Flux Hamiltonians, Lie Algebras and Root Lattices With Minuscule Decorations

We study a family of Hamiltonians of fermions hopping on a set of lattices in the presence of a background gauge field. The lattices are constructed by decorating the root lattices of various Lie algebras with their minuscule representations. The Hamiltonians are, in momentum space, themselves elements of the Lie algebras in these same representations. We describe various interesting aspects of the spectra--which exhibit a family resemblance to the Dirac spectrum, and in many cases are able to relate them to known facts about the relevant Lie algebras. Interestingly, various realizable lattices such as the kagom\'{e} and pyrochlore can be given this Lie algebraic interpretation and the particular flux Hamiltonians arise as mean-field Hamiltonians for spin-1/2 Heisenberg models on these lattices

η−η′\eta-\eta^\prime mixing and the next-to-leading-order power correction

The next-to-leading-order $O(1/Q^4)$ power correction for $\eta\gamma$ and $\eta^\prime\gamma$ form factors are evaluated and employed to explore the $\eta-\eta^\prime$ mixing. The parameters of the two mixing angle scheme are extracted from the data for form factors, two photon decay widths and radiative $J/\psi$ decays. The $\chi^2$ analysis gives the result: $f_{\eta_1}=(1.16\pm0.06)f_\pi, f_{\eta_8}=(1.33\pm0.23)f_\pi, \theta_1=-9^\circ\pm 3^\circ, \theta_8=-21.3^\circ\pm 2.3^\circ$, where $f_{\eta_{1(8)}}$ and $\theta_{1(8)}$ are the decay constants and the mixing angles for the singlet (octet) state. In addition, we arrive at a stringent range for $f_{\eta^\prime}^c:-10$ MeV$\le f_{\eta^\prime}^c\le -4$ MeV.Comment: 23 pages, 9 figures, To be publshied in Phys. Rev.

Maximum likelihood soft-output detection through Sphere Decoding combined with box optimization

This is the author’s version of a work that was accepted for publication in Signal Processing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Signal Processing 125 (2016) 249–260. DOI 10.1016/j.sigpro.2016.02.006.This paper focuses on the improvement of known algorithms for maximum likelihood soft-output detection. These algorithms usually have large computational complexity, that can be reduced by using clipping. Taking two well-known soft-output maximum likelihood algorithms (Repeated Tree Search and Single Tree Search) as a starting point, a number of modifications (based mainly on box optimization techniques) are proposed to improve the efficiency of the search. As a result, two new algorithms are proposed for soft-output maximum likelihood detection. One of them is based on Repeated Tree Search (which can be applied with and without clipping). The other one is based on Single Tree Search, which can only be applied to the case with clipping. The proposed algorithms are compared with the Single Tree Search algorithm, and their efficiency is evaluated in standard detection problems (4 4 16-QAM and 4 4 64-QAM) with and without clipping. The results show that the efficiency of the proposed algorithms is similar to that of the Single Tree Search algorithm in the case 4 4 16-QAM; however, in the case 4 4 64- QAM, the new algorithms are far more efficient than the Single Tree Search algorithm. & 2016 Elsevier B.V. All rights reserved.This work has been partially funded by Generalitat Valenciana through the projects ISIC/2012/006 and PROMETEO II/2014/003, and by Ministerio Espanol de Economia y Competitividad through the project TEC2012-38142-C04 and through the Grant RACHEL TEC2013-47141-C4-4-R.García Mollá, VM.; Simarro Haro, MDLA.; Martínez Zaldívar, FJ.; González Salvador, A.; Vidal Maciá, AM. (2016). Maximum likelihood soft-output detection through Sphere Decoding combined with box optimization. Signal Processing. 125:249-260. https://doi.org/10.1016/j.sigpro.2016.02.006S24926012

Variable-range hopping in quasi-one-dimensional electron crystals

We study the effect of impurities on the ground state and the low-temperature dc transport in a 1D chain and quasi-1D systems of many parallel chains. We assume that strong interactions impose a short-range periodicicity of the electron positions. The long-range order of such an electron crystal (or equivalently, a $4 k_F$ charge-density wave) is destroyed by impurities. The 3D array of chains behaves differently at large and at small impurity concentrations $N$. At large $N$, impurities divide the chains into metallic rods. The low-temperature conductivity is due to the variable-range hopping of electrons between the rods. It obeys the Efros-Shklovskii (ES) law and increases exponentially as $N$ decreases. When $N$ is small, the metallic-rod picture of the ground state survives only in the form of rare clusters of atypically short rods. They are the source of low-energy charge excitations. In the bulk the charge excitations are gapped and the electron crystal is pinned collectively. A strongly anisotropic screening of the Coulomb potential produces an unconventional linear in energy Coulomb gap and a new law of the variable-range hopping $-\ln\sigma \sim (T_1 / T)^{2/5}$. $T_1$ remains constant over a finite range of impurity concentrations. At smaller $N$ the 2/5-law is replaced by the Mott law, where the conductivity gets suppressed as $N$ goes down. Thus, the overall dependence of $\sigma$ on $N$ is nonmonotonic. In 1D, the granular-rod picture and the ES apply at all $N$. The conductivity decreases exponentially with $N$. Our theory provides a qualitative explanation for the transport in organic charge-density wave compounds.Comment: 20 pages, 7 figures. (v1) The abstract is abridged to 24 lines. For the full abstract, see the manuscript (v2) several changes in presentation per referee's comments. No change in result

