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Register a new userElectromagnetic currents for dressed hadrons
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Helmut Haberzettl
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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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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.
In this talk we briefly summarize our theoretical understanding of in-medium selfenergies of hadrons. With the special case of the $omega$ meson we demonstrate that earlier calculations that predicted a significant lowering of the mass in medium are based on an incorrect treatment of the model Lagrangian; more consistent calculations lead to a significant broadening, but hardly any mass shift. We stress that the experimental reconstruction of hadron spectral functions from measured decay products always requires knowledge of the decay branching ratios which may also be strongly mass-dependent. It also requires a quantitatively reliable treatment of final state interactions which has to be part of any reliable theory.
Heavy ion collisions (HIC) at high energies are excellent ways for producing heavy hadrons and composite particles. With upgraded detectors at RHIC and LHC, it has become possible to measure hadrons beyond their ground states. Therefore, HIC provide a new method for studying exotic hadrons that are either hadronic molecular states or compact multiquark systems. Because their structures are related to the fundamental properties of QCD, studying exotic hadrons is currently one of the most active areas of research in hadron physics. Experiments carried out at various accelerator facilities have indicated that some exotic hadrons may have already been produced. The present review is a summary of the current understanding of a selected set of exotic particle candidates that can be potentially measured in HIC. It also includes discussions on the production of exotic hadrons in HIC based on the coalescence and statistical models. A more detailed discussion leads to the conclusion that the yield of a hadron is typically an order of magnitude smaller when it is a compact multiquark state than that of an excited hadronic state with normal quark numbers and/or a molecular configuration. Attention is also given to some of the proposed heavy exotic hadrons that could be produced with sufficient abundance in HIC because of the significant numbers of charm and bottom quarks produced at RHIC and LHC, making it possible to study them in these experiments. Further included in the discussion are the general formalism for the coalescence model that involves resonance particles and its implication on the present estimated yield for resonance production. Finally, a review is given on recent studies to constrain the hadron-hadron interaction through correlation measurements in HIC and their implications on the interpretation and the possible existence of exotic states in hadronic interactions.
We propose an improved quark coalescence model for spin alignment of vector mesons and polarization of baryons by spin density matrix with phase space dependence. The spin density matrix is defined through Wigner functions. Within the model we propose an understanding of spin alignments of vector mesons $phi$ and $K^{*0}$ (including $bar{K}^{*0}$) in the static limit: a large positive deviation of $rho_{00}$ for $phi$ mesons from 1/3 may come from the electric part of the vector $phi$ field, while a negative deviation of $rho_{00}$ for $K^{*0}$ may come from the electric part of vorticity tensor fields. Such a negative contribution to $rho_{00}$ for $K^{*0}$ mesons, in comparison with the same contribution to $rho_{00}$ for $phi$ mesons which is less important, is amplified by a factor of the mass ratio of strange to light quark times the ratio of $leftlangle mathbf{p}_{b}^{2}rightrangle $ on the wave function of $K^{*0}$ to $phi$ ($mathbf{p}_{b}$ is the relative momentum of two constituent quarks of $K^{*0}$ and $phi$). These results should be tested by a detailed and comprehensive simulation of vorticity tensor fields and vector meson fields in heavy ion collisions.
The decay widths of the charmonium states to $Dbar D$ in isospin asymmetric nuclear matter in the presence of a magnetic field are studied, using a field theoretical model for composite hadrons with quark/antiquark constituents. The medium modifications of these partial decay widths arise due to the changes in the masses of the decaying charmonium state and the produced $D$ and $bar D$ mesons in the magnetized hadronic matter, calculated within a chiral effective model. The decay widths are computed using the light quark--antiquark pair creation term of the free Dirac Hamiltonian in terms of the constituent quark field operators. The results of the present investigation are compared with the in-medium decay widths obtained within the $^3P_0$ model. Within the $^3P_0$ model, the charmonium decay widths are calculated using the creation of a light quark--antiquark pair in the $^3P_0$ state. In the presence of a magnetic field, the Landau level contributions give rise to positive shifts in the masses of the charged $D$ and $bar D$ mesons. This leads to the decay of charmonium to the charged $D^+ D^-$ to be suppressed as compared to the neutral $Dbar D$ pair in symmetric nuclear matter, whereas in asymmetric nuclear matter, the larger mass drop of the $D^+D^-$ pair, as compared to the $D^0 bar {D^0}$ pair leads to the production of charged open charm meson pairs to be enhanced as compared to the charmonium decay channel to $D^0 {bar {D^0}}$.
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