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I. R. Afnan

Publications and source records attributed to I. R. Afnan.

At least 19 recordsLinked to original sources
arXiv2012

Variations of nuclear binding with quark masses

We investigate the variation with light quark mass of the mass of the nucleon as well as the masses of the mesons commonly used in a one-boson-exchange model of the nucleon-nucleon force. Care is taken to evaluate the meson mass shifts at the kinematic point relevant to that problem. Using these results, the corresponding changes in the energy of the 1 S0 anti-bound state, the binding energies of the deuteron, triton and selected finite nuclei are evaluated using a one-boson exchange model. The results are discussed in the context of possible corrections to the standard scenario for big bang nucleosynthesis in the case where, as suggested by recent observations of quasar absorption spectra, the quark masses may have changed over the age of the Universe.

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arXiv2004

The three-body problem with short-range forces: renormalized equations and regulator-independent results

We discuss effective field theory treatments of the problem of three particles interacting via short-range forces. One case of such a system is neutron-deuteron scattering at low energies. We demonstrate that in attractive channels the renormalization-group evolution of the 1+2 scattering amplitude may be complicated by the presence of eigenvalues greater than unity in the kernel. We also show that these eigenvalues can be removed from the kernel by one subtraction, resulting in an equation which is renormalization-group invariant. A unique solution for 1+2 scattering phase shifts is then obtained. We give an explicit demonstration of our procedure for both the case of three spinless bosons and the case of the doublet channel in nd scattering. After the contribution of the two-body effective range is included in the effective field theory, it gives a good description of the nd doublet phase shifts below deuteron breakup threshold.

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arXiv2003

Deep inelastic scattering from A=3 nuclei and the neutron structure function

We present a comprehensive analysis of deep inelastic scattering from He-3 and H-3, focusing in particular on the extraction of the free neutron structure function, F_2^n. Nuclear corrections are shown to cancel to within 1-2% for the isospin-weighted ratio of He-3 to H-3 structure functions, which leads to more than an order of magnitude improvement in the current uncertainty on the neutron to proton ratio F_2^n/F_2^p at large x. Theoretical uncertainties originating from the nuclear wave function, including possible non-nucleonic components, are evaluated. Measurement of the He-3 and H-3 structure functions will, in addition, determine the magnitude of the EMC effect in all A < 4 nuclei.

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arXiv2002

Unitarity and the Bethe-Salpeter Equation

We investigate the relation between different three-dimensional reductions of the Bethe-Salpeter equation and the analytic structure of the resultant amplitudes in the energy plane. This correlation is studied for both the $ϕ^2σ$ interaction Lagrangian and the $πN$ system with $s$-, $u$-, and $t$-channel pole diagrams as driving terms. We observe that the equal-time equation, which includes some of the three-body unitarity cuts, gives the best agreement with the Bethe-Salpeter result. This is followed by other 3-D approximations that have less of the analytic structure.

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arXiv2002

The Lambda-Lambda Interaction and ^{6}_{Lambda Lambda}He

An OBE potential model for the ^{1}S_0 S = -2 interaction is analyzed with emphasis on the role of coupling between the Lambda Lambda, N Xi, and Sigma Sigma channels. Singlet scalar exchange, an approximation to two-pion exchange, is significant in all channels; surprisingly, the one-pion exchange component is almost negligible. The size of the channel coupling as a function of the overall strength of the OBE model potential is examined. Implications of the analysis for the binding energy of ^{6}_{Lambda Lambda}He are considered; the new experimental datum may suggest a consistency between the extracted Lambda Lambda matrix element and the relation implied by SU(3) among OBE baryon-baryon interactions. \\

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arXiv2001

Pion-nucleon scattering in a Bethe-Salpeter approach

A covariant model of elastic pion-nucleon scattering based on the Bethe-Salpeter equation is presented. We obtain a good description of the S- and P-wave phase shifts up to 360 MeV laboratory energy. We also compare results from the K-matrix approach and several 3-dimensional quasipotential equations to the Bethe-Salpeter equation.

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arXiv2000

Structure functions for the three nucleon system

The spectral functions and light-cone momentum distributions of protons and neutrons in 3He and 3H are given in terms of the three-nucleon wave function for realistic nucleon-nucleon interactions. To reduce computational complexity, separable expansions are employed for the nucleon-nucleon potentials. The results for the light-cone momentum distributions suggest that they are not very sensitive to the details of the two-body interaction, as long as it has reasonable short-range repulsion. The unpolarised and polarised structure functions are examined for both 3He and 3H in order to test the usefulness of 3He as a neutron target. It is found that the measurement of the spin structure function of polarised 3H would provide a very clear test of the predicted change in the polarised parton distributions of a bound proton.

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arXiv2000

Measurement of the F2n/F2p and d/u Ratios in Deep Inelastic Electron Scattering off 3H and 3He

We discuss a possible measurement of the ratio of the nucleon structure functions, F2n/F2p, and the ratio of the up to down quark distributions, u/d, at large x, by performing deep inelastic electron scattering from the 3H and 3He mirror nuclei with the 11 GeV upgraded beam of Jefferson Lab. The measurement is expected to be almost free of nuclear effects, which introduce a significant uncertainty in the extraction of these two ratios from deep inelastic scattering off the proton and deuteron. The results are expected to test perturbative and non-perturbative mechanisms of spin-flavor symmetry breaking in the nucleon, and constrain the structure function parameterizations needed for the interpretation of high energy e-p, p-p and p-pbar collider data. The precision of the expected data can also allow for testing competing parameterizations of the nuclear EMC effect and provide valuable constraints on models of its dynamical origin.

