Investigation of Hadronic Quasi-Three-Body B Decays

We interest to investigate of the quasi-three-body decays of B⁰ meson to \({f_0}(980){K^ + }{\pi ^ - }({f_0}(980) \to \pi \pi )\) and \({\bar D_1}{(2420)^0}{\pi ^ + }{\pi ^ - }(\bar D_1^0) \to D{^{*-} }{\pi ^ + }\). The analysis of mentioned four-body decays is such as to factorize into the three-body decay and several channels observed. Hadronic three-body decays include both non-resonant and resonant contributions, on the basis of the factorization approach. In the case of B⁰ to vector pseudoscalar states appeared in factorized terms, the B* pole contribution is considered. Hence the matrix element of the B* → D₁ weak transition and strong vertex is computed. Therefore the theoretical values are (1.418 ± 0.21) × 10^?6 and (1.44 ± 0.2) × 10^?4, while the experimental results of them are \((1.4_{-0.6}^{+0.5})\times10^{-6}\), respectively. Comparing computational analysis values with experimental values show that our results are in agreement with them.     

The $$\tau\rightarrow\bar{K}^{*0}(892)\pi^{-}\nu_\tau$$ Decay in the Nambu–Jona-Lasinio Model

The width of the \(\tau\rightarrow\bar{K}^{*0}(892)\pi^{-}\nu_\tau\) decay is calculated within the Nambu–Jona-Lasinio model taking into account four channels of the formation of the \(\tau\rightarrow\bar{K}^{*0}(892)\pi^{-}\) pair—the contact interaction and three channels with intermediate axial-vector, vector, and pseudoscalar mesons. Leading contributions arise from the contact interaction and axial-vector channel with an intermediate ground-state K₁(1270) meson. Our theoretical estimate adequately reproduces the measured \(\tau\rightarrow\bar{K}^{*0}(892)\pi^{-}\nu_\tau\) decay width.     

Sbottom signature of supersymmetric golden region

The experimental search limit on the Higgs boson mass points to a “golden region” in the Minimal Supersymmetric Standard Model parameter space in which the fine-tuning in the electroweak sector is minimized. One of the sbottoms is relatively light since its mass parameter is related to that of the stop. The decay products of the light sbottom typically include a W boson and a b jet. We studied the pair production of the light sbottoms at the Large Hadron Collider and examined its discovery potential via collider signature of 4 jets + 1 lepton + missing E _T . Such channel differs from conventional sbottom searches of either \(\tilde{b}_{1} \rightarrow b \chi_{2}^{0} \rightarrow b \ell^{+}\ell^{-} \chi_{1}^{0}\) or \(\tilde{b}_{1} \rightarrow t \chi_{1}^{-}\) with reconstructed top quark. We analyzed the Standard Model backgrounds for this channel and developed a set of cuts to identify the signal and suppress the backgrounds. We showed that with 100 fb^?1 integrated luminosity, a significance level of 5–6 σ could be reached for the light sbottom discovery at the LHC.     

Asymptotic Behavior of the Selberg Zeta Functions for Degenerating Families of Hyperbolic Manifolds

Let {M _k } be a degenerating sequence of finite volume, hyperbolic manifolds of dimension d, with d = 2 or d = 3, with finite volume limit M _∞. Let \({Z_{M_{k}} (s)}\) be the associated sequence of Selberg zeta functions, and let \({{\mathcal{Z}}_{k} (s)}\) be the product of local factors in the Euler product expansion of \({Z_{M_{k}} (s)}\) corresponding to the pinching geodesics on M _k . The main result in this article is to prove that \({Z_{M_{k}} (s)/{\mathcal{Z}}_{k} (s)}\) converges to \({Z_{M_{\infty}} (s)}\) for all \({s \in \mathbf{C}}\)with Re(s) > (d ? 1)/2. The significant feature of our analysis is that the convergence of \({Z_{M_{k}} (s)/{\mathcal{Z}}_{k} (s)}\) to \({Z_{M_{\infty}} (s)}\) is obtained up to the critical line, including the right half of the critical strip, a region where the Euler product definition of the Selberg zeta function does not converge. In the case d = 2, our result reproves by different means the main theorem in Schulze (J Funct Anal 236:120–160, 2006).     

