The Isospin Mixing in the X(3872) Decay Spectrum

The large isospin symmetry breaking found in the X(3872) decay is investigated by looking into the transfer strength from the \({{c}\bar{c}}\) quarkonium to the two-meson states: \({c\bar{c} \rightarrow D^{0}\overline{D}^{*0}, D^{+} D^{*-} , J /\psi\omega, {\rm and} \, J /\psi\rho}\) . The widths of the \({\rho}\) and \({\omega}\) mesons are taken into account in the calculation. It is found that very narrow \({J /\psi\omega}\) and \({J /\psi\rho}\) peaks appear at the \({D^{0}\overline{D}^{*0}}\) threshold. These narrow peaks appear provided that the strength of the \({D^{0}\overline{D}^{*0}}\) component is large around the threshold. The large width of the \({\rho}\) meson enhances the isospin-one component in the transfer strength considerably, which reduces the ratio \({{\rm Br}(X \rightarrow J /\psi\omega)/{\rm Br}(X \rightarrow J /\psi\rho)}\) down to 2.5.     

Blow Up Dynamics for Equivariant Critical Schrödinger Maps

For the Schrödinger map equation \({u_t = u \times \triangle u \, {\rm in} \, \mathbb{R}^{2+1}}\) , with values in S ², we prove for any \({\nu > 1}\) the existence of equivariant finite time blow up solutions of the form \({u(x, t) = \phi(\lambda(t) x) + \zeta(x, t)}\) , where \({\phi}\) is a lowest energy steady state, \({\lambda(t) = t^{-1/2-\nu}}\) and \({\zeta(t)}\) is arbitrary small in \({\dot H^1 \cap \dot H^2}\) .     

The Charmonium-Molecule Hybrid Structure of the X(3872)

In order to understand the structure of the X(3872) the effects of the ${{\rm c\overline{c}}}$ charmonium core state coupling to the ${D^0\overline{D}^{*0}}$ and D ⁺ D ^*? molecule states are studied. The obtained structure of the X(3872) is about 9 % of ${{\rm c}\overline{{\rm c}}}$ charmonium, 75 % of the isoscalar ${D\overline{D}}$ molecule and 16 % of the isovector ${D\overline{D}}$ molecule which explains observed properties of the X(3872) well.     

Renormalization of Critical Gaussian Multiplicative Chaos and KPZ Relation

Gaussian Multiplicative Chaos is a way to produce a measure on \({\mathbb{R}^d}\) (or subdomain of \({\mathbb{R}^d}\) ) of the form \({e^{\gamma X(x)} dx}\) , where X is a log-correlated Gaussian field and \({\gamma \in [0, \sqrt{2d})}\) is a fixed constant. A renormalization procedure is needed to make this precise, since X oscillates between ?∞ and ∞ and is not a function in the usual sense. This procedure yields the zero measure when \({\gamma = \sqrt{2d}}\) . Two methods have been proposed to produce a non-trivial measure when \({\gamma = \sqrt{2d}}\) . The first involves taking a derivative at \({\gamma = \sqrt{2d}}\) (and was studied in an earlier paper by the current authors), while the second involves a modified renormalization scheme. We show here that the two constructions are equivalent and use this fact to deduce several quantitative properties of the random measure. In particular, we complete the study of the moments of the derivative multiplicative chaos, which allows us to establish the KPZ formula at criticality. The case of two-dimensional (massless or massive) Gaussian free fields is also covered.     

Study of 3He Nuclei by Polarization Observables in Quasi-Elastic Electron Scattering

In a recent set of measurements at Jefferson Laboratory, we have studied the missing-momentum dependence of beam-target asymmetries in exclusive \({\overrightarrow{^3{{\rm He}}}({{\rm e}},{\rm e}'{\rm p}){\rm pn}, \overrightarrow{^3{{\rm He}}}({{\rm e}},{\rm e}'{\rm p}){\rm d} }\) , and \({\overrightarrow{^3{{\rm He}}}({{\rm e}},{\rm e}'{\rm d}){\rm p}}\) channels at a previously unattainable level of precision and unreached range in missing momenta. We have also measured single-spin asymmetries in the processes \({\overrightarrow{^3{{\rm He}}}({\vec{{\rm e}}},{\rm e}')}\) and \({\overrightarrow{^3{{\rm He}}}({{\rm \vec{e}}},{\rm e}'{\rm n})}\) , where the nuclei were polarized vertically. Preliminary results are presented.     

