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.     

Standard Model Higgs boson mass from inflation

We analyse one-loop radiative corrections to the inflationary potential in the theory, where inflation is driven by the Standard Model Higgs field. We show that inflation is possible provided the Higgs mass mH$m_H$ lies in the interval mmin<mH<mmax$m_{\min }<m_H<m_{\max }$, where mmin=[136.7+(mt−171.2)×1.95] GeV$m_{\min }=[136.7+(m_t-171.2)\times 1.95]\text{GeV}$, mmax=[184.5+(mt−171.2)×0.5] GeV$m_{\max }=[184.5+(m_t-171.2)\times 0.5]\text{GeV}$ and mt$m_t$ is the mass of the top quark. In the renormalization scheme associated with the Einstein frame the predictions of the spectral index of scalar fluctuations and of the tensor-to-scalar ratio practically do not depend on the Higgs mass within the admitted region and are equal to ns=0.97$n_s=0.97$ and r=0.0034$r=0.0034$ correspondingly.     

Phantom and non-phantom dark energy: The cosmological relevance of non-locally corrected gravity

In this Letter we have investigated the cosmological dynamics of non-locally corrected gravity involving a function of the inverse d'Alembertian of the Ricci scalar, f(^□−1R)$f({\square }^{\mathrm{-1}}R)$. Casting the dynamical equations into local form, we derive the fixed points of the dynamics and demonstrate the existence and stability of a one parameter family of dark energy solutions for a simple choice, f(^□−1R)∼exp(α^□−1R)$f({\square }^{\mathrm{-1}}R)\sim \exp (\alpha {\square }^{\mathrm{-1}}R)$. The effective EoS parameter is given by, weff=(α−1)/(3α−1)$w_{\mathrm{eff}}=(\alpha -1)/(3\alpha -1)$ and the stability of the solutions is guaranteed provided that 1/3<α<2/3$1/3<\alpha <2/3$. For 1/3<α<1/2$1/3<\alpha <1/2$ and 1/2<α<2/3$1/2<\alpha <2/3$, the underlying system exhibits phantom and non-phantom behavior respectively; the de Sitter solution corresponds to α=1/2$\alpha =1/2$. For a wide range of initial conditions, the system mimics dust like behavior before reaching the stable fixed point. The late time phantom phase is achieved without involving negative kinetic energy fields. A brief discussion on the entropy of de Sitter space in non-local model is included.     

Chaotic inflation,radiative corrections and precision cosmology

We employ chaotic (?²${?}^2$ and ?⁴${?}^4$) inflation to illustrate the important role radiative corrections can play during the inflationary phase. Yukawa interactions of ?  , in particular, lead to corrections of the form −κ?⁴ln(?/μ)$-\kappa {?}^4\ln (?/\mu )$, where κ>0$\kappa >0$ and μ   is a renormalization scale. For instance, ?⁴${?}^4$ chaotic inflation with radiative corrections looks compatible with the most recent WMAP (5 year) analysis, in sharp contrast to the tree level case. We obtain the 95% confidence limits 2.4×¹⁰⁻¹⁴?κ?5.7×¹⁰⁻¹⁴$2.4\times {10}^{\mathrm{-14}}?\kappa ?5.7\times {10}^{\mathrm{-14}}$, 0.931?ns?0.958$0.931?n_s?0.958$ and 0.038?r?0.205$0.038?r?0.205$, where ns$n_s$ and r   respectively denote the scalar spectral index and scalar to tensor ratio. The limits for ?²${?}^2$ inflation are κ?7.7×¹⁰⁻¹⁵$\kappa ?7.7\times {10}^{\mathrm{-15}}$, 0.929?ns?0.966$0.929?n_s?0.966$ and 0.023?r?0.135$0.023?r?0.135$. The next round of precision experiments should provide a more stringent test of realistic chaotic ?²${?}^2$ and ?⁴${?}^4$ inflation.     

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.     

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.     

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.     

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.     

