Anomalous dipion invariant mass distribution of the ?(4S) decays into ?(1S)π+π? and ?(2S)π+π?

To solve the discrepancy between the experimental data on the partial widths and lineshapes of the dipion emission of ϒ(4S) and the theoretical predictions, we suggest that there is an additional contribution, which had not been taken into account in previous calculations. Noticing that the mass of ϒ(4S) is above the production threshold of B[`(B)]B\bar{B}, the contribution of the sequential process \varUpsilon(4S)? B[`(B)]? \varUpsilon(nS)+S?\varUpsilon(nS)+p⁺p^-\varUpsilon(4S)\to B\bar{B}\to \varUpsilon(nS)+S\to\varUpsilon(nS)+\pi^{+}\pi^{-} (n=1,2) may be sizable, and its interference with that from the direct production would be important. The goal of this work is to investigate if a sum of the two contributions with a relative phase indeed reproduces the data. Our numerical results on the partial widths and the lineshapes d\varGamma(\varUpsilon(4S)?\varUpsilon(2S,1S)p⁺p^-)/d(m_p⁺p^-)d\varGamma(\varUpsilon(4S)\to\varUpsilon(2S,1S)\pi^{+}\pi^{-})/d(m_{\pi ^{+}\pi^{-}}) are satisfactorily consistent with the measurements; thus the role of this mechanism is confirmed. Moreover, with the parameters obtained by fitting the data of the Belle and BaBar collaborations, we predict the distributions dΓ(ϒ(4S)→ϒ(2S,1S)π ⁺ π ⁻)/dcosθ, which have not been measured yet.     

Low Temperature Properties for Correlation Functions in Classical N-Vector Spin Models

We obtain convergent multi-scale expansions for the one-and two-point correlation functions of the low temperature lattice classical N - vector spin model in d S 3 dimensions, N S 2. The Gibbs factor is taken as exp[-b(1/2 ||?f||² +l/8 || |f|² - 1 ||² + v/2||f- h||²)], \exp [-\beta (1/2 ||\partial \phi||^2 +\lambda/8 ||\, |\phi|^2 - 1 ||^2 + v/2||\phi - h||^2)], where f(x), h ? R^N\phi(x), h \in R^N, x ? Z^dx \in Z^d, |h|=1, b < ￥|h|=1, \beta < \infty, l 3 ￥\lambda \geq \infty are large and 0 < v h 1. In the thermodynamic and v ˉ 0v \downarrow 0 limits, with h = e₁, and j L ‘^½ ‘, the expansion gives áf₁(x)? = 1+0(1/b^1/2)\langle \phi_1(x)\rangle = 1+0(1/\beta^{1/2}) (spontaneous magnetization), áf₁(x)f_i(y)? = 0\langle \phi_1(x)\phi_i(y)\rangle=0, áf_i (x)f_i (y)? = c₀ D^-1(x,y)+R(x,y)\langle \phi_i (x)\phi_i (y)\rangle = c_0 \Delta^{-1}(x,y)+R(x,y) (Goldstone Bosons), i = 2, 3, ?, Ni= 2, 3,\,\ldots, N, and áf₁(x)f₁(y)?^T=R￠(x,y)\langle \phi_1(x)\phi_1(y)\rangle^T=R'(x,y), where |R(x,y)||R(x,y)|, |R￠(x,y)| < 0(1)(1+|x-y|)^d-2+r|R'(x,y)|< 0(1)(1+|x-y|)^{d-2+\rho} for some „ > 0, and c₀ is aprecisely determined constant.     

