Weak Decays Research Articles

Feasibility of the experimental study of D_{s}^{*}rightarrow {phi }{pi } decay

The current knowledge on the D_{s}^{*} meson are very limited. Besides the dominant electromagnetic decays, the D_{s}^{*} weak decays are legal and offer the valuable opportunities to explore the wanted D_{s}^{*} meson. In this paper, the D_{s}^{*}rightarrow {phi }{pi } decay was studied with the factorization approach. It is found that the branching ratio {mathcal {B}}(D_{s}^{*}rightarrow {phi }{pi }){sim }{mathcal {O}}(10^{-7}), which corresponds to several thousands of events at the e^{+}e^{-} collider experiments including STCF, SuperKEKB, CEPC and FCC-ee, and several millions of events at the hadron collider experiments, such as LHCb@HL-LHC. It is feasible to experimentally study the D_{s}^{*}rightarrow {phi }{pi } weak decay in the future, even considering the identification efficiency.

On the stability of the open-string QED neutron and dark matter

We study the stability of a hypothetical QED neutron, which consists of a color-singlet system of two $d$ quarks and a $u$ quark interacting with the QED interaction. As a quark cannot be isolated, the intrinsic motion of the three quarks in the lowest-energy state may lie predominantly in 1+1 dimensions, as in a $d$-$u$-$d$ open string. The attractive $d$-$u$ and $u$-$d$ QED interactions may overcome the weaker repulsive $d$-$d$ QED interaction to bind the three quarks together. We examine the QED neutron in a phenomenological three-body problem in 1+1 dimensions with an effective interaction extracted from Schwinger's exact QED solution in 1+1 dimensions. The phenomenological model in a variational calculation yields a stable QED neutron at 44.5 MeV. The analogous QED proton with two $u$ quarks and a $d$ quark has been found to be too repulsive to be stable and does not have a bound or continuum state, onto which the QED neutron can decay via the weak interaction. Consequently, the QED neutron is stable against the weak decay, has a long lifetime, and is in fact a QED dark neutron. It may be produced following the deconfinement-to-confinement phase transition of the quark gluon plasma in high-energy heavy-ion collisions. Because of the long lifetime of the QED dark neutron, self-gravitating assemblies of QED dark neutrons or dark antineutrons may be good candidates for a part of the primordial dark matter produced during the phase transition of the quark gluon plasma in the evolution of the early Universe.

Searching systematics for nonfactorizable contributions to and hadronic decays

The two-body weak decays / and are examined using isospin analysis to study nonfactorizable contributions. After determining strong interaction phases and obtaining factorizable contributions from spectator-quark diagrams for N c =3, we determine nonfactorizable isospin amplitudes from the experimental data for these modes. Our results support the universality of the ratio of nonfactorizable isospin reduced amplitudes for these decays within experimental errors. To demonstrate that these systematics are not coincidental, we also plot our results w. r. t. this ratio.

Production characteristics of light (anti-)nuclei from (anti-)nucleon coalescence in heavy ion collisions at energies employed at the RHIC beam energy scan

With the kinetic freeze-out nucleons and antinucleons obtained from the quark combination model, we study the production of light nuclei and antinuclei in the (anti-)nucleon coalescence mechanism in relativistic heavy ion collisions. We derive analytic formulas of the momentum distributions of different light nuclei and apply them to compute transverse momentum ($p_T$) spectra of (anti-)deuterons ($d$, $\bar d$) and (anti-)tritons ($t$, $\bar t$) in Au-Au collisions at $\sqrt{s_{NN}}=$7.7, 11.5, 19.6, 27, 39, 54.4 GeV. We find that the experimental data available for these $p_T$ spectra can be well reproduced. We further study the yields and yield ratios of different light (anti-)nuclei and naturally explain their interesting behaviors as a function of the collision energy. We especially point out that the multi-particle yield ratio $tp/d^2$ should be carefully corrected from hyperon weak decays for protons to probe the production characteristics of light nuclei. All of our results show that the coalescence mechanism for (anti-)nucleons plays a dominant role for the production of light nuclei and antinuclei at the RHIC beam energy scan energies.

