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.     

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 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.     

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 \({\mathcal{D}_\Gamma^\prime}\) .     

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.     

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 \({\lambda \leq 0}\) .     

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.     

Classical {\mathcal{W}}-Algebras and Generalized Drinfeld–Sokolov Hierarchies for Minimal and Short Nilpotents

We derive explicit formulas for λ-brackets of the affine classical \({\mathcal{W}}\) -algebras attached to the minimal and short nilpotent elements of any simple Lie algebra \({\mathfrak{g}}\) . This is used to compute explicitly the first non-trivial PDE of the corresponding integrable generalized Drinfeld–Sokolov hierarchies. It turns out that a reduction of the equation corresponding to a short nilpotent is Svinolupov’s equation attached to a simple Jordan algebra, while a reduction of the equation corresponding to a minimal nilpotent is an integrable Hamiltonian equation on 2h ˇ?3 functions, where h ˇ is the dual Coxeter number of \(\mathfrak{g}\) . In the case when \(\mathfrak{g}\) is \({\mathfrak{sl}_2}\) both these equations coincide with the KdV equation. In the case when \(\mathfrak{g}\) is not of type \({C_n}\) , we associate to the minimal nilpotent element of \(\mathfrak{g}\) yet another generalized Drinfeld–Sokolov hierarchy.     

Antineutrino science in KamLAND

The primary goal of KamLAND is a search for the oscillation of \({\bar{\nu }}_\mathrm{e}\) ’s emitted from distant power reactors. The long baseline, typically 180 km, enables KamLAND to address the oscillation solution of the “solar neutrino problem” with \({\bar{\nu }}_{e} \) ’s under laboratory conditions. KamLAND found fewer reactor \({\bar{\nu }}_{e} \) events than expected from standard assumptions about \(\overline{\nu }_e\) propagation at more than 9 \(\sigma \) confidence level (C.L.). The observed energy spectrum disagrees with the expected spectral shape at more than 5 \(\sigma \) C.L., and prefers the distortion from neutrino oscillation effects. A three-flavor oscillation analysis of the data from KamLAND and KamLAND + solar neutrino experiments with CPT invariance, yields \(\Delta m_{21}^2 \) = [ \(7.54_{-0.18}^{+0.19} \times \) 10 \(^{-5}\) eV \(^{2}\) , \(7.53_{-0.18}^{+0.19} \times \) 10 \(^{-5}\) eV \(^{2}\) ], tan \(^{2}\theta _{12}\) = [ \(0.481_{-0.080}^{+0.092} \) , \(0.437_{-0.026}^{+0.029} \) ], and sin \(^{2}\theta _{13}\) = [ \(0.010_{-0.034}^{+0.033} \) , \(0.023_{-0.015}^{+0.015} \) ]. All solutions to the solar neutrino problem except for the large mixing angle region are excluded. KamLAND also demonstrated almost two cycles of the periodic feature expected from neutrino oscillation effects. KamLAND performed the first experimental study of antineutrinos from the Earth’s interior so-called geoneutrinos (geo \({\bar{\nu }}_{e} \) ’s), and succeeded in detecting geo \({\bar{\nu }}_{e} \) ’s produced by the decays of \(^{238}\) U and \(^{232}\) Th within the Earth. Assuming a chondritic Th/U mass ratio, we obtain \(116_{-27}^{+28} {\bar{\nu }}_{e}\) events from \(^{238}\) U and \(^{232}\) Th, corresponding a geo \({\bar{\nu }}_{e}\) flux of \(3.4_{-0.8}^{+0.8}\times \) 10 \(^{6}\) cm \(^{-2}\)  s \(^{-1}\) at the KamLAND location. We evaluate various bulk silicate Earth composition models using the observed geo \({\bar{\nu }}_{e} \) rate.     

Radiative X(3872) Decays in Charmonium-Molecule Hybrid Model

We study the radiative decays of the X(3872) in the charmonium-molecule model combined with the quark potential model. We obtain \({\Gamma(X(3872) \to J/\psi \, \gamma) = 29.2\,{\rm keV}}\) and \({\Gamma(X(3872) \to \psi' \, \gamma) = 6.3\,{\rm keV}}\) . The ratio of these two is 0.22, which is much smaller than the BABAR observation. We find that the result is very sensitive to the amount of the \({\chi_{c1}(1P)}\) component in the X(3872).     

