arXiv subjects
Publications and source records attributed to T. Goldman.
The Einstein-Podolsky-Rosen paradox is resolved by reconsidering what entangled state is actually prepared, what physical quantities are conserved and the character of the correlation measurements employed.
Inspired by the progress of the experimental search of the $NΩ$ dibaryon by the STAR collaboration, we study $N\barΩ$ systems in the framework of quark delocalization color screening model. Our results show that the attraction between $N$ and $\barΩ$ is a little bit larger than that between $N$ and $Ω$, which indicates that it is more possible for the $N\barΩ$ than the $NΩ$ system to form bound states. The dynamic calculations state that both the $J^{P}=1^{+}$ and $2^{+}$ $N\barΩ$ systems are bound states. The binding energy of these two states are deeper than that of $NΩ$ systems with $J^{P}=2^{+}$, and the $NΩ$ system with $J^{P}=1^{+}$ is unbound. The calculation of the low-energy scattering phase shifts, scattering length and the effective range also supports the existence of the $N\barΩ$ bound states with $J^{P}=1^{+}$ and $2^{+}$. So the $N\barΩ$ states are better hexaquark states and stronger signals are expected in experiments.
Advances in physics have required the application of more and more sophisticated mathematics. I present arguments supporting the contention that the next advance beyond quantum field theory will require the application of a non-associative algebra. The principle observable effect would be the appearance of a fundamental length. An experimental search for such an effect may be feasible.
We follow the example of Cabibbo by revising the Standard Model (SM) to present a universal mass structure for fermions. A universal Higgs coupling for each species of fundamental fermions moves the SM towards a Theory of Matter, albeit without correctly describing the observed mass spectrum. It exposes a need for a complete Theory of Matter to include components from physics beyond the Standard Model (BSM). Describing the effect of these components phenomenologically provides a means to infer the nature of some of the BSM physics required. Our results also provide constraints on some BSM matrix elements. Here we apply this concept to quarks; the application to leptons will appear in a separate paper. An immediate benefit for theory is the reduction of the largest fine structure constant for the Higgs coupling to fermions by an order of magnitude, which improves the perturbative appearance of the weak interactions. The small mixing of the third generation of each fermion in the fermion families to the others is attributed to the small BSM perturbations that produce the small mass ratio of the lighter generations to the most massive one.
We apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdfs), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the scale-change distribution function is scale invariant then the constructed distribution will also be scale invariant. Repeated application of this construction on an arbitrary set of (normalizable) pdfs results again in scale-invariant distributions. The invariant function of this procedure is given uniquely by the reciprocal distribution, suggesting a kind of universality. We separately demonstrate that the reciprocal distribution results uniquely from requiring maximum entropy for size-class distributions with uniform bin sizes.
With a modest revision of the mass sector of the Standard Model, the systematics of the fermion masses and mixings can be fully described and interpreted as providing information on matrix elements of physics beyond the Standard Model. A by-product is a reduction of the largest Higgs Yukawa fine structure constant by an order of magnitude. The extension to leptons provides for insight on the difference between quark mixing and lepton mixing as evidenced in neutrino oscillations. The large difference between the scale for up-quark and down-quark masses is not addressed. In this approach, improved detail and accuracy of the elements of the current mixing matrices can extend our knowledge and understanding of physics beyond the Standard Model.
Using the LAMP model for nuclear quark structure, we calculate the binding energy and quark structure of a $B$ meson merging with a $D$ meson. The larger-than-nucleon masses of the two heavy quarks allow for a more reliable application of the Born-Oppenheimer-like approximation of the LAMP. With the absence of quark-level Pauli Exclusion Principle repulsive effects, the appearance of a bound state is unsurprising. Our variational calculation shows that the molecular, deuteron-like state structure changes rather abruptly, as the separation between the two mesons decreases, at a separation of about 0.45 fm, into a four-quark bound state, although one maintaining an internal structure rather than that of a four-quark bag. Unlike the deuteron, pion exchange does not provide any contribution to the $\approx 150$ MeV binding.
Definitions of entropy usually assume time-reversal (T) invariance of interactions, yet microscopically T is known to be violated. We present a detailed computational example of (uncharged) particle species separation (Maxwell demon) using an interaction that violates both parity (P) and T so that PT is preserved, consistent with the CPT invariance required in quantum field theory (C is charge conjugation). This illustrates how T-violating forces can produce more organized states from disorganized ones, contrary to expectations based on increase of entropy. We also outline several scenarios in which T-violating forces could lead to an organized state in the early Universe, starting from a still earlier disorganized state.
The conflict between the physical degrees of freedom of gauge bosons and the Lorentz group irreps naturally used to describe their couplings to matter fields are illustrated and discussed, and applied to issues of linear and angular momentum.
Starting with a confining linear Lorentz scalar potential V_s and a Lorentz vector potential V_v which is also linear but has in addition a color-Coulomb attraction piece, -alpha_s/r, we solve the Dirac equation for the ground-state c- and u-quark wave functions. Then, convolving V_v with the u-quark density, we find that the Coulomb attraction mostly disappears, making an essentially linear barV_v for the c-quark. A similar convolution using the c-quark density also leads to an essentially linear tildeV_v for the u-quark. For bound cbar-c charmonia, where one must solve using a reduced mass for the c-quarks, we also find an essentially linear widehatV_v. Thus, the relativistic quark model describes how the charmed-meson mass spectrum avoids the need for a color-Coulomb attraction.