Heavy-flavor-conserving hadronic weak decays of charmed and bottom baryons

Three decades ago, heavy-flavor-conserving (HFC) weak decays of heavy baryons such as ${\mathrm{\ensuremath{\Xi}}}_{Q}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{Q}\ensuremath{\pi}$ and ${\mathrm{\ensuremath{\Omega}}}_{Q}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{Q}\ensuremath{\pi}$ for $Q=c$, $b$ had been studied within the framework that incorporates both heavy quark and chiral symmetries. It was pointed out that if the heavy quark in the HFC process behaves as a spectator, then the $P$-wave amplitude of ${\mathcal{B}}_{\overline{3}}\ensuremath{\rightarrow}{\mathcal{B}}_{\overline{3}}+\ensuremath{\pi}$, with ${\mathcal{B}}_{\overline{3}}$ being an antitriplet heavy baryon, will vanish in the heavy quark limit. Indeed, this is the case for ${\mathrm{\ensuremath{\Xi}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\pi}$ decays. For ${\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}\ensuremath{\pi}$ decays, they receive additional nonspectator contributions arising from the $W$-exchange diagrams through the $cs\ensuremath{\rightarrow}dc$ transition. Spectator and nonspectator $W$-exchange contributions to the $S$-wave amplitude of ${\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}\ensuremath{\pi}$ are destructive, rendering the $S$-wave contribution even smaller. However, the nonspectator effect on the $P$-wave amplitude was overlooked in all the previous model calculations until a very recent investigation within the framework of a constituent quark model in which the parity-conserving pole terms were found to be dominant in ${\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}\ensuremath{\pi}$ decays. Since the pion produced in the HFC process is soft, we apply current algebra to study both $S$- and $P$-wave amplitudes and employ the bag and diquark models to estimate the matrix elements of four-quark operators. We confirm that ${\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}\ensuremath{\pi}$ decays are indeed dominated by the parity-conserving transition induced from nonspectator $W$-exchange and that they receive largest contributions from the intermediate ${\mathrm{\ensuremath{\Sigma}}}_{c}$ pole terms. We also show that the $S$-wave of ${\mathrm{\ensuremath{\Omega}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{b}\ensuremath{\pi}$ decays vanishes in the heavy quark limit, while ${\mathrm{\ensuremath{\Omega}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\pi}$ receive additional $W$-exchange contributions via $cs\ensuremath{\rightarrow}dc$ transition. The $P$-wave contribution to ${\mathrm{\ensuremath{\Omega}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\pi}$ is enhanced by the ${{\mathrm{\ensuremath{\Xi}}}^{\ensuremath{'}}}_{c}$ pole, though it is not so dramatic as in the case of ${\mathrm{\ensuremath{\Xi}}}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}\ensuremath{\pi}$. The asymmetry parameter $\ensuremath{\alpha}$ is found to be positive, of order 0.70 and 0.74 for ${\mathrm{\ensuremath{\Xi}}}_{c}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${\mathrm{\ensuremath{\Xi}}}_{c}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{+}{\ensuremath{\pi}}^{0}$, respectively. The predicted branching fraction is of order $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ for ${\mathrm{\ensuremath{\Omega}}}_{c}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ for ${\mathrm{\ensuremath{\Omega}}}_{c}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{0}{\ensuremath{\pi}}^{0}$ both with the asymmetry parameter close to $\ensuremath{-}1$.

