Constraining cosmological parameters with observational data including weak lensing effects

In this Letter, we study the cosmological implications of the 100 square degree Weak Lensing survey (the CFHTLS-Wide, RCS, VIRMOS-DESCART and GaBoDS surveys). We combine these weak lensing data with the cosmic microwave background (CMB) measurements from the WMAP5, BOOMERanG, CBI, VSA, ACBAR, the SDSS LRG matter power spectrum and the Type Ia Supernoave (SNIa) data with the “Union” compilation (307 sample), using the Markov Chain Monte Carlo method to determine the cosmological parameters, such as the equation-of-state (EoS) of dark energy w  , the density fluctuation amplitude σ₈${\sigma }_8$, the total neutrino mass ∑mν$\sum m_{\nu }$ and the parameters associated with the power spectrum of the primordial fluctuations. Our results show that the ΛCDM model remains a good fit to all of these data. In a flat universe, we obtain a tight limit on the constant EoS of dark energy, w=−0.97±0.041$w=-0.97\pm 0.041$ (1σ  ). For the dynamical dark energy model with time evolving EoS parameterized as wde(a)=w₀+wa(1−a)$w_{\mathrm{de}}(a)=w_0+w_a(1-a)$, we find that the best-fit values are w₀=−1.064$w_0=-1.064$ and wa=0.375$w_a=0.375$, implying the mildly preference of Quintom model whose EoS gets across the cosmological constant boundary during evolution. Regarding the total neutrino mass limit, we obtain the upper limit, ∑mν<0.471 eV$\sum m_{\nu }<0.471\text{eV}$ (95% C.L.) within the framework of the flat ΛCDM model. Due to the obvious degeneracies between the neutrino mass and the EoS of dark energy model, this upper limit will be relaxed by a factor of 2 in the framework of dynamical dark energy models. Assuming that the primordial fluctuations are adiabatic with a power law spectrum, within the ΛCDM model, we find that the upper limit on the ratio of the tensor to scalar is r<0.35$r<0.35$ (95% C.L.) and the inflationary models with the slope ns?1$n_s?1$ are excluded at more than 2σ   confidence level. In this Letter we pay particular attention to the contribution from the weak lensing data and find that the current weak lensing data do improve the constraints on matter density Ωm${\Omega }_m$, σ₈${\sigma }_8$, ∑mν$\sum m_{\nu }$, and the EoS of dark energy.     

Implications of neutrino mass generation from QCD confinement

We consider the possibility that the quark condensate formed by QCD confinement generates Majorana neutrino masses mν$m_{\nu }$ via dimension seven operators. No degrees of freedom beyond the Standard Model are necessary, below the electroweak scale. Obtaining experimentally acceptable neutrino masses requires the new physics scale Λ∼TeV$\Lambda \sim \text{TeV}$, providing a new motivation for weak-scale discoveries at the LHC. We implement this mechanism using a Z₃$Z_3$ symmetry which leads to a massless up quark above the QCD chiral condensate scale. We use non-helicity-suppressed light meson rare decay data to constrain Λ. Experimental constraints place a mild hierarchy on the flavor structure of dimension seven operators and the resulting neutrino mass matrix.     

Evaluation of charged current neutrino–nucleon interaction differential cross section

The charged current neutrino–nucleon interaction differential cross section are evaluated in the kinematical range 30<Eν<300 GeV$30<E_{\nu }<300\text{GeV}$, 0.1<x<0.8$0.1<x<0.8$ and 0<y<1$0<y<1$ using QCD inspired Thermodynamic Bag Model (TBM). We also discuss the x   and Q²$Q^2$ dependence of nucleon structure functions F₂(x,Q²)$F_2(x,Q^2)$ and xF₃(x,Q²)$x{F}_3(x,Q^2)$ estimated with statistical approach. The contribution of strange quark distribution function to the cross section is explored and the results obtained have been compared with relevant data from NuTeV and CHORUS experiments.     

Is space-time symmetry a suitable generalization of parity-time symmetry?

We discuss space-time symmetric Hamiltonian operators of the form H=H₀+igH^′$H=H_0+ig{H}^{\prime }$, where H₀$H_0$ is Hermitian and g$g$ real. H₀$H_0$ is invariant under the unitary operations of a point group G$G$ while H^′$H^{\prime }$ is invariant under transformation by elements of a subgroup G^′$G^{\prime }$ of G$G$. If G$G$ exhibits irreducible representations of dimension greater than unity, then it is possible that H$H$ has complex eigenvalues for sufficiently small nonzero values of g$g$. In the particular case that H$H$ is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<g_c$0<g<g_c$, where g_c$g_c$ is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H$H$ may exhibit real or complex eigenvalues for g>0$g>0$. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.     

