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Register a new userModel-independent form-factor constraints for electromagnetic spin-1 currents
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Authors
Helmut Haberzettl
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Using local gauge invariance in the form of the Ward-Takahashi identity and the fact that properly constructed current operators must be free of kinematic singularities, it is shown that the magnetic moment $mu$ and the quadrupole moment $Q$ of an elementary spin-1 particle with mass $m$ and charge $e$ are related by $2 mmu + m^2 Q = e$, thus constraining the normalizations of the Sachs form factors. This relation holds true as a matter of course at the tree level in the standard model, but we prove it remains true in general for dressed spin-1 states derived from elementary fields. General expressions for spin-1 propagators and currents with arbitrary hadronic dressing are given showing the result to be independent of any dressing effect or model approach.
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A novel method is employed to compute the pion electromagnetic form factor, F_pi(Q^2), on the entire domain of spacelike momentum transfer using the Dyson-Schwinger equation (DSE) framework in quantum chromodynamics (QCD). The DSE architecture unifies this prediction with that of the pions valence-quark parton distribution amplitude (PDA). Using this PDA, the leading-order, leading-twist perturbative QCD result for Q^2 F_pi(Q^2) underestimates the full computation by just 15% on Q^2>~8GeV^2, in stark contrast with the result obtained using the asymptotic PDA. The analysis shows that hard contributions to the pion form factor dominate for Q^2>~8GeV^2 but, even so, the magnitude of Q^2 F_pi(Q^2) reflects the scale of dynamical chiral symmetry breaking, a pivotal emergent phenomenon in the Standard Model.
We propose an extension of the minimal-substitution prescription for coupling the electromagnetic field to hadronic systems with internal structure. The resulting rules of extended substitution necessarily distinguish between couplings to scalar and Dirac particles. Moreover, they allow for the incorporation of electromagnetic form factors for virtual photons in an effective phenomenological framework. Applied to pions and nucleons, assumed to be fully dressed to all orders, the resulting dressed currents are shown to be locally gauge invariant. Moreover, half-on-shell expressions of (hadron propagator)$times$(electromagnetic current) needed in all descriptions of physical processes will lose textit{all} information about hadronic dressing for real photons. The Ball-Chiu ansatz for the spin-1/2 current is seen to suffer from an incomplete coupling procedure where some essential aspects of the Dirac particle are effectively treated as those of a scalar particle. Applied to real Compton scattering on pions and nucleons, we find that emph{all} dressing information cancels exactly when external hadrons are on shell, leaving only gauge-invariant bare Born-type contributions with physical masses. Hence, nontrivial descriptions necessarily require contact-type two-photon processes obtained by hadrons looping around two photon insertion points.
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J. P. B. C. de Melo
, Anace N. da Silva (Laboratorio de Fisican Teorica e Computac{c}~ao Cientifica
, Universidade Cruzeiro do Sul
2014
The electromagnetic current~$J^+$ for spin-1, is used here to extract the electromagnetic form-factors of a light-front constituent quark model. The charge ($G_0$), magnetic ($G_1$) and quadrupole $G_2$ form factors are calculated using different prescriptions known in the literature, for the combinations of the four independent matrix elements of the current between the polarisations states in the Drell-Yan frame. However, the results for some prescriptions relying only on the valence contribution breaks the rotational symmetry as they violate the angular condition. In the present work, we use some relations between the matrix elements of the electromagnetic current in order to eliminate the breaking of the rotational symmetry, by computing the zero-mode contributions to matrix elements resorting only to the valence ones.
We use the Nambu-Jona-Lasinio model as an effective quark theory to investigate the medium modifications of the nucleon electromagnetic form factors. By using the equation of state of nuclear matter derived in this model, we discuss the results based on the naive quark-scalar diquark picture, the effects of finite diquark size, and the meson cloud around the constituent quarks. We apply this description to the longitudinal response function for quasielastic electron scattering. RPA correlations, based on the nucleon-nucleon interaction derived in the same model, are also taken into account in the calculation of the response function.
We study the Wigner function for massive spin-1/2 fermions in electromagnetic fields. Dirac form kinetic equation and Klein-Gordon form kinetic equation are obtained for the Wigner function, which are derived from the Dirac equation. The Wigner function and its kinetic equations are expanded in terms of the generators of Clifford algebra and a complicated system of partial differential equations is obtained. We prove that some component equations are automattically satisfied if the rest ones are fulfilled. In this thesis two methods are proposed for calculating the Wigner function, which are proved to be equivalent. The Wigner function is analytically calculated following the standard second-quantization procedure in the following cases: free fermions with or without spin imbalance, in constant magnetic field, in constant electric field, and in constant parallel electromagnetic field. Strong-field effects, such as the Landau levels and Schwinger pair-production are reproduced using the Wigner function approach. For an arbitrary space-time dependent field configuration, a semi-classical expansion with respect to the reduced Plancks constant $hbar$ is performed. We derive general expressions for the Wigner function components at linear order in $hbar$, in which order the spin corrections start playing a role. A generalized Bargmann-Michel-Telegdi (BMT) equation and a generalized Boltzmann equation are obtained for the undetermined polarization density and net fermion number density, which can be used to construct spin-hydrodynamics in the future. We also make a comparison between analytical results and the ones from semi-classical expansion, which shows coincidence for weak electromagnetic fields and small spin imbalance.
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