Point-form analysis of elastic deuteron form factors

Allen, Thomas W.; Klink, William H.; Polyzou, W. N.

doi:10.1103/physrevc.63.034002

Cited by 54 publications

(70 citation statements)

References 55 publications

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“…As can be checked in the small binding limit, this factor is identical to the one already found in [6], reminded at the beginning of this subsection. It is noticed that the front-form case with q + = 0 gives the asymptotic behavior 4 g 2 Q −4 , in agreement with the exact result, while the instant-form one gives an extra factor 16/9, requiring in any case two-body currents to get it.…”

Section: • Change Of Variables In Different Formssupporting

confidence: 67%

“…For the ground state of a system made of scalar constituents, the asymptotic behavior is Q −8 , instead of Q −4 [10,11]. The difference can be traced back to a peculiarity of the formalism that changes the dependence on a factor Q 2 into a dependence on Q 2 (1 + Q 2 /(4 M 2 )) [6]. A fast fall off also appears in the case where the mass of the system is small compared to the sum of the constituent masses (the pion for instance) with the result that the charge radius scales like the inverse of the mass [8].…”

Section: • Change Of Variables In Different Formsmentioning

confidence: 99%

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Relativistic quantum mechanics: a Dirac's point-form inspired approach

Desplanques

2005

Nuclear Physics A

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This paper describes a tentative relativistic quantum mechanics approach inspired by Dirac's point-form, which is based on the physics description on a hyperboloid surface. It is mainly characterized by a non-standard relation of the constituent momenta of some system to its total momentum. Contrary to instantand front-form approaches, where it takes the form of a 3-dimensional δ(· · ·) function, the relation is given here by a Lorentz-scalar constraint. Thus, in the c.m. frame, the sum of the constituent momenta, which differs from zero off-energy shell, has no fixed direction, in accordance with the absence of preferred direction on a hyperboloid surface. To some extent, this gives rise to an extra degree of freedom entering the description of the system of interest. The development of a consistent formalism within this picture is described. Comparison with other approaches is made.

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Section: • Change Of Variables In Different Formssupporting

confidence: 67%

Section: • Change Of Variables In Different Formsmentioning

confidence: 99%

Relativistic quantum mechanics: a Dirac's point-form inspired approach

Desplanques

2005

Nuclear Physics A

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“…For the deuteron case, which is less relativistic than the previous systems, a conclusion supposes to disentangle the role of dynamics, nucleon form factors and relativistic approaches. One can nevertheless guess that the drop off of form factors at very high momentum transfer in the "point-form" [7] is faster than in other forms [8,9], emphasizing an effect mentioned in the first reference. The lack of convergence in all cases indicates that many-body currents should play a significant and sometimes essential role.…”

Section: Introductionmentioning

confidence: 99%

“…It evidences a change in the power-law asymptotic behavior of the uncorrected form factors, which shows up as soon as the momentum transfer is large enough (a few constituent masses, see ref. [7] about the deuteron case and refs. [3,20] for a system similar to the one considered in this work).…”

Section: "Point Form"mentioning

confidence: 99%

Form factors in RQM approaches: Constraints from space-time translations

Desplanques

Dong

2008

Eur. Phys. J. A

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Different relativistic quantum mechanics approaches have recently been used to calculate properties of various systems, form factors in particular. It is known that predictions, which most often rely on a single-particle current approximation, can lead to predictions with a very large range. It was shown that accounting for constraints related to space-time translations could considerably reduce this range. It is shown here that predictions can be made identical for a large range of cases. These ones include the following approaches: instant form, front form, and "pointform" in arbitrary momentum configurations and a dispersion-relation approach which can be considered as the approach which the other ones should converge to. This important result supposes both an implementation of the above constraints and an appropriate single-particle-like current. The change of variables that allows one to establish the equivalence of the approaches is given. Some points are illustrated with numerical results for the ground state of a system consisting of scalar particles.

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“…Supposed to be based on the point-form approach, it essentially relies on kinematical boost transformations. It has been applied for calculating form factors of the deuteron [23], the nucleon [24], a two-body system composed of scalar particles exchanging a zero-mass boson [11] and a system corresponding to a zero-range interaction [12]. In the first case, there is no significant improvement with respect to a non-relativistic calculation.…”

Section: Introductionmentioning

confidence: 99%

Comparison of form factors calculated with different expressions for the boost transformation

2003

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The effect of different boost expressions is considered for the calculation of the ground-state form factor of a two-body system made of scalar particles interacting via the exchange of a scalar boson. The aim is to provide an uncertainty range on methods employed in implementing these effects as well as an insight on their relevance when an "exact" calculation is possible. Using a wave function corresponding to a mass operator that has the appropriate properties to construct the generators of the Poincaré algebra in the framework of relativistic quantum mechanics, form factors are calculated using the boost transformations pertinent to the instant, front and point forms of this approach. Moderately and strongly bound systems are considered with masses of the exchanged boson taken as zero, 0.15 times the constituent mass m, and infinity. In the first and last cases, a comparison with "exact" calculations is made (Wick-Cutkosky model and Feynman triangle diagram). Results with a Galilean boost are also given. Momentum transfers up to Q 2 = 100 m 2 are considered. Emphasis is put on the contribution of the single-particle current, as usually done. It is found that the present point-form calculations of form factors strongly deviate from all the other ones, requiring large contributions from two-body currents. Different implementations of the point-form approach, where the role of these two-body currents would be less important, are sketched.

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Point-form analysis of elastic deuteron form factors

Cited by 54 publications

References 55 publications

Relativistic quantum mechanics: a Dirac's point-form inspired approach

Relativistic quantum mechanics: a Dirac's point-form inspired approach

Form factors in RQM approaches: Constraints from space-time translations

Comparison of form factors calculated with different expressions for the boost transformation

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