{^6_{\Lambda} \rm{H}} Modeled as {^4_{\Lambda} \rm{H}} + n + n

A three-body calculation for the \({^4_{\Lambda} \rm{He}}\) and \({^6_{\Lambda}{\rm H}}\) hypernuclei has been undertaken. The respective cores are \({^4_{\Lambda}{\rm H}}\) . The interactions in the \({^6_{\Lambda}{\rm He}}\) system, modeled as \({^4_{\Lambda} {\rm H+p+n}}\) , are reasonably well known. For example, the p n interaction is well determined by the p n scattering data, the \({^4_{\Lambda}{\rm H}}\) –p interaction can be fitted to the \({^5_{\Lambda}{\rm He}}\) binding energy. The \({^4_{\Lambda}{\rm He}}\) –n interaction can be fitted to α–n scattering data. For the ⁴He–n system the s-wave can be modeled alternatively as a repulsive potential or as an attractive potential with a forbidden bound state. We explore these alternatives in ⁶He, because the interaction comes into play in modeling \({^6_{\Lambda}{\rm He}}\) as well as in our \({^4_{\Lambda}{\rm H}}\) + n + n model of \({^6_{\Lambda}{\rm H}}\) , where the valence neutrons are Pauli blocked from the s-shell of the core nucleus.     

Antiproton low-energy collisions with Ps-atoms and true muonium atoms (μ + μ −)

Three-charge-particle collisions with participation of ultra-slow antiprotons ( \(\overline {\rm {p}}\) ) is the subject of this work. Specifically we compute the total cross sections and corresponding thermal rates of the following three-body reactions: \(\overline {\rm p}+(e^+e^-) \rightarrow \overline {\rm {H}} + e^-\) and \(\overline {\rm p}+(\mu ^+\mu ^-) \rightarrow \overline {\rm {H}}_{\mu } + \mu ^-\) , where \(e^-(\mu ^-)\) is an electron (muon) and \(e^+(\mu ^+)\) is a positron (antimuon) respectively, \(\overline {\rm {H}}=(\overline {\rm p}e^+)\) is an antihydrogen atom and \(\overline {\rm {H}}_{\mu }=(\overline {\rm p}\mu ^+)\) is a muonic antihydrogen atom, i.e. a bound state of \(\overline {\rm {p}}\) and μ ⁺. A set of two-coupled few-body Faddeev-Hahn-type (FH-type) equations is numerically solved in the framework of a modified close-coupling expansion approach.     

Charmonium and Meson–Molecule Hybrid Tetraquarks

In the X (3872) decay, both of the ${{J/{\psi\pi\pi}}}$ and ${{J/{\psi\pi\pi\pi}}}$ branching fractions are observed experimentally, and their sizes are comparable to each other. In order to clarify the mechanism to cause such a large isospin violation, we investigate X(3872) employing a model of coupled-channel two-meson scattering with a ${{\rm c}\bar{c}}$ core. The two-meson states consist of ${{D^0\overline{D}^{*0}}}$ , D ⁺ D ^*?, ${{J/{\psi\rho}}}$ , and ${{J/{\psi\omega}}}$ . The effects of the ρ and ω meson width are also taken into account. We calculate the transfer strength from the ${{{\rm c}\bar{c}}}$ core to the final two-meson states. It is found that very narrow ${{J/{\psi\rho}}}$ and ${{J/{\psi\omega}}}$ peaks appear very close to the ${{D^0\overline{D}^{*0}}}$ threshold for a wide range of variation in the parameter sets. The size of the ${{J/{\psi\rho}}}$ peak is almost the same as that of ${{J/{\psi\omega}}}$ , which is consistent with the experiments. The large width of the ρ meson makes the originally small isospin violation by about five times larger.     

