Exact classical solutions of nonlinear sigma models on supermanifolds

We study two-dimensional nonlinear sigma models with target spaces being the complex super-Grassmannian manifolds, that is, coset supermanifolds G(m,p|n,q)≅U(m|n)/[U(p|q)⊗U(m−p|n−q)]$G(m,p|n,q)\cong U(m|n)/[U(p|q)\otimes U(m-p|n-q)]$ for 0?p?m$0?p?m$, 0?q?n$0?q?n$ and 1?p+q$1?p+q$. The projective superspace CPm−1|n${\mathbf{CP}}^{m-1|n}$ is a special case of p=1$p=1$, q=0$q=0$. For the two-dimensional Euclidean base space, a wide class of exact classical solutions (or harmonic maps) are constructed explicitly and elementarily in terms of Gramm–Schmidt orthonormalisation procedure starting from holomorphic bosonic and fermionic supervector input functions. The construction is a generalisation of the non-super-case published more than twenty years ago by one of the present authors.     

New exact solution structures and nonlinear dispersion in the coupled nonlinear wave systems

In this Letter, to further understand the role of nonlinear dispersion in coupled nonlinear wave systems in both real and complex fields, we study the coupled Klein–Gordon equations with nonlinear dispersion in real field (called CKG(m,n,k)$\mathrm{CKG}(m,n,k)$ equation) and (2+1)$(2+1)$-dimensional generalization of coupled nonlinear Schrödinger equation with nonlinear dispersion in complex field (called GCNLS(m,n,k)$\mathrm{GCNLS}(m,n,k)$ equation) via some transformations. As a consequence, some types of solutions are obtained, which contain compactons, solitary pattern solutions, envelope compacton solutions, envelope solitary pattern solutions, solitary wave solutions and rational solutions.     

Differential operator realizations of superalgebras and free field representations of corresponding current algebras

Based on the particular orderings introduced for the positive roots of finite-dimensional basic Lie superalgebras, we construct the explicit differential operator representations of the osp(2r|2n)$\mathit{osp}(2r|2n)$ and osp(2r+1|2n)$\mathit{osp}(2r+1|2n)$ superalgebras and the explicit free field realizations of the corresponding current superalgebras ospk_(2r|2n)$\mathit{osp}{(2r|2n)}_k$ and ospk_(2r+1|2n)$\mathit{osp}{(2r+1|2n)}_k$ at an arbitrary level k. The free field representations of the corresponding energy–momentum tensors and screening currents of the first kind are also presented.     

Zero modes for the boundary giant magnons

We study the fermion zero-mode dynamics for open strings ending on the giant graviton branes. For the open string ending on the Z=0$Z=0$ brane, the quantization of the fermion zero-modes of boundary giant magnons reproduces the 256 states of the boundary degrees with the precise realization of the SU(2|2)×SU(2|2)$\mathit{SU}(2|2)\times \mathit{SU}(2|2)$ symmetry algebra. Also for the open string ending on the Y=0$Y=0$ brane, we reproduce the unique vacuum state from the fermion zero-modes.     

Generalizations of Maxwell (super)algebras by the expansion method

The Lie algebras expansion method is used to show that the four-dimensional spacetime Maxwell (super)algebras and some of their generalizations can be derived in a simple way as particular expansions of o(3,2)$o(3,2)$ and osp(N|4)$\mathit{osp}(N|4)$.     

Comment on reparametrization invariance of quark–lepton complementarity

We study the complementarity between quark and lepton mixing angles (QLC), the sum of an angle in quark mixing and the corresponding angle in lepton mixing is π/4$\pi /4$. Experimentally in the standard PDG parametrization, two such relations exist approximately. These QLC relations are accidental which only manifest themselves in the PDG parametrization. We propose reparametrization invariant expressions for the complementarity relations in terms of the magnitude of the elements in the quark and lepton mixing matrices. In the exact QLC limit, it is found that |_Vus/_Vud|+|_Ve2/_Ve1|+|_Vus/_Vud||_Ve2/_Ve1|=1$|V_{us}/V_{ud}|+|V_{e2}/V_{e1}|+|V_{us}/V_{ud}||V_{e2}/V_{e1}|=1$ and |_Vcb/_Vtb|+|_Vμ3/_Vτ3|+|_Vcb/_Vtb||_Vμ3/_Vτ3|=1$|V_{cb}/V_{tb}|+|V_{\mu 3}/V_{\tau 3}|+|V_{cb}/V_{tb}||V_{\mu 3}/V_{\tau 3}|=1$. Expressions with deviations from exact complementarity are obtained. Implications of these relations are also discussed.     

