Analysis of the \frac{1} {2}^ - and \frac{3} {2}^ - heavy and doubly heavy baryon states with QCD sum rules

In this article, we study the $\frac{1} {2}^ -$ and $\frac{3} {2}^ -$ heavy and doubly heavy baryon states $\Sigma _Q \left( {\frac{1} {2}^ - } \right)$ , $\Xi '_Q \left( {\frac{1} {2}^ - } \right)$ , $\Omega _Q \left( {\frac{1} {2}^ - } \right)$ , $\Xi _{QQ} \left( {\frac{1} {2}^ - } \right)$ , $\Omega _{QQ} \left( {\frac{1} {2}^ - } \right)$ , $\Sigma _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Xi _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Omega _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Xi _{QQ}^* \left( {\frac{3} {2}^ - } \right)$ and $\Omega _{QQ}^* \left( {\frac{3} {2}^ - } \right)$ by subtracting the contributions from the corresponding $\frac{1} {2}^ +$ and $\frac{3} {2}^ +$ heavy and doubly heavy baryon states with the QCD sum rules in a systematic way, and make reasonable predictions for their masses.     

The Higgs boson inclusive decay channels H \rightarrow b\bar{b} and H \rightarrow gg up to four-loop level

The principle of maximum conformality (PMC) has been suggested to eliminate the renormalization scheme and renormalization scale uncertainties, which are unavoidable for the conventional scale setting and are usually important errors for theoretical estimations. In this paper, by applying PMC scale setting, we analyze two important inclusive Standard Model Higgs decay channels, $H\rightarrow b\bar{b}$ and $H\rightarrow gg$ , up to four-loop and three-loop levels, respectively. After PMC scale setting, it is found that the conventional scale uncertainty for these two channels can be eliminated to a high degree. There is small residual initial scale dependence for the Higgs decay widths due to unknown higher-order $\{\beta _i\}$ terms. Up to four-loop level, we obtain $\Gamma (H\rightarrow b\bar{b}) = 2.389\pm 0.073 \pm 0.041$ MeV and up to three-loop level, we obtain $\Gamma (H\rightarrow gg) = 0.373\pm 0.030$ MeV, where the first error is caused by varying $M_H=126\pm 4$ GeV and the second error for $H\rightarrow b\bar{b}$ is caused by varying the $\overline{\mathrm{MS}}$ -running mass $m_b(m_b)=4.18\pm 0.03$ GeV. Taking $H\rightarrow b\bar{b}$ as an example, we present a comparison of three BLM-based scale-setting approaches, e.g. the PMC-I approach based on the PMC–BLM correspondence, the $R_\delta $ -scheme and the seBLM approach, all of which are designed to provide effective ways to identify non-conformal $\{\beta _i\}$ -series at each perturbative order. At four-loop level, all those approaches lead to good pQCD convergence, they have almost the same pQCD series, and their predictions are almost independent on the initial renormalization scale. In this sense, those approaches are equivalent to each other.     

On the Quasi-linear Elliptic PDE {-\nabla \cdot ( \nabla{u}/ \sqrt{1-| \nabla{u} |^2}) = 4 \pi \sum_k a_k \delta_{s_k}} in Physics and Geometry

It is shown that for each finite number N of Dirac measures ${\delta_{s_n}}$ supported at points ${s_n \in {\mathbb R}^3}$ with given amplitudes ${a_n \in {\mathbb R} \backslash\{0\}}$ there exists a unique real-valued function ${u \in C^{0, 1}({\mathbb R}^3)}$ , vanishing at infinity, which distributionally solves the quasi-linear elliptic partial differential equation of divergence form ${-\nabla \cdot ( \nabla{u}/ \sqrt{1-| \nabla{u} |^2}) = 4 \pi \sum_{n=1}^N a_n \delta_{s_n}}$ . Moreover, ${u \in C^{\omega}({\mathbb R}^3\backslash \{s_n\}_{n=1}^N)}$ . The result can be interpreted in at least two ways: (a) for any number N of point charges of arbitrary magnitude and sign at prescribed locations s _n in three-dimensional Euclidean space there exists a unique electrostatic field which satisfies the Maxwell-Born-Infeld field equations smoothly away from the point charges and vanishes as |s| ?? ??; (b) for any number N of integral mean curvatures assigned to locations ${s_n \in {\mathbb R}^3 \subset{\mathbb R}^{1, 3}}$ there exists a unique asymptotically flat, almost everywhere space-like maximal slice with point defects of Minkowski spacetime ${{\mathbb R}^{1, 3}}$ , having lightcone singularities over the s _n but being smooth otherwise, and whose height function vanishes as |s| ?? ??. No struts between the point singularities ever occur.     