Prospects for studies of {D^{*0}} rightarrow {mu ^+}{mu ^-} and {B^{{*0}}_{(s)}}rightarrow {mu ^+}{mu ^-} decays

Weak decays of the vector {{D} ^*} ^0 and {{B} ^{*0}_{({s})}} mesons to the {mu ^+mu ^-} final state provide novel potential to test the Standard Model of particle physics. Such processes have extremely small branching fractions as the vector mesons are able to decay through electromagnetic and (for the {{D} ^*} ^0 meson) strong interactions. Nonetheless, the production of copious quantities of these particles in LHC collisions, and the ability to exploit experimental techniques that can suppress background to low levels, provides good potential to reach interesting sensitivity. The possibility to reconstruct these processes as part of the decay chain of {{{B} ^-}} or {{B} _{c} ^+} mesons appears particularly attractive due to the clean experimental signature of the displaced vertex. Indeed, published LHCb data on {{{B} ^-}} rightarrow {{pi } ^-} {mu ^+mu ^-} decays already implies a stringent limit on the branching fraction of {{D} ^{*0}} rightarrow {mu ^+mu ^-} . Estimates are made on the achievable sensitivity to {{D} ^{*0}} rightarrow {mu ^+mu ^-} and {{B} ^{*0}_{({s})}} rightarrow {mu ^+mu ^-} decays with the LHCb experiment.

Test of nuclear decay rate variation due to an antineutrino flux

Unexplained variations of the decay rate for weak interaction decays such as $\beta^{\pm}$-decay, electron capture, as well as strong interaction $\alpha$-decay have been reported. Some researcher interpreted these variations as caused by an unexplained fundamental interaction. The purpose of the paper is to review decay rate parameter variations experiments and place them into a common comparable context and to make decay parameter measurements at the level of 10$^{-5}$ in the presences of an antineutrino flux, $\sim 3 \times10^{12}$ $\overline{\nu} \, cm^{-2} \, sec^{-1}$, 6.5 meters from the High Flux Isotope Reactor(HFIR) reactor core having an on-off cycle time of $\sim$30 days. Two weak interaction decays, one via electron capture and the other via $\beta^-$ decay were selected because the final state and the time reverse state each contain a neutrino and anti-neutrino, covering arguments that the anti-neutrino flux may interact differently or not at all in one of the cases. The experiment searched for variation of the $^{54}_{25}$Mn, e$^-$ capture and $^{137}_{~55}$Cs, $\beta^-$ decay rate parameters. The measured variation in the decay rate parameters are found to be $\delta \lambda/ \lambda = (0.034\pm 1.38)\times 10^{-5}$ for $^{54}_{25}$Mn and $\delta \lambda/ \lambda = (0.67\pm 1.56)\times 10^{-5}$ for $^{137}_{~55}$Cs. These results are consistent with no measurable decay rate parameter variation due to an antineutrino flux, yielding a $68\%$ confidence level upper limit sensitivity for $^{54}_{25}$Mn, $\delta \lambda/ \lambda \leq 1.31\times10^{-5}$ or $\sigma \leq 1.29\times10^{-25}\,cm^{2}$ in cross section and for $^{137}_{~55}$Cs, $\delta \lambda/ \lambda \leq 2.23\times10^{-5}$ or $\sigma \leq 5.69\times10^{-27}\,cm^{2}$. These null or no observable effect measurements places cross-section upper limits $\sim 10^{4}$ times more sensitive than past experiments.

Lifshitz Tails for Random Diagonal Perturbations of Laurent Matrices

We study the Integrated Density of States of one-dimensional random operators acting on $\ell^2(\mathbb Z)$ of the form $T + V_\omega$ where $T$ is a Laurent (also called bi-infinite Toeplitz) matrix and $V_\omega$ is an Anderson potential generated by i.i.d. random variables. We assume that the operator $T$ is associated to a bounded, H\"older-continuous symbol $f$, that attains its minimum at a finite number of points. We allow for $f$ to attain its minima algebraically. The resulting operator $T$ is long-range with weak (algebraic) off-diagonal decay. We prove that this operator exhibits Lifshitz tails at the lower edge of the spectrum with an exponent given by the Integrated Density of States of $T$ at the lower spectral edge. The proof relies on generalizations of Dirichlet-Neumann bracketing to the long-range setting and a generalization of Temple's inequality to degenerate ground state energies.

