Projected Shell Model Analysis of Multi—Quasiparticle High—K Isomers in ^174Hf

Multi-quasiparticle high-K states in ^174Hf are studied in the framework of the projected shell model.The calculation reproduces well the observed ground-state band as well as most of the two-and four-quasiparticle rotational bands.Some as yet unobserved high-K isomeric states in ^174Hf are predicted.Possible reasons for the existing discrepancies between calculation and experiment are discussed.It is suggested that the projected shell model may be a useful method for studying multi-quasiparticle high-K isomers and the K-mixing phenomenon in heavy deformed nuclei.     

Exotic ■_s~((*))D~((*)) molecular states and sc■ tetraquark states with J~P=0~+,1~+,2~+

We have calculated the mass spectra for the ■_s~((*))D~((*)) molecular states and sc■ tetraquark states with J~P=0~+,1~+,2~+.The masses of the axial-vector ■_sD~*,■_s~*D molecular states and ■ tetraquark states are predicted to be approximately 3.98 GeV,in good agreement with the mass of Z_(cs)(3985)~- from BESⅢ.In both the molecular and diquark-antidiquark scenarios,our results suggest that there may exist two almost degenerate states,as the strange partners of X(3872) and Z_c(3900).We propose to carefully examine Z_(cs)(3985) in future experiments to verify this.One may also search for more hidden-charm four-quark states with strangeness in not only the open-charm ■_s~((*))D~((*)) channels but also the hidden-charm channels η_cK/K~*,J/ψK/K~*.     

Molecular picture for X_0(2900) and X_1(2900)

Inspired by the newly observed X_0(2900) and X_1(2900) states at LHCb,the K~*■ and K■ interactions are studied in the quasipotential Bethe-Salpeter equation approach combined with the one-bo son-exchange model.The bound and virtual states from the interactions are searched for as poles in the complex energy plane of scattering amplitude.A bound state with I(J~P)=0(0~+) and a virtual state with 0(1~-) are produced from the K~*■ interaction and K■ interaction,and can be related to the X_0(2900) and X_1(2900) observed at LHCb,respectively.A bound state with I(J~P)=0(1~+) and a virtual state with I(J~P)=0(2~+) are also predicted from the K~*■ interaction,with the same α value,to reproduce the X_(0,1)(2900),which can be searched for in future experiments.     

Quasi Three-Body Decay of D Meson

The aim of this work is to provide a phenomenological analysis of the contribution of D~0 meson to K*(892)~0π~+π~-(K*(892)~0-→π~+K~-), K~-π~+ω(ω-→π~+π~-π~0) and K~-π~+?(?(1020)-→ K~+K~-) quasi-three-body decays. The analysis of mentioned multi-body decays is such as to factorize into the three-body decay and several channels observed. Hadronic three-body decays receive both resonant and non-resonant contribution. Based on the factorization method, there are tree and emission annihilation diagrams for these decay modes. In the case of D~0 to vector pseudoscalar states appeared in factored terms, the matrix elements of the vector and axial vector currents between the D~0 and PV mesons can be computed by using D~(*+)pole. Considering the non-resonant and resonant amplitude in our computation,the theoretical values of the branching ratio are(9.78 ± 0.46) × 10~(-3),(2.74 ± 0.17) × 10~(-2), and(3.53 ± 0.23) × 10~(-5), while the experimental results of them are(9.9 ±2.3) × 10~(-3),(2.7 ± 0.5) × 10~(-2), and(4 ± 1.7) × 10~(-5) respectively. Comparing computational analysis values with experimental values show that our results are in approximately agreement with them.     

Cross sections for inelastic 2-to-2 meson-meson scattering in hadronic matter

With quark-antiquark annihilation and creation in the first Born approximation, we study the reactions:K■→K■~*,K■→K~*■, πK→πK~*, πK→ρK, ππ→ K■~*, ππ→K~*■,ππ→K~*■~*,πρ→K■, πρ→K~*■~*,ρρ→K~*■~*, K■~*→ρρ, and K~*■→pp. Unpolarized cross sections for the reactions are obtained from transition amplitudes that are composed of mesonic quark-antiquark relative-motion wave functions and the transition potential for quark-antiquark annihilation and creation. Using a quark-antiquark potential that is equivalent to the transition potential, we prove that the total spin of the two final mesons may not be equal to the total spin of the two initial mesons. Based on flavor matrix elements, cross sections for some isospin channels of reactions can be obtained from other isospin channels of the reactions. Remarkable temperature dependence of the cross sections was observed.     