Lifshitz-point correlation length exponents from the large-n expansion

The large-n expansion is applied to the calculation of thermal critical exponents describing the critical behavior of spatially anisotropic d-dimensional systems at m  -axial Lifshitz points. We derive the leading non-trivial 1/n$1/n$ correction for the perpendicular correlation-length exponent _νL2${\nu }_{L2}$ and hence several related thermal exponents to order O(1/n)$O(1/n)$. The results are consistent with known large-n expansions for d  -dimensional critical points and isotropic Lifshitz points, as well as with the second-order epsilon expansion about the upper critical dimension d^?=4+m/2$d^{?}=4+m/2$ for generic m∈[0,d]$m\in [0,d]$. Analytical results are given for the special case d=4$d=4$, m=1$m=1$. For uniaxial Lifshitz points in three dimensions, 1/n$1/n$ coefficients are calculated numerically. The estimates of critical exponents at d=3$d=3$, m=1$m=1$ and n=3$n=3$ are discussed.     

Pion radiative weak decays in nonlocal chiral quark models

We analyze the radiative pion decay π⁺→e⁺νeγ${\pi }^{+}\to e^{+}{\nu }_e\gamma$ within nonlocal chiral quark models that include wave function renormalization. In this framework we calculate the vector and axial-vector form factors FV$F_V$ and FA$F_A$ at q²=0$q^2=0$ — where q²$q^2$ is the e⁺νe$e^{+}{\nu }_e$ squared invariant mass — and the slope a   of FV(q²)$F_V(q^2)$ at q²→0$q^2\to 0$. The calculations are carried out considering different nonlocal form factors, in particular those taken from lattice QCD evaluations, showing a reasonable agreement with the corresponding experimental data. The comparison of our results with those obtained in the (local) NJL model and the relation of FV$F_V$ and a   with the form factor in π⁰→γ^?γ${\pi }^0\to {\gamma }^{?}\gamma$ decays are discussed.     

Quantum phase diagram of the half filled Hubbard model with bond-charge interaction

Using quantum field theory and bosonization, we determine the quantum phase diagram of the one-dimensional Hubbard model with bond-charge interaction X in addition to the usual Coulomb repulsion U at half-filling, for small values of the interactions. We show that it is essential to take into account formally irrelevant terms of order X  . They generate relevant terms proportional to X²$X^2$ in the flow of the renormalization group (RG). These terms are calculated using operator product expansions. The model shows three phases separated by a charge transition at U=Uc$U=U_c$ and a spin transition at U=Us>Uc$U=U_s>U_c$. For U<Uc$U<U_c$ singlet superconducting correlations dominate, while for U>Us$U>U_s$, the system is in the spin-density wave phase as in the usual Hubbard model. For intermediate values Uc<U<Us$U_c<U<U_s$, the system is in a spontaneously dimerized bond-ordered wave phase, which is absent in the ordinary Hubbard model with X=0$X=0$. We obtain that the charge transition remains at Uc=0$U_c=0$ for X≠0$X\ne 0$. Solving the RG equations for the spin sector, we provide an analytical expression for Us(X)$U_s(X)$. The results, with only one adjustable parameter, are in excellent agreement with numerical ones for X<t/2$X<t/2$ where t is the hopping.     

On analogues of black brane solutions in the model with multicomponent anisotropic fluid

A family of spherically symmetric solutions with horizon in the model with m  -component anisotropic fluid is presented. The metrics are defined on a manifold that contains a product of n−1$n-1$ Ricci-flat “internal” spaces. The equation of state for any s  -th component is defined by a vector Us$U^s$ belonging to Rn+1${\mathbb{R}}^{n+1}$. The solutions are governed by moduli functions Hs$H_s$ obeying non-linear differential equations with certain boundary conditions imposed. A simulation of black brane solutions in the model with antisymmetric forms is considered. An example of solution imitating M₂–M₅$M_2\text{–}{M}_5$ configuration (in D=11$D=11$ supergravity) corresponding to Lie algebra A₂$A_2$ is presented.     

