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In a recent comment [1] Blankleider and Kvinikhidze claim that our work [2] is based on a set of inconsistent Bethe-Salpeter equations for the coupling of four-quark to two-quark states. Here we demonstrate that their argument is insubstantial., Comment: 3 pages, 1 figure

In a recent comment [1] Blankleider and Kvinikhidze claim that our work [2] is based on a set of inconsistent Bethe-Salpeter equations for the coupling of four-quark to two-quark states. Here we demonstrate that their argument is insubstantial., 3 pages, 1 figure

We study the dynamical generation of resonances in isospin singlet channels with mixing between two- and four-quark states. To this end we generalise a Bethe-Salpeter approach to four-quark states employed previously \cite{Heupel:2012ua} to accommodate for mixing diagrams. The $q\bar{q}q\bar{q}$ and $q\bar{q}$ components of the Bethe-Salpeter wave function (with light quarks $q\in\{u,d\}$) are determined consistently in a symmetry-preserving truncation of the underlying Dyson-Schwinger equations. As a prominent example we deal with the isospin-singlet $0^{++}$ meson with light quark content. We find that the $\pi\pi$ contribution of the four-quark component is mainly responsible for the low (real part of the) mass of the resulting state. We also study the analytic structure in the complex momentum plane and find a branch cut at the two-pion threshold and a singularity in the second Riemann sheet indicating a considerable decay width. Our findings are in excellent qualitative agreement with the general picture for the $\sigma/f_0(500)$ that emerged in the past two decades from dispersive approaches \cite{Pelaez:2015qba}., Comment: 10 pages, 7 figures, v2: minor changes, version accepted by PRD

We study the dynamical generation of resonances in isospin singlet channels with mixing between two- and four-quark states. To this end we generalise a Bethe-Salpeter approach to four-quark states employed previously \cite{Heupel:2012ua} to accommodate for mixing diagrams. The $q\bar{q}q\bar{q}$ and $q\bar{q}$ components of the Bethe-Salpeter wave function (with light quarks $q\in\{u,d\}$) are determined consistently in a symmetry-preserving truncation of the underlying Dyson-Schwinger equations. As a prominent example we deal with the isospin-singlet $0^{++}$ meson with light quark content. We find that the $����$ contribution of the four-quark component is mainly responsible for the low (real part of the) mass of the resulting state. We also study the analytic structure in the complex momentum plane and find a branch cut at the two-pion threshold and a singularity in the second Riemann sheet indicating a considerable decay width. Our findings are in excellent qualitative agreement with the general picture for the $��/f_0(500)$ that emerged in the past two decades from dispersive approaches \cite{Pelaez:2015qba}., 10 pages, 7 figures, v2: minor changes, version accepted by PRD

We generalise the framework of Dyson-Schwinger and Bethe-Salpeter equations for four-quark states to accommodate the case of unequal quark masses. As a first application, we consider the quantum numbers $I(J^{PC})=0(1^{++})$ of the $X(3872)$ and study the four-quark states with quark contents $cq\bar{q}\bar{c}$ and $cs\bar{s}\bar{c}$. Their Bethe-Salpeter amplitudes are represented by a basis of heavy-light meson-meson, hadro-charmonium and diquark-antidiquark operators, which allows for a dynamical distinction between different internal configurations. In both cases we find the heavy-light meson-meson component to be dominant. For the putative $X(3872)$ we obtain a mass of $3916(74)$ MeV; the corresponding $cs\bar{s}\bar{c}$ state is predicted at $4068(61)$ MeV., 8 pages, 2 figures; v2: minor typos corrected