Pinning down |Delta c|=|Delta u|=1 couplings with rare charm baryon decays

We study the full angular distribution of semileptonic rare charm baryon decays in which the secondary baryon undergoes weak decay with sizable polarization parameter, Xi _c^+rightarrow Sigma ^+,(rightarrow ppi ^0)ell ^+ell ^-, Xi _c^0rightarrow Lambda ^0,(rightarrow p pi ^-)ell ^+ell ^- and Omega _c^0rightarrow Xi ^0,(rightarrow Lambda ^{0} pi ^0)ell ^+ell ^-. Such self-analyzing decay chains allow for seven additional observables compared to three-body decays such as Lambda _c rightarrow p ell ^+ ell ^-, with different sensitivities to the |Delta c|=|Delta u|=1 weak couplings. Opportunities to test the standard model in c rightarrow u transitions with standard model null tests and other angular observables are worked out. We show that a joint model-independent analysis of the leptonic A_{text {FB}}^ell , hadronic A_{text {FB}}^{text {H}}, and combined forward–backward asymmetry A_{text {FB}}^{ell text {H}} together with the fraction of longitudinally produced leptons, F_L, is able to pin down the dipole couplings C_{7},C^prime _{7} and the semileptonic (axial-) vector ones C_{10},C^prime _{9},C^prime _{10}. A_{text {FB}}^{text {H}} is also accessible with dineutrino c rightarrow u nu {bar{nu }} modes and probes right-handed currents.

NLO QCD corrections to inclusive b→cℓν¯ decay spectra up to 1/mQ3

We present analytical results for higher order corrections to the decay spectra of inclusive semileptonic heavy hadron weak decays, using the heavy quark expansion (HQE). We compute analytically the spectrum of the leptonic invariant mass for $B\ensuremath{\rightarrow}{X}_{c}\ensuremath{\ell}\overline{\ensuremath{\nu}}$ up to and including terms of order $1/{m}_{Q}^{3}$ within the HQE at next-to-leading order in ${\ensuremath{\alpha}}_{s}$. The full dependence of the differential rate on the mass of the final-state quark is taken into account. We discuss the implications of our results for the precision determination of the Cabbibo-Kobayashi-Maskawa matrix element $|{V}_{cb}|$.

Lattice dynamics and its effects on magnetocrystalline anisotropy energy of pristine and hole-doped YCo5 from first principles

We study the lattice dynamics effects on the phase stability and magnetocrystalline anisotropy (MCA) energy of CaCu$_5$-type YCo$_5$ at finite temperatures using first-principles calculations based on density functional theory (DFT). Harmonic lattice dynamics (HLD) calculations indicate that YCo$_5$ with 56 full valance electrons is dynamically unstable and this instability can be cured by reducing the number of electrons ($N_e$). Crystal orbital Hamilton population analysis reveals that the observed phonon instability originates from the large population of antibonding states near the Fermi level, which is dominated by the Co atoms in the honeycomb layer. The antibonding state depopulates with decreasing $N_e$, resulting in stable phonons for hole-doped YCo$_5$ with $N_e$ $\leq$ 55. We then evaluate the temperature-dependent MCA energy using both HLD and $ab$ $initio$ molecular dynamics (AIMD) methods. For the pristine YCo$_5$, we observe a very weak temperature decay of the MCA energy, indicating little effect of lattice dynamics. Also, the MCA energies evaluated with AIMD at all target temperatures are larger than that of the static hexagonal lattice at 0 K, which is mainly attributed to the structural distortion driven by soft phonon modes. In the hole-doped YCo$_5$, where the distortion is suppressed, a considerable temperature decay in MCA energy is obtained both in HLD and AIMD methods, showing that lattice dynamics effects on MCA energy are non-negligible.

