Matching Excluded Volume Hadron Resonance Gas Models and Perturbative QCD to Lattice Calculations

We match three hadronic equations of state at low energy densities to a perturbatively computed equation of state of quarks and gluons at high energy densities. One of them includes all known hadrons treated as point particles, which approximates attractive interactions among hadrons. The other two include, in addition, repulsive interactions in the form of excluded volumes occupied by the hadrons. A switching function is employed to make the crossover transition from one phase to another without introducing a thermodynamic phase transition. A chi-square fit to accurate lattice calculations with temperature $100 < T < 1000$ MeV determines the parameters. These parameters quantify the behavior of the QCD running gauge coupling and the hard core radius of protons and neutrons, which turns out to be $0.62 \pm 0.04$ fm. The most physically reasonable models include the excluded volume effect. Not only do they include the effects of attractive and repulsive interactions among hadrons, but they also achieve better agreement with lattice QCD calculations of the equation of state. The equations of state constructed in this paper do not result in a phase transition, at least not for the temperatures and baryon chemical potentials investigated. It remains to be seen how well these equations of state will represent experimental data on high energy heavy ion collisions when implemented in hydrodynamic simulations.Comment: 19 pages, 9 figure

Net Baryon Fluctuations from a Crossover Equation of State

We have constructed an equation of state which smoothly interpolates between an excluded volume hadron resonance gas at low energy density to a plasma of quarks and gluons at high energy density. This crossover equation of state agrees very well with lattice calculations at both zero and nonzero baryon chemical potential. We use it to compute the variance, skewness, and kurtosis of fluctuations of baryon number, and compare to measurements of proton number fluctuations in central Au-Au collisions as measured by the STAR collaboration in a beam energy scan at the Relativistic Heavy Ion Collider. The crossover equation of state can reproduce the data if the fluctuations are frozen out at temperatures well below than the average chemical freeze-out.Comment: 5 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1506.0340

Construction of a Minimal Higgs SO(10) SUSY GUT Model

A full account is given of the procedure used by the authors to construct an SO(10) supersymmetric grand unified model of the fermion mass matrices. Various features of the model which gives remarkably accurate results for the quark and lepton masses and mixings were presented earlier in separate publications. The construction of the matrices is first discussed in the framework of effective operators, from which one naturally obtains the maximal \nu_\mu - \nu_\tau mixing, while the small angle or maximal mixing solutions for the solar neutrinos depend upon the nature of the Majorana matrix. A set of Higgs and fermion superfields is then introduced from which the Higgs and Yukawa superpotentials uniquely give the structure of the mass matrices previously obtained. The right-handed Majorana matrix arises from one Higgs field coupling to several pairs of superheavy conjugate neutrino singlets. For the simple version considered, 10 input parameters accurately yield the 20 masses and mixings of the quarks and leptons, and the 3 masses of the right-handed neutrinos.Comment: 37 pages including 4 figures, corrected a misprint in Table I and several misprints in Fig.

Predicting quark and lepton masses and mixings

A model is presented that fits the quark and lepton masses and mixings wherein five dimensionless parameters and a phase account for fifteen dimensionless observables. Among these are the Wolfenstein parameters $\rho$ and $\eta$, the $\nu_e-\nu_{\mu}$ and $\nu_e-\nu_{\tau}$ mixing angles which are predicted to be small and comparable while the $\nu_{\mu}-\nu_{\tau}$ mixing angle is predicted to be large. The model is based on supersymmetric SO(10) with the form of the mass matrices motivated by simplicity at the level of grand unification.Comment: 15 pages, LaTe

Handling employee problems

The most effective means of handling employee problems is to recognize and eliminate their probable cause before they arise. The authors of other papers included in these proceedings have provided guidance for avoiding manager/employee problems on a daily basis. If the conditions they discuss are monitored, there should be little need for "handling employee problems." In order to identify a problem, a supervisor must know and be sensitive to employees' needs as well as have a comprehensive view of organizational goals. The way in which each employee's role fits into the overall plan of service should be well defined. With this information, an insightful manager can identify both real and potential problems and deal with them appropriately.published or submitted for publicatio

Lifting a Realistic SO(10) Grand Unified Model to Five Dimensions

It has been shown recently that the problem of rapid proton decay induced by dimension five operators arising from the exchange of colored Higgsinos can be simply avoided in grand unified models where a fifth spatial dimension is compactified on an orbifold. Here we demonstrate that this idea can be used to solve the Higgsino-mediated proton decay problem in any realistic SO(10) model by lifting that model to five dimensions. A particular SO(10) model that has been proposed to explain the pattern of quark and lepton masses and mixings is used as an example. The idea is to break the SO(10) down to the Pati-Salam symmetry by the orbifold boundary conditions. The entire four-dimensional SO(10) model is placed on the physical SO(10) brane except for the gauge fields, the 45 and a single 10 of Higgs fields, which are placed in the five-dimensional bulk. The structure of the Higgs superpotential can be somewhat simplified in doing so, while the Yukawa superpotential and mass matrices derived from it remain essentially unaltered.Comment: 17 pages, version to be published in Phys. Rev. D with expanded discussion of the suppression of dim-5 proton decay operator

SO(10) and Large nu_mu - nu_tau Mixing

A general approach to understanding the large mixing seen in atmospheric neutrinos is explained, as well as a highly predictive SO(10) model which implements this approach. It is also seen how bimaximal mixing naturally arises in this scheme. (Talk presented at NNN99, SUNY Stony Brook, Sept. 22-26, 1999)Comment: 10 pages, LaTe