We present the first Dyson-Schwinger calculation of the three-gluon vertex in Landau-gauge QCD in which its full covariant structure is back-coupled self-consistently. We truncate a Bose-symmetrized version of the DSE at the level of one-loop diagrams, model the four-gluon vertex, and neglect terms that contain non-primitively divergent n-point functions; the ghost-gluon vertex is taken bare to good approximation. Fit functions for the ghost and gluon propagators that interpolate between scaling and decoupling are presented. In all aspects of our study Bose symmetry is manifest, from the truncation to the basis decomposition and to the momentum invariants. We explore the uniform and soft-collinear infrared limits and obtain the expected infrared exponents. The presence of a zero crossing in the tree-level component of the vertex is confirmed for both scaling- and decoupling-type scenarios. The zero crossing appears at a scale ~1 GeV; however, its location might be sensitive to the four-gluon vertex and missing components in the DSE., 20 pages, 13 figures

We summarize results from our recent paper* on nucleon Compton scattering in the Dyson-Schwinger approach. We study the Compton scattering phase space and its various kinematic limits, and we introduce a covariant, transverse tensor basis for the scattering amplitude that is free of kinematic singularities. We illustrate the decomposition of the Compton amplitude at the quark-gluon level and calculate its nonperturbative handbag part, which also includes all t-channel meson resonances. The calculation requires numerical solutions for the dressed quark propagator, the nucleon's Faddeev amplitude and the quark Compton vertex as its input; they are consistently obtained from Dyson-Schwinger, Bethe-Salpeter and Faddeev equations. As a first application, we verify that the result for the Compton scattering amplitude reproduces the pi-gamma-gamma transition form factor when the pion pole in the t channel is approached. *G. Eichmann and C. S. Fischer, arXiv:1212.1761 [hep-ph]., 8 pages, 4 figures, 1 table. Proceedings of the Xth Quark Confinement and the Hadron Spectrum, October 7-12, Munich, Germany

We summarize recent results for the spectrum and properties of light pseudoscalar and scalar hadrons in a functional approach to QCD using Dyson-Schwinger and Bethe-Salpeter equations. We focus in particular on the role of pions as virtual constituents in light mesons ('pion cloud effects') as well as their role as constituents of tetraquark bound states. An extension of our framework into the charm quark sector reveals an all-charm tetraquark in the mass region around 5.5 GeV., Comment: 10 pages, 7 figures, contribution to the 51st International Winter Meeting on Nuclear Physics, 21-25 January 2013, Bormio (Italy)

We compute the vector-meson, nucleon and delta/omega-baryon masses and their evolution with the current-quark mass using a covariant generalized Bethe-Salpeter equation approach. The interaction kernel is truncated to a dressed gluon exchange. We study the model dependence of our results with the quark-gluon dressing to assess the validity of the truncation., 8 pages, 1 figure, 1 table. Talk presented by H. Sanchis-Alepuz at the International Workshop on QCD Green's Functions, Confinement, and Phenomenology - QCD-TNT II, September 05-09 2011, ECT* Trento, Italy

This thesis presents an investigation of meson and baryon properties in the framework of covariant bound-state equations based on the Dyson-Schwinger equations of QCD. Pion and rho-meson, diquark, nucleon and delta-baryon masses are obtained as self-consistent solutions of the respective equations for $q\bar{q}$, $qq$, $qqq$ and $q(qq)$ systems. The common parenthesis is given by a rainbow-ladder truncation in the quark-(anti-)quark channel. It includes an effective quark-gluon coupling as the only phenomenological input and inherent link in the calculation of meson and baryon observables. Results for hadron masses and the pion's and nucleon's static electromagnetic properties as a function of a self-consistently calculated pion mass are presented and compared to lattice results and their chiral extrapolations. The evolution of the nucleon electromagnetic form factors with larger photon momentum is investigated. The impact of further contributions beyond rainbow-ladder, e.g. pionic corrections, and possible future applications are discussed., PhD thesis, University of Graz, 139 pages

I briefly summarize recent results for nucleon and [Formula: see text] electromagnetic, axial and transition form factors in the Dyson-Schwinger approach. The calculation of the current diagrams from the quark-gluon level enables a transparent discussion of common features such as: the implications of dynamical chiral symmetry breaking and quark orbital angular momentum, the timelike structure of the form factors, and their interpretation in terms of missing pion-cloud effects.