Preliminary studies of the Raman spectra of \hbox {Ag}_{2}\hbox {Te}\hbox { and }\hbox {Ag}_{5}\hbox {Te}_{3}

The theoretical calculations indicated that the monoclinic low-temperature phase of silver telluride $(\upbeta \hbox {-Ag}_{2}\hbox {Te})$ is a new binary topological insulator with highly anisotropic single Dirac cone surface. We obtained $\upbeta \hbox {-Ag}_{2}\hbox {Te}$ crystal ingots containing few grains by the Bridgman method. We also deposited thin films of tellurium, $\hbox {Ag}_{5}\hbox {Te}_{3}\hbox { and }(\hbox {Te+Ag}_{5}\hbox {Te}_{3})$ by thermal evaporation method. The Raman spectra of $\upbeta \hbox {-Ag}_{2}\hbox {Te}$ , tellurium and $\hbox {Ag}_{5}\hbox {Te}_{3}$ were measured at three excitation wave lengths: 633, 515 and 488 nm. The Raman active modes of $\upbeta \hbox {-Ag}_{2}\hbox {Te}$ , tellurium and $\hbox {Ag}_{5}\hbox {Te}_{3}$ are situated at frequencies below 300  $\hbox {cm}^{-1}$ while vibrations of other phases appear at higher frequencies.     

Thin-shell wormholes from the regular Hayward black hole

We discuss the formalism of the two Higgs doublet model of type III with CP violation from CP-even CP-odd mixing in the neutral Higgs bosons. The flavor-changing interactions among neutral Higgs bosons and fermions are presented at tree level in this type of model. These assumptions allow the study of rare top decays mediated by a neutral Higgs boson; particularly we are interested in $t\rightarrow c l^+l^-$ . For this process we estimate the upper bounds of the branching ratios $\mathrm{Br }(t\rightarrow c \tau ^+\tau ^-)$ of the order of $10^{-9}\sim 10^{-7}$ for a neutral Higgs boson mass equal to 125 GeV and $\tan \beta =1$ , 1.5, 2, 2.5. For the case of $t\rightarrow c \tau ^+\tau ^-$ the number of possible events is estimated to range from 1 to 10 events, which could be observed in future experiments at LHC with a luminosity of 300  $\hbox {fb}^{-1}$ and 14 TeV for the energy of the center of mass. Also we estimate that the number of events for the process $t\rightarrow c l^+l^-$ in different scenarios is of the order of 2,500.     

Structure of Neutron-Rich Be Hyper Isotopes

The deformation change of ${^{9}_\Lambda}$ Be and the low-lying states of ${^{12}_{\Lambda}}$ Be are studied by using the antisymmetrized molecular dynamics for hypernuclei (HyperAMD). In ${^{9}_{\Lambda}}$ Be, the Λ hyperon in p orbit enhances nuclear quadrupole deformation, while the Λ hyperon in s orbit reduces it. In ${^{12}_{\Lambda}}$ Be, the ground state parity inverted in ¹¹Be is reverted in ${^{12}_{\Lambda}}$ Be by adding a Λ hyperon as an impurity (impurity effect).     

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.     