Sum rule for the partial decay rates of bottom hadrons based on the dynamical supersymmetry of the s¯ quark and the ud diquark

We investigate the weak decays of ${\overline{B}}_{s}^{0}$ and ${\mathrm{\ensuremath{\Lambda}}}_{b}$ to charm hadrons based on the dynamical supersymmetry between the $\overline{s}$ quark and the $ud$ diquark. We derive a new sum rule relating the decay rates of the processes ${\overline{B}}_{s}^{0}\ensuremath{\rightarrow}{D}_{s}^{+}{P}^{\ensuremath{-}}$, ${\overline{B}}_{s}^{0}\ensuremath{\rightarrow}{D}_{s}^{*+}{P}^{\ensuremath{-}}$, and ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}{P}^{\ensuremath{-}}$, where ${P}^{\ensuremath{-}}$ is a negatively charged meson, such as ${\ensuremath{\pi}}^{\ensuremath{-}}$ and ${K}^{\ensuremath{-}}$. It is found that the observed decay rates satisfy the sum rule very well. This implies that the supersymmetry between the $\overline{s}$ quark and the $ud$ diquark is also seen in the wave functions of the heavy hadrons and suggests that the $ud$ diquark can be regarded as a valid effective constituent for heavy hadrons.

Prospects for discovering new physics in charm sector through low-energy scattering processes e−p→e−(μ−)Λc

We investigate the potential for discovering new physics through the low-energy scattering processes $e^-p\to e^-(\mu^-)\Lambda_c$, which could be accessible in the forthcoming $ep$ scattering experiments once adapted to our proposed setups. In the framework of a general low-energy effective Lagrangian, we demonstrate that, compared with the conventional flavor-changing neutral-current weak decays of charmed hadrons and the dilepton productions at high-energy colliders, the low-energy scattering processes can provide more competitive potentials for hunting the underlying new physics. In some specific leptoquark models, we also show that promising event rates can be expected for both the scattering processes, and point out a possible way to distinguish the experimental signals due to the scalar leptoquarks from those of the vector ones.

Study of heavy quark conserving weak decays in the quark model

Within the framework of a constituent quark model, we investigate the heavy quark conserving weak decays of Ξc and Ξb. This process involves elementary transitions of us→du or s→udu¯ with the heavy quark as a spectator, while for the charmed baryon in the initial state it can also occur via cs→dc to conserve the heavy quark flavor in the weak decays. It shows that the heavy quark symmetry (HQS) plays an essential role in the processes where the heavy quark acts as a spectator. For the Ξc decays, the dominance of the pole terms in the parity-conserving transitions is evident. This can naturally explain the sizable branching ratio for Ξc0→Λcπ− as recently reported by LHCb. The same mechanism predicts a large branching ratio for Ξc+→Λcπ0. In contrast, the decays of Ξb will only go through the parity-violating processes because of the HQS. In addition, the branching ratios of the Ξc+→Λcπ0 and Ξb0→Λbπ0 processes are also predicted for the further experimental measurement.

Competition between weak and α -decay modes in superheavy nuclei

The competition between $\ensuremath{\alpha}$- and ${\ensuremath{\beta}}^{+}/\text{EC}$-decay modes is studied systematically in nuclei along the $\ensuremath{\alpha}$-decay chains following the synthesis of superheavy nuclei with $Z=119$ and $Z=120$. A microscopic approach based on deformed self-consistent Hartree-Fock mean-field calculations with Skyrme forces and pairing correlations is used to describe the ${\ensuremath{\beta}}^{+}$ and electron capture weak decays, whereas the $\ensuremath{\alpha}$ decay is estimated from existing phenomenological expressions. It is shown that $\ensuremath{\alpha}$ decay is in most cases the dominant decay mode, but interesting instances are identified where the half-lives are comparable, opening the possibility of new pathways towards more neutron-rich nuclei in this region.