Photon Asymmetries in {nd\rightarrow} 3 Hγ Using EFT({/\!\!\!\pi}) Approach

The parity-violating Lagrangian of the weak nucleon-nucleon (NN) interaction in the pionless effective field theory (EFT( \({/\!\!\!\pi}\) )) approach contains five independent unknown low-energy coupling constants (LECs). The photon asymmetry with respect to neutron polarization in \({np\rightarrow d\gamma A_\gamma^{np}}\) , the circular polarization of outgoing photon in \({np\rightarrow d\gamma P_\gamma^{np}}\) , the neutron spin rotation in hydrogen \({\frac{1}{\rho}\frac{d\phi^{np}}{dl}}\) , the neutron spin rotation in deuterium \({\frac{1}{\rho}\frac{d\phi^{nd}}{dl}}\) and the circular polarization of γ-emission in \({nd\rightarrow}\) ³ Hγ \({P^{nd}_\gamma}\) are the parity-violating observables which have been recently calculated in terms of parity-violating LECs in the EFT( \({/\!\!\!\pi}\) ) framework. We obtain the LECs by matching the parity-violating observables to the Desplanques, Donoghue, and Holstein (DDH) best value estimates. Then, we evaluate photon asymmetry with respect to the neutron polarization \({a^{nd}_\gamma}\) and the photon asymmetry in relation to deuteron polarization \({A^{nd}_\gamma}\) in \({nd\rightarrow}\) ³ Hγ process. We finally compare our EFT( \({/\!\!\!\pi}\) ) photon asymmetries results with the experimental values and the previous calculations based on the DDH model.     

The NLS Equation in Dimension One with Spatially Concentrated Nonlinearities: the Pointlike Limit

In the present paper, we study the following scaled nonlinear Schrödinger equation (NLS) in one space dimension: $$ i\frac{\rm d}{{\rm d}t}\psi^{\varepsilon}(t)=-\Delta\psi^{\varepsilon}(t) +\frac{1}{\varepsilon}V\left(\frac{x}{\varepsilon} \right)|\psi^{\varepsilon}(t)|^{2\mu}\psi^{\varepsilon}(t)\quad \varepsilon > 0\,\quad V\in L^1(\mathbb{R},(1+|x|){\rm d}x) \cap L^\infty(\mathbb{R}).$$ This equation represents a nonlinear Schrödinger equation with a spatially concentrated nonlinearity. We show that in the limit \({\varepsilon\to 0}\) the weak (integral) dynamics converges in \({H^1(\mathbb{R})}\) to the weak dynamics of the NLS with point-concentrated nonlinearity: $$ i\frac{{\rm d}}{{\rm d}t} \psi(t) =H_{\alpha} \psi(t) .$$ where H _α is the Laplacian with the nonlinear boundary condition at the origin \({\psi'(t,0+)-\psi'(t,0-)=\alpha|\psi(t,0)|^{2\mu}\psi(t,0)}\) and \({\alpha=\int_{\mathbb{R}}V{\rm d}x}\) . The convergence occurs for every \({\mu\in \mathbb{R}^+}\) if V ≥  0 and for every  \({\mu\in (0,1)}\) otherwise. The same result holds true for a nonlinearity with an arbitrary number N of concentration points.     

Functional Properties of Hörmander’s Space of Distributions Having a Specified Wavefront Set

The space \({\mathcal{D}_\Gamma^\prime}\) of distributions having their wavefront sets in a closed cone \({\Gamma}\) has become important in physics because of its role in the formulation of quantum field theory in curved spacetime. In this paper, the topological and bornological properties of \({\mathcal{D}_\Gamma^\prime}\) and its dual \({\mathcal{E}_\Lambda^\prime}\) are investigated. It is found that \({\mathcal{D}_\Gamma^\prime}\) is a nuclear, semi-reflexive and semi-Montel complete normal space of distributions. Its strong dual \({\mathcal{E}_\Lambda^\prime}\) is a nuclear, barrelled and (ultra)bornological normal space of distributions which, however, is not even sequentially complete. Concrete rules are given to determine whether a distribution belongs to \({\mathcal{D}_\Gamma^\prime}\) , whether a sequence converges in \({\mathcal{D}_\Gamma^\prime}\) and whether a set of distributions is bounded in \({\mathcal{D}_\Gamma^\prime}\) .     

Coupling constant in dispersive model

The average of the moments for event shapes in e ^?+? e??→hadrons within the context of next-to-leading order (NLO) perturbative QCD prediction in dispersive model is studied. Moments used in this article are $\langle {1-T}\rangle$ , $\langle \rho\rangle$ , $\langle {B_{\rm T}}\rangle$ and $\langle {B_{\rm W} }\rangle$ . We extract α _s, the coupling constant in perturbative theory and α ₀ in the non-perturbative theory using the dispersive model. By fitting the experimental data, the values of $\alpha_{\rm s} ({M_{\rm Z^0} })=0.1171\pm 0.00229$ and $\alpha_0 \left( {\mu_{\rm I} =2\,{\rm GeV}} \right)=0.5068\pm 0.0440$ are found. Our results are consistent with the above model. Our results are also consistent with those obtained from other experiments at different energies. All these features are explained in this paper.     

