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G. A. Miller

Publications and source records attributed to G. A. Miller.

At least 55 records · Page 3Linked to original sources
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.

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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.

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arXiv2002

Spontaneously Broken Chiral Symmetry and Hard QCD Phenomena

These are the mini-proceedings of the workshop ``Spontaneously Broken Chiral Symmetry and Hard QCD Phenomena" held at the Physikzentrum Bad Honnef from July 15 to 19, 2002. Every author presents a summary of his talk. The transparencies of all speakers and further information on the workshop can be found on the website: http://www.tp2.ruhr-uni-bochum.de/hardreactions.html

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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.

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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.

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arXiv2002

Hadrons in the Nuclear Medium

Quantum Chromodynamics, the microscopic theory of strong interactions, has not yet been applied to the calculation of nuclear wave functions. However, it certainly provokes a number of specific questions and suggests the existence of novel phenomena in nuclear physics which are not part of the the traditional framework of the meson-nucleon description of nuclei. Many of these phenomena are related to high nuclear densities and the role of color in nucleonic interactions. Quantum fluctuations in the spatial separation between nucleons may lead to local high density configurations of cold nuclear matter in nuclei, up to four times larger than typical nuclear densities. We argue here that experiments utilizing the higher energies available upon completion of the Jefferson Laboratory energy upgrade will be able to probe the quark-gluon structure of such high density configurations and therefore elucidate the fundamental nature of nuclear matter. We review three key experimental programs: quasi-elastic electro-disintegration of light nuclei, deep inelastic scattering from nuclei at $x>1$, and the measurement of tagged structure functions. These interrelated programs are all aimed at the exploration of the quark structure of high density nuclear configurations. The study of the QCD dynamics of elementary hard processes is another important research direction and nuclei provide a unique avenue to explore these dynamics. We argue that the use of nuclear targets and large values of momentum transfer at would allow us to determine whether the physics of the nucleon form factors is dominated by spatially small configurations of three quarks.

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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.

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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.

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arXiv2002

Coherent QCD phenomena in the Coherent Pion-Nucleon and Pion-Nucleus Production of Two Jets at High Relative Momenta

We use QCD to compute the cross section for coherent production of a di-jet (treated as a $q\bar q$ moving at high relative transverse momentum,$κ_t $). In the target rest frame,the space-time evolution of this reaction is dominated by the process in which the high $κ_t$ $q\bar q$ component of the pion wave function is formed before reaching the target. It then interacts through two gluon exchange. In the approximation of keeping the leading order in powers of $α_s$ and all orders in $α_{s}\ln(κ_{t}^2/k_{0}^2),$ the amplitudes for other processes are shown to be smaller at least by a power of $α_{s}$. The resulting dominant amplitude is proportional to $z(1-z) κ_t^{-4}$ ($z$ is the fraction light-cone(+)momentum carried by the quark in the final state) times the skewed gluon distribution of the target. For the pion scattering by a nuclear target, this means that at fixed $x_{N}= 2κ_{t}^2/s$ (but $κ_{t}^2\to \infty$) the nuclear process in which there is only a single interaction is the most important one to contribute to the reaction. Thus in this limit color transparency phenomena should occur.These findings are in accord with E971 experiment at FNAL. We also re-examine a potentially important nuclear multiple scattering correction which is positive and $\propto A^{1/3}/κ_t^4$. The meaning of the signal obtained from the experimental measurement of pion diffraction into two jets is also critically examined and significant corrections are identified.We show also that for values of $κ_t$ achieved at fixed target energies, di-jet production by the e.m. field of the nucleus leads to an insignificant correction which gets more important as $κ_t$ increases.

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arXiv2002

Return of the EMC Effect: Finite Nuclei

A light front formalism for deep inelastic lepton scattering from finite nuclei is developed. In particular, the nucleon plus momentum distribution and a finite system analog of the Hugenholtz-van Hove theorem are presented. Using a relativistic mean field model, numerical results for the plus momentum distribution and ratio of bound to free nucleon structure functions for Oxygen, Calcium and Lead are given. We show that we can incorporate light front physics with excellent accuracy while using easily computed equal time wavefunctions. Assuming nucleon structure is not modified in-medium we find that the calculations are not consistent with the binding effect apparent in the data not only in the magnitude of the effect, but in the dependence on the number of nucleons.

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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.

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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.

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arXiv2001

Perturbative QCD and factorization of coherent pion photoproduction on the deuteron

We analyze the predictions of perturbative QCD for pion photoproduction on the deuteron, gamma D -> pi^0 D, at large momentum transfer using the reduced amplitude formalism. The cluster decomposition of the deuteron wave function at small binding only allows the nuclear coherent process to proceed if each nucleon absorbs an equal fraction of the overall momentum transfer. Furthermore, each nucleon must scatter while remaining close to its mass shell. Thus the nuclear photoproduction amplitude, M_{gamma D -> pi^0 D}(u,t), factorizes as a product of three factors: (1) the nucleon photoproduction amplitude, M_{gamma N_1 -> pi^0 N_1}(u/4,t/4), at half of the overall momentum transfer, (2) a nucleon form factor, F_{N_2}(t/4), at half the overall momentum transfer, and (3) the reduced deuteron form factor, f_d(t), which according to perturbative QCD, has the same monopole falloff as a meson form factor. A comparison with the recent JLAB data for gamma D -> pi^0 D of Meekins et al. [Phys. Rev. C 60, 052201 (1999)] and the available gamma p -> pi^0 p data shows good agreement between the perturbative QCD prediction and experiment over a large range of momentum transfers and center of mass angles. The reduced amplitude prediction is consistent with the constituent counting rule, p^11_T M_{gamma D -> pi^0 D} -> F(theta_cm), at large momentum transfer. This is found to be consistent with measurements for photon lab energies E_gamma > 3 GeV at theta_cm=90 degrees and $\elab > 10$ GeV at 136 degrees.

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arXiv2001

Return of the EMC Effect

The relationship between the properties of nuclear matter and structure functions measured in lepton-nucleus deep inelastic scattering is investigated using light front dynamics. We find that relativistic mean field models such as the Walecka, Zimanyi-Moszkowski (and point-coupling versions of the same) and Rusnak-Furnstahl models contain essentially no binding effect, in accord with an earlier calculation by Birse. These models are found to obey the Hugenholtz-van Hove theorem, which is applicable if nucleons are the only degrees of freedom. Any model in which the entire Fock space wave function can be represented in terms of free nucleons must obey this theorem, which implies that all of the plus momentum is carried by nucleons, and therefore that there will be essentially no binding effect. The explicit presence of nuclear mesons allows one to obtain a modified form of the Hugenholtz-van Hove theorem, which is equivalent to the often-used momentum sum rule. These results argue in favor of a conclusion that the depletion of the deep inelastic structure function observed in the valence quark regime is due to some interesting effect involving dynamics beyond the conventional nucleon-meson treatment of nuclear physics.

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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.

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arXiv2000

Charge Symmetry Violation in $pn\to d π^0$ as a Test of Chiral Effective Field Theory

Chiral effective field theory predicts a specific charge symmetry violating amplitude for pion production. This term is shown to provide the dominant contribution to the forward-backward asymmetry in the angular distribution for the reaction $pn\to dπ^0$, for reasonable values of the mass difference between down and up quarks, $δm_N$. Using a value $δm_N\approx$ 3 MeV leads to a prediction of a 10 standard deviation effect for a TRIUMF experiment.

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