Analysis of the X(1835) and related baryonium states with Bethe-Salpeter equation

In this article, we study the mass spectrum of the baryon-antibaryon bound states p [`(p)] \bar{{p}} , S \Sigma [`(S)] \bar{{\Sigma}} , X \Xi [`(X)] \bar{{\Xi}} , L \Lambda [`(L)] \bar{{\Lambda}} , p [`(N)] \bar{{N}}(1440) , S \Sigma [`(S)] \bar{{\Sigma}}(1660) , X \Xi [`(X)]<sup>￠</sup> \bar{{\Xi}}^{{\prime}}_{} and L \Lambda [`(L)] \bar{{\Lambda}}(1600) with the Bethe-Salpeter equation. The numerical results indicate that the p [`(p)] \bar{{p}} , S \Sigma [`(S)] \bar{{\Sigma}} , X \Xi [`(X)] \bar{{\Xi}} , p [`(N)] \bar{{N}}(1440) , S \Sigma [`(S)] \bar{{\Sigma}}(1660) , X \Xi [`(X)]^￠ \bar{{\Xi}}^{{\prime}}_{} bound states maybe exist, and the new resonances X(1835) and X(2370) can be tentatively identified as the p [`(p)] \bar{{p}} and p [`(N)] \bar{{N}}(1440) (or N(1400)[`(p)] \bar{{p}} bound states, respectively, with some gluon constituents, and the new resonance X(2120) may be a pseudoscalar glueball. On the other hand, the Regge trajectory favors identifying the X(1835) , X(2120) and X(2370) as the excited h^￠ \eta^{{\prime}}_{}(958) mesons with the radial quantum numbers n = 3 , 4 and 5, respectively.     

A close look at the competition of isovector and isoscalar pairing in A=18 and 20 even-even N≈Z nuclei

competition of isovector and isoscalar pairing in A=18 and 20 even-even N≈Z nuclei is analyzed in the framework of the mean-field plus the dynamic quadurpole-quadurpole, pairing and particle-hole interactions, whose Hamiltonian is diagonalized in the basis U(24) ?(U(6) ? S U(3) ? S O(3))■(U(4) ? S US(2)■ S UT(2)) in the L = 0 configuration subspace. Besides the pairing interaction, it is observed that the quadurpole-quadurpole and particlehole interactions also play a significant role in determining the relative positions of low-lying excited 0~+ and 1~+ levels and their energy gaps, which can result in the ground state first-order quantum phase transition from J = 0 to J = 1.The strengths of the isovector and isoscalar pairing interactions in these even-even nuclei are estimated with respect to the energy gap and the total contribution to the binding energy. Most importantly, it is shown that although the mechanism of the particle-hole contribution to the binding energy is different, it is indirectly related to the Wigner term in the binding energy.     

Light meson mass dependence of the positive-parity heavy-strange mesons

We calculate the masses of the resonances D_s0^*(2317)\ensuremath D_{s0}^{\ast}(2317) and D_s1(2460)\ensuremath D_{s1}(2460) as well as their bottom partners as bound states of a kaon and a D^(*)\ensuremath D^{(\ast)} - and B^(*)\ensuremath B^{(\ast)} -meson, respectively, in unitarized chiral perturbation theory at next-to-leading order. After fixing the parameters in the D_s0^*(2317)\ensuremath D_{s0}^{\ast}(2317) channel, the calculated mass for the D_s1(2460)\ensuremath D_{s1}(2460) is found in excellent agreement with experiment. The masses for the analogous states with a bottom quark are predicted to be M_B^*s0=(5696±40)\ensuremath M_{B^{\ast}_{s0}}=(5696\pm 40) MeV and M_Bs1=(5742±40)\ensuremath M_{B_{s1}}=(5742\pm 40) MeV in reasonable agreement with previous analyses. In particular, we predict M_Bs1-M_Bs0^*=46±1\ensuremath M_{B_{s1}}{-}M_{B_{s0}^{\ast}}=46\pm 1 MeV. We also explore the dependence of the states on the pion and kaon masses. We argue that the kaon mass dependence of a kaonic bound state should be almost linear with slope about unity. Such a dependence is specific to the assumed molecular nature of the states. We suggest to extract the kaon mass dependence of these states from lattice QCD calculations.     