Effect of FCNC mediated <Emphasis Type="Italic">Z</Emphasis> boson on lepton flavor violating decays

We study the three body lepton flavor violating (LFV) decays μ ^?→e ^? e ⁺ e ^?, \(\tau^{-} \to l_{i}^{-} l_{j}^{+} l_{j}^{-}\) and the semileptonic decay τ→μφ in the flavor changing neutral current (FCNC) mediated Z boson model. We also calculate the branching ratios for LFV leptonic B decays, B _d,s →μe, B _d,s →τe, B _d,s →τμ and the conversion of muon to electron in Ti nucleus. The new physics parameter space is constrained by using the experimental limits on μ ^?→e ^? e ⁺ e ^? and τ ^?→μ ^? μ ⁺ μ ^?. We find that the branching ratios for τ→eee and τ→μφ processes could be as large as \({\sim}{\mathcal{O}}(10^{-8})\) and \(\mathrm{Br}(B_{d,s} \to \tau \mu,~ \tau e) \sim {\mathcal{O}}(10^{-10})\). For other LFV B decays the branching ratios are found to be too small to be observed in the near future.     

Angular distributions in the decays of the triplet <Emphasis Type="Italic">D</Emphasis><Subscript>2</Subscript> state of charmonium directly produced in polarized proton–antiproton collisions

Using the helicity formalism, we calculate the combined angular distribution function of the two gamma photons and the electron in the cascade process \({\bar{p}p}\to{}^{3}{D}_{2}\to\chi_{J}+\gamma_{1}\to(\psi +\gamma_{2})+\gamma_{1}\to({e}^{+}+{e}^{-})+\gamma_{1}+\gamma_{2}\) (J=0,1,2), when \({\bar{p}}\) and p are arbitrarily polarized. We also present the partially integrated angular distribution functions in six different cases. Our results show that by measuring the two-particle angular distribution of γ ₁ and γ ₂ and that of γ ₁ and e ^?, one can determine the relative magnitudes as well as the relative phases of all the helicity amplitudes in the two radiative decay processes ³ D ₂→χ _J +γ ₁ and χ _J →ψ+γ ₂.     

<Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> meson rare decays in the light-cone quark model

We investigate the rare decays \(B_{c} \rightarrow D_{s}(1968)\ell \overline{\ell}\) and \(B_{c}\rightarrow D_{s}^{*}(2317) \ell \overline{\ell}\) in the framework of the light-cone quark model (LCQM). The transition form factors are calculated in the space-like region and then analytically continued to the time-like region via exponential parametrization. The branching ratios and longitudinal lepton polarization asymmetries (LPAs) for the two decays are given and compared with each other. The results are helpful for investigating the structure of B _c meson and for testing the unitarity of CKM quark mixing matrix. All these results can be tested in the future experiments at the LHC.     

Single-photon laser spectroscopy of cold antiprotonic helium

Some laser spectroscopy experiments carried out by the Atomic Spectroscopy and Collisions Using Slow Antiprotons (ASACUSA) collaboration to measure the single-photon transition frequencies of antiprotonic helium (\(\overline {p}\text {He}^{+}\equiv \overline {p}+\text {He}^{2+}+e^{-}\)) atoms are reviewed. The \(\overline {p}\text {He}^{+}\) were cooled to temperature T =?1.5–1.7 K by buffer-gas cooling in a cryogenic gas target, thus reducing the thermal Doppler width in the single-photon resonance lines. The antiproton-to-electron mass ratio was determined as \(M_{\overline {p}}/m_{e}=?1836.1526734(15)\) by comparisons with the results of three-body quantum electrodynamics calculations. This agreed with the known proton-to-electron mass ratio.     