Pesin’s Entropy Formula for Systems Between C^1 and C^{1+\alpha }

In this article we give a new observation of Pesin’s entropy formula, motivated from Mañé’s proof of (Ergod Theory Dyn Sys 1:95–102, 1981). Let \(M\) be a compact Riemann manifold and \(f:\,M\rightarrow M\) be a \(C^1\) diffeomorphism on \(M\) . If \(\mu \) is an \(f\) -invariant probability measure which is absolutely continuous relative to Lebesgue measure and nonuniformly-H \(\ddot{\text {o}}\) lder-continuous(see Definition 1.1), then we have Pesin’s entropy formula, i.e., the metric entropy \(h_\mu (f)\) satisfies $$\begin{aligned} h_{\mu }(f)=\int \sum _{\lambda _i(x)> 0}\lambda _i(x)d\mu , \end{aligned}$$ where \(\lambda _1(x)\ge \lambda _2(x)\ge \cdots \ge \lambda _{dim\,M}(x)\) are the Lyapunov exponents at \(x\) with respect to \(\mu .\) Nonuniformly-H \(\ddot{\text {o}}\) lder-continuous is a new notion from probabilistic perspective weaker than \(C^{1+\alpha }.\)      

Asymptotic Quantum Many-Body Localization from Thermal Disorder

We consider a quantum lattice system with infinite-dimensional on-site Hilbert space, very similar to the Bose–Hubbard model. We investigate many-body localization in this model, induced by thermal fluctuations rather than disorder in the Hamiltonian. We provide evidence that the Green–Kubo conductivity κ(β), defined as the time-integrated current autocorrelation function, decays faster than any polynomial in the inverse temperature β as \({\beta \to 0}\) . More precisely, we define approximations \({\kappa_{\tau}(\beta)}\) to κ(β) by integrating the current-current autocorrelation function up to a large but finite time \({\tau}\) and we rigorously show that \({\beta^{-n}\kappa_{\beta^{-m}}(\beta)}\) vanishes as \({\beta \to 0}\) , for any \({n,m \in \mathbb{N}}\) such that m?n is sufficiently large.     

On Energy-Momentum Transfer of Quantum Fields

We prove the following theorem on bounded operators in quantum field theory: if \({\|[B,B^*(x)]\|\leqslant{\rm const}D(x)}\) , then \({\|B^k_\pm(\nu)G(P^0)\|^2\leqslant{\rm const}\int D(x - y){\rm d}|\nu|(x){\rm d}|\nu|(y)}\) , where D(x) is a function weakly decaying in spacelike directions, \({B^k_\pm}\) are creation/annihilation parts of an appropriate time derivative of B, G is any positive, bounded, non-increasing function in \({L^2(\mathbb{R})}\) , and \({\nu}\) is any finite complex Borel measure; creation/annihilation operators may be also replaced by \({B^k_t}\) with \({\check{B^k_t}(p)=|p|^k\check{B}(p)}\) . We also use the notion of energy-momentum scaling degree of B with respect to a submanifold (Steinmann-type, but in momentum space, and applied to the norm of an operator). These two tools are applied to the analysis of singularities of \({\check{B}(p)G(P^0)}\) . We prove, among others, the following statement (modulo some more specific assumptions): outside p = 0 the only allowed contributions to this functional which are concentrated on a submanifold (including the trivial one—a single point) are Dirac measures on hypersurfaces (if the decay of D is not to slow).     

Self-Dual Noncommutative {\phi^4} -Theory in Four Dimensions is a Non-Perturbatively Solvable and Non-Trivial Quantum Field Theory