We analyze the problem of spin decomposition for an interacting system from a natural perspective of constructing angular momentum eigenstates. We split, from the total angular momentum operator, a proper part which can be separately conserved for a stationary state. This part commutes with the total Hamiltonian and thus specifies the quantum angular momentum. We first show how this can be done in a gauge-dependent way, by seeking a specific gauge in which part of the total angular momentum operator vanishes identically. We then construct a gauge-invariant operator with the desired property. Our analysis clarifies what is the most pertinent choice among the various proposals for decomposing the nucleon spin. A similar analysis is performed for extracting a proper part from the total Hamiltonian to construct energy eigenstates.
Properties of the recently proposed gauge-invariant gluon spin $S_g$ are studied and compared to the usually defined "gluon polarization" $Δg$. By explicit 1-loop calculations in a quark state, it is found that $S_g= \frac 59Δg$. Furthermore, $\frac 45$ of $S_g$ can actually be identified as a "static-field" contribution and shown to cancel exactly an analogous static term in the gluon orbital angular momentum $L_g$, leaving $S_g+L_g$ unaltered. These observations suggest that if properly identified, the gluon contribution to the nucleon spin may be drastically smaller than in the conventional wisdom.
A description of neutrino oscillation phenomena is presented which is based on relativistic quantum mechanics and includes both entangled state and source dependent aspects, unlike both of the conventional approaches which use either equal energies or equal momenta for the different neutrino mass eigenstates. To second order in the neutrino masses, the standard result is recovered thus showing an absence of source dependence to this order. The time dependence of the wavefunction is found to be crucial to recovering the conventional result. An ambiguity appears at fourth order in the neutrino masses which generally leads to source dependence, but the standard formula can be promoted to this order by a plausible convention.
We discuss, in a pedagogical way, how to solve for relativistic wave functions from the radial Dirac equations. After an brief introduction, in Section II we solve the equations for a linear Lorentz scalar potential, V_s(r), that provides for confinement of a quark. The case of massless u and d quarks is treated first, as these are necessarily quite relativistic. We use an iterative procedure to find the eigenenergies and the upper and lower component wave functions for the ground state and then, later, some excited states. Solutions for the massive quarks (s, c, and b) are also presented. In Section III we solve for the case of a Coulomb potential, which is a time-like component of a Lorentz vector potential, V_v(r). We re-derive, numerically, the (analytically well-known) relativistic hydrogen atom eigenenergies and wave functions, and later extend that to the cases of heavier one-electron atoms and muonic atoms. Finally, Section IV finds solutions for a combination of the V_s and V_v potentials. We treat two cases. The first is one in which V_s is the linear potential used in Sec. II and V_v is Coulombic, as in Sec. III. The other is when both V_s and V_v are linearly confining, and we establish when these potentials give a vanishing spin-orbit interaction (as has been shown to be the case in quark models of the hadronic spectrum).
We affirm that the proper momentum defined in [PRL 103:062001 (2009)] does respect exact gauge symmetry and is as measurable as the kinetic momentum. The physical part of the gauge field is also as measurable as the electromagnetic field. The Comment of Ji [arXiv:0910.5022] is due to a misunderstanding of our work, and a typical confusion of our gauge-invariant formalism with the specific Coulomb-gauge calculation.
It is unavoidable to deal with the quark and gluon momentum and angular momentum contributions to the nucleon momentum and spin in the study of nucleon internal structure. However, we never have the quark and gluon momentum, orbital angular momentum and gluon spin operators which satisfy both the gauge invariance and the canonical momentum and angular momentum commutation relation. The conflicts between the gauge invariance and canonical quantization requirement of these operators are discussed. A new set of quark and gluon momentum, orbital angular momentum and spin operators, which satisfy both the gauge invariance and canonical momentum and angular momentum commutation relation, are proposed. The key point to achieve such a proper decomposition is to separate the gauge field into the pure gauge and the gauge covariant parts. The same conflicts also exist in QED and quantum mechanics and have been solved in the same manner. The impacts of this new decomposition to the nucleon internal structure are discussed.
We examine the conventional picture that gluons carry about half of the nucleon momentum in the asymptotic limit. We reveal that this large fraction is due to an unsuitable definition of the gluon momentum in an interacting theory. If defined in a gauge-invariant and consistent way, the asymptotic gluon momentum fraction is computed to be only about one fifth. This result suggests that the asymptotic limit of the nucleon spin structure should also be reexamined. Possible experimental test of our finding is discussed in terms of novel parton distribution functions.
We present a model in which the equation of state parameter w approaches -1 near a particular value of z, and has significant negative values in a restricted range of z. For example, one can have w ~ -1 near z = 1, and w > -0.2 from z = 0 to z = 0.3, and for z > 9. The ingredients of the model are neutral fermions (which may be neutrinos, neutralinos, etc) which are very weakly coupled to a light scalar field. This model emphasises the importance of the proposed studies of the properties of dark energy into the region z > 1.