[Paper Review] Poincare-invariant spectator-model currents for electroweak nucleon form factors

R. F. Wagenbrunn, T. Melde+1 more|ArXiv.org|Sep 6, 2005

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper presents Poincaré-invariant spectator-model currents within relativistic constituent quark models (RCQMs) to describe electroweak nucleon form factors, employing the point-form relativistic dynamics to ensure manifest covariance and symmetry constraints. It achieves excellent agreement with experimental data for proton and neutron electromagnetic and axial form factors across low to moderate momentum transfers, demonstrating that relativistic effects and proper current normalization are essential for consistency, with minimal differences between one-gluon-exchange and Goldstone-boson-exchange RCQM dynamics in ground states.

ABSTRACT

The relativistic constituent quark model of low-energy quantum chromodynamics is found to yield a consistent picture of the electroweak structure of the nucleons. Notably, the electromagnetic and axial form factors of both the proton and the neutron can be described in close agreement with existing experimental data in the domain of low to moderate momentum transfers. For the theory it is mandatory to respect Poincare invariance and to fulfill additional conditions like charge normalization. Here we present covariant predictions of the one-gluon-exchange and Goldstone-boson-exchange constituent quark models for the electroweak form factors of the nucleons and give a critical discussion of the results in view of the point-form spectator model employed for the electromagnetic and axial current operators.

Motivation & Objective

• To develop a Poincaré-invariant formulation of spectator-model currents for electroweak nucleon form factors within relativistic constituent quark models (RCQMs).
• To ensure that the current operators satisfy fundamental symmetries, including Lorentz invariance, translational and time-reversal invariance, and charge normalization.
• To compare predictions from two distinct RCQM dynamics—one-gluon-exchange (OGE) and Goldstone-boson-exchange (GBE)—for nucleon form factors.
• To assess the role of relativistic effects and the validity of the point-form spectator model (PFSM) against nonrelativistic impulse approximation (NRIA).
• To determine optimal normalization factors in the current operator that preserve symmetry and physical constraints across all reference frames.

Proposed method

• The study employs the point-form relativistic dynamics framework, which ensures manifest Poincaré invariance of transition amplitudes across all reference frames.
• The current operator is constructed as a spectator model where the intermediate boson couples only to one quark, while momentum transfer is conserved for the entire three-quark system.
• The reduced matrix elements of the current are expressed using a normalization factor $ N(x,y) $, which depends on initial and final baryon masses and is tuned to satisfy charge normalization and time-reversal invariance.
• The electromagnetic current uses the standard Dirac vertex $ e_1 \bar{u}\gamma^\mu u $, while the axial current includes a pion-pole term with coupling constants $ g_{A}^{q} $ and $ g_{qq\pi} $.
• The normalization factor $ N(x,y) = \left(\frac{M}{\sum \omega_i}\right)^{xy} \left(\frac{M'}{\sum \omega'_i}\right)^{x(1-y)} $ is used, with $ x=3 $ fixed by proton charge normalization and $ y=1/2 $ selected by time-reversal invariance in the Breit frame.
• Calculations are performed for both OGE and GBE RCQMs, with results compared to NRIA and experimental data across $ Q^2 $-dependent form factors.

Experimental results

Research questions

• RQ1 Can Poincaré-invariant spectator-model currents in RCQMs accurately describe the electromagnetic and axial form factors of the proton and neutron across low to moderate momentum transfers?
• RQ2 How do predictions from OGE and GBE RCQMs compare in their description of nucleon form factors, particularly in the ground state?
• RQ3 To what extent do relativistic effects and proper current normalization—beyond mere Poincaré invariance—improve agreement with experimental data compared to nonrelativistic approximations?
• RQ4 What is the role of the normalization factor $ N(x,y) $ in ensuring charge normalization and time-reversal invariance in the point-form spectator model?
• RQ5 Why does the PFSM approach yield such good agreement with data despite using a simplified current structure?

Key findings

• The Poincaré-invariant spectator-model currents in RCQMs yield excellent agreement with experimental data for both proton and neutron electromagnetic and axial form factors across the low to moderate $ Q^2 $ range.
• The predictions from the OGE and GBE RCQMs are nearly indistinguishable for ground-state form factors, except for the neutron electric form factor $ G_E^n $, indicating similar quark wave function components in both models.
• The nonrelativistic impulse approximation (NRIA) fails completely, underscoring the paramount importance of relativistic effects in nucleon structure calculations.
• The normalization factor $ N(x,y) $, with $ x=3 $ and $ y=1/2 $, ensures proper proton charge normalization and satisfies time-reversal invariance in the Breit frame, validating its use in the current operator.
• The PFSM current is effective many-body due to the non-separable dependence on interacting baryon masses, despite its spectator-model origin, and maintains all symmetries across all reference frames.
• The success of the PFSM approach is attributed to the strict enforcement of Poincaré invariance, charge normalization, and time-reversal invariance, which are not satisfied in simpler models.