CP violation in Bd,s→l+l−B_{d,s} \to l^+l^- in the model III 2HDM

We have calculated the Wilson coefficients $C_{10}, C_{Q_i}$ (i=1,2) in the $\bar{MS}$ renormalization scheme in the model III 2HDM. Using the obtained Wilson coefficients, we have analyzed the CP violation in decays $B^0_q\to l^+l^-$ (q=d,s) in the model. The CP asymmetry, $A_{CP}$, depends on the parameters of models and $A_{CP}$ in $B_d\to l^+l^-$ can be as large as 40% and 35% for $l=\tau$ and $l=\mu$ respectively. It can reach 4% for $B^0_s$ decays. Because in SM CP violation is smaller than or equal to O($10^{-3}$) which is unobservably small, an observation of CP asymmetry in the decays $B^0_q \to l^+l^- (q=d,s)$ would unambiguously signal the existence of new physics.Comment: revtex4, 16 pages, 7 figure

The Mathematical Universe

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.Comment: Replaced to match accepted Found. Phys. version, 31 pages, 5 figs; more details at http://space.mit.edu/home/tegmark/toe.htm

Tri-meson-mixing of π\pi-η\eta-η′\eta' and ρ\rho-ω\omega-ϕ\phi in the light-cone quark model

The radiative transition form factors of the pseudoscalar mesons {$\pi$, $\eta$, $\eta'$} and the vector mesons {$\rho$, $\omega$, $\phi$} are restudied with $\pi$-$\eta$-$\eta'$ and $\rho$-$\omega$-$\phi$ in tri-meson-mixing pattern, which is described by tri-mixing matrices in the light-cone constituent quark model. The experimental transition decay widths are better reproduced with tri-meson-mixing than previous results in a two-mixing-angle scenario of only two-meson $\eta$-$\eta'$ mixing and $\omega$-$\phi$ mixing.Comment: 8 pages, 6 figures, final version to appear in EPJ

Measurement of the polarisation of W bosons produced with large transverse momentum in pp collisions at sqrt(s) = 7 TeV with the ATLAS experiment

This paper describes an analysis of the angular distribution of W->enu and W->munu decays, using data from pp collisions at sqrt(s) = 7 TeV recorded with the ATLAS detector at the LHC in 2010, corresponding to an integrated luminosity of about 35 pb^-1. Using the decay lepton transverse momentum and the missing transverse energy, the W decay angular distribution projected onto the transverse plane is obtained and analysed in terms of helicity fractions f0, fL and fR over two ranges of W transverse momentum (ptw): 35 < ptw < 50 GeV and ptw > 50 GeV. Good agreement is found with theoretical predictions. For ptw > 50 GeV, the values of f0 and fL-fR, averaged over charge and lepton flavour, are measured to be : f0 = 0.127 +/- 0.030 +/- 0.108 and fL-fR = 0.252 +/- 0.017 +/- 0.030, where the first uncertainties are statistical, and the second include all systematic effects.Comment: 19 pages plus author list (34 pages total), 9 figures, 11 tables, revised author list, matches European Journal of Physics C versio

Observation of a new chi_b state in radiative transitions to Upsilon(1S) and Upsilon(2S) at ATLAS

The chi_b(nP) quarkonium states are produced in proton-proton collisions at the Large Hadron Collider (LHC) at sqrt(s) = 7 TeV and recorded by the ATLAS detector. Using a data sample corresponding to an integrated luminosity of 4.4 fb^-1, these states are reconstructed through their radiative decays to Upsilon(1S,2S) with Upsilon->mu+mu-. In addition to the mass peaks corresponding to the decay modes chi_b(1P,2P)->Upsilon(1S)gamma, a new structure centered at a mass of 10.530+/-0.005 (stat.)+/-0.009 (syst.) GeV is also observed, in both the Upsilon(1S)gamma and Upsilon(2S)gamma decay modes. This is interpreted as the chi_b(3P) system.Comment: 5 pages plus author list (18 pages total), 2 figures, 1 table, corrected author list, matches final version in Physical Review Letter