22 research outputs found
Non-perturbative QCD Correlation Functions
Functional methods provide access to the non-perturbative regime of quantum chromo- dynamics. Hence, they allow investigating confinement and chiral symmetry breaking. In this dissertation, correlation functions of Yang-Mills theory and unquenched two-flavor QCD are computed from the functional renormalization group. Employing a self-consistent vertex expansion of the effective action, Yang-Mills correlation functions are obtained in four as well as in three spacetime dimensions. To this end, confinement and Slavnov-Taylor identities are discussed. Our numerical results show very good agreement with corresponding lattice results. Next, unquenched two-flavor QCD is considered where it is shown that the unquenched two-flavor gluon propagator is insensitive to the pion mass. Furthermore, the necessity for consistent truncations is emphasized. Finally, correlation functions of finite-temperature Yang-Mills theory are computed in a truncation that includes the splitting of the gluon field into directions that are transverse and longitudinal to the heat bath. In particular, it includes the splitting of the three- and four-gluon vertices. The obtained gluon propagator allows to extract a Debye screening mass that coincides with the hard thermal loop screening mass at high temperatures, but is meaningful also at temperatures below the phase transition temperature
FeynOnium: Using FeynCalc for automatic calculations in Nonrelativistic Effective Field Theories
We present new results on FeynOnium, an ongoing project to develop a general
purpose software toolkit for semi-automatic symbolic calculations in
nonrelativistic Effective Field Theories (EFTs). Building upon FeynCalc, an
existing Mathematica package for symbolic evaluation of Feynman diagrams, we
have created a powerful framework for automatizing calculations in
nonrelativistic EFTs (NREFTs) at tree- and 1-loop level. This is achieved by
exploiting the novel features of FeynCalc that support manipulations of
Cartesian tensors, Pauli matrices and nonstandard loop integrals. Additional
operations that are common in nonrelativistic EFT calculations are implemented
in a dedicated add-on called FeynOnium. While our current focus is on EFTs for
strong interactions of heavy quarks, extensions to other systems that admit a
nonrelativistic EFT description are planned for the future. All our codes are
open-source and publicly available. Furthermore, we provide several example
calculations that demonstrate how FeynOnium can be employed to reproduce known
results from the literature.Comment: 61 pages, no figures, matches the version accepted in JHEP. To obtain
the programs, see https://github.com/FeynCal
Quantum Gravity from dynamical metric fluctuations
In this contribution, we discuss the asymptotic safety scenario for quantum
gravity by evaluating the correlation functions of dynamical metric
fluctuations. This is done with a functional renormalisation group approach
that disentangles dynamical metric fluctuations from the background metric. We
detail the derivation of the respective flow equations on space-time manifolds
with Euclidean and Lorentzian signatures and discuss the diffeomorphism
symmetry constraints on the flow as well as the convergence of systematic
vertex expansion schemes. We then proceed with a comprehensive review of
results of momentum-dependent correlation functions at vanishing cutoff scale,
the phase structure of the asymptotically safe Standard Model, and spectral
properties of asymptotically safe gravity from direct computations in
space-times with Lorentzian signatures such as the graviton spectral function.Comment: 47 pages, 15 figures. Invited chapter for the "Handbook of Quantum
Gravity" (Eds. C. Bambi, L. Modesto and I.L. Shapiro, Springer Singapore
Refined Gribov-Zwanziger theory coupled to scalar fields in the Landau gauge
The Refined Gribov-Zwanziger (RGZ) action in the Landau gauge accounts for
the existence of infinitesimal Gribov copies as well as the dynamical formation
of condensates in the infrared of Euclidean Yang-Mills theories. We couple
scalar fields to the RGZ action and compute the one-loop scalar propagator in
the adjoint representation of the gauge group. We compare our findings with
existing lattice data. The fate of BRST symmetry in this model is discussed,
and we provide a comparison to a previous proposal for a non-minimal coupling
between matter and the RGZ action. We find good agreement with the lattice data
of the scalar propagator for the values of the mass parameters that fit the RGZ
gluon propagator to the lattice. This suggests that the non-perturbative
information carried by the gluon propagator in the RGZ framework provides a
suitable mechanism to reproduce the behavior of correlation functions of
colored matter fields in the infrared.Comment: 18 pages + refs.; 6 figures; Matches the journal versio
Four-quark scatterings in QCD I
We investigate dynamical chiral symmetry breaking and the emergence of
mesonic bound states from the infrared dynamics of four-quark scatterings. Both
phenomena originate from the resonant scalar-pseudoscalar channel of the
four-quark scatterings, and we compute the functional renormalisation group
(fRG) flows of the Fierz-complete four-quark interaction of up and down quarks
with its channel momentum dependence. This is done in the isospin symmetric
case, also including the flow of the quark two-point function. This system can
be understood as the fRG analogues of the complete Bethe-Salpeter equations and
quark gap equation. The pole mass of the pion is determined from both direct
calculations of the four-quark flows in the Minkowski regime of momenta and the
analytic continuation based on results in the Euclidean regime, which are
consistent with each other.Comment: 26 pages, 20 figures, 3 tables; v2: minor typos correcte