arXiv subjects
Publications and source records attributed to Jerrold Franklin.
We show that a form for the second partial derivative of $1/r$ proposed by Frahm and subsequently used by other workers applies only when averaged over smooth functions. We use dyadic notation to derive a more general form without that restriction.
We show that the conclusion of a recent experiment [arXiv:0912.3934] that claims to have discovered that "the speed of light seems to depend on the motion of the observer" is wrong.
The meaning of Lorentz contraction in special relativity and its connection with Bell's spaceships parable is discussed. The motion of Bell's spaceships is then compared with the accelerated motion of a rigid body. We have tried to write this in a simple form that could be used to correct students' misconceptions due to conflicting earlier treatments.
Model independent sum rules for heavy baryon masses are tested for baryons containing charmed or bottom quarks. The sum rules depend only on the assumption that baryon mass differences are determined by spin-dependent two-body energies of quark pairs that do not depend on which baryon the quark pair is in. No assumption is made about the details of the quark-quark interaction. The sum rules are generally well satisfied, although better experimental accuracy would be required for a quantitative test of some of the sum rules. The success of the sum rules is evidence that "baryon independence" of quark-quark interaction is a good assumption for baryon mass calculations. It also means that the success of some detailed baryon mass calculations may not depend on the specific mechanism used in the calculation.
The absence of any tendency toward rotation in a moving right angle lever is given a simple explanation.
The absence of any tendency toward rotation in the Trouton-Noble experiment is given a simple explanation.
A general three quark bound state satisfying the Pauli principle, and conserving angular momentum and isospin, is used to investigate the spin structure of nucleons at high $x$. It is shown that, if a spin up quark dominates as $x$$\to$1 for a spin up proton, it must be a u quark. Then both $A_{1p}$ and $A_{1n}$, as well as the quark spin distribution $Δu/u$, will approach 1 as $x$$\to$1. The spin distribution $Δd/d$ does not approach 1, but is bound by the limits $-{1/3}\leΔd/d\le 0$ for any $x$. The ratio {$F_{1n}/F_{1p}$ will approach 1/4} (not3/7).
A general three quark bound state satisfying the Pauli principle, and conserving angular momentum and isospin, is used to investigate the spin structure of nucleons at high $x$. It is shown if {$F_{1n}/F_{1p}$$\to$1/4}, then both $A_{1p}$ and $A_{1n}$, as well as quark spin distribution $Δu/u$, will approach 1 as $x$$\to$1 in polarized deep inelastic scattering. The spin distribution $Δd/d$ does not approach 1, but is bound by the limits $-{1/3}\leΔd/d\le 0$ for any $x$.
Baryon magnetic moments and beta decay ratios ($G_A/G_V$) are calculated in a phenomenological quark model. Non-static effects of pion exchange and orbital excitation are included. Good agreement with experiment is found for a combined fit to all measured baryon magnetic moments and beta decay ratios. The model predicts an antiquark content for the proton that is consistent with the Gottfried sum rule.
Exact solutions are found to the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions. The method works for the ground state or for the lowest orbital state with l=j-{1/2}, for any j.
New experimental measurements are used to test model independent sum rules for charmed baryon masses. Sum rules for medium-strong mass differences are found to be reasonably well satisfied with increasing accuracy, and the new measurements permit an improved prediction of $2778\pm 9$ MeV for the mass of the $Ω_c^{*0}$. But an isospin breaking sum rule for the $Σ_c$ mass splittings is still in significant disagreement posing a serious problem for the quark model of charmed baryons. Individual $Σ_c$ mass splittings are investigated, using the new CLEO measurement of the $Ξ_c^\prime$ mass splitting, but the accuracy is not yet sufficient for a good test.
A simple analytical solution is found to the Dirac equation for the combination of a Coulomb potential with a linear confining potential. An appropriate linear combination of Lorentz scalar and vector linear potentials, with the scalar part dominating, can be chosen to give a simple Dirac wave function. The binding energy depends only on the Coulomb strength, and is not affected by the linear potential. The method works for the ground state, or for the lowest state with $l=j-{1/2}$, for any $j$.
The importance of exchange currents, and of conserving isotopic spin at both the quark and baryon levels in application of the chiral quark model to any calculation of baryon magnetic moments is emphasized.
The new designation of heavy baryons proposed by Falk (hep-ph/9603389) is shown to violate minimal symmetry sum rules.
The mixing angle between the Xi_c and Xi_c' baryons is shown to be small, with a negligible shift in the Xi_c masses.
Model independent sum rules are applied to recent measurements of heavy c-baryon and d-baryon masses. The sum rules are generally satisfied to the same degree as for the light (u,d,s) baryons.
A rest frame valence quark model is applied to the deep inelastic scattering of charged leptons by protons. The parameters of the model are determined by a fit to unpolarized electron cross sections. The model then can be used to calculate the asymmetry in polarized deep inelastic scattering. The predicted spin-dependent structure function g1p is in good agreement with recent measurements. This indicates that, in the proton rest system, the spin of the proton is carried by the valence quarks.
The spin dependent structure functions, g$_{1p}$ of the proton and g$_{1n}$ of the neutron, calculated in the nucleon rest frame using a relativistic quark model wave function, are compared with recent experiments.