Restudy of the color-allowed two-body nonleptonic decays of bottom baryons Ξb and Ωb supported by hadron spectroscopy

In this work, we calculate the branching ratios of the color-allowed two-body nonleptonic decays of the bottom baryons, which include the ${\mathrm{\ensuremath{\Xi}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Xi}}}_{c}^{(*)}$ and ${\mathrm{\ensuremath{\Omega}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Omega}}}_{c}^{(*)}$ weak transitions by emitting a pseudoscalar meson (${\ensuremath{\pi}}^{\ensuremath{-}}$, ${K}^{\ensuremath{-}}$, ${D}^{\ensuremath{-}}$, and ${D}_{s}^{\ensuremath{-}}$) or a vector meson (${\ensuremath{\rho}}^{\ensuremath{-}}$, ${K}^{*\ensuremath{-}}$, ${D}^{*\ensuremath{-}}$, and ${D}_{s}^{*\ensuremath{-}}$). For achieving this aim, we adopt the three-body light-front quark model with the support of hadron spectroscopy, where the spatial wave functions of these heavy baryons involved in these weak decays are obtained by a semirelativistic potential model associated with the Gaussian expansion method. Our results show that these decays with the ${\ensuremath{\pi}}^{\ensuremath{-}}$, ${\ensuremath{\rho}}^{\ensuremath{-}}$, and ${D}_{s}^{(*)\ensuremath{-}}$-emitted mode have considerable widths, which could be accessible at the ongoing LHCb and Belle II experiments.

Dynamics of microbial communities, flavor, and physicochemical properties of pickled chayote during an industrial-scale natural fermentation: Correlation between microorganisms and metabolites

Pickled chayote is a Chinese fermented vegetable with unique flavors and is favored by local consumers. However, little is known about its quality changes and microbial community succession during fermentation and the relationship between microbes and quality. In the work, the physicochemical quality attributes (pH, acidity, nitrite, texture, and color) and flavor properties (sugars, organic acids, free amino acid [FAA], and volatiles) were investigated. The results revealed that organic acids, FAAs, and key volatiles (esters, terpenes, alcohols, and phenols) significantly increased during fermentation. Lactobacillus was the dominant bacterial genus with Lactobacillus alimentarius being the prevalent species; Kazachstania and Pichia were dominant fungal genera with Kazachstania humilis and Pichia membranifaciens being the prevalent species. The microbial metabolic network found that bacteria (L. alimentarius, L. futsaii, and L. paralimentarius) and fungi (K. humilis and P. membranifaciens) played significant roles in the physicochemical changes and flavor production of pickled chayote.

Development of a triple coincidence method of reaction, gamma-ray, and weak decay in the hypernuclear gamma-ray spectroscopy at J-PARC

To understand the mechanism of the charge symmetry breaking between 4ΛH and 4ΛHe, we plan to measure the gamma-transition energy of 4ΛH (1+ → 0+) with a Ge detector array. For identification of the hypernucleus, we will perform triple coincidence with the reaction, γ-ray, and weak decay for the first time. We measure the pion from weak decay with a range counter. This method will enable γ-ray spectroscopy of various hyperfragments which cannot be directly produced by (K−, π−) or (π+, K+) reactions.

Properties of doubly heavy baryons in QCD

The study of the properties of doubly heavy baryons represents a promising area in particle physics. It can provide us with information about Cabibbo-Kobayashi-Maskawa (CKM) matrix elements and the low energy dynamics of QCD. They have a very rich phenomenology. The investigation of weak, electromagnetic, and strong decays has a vital importance for understanding the dynamics of doubly heavy baryons. The main ingredients of such studies are the spectroscopic parameters, the strong coupling constants, and the transition form factors. For calculations of these quantities, non-perturbative methods are needed. One of these methods is the QCD sum rules. In the present work, we review our studies on the properties of the doubly heavy baryons within the sum rules method, focusing mainly on the mass and strong coupling constants of the doubly heavy baryons. In addition, the radiative decays of doubly heavy baryons are estimated using the vector dominance model. We also make few remarks on the semileptonic decays of the doubly heavy baryons

Exponential decay for 2D reduced gravity two-and-a-half layer model with quantum potential and drag force

<p style='text-indent:20px;'>In this paper, we study the global weak solutions to a reduced gravity two-and-a-half layer model with quantum potential and drag force in two-dimensional torus. Inspired by Bresch, Gisclon, