We investigate the impact of unquenching effects on QCD Green's functions, in the form of quark-loop contributions to both the gluon propagator and three-gluon vertex, in a three-loop inspired ...truncation of the three-particle irreducible (3PI) effective action. The fully coupled system of Dyson-Schwinger equations for the quark-gluon, ghost-gluon and three-gluon vertices, together with the quark propagator, are solved self-consistently; our only input are the ghost and gluon propagators themselves that are constrained by calculations within lattice QCD. We find that the two different unquenching effects have roughly equal, but opposite, impact on the quark-gluon vertex and quark propagator, with an overall negative impact on the latter. By taking further derivatives of the 3PI effective action, we construct the corresponding quark-antiquark kernel of the Bethe-Salpeter equation for mesons. The leading component is gluon exchange between two fully dressed quark-gluon vertices, thus introducing for the first time an obvious scalar-scalar component to the binding. We gain access to time-like properties of bound states by analytically continuing the coupled system of Dyson-Schwinger equations to the complex plane. We observe that the vector axial-vector splitting is in accord with experiment and that the lightest quark-antiquark scalar meson is above 1 GeV in mass.
We present results for the charged kaon-box contributions to the hadronic light-by-light (HLBL) correction of the muon's anomalous magnetic moment. To this end we determine the kaon electromagnetic ...form factor within the functional approach to QCD using Dyson-Schwinger and Bethe-Salpeter equations and evaluate the kaon-box contribution as defined in the dispersive approach to HLBL. As an update to previous work we also reevaluate the charged pion-box contribution taking effects due to isospin breaking into account. Our results are aπ±−boxμ = −15.7 (2) (3) × 10−11 and aK±−boxμ = −0.48 (2) (4) × 10−11 thus confirming the large suppression of box contributions beyond the leading pion box.
We review results for the phase diagram of QCD, the properties of quarks and gluons and the resulting properties of strongly interacting matter at finite temperature and chemical potential. The ...interplay of two different but related transitions in QCD, chiral symmetry restoration and deconfinement, leads to a rich phenomenology when external parameters such as quark masses, volume, temperature and chemical potential are varied. We discuss the progress in this field from a theoretical perspective, focusing on non-perturbative QCD as encoded in the functional approach via Dyson–Schwinger and Bethe–Salpeter equations. We aim at a pedagogical overview on the physics associated with the structure of this framework and explain connections to other approaches, in particular with the functional renormalisation group and lattice QCD. We discuss various aspects associated with the variation of the quark masses, assess recent results for the QCD phase diagram including the location of a putative critical end-point for Nf=2+1 and Nf=2+1+1, discuss results for quark spectral functions and summarise aspects of QCD thermodynamics and fluctuations.
The analytic structure of the nonperturbative gluon propagator contains information on the absence of gluons from the physical spectrum of the theory. We study this structure from numerical solutions ...in the complex momentum plane of the gluon and ghost Dyson-Schwinger equations in Landau gauge Yang-Mills theory. The resulting ghost and gluon propagators are analytic apart from a distinct cut structure on the real, timelike momentum axis. The propagator violates the Osterwalder-Schrader positivity condition, confirming the absence of gluons from the asymptotic spectrum of the theory.
In buyer–seller relationships, offering trade credit to buyers fosters long‐term collaboration but seller provision varies systematically as relationships evolve. We study the optimal provision ...dynamics of trade credit when the seller's information about the buyer is incomplete. We show how the interaction of self‐enforcing relational contracts and formal contracts determines optimal payment contract choice. We find that payment contracts can be interpreted as screening technologies and imply distinct learning opportunities about the buyer's type. In line with empirical evidence, the model predicts that all transitions between payment terms lead to seller trade credit provision in the long run.
We study the internal structure of a range of four-quark states with charm quark contributions using a two-body Bethe–Salpeter equation. Thereby, we examine charmonium-like states with hidden charm ...and quark content
c
c
¯
q
q
¯
, open-charm states with quark content
c
c
q
¯
q
¯
and all-charm states with
c
c
c
¯
c
¯
. In particular we study the internal competition between meson–meson components and diquark–antidiquark components in the wave functions of these states. Our results indicate that the
χ
c
1
(
3872
)
and the
Z
c
(
3900
)
are predominantly
D
D
¯
∗
states and that the recently discovered open-charm state
T
cc
+
is dominated by an internal
D
D
∗
component. In both cases the diquark components are negligible. For the all-charm state
X
(6900) with as yet unknown quantum numbers we identify candidates in the excitation spectra of
0
+
and
1
+
states. Furthermore, our framework serves to provide predictions for further, yet undiscovered open and hidden charm four-quark states.
We present results for fluctuations of the baryon number for QCD at nonzero temperature and chemical potential. These are extracted from solutions to a coupled set of truncated Dyson-Schwinger ...equations for the quark and gluon propagators of Landau-gauge QCD with Nf = 2 + 1 quark flavors, that has been studied previously. We discuss the changes of fluctuations and ratios thereof up to fourth order for several temperatures and baryon chemical potential up to and beyond the critical endpoint. In the context of preliminary STAR data for the skewness and kurtosis ratios, the results are compatible with the scenario of a critical endpoint at large chemical potential and slightly offset from the freeze-out line. We also discuss the caveats involved in this comparison.
We calculate the dressed gluon and ghost propagators of Landau gauge Yang-Mills theory in the complex momentum plane from their Dyson-Schwinger equations. To this end, we develop techniques for a ...direct calculation such that no mathematically ill-posed inverse problem needs to be solved. We provide a detailed account of the employed ray technique and discuss a range of tools to monitor the stability of the numerical calculation. Within a truncation employing model Ansätze for the three-point vertices and neglecting effects due to four-point functions, we find a singularity in the gluon propagator in the second quadrant of the complex p2 plane. Although the location of this singularity turns out to be strongly dependent on the model for the three-gluon vertex, it always occurs at complex momenta for the range of models considered.
We study the dual quark condensate as a signal for the confinement-deconfinement phase transition of QCD. This order parameter for center symmetry has been defined recently by Bilgici et al. within ...the framework of lattice QCD. In this work we determine the ordinary and the dual quark condensate with functional methods using a formulation of the Dyson-Schwinger equations for the quark propagator on a torus. The temperature dependence of these condensates serves to investigate the interplay between the chiral and deconfinement transitions of quenched QCD.
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