arXiv subjects

B. C. Tiburzi

Publications and source records attributed to B. C. Tiburzi.

33 records · Page 2Linked to original sources

arXiv2006

Electromagnetic and spin polarisabilities in lattice QCD

We discuss the extraction of the electromagnetic and spin polarisabilities of nucleons from lattice QCD. We show that the external field method can be used to measure all the electromagnetic and spin polarisabilities including those of charged particles. We then turn to the extrapolations required to connect such calculations to experiment in the context of finite volume chiral perturbation theory. We derive results relevant for lattice simulations of QCD, partially-quenched QCD and quenched QCD. Our results for the polarisabilities show a strong dependence on the lattice volume and quark masses, typically differing from the infinite volume limit by ~10% for current lattice volumes and quark masses.

hep-lat↗

arXiv2005

Estimates for Pion-Photon Transition Distributions

In the scaling regime, amplitudes for backward virtual Compton scattering and hadron annihilation into two photons depend on structure functions that describe the hadron-photon transition at the partonic level. We construct simple analytical models for the vector and axial-vector pion-photon transition distribution amplitudes based on double distributions. Via a sum rule, these models are tuned to reproduce the pion-photon transition form factors. To obtain reasonable estimates of the distributions at a low scale, we modify the models to saturate the positivity bounds using empirically parametrized parton distributions. We also determine a model-independent contribution to the axial-vector transition distribution using chiral perturbation theory.

hep-ph↗

arXiv2004

Double distributions for the proton

We derive double distributions for the proton in a simple model that contains scalar as well as axial-vector diquark correlations. The model parameters are tuned so that the experimentally measured electromagnetic form factors are reproduced for small momentum transfer. Resulting generalized parton distributions satisfy known constraints, including the positivity bounds.

hep-ph↗

arXiv2004

Light-Front Dynamics and Generalized Parton Distributions

In this work we report on using light-front dynamics to describe generalized parton distributions, which are correlation functions encountered in virtual Compton scattering at large momentum transfer. This two photon process requires pair annihilation contributions which are subtle to handle in light-front dynamics. We are careful to derive such contributions in the light-front Bethe-Salpeter formalism. This derivation highlights the connection to the Fock space picture as well as provides a toy model for generalized parton distributions.Ultimately we use light-front dynamics to build a phenomenological parametrization for the proton's generalized parton distributions. This task is non-trivial due to the field theoretic constraints required of these distributions. To meet the constraints imposed by Lorentz covariance, we approach generalized parton distributions from the perspective of double distributions. Despite avid phenomenological use, surprisingly little work has been done to calculate double distributions. We first focus on a number of simple pedagogical examples and demonstrate how double distributions can be correctly determined. The double distributions we derive, including those for the proton, satisfy known constraints and are adequate for phenomenological estimates of cross sections. The models used allow one to study the interplay between the light-front formulation and Lorentz covariance.

nucl-th↗

arXiv2004

Double distributions: Loose ends

We point out that double distributions need not vanish at their boundary. Boundary terms do not change the ambiguity inherent in defining double distributions; instead, boundary conditions must be satisfied in order to switch between different decompositions. We analyze both the spin zero and spin one-half cases.

hep-ph↗

arXiv2003

Complex conjugate poles and parton distributions

We calculate parton and generalized parton distributions in Minkowski space using a scalar propagator with a pair of complex conjugate poles. Correct spectral and support properties are obtained only after careful analytic continuation from Euclidean space. Alternately the quark distribution function can be calculated from modified cutting rules, which put the intermediate state on its complex mass shells. Distribution functions agree with those resulting from the model's Euclidean space double distribution which we calculate via non-diagonal matrix elements of twist-two operators. Thus one can use a wide class of analytic parameterizations of the quark propagator to connect Euclidean space Green functions to light-cone dominated amplitudes.

hep-ph↗

arXiv2002

Generalized parton distributions and double distributions for q q-bar pions

We consider two simple covariant models for pions (one with scalar and the other with spin-1/2 constituents). Pion generalized parton distributions are derived by integration over the light-cone energy. The model distributions are consistent with all known properties of generalized parton distributions, including positivity. We also construct the corresponding double distributions by appealing to Lorentz invariance. These ostensibly constructed double distributions lead to different generalized parton distributions that need not respect the positivity constraints. This inconsistency arises from the ambiguity inherent in defining double distributions in a one-component formalism (even in the absence of the Polyakov-Weiss term). We demonstrate that the correct model double distributions can be calculated from non-diagonal matrix elements of twist-two operators.

hep-ph↗

arXiv2002

Current in the light-front Bethe-Salpeter formalism I: Replacement of non-wave function vertices

We apply the light-front reduction of the Bethe-Salpeter equation to matrix elements of the electromagnetic current between bound states. Using a simple (1+1)-dimensional model to calculate form factors, we focus on two cases. In one case, the interaction is dominated by a term instantaneous in light-cone time. Here effects of higher Fock states are negligible and the form factor can be effectively expressed using non-wave function vertices and crossed interactions. If the interaction is not instantaneous, non-wave function vertices are replaced by contributions from higher Fock states. These higher Fock components arise from the covariant formalism via the energy poles of the Bethe-Salpeter vertex and the electromagnetic vertex. The replacement of non-wave function vertices in time-ordered perturbation theory is a theorem which directly extends to generalized parton distributions, e.g., in (3+1) dimensions.