Higgs-boson couplings beyond the Standard Model

The implications for Higgs decays of potential new physics beyond the Standard Model (BSM) are considered in the context of effective field theory, assuming perturbative decoupling. Using existing data to restrict which dimension-six operators can arise, it is shown that, given the existing experimental constraints, only a small number of operators can affect the decays of the Higgs: those that may be potentially-tree-generated (PTG) and modify the Higgs–fermion couplings, or those that may be loop-generated (LG) that modify the Higgs couplings to γγ, Zγ and GG  . Implications for specific branching ratios are given in terms of the coefficients of various dimension-six operators. In such a scenario, the ratios Γ(H→WW^?)/Γ(H→ZZ^?)$\Gamma (H\to W{W}^{?})/\Gamma (H\to Z{Z}^{?})$ and Γ(H→W?ν)/Γ(H→Z??)$\Gamma (H\to W?\nu )/\Gamma (H\to Z??)$ equal to their Standard Model values to an accuracy of O(1%)$O(1\text{\%})$ or less.     

Exact height distributions for the KPZ equation with narrow wedge initial condition

We consider the KPZ equation in one space dimension with narrow wedge initial condition, h(x,t=0)=−|x|/δ$h(x,t=0)=-|x|/\delta$, δ?1$\delta ?1$, evolving into a parabolic profile with superimposed fluctuations. Based on previous results for the weakly asymmetric simple exclusion process with step initial conditions, we obtain a determinantal formula for the one-point distribution of the solution h(x,t)$h(x,t)$ valid for any x   and t>0$t>0$. The corresponding distribution function converges in the long time limit, t→∞$t\to \infty$, to the Tracy–Widom distribution. The first order correction is a shift of order t−1/3$t^{-1/3}$. We provide numerical computations based on the exact formula.     

Single eta production in heavy quarkonia: Breakdown of multipole expansion

The η   production in the (n,n^′)$(n,n^{\prime })$ bottomonium transitions ?(n)→?(n^′)η$?(n)\to ?(n^{\prime })\eta$, is studied in the method used before for dipion heavy quarkonia transitions. The widths Γη(n,n^′)${\Gamma }_{\eta }(n,n^{\prime })$ are calculated without fitting parameters for n=2,3,4,5$n=2,3,4,5$, n^′=1$n^{\prime }=1$. Resulting Γη(4,1)${\Gamma }_{\eta }(4,1)$ is found to be large in agreement with recent data. Multipole expansion method is shown to be inadequate for large size systems considered.     

Dilaton field and cosmic wave propagation

We study the electromagnetic wave propagation in the joint dilaton field and axion field. Dilaton field induces amplification/attenuation in the propagation while axion field induces polarization rotation. The amplification/attenuation induced by dilaton is independent of the frequency (energy) and the polarization of electromagnetic waves (photons). From observations, the agreement with and the precise calibration of the cosmic microwave background (CMB) to blackbody radiation constrains the fractional change of dilaton |Δψ|/ψ$|\mathrm{\Delta }\psi |/\psi$ to less than about 8×10⁻⁴$8\times {10}^{-4}$ since the time of the last scattering surface of the CMB.     

On hydrogen transport in the first wall material of fusion devices in the presence of a broadband distribution of traps over the trapping energy

The dynamics of hydrogen dissolved in a sample with continuous distribution of traps over trapping energy φ(ε)∝exp(−αε)$\phi (\epsilon )\propto \exp (-\alpha \epsilon )$ (ε=E/T$\epsilon =E/T$ is the ratio of trapping energy E to the sample's temperature T  ) is considered. Assuming that the hydrogen density is smaller than the trap density and the most of hydrogen is trapped, we found that the dynamics of hydrogen transport can be described by either sub-diffusion or non-linear diffusion equations. Analysis of the outgassing of the sample homogeneously loaded with hydrogen gives, in the most important cases, both power-law, _ΓH∝t^−p${\Gamma }_{\mathrm{H}}\propto t^{-p}$ (p≥1/2$p\ge 1/2$) and exponential, ln(_ΓH)∝−t^α$\ln ({\Gamma }_{\mathrm{H}})\propto -t^{\alpha }$, time dependencies of the outgassing flux, _ΓH(t)${\Gamma }_{\mathrm{H}}(t)$.     