We study quartic matrix models with partition function \({\mathcal{Z}[E, J] = \int dM}\) exp(trace \({(JM - EM^{2} - \frac{\lambda}{4} M^4)}\) ). The integral is over the space of Hermitean \({\mathcal{N} \times \mathcal{N}}\) -matrices, the external matrix E encodes the dynamics, \({\lambda > 0}\) is a scalar coupling constant and the matrix J is used to generate correlation functions. For E not a multiple of the identity matrix, we prove a universal algebraic recursion formula which gives all higher correlation functions in terms of the 2-point function and the distinct eigenvalues of E. The 2-point function itself satisfies a closed non-linear equation which must be solved case by case for given E. These results imply that if the 2-point function of a quartic matrix model is renormalisable by mass and wavefunction renormalisation, then the entire model is renormalisable and has vanishing β-function. As the main application we prove that Euclidean \({\phi^4}\) -quantum field theory on four-dimensional Moyal space with harmonic propagation, taken at its self-duality point and in the infinite volume limit, is exactly solvable and non-trivial. This model is a quartic matrix model, where E has for \({\mathcal{N} \to \infty}\) the same spectrum as the Laplace operator in four dimensions. Using the theory of singular integral equations of Carleman type we compute (for \({\mathcal{N} \to \infty}\) and after renormalisation of \({E, \lambda}\) ) the free energy density (1/volume) log \({(\mathcal{Z}[E, J]/\mathcal{Z}[E, 0])}\) exactly in terms of the solution of a non-linear integral equation. Existence of a solution is proved via the Schauder fixed point theorem. The derivation of the non-linear integral equation relies on an assumption which in subsequent work is verified for coupling constants \({\lambda \leq 0}\) .     

Identification of \mathrm{\ensuremath J^{\pi} = 19/2^+} and \mathrm{\ensuremath 23/2^+} isomeric states in 127Sb

The nucleus $\ensuremath {\rm ^{127}Sb}$ , which is on the neutron-rich periphery of the $\ensuremath \beta$ -stability region, has been populated in complex nuclear reactions involving deep-inelastic and fusion-fission processes with $\ensuremath {\rm {}^{136}Xe}$ beams incident on thick targets. The previously known isomer at 2325 keV in $\ensuremath {\rm {}^{127}Sb}$ has been assigned spin and parity $\ensuremath 23/2^+$ , based on the measured $\ensuremath \gamma$ - $\ensuremath \gamma$ angular correlations and total internal conversion coefficients. The half-life has been determined to be 234(12) ns, somewhat longer than the value reported previously. The 2194 keV state has been assigned $\ensuremath J^{\pi} = 19/2^+$ and identified as an isomer with $\ensuremath T_{1/2} = 14(1) {\rm ns}$ , decaying by two $\ensuremath E2$ branches. The observed level energies and transition strengths are compared with the predictions of a shell model calculation. Two $\ensuremath 15/2^+$ states have been identified close in energy, and their properties are discussed in terms of mixing between vibrational and three-quasiparticle configurations.     

Light Hypernuclei Based on Chiral Interactions at Next-to-Leading Order

We present predictions for the binding energies of the light hypernuclei \({^3_\Lambda{\rm H},\, ^4_\Lambda{\rm He}}\) and \({^4_\Lambda{\rm H}}\) based on Faddeev- and Yakubovsky equations in momentum space. We discuss how such results can help to test the existing hyperon–nucleon (Y N) potential models and effective field theory based Y N interactions. Especially, we show results for the chiral interactions at next-to-leading order.     

Possible Existence of {(c\bar{c})} –Nucleus Bound States

Charmonium ( \({c \bar{c}}\) ) bound states in few-nucleon systems, ²H, ⁴He and ⁸Be, are studied via Gaussian Expansion Method (GEM). We adopt a Gaussian potential as an effective \({(c \bar{c})}\) –nucleon (N) interaction. The relation between two-body \({(c \bar{c})}\) –N scattering length \({a_{c\bar{c}-N}}\) and the binding energies B of \({(c \bar{c})}\) –nucleus bound states are given. Recent lattice QCD data of \({a_{c\bar{c}-N}}\) corresponds to \({B \simeq 0.5}\) MeV for \({(c \bar{c})-^{4}}\) He and 2 MeV for \({(c \bar{c})-^{8}}\) Be in our results.     

Determinantal Quintics and Mirror Symmetry of Reye Congruences

We study a certain family of determinantal quintic hypersurfaces in \({\mathbb{P}^{4}}\) whose singularities are similar to the well-studied Barth–Nieto quintic. Smooth Calabi–Yau threefolds with Hodge numbers (h ^1,1,h ^2,1) = (52, 2) are obtained by taking crepant resolutions of the singularities. It turns out that these smooth Calabi–Yau threefolds are in a two dimensional mirror family to the complete intersection Calabi–Yau threefolds in \({\mathbb{P}^{4}\times\mathbb{P}^{4}}\) which have appeared in our previous study of Reye congruences in dimension three. We compactify the two dimensional family over \({\mathbb{P}^{2}}\) and reproduce the mirror family to the Reye congruences. We also determine the monodromy of the family over \({\mathbb{P}^{2}}\) completely. Our calculation shows an example of the orbifold mirror construction with a trivial orbifold group.