Warped string compactification via singular Calabi–Yau conformal field theory

We construct spacetime supersymmetric, modular invariant partition functions of strings on the conifold-type singularities which include contributions from the discrete-series representations of SL(2,R)$\mathit{SL}(2,\mathbf{R})$. The discrete spectrum is automatically consistent with the GSO projection in the continuous sector, and contains massless matter fields localized on a four-dimensional submanifold at the tip of a cigar. In particular, they are in the 27⊕1$27\oplus 1$ of E₆$E_6$ for the E₈×E₈$E_8\times E_8$ heterotic string. We speculate about a possible realization of local E₆$E_6$ GUT by using this framework.     

The QCD spin chain S matrix

Beisert et al. have identified an integrable SU(2,2)$\mathit{SU}(2,2)$ quantum spin chain which gives the one-loop anomalous dimensions of certain operators in large Nc$N_c$ QCD. We derive a set of nonlinear integral equations (NLIEs) for this model, and compute the scattering matrix of the various (in particular, magnon) excitations.     

The effect of quenched bond disorder on first-order phase transitions

We investigate the effect of quenched bond disorder on the two-dimensional three-color Ashkin–Teller model, which undergoes a first-order phase transition in the absence of impurities. This is one of the simplest and striking models in which quantitative numerical simulations can be carried out to investigate emergent criticality due to disorder rounding of first-order transition. Utilizing extensive cluster Monte Carlo simulations on large lattice sizes of up to 128×128$128\times 128$ spins, each of which is represented by three colors taking values ±1$\pm 1$, we show that the rounding of the first-order phase transition is an emergent criticality. We further calculate the correlation length critical exponent, ν$\nu$, and the magnetization critical exponent, β$\beta$, from finite size scaling analysis. We find that the critical exponents, ν$\nu$ and β$\beta$, change as the strength of disorder or the four-spin coupling varies, and we show that the critical exponents appear not to be in the Ising universality class. We know of no analytical approaches that can explain our non-perturbative results. However our results should inspire further work on this important problem, either numerical or analytical.     

Kurtosis and compressibility near the chiral phase transition

The properties of net quark number fluctuations in the vicinity of the QCD chiral phase transition are discussed in terms of an effective chiral model in the mean-field approximation. We focus on the ratio of the fourth- to second-order cumulants (kurtosis) and the compressibility of the system and discuss their dependence on the pion mass. It is shown that near the chiral phase transition, both observables are sensitive to the value of mπ$m_{\pi }$. For physical mπ$m_{\pi }$, the kurtosis exhibits a peak whereas the inverse compressibility shows a dip at the pseudocritical temperature. These structures disappear for large mπ$m_{\pi }$. Our results, obtained in an effective model with two flavors, are qualitatively consistent with recent results of 2+1$2+1$ flavor lattice gauge theory. We also discuss the high- and low-temperature properties of these observables and the role of the coupling of the quark degrees of freedom to the Polyakov loop.     

Higher dimensional Yang–Mills black holes in third order Lovelock gravity

By employing the higher (N>5$N>5$)-dimensional version of the Wu–Yang ansatz we obtain magnetically charged new black hole solutions in the Einstein–Yang–Mills–Lovelock (EYML) theory with second (α₂${\alpha }_2$) and third (α₃${\alpha }_3$) order parameters. These parameters, where α₂${\alpha }_2$ is also known as the Gauss–Bonnet parameter, modify the horizons (and the resulting thermodynamical properties) of the black holes. It is shown also that asymptotically (r→∞$r\to \infty$), these parameters contribute to an effective cosmological constant—without cosmological constant—so that the solution behaves de-Sitter (anti de-Sitter) like.     

Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.     

Anomalous anomalous scaling?

Motivated by speculations about infrared deviations from the standard behavior of local quantum field theories, we explore the possibility that such effects might show up as an anomalous running of coupling constants. The most sensitive probes are presently given by the anomalous magnetic moments of the electron and the muon, that suggest that αem${\alpha }_{\mathrm{em}}$ runs 1.00047±0.00018$1.00047\pm 0.00018$ times faster than predicted by the Standard Model. The running of αem${\alpha }_{\mathrm{em}}$ and αs${\alpha }_{\mathrm{s}}$ up to the weak scale is confirmed with a precision at the % level.     

Holomorphic Cartan geometries and Calabi–Yau manifolds

Let M$M$ be a connected complex projective manifold such that _c1(T^(1,0)M)=0$c_1\left(T^{(1,0)}M\right)=0$. If M$M$ admits a holomorphic Cartan geometry, then we show that M$M$ is holomorphically covered by an abelian variety.