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Register a new userCovariance, Dynamics and Symmetries, and Hadron Form Factors
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We summarise applications of Dyson-Schwinger equations to the theory and phenomenology of hadrons. Some exact results for pseudoscalar mesons are highlighted with details relating to the U_A(1) problem. We describe inferences from the gap equation relating to the radius of convergence for expansions of observables in the current-quark mass. We recapitulate upon studies of nucleon electromagnetic form factors, providing a comparison of the ln-weighted ratios of Pauli and Dirac form factors for the neutron and proton.
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We provide a snapshot of Dyson-Schwinger equation applications to the theory and phenomenology of hadrons. Exact results for pseudoscalar mesons are highlighted, with details relating to the U_A(1) problem. Calculated masses of the lightest J=0,1 states are discussed. We recapitulate upon studies of nucleon properties and give a perspective on the contribution of quark orbital angular momentum to the spin of a nucleon at rest.
A synopsis exemplifying the employment of Dyson-Schwinger equations in the calculation and explanation of hadron electromagnetic form factors and related phenomena. In particular the contribution: presents the pion form factor computed simultaneously at spacelike and timelike momenta; reports aspects of the evolution of the nucleon and Delta masses with current-quark mass and the correlation of their mass difference with that between scalar and axial-vector diquarks; describes an estimate of the s-quark content of a dressed u-quark and its impact on the nucleons strangeness magnetic moment; and comments upon the domain within which a pseudoscalar meson cloud can materially contribute to hadron form factors.
We compute nucleon and Roper e.m. elastic and transition form factors using a symmetry-preserving treatment of a contact-interaction. Obtained thereby, the e.m. interactions of baryons are typically described by hard form factors. In contrasting this behaviour with that produced by a momentum-dependent interaction, one achieves comparisons which highlight that elastic scattering and resonance electroproduction experiments probe the infrared evolution of QCDs running masses; e.g., the existence, and location if so, of a zero in the ratio of nucleon Sachs form factors are strongly influenced by the running of the dressed-quark mass. In our description of baryons, diquark correlations are important. These correlations are instrumental in producing a zero in the Dirac form factor of the protons d-quark; and in determining d_v/u_v(x=1), as we show via a formula that expresses d_v/u_v(x=1) in terms of the nucleons diquark content. The contact interaction produces a first excitation of the nucleon that is constituted predominantly from axial-vector diquark correlations. This impacts greatly on the gamma*p->P_{11}(1440) form factors. Notably, our quark core contribution to F_2*(Q^2) exhibits a zero at Q^2~0.5mN^2. Faddeev equation treatments of a hadrons quark core usually underestimate its magnetic properties, hence we consider the effect produced by a dressed-quark anomalous e.m. moment. Its inclusion much improves agreement with experiment. On the domain 0<Q^2<2GeV^2, meson-cloud effects are important in making a realistic comparison between experiment and hadron structure calculations. Our computed helicity amplitudes are similar to the bare amplitudes in coupled-channels analyses of the electroproduction process. Thus supports a view that extant structure calculations should directly be compared with the bare-couplings, etc., determined via coupled-channels analyses.
A dressed-quark core contribution to nucleon electromagnetic form factors is calculated. It is defined by the solution of a Poincare covariant Faddeev equation in which dressed-quarks provide the elementary degree of freedom and correlations between them are expressed via diquarks. The nucleon-photon vertex involves a single parameter; i.e., a diquark charge radius. It is argued to be commensurate with the pions charge radius. A comprehensive analysis and explanation of the form factors is built upon this foundation. A particular feature of the study is a separation of form factor contributions into those from different diagram types and correlation sectors, and subsequently a flavour separation for each of these. Amongst the extensive body of results that one could highlight are: r_1^{n,u}>r_1^{n,d}, owing to the presence of axial-vector quark-quark correlations; and for both the neutron and proton the ratio of Sachs electric and magnetic form factors possesses a zero.
We present a calculation of the SU(3)-breaking corrections to the hyperon transition vector form factors to $mathcal{O}(p^4)$ in heavy baryon chiral perturbation theory with finite-range regularisation. Both octet and decuplet degrees of freedom are included. We formulate a chiral expansion at the kinematic point $Q^2=-(M_{B_1}-M_{B_2})^2$, which can be conveniently accessed in lattice QCD. The two unknown low-energy constants at this point are constrained by lattice QCD simulation results for the $Sigma^-rightarrow n$ and $Xi^0rightarrow Sigma^+$ transition form factors. Hence we determine lattice-informed values of $f_1$ at the physical point. This work constitutes progress towards the precise determination of $|V_{us}|$ from hyperon semileptonic decays.
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