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Register a new userElectromagnetic spin-1 form-factor free of zero-modes
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Joao Pacheco B. C. de Melo Dr.
Publication date
2014
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and research's language is
English
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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.
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We use recent data on K^+ -> pi^+ e^+ e^-, together with known values for the pion form factor, to derive experimental values for the kaon electromagnetic form factor for 0 < q^2 < 0.125 (GeV/c)^2. The results are then compared with the predictions of the Vector Meson Dominance model, which gives a good fit to the experimental results.
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.
The electromagnetic form factor of the pion in the space-like region, and at finite temperature, $F_{pi}(Q^{2},T)$, is obtained from a QCD Finite Energy Sum Rule. The form factor decreases with increasing T, and vanishes at some critical temperature, where the pion radius diverges. This divergence may be interpreted as a signal for quark deconfinement.
The measured electromagnetic form factors of $Lambda$ hyperon in the time-like region are significantly deviated from pQCD prediction. We attribute the non-vanishing cross section near threshold to be the contribution of below-threshold $phi$(2170) state, supporting its exotic structure. Above the threshold, we find significant role of a wide vector meson with the mass of around 2.34 GeV, which would be the same state present in $pbar{p}$ annihilation reactions. As a result, we give a satisfactory description of the behavior of existing data without modifying pQCD expectation.
The inclusion of the unstable features of a spin-1 particle, without breaking the electromagnetic gauge invariance, can be properly accomplished by including higher order contributions as done in the so-called fermion loop scheme (for the W gauge boson), and the boson loop scheme (for vector mesons). This induces a non trivial modification to the electromagnetic vertex of the particle, which must be considered in addition to any other contribution computed as stable particles. Considering the modified electromagnetic vertex, we obtain general expressions for the corresponding corrections to the multipoles as a function of the mass of the particles in the loop. For the W gauge boson no substantial deviations from the stable case is observed. For the rho and K* mesons the mass of the particles in the loop makes a significant effect, and can be comparable with corrections of different nature .
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