Laser-based measurements of line strength, self- and pressure-broadening coefficients of the H35Cl R(3) absorption line in the first overtone region for pressures up to 1 MPa

A high-resolution spectrometer based on a vertical-cavity surface-emitting laser (VCSEL) was developed and used to determine the line strength S(T ₀)=12.53(11)×10⁻²¹ cm⁻¹/(molec cm⁻²) and the self-broadening coefficient g⁰_HCl=0.021787(61)\gamma^{0}_{\mathrm{HCl}}=0.021787(61)  cm⁻¹/atm of the R(3) absorption line in the first rovibrational overtone (2←0) band of H³⁵Cl. Furthermore, the first laser-based high-pressure study on the pressure broadening of HCl by He, N₂ and O₂(g⁰_N2=0.07292(5)\mathrm{O}_{2}(\gamma^{0}_{\mathrm{N}_{2}}=0.07292(5)  cm⁻¹/atm, g⁰_He=0.02113(1)\gamma^{0}_{\mathrm{He}}=0.02113(1)  cm⁻¹/atm, g⁰_O2=0.03978(6)\gamma^{0}_{\mathrm{O}_{2}}=0.03978(6)  cm⁻¹/atm) is presented covering pressures of up to 1 MPa. The results are compared to previously available low-pressure data.     

Bounds on the Minimal Energy of Translation Invariant N-Polaron Systems

For systems of N charged fermions (e.g. electrons) interacting with longitudinal optical quantized lattice vibrations of a polar crystal we derive upper and lower bounds on the minimal energy within the model of H. Fröhlich. The only parameters of this model, after removing the ultraviolet cutoff, are the constants U > 0 and α > 0 measuring the electron-electron and the electron-phonon coupling strengths. They are constrained by the condition ${\sqrt{2}\alpha < U}For systems of N charged fermions (e.g. electrons) interacting with longitudinal optical quantized lattice vibrations of a polar crystal we derive upper and lower bounds on the minimal energy within the model of H. Fr?hlich. The only parameters of this model, after removing the ultraviolet cutoff, are the constants U > 0 and α > 0 measuring the electron-electron and the electron-phonon coupling strengths. They are constrained by the condition ?2a < U{\sqrt{2}\alpha < U}, which follows from the dependence of U and α on electrical properties of the crystal. We show that the large N asymptotic behavior of the minimal energy E _N changes at ?2a = U{\sqrt{2}\alpha=U} and that ?2a ￡ U{\sqrt{2}\alpha\leq U} is necessary for thermodynamic stability: for ${\sqrt{2}\alpha > U}${\sqrt{2}\alpha > U} the phonon-mediated electron-electron attraction overcomes the Coulomb repulsion and E _N behaves like −N ^7/3.     

On Spectral Polynomials of the Heun Equation. II

The well-known Heun equation has the form

A fresh look at hadronic light-by-light scattering in the muon g - 2 with the Dyson-Schwinger approach

Using the Dyson-Schwinger and Bethe-Salpeter equations, we calculate the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon a_m\ensuremath a_\mu , using a phenomenological model for the gluon and quark-gluon interaction. We find a_m=(84 ±13)×10^-11\ensuremath a_\mu=(84 \pm 13)\times 10^{-11} for meson exchange, and a_m = (107 ±2 ±46)×10^-11\ensuremath a_\mu = (107 \pm 2 \pm 46)\times 10^{-11} for the quark loop. The former is commensurate with past calculations; the latter much larger due to dressing effects. This leads to a revised estimate of a_m=116 591 865.0(96.6)×10^-11\ensuremath a_\mu=116 591 865.0(96.6)\times 10^{-11} , reducing the difference between theory and experiment to ≃ 1.9s \sigma .     