hep-ph↗

arXiv2002

Current in the light-front Bethe-Salpeter formalism II: Applications

We pursue applications of the light-front reduction of current matrix elements in the Bethe-Salpeter formalism. The normalization of the reduced wave function is derived from the covariant framework and related to non-valence probabilities using familiar Fock space projection operators. Using a simple model, we obtain expressions for generalized parton distributions that are continuous. The non-vanishing of these distributions at the crossover between kinematic regimes (where the plus component of the struck quark's momentum is equal to the plus component of the momentum transfer) is tied to higher Fock components. Moreover continuity holds due to relations between Fock components at vanishing plus momentum. Lastly we apply the light-front reduction to time-like form factors and derive expressions for the generalized distribution amplitudes in this model.

hep-ph↗

arXiv2002

Generalized parton distributions for $q\bar{q}$ pions

We use a two-body, light-cone pion wave function (which vanishes when one of the constituents carries all of the plus-momentum) to construct a double distribution. We show that the resulting generalized parton distribution has incorrect behavior at the crossover between kinematic regions. Furthermore the positivity constraints are not respected. On the other hand, the field-theoretic, two-body double distribution gives generalized parton distributions that have physically correct crossover behavior and respect the positivity constraints independent of the model wave function used. However, the sum rule and polynomiality conditions cannot be satisfied with a two-body wave function alone since Lorentz symmetry is not maintained.

hep-ph↗

arXiv2002

Generalized parton distributions for weakly bound systems from light-front quantum mechanics

We present generalized parton distributions for weakly bound systems on the light cone in order to build intuition about the light-front formalism. Physics at the crossover is reviewed in terms of the light-cone Fock space representation. Furthermore, we link light-cone Fock components to the equal (light-cone) time projection of the covariant Bethe-Salpeter amplitude. Continuity of the distributions arises naturally in this weak binding model.

hep-ph↗

arXiv2002

Light front Bethe-Salpeter equation applied to form factors, generalized parton distributions and generalized distribution amplitudes

We present an intuitive, light front reduction scheme for the Bethe-Salpeter equation that consists of iterations of the (light front) energy dependent covariant equation followed by an instantaneous approximation. This scheme is equivalent to and motivates the form of a standard reduction that reproduces light front, time ordered perturbation theory for bound states. We use this three-dimensional light front formalism to compute electromagnetic form factors between bound states to show how higher, light front Fock components arise from the covariant Bethe-Salpeter wave function. Moreover, we show that non-wave function vertices, which arise after integration over the minus momenta, are completely removed in favor of higher Fock states when one correctly takes into account all contributions at a given order in perturbation theory. Such non-wave function vertices are shown only to occur in models in which the interactions are instantaneous. These models lack true higher Fock states. The normalization of the reduced wave function is derived from the covariant framework and related to nonvalence probabilities using familiar Fock space projection operators. Using a simple model, we obtain expressions for generalized parton distributions that are continuous. The nonvanishing of these distributions at the crossover between kinematic regimes (where the plus component of the struck quark's momentum is equal to the plus component of the momentum transfer) is tied to higher Fock components. Lastly we apply the light front reduction to timelike form factors and derive expressions for the generalized distribution amplitudes in this model.

hep-ph↗

arXiv2001

Exploring skewed parton distributions with two body models on the light front II: covariant Bethe-Salpeter approach

We explore skewed parton distributions for two-body, light-front wave functions. In order to access all kinematical regimes, we adopt a covariant Bethe-Salpeter approach, which makes use of the underlying equation of motion (here the Weinberg equation) and its Green's function. Such an approach allows for the consistent treatment of the non-wave function vertex (but rules out the case of phenomenological wave functions derived from ad hoc potentials). Our investigation centers around checking internal consistency by demonstrating time-reversal invariance and continuity between valence and non-valence regimes. We derive our expressions by assuming the effective qq potential is independent of the mass squared, and verify the sum rule in a non-relativistic approximation in which the potential is energy independent. We consider bare-coupling as well as interacting skewed parton distributions and develop approximations for the Green's function which preserve the general properties of these distributions. Lastly we apply our approach to time-like form factors and find similar expressions for the related generalized distribution amplitudes.

hep-ph↗

arXiv2001

Exploring Skewed Parton Distributions with Two-body Models on the Light Front I: bimodality

We explore skewed parton distributions for simple, model wave-functions in a truncated two-body Fock space. Consideration of non-Gaussian wave functions is our main emphasis, from which we observe the distributions are bimodal (there can be two distinct peaks) in the Fock-space diagonal overlap region (x > xi). We demonstrate that this behavior arises from convoluting two light-front wave functions to form the skewed parton distribution. Furthermore, the factorization Ansaetze, which have been used often, are shown not to hold. At high t, we can write the skewed parton distribution in terms of quark distribution amplitudes and perturbative wave functions thereby providing new tests.

hep-ph↗

arXiv2001

Trouble in Asymptopia---the Hulthen Model on the Light Front

We use light-front dynamics to calculate the electromagnetic form-factor for the Hulthen model of the deuteron. For small momentum transfer Q^2 < 5 GeV^2 the relativistic effects are quite small. For Q^2 = 11 GeV^2 there is about a 13% discrepancy between the relativistic and non-relativistic approaches. For asymptotically large momentum transfer, however, the light-front form factor, log Q^2 /Q^4, markedly differs from the non-relativistic version, 1/Q^4. This behavior is also present for any wave function, such as those obtained from realistic potential models, which can be represented as a sum of Yukawa functions. Furthermore, the asymptotic behavior is in disagreement with the Drell-Yan-West relation. We investigate precisely how to determine the asymptotic behavior and confront the problem underlying troublesome form factors on the light front.

nucl-th↗