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arXiv2000

Neutron Structure Function and A=3 Mirror Nuclei

We investigate deep inelastic scattering from He-3 and H-3 within a conventional convolution treatment of binding and Fermi motion effects. Using realistic Faddeev wave functions together with a nucleon spectral function, we demonstrate that the free neutron structure function can be extracted in deep-inelastic scattering from A=3 mirror nuclei, with nuclear effects canceling to within 2% for x < 0.85.

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arXiv2000

Deep inelastic scattering on asymmetric nuclei

We study deep inelastic scattering on isospin asymmetric nuclei. In particular, the difference of the nuclear structure functions and the Gottfried sum rule for the lightest mirror nuclei, 3He and 3H, are investigated. It is found that such systems can provide significant information on charge symmetry breaking and flavor asymmetry in the nuclear medium. Furthermore, we propose a new method to extract the neutron structure function from radioactive isotopes far from the line of stability. We also discuss the flavor asymmetry in the Drell-Yan process with isospin asymmetric nuclei.

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arXiv2000

Comment on ``Parton distributions, d/u, and higher twist effects at high x''

In a recent paper Yang and Bodek extracted the free neutron structure function at large x by extrapolating the density dependence of the nuclear EMC ratios to the deuteron. We clarify why this approach is ill-defined for light nuclei, and introduces a large theoretical bias into the extraction of F_2n at large x.

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arXiv2000

Numerical renormalization using dimensional regularization: a simple test case in the Lippmann-Schwinger equation

Dimensional regularization is applied to the Lippmann-Schwinger equation for a separable potential which gives rise to logarithmic singularities in the Born series. For this potential a subtraction at a fixed energy can be used to renormalize the amplitude and produce a finite solution to the integral equation for all energies. This can be done either algebraically or numerically. In the latter case dimensional regularization can be implemented by solving the integral equation in a lower number of dimensions, fixing the potential strength, and computing the phase shifts, while taking the limit as the number of dimensions approaches three. We demonstrate that these steps can be carried out in a numerically stable way, and show that the results thereby obtained agree with those found when the renormalization is performed algebraically to four significant figures.

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arXiv1999

Solution of the Bethe-Salpeter equation for pion-nucleon scattering

A relativistic description of pion-nucleon scattering based on the four-dimensional Bethe-Salpeter equation is presented. The kernel of the equation consists of s- and u-channel nucleon and delta pole diagrams, as well as rho and sigma exchange in the t-channel. The Bethe-Salpeter equation is solved by means of a Wick rotation, and good fits are obtained to the s- and p-wave phase shifts up to 360 MeV pion laboratory energy. The coupling constants determined by the fits are consistent with the commonly accepted values in the literature.

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arXiv1999

The $ΛΛ-ΞN$ Coupling and the Binding Energy of $_{ΛΛ}^{6}}$He

To understand the difference between the value of the nn and Lambda-Lambda two-body matrix elements, we examine the role of the coupling between the Lambda-Lambda and Xi-N channels, first within the framework of SU(3), and second in the numerical results for the binding energy of Lambda-Lambda 6He. We find that it is essential to include the coupled channel nature of the BB interaction as we proceed from strangeness zero to the strangeness -1 and -2 channels if we are to understand the relative magnitude of the two-body matrix elements in the different strangeness channels.

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arXiv1998

Covariant formulation of pion-nucleon scattering

A covariant model of elastic pion-nucleon scattering based on the Bethe-Salpeter equation is presented. The kernel consists of s- and u-channel nucleon and delta poles, along with rho and sigma exchange in the t-channel. A good fit is obtained to the s- and p-wave phase shifts up to the two-pion production threshold.

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arXiv1997

$Ξ^{-} d\to nΛΛ$ and the $ΛΛ$ final state interaction

The reaction $Ξ^-d\to nΛΛ$ is studied within the framework of the Faddeev equations as a possible tool to gain insight into the final state $Λ$--$Λ$ interaction. The neutron differential energy spectrum gives a final state interaction that is sensitive to both the $Λ$--$Λ$ amplitude at threshold, and the coupling between the $Λ$--$Λ$ and $Ξ$--$N$ channels. The latter is a result of interference between two mechanisms for the production of the final state, which suggests that this reaction could give a measure of flavor SU(3) violation in the two-baryon system.

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arXiv1997

The $Ξ^- +d\to n+Λ+Λ$ reaction as a probe of the $ΛΛ$ interaction

Within the framework of the Faddeev equations we demonstrate that a $ΛΛ-ΞN$ interaction that gives a $ΛΛ$ scattering length comparable to the $nn$ scattering length, and the binding energy of $^{\ 6}_{ΛΛ}$He as an $αΛΛ-αΞN$ system, produces a final state interaction peak in the neutron spectrum for the reaction $Ξ^- d \to nΛΛ$. This suggests that this reaction could be used to constrain the $ΛΛ$ scattering length.

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