Nucleon and Pion Form Factors in Different Forms of Relativistic Quantum Mechanics

Calculations of form factors in different forms of relativistic kinematics are presented. They involve the instant, front and point forms. In the two first cases, different kinematical conditions are considered while in the latter case, both a Dirac-inspired approach and a hyperplane-based one are incorporated in our study. Numerical results are presented for the pion form factors with emphasis on both the low and high Q**2 range. A new argument is presented, explaining why some approaches do considerably much better than other ones whenonly a single-particle current is considered.Comment: To appear in the proceedings of MENU04 (Beijing, Aug. 29- Sept. 4, 2004

Pion charge form factor and constraints from space-time translations

The role of Poincar\'e covariant space-time translations is investigated in the case of a relativistic quantum mechanics approach to the pion charge form factor. It is shown that the related constraints are generally inconsistent with the assumption of a single-particle current, which is most often referred to. The only exception is the front-form approach with $q^+=0$. How accounting for the related constraints, as well as restoring the equivalence of different RQM approaches in estimating form factors, is discussed. Some extensions of this work and, in particular, the relationship with a dispersion-relation approach, are presented. Conclusions relative to the underlying dynamics are given.Comment: 6 pages, 2 figures, proceedings of the QNP2009 international conference (Beijing, oct. 2009), to be published in Chinese Physics

Dirac's inspired point form and hadron form factors

Noticing that the point-form approach referred to in many recent works implies physics described on hyperplanes, an approach inspired from Dirac's one, which involves a hyperboloid surface, is presented. A few features pertinent to this new approach are emphasized. Consequences as for the calculation of form factors are discussed.Comment: 4 pages, 2 figures, to be published in the proceedings of BARYON0

Form factors of hadronic systems in various forms of relativistic quantum mechanics

The form factor of hadronic systems in various forms of relativistic quantum mechanics is considered. Motivated by the agreement of the nucleon ``point-form'' results with experiment, results for a toy model corresponding to the simplest Feynman diagram are first presented. These ones include the results for this diagram, which plays the role of an experiment, for the front-form and instant-form in standard kinematics (q^+=0 and Breit frame), but also in unconventional kinematics and finally a Dirac's point-form inspired approach. Results for an earlier ``point-form'' approach are reminded. Results are also presented for the pion charge form factor. Conclusions as for the efficiency of various approaches are given.Comment: 8 pages, 5 figures; invited talk at N*2004, Grenoble, March 24-27 (2004); to be published in the proceedings (World Scientific

Two-pion-exchange parity-violating potential and n⃗p→dγ\vec{n} p \to d \gamma

We calculate the parity-violating nucleon-nucleon potential in heavy-baryon chiral perturbation theory up to the next-to-next-to-leading order. The one-pion exchange comes in the leading order and the next-to-next-to-leading order consists of two-pion-exchange and the two-nucleon contact terms. In order to investigate the effect of the higher order contributions, we calculate the parity-violating asymmetry in $\vec{n} p \to d \gamma$ at the threshold. The one-pion dominates the physical observable and the two-pion contribution is about or less than 10% of the one-pion contribution.Comment: 3 pages, contribution to the workshop PAVI06 held in Milos island, Greece, May 16-20, 200

About the parity-non-conserving asymmetry in n+p--->d+gamma

The parity-non-conserving (pnc) asymmetry in \vec{n} + p \to d+\gamma at thermal energies has recently been calculated using effective field-theory methods. A comparison of this calculation with much more elaborate calculations performed in the 70's is made. This allows one to assess the validity of this new approach as presently used. It is found to overshoot the almost exact calculations by a factor close to 2 for the contribution involving the ^3S_1 component of both the initial and final states. This is much larger than anticipated by the authors. This discrepancy is analyzed and found to originate from the over-simplified description of the deuteron and capture states which underlies the new approach. The claim that earlier determinations of the sign would be in error is also examined. It is found that the sign discrepancy is most probably due, instead, to the fact that the pion-nucleon interaction referred to by the authors corresponds to a parity-non-conserving potential with a sign opposite to what is currently used. Some estimates and constraints relative to the pnc piNN coupling, h^1_{\pi}, which the above asymmetry is dependent on, are reviewed. Further details are given in an Appendix.Comment: 17 pages, 3 figures, submitted for publication in a shorter versio

Relationship of field-theory based single boson exchange potentials to current ones

It is shown that field-theory based single boson exchange potentials cannot be identified to those of the Yukawa or Coulomb type that are currently inserted in the Schr\"odinger equation. The potential which is obtained rather corresponds to this current single boson exchange potential corrected for the probability that the system under consideration is in a two-body component, therefore missing contributions due to the interaction of these two bodies while bosons are exchanged. The role of these contributions, which involve at least two boson exchanges, is examined. The conditions that allow one to recover the usual single boson exchange potential are given. It is shown that the present results have some relation: i) to the failure of the Bethe-Salpeter equation in reproducing the Dirac or Klein-Gordon equations in the limit where one of the constituent has a large mass, ii) to the absence of corrections of relative order alpha log(1/alpha) to a full calculation of the binding energy in the case of neutral massless bosons or iii) to large corrections of wave-functions calculated perturbatively in some light-front approaches.Comment: LaTeX, 37 pages, 14 figures, submitted for publicatio

Form factors in relativistic quantum mechanics: constraints from space-time translations

The comparison of form factors calculated from a single-particle current in different relativistic quantum mechanic approaches evidences tremendous discrepancies. The role of constraints coming from space-time translations is considered here with this respect. It is known that invariance under these translations implies the energy-momentum conservation relation that is usually assumed to hold globally. Transformations of the current under these translations, which lead to this result, also imply constraints that have been ignored so far in relativistic quantum mechanic approaches. An implementation of these constraints is discussed in the case of a model with two scalar constituents. It amounts to incorporate selected two-body currents to all orders in the interaction. Discrepancies for form factors in different approaches can thus be removed, contributing to restore the equivalence of different approaches. Results for the standard front-form approach ($q^+=0$) are found to fulfill the constraints and are therefore unchanged. The relation with results from a dispersion-relation approach is also made.Comment: 8 pages, 5 figures; to be published in the proceedings of LC2008; Light Cone 2008. Relativistic Nuclear and Particle Physics, Mulhouse : France (2008

Validity of the one-body current for the calculation of form factors in the point form of relativistic quantum mechanics

Form factors are calculated in the point form of relativistic quantum mechanics for the lowest energy states of a system made of two scalar particles interacting via the exchange of a massless boson. They are compared to the exact results obtained by using solutions of the Bethe-Salpeter equation which are well known in this case (Wick-Cutkosky model). Deficiencies of the point-form approach together with the single-particle current are emphasised. They point to the contribution of two-body currents which are required in any case to fulfil current conservation.Comment: 11 pages, 1 eps figur