Study of the weak annihilation contributions in charmless $$\varvec{B_s\rightarrow VV}$$ decays

In this paper, in order to probe the spectator-scattering and weak annihilation contributions in charmless \(B_s\rightarrow VV\) (where V stands for a light vector meson) decays, we perform the \(\chi ^2\)-analyses for the endpoint parameters within the QCD factorization framework, under the constraints from the measured \(\bar{B}_{s}\rightarrow \) \(\rho ^0\phi \), \(\phi K^{*0}\), \(\phi \phi \) and \(K^{*0}\bar{K}^{*0}\) decays. The fitted results indicate that the endpoint parameters in the factorizable and nonfactorizable annihilation topologies are non-universal, which is also favored by the charmless \(B\rightarrow PP\) and PV (where P stands for a light pseudo-scalar meson) decays observed in previous work. Moreover, the abnormal polarization fractions \(f_{L,\bot }(\bar{B}_{s}\rightarrow K^{*0}\bar{K}^{*0})=(20.1\pm 7.0)\%,(58.4\pm 8.5)\%\) measured by the LHCb collaboration can be reconciled through the weak annihilation corrections. However, the branching ratio of \(\bar{B}_{s}\rightarrow \phi K^{*0}\) decay exhibits a tension between the data and theoretical result, which dominates the contributions to \(\chi _\mathrm{min}^2\) in the fits. Using the fitted endpoint parameters, we update the theoretical results for the charmless \(B_s\rightarrow VV\) decays, which will be further tested by the LHCb and Belle-II experiments in the near future.     

Inverse Scattering at Fixed Energy on Surfaces with Euclidean Ends

On a fixed Riemann surface (M ₀, g ₀) with N Euclidean ends and genus g, we show that, under a topological condition, the scattering matrix S _V (λ) at frequency λ > 0 for the operator Δ+V determines the potential V if \({V\in C^{1,\alpha}(M_0)\cap e^{-\gamma d(\cdot,z_0)^j}L^\infty(M_0)}\) for all γ > 0 and for some \({j\in\{1,2\}}\) , where d(z, z ₀) denotes the distance from z to a fixed point \({z_0\in M_0}\) . The topological condition is given by \({N\geq \max(2g+1,2)}\) for j = 1 and by N ≥ g + 1 if j = 2. In \({\mathbb {R}^2}\) this implies that the operator S _V (λ) determines any C ^{1, α} potential V such that \({V(z)=O(e^{-\gamma|z|^2})}\) for all γ > 0.     

Analysis of charmless two-body <Emphasis Type="Italic">B</Emphasis> decays in factorization-assisted topological-amplitude approach

We analyze charmless two-body non-leptonic B decays \(B \rightarrow PP, PV\) under the framework of a factorization-assisted topological-amplitude approach, where P(V) denotes a light pseudoscalar (vector) meson. Compared with the conventional flavor diagram approach, we consider the flavor SU(3) breaking effect assisted by a factorization hypothesis for topological diagram amplitudes of different decay modes, factorizing out the corresponding decay constants and form factors. The non-perturbative parameters of topology diagram magnitudes \(\chi \) and the strong phase \(\phi \) are universal; they can be extracted by \(\chi ^2\) fit from current abundant experimental data of charmless Bdecays. The number of free parameters and the \(\chi ^2\) per degree of freedom are both reduced compared with previous analyses. With these best fitted parameters, we predict branching fractions and CP asymmetry parameters of nearly 100 \(B_{u,d}\) and \(B_s\) decay modes. The long-standing \(\pi \pi \) and \(\pi K\)-CP puzzles are solved simultaneously.     

Parabolic Presentations of the Super Yangian {Y(\mathfrak{gl}_{M|N})} Associated with Arbitrary 01-Sequences

Let μ be an arbitrary composition of M + N and let \({\mathfrak{s}}\) be an arbitrary \({0^{M}1^{N}}\)- sequence. A new presentation, depending on \({\mu \rm and \mathfrak{s}}\), of the super Yangian Y_M|N associated to the general linear Lie superalgebra \({\mathfrak{gl}_{M|N}}\) is obtained.     

Spectral Deformation for Two-Body Dispersive Systems with e.g. the Yukawa Potential

We find an explicit closed formula for the k’th iterated commutator \({\text{ad}_{A}^{k}}(H_{V}(\xi ))\) of arbitrary order k ? 1 between a Hamiltonian \(H_{V}(\xi )=M_{\omega _{\xi }}+S_{\check V}\) and a conjugate operator \(A=\frac{\mathfrak{i}}{2}(v_{\xi}\cdot\nabla+\nabla\cdot v_{\xi})\), where \(M_{\omega _{\xi }}\) is the operator of multiplication with the real analytic function ω _ξ which depends real analytically on the parameter ξ, and the operator \(S_{\check V}\) is the operator of convolution with the (sufficiently nice) function \(\check V\), and v _ξ is some vector field determined by ω _ξ . Under certain assumptions, which are satisfied for the Yukawa potential, we then prove estimates of the form \(\| {{\text{ad}_{A}^{k}}(H_{V}(\xi ))(H_{0}(\xi )+\mathfrak{i} )}\|\leqslant C_{\xi }^{k}k!\) where C _ξ is some constant which depends continuously on ξ. The Hamiltonian is the fixed total momentum fiber Hamiltonian of an abstract two-body dispersive system and the work is inspired by a recent result [3] which, under conditions including estimates of the mentioned type, opens up for spectral deformation and analytic perturbation theory of embedded eigenvalues of finite multiplicity.     

ψ(4040) and ψ(4160) Decays into the Dd± Ds∓$ D_{d}^{\pm } D_{s}^{\mp }$ Pair and the S- D Mixing Effects

The ψ(4040) and ψ(4160) →\(D_{d}^{\pm }D_{s}^{\mp }\) decays are studied with the perturbative QCD approach phenomenologically. It is found that branching ratios for these decays are insensitive to the S-D mixing angle ?? ∈ [?30^°,30^°], and too tiny to be measured in the near future experiments.     

A Note on Quantum Coherence

In this paper, we discuss the coherence of the reduced state in system H _A ?H _B under taking different quantum operations acting on subsystem H _B . Firstly, we show that for a pure bipartite state, the coherence of the final subsystem H _A under the sum of two orthonormal rank 1 projections acting on H _B is less than or equal to the sum of the coherence of the state after two orthonormal projections acting on H _B , respectively. Secondly, we obtain that the coherence of reduced state in subsystem H _A under random unitary channel \({\Phi }(\rho )={\sum }_{s}\lambda _{s}U_{s}\rho U_{s}^{\ast }\) acting on H _B , is equal to the coherence of the state after each operation \({\Phi }_{s}(\rho )=\lambda _{s}U_{s}\rho U_{s}^{\ast }\) acting on H _B for every s. In addition, for general quantum operation \({\Phi }(\rho )={\sum }_{s}F_{s}\rho F_{s}^{\ast }\) on H _B , we get the relation

$$ C\left (\left ((I\otimes {\Phi })\rho ^{AB}\right )^{A}\right )\leq \sum \limits _{s}C\left (\left ((I\otimes {\Phi }_{s})\rho ^{AB}\right )^{A}\right ). $$

     

Ground State Energy of the One-Dimensional Discrete Random Schrödinger Operator with Bernoulli Potential

In this paper we show the that the ground state energy of the one-dimensional discrete random Schrödinger operator with Bernoulli potential is controlled asymptotically as the system size N goes to infinity by the random variable ? _N , the length the longest consecutive sequence of sites on the lattice with potential equal to zero. Specifically, we will show that for almost every realization of the potential the ground state energy behaves asymptotically as \({\frac{\pi^{2}}{(\ell_{N} +1)^{2}}} \) in the sense that the ratio of the quantities goes to one.     

Four-Leptonic Decays of Charged and Neutral <Emphasis Type="Italic">B</Emphasis> Mesons within the Standard Model

The branching ratios and differential distributions for the four-leptonic decays \({B^ - } \to {\mu ^ + }{\mu ^ - }{\bar v_e}{e^ - }\), \({B^ - } \to {e^ + }{e^ - }{\bar v_\mu }{\mu ^ - }\), and \({B^ - } \to {\mu ^ + }{\bar v_\mu }{\mu ^ - }{\mu ^ - }\) are calculated within the Standard Model. The branching ratios for the rare decays B_d,s → e⁺e^?μ⁺μ^? and B_d,s → μ⁺μ^?μ⁺μ^? are estimated. Methods for testing the lepton universality in rare multileptonic decays of charged and neutral B mesons are proposed.     

Determinations of $$|V_{cb}|$$ and $$|V_{ub}|$$|Vub| from baryonic $$\Lambda _b$$Λb decays

We present the first attempt to extract \(|V_{cb}|\) from the \(\Lambda _b\rightarrow \Lambda _c^+\ell \bar{\nu }_\ell \) decay without relying on \(|V_{ub}|\) inputs from the B meson decays. Meanwhile, the hadronic \(\Lambda _b\rightarrow \Lambda _c M_{(c)}\) decays with \(M=(\pi ^-,K^-)\) and \(M_c=(D^-,D^-_s)\) measured with high precisions are involved in the extraction. Explicitly, we find that \(|V_{cb}|=(44.6\pm 3.2)\times 10^{-3}\), agreeing with the value of \((42.11\pm 0.74)\times 10^{-3}\) from the inclusive \(B\rightarrow X_c\ell \bar{\nu }_\ell \) decays. Furthermore, based on the most recent ratio of \(|V_{ub}|/|V_{cb}|\) from the exclusive modes, we obtain \(|V_{ub}|=(4.3\pm 0.4)\times 10^{-3}\), which is close to the value of \((4.49\pm 0.24)\times 10^{-3}\) from the inclusive \(B\rightarrow X_u\ell \bar{\nu }_\ell \) decays. We conclude that our determinations of \(|V_{cb}|\) and \(|V_{ub}|\) favor the corresponding inclusive extractions in the B decays.     

Polarized angular distributions in the decays of the singlet D2 state of charmonium originating from $\bar{p}p$ collisions

Using the helicity formalism, we calculate the combined angular distribution function of the neutral pion (π ⁰) and the polarized electron (e ^?) and photon (γ) produced in the triple cascade process \(\bar{p}+p\rightarrow{}^{1}D_{2}\rightarrow{}^{1}P_{1}+\gamma\rightarrow(\psi +\pi^{0})+\gamma \rightarrow(e^{-}+e^{+})+\pi^{0}+\gamma\), when \(\bar{p}\) and p are unpolarized. We also present the partially integrated angular distribution functions in three different cases where the combined angular distribution function of the three particles is integrated over the direction of one of the particles. Our results show that by measuring the two-particle angular distribution of the electron and the photon with the polarization of either particle, one can determine the relative magnitudes as well as the relative phases of all the angular-momentum helicity amplitudes in the two decay processes ¹ D ₂→¹ P ₁+γ and ¹ P ₁→ψ+π ⁰.     

Infinitive Operator-Sum Representation for Damping in a Squeezed Heat Reservoir via the Thermo Entangled State Approach

Using the thermo entangled state approach, we successfully solve the master equation of a damped harmonic oscillator affected by a linear resonance force in a squeezed heat reservoir, and obtain the analytical evolution formula for the density operator in the infinitive Kraus operator-sum representation. Interestingly, the Kraus operators M_l,m,n,r and \(\mathfrak {M}_{l,m,n,r}^{\dag }\) are not Hermite conjugate, but they are still trace-preserving quantum operations because of the normalization condition. We also investigate the evolution for an initial coherent state for damping in a squeezed heat reservoir, which shows that the initial coherent state decays to a complex mixed state as a result of damping and thermal noise.