other related four-loop results, we can extend our calculations exactly to $N^4LO$ (five-loops) RGOPT, and partially to $N^5LO$ (six-loops), the latter within a well-defined approximation accounting for all six-loop contents exactly predictable from five-loops RG properties. The RGOPT results overall show a very good stability and convergence, giving primarily the RG invariant condensate, $langle bar q qrangle^{1/3}_{RGI}(n_f=0) = -(0.840_{-0.016}^{+0.020}) barLambda_0 $, $langlebar q qrangle^{1/3}_{RGI}(n_f=2) = -(0.781_{-0.009}^{+0.019}) barLambda_2 $, $langlebar q qrangle^{1/3}_{RGI}(n_f=3) = -(0.751_{-.010}^{+0.019}) barLambda_3 $, where $barLambda_{n_f}$ is the basic QCD scale in the overline{MS} scheme for $n_f$ quark flavors, and the range spanned is our rather conservative estimated theoretical error. This leads {it e.g.} to $ langlebar q qrangle^{1/3}_{n_f=3}(2, {rm GeV}) = -(273^{+7}_{-4}pm 13)$ MeV, using the latest $barLambda_3$ values giving the second uncertainties. We compare our results with some other recent determinations. As a by-product of our analysis we also provide complete five-loop and partial six-loop expressions of the perturbative QCD spectral density, that may be useful for other purposes.
Our recently developed variant of variationnally optimized perturbation (OPT), in particular consistently incorporating renormalization group properties (RGOPT), is adapted to the calculation of the QCD spectral density of the Dirac operator and the related chiral quark condensate $langle bar q q rangle$ in the chiral limit, for $n_f=2$ and $n_f=3$ massless quarks. The results of successive sequences of approximations at two-, three-, and four-loop orders of this modified perturbation, exhibit a remarkable stability. We obtain $langle bar q qrangle^{1/3}_{n_f=2}(2, {rm GeV}) = -(0.833-0.845) barLambda_2 $, and $ langlebar q qrangle^{1/3}_{n_f=3}(2, {rm GeV}) = -(0.814-0.838) barLambda_3 $ where the range spanned by the first and second numbers (respectively four- and three-loop order results) defines our theoretical error, and $barLambda_{n_f}$ is the basic QCD scale in the $overline{MS}$-scheme. We obtain a moderate suppression of the chiral condensate when going from $n_f=2$ to $n_f=3$. We compare these results with some other recent determinations from other nonperturbative methods (mainly lattice and spectral sum rules).
We apply the renormalization group optimized perturbation theory (RGOPT) to evaluate the quark contribution to the QCD pressure at finite temperatures and baryonic densities, at next-to-leading order (NLO). Our results are compared to NLO and state-of-the-art higher orders of standard perturbative QCD (pQCD) and hard thermal loop perturbation theory (HTLpt). The RGOPT resummation provides a nonperturbative approximation, exhibiting a drastically better remnant renormalization scale dependence than pQCD, thanks to built-in renormalization group invariance consistency. At NLO, upon simply adding to the RGOPT-resummed quark contributions the purely perturbative NLO glue contribution, our results show a remarkable agreement with ab initio lattice simulation data for temperatures $0.25 lesssim T lesssim 1 , {rm GeV}$, with a remnant scale dependence drastically reduced as compared to HTLpt.
We present results for in-medium spectral functions obtained within the Functional Renormalization Group framework. The analytic continuation from imaginary to real time is performed in a well-defined way on the level of the flow equations. Based on this recently developed method, results for the sigma and the pion spectral function for the quark-meson model are shown at finite temperature, finite quark-chemical potential and finite spatial momentum. It is shown how these spectral function become degenreate at high temperatures due to the restoration of chiral symmetry. In addition, results for vector- and axial-vector meson spectral functions are shown using a gauged linear sigma model with quarks. The degeneration of the $rho$ and the $a_1$ spectral function as well as the behavior of their pole masses is discussed.
We employ the functional renormalization group approach formulated on the Schwinger-Keldysh contour to calculate real-time correlation functions in scalar field theories. We provide a detailed description of the formalism, discuss suitable truncation schemes for real-time calculations as well as the numerical procedure to self-consistently solve the flow equations for the spectral function. Subsequently, we discuss the relations to other perturbative and non-perturbative approaches to calculate spectral functions, and present a detailed comparison and benchmark in $d=0+1$ dimensions.
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