On minimum-bias effects at the LHC

In general, minimum-bias triggers planned for experiments at the LHC miss a considerable fraction of the total number of events. We exemplify the rejection rate using the Durham model of soft high-energy interactions to obtain quantitative estimates of the signals arising from the ATLAS scintillation counters positioned in the rapidity intervals 2<|η|<4$2<|\eta |<4$, and also from TOTEM detectors covering the intervals 3.1<|η|<6.5$3.1<|\eta |<6.5$. Typically we find that the expected signal is about half of the total cross section, σtot${\sigma }_{\mathrm{tot}}$. We also calculate the cross section for the so-called zero-bias measurement planned by CMS in the extended rapidity interval −5<η<7$-5<\eta <7$. We emphasize that only models which give satisfactory predictions for the measured minimum-bias or zero-bias cross sections can be used to obtain the value of the total inelastic cross section.     

The first application of the Vogel–Fulcher–Tammann equation to biological problem: A new interpretation of the temperature dependent hydrogen exchange rates of the thrombin-binding DNA

The Vogel–Fulcher–Tammann equation, which is widely applied in condensed matter physics, is for the first time applied to analysis of the hydrogen exchange rates of DNA as a function of temperature. The VFT equation, which for hydrogen exchange should read kex=Aexp[−(E/R)/(T−T₀)]$k_{\mathrm{ex}}=A\exp [-(E/R)/(T-T_0)]$, contains a constant temperature T₀$T_0$. When we analyzed the hydrogen exchange rates for the thrombin binding DNA aptamer d  (GGTTGGTGTGGTTGG) as a function of temperature using the VFT equation, we found that T₀$T_0$ happens to be the melting temperature of the DNA. A quantitative relationship is established between the VFT equation and the Arrhenius equation. Under suitable conditions the VFT equation can be reduced to the Arrhenius equation.     

Asymptotic forms for hard and soft edge general β conditional gap probabilities

An infinite log-gas formalism, due to Dyson, and independently Fogler and Shklovskii, is applied to the computation of conditioned gap probabilities at the hard and soft edges of random matrix β-ensembles. The conditioning is that there are n   eigenvalues in the gap, with n?|t|$n?|t|$, t   denoting the end point of the gap. It is found that the entropy term in the formalism must be replaced by a term involving the potential drop to obtain results consist with known asymptotic expansions in the case n=0$n=0$. With this modification made for general n  , the derived expansions — which are for the logarithm of the gap probabilities — are conjectured to be correct up to and including terms O(log|t|)$\mathrm{O}(\log |t|)$. They are shown to satisfy various consistency conditions, including an asymptotic duality formula relating β   to 4/β$4/\beta$.     

A maximal atmospheric mixing from a maximal CP violating phase

We point out an elegant mechanism to predict a maximal atmospheric angle, which is based on a maximal CP violating phase difference between second and third lepton families in the flavour symmetry basis. In this framework, a discussion of the general formulas for θ₁₂${\theta }_{12}$, |U_e3|$|U_{e3}|$, δ   and their possible correlations in some limiting cases is provided. We also present an explicit realisation in terms of an SO(3)$\mathit{SO}(3)$ flavour symmetry model.     

The constraint on FCNC coupling of the top quark with a gluon from ep-collisions

Using the constraint on the single top production cross-section obtained at the HERA collider, σ(ep→etX)$\sigma (ep\to etX)$, we evaluate an upper limit on coupling constant of the anomalous top quark interaction with a gluon via flavor-changing neutral current: |κ_tgq/Λ|?0.4 TeV⁻¹$|{\kappa }_{tgq}/\Lambda |?0.4{\text{TeV}}^{\mathrm{-1}}$, BR(t→gq)<13%$\mathrm{BR}(t\to gq)<13\mathrm{\%}$.