The Baker–Akhiezer Function and Factorization of the Chebotarev–Khrapkov Matrix

A new technique is proposed for the solution of the Riemann–Hilbert problem with the Chebotarev–Khrapkov matrix coefficient \({G(t) = \alpha_{1}(t)I + \alpha_{2}(t)Q(t)}\) , \({\alpha_{1}(t), \alpha_{2}(t) \in H(L)}\) , I = diag{1, 1}, Q(t) is a \({2\times2}\) zero-trace polynomial matrix. This problem has numerous applications in elasticity and diffraction theory. The main feature of the method is the removal of essential singularities of the solution to the associated homogeneous scalar Riemann–Hilbert problem on the hyperelliptic surface of an algebraic function by means of the Baker–Akhiezer function. The consequent application of this function for the derivation of the general solution to the vector Riemann–Hilbert problem requires the finding of the \({\rho}\) zeros of the Baker–Akhiezer function ( \({\rho}\) is the genus of the surface). These zeros are recovered through the solution to the associated Jacobi problem of inversion of abelian integrals or, equivalently, the determination of the zeros of the associated degree- \({\rho}\) polynomial and solution of a certain linear algebraic system of \({\rho}\) equations.     

Self-Avoiding Walk is Sub-Ballistic

We prove that self-avoiding walk on ${\mathbb{Z}^d}$ is sub-ballistic in any dimension d ≥ 2. That is, writing ${\| u \|}$ for the Euclidean norm of ${u \in \mathbb{Z}^d}$ , and ${\mathsf{P_{SAW}}_n}$ for the uniform measure on self-avoiding walks ${\gamma : \{0, \ldots, n\} \to \mathbb{Z}^d}$ for which γ ₀ = 0, we show that, for each v > 0, there exists ${\varepsilon > 0}$ such that, for each ${n \in \mathbb{N}, \mathsf{P_{SAW}}_n \big( {\rm max}\big\{\| \gamma_k \| : 0 \leq k \leq n\big\} \geq vn \big) \leq e^{-\varepsilon n}}$ .     

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.     

Universality of the Local Regime for the Block Band Matrices with a Finite Number of Blocks

We consider the block band matrices, i.e. the Hermitian matrices $H_N$ , $N=|\Lambda |W$ with elements $H_{jk,\alpha \beta }$ , where $j,k \in \Lambda =[1,m]^d\cap \mathbb {Z}^d$ (they parameterize the lattice sites) and $\alpha , \beta = 1,\ldots , W$ (they parameterize the orbitals on each site). The entries $H_{jk,\alpha \beta }$ are random Gaussian variables with mean zero such that $\langle H_{j_1k_1,\alpha _1\beta _1}H_{j_2k_2,\alpha _2\beta _2}\rangle =\delta _{j_1k_2}\delta _{j_2k_1} \delta _{\alpha _1\beta _2}\delta _{\beta _1\alpha _2} J_{j_1k_1},$ where $J=1/W+\alpha \Delta /W$ , $\alpha < 1/4d$ . This matrices are the special case of Wegner’s $W$ -orbital models. Assuming that the number of sites $|\Lambda |$ is finite, we prove universality of the local eigenvalue statistics of $H_N$ for the energies $|\lambda _0|< \sqrt{2}$ .     

Tail Asymptotics of Free Path Lengths for the Periodic Lorentz Process: On Dettmann’s Geometric Conjectures

In the simplest case, consider a \({\mathbb{Z}^d}\) -periodic (d ≥ 3) arrangement of balls of radii < 1/2, and select a random direction and point (outside the balls). According to Dettmann’s first conjecture, the probability that the so determined free flight (until the first hitting of a ball) is larger than t >  > 1 is \({\sim\frac{C}{t}}\) , where C is explicitly given by the geometry of the model. In its simplest form, Dettmann’s second conjecture is related to the previous case with tangent balls (of radii 1/2). The conjectures are established in a more general setup: for \({\mathcal{L}}\) -periodic configuration of—possibly intersecting—convex bodies with \({\mathcal{L}}\) being a non-degenerate lattice. These questions are related to Pólya’s visibility problem (Arch Math Phys Ser 2:135–142, 1918), to theories of Bourgain et al. (Commun Math Phys 190:491–508,1998), and of Marklof–Strömbergsson (Ann Math 172:1949–2033,2010). The results also provide the asymptotic covariance of the periodic Lorentz process assuming it has a limit in the super-diffusive scaling, a fact if d = 2 and the horizon is infinite.     

