Melosh Rotation Research Articles

Relativistic corrections to the vector meson light front wave function

We compute a light front wave function for heavy vector mesons based on long distance matrix elements constrained by decay width analyses in the Non Relativistic QCD framework. Our approach provides a systematic expansion of the wave function in quark velocity. The first relativistic correction included in our calculation is found to be significant, and crucial for a good description of the HERA exclusive $\mathrm{J}/\psi$ production data. When looking at cross section ratios between nuclear and proton targets, the wave function dependence does not cancel out exactly. In particular the fully non-relativistic limit is found not to be a reliable approximation even in this ratio. The important role of the Melosh rotation to express the rest frame wave function on the light front is illustrated.

Point form electrodynamics and the Gupta–Bleuler formalism

The Gupta–Bleuler formalism for photons is generalized by choosing the representation of the little group for massless particles, the two-dimensional Euclidean group, to be the four-dimensional nonunitary representation obtained by restricting elements of the Lorentz group to the Euclidean group. Though the little group representation is nonunitary, it is shown that the representation of the Poincaré group is unitary. Under Lorentz transformations photon creation and annihilation operators transform as irreducible representations of massless particles, and not as four-vectors. As a consequence the polarization vector, which connects the four-vector potential with creation and annihilation operators, is given in terms of boosts, coset representatives of the Lorentz group with respect to the Euclidean group. Several polarization vectors (boost choices) are worked out, including a front form polarization vector. The different boost choices are shown to be related by the analogue of Melosh rotations, namely Euclidean group transformations

Axial vector form factor of nucleons in a light-cone diquark model

The nucleon axial vector form factor is investigated in a light-cone quark spectator diquark model, in which Melosh rotations are applied to both the quark and vector diquark. It is found that this model gives a very good description of available experimental data and the results have very little dependence on the parameters of the model. The relation between the nucleon axial constant and the anomalous magnetic moment of nucleons is also discussed.

The interplay of soft and hard contributions in the electromagnetic pion form factor

We consider various relativistic models for the valence Fock-state wave function of the pion. These models are obtained from simple instant-form wave functions by applying a Melosh rotation to the spin part and by imposing physical constraints on the parameters. We discuss how the soft and the hard (perturbative) parts of the electromagnetic form factor are affected by the choice of the model and by the Melosh rotation.

Electromagnetic form factors of nucleons in a light-cone diquark model

We investigate the electromagnetic form factors of nucleons within a simple relativistic quark spectator-diquark model using the light-cone formalism. Melosh rotations are applied to both quark and vector diquark. It is shown that the difference between vector and scalar spectator diquarks reproduces the right electric form factor of neutrons, and both the form factors ${G}_{E}{(Q}^{2})$ and ${G}_{M}{(Q}^{2})$ of the proton and neutron agree with experimental data well up to ${Q}^{2}=2 {\mathrm{GeV}}^{2}$ in this simple model.

SU(6) breaking effects in the nucleon elastic electromagnetic form factors

The effects of SU(6) breaking on the nucleon elastic form factors are investigated within the constituent quark model formulated on the light-front. It is shown that the kinematical SU(6) breaking caused by the Melosh rotations of the quark spins as well as the dynamical SU(6) breaking due to the mixed-symmetry component generated in the nucleon wave function by the spin-dependent terms of the quark-quark interaction, can affect both GEn(Q**2) and GMp(Q**2)/GMn(Q**2). The calculated GEn(Q**2) is found to be qualitatively consistent with existing data. while the calculations of GM(Q**2) based on the plus component of the current are found to be plagued by spurious effects related to the loss of the rotational covariance in the light-front formalism. These unwanted effects can be avoided by considering the transverse y-component of the current. In this way our light-front predictions are found to be consistent with the data on both GEn(Q**2) and GMp(Q**2)/GMn(Q**2). Finally, it is shown that a suppression of the ratio GEp(Q**2)/GMp(Q**2) with respect to the dipole-fit prediction can be expected in the constituent quark model provided the relativistic effects generated by the Melosh rotations of the constituent spins are taken into account.

Probing relativistic spin effects in the nucleon by means of Drell-Yan processes

Significant differences between transverse and longitudinal polarized parton distributions are found at low energies within a light-front covariant quark model of the nucleon. These differences are due to relativistic spin effects introduced by the Melosh rotations and survive evolution to higher $Q^2$ scales. A specific observable related to double-spin asymmetries in lepton pair production in polarized hadron-hadron collisions is defined. The possibility of assessing the relevance of these relativistic spin effects in future experiments at RHIC and HERA--$\vec{N}$ is discussed.