Beyond mean-field approach for pear-shaped hypernuclei

We develop both relativistic mean field and beyond approaches for hypernuclei with possible quadrupole-octupole deformation or pear-like shapes based on relativistic point-coupling energy density functionals. The symmetries broken in the mean-field states are recovered with parity, particle-number and angular momentum projections. We take_Λ~(21)Ne as an example to illustrate the method, where the Λ hyperon is put on one of the two lowest-energy orbits(labeled as Λ_s, Λ_p), respectively. We find that the Λ hyperon in both cases disfavors the formation of a reflection-asymmetric molecular-like~(16)O+α structure in~(20)Ne, which is consistent with the Nilsson diagram for the hyperon in(β_2, β_3) deformation plane. In particular, we show that the negative-parity states with the configuration~(20)Ne(K~π= 0~-)  Λ_s are close in energy to those with the configuration~(20)Ne(K~π= 0~+)Λ_p, even though they have very different structures. The Λ_s(Λ_p) becomes more and more concentrated around the bottom(top) of the"pear" with the increase of octupole deformation.     

Phenomenological studies on B~0 → [K~-π~+]_(S/V)[π~+π~-]_(V/S) → K~-π~+π~+π~- decay

Within the quasi-two-body decay model,we study the localized CP violation and branching fraction of the four-body decay B~0→[K~-π~+]_(s/V)[π~+π~-]_(V/)S→K-π~+π~-π~+ when the K~-π~+and π~-π~+ pair invariant masses are0.35 m(K~-π~+)2.04 GeV and 0 mπ~-π~+1.06 GeV,with the pairs being dominated by the K_0~*(700)~0,K~*(892)~0,K~*(1410)~0,K_0~*(1430) and K~*(1680)~0,and fo(500),ρ~0(770),ω(782) and fo(980) resonances,respectively.When dealing with the dynamical functions of these resonances,fo(500),ρ~0(770),fo(980) and K_0~*(1430) are modeled with the Bugg model,Gounaris-Sakurai function,Flatte formalism and LASS lineshape,respectively,while the others are described by the relativistic Breit-Wigner function.Adopting the end point divergence parameters ρA ∈[0,0.5] andΦ_A∈[0,2π],our predicted results are F_(CP)(B~0→K~-π~+π~+π~-)∈[-0.365,0.447] and B(B~0→K-π~+π~+π~-)∈[6.11,185.32] x 10~(-8),based on the hypothetical qq structures for the scalar mesons in the QCD factorization approach.Meanwhile,we calculate the CP violating asymmetries and branching fractions of the two-body decays B~0→SV(VS) and all the individual four-body decays B~0→SV(VS)→K~-π~+π~-π~+,respectively.Our theoretical results for the two-body decays B~0→K~*(892)~0 fo(980),B~0→K_0~*(1430)~0ω(782),B~0→K~*(892)~0 f~0(980),B~0→K_0~*(1430)~0ρ,and B~0→(1430)~0ω are consistent with the available experimental data,with the remaining predictions await testing in future high precision experiments.     

Molecular opacities of low-lying states of oxygen molecule

The X~3∑_g~-,A'~3△_u,A~3∑_u~+,1~3Π_g,and B~3∑_u~-electronic states of oxygen molecule(O_2) are calculated by the multiconfiguration self-consisted filed(MRCI)+Q method with the scalar relativistic correction and core-valence correlation correction.The obtained spectroscopic constants of the low-lying bound states are in excellent agreement with measurements.Based on the accurately calculated structure parameters,the opacities of the oxygen molecule at the temperatures of 1000 K,2000 K,2500 K,and 5000 K under a pressure of 100 atm(1 atm=1.01325×10~5 Pa) and the partition functions between 10 K and 104 K are obtained.It is found that with the increase of temperature,the opacities for transitions in a long wavelength range are enlarged because of the larger population on excited electronic states at the higher temperatures.     

Radiative lifetimes of Rydberg 6pnd J=2 states of Pb I by multichannel quantum defect theory

Energy levels of the odd-parity 6pnd J=2 Rydberg states of Pb I are analysed by the multichannel quantum defect theory (MQDT) in the frame of a five-channel three-limit calculation model. With optimal MQDT parameters, channel admixture coefficients are obtained and used to calculate the theoretical lifetimes of the levels by comparing to the previously measured lifetimes. The predicted lifetimes for higher-lying Rydberg states are given and discussed. These predicted lifetimes are very different from those obtained by the four-channel two-limit model pl:eviously used, which means that introduction of the additional interacting channel is important for studying the 6pnd J=2 Rydberg states of Pb I.     