Solutions of the Maxwell and Yang-Mills equations associated with hopf fibrings

It is shown that the magnetic pole of lowest strength and the pseudoparticle solution of the Yang-Mills equations correspond to natural connections defined on the principal bundlesU(2)/U(1)=S ₃ S ₂ andSp(2)/Sp(1)=S ₇ S ₄, respectively. This observation leads to a general methods of constructing new, topologically nontrivial solutions of the Maxwell and Yang-Mills equations. Among them is an electromagnetic instanton defined over the two-dimensional complex projective space endowed with the Fubini-Study metric.On leave from the Institute of Theoretical Physics, Warsaw University, Hoza 69, Warsaw, Poland.     

On parity-violating three-nucleon interactions and the predictive power of few-nucleon EFT at very low energies

We address the typical strengths of hadronic parity-violating three-nucleon interactions in “pion-less” Effective Field Theory (EFT) in the nucleon-deuteron (iso-doublet) system. By analysing the superficial degree of divergence of loop diagrams, we conclude that no such interactions are needed at leading order, O(eQ^-1)\ensuremath {O}(\epsilon Q^{-1}) . The only two distinct parity-violating three-nucleon structures with one derivative mix ²S_\frac12\ensuremath ^2S_{\frac{1}{2}} and ²P_\frac12\ensuremath ^2P_{\frac{1}{2}} waves with iso-spin transitions D \Delta I = 0 or 1. Due to their structure, they cannot absorb any divergence ostensibly appearing at next-to-leading order, O(eQ⁰)\ensuremath {O}(\epsilon Q^0) . This observation is based on the approximate realisation of Wigner’s combined SU(4) spin-isospin symmetry in the two-nucleon system, even when effective-range corrections are included. Parity-violating three-nucleon interactions thus only appear beyond next-to-leading order. This guarantees renormalisability of the theory to that order without introducing new, unknown coupling constants and allows the direct extraction of parity-violating two-nucleon interactions from three-nucleon experiments.     

Fredholm Determinants and Pole-free Solutions to the Noncommutative Painlevé II Equation

We extend the formalism of integrable operators à la Its-Izergin-Korepin-Slavnov to matrix-valued convolution operators on a semi–infinite interval and to matrix integral operators with a kernel of the form \fracE₁^T(l) E₂(m)l+m{\frac{E_1^T(\lambda) E_2(\mu)}{\lambda+\mu}}, thus proving that their resolvent operators can be expressed in terms of solutions of some specific Riemann-Hilbert problems. We also describe some applications, mainly to a noncommutative version of Painlevé II (recently introduced by Retakh and Rubtsov) and a related noncommutative equation of Painlevé type. We construct a particular family of solutions of the noncommutative Painlevé II that are pole-free (for real values of the variables) and hence analogous to the Hastings-McLeod solution of (commutative) Painlevé II. Such a solution plays the same role as its commutative counterpart relative to the Tracy–Widom theorem, but for the computation of the Fredholm determinant of a matrix version of the Airy kernel.     

Boundary Concentration for Eigenvalue Problems Related to the Onset of Superconductivity

We examine the asymptotic behavior of the eigenvalue w(h) and corresponding eigenfunction associated with the variational problem m(h) o inf_{y ? H¹(W;C )} \fracò_W \abs(i?+hA)y² dx dy ò_W\absy² dx dy \mu(h)\equiv\inf_{\psi\in H^{1}(\Omega;{\bf C} )} \frac{\int_{\Omega } \abs{(i\nabla+h{\bf A})\psi}^{2}\,dx\,dy} {\int_{\Omega }\abs{\psi}^{2}\,dx\,dy} in the regime h>>1. Here A is any vector field with curl equal to 1. The problem arises within the Ginzburg-Landau model for superconductivity with the function w(h) yielding the relationship between the critical temperature vs. applied magnetic field strength in the transition from normal to superconducting state in a thin mesoscopic sample with cross-section W ì \R²\Omega\subset\R^{2}. We first carry out a rigorous analysis of the associated problem on a half-plane and then rigorously justify some of the formal arguments of [BS], obtaining an expansion for w while also proving that the first eigenfunction decays to zero somewhere along the sample boundary ?W\partial \Omega when z is not a disc. For interior decay, we demonstrate that the rate is exponential.     

