Splitting Methods for SU(N) Loop Approximation

The problem of finding the correct asymptotic rate of approximation by polynomial loops in dependence of the smoothness of the elements of a loop group seems not well-understood in general. For matrix Lie groups such as SU(N), it can be viewed as a problem of nonlinearly constrained trigonometric approximation. Motivated by applications to optical FIR filter design and control, we present some initial results for the case of SU(N)-loops, N>1. In particular, using representations via the exponential map and ideas from splitting methods, we prove that the best approximation of an SU(N)-loop belonging to a Hoelder-Zygmund class Lip_alpha with alpha>1/2 by a polynomial SU(N)-loop of degree n is of the order O(n^{-\alpha/(1+\alpha)}) as n tends to infinity. Although this approximation rate is not considered final (and can be improved in special cases), to our knowledge it is the first general, nontrivial result of this type.Comment: 14 pages, still submitted to J. Approx. Th. typos corrected, part of the proof of Lemma 4 concerning the auxiliary statement on page 8 rewritten in a clearer wa

Chiral Analysis of Quenched Baryon Masses

We extend to quenched QCD an earlier investigation of the chiral structure of the masses of the nucleon and the delta in lattice simulations of full QCD. Even after including the meson-loop self-energies which give rise to the leading and next-to-leading non-analytic behaviour (and hence the most rapid variation in the region of light quark mass), we find surprisingly little curvature in the quenched case. Replacing these meson-loop self-energies by the corresponding terms in full QCD yields a remarkable level of agreement with the results of the full QCD simulations. This comparison leads to a very good understanding of the origins of the mass splitting between these baryons.Comment: 23 pages, 6 figure

Non-minimal Split Supersymmetry

We present an extension of the minimal split supersymmetry model, which is capable of explaining the baryon asymmetry of the Universe. Instead of MSSM we start from NMSSM and split its spectrum in such a way that the low energy theory contains neutral particles, in addition to the content of minimal split supersymmetry. They trigger the strongly first order electroweak phase transition (EWPT) and provide an additional source of CP-violation. In this model, we estimate the amount of the baryon asymmetry produced during EWPT, using WKB approximation for CP-violating sources in diffusion equations. We also examine the contribution of CP-violating interactions to the electron and neutron electric dipole moments and estimate the production of the neutralino dark matter. We find that both phenomenological and cosmological requirements can be fulfilled in this model.Comment: 31 pages, 9 figures, typos correcte

Not Even Decoupling Can Save Minimal Supersymmetric SU(5)

We make explicit the statement that Minimal Supersymmetric SU(5) has been excluded by the Super-Kamiokande search for the process $p \to K^{+} \overline{\nu}$. This exclusion is made by first placing limits on the colored Higgs triplet mass, by forcing the gauge couplings to unify. We also show that taking the superpartners of the first two generations to be very heavy in order to avoid flavor changing neutral currents, the so-called ``decoupling'' idea, is insufficient to resurrect the Minimal SUSY SU(5). We comment on various mechanisms to further suppress proton decay in SUSY SU(5). Finally, we address the contributions to proton decay from gauge boson exchange in the Minimal SUSY SU(5) and flipped SU(5) models.Comment: 8 pages, 4 figure

Heavy Quark Spectroscopy and Matrix Elements: A Lattice Study using the Static Approximation

We present results of a lattice analysis of the $B$ parameter, $B_B$, the decay constant $f_B$, and several mass splittings using the static approximation. Results were obtained for 60 quenched gauge configurations computed at $\beta=6.2$ on a lattice size of $24^3\times48$. Light quark propagators were calculated using the $O(a)$-improved Sheikholeslami-Wohlert action. We find \Bbstat(m_b) = 0.69\er{3}{4} {\rm(stat)}\er{2}{1} {\rm(syst)}, corresponding to \Bbstat = 1.02\er{5}{6}\er{3}{2}, and \fbstat = 266\err{18}{20}\err{28}{27} \mev, f_{B_s}^2 B_{B_s}/f_B^2 B_B = 1.34\er{9}{8}\er{5}{3}, where a variational fitting technique was used to extract \fbstat. For the mass splittings we obtain M_{B_s}-M_{B_d} = 87\err{15}{12}\err{6}{12} \mev, M_{\Lambda_b}-M_{B_d} = 420\errr{100}{90}\err{30}{30} \mev and M_{B^*}^2-M_B^2 = 0.281\err{15}{16}\err{40}{37} \gev^2. We compare different smearing techniques intended to improve the signal/noise ratio. From a detailed assessment of systematic effects we conclude that the main systematic uncertainties are associated with the renormalisation constants relating a lattice matrix element to its continuum counterpart. The dependence of our findings on lattice artefacts is to be investigated in the future.Comment: 40 pages, uuencoded compressed tar file, containing one LaTeX file and 14 postscript files (to be included with epsf). Minor change in the value of the B parameter. Contains corrected value for the B*-B mass splitting. Version accepted for publication in Phys. Rev.

On membrane interactions and a three-dimensional analog of Riemann surfaces

Membranes in M-theory are expected to interact via splitting and joining processes. We study these effects in the pp-wave matrix model, in which they are associated with transitions between states in sectors built on vacua with different numbers of membranes. Transition amplitudes between such states receive contributions from BPS instanton configurations interpolating between the different vacua. Various properties of the moduli space of BPS instantons are known, but there are very few known examples of explicit solutions. We present a new approach to the construction of instanton solutions interpolating between states containing arbitrary numbers of membranes, based on a continuum approximation valid for matrices of large size. The proposed scheme uses functions on a two-dimensional space to approximate matrices and it relies on the same ideas behind the matrix regularisation of membrane degrees of freedom in M-theory. We show that the BPS instanton equations have a continuum counterpart which can be mapped to the three-dimensional Laplace equation through a sequence of changes of variables. A description of configurations corresponding to membrane splitting/joining processes can be given in terms of solutions to the Laplace equation in a three-dimensional analog of a Riemann surface, consisting of multiple copies of R^3 connected via a generalisation of branch cuts. We discuss various general features of our proposal and we also present explicit analytic solutions.Comment: 64 pages, 17 figures. V2: An appendix, a figure and references added; various minor changes and improvement

QCD Thermodynamics from the Lattice

We review the current methods and results of lattice simulations of quantum chromodynamics at nonzero temperatures and densities. The review is intended to introduce the subject to interested nonspecialists and beginners. It includes a brief overview of lattice gauge theory, a discussion of the determination of the crossover temperature, the QCD phase diagram at zero and nonzero densities, the equation of state, some in-medium properties of hadrons including charmonium, and some plasma transport coefficients.Comment: 74 pp. 31 figs. To appear in the European Physical Journal A and Advances in Physics of Particles and Nuclei. Added references, corrected typos, and updated the discussion of the thermal heavy quark/antiquark potential. Added and updated references. Final versio