Partition function zeros of the antiferromagnetic Ising model on triangular lattice in the complex temperature plane for nonzero magnetic field

The grand partition functions Z(T,B)$Z(T,B)$ of the Ising model on L×L$L\times L$ triangular lattices with fully periodic boundary conditions, as a function of temperature T and magnetic field B  , are evaluated exactly for L<12$L<12$ (using microcanonical transfer matrix) and approximately for L?12$L?12$ (using Wang–Landau Monte Carlo algorithm). From Z(T,B)$Z(T,B)$, the distributions of the partition function zeros of the triangular-lattice Ising model in the complex temperature plane for real B≠0$B\ne 0$ are obtained and discussed for the first time. The critical points aN(x)$a_N(x)$ and the thermal scaling exponents yt(x)$y_t(x)$ of the triangular-lattice Ising antiferromagnet, for various values of x=e−2βB$x=e^{-2\beta B}$, are estimated using the partition function zeros.     

Probing photon helicity in radiative B decays via charmonium resonance interference

We investigate a new method to probe the helicity of the photon emitted in the b→sγ$b\to s\gamma$ transition. The method relies on the observation of interference effects between two resonance contributions, B→K^∗(Kγ)γ$B\to K^{\ast }(K\gamma )\gamma$ and B→ηc(γγ)K$B\to {\eta }_c(\gamma \gamma )K$ or B→χ_c0(γγ)K$B\to {\chi }_{c0}(\gamma \gamma )K$ to the same final state Kγγ  . Decays of the type B→Kres(Kγ)γ$B\to K_{\mathrm{res}}(K\gamma )\gamma$ dominate the B→Kγγ$B\to K\gamma \gamma$ yield throughout most of the phase space, and may be accessible at current B meson facilities already.     

Can density functional theory make use of experimentally determined ground-state electron densities via the Dirac density matrix for molecules of biological interest?

More than four decades ago, March and Murray gave a perturbation theory of the single-particle(s) Dirac density matrix γs(r,r^′)${\gamma }_s(r,r^{\prime })$ to all orders in a given one-body potential energy V(r)$V(r)$. However, for density functional theory in orbital-free form, one requires the functional γs[ρ]${\gamma }_s[\rho ]$ where ρ(r)$\rho (r)$ is the ground-state electron density. Therefore, in the present study, a first-order non-linear differential equation is proposed for γs${\gamma }_s$ in terms of ρ(r)$\rho (r)$ and ∇ρ(r)$\mathrm{\nabla }\rho (r)$, plus the single-particle kinetic energy. Since this latter quantity is itself known to be a functional of ρ  , the existence of such an equation for γs${\gamma }_s$ would be a significant step along the road to determining the desired functional γs[ρ]${\gamma }_s[\rho ]$. As yet, we have succeeded in giving a rigorous proof of the proposed differential equation for γs(r,r^′)${\gamma }_s(r,r^{\prime })$ only for one- and two-level molecules. If it is subsequently proved for an arbitrary number of levels, which we believe should be possible, it would then allow γs${\gamma }_s$ to be calculated for molecules of biological interest, from experimentally measured ground-state densities ρ(r)$\rho (r)$, as the approach is entirely orbital-free.     

Vacuum phase transition at nonzero baryon density

It is argued that the dominant contribution to the interaction of quark–gluon plasma at moderate T?Tc$T?T_c$ is given by the nonperturbative vacuum field correlators. Basing on that nonperturbative equation of state of quark–gluon plasma is computed and in the lowest approximation expressed in terms of absolute values of Polyakov lines for quarks and gluons Lfund(T),Ladj(T)=(Lfund)^9/4$L_{\mathrm{fund}}(T),L_{\mathrm{adj}}(T)={(L_{\mathrm{fund}})}^{9/4}$ known from lattice and analytic calculations. Phase transition at any μ   is described as a transition due to vanishing of one of correlators, DE(x)$D^E(x)$, which implies the change of gluonic condensate ΔG₂$\mathrm{\Delta }{G}_2$. Resulting transition temperature Tc(μ)$T_c(\mu )$ is calculated in terms of ΔG₂$\mathrm{\Delta }{G}_2$ and Lfund(Tc)$L_{\mathrm{fund}}(T_c)$. The phase curve Tc(μ)$T_c(\mu )$ is in a good agreement with lattice data. In particular Tc(0)=0.27$T_c(0)=0.27$; 0.19; 0.17 GeV$0.17\text{ GeV}$ for nf=0,2,3$n_f=0,2,3$ and fixed ΔG₂=0.0035 GeV⁴$\mathrm{\Delta }{G}_2=0.0035{\text{ GeV}}^4$.     

Single spin asymmetry in πp Drell–Yan process

We study the single spin asymmetries for the πp^↑→μ⁺μ⁻X$\pi p^{\uparrow }\to {\mu }^{+}{\mu }^{-}X$ process. We consider the asymmetries contributed by the coupling of the Boer–Mulders function with the transversity distribution and the pretzelosity distribution, characterized by the sin(?+?S)$\sin (?+{?}_S)$ and sin(3?−?S)$\sin (3?-{?}_S)$ azimuthal angular dependence, respectively. We estimate the magnitude of these asymmetries at COMPASS by using proper weighting functions. We find that the sin(?+?S)$\sin (?+{?}_S)$ asymmetry is of the size of a few percent and can be measured through the experiment. The sin(3?−?S)$\sin (3?-{?}_S)$ asymmetry is smaller than the sin(?+?S)$\sin (?+{?}_S)$ asymmetry. After a cut on qT$q_T$, we succeed in enhancing the asymmetry.     

Quantum Regge Calculus of Einstein–Cartan theory

We study the Quantum Regge Calculus of Einstein–Cartan theory to describe quantum dynamics of Euclidean space–time discretized as a 4-simplices complex. Tetrad field eμ(x)$e_{\mu }(x)$ and spin-connection field ωμ(x)${\omega }_{\mu }(x)$ are assigned to each 1-simplex. Applying the torsion-free Cartan structure equation to each 2-simplex, we discuss parallel transports and construct a diffeomorphism and local   gauge-invariant Einstein–Cartan action. Invariant holonomies of tetrad and spin-connection fields along large loops are also given. Quantization is defined by a bounded partition function with the measure of SO(4)$\mathit{SO}(4)$-group valued ωμ(x)${\omega }_{\mu }(x)$ fields and Dirac-matrix valued eμ(x)$e_{\mu }(x)$ fields over 4-simplices complex.     

Suppression of flavor symmetry breaking in B decay sum rules

While flavor symmetries are useful for studying hadronic B   decays, symmetry relations for amplitudes and decay rates are usually violated by first order symmetry breaking corrections. We point out two cases in which first order symmetry breaking is suppressed by a small ratio of amplitudes: (1) An isospin sum rule for four B→Kπ$B\to K\pi$ decays, where isospin breaking is shown to be negligible. (2) An SU(3)$\mathrm{SU}(3)$ sum rule for pairs of B→Kπ$B\to K\pi$ and B→Kη₈$B\to K{\eta }_8$, generalized to pairs of B→Kπ$B\to K\pi$, B→Kη$B\to K\eta$ and B→Kη^′$B\to K{\eta }^{\prime }$.     

Understanding the radiative decays of vector charmonia to light pseudoscalar mesons

We show that the newly measured branching ratios of vector charmonia (J/ψ$J/\psi$, ψ^′${\psi }^{\prime }$ and ψ(3770)$\psi (3770)$) into γP, where P   stands for light pseudoscalar mesons π⁰${\pi }^0$, η  , and η^′${\eta }^{\prime }$, can be well understood in the framework of vector meson dominance (VMD) in association with the ηc–η(η^′)${\eta }_c\text{–}\eta ({\eta }^{\prime })$ mixings due to the axial gluonic anomaly. These two mechanisms behave differently in J/ψ$J/\psi$ and ψ^′→γP${\psi }^{\prime }\to \gamma P$. A coherent understanding of the branching ratio patterns observed in J/ψ(ψ^′)→γP$J/\psi ({\psi }^{\prime })\to \gamma P$ can be achieved by self-consistently including those transition mechanisms at hadronic level. The branching ratios for ψ(3770)→γP$\psi (3770)\to \gamma P$ are predicted to be rather small.     

Renormalization-group flow for the field strength in scalar self-interacting theories

We consider the renormalization-group coupled equations for the effective potential V(?)$V(?)$ and the field strength Z(?)$Z(?)$ in the spontaneously broken phase as a function of the infrared cutoff momentum k  . In the k→0$k\to 0$ limit, the numerical solution of the coupled equations, while consistent with the expected convexity property of V(?)$V(?)$, indicates a sharp peaking of Z(?)$Z(?)$ close to the end points of the flatness region that define the physical realization of the broken phase. This might represent further evidence in favor of the non-trivial vacuum field renormalization effect already discovered with variational methods.     

First-order density matrices in one dimension for independent fermions and impenetrable bosons in harmonic traps

To complement existing knowledge of the density matrix γF(x,y)${\gamma }_{\mathrm{F}}(x,y)$ of independent fermions for N   particles in one dimension under harmonic confinement, the corresponding matrix γIB(x,y)${\gamma }_{\mathrm{IB}}(x,y)$ for impenetrable bosons is given for N=2$N=2$ and 3 (with the N=4$N=4$ form available also). For fermions the momentum density is then obtained and illustrated numerically for N=10$N=10$. The boson momentum density is studied analytically at high momentum p  , the coefficients of the p⁻⁴$p^{\mathrm{-4}}$ and p⁻⁶$p^{\mathrm{-6}}$ terms being tabulated for N=2–5$N=2\text{–}5$ inclusive. Their dependence on powers of N   is exhibited numerically. Finally, the functional relationship between γIB(x,y)${\gamma }_{\mathrm{IB}}(x,y)$ and γF(x,y)${\gamma }_{\mathrm{F}}(x,y)$ is formally set out and illustrated.     

Probing dark energy using its density instead of its equation of state

The variation of dark energy density with redshift, ρX(z)${\rho }_X(z)$, provides a critical clue to the nature of dark energy. Since ρX(z)${\rho }_X(z)$ depends on the dark energy equation of state wX(z)$w_X(z)$ through an integral, ρX(z)${\rho }_X(z)$ can be constrained more tightly than wX(z)$w_X(z)$ given the same observational data. We demonstrate this explicitly using current type Ia supernova (SN Ia) data [the Tonry/Barris sample], together with the Cosmic Microwave Background (CMB) shift parameter from CMB data (WMAP, CBI, and ACBAR), and the large scale structure (LSS) growth factor from 2dF galaxy survey data. We assume a flat universe, and use Markov Chain Monte Carlo (MCMC) technique in our analysis. We find that, while wX(z)$w_X(z)$ extracted from current data is consistent with a cosmological constant at 68% C.L., ρX(z)${\rho }_X(z)$ (which has far smaller uncertainties) is not. Our results clearly show the advantage of using ρX(z)${\rho }_X(z)$, instead of wX(z)$w_X(z)$, to probe the variation of dark energy.     

Rational r-matrices,higher rank Lie algebras and integrable proton–neutron BCS models

We study integrable cases of pairing BCS hamiltonians containing several types of fermions. We prove that there exist three classes of such integrable models associated with classical rational r  -matrices and Lie algebras gl(2m)$\mathit{gl}(2m)$, sp(2m)$\mathit{sp}(2m)$ and so(2m)$\mathit{so}(2m)$ correspondingly. We diagonalize the constructed hamiltonians by means of the algebraic Bethe ansatz. In the partial case of two types of fermions (m=2$m=2$) the obtained models may be interpreted as N=Z$N=Z$ proton–neutron integrable models. In particular, in the case of sp(4)$\mathit{sp}(4)$ we recover the famous integrable proton–neutron model of Richardson.     

Hadro-charmonium

We argue that relatively compact charmonium states, J/ψ$J/\psi$, ψ(2S)$\psi (2S)$, χc${\chi }_c$, can very likely be bound inside light hadronic matter, in particular inside higher resonances made from light quarks and/or gluons. The charmonium state in such binding essentially retains its properties, so that the bound system decays into light mesons and the particular charmonium resonance. Thus such bound states of a new type, which we call hadro-charmonium, may explain the properties of some of the recently observed resonant peaks, in particular of Y(4.26)$Y(4.26)$, Y(4.32–4.36)$Y(4.32\text{–}4.36)$, Y(4.66)$Y(4.66)$, and Z(4.43)$Z(4.43)$. We discuss further possible implications of the suggested picture for the observed states and existence of other states of hadro-charmonium and hadro-bottomonium.     

Constraints on kinematic models from the latest observational data

Kinematical models are constrained by the latest observational data from geometry-distance measurements, which include 557 type Ia supernovae (SNIa) Union2 data and 15 observational Hubble data. Considering two parameterized deceleration parameter, the values of current deceleration parameter q₀$q_0$, jerk parameter j₀$j_0$ and transition redshift zT$z_T$, are obtained. Furthermore, we show the departures for two parameterized kinematical models from ΛCDM model according to the evolutions of jerk parameter j(z)$j(z)$. Also, it is shown that the constraint on jerk parameter j(z)$j(z)$ is weak by the current geometrical observed data.     

The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution

Lattice artifacts in the 2d O(n) non-linear σ  -model are expected to be of the form O(a²)$\mathrm{O}(a^2)$, and hence it was (when first observed) disturbing that some quantities in the O(3)$\mathrm{O}(3)$ model with various actions show parametrically stronger cutoff dependence, apparently O(a)$\mathrm{O}(a)$, up to very large correlation lengths. In a previous letter Balog et al. (2009) [1] we described the solution to this puzzle. Based on the conventional framework of Symanzik's effective action, we showed that there are logarithmic corrections to the O(a²)$\mathrm{O}(a^2)$ artifacts which are especially large (ln³a${\ln }^{3}a$) for n=3$n=3$ and that such artifacts are consistent with the data. In this paper we supply the technical details of this computation. Results of Monte Carlo simulations using various lattice actions for O(3)$\mathrm{O}(3)$ and O(4)$\mathrm{O}(4)$ are also presented.     

Dynamical SUSY breaking in heterotic M-theory

It is shown that four-dimensional N=1$N=1$ supersymmetric QCD with massive flavors in the fundamental representation of the gauge group can be realized in the hidden sector of E₈×E₈$E_8\times E_8$ heterotic string vacua. The number of flavors can be chosen to lie in the range of validity of the free-magnetic dual, using which one can demonstrate the existence of long-lived meta-stable non-supersymmetric vacua. This is shown explicitly for the gauge group Spin(10)$\mathit{Spin}(10)$, but the methods are applicable to Spin(Nc)$\mathit{Spin}(N_c)$, SU(Nc)$\mathit{SU}(N_c)$ and Sp(Nc)$\mathit{Sp}(N_c)$ for a wide range of color index Nc$N_c$. Hidden sectors of this type can potentially be used as a mechanism to break supersymmetry within the context of heterotic M-theory.