Noncommutative Sine-Gordon Model

The sine-Gordon model may be obtained by dimensional and algebraic reduction from (2+2)-dimensional self-dual U(2) Yang-Mills through a (2+1)-dimensional integrable U(2) sigma model. It is argued that the noncommutative (Moyal) deformation of this procedure should relax the algebraic reduction from U(2) U(1) to U(2)U(1) × U(1). The result are novel noncommutative sine-Gordon equations for a pair of scalar fields. The dressing method is outlined for constructing its multi-soliton solutions. Finally, the tree-level amplitudes demonstrate that this model possesses a factorizable and causal S-matrix in spite of its time-space noncommutativity.     

Asymptotics for the Covariance of the Airy<Subscript>2</Subscript> Process

In this paper we compute some of the higher order terms in the asymptotic behavior of the two point function \mathbbP(A₂(0) ￡ s₁,A₂(t) ￡ s₂)\mathbb{P}(\mathcal {A}_{2}(0)\leq s_{1},\mathcal{A}_{2}(t)\leq s_{2}), extending the previous work of Adler and van Moerbeke (; Ann. Probab. 33, 1326–1361, 2005) and Widom (J. Stat. Phys. 115, 1129–1134, 2004). We prove that it is possible to represent any order asymptotic approximation as a polynomial and integrals of the Painlevé II function q and its derivative q′. Further, for up to tenth order we give this asymptotic approximation as a linear combination of the Tracy-Widom GUE density function f ₂ and its derivatives. As a corollary to this, the asymptotic covariance is expressed up to tenth order in terms of the moments of the Tracy-Widom GUE distribution.     

Projectively Equivariant Quantizations over the Superspace $${\mathbb{R}^{p|q}}$$

We investigate the concept of projectively equivariant quantization in the framework of super projective geometry. When the projective superalgebra \mathfrakpgl(p+1|q){\mathfrak{pgl}(p+1|q)} is simple, our result is similar to the classical one in the purely even case: we prove the existence and uniqueness of the quantization except in some critical situations. When the projective superalgebra is not simple (i.e. in the case of \mathfrakpgl(n|n)\not @ \mathfraksl(n|n){\mathfrak{pgl}(n|n)\not\cong \mathfrak{sl}(n|n)}), we show the existence of a one-parameter family of equivariant quantizations. We also provide explicit formulas in terms of a generalized divergence operator acting on supersymmetric tensor fields.     

Universality in the Two Matrix Model with a Monomial Quartic and a General Even Polynomial Potential

In this paper we studied the asymptotic eigenvalue statistics of the 2 matrix model with the probability measure

Stochastic Porous Media Equations and Self-Organized Criticality: Convergence to the Critical State in all Dimensions

If X = X(t, ξ) is the solution to the stochastic porous media equation in O ì R^d, 1 ￡ d ￡ 3,{\mathcal{O}\subset \mathbf{R}^d, 1\le d\le 3,} modelling the self-organized criticality (Barbu et al. in Commun Math Phys 285:901–923, 2009) and X _c is the critical state, then it is proved that ò^￥₀m(O\O^t₀)dt < ￥,\mathbbP-a.s.{\int^{\infty}_0m(\mathcal{O}{\setminus}\mathcal{O}^t_0)dt<{\infty},\mathbb{P}\hbox{-a.s.}} and lim_t?￥ ò_O|X(t)-X_c|dx = l < ￥, \mathbbP-a.s.{\lim_{t\to{\infty}} \int_\mathcal{O}|X(t)-X_c|d\xi=\ell<{\infty},\ \mathbb{P}\hbox{-a.s.}} Here, m is the Lebesgue measure and O^t_c{\mathcal{O}^t_c} is the critical region {x ? O; X(t,x)=X_c(x)}{\{\xi\in\mathcal{O}; X(t,\xi)=X_c(\xi)\}} and X _c (ξ) ≤ X(0, ξ) a.e. x ? O{\xi\in\mathcal{O}}. If the stochastic Gaussian perturbation has only finitely many modes (but is still function-valued), lim_{t ? ￥} ò_K|X(t)-X_c|dx = 0{\lim_{t \to {\infty}} \int_K|X(t)-X_c|d\xi=0} exponentially fast for all compact K ì O{K\subset\mathcal{O}} with probability one, if the noise is sufficiently strong. We also recover that in the deterministic case ℓ = 0.     