Relativistic effects on the neutron charge form factor in the constituent quark model

The neutron charge form factor G E n ( Q 2) is investigated within a constituent quark model formulated on the light-front. It is shown that, if the quark initial motion is neglected in the Melosh rotations, the Dirac neutron form factor F 1 n ( Q 2) receives a relativistic correction which cancels exactly against the Foldy term in G E n ( Q 2), as it has been recently argued by Isgur. Moreover, at the same level of approximation the ratio of the proton to neutron magnetic form factors G M p ( Q 2)/ G M n ( Q 2) is still given by the naive SU(6)-symmetry expectation, −3/2. However, it is also shown that the full Melosh rotations break SU(6) symmetry, giving rise to G E n ( Q 2)≠0 and G M p ( Q 2)/ G M n ( Q 2)≠−3/2 even when a SU(6)-symmetric canonical wave function is assumed. It turns out that relativistic effects alone cannot explain simultaneously the experimental data on G E n ( Q 2) and G M p ( Q 2)/ G M n ( Q 2).

Feynman versus Bakamjian-Thomas in light-front dynamics

We compare the Bakamjian-Thomas (BT) formulation of relativistic few-body systems with light-front field theories that maintain closer contact with Feynman diagrams. We find that Feynman diagrams distinguish Melosh rotations and other kinematical quantities belonging to various composite subsystem frames that correspond to different loop integrals. The BT formalism knows only the rest frame of the whole composite system, where everything is evaluated.

The nucleon wave function in light-front dynamics

The general spin structure of the relativistic nucleon wave function in the 3 q-model is found. It contains 16 spin components, in contrast to the 8 already known. This follows from the fact that in a many-body system parity conservation does not reduce the number of components. The explicitly covariant form of the wave function automatically takes into account the relativistic spin rotations, without introducing any Melosh rotation matrices. It also reduces the calculations to the standard routine of the Dirac matrices and of the trace techniques. In examples of the proton magnetic moment and of the axial nucleon form factor, with a particular wave function, we reproduce the results of the standard approach. Calculations beyond the standard assumptions give different results.

Melosh rotation and the nucleon tensor charge

By making use of the effect of the Melosh rotation, we show that one can estimate, in a simple way, the nucleon tensor charge in a relativistic quark model formulated on the light-cone. We discuss the physical significance of our results and compare them with those recently obtained in different phenomenological models.

Note on restoring manifest rotational symmetry in hyperfine and fine structure in light-front QED.

We study the part of the renormalized, cutoff QED light-front Hamiltonian that does not change particle number. The Hamiltonian contains interactions that must be treated in second-order bound state perturbation theory to obtain hyperfine structure. We show that a simple unitary transformation leads directly to the familiar Breit-Fermi spin-spin and tensor interactions, which can be treated in degenerate first-order bound-state perturbation theory, thus simplifying analytic light-front QED calculations. To the order in momenta we need to consider, this transformation is equivalent to a Melosh rotation. We also study how the similarity transformation affects spin-orbit interactions.

Calculation of the Isgur-Wise function from a light-front constituent quark model

The space-like elastic form factor of heavy-light pseudoscalar mesons is investigated within a light-front constituent quark model in order to evaluate the Isgur-Wise form factor. The relativistic composition of the constituent quark spins is properly taken into account using the Melosh rotations, and various heavy-meson wave function are considered, including the eigenfunctions of an effective light-front mass operator reproducing meson mass spectra. It is shown that in a wide range of values of the recoil the Isgur-Wise form factor exhibits a moderate dependence upon the choice of the heavy-meson wave function and is mainly governed by the effects of the confinement scale.

Analysis of the pion wave function in the light-cone formalism.

Several general constraints are suggested to analyze the pionic valence-state wave function. It is found that the present model wave functions used in light-cone formalism of perturbative quantum chromodynamics have failed these requirements to fit the pionic form factor data and the reasonable valence-state structure function which does not exceed the pionic structure function data for $x \rightarrow 1$ simultaneously. Furthermore, it is pointed out that there is a possibility to find model wave functions which can satisfy all of general constraints. Also we show that there are two higher helicity $(\lambda_{1} + \lambda_{2} =\pm1)$ components in the light-cone wave function for the pion as a natural consequence from the Melosh rotation and it is speculated that these components should be incorporated into the perturbative quantum chromodynamics.

Spin structure of the pion in a light-cone representation

The spin structure of the pion is discussed by transforming the wave function for the pion in the naive quark model into a light-cone representation. It is shown that there are higher helicity (λ 1+λ 2=±1) states in the full light-cone wave function for the pion besides the ordinary helicity (λ 1+λ 2=0) component wave functions as a consequence from the Melosh rotation relating spin states in light-front dynamics and those in instantform dynamics. Some low energy properties of the pion, such as the electromagnetic form factor, the charged mean square radius, and the weak decay constant, could be interrelated in this representation with reasonable parameters.