D~0-~0 mixing sensitivity estimation at Belle II in wrong-sign decays D~0→K~+π~-π~0 via time-dependent amplitude analysis

The sensitivity of the D~0-~0 mixing parameters x and y is estimated in the wrong-sign decay D~0→K~+π~-π~0 by time-dependent amplitude analysis. The resolution of the D~0 lifetime is essential in time-dependent Dalitz analyses. The Belle II detector, which aims to collect a total integrated luminosity of 50 ab~(-1) of data, has σ = 140 fs in Monte Carlo studies, a factor of two improvement over that of Belle and Ba Bar, so the produced Dalitz signal Monte Carlo samples are smeared with this resolution. Then a time-dependent Dalitz plot fitting is performed on these smeared samples, and the sensitivity of D~0-~0mixing parameters are σ_x = 0.057% and σ_y = 0.049%. These are about an order of magnitude improvement on current experimental results, without considering background effects.     

High-K isomers as probes of octupole collectivity in heavy nuclei

The influence of the octupole deformation on the structure of high-K isomeric states in the region of heavy even–even actinide nuclei is studied through a reflection asymmetric deformed shell model (DSM). Two-quasiparticle states with high-K values are constructed by taking into account the pairing effect through a DSM + BCS procedure with constant pairing interaction. The behaviour of two-quasiparticle energies and magnetic dipole moments of Kπ=⁶⁺$K^{\pi }=6^{+}$, ⁶⁻$6^{-}$ and ⁸⁻$8^{-}$ configurations, applicable to mass numbers in the range A=234–252$A=234\text{–}252$, was examined over a wide range of quadrupole and octupole deformations. A pronounced sensitivity of the magnetic moments to the octupole deformation is found. The result suggests a possibly important role for high-K isomers in determining the degree of octupole deformation in heavy actinide nuclei.     

Energy levels of the nucleus 250Bk from residual interaction studies

The bandhead energies of twenty two-quasiparticle states expected to occur in the low-energy excitation spectrum of the doubly odd nucleus ²⁵⁰Bk are calculated using a zero-range residual interaction and the results are compared with the available experimental information. Configuration assignments to nine intrinsic states reported in earlier studies are confirmed. Our calculations support the excitation energy of 115 keV for the K^π = 3⁺ state and also the characterisation of the 317 keV 5⁺ state as the K^π = 5⁺ bandhead. In addition, we suggest acceptable two-particle configurations for the 175 keV 1⁺ state and the 216 keV 0⁺ state. The expected location of eight as yet unobserved two-quasiparticle states is predicted.     

Study of X(5568) in a unitary coupled-channel approximation of BK and B_sπ

The potential of the B meson and the pseudoscalar meson is constructed up to the next-to-leading order Lagrangian, and then the BK and B_sπ interaction is studied in the unitary coupled-channel approximation. A resonant state with a mass about 5568 MeV and J~P= 0~+is generated dynamically, which can be associated with the X(5568) state announced by the D0 Collaboration recently. The mass and the decay width of this resonant state depend on the regularization scale in the dimensional regularization scheme, or the maximum momentum in the momentum cutoff regularization scheme. The scattering amplitude of the vector B meson and the pseudoscalar meson is calculated, and an axial-vector state with a mass near 5620 MeV and J~P= 1~+is produced. Their partners in the charm sector are also discussed.     

A spin-parity analysis of the K+K+K− system produced in the reaction K+p → K+K+K−p

We present the first spin-parity analysis of the K⁺K⁺K^?) system produced in the reaction K⁺p → K⁺K⁺K^?p, and show that the general features of this system resemble those of the (ππ⁺π^?) and Kπ⁺π^?) systems produced in the reactions π(K)p → π(K)π⁺π^?p. There is a low mass enhancement, (47 ± 11)% of which corresponds to 1⁺ states decaying to Kø. At higher (K⁺K⁺K^?) masses 2^? → Kf′ becomes increasingly significant and at all masses there is a 0^? contribution of roughly 30%.     

M1 and E2 band structures in the Sn-Xe-Ba region

In the present talk I will discuss some ‘rare’ aspects of the E2 band structures and the novel features concerning the dipole bands in this mass region. Reliable and accurate lifetimes have been measured using coincidence recoil distance method. The results of ^129,130Ba will be discussed. In contrast to the predictions of the tilted axis cranking model, the dipole bands in Sb-Xe-Ba nuclei can be nicely described as high-K prolate bands. New data from multi-detector arrays has established extended bands structure, their decay to low lying states have been established and the angular correlation supports the predominant, ΔI=1 character. Finally the sensitive measures, i.e. B(M1) rates of the tilted axis model are compared with the high-K formula based on 1-dim cranking model.     

A partial-wave analysis of the reaction π−p → K+K−n measured on a polarized target at ∼18 GeV/c

The reaction π^?p→K⁺K^?n has been studied on a hydrogen target (27 000 events) at 18.4 GeV/c and on a polarized target (54 000 events) at 17.2 GeV/c. A combination of results of both experiments allows a partial-wave analysis of the K⁺K^? system between 1.1 and 1.74 GeV mass without any model assumptions. In general our fits yield unique solutions. Using results of our previous analysis of π⁺π^? final states and assuming the dominance of the positive G-parity states in the K⁺K^? system, the branching ratios $\text{BR}\text{(}\text{K}\text{K}\text{/ππ)}$ of partial waves into $\text{K}\text{K}\text{and}\text{ππ}$ are determined. The S-wave appears to be mainly a broad ε (1300) with $\text{BR}\text{(}\text{K K}\text{/ππ) = 0.068}{}_{\mathrm{?0.021}}{}^{\mathrm{+0.017}}$. The weak P-wave can be described by a tail of the $\text{?(770)}\text{with BR}\text{(}\text{K K}\text{/ππ) = 0.081}{}_{\mathrm{?0.025}}{}^{\mathrm{+0.029}}$. The D-wave is interpreted in terms of a superposition of f(1270) + A₂(1310) + f′(1515) resonances. The fit yields $\text{BR}\text{(}\text{K K}\text{/ππ) = 0.069}{}_{\mathrm{?0.031}}{}^{\mathrm{+0.023}}$ for the f(1270) and BR(ππ/all) = 0.027_?0.013^+0.071 for the f′(1515). The F-wave shows the g(1690) meson with $\text{BR}\text{(}\text{K K}\text{/ππ) = 0.191}{}_{\mathrm{?0.037}}{}^{\mathrm{+0.040}}$. All the above values refer to the t bin between 0.01 and 0.20 (GeV/c)². Some results are also given for the high-t region.     

Isomeric states in180Os

Two new isomers have been observed in¹⁸⁰Os. A high-K isomer withI, K ≧20 and a half-life ofT _1/2=12+4 ns have been established. It deexcites via two transitions into the 18⁺ level of the yrare band indicating an unusually smallK-hindrance factor. Evidence for an isomer withI, K>16 and a half-life ofT _1/2=41±10 ns was found. A half-life of 17±3 ns was measured for the previously known 7^? state at 1862 keV. The decay scheme of the previously known 7^? isomer at 1928 keV has been extended and a revised version is presented.     

Study of the missing-mass spectra in the reactions π−d → K+ + MM and K−d → π+ + MM at 1.4 GeV/c to search for strange dibaryon states

The reactions π^?d → K⁺ + MM and K^?d → π⁺ + MM have been studied at 1.4 GeV/c to search for strange dibaryon states with quantum numbers Q = ?1, and S = ?1. No structures are found which could indicate the production of such states and upper limits for the cross sections are established.     

Theoretical determination of the K2 electronic structure

A theoretical study of the electronic structure of K₂⁺ is presented. Potential energy curves for the ground and various electronic excited states have been computed in the framework of a model potential method over a wide range of internuclear distances. Spectroscopic constants for the lowest short-range bound states have been determined and they are compared with available experimental and theoretical values. Long-range structures (wells and humps) have been also predicted, some of which being described from a long-range model.     

Lepton number violation in D meson decay

The lepton number violation(LNV) process can be induced by introducing a fourth generation heavy Majorana neutrino,which is coupled to the charged leptons of the Standard Model(SM). There have been many previous studies on the leptonic number violating decay processes with this mechanism. We follow the trend to study the process: D→Kllπ with the same-sign dilepton final states. We restrict ourselves to certain neutrino mass regions,in which the heavy neutrino could be on-shell and the dominant contribution to the branching fraction comes from the resonance enhanced effect. Applying the narrow width approximation(NWA),we found that the upper limit for the branching fractions for D0→ K-l+l+π-are generally at the order of 10-12 to 10-9,if we take the most stringent upper limit bound currently available in the literature for the mixing matrix elements. We also provide the constraints,which is competitive compared to the LNV B decays,on the mixing matrix element |VeN|2 based on the upper limit of D0→ K-e+e+π-estimated from the Monte-Carlo(MC) study at BESⅢ. Although the constraints are worse than the ones from(0νββ) decay in the literature,the future experiment at the charm factory may yield more stringent constraints.