Production of the P-wave excited Bc-states through the Z0 boson decays

In Deng et al. (Eur. Phys. J. C 70:113, 2010), we have dealt with the production of the two color-singlet S-wave (c[`(b)])(c\bar{b})-quarkonium states B<sub>c</sub>(|(c[`(b)])₁[¹S₀]?)B_{c}(|(c\bar {b})_{\mathbf{1}}[^{1}S_{0}]\rangle) and B^*_c(|(c[`(b)])<sub>1</sub>[<sup>3</sup>S<sub>1</sub>]?)B^{*}_{c}(|(c\bar{b})_{\mathbf{1}}[^{3}S_{1}]\rangle) through the Z <sup>0</sup> boson decays. As an important sequential work, we make a further discussion on the production of the more complicated P-wave excited (c[`(b)])(c\bar{b})-quarkonium states, i.e. |(c[`(b)])<sub>1</sub>[<sup>1</sup>P<sub>1</sub>]?|(c\bar{b})_{\mathbf{1}}[^{1}P_{1}]\rangle and |(c[`(b)])₁[³P_J]?|(c\bar{b})_{\mathbf{1}}[^{3}P_{J}]\rangle (with J=(1,2,3)). More over, we also calculate the channel with the two color-octet quarkonium states |(c[`(b)])<sub>8</sub>[<sup>1</sup>S<sub>0</sub>]g?|(c\bar{b})_{\mathbf{8}}[^{1}S_{0}]g\rangle and |(c[`(b)])₈[³S₁]g?|(c\bar{b})_{\mathbf{8}}[^{3}S_{1}]g\rangle, whose contributions to the decay width maybe at the same order of magnitude as that of the color-singlet P-wave states according to the naive nonrelativistic quantum chromodynamics scaling rules. The P-wave states shall provide sizable contributions to the B _c production, whose decay width is about 20% of the total decay width \varGamma _{Z⁰? Bc}\varGamma _{Z^{0}\to B_{c}}. After summing up all the mentioned (c[`(b)])(c\bar {b})-quarkonium states’ contributions, we obtain \varGamma _{Z⁰? Bc}=235.9^+352.8_-122.0\varGamma _{Z^{0}\to B_{c}}=235.9^{+352.8}_{-122.0} KeV, where the errors are caused by the main sources of uncertainty.     

Upper Bounds for Coarsening for the Deep Quench Obstacle Problem

The deep quench obstacle problem models phase separation at low temperatures. During phase separation, domains of high and low concentration are formed, then coarsen or grow in average size. Of interest is the time dependence of the dominant length scales of the system. Relying on recent results by Novick-Cohen and Shishkov (Discrete Contin. Dyn. Syst. B 25:251–272, 2009), we demonstrate upper bounds for coarsening for the deep quench obstacle problem, with either constant or degenerate mobility. For the case of constant mobility, we obtain upper bounds of the form t ^1/3 at early times as well as at times t for which E(t) ￡ \frac(1-[`(u)]<sup>2</sup>)4E(t)\le\frac{(1-\overline{u}^{2})}{4}, where E(t) denotes the free energy. For the case of degenerate mobility, we get upper bounds of the form t <sup>1/3</sup> or t <sup>1/4</sup> at early times, depending on the value of E(0), as well as bounds of the form t <sup>1/4</sup> whenever E(t) ￡ \frac(1-[`(u)]²)4E(t)\le\frac{(1-\overline{u}^{2})}{4}.