Pairs in the light-front and covariance

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The frame dependence of the pair-term contribution to the electromagnetic form factor of the pion is studied within the Light Front approach. A symmetric ansatz for the pion Bethe-Salpeter amplitude with a pseudo scalar coupling of the constituent to the pion field is used. In this model, the pair term vanishes for the DrellYan condition, while it is dominant for momentum transfer along the light-front direction. I IntroductionWithin the Front Form dynamics [1], where the state of the system is defined at x + = t + z = 0, if one uses the impulse approximation of the plus component of the electromagnetic current (j + ) in the Drell-Yan frame to calculate the form factors, the pair production from the incoming photon (pair-term contribution) is in general suppressed by lightfront momentum conservation (see, e.g., [2]). This was seen in schematic covariant models for spin-zero composite systems [3,4,5]. However, even in the Drell-Yan frame the pair term is present in j + for spin-one systems and is necessary to keep the rotational properties of the matrix element of the current [6,7].To avoid the difficulties associated with the rotational properties of the impulse approximation some physically motivated schemes to extract form factors from the current were used [8,9,10]. In another approach, free of these ambiguities [11], the plus component of the momentum transfer is non zero while the transverse momentum transfer vanishes in the Breit frame. This can be achieved by departing from the Drell-Yan condition by rotating the system around the y-direction, i.e, a non-kinematical transformation, and thus changing the direction of the momentum transfer in the z − x plane.However, by relaxing the Drell-Yan condition, a lightfront pair term can contribute to the plus component of the current, which can be studied in the pion example, as a prototype of a relativistic system of bound constituents. In this work, the composite system of a constituent quark and antiquark, is described by an ansatz for the Bethe-Salpeter amplitude which is nonconstant and symmetric with a pseudo scalar coupling of the constituent to the pion field. Our aim here is to discuss, within that model, the magnitude of the pair contribution to the pion electromagnetic form factor for momentum transfers in the z − x plane in the Breit-frame, as has been done in Ref. [5].The work is organized as follows. In Sec. II, we present the model of the pion Bethe-Salpeter amplitude and its eletromagnetic current in impulse approximation. In Sec. III, we discuss the numerical results for the pion electromagnetic form factor where the separate contribution of the pair term is given. We also present our summary in Sec. III. II Pion Model and Electromagnetic CurrentThe electromagnetic current of the pion is calculated in impulse approximation, using a pseudoscalar coupling between pion and quark fields, given by the effective Lagrangian (see, e.g.[12]):where g = m/f π is the coupling constant from the Goldberg-Treiman relation at the quark level, and m is the

“…(6). The probability of the valence component in the pion, η, is identified to F (W F ) π (0, 0) The pion decay constant is one constraint to fix the free parameters of the model:…”

Section: Pion Model and Electromagnetic Currentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

mentioning

confidence: 98%

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Frame dependence of the pair contribution to the pion electromagnetic form factor in a light-front approach

Melo¹,

Frederico²,

Pace³

et al. 2003

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“…In some cases, as for vector mesons in the present model, it is necessary to perform a careful analysis of the light-front calculation of the photo-absorption amplitude which accounts for pair terms or Z-diagrams that survive in the Drell-Yan frame (see, e.g., Ref. [22]). The Z-diagram vanishes in the calculation of the plus component of the electromagnetic current ( j + ) with q + = 0 for pseudoscalar mesons with γ5 coupling and the momentum component of the BS vertices from Eqs.…”

Section: Light-front Constituent Quark Modelmentioning

confidence: 99%

Modeling electromagnetic form factors of light and heavy pseudoscalar mesons

El-Bennich¹,

Melo²,

Loiseau³

et al. 2008

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“…However, the light-front description in a truncated Fock-space breaks the rotational symmetry because the associated transformation is a dynamical boost [3,4,5]. It is a formidable task to study the properties under dynamical boosts in light-front quantization [2].…”

Section: Introductionmentioning

confidence: 99%

Spin-1 particle in the light-front approach

Melo¹,

Frederico²

2004

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The electromagnetic current of spin-1 composite particles does not transform properly under rotations if only the valence contribution is considered in the light-front model. In particular, the plus component of the current, evaluated only for the valence component of the wave function, in the Drell-Yan frame violates rotational symmetry, which does not allow a unique calculation of the electromagnetic form-factors. The prescription suggested by Grach and Kondratyuk [Sov. J. Nucl. Phys. 38, 198 (1984)] to extract the form factors from the plus component of the current, eliminates contributions from pair diagrams or zero modes, which if not evaluated properly cause the violation of the rotational symmetry. We address this problem in an analytical and covariant model of a spin-1 composite particle.