Quasi solid state dye-sensitized solar cells based on polyvinyl alcohol (PVA) electrolytes containing \mathbf{I}^{\mathbf{-}}/\mathbf{I}_{\mathbf{3}}^{\mathbf{-}} redox couple

Quasi solid state dye-sensitized solar cells (DSSCs) have been fabricated with electrolytes containing $\text{ I }^{-}/\text{ I }_{3}^{-}$ redox couple using 80 % hydrolyzed polyvinyl alcohol (PVA) doped with potassium iodide (KI) and a mixture of potassium iodide and tetrapropyl ammonium iodide ( $\text{ Pr }_{4}\text{ NI }$ ) salts. The quasi solid state gel polymer electrolytes were prepared using 1:1 ethylene carbonate (EC):propylene carbonate (PC) mixture. The solar cells have the structure of ITO/ $\text{ TiO }_{2}$ /N3-Dye/electrolyte/Pt/ITO. The conductivity of the electrolytes has been calculated from the bulk resistance value determined using the electrochemical impedance spectroscopy. The performance of the DSSCs has been studied by varying the concentration of the doping salts in the electrolyte and incident light intensity. The DSSC fabricated with the KI salt electrolyte containing 9.9 wt% PVA, 39.6 wt% EC, 39.6 wt% PC, 10.9 wt% KI $(+\text{ I }_{2})$ exhibited the best power conversion efficiency of 1.97 %. However, the DSSC with a double-salt electrolyte containing 9.9 wt% PVA: 39.6 wt% EC: 39.6 wt% PC: (6.5 wt% KI: 4.4 wt% $\text{ Pr }_{4}\text{ NI }$ ) ( $+\text{ I }_{2}$ ) exhibited a higher efficiency of 3.27% under $100 \text{ mW/cm }^{2}$ light intensity. The efficiency of this cell increased to 4.59 % under dimmer light of intensity of $54 \text{ mW/cm }^{2}$ .     

Towards Asymptotic Completeness of Two-Particle Scattering in Local Relativistic QFT

We consider the problem of existence of asymptotic observables in local relativistic theories of massive particles. Let ${\tilde{p}_1}$ and ${\tilde{p}_2}$ be two energy-momentum vectors of a massive particle and let ${\Delta}$ be a small neighbourhood of ${\tilde{p}_1 + \tilde{p}_2}$ . We construct asymptotic observables (two-particle Araki–Haag detectors), sensitive to neutral particles of energy-momenta in small neighbourhoods of ${\tilde{p}_1}$ and ${\tilde{p}_2}$ . We show that these asymptotic observables exist, as strong limits of their approximating sequences, on all physical states from the spectral subspace of ${\Delta}$ . Moreover, the linear span of the ranges of all such asymptotic observables coincides with the subspace of two-particle Haag–Ruelle scattering states with total energy-momenta in ${\Delta}$ . The result holds under very general conditions which are satisfied, for example, in ${\lambda{\phi}_{2}^{4}}$ . The proof of convergence relies on a variant of the phase-space propagation estimate of Graf.     

Femtosecond relaxation kinetics of highly excited \mathrm{M}_{\mathrm{Na}}^{**} states in CaF2 at 3.2 eV and 4.7 eV

Femtosecond (fs) laser pulses at variable delay times allowed us to track the fast non-radiative transitions between the manifold of highly excited $\mathrm{M}_{\mathrm{Na}}^{**}$ states to the lower lying fluorescent $\mathrm{M}_{\mathrm{Na}}^{*}$ state in CaF₂. Two distinct $\mathrm{M}_{\mathrm{Na}}^{**}$ states of the manifold at 3.16?eV ( $\mathrm{M}_{\mathrm{Na}2}^{**}$ ) and 4.73?eV ( $\mathrm{M}_{\mathrm{Na}3}^{**}$ ) were populated using the second (SH) and third harmonics (TH) of fs laser light at 785?nm. The population kinetics of the fluorescent $\mathrm{M}_{\mathrm{Na}}^{*}$ state in the 2?eV excitation energy range was revealed by depleting its fluorescence centered at 740?nm using fundamental near infrared (NIR) fs laser pulses. The related time constants for $\mathrm{M}_{\mathrm{Na}2,3}^{**}{\sim}{>} \mathrm{M}_{\mathrm{Na}}^{*}$ relaxation amounted to 1.0±0.14?ps and 3.0±0.3?ps upon SH and TH excitation, respectively.     