If Gauss–Bonnet interaction plays the role of dark energy

A cosmological model has been constructed with Gauss–Bonnet-scalar interaction, where the Universe starts with exponential expansion but encounters infinite deceleration, q→∞$q\to \infty$ and infinite equation of state parameter, w→∞$w\to \infty$. During evolution it subsequently passes through the stiff fluid era, q=2$q=2$, w=1$w=1$, the radiation dominated era, q=1$q=1$, w=1/3$w=1/3$ and the matter dominated era, q=1/2$q=1/2$, w=0$w=0$. Finally, deceleration halts, q=0$q=0$, w=−1/3$w=-1/3$, and it then encounters a transition to the accelerating phase. Asymptotically the Universe reaches yet another inflationary phase q→−1$q\to -1$, w→−1$w\to -1$. Such evolution is independent of the form of the potential and the sign of the kinetic energy term, i.e., even a non-canonical kinetic energy is unable to phantomize (w<−1)$(w<-1)$ the model.     

Commuting conformal and dual conformal symmetries in the Regge limit

In this paper we continue our study of the dual SL(2,C)$\mathit{SL}(2,C)$ symmetry of the BFKL equation, analogous to the dual conformal symmetry of N=4$N=4$ super-Yang–Mills. We find that the ordinary and dual SL(2,C)$\mathit{SL}(2,C)$ symmetries do not generate a Yangian, in contrast to the ordinary and dual conformal symmetries in the four-dimensional gauge theory. The algebraic structure is still reminiscent of that of N=4$N=4$ SYM, however, and one can extract a generator from the dual SL(2,C)$\mathit{SL}(2,C)$ close to the bi-local form associated with Yangian algebras. We also discuss the issue of whether the dual SL(2,C)$\mathit{SL}(2,C)$ symmetry, which in its original form is broken by IR effects, is broken in a controlled way, similar to the way the dual conformal symmetry of N=4$N=4$ satisfies an anomalous Ward identity. At least for the lowest orders it seems possible to recover the dual SL(2,C)$\mathit{SL}(2,C)$ by deforming its representation, keeping open the possibility that it is an exact symmetry of BFKL. Independently of a possible relation to N=4$N=4$ scattering amplitudes, this opens an avenue for explaining the integrability of BFKL in terms of two finite-dimensional subalgebras.     

Primordial perturbation in Hořava–Lifshitz cosmology

Recently, Ho?ava has proposed a renormalizable theory of gravity with critical exponent z=3$z=3$ in the UV. This proposal might imply that the scale invariant primordial perturbation can be generated in any expansion of early universe with a∼tn$a\sim t^n$ and n>1/3$n>1/3$, which, in this Letter, will be confirmed by solving the motion equation of perturbation mode on super sound horizon scale for any background evolution of early universe. It is found that if enough efolding number of primordial perturbation suitable for observable universe is required, then n?1$n?1$ needs to be satisfied, unless the scale of UV regime is quite low. However, the possible UV completeness of HL gravity helps to relax this bound.     

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.     

A new model of agegraphic dark energy

In this note, we propose a new model of agegraphic dark energy based on the Károlyházy relation, where the time scale is chosen to be the conformal time η   of the Friedmann–Robertson–Walker (FRW) universe. We find that in the radiation-dominated epoch, the equation-of-state parameter of the new agegraphic dark energy wq=−1/3$w_q=-1/3$ whereas Ωq=n²a²${\Omega }_q=n^2{a}^2$; in the matter-dominated epoch, wq=−2/3$w_q=-2/3$ whereas Ωq=n²a²/4${\Omega }_q=n^2{a}^2/4$; eventually, the new agegraphic dark energy dominates; in the late time wq→−1$w_q\to -1$ when a→∞$a\to \infty$, and the new agegraphic dark energy mimics a cosmological constant. In every stage, all things are consistent. The confusion in the original agegraphic dark energy model proposed in [R.G. Cai, Phys. Lett. B 657 (2007) 228, arXiv: 0707.4049 [hep-th]] disappears in this new model. Furthermore, Ωq?1${\Omega }_q?1$ is naturally satisfied in both radiation-dominated and matter-dominated epochs where a?1$a?1$. In addition, we further extend the new agegraphic dark energy model by including the interaction between the new agegraphic dark energy and background matter. In this case, we find that wq$w_q$ can cross the phantom divide.