Phase Transitions in Layered Systems

We consider the Ising model on \(\mathbb Z\times \mathbb Z\) where on each horizontal line \(\{(x,i), x\in \mathbb Z\}\) , called “layer”, the interaction is given by a ferromagnetic Kac potential with coupling strength \(J_{ \gamma }(x,y)={ \gamma }J({ \gamma }(x-y))\) , where \(J(\cdot )\) is smooth and has compact support; we then add a nearest neighbor ferromagnetic vertical interaction of strength \({ \gamma }^{A}\) , where \(A\ge 2\) is fixed, and prove that for any \(\beta \) larger than the mean field critical value there is a phase transition for all \({ \gamma }\) small enough.     

QCD analysis of forward neutron production in DIS

Observing light-by-light scattering at the large hadron collider (LHC) has received quite some attention and it is believed to be a clean and sensitive channel to possible new physics. In this paper, we study the diphoton production at the LHC via the process \({{pp}}\rightarrow {{p}}\gamma \gamma {{p}}\rightarrow {{p}}\gamma \gamma {{p}}\) through graviton exchange in the large extra dimension (LED) model. Typically, when we do the background analysis, we also study the double Pomeron exchange of \(\gamma \gamma \) production. We compare its production in the quark–quark collision mode to the gluon–gluon collision mode and find that contributions from the gluon–gluon collision mode are comparable to the quark–quark one. Our result shows, for extra dimension \(\delta =4\) , with an integrated luminosity \(\mathcal{L} = 200\,\mathrm{fb}^{-1}\) at the 14 TeV LHC, that diphoton production through graviton exchange can probe the LED effects up to the scale \({M}_{S}=5.06 (4.51, 5.11)\,\mathrm{TeV}\) for the forward detector acceptance \(\xi _1 (\xi _2, \xi _3)\) , respectively, where \(0.0015<\xi _1<0.5\) , \(0.1<\xi _2<0.5\) , and \(0.0015<\xi _3<0.15\) .     

Nucleon and {\Delta} Elastic and Transition Form Factors

We present a unified study of nucleon and \({\Delta}\) elastic and transition form factors, and compare predictions made using a framework built upon a Faddeev equation kernel and interaction vertices that possess QCD-like momentum dependence with results obtained using a symmetry-preserving treatment of a vector \({\otimes}\) vector contact-interaction. The comparison emphasises that experiments are sensitive to the momentum dependence of the running couplings and masses in the strong interaction sector of the Standard Model and highlights that the key to describing hadron properties is a veracious expression of dynamical chiral symmetry breaking in the bound-state problem. Amongst the results we describe, the following are of particular interest: \({G_{E}^{p}(Q^{2})/G_{M}^{p}(Q^{2})}\) possesses a zero at Q ² = 9.5 GeV²; any change in the interaction which shifts a zero in the proton ratio to larger Q ² relocates a zero in \({G_{E}^{n}(Q^{2})/G_M^{n}(Q^{2})}\) to smaller Q ²; there is likely a value of momentum transfer above which \({G_{E}^{n} > G_{E}^{p}}\) ; and the presence of strong diquark correlations within the nucleon is sufficient to understand empirical extractions of the flavour-separated form factors. Regarding the \({\Delta(1232)}\) -baryon, we find that, inter alia: the electric monopole form factor exhibits a zero; the electric quadrupole form factor is negative, large in magnitude, and sensitive to the nature and strength of correlations in the \({\Delta(1232)}\) Faddeev amplitude; and the magnetic octupole form factor is negative so long as rest-frame P- and D-wave correlations are included. In connection with the \({N \to \Delta}\) transition, the momentum-dependence of the magnetic transition form factor, \({G_{M}^{*}}\) , matches that of \({G_{M}^{n}}\) once the momentum transfer is high enough to pierce the meson-cloud; and the electric quadrupole ratio is a keen measure of diquark and orbital angular momentum correlations, the zero in which is obscured by meson-cloud effects on the domain currently accessible to experiment. Importantly, within each framework, identical propagators and vertices are sufficient to describe all properties discussed herein. Our analysis and predictions should therefore serve as motivation for measurement of elastic and transition form factors involving the nucleon and its resonances at high photon virtualities using modern electron-beam facilities.     

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).