Existence of a Non-Averaging Regime for the Self-Avoiding Walk on a High-Dimensional Infinite Percolation Cluster

Let $Z_N$ be the number of self-avoiding paths of length $N$ starting from the origin on the infinite cluster obtained after performing Bernoulli percolation on ${\mathbb Z} ^d$ with parameter $p>p_c({\mathbb Z} ^d)$ . The object of this paper is to study the connective constant of the dilute lattice $\limsup _{N\rightarrow \infty } Z_N^{1/N}$ , which is a non-random quantity. We want to investigate if the inequality $\limsup _{N\rightarrow \infty } (Z_N)^{1/N} \le \lim _{N\rightarrow \infty } {\mathbb E} [Z_N]^{1/N}$ obtained with the Borel–Cantelli Lemma is strict or not. In other words, we want to know if the quenched and annealed versions of the connective constant are equal. On a heuristic level, this indicates whether or not localization of the trajectories occurs. We prove that when $d$ is sufficiently large there exists $p^{(2)}_c>p_c$ such that the inequality is strict for $p\in (p_c,p^{(2)}_c)$ .     

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 ${n \in \mathbb{N}, \mathsf{P_{SAW}}_n \big( {\rm max}\big\{\| \gamma_k \| : 0 \leq k \leq n\big\} \geq vn \big) \leq e^{-\varepsilon n}}$ .     

Split supersymmetry under GUT and current dark matter constraints

There are four types of two-Higgs doublet models under a discrete \(Z_2\) symmetry imposed to avoid tree-level flavor-changing neutral current, i.e. type-I, type-II, type-X, and type-Y models. We investigate the possibility to discriminate the four models in the light of the flavor physics data, including \(B_s\) – \(\bar{B}_s\) mixing, \(B_{s,d} \rightarrow \mu ^+ \mu ^-\) , \(B\rightarrow \tau \nu \) and \(\bar{B} \rightarrow X_s \gamma \) decays, the recent LHC Higgs data, the direct search for charged Higgs at LEP, and the constraints from perturbative unitarity and vacuum stability. After deriving the combined constraints on the Yukawa interaction parameters, we have shown that the correlation between the mass eigenstate rate asymmetry \(A_{\Delta \Gamma }\) of \(B_{s} \rightarrow \mu ^+ \mu ^-\) and the ratio \(R=\mathcal{B}(B_{s} \rightarrow \mu ^+ \mu ^-)_\mathrm{exp}/ \mathcal{B}(B_{s} \rightarrow \mu ^+ \mu ^-)_\mathrm{SM}\) could be a sensitive probe to discriminate the four models with future precise measurements of the observables in the \(B_{s} \rightarrow \mu ^+ \mu ^-\) decay at LHCb.     

Absolute E3 and M2 transition probabilities for the electromagnetic decay of the \mathrm{\ensuremath I^{\pi}=K^{\pi}=8^{-}} isomeric state in 132Ce

The decay of the $\ensuremath I^{\pi}=K^{\pi}=8^{-}$ isomeric state at 2340keV in ¹³²Ce has been investigated in the ¹²⁰Sn(¹⁶O, 4n)¹³²Ce reaction. The measurements were carried out in e - $ \gamma$ and $ \gamma$ - $ \gamma$ coincidence modes using an electron spectrometer coupled to the OSIRIS II gamma-ray array at the Heavy Ion Laboratory of the University of Warsaw. Experimentally obtained internal conversion coefficients for the $\ensuremath 8^{-} \rightarrow 6^{+}$ and $\ensuremath 8^{-} \rightarrow 5^{+}$ transitions allowed the multipolarities, mixing ratios, reduced transition probabilities and hindrance factors to be determined.     

Universality of identified hadron production in pp collisions

The shapes of invariant differential cross section for identified $\pi ^{\pm },K^{\pm }, p$ and $\overline{p}$ production as a function of transverse momentum measured in $pp$ collisions by the PHENIX detector are analyzed in terms of a recently introduced approach. Simultaneous fits of these data to the sum of exponential and power-law terms show a significant difference in the exponential term contributions. This effect qualitatively explains the observed shape of the experimental $K/\pi $ and $p/\pi $ yield ratios measured as a function of transverse momentum of produced hadrons. A picture with two types of mechanisms for hadron production is presented. Universality of the power-law term behavior for $\pi ^{\pm },K^{\pm }, p$ , and $\overline{p}$ production is shown.     

On Dirichlet-to-Neumann Maps, Nonlocal Interactions, and Some Applications to Fredholm Determinants

We consider Dirichlet-to-Neumann maps associated with (not necessarily self-adjoint) Schrödinger operators describing nonlocal interactions in ${L^2(\Omega; d^n x)}$ , where ${\Omega \subset \mathbb{R}^n}$ , ${n\in\mathbb{N}}$ , ${n\geq 2}$ , are open sets with a compact, nonempty boundary ${\partial\Omega}$ satisfying certain regularity conditions. As an application we describe a reduction of a certain ratio of Fredholm perturbation determinants associated with operators in ${L^2(\Omega; d^{n} x)}$ to Fredholm perturbation determinants associated with operators in ${L^2(\partial\Omega; d^{n-1} \sigma)}$ , ${n\in\mathbb{N}}$ , ${n\geq 2}$ . This leads to an extension of a variant of a celebrated formula due to Jost and Pais, which reduces the Fredholm perturbation determinant associated with a Schrödinger operator on the half-line ${(0,\infty)}$ , in the case of local interactions, to a simple Wronski determinant of appropriate distributional solutions of the underlying Schrödinger equation.     

Finite W-Superalgebras and Truncated Super Yangians

Let ${Y_{m|n}^{\ell}}$ be the super Yangian of general linear Lie superalgebra for ${\mathfrak{gl}_{m|n}}$ . Let ${e \in \mathfrak{gl}_{m\ell|n\ell}}$ be a “rectangular” nilpotent element and ${\mathcal{W}_e}$ be the finite W-superalgebra associated to e. We show that ${Y_{m|n}^{\ell}}$ is isomorphic to ${\mathcal{W}_e}$ .     

Quantum Sphere {\mathbb{S}^4} as a Non-Levi Conjugacy Class

We construct a ${U_\hbar(\mathfrak{sp}(4))}$ -equivariant quantization of the four-dimensional complex sphere ${\mathbb{S}^4}$ regarded as a conjugacy class, Sp(4)/Sp(2) ×?Sp(2), of a simple complex group with non-Levi isotropy subgroup, through an operator realization of the quantum polynomial algebra ${\mathbb{C}_\hbar[\mathbb{S}^4]}$ on a highest weight module of ${U_\hbar(\mathfrak{sp}(4))}$ .     

Structure of neutron-rich nuclei around the N = 126 closed shell; the yrast structure of 205Au126 up to spin-parity I^{\pi} = (19/2+)

Heavy neutron-rich nuclei have been populated through the relativistic fragmentation of a $\ensuremath ^{208}_{\ 82}{\rm Pb}$ beam at $\ensuremath E/A = 1$ GeV on a $\ensuremath 2.5 {\rm g/cm^2}$ thick Be target. The synthesised nuclei were selected and identified in-flight using the fragment separator at GSI. Approximately 300 ns after production, the selected nuclei were implanted in an $\ensuremath \sim 8$ mm thick perspex stopper, positioned at the centre of the RISING $\ensuremath \gamma$ -ray detector spectrometer array. A previously unreported isomer with a half-life $\ensuremath T_{1/2} = 163(5)$ ns has been observed in the N = 126 closed-shell nucleus $\ensuremath ^{205}_{\ 79}{\rm Au}$ . Through $ \gamma$ -ray singles and $ \gamma$ - $ \gamma$ coincidence analysis a level scheme was established. The comparison with a shell model calculation tentatively identifies the spin-parity of the excited states, including the isomer itself, which is found to be $\ensuremath I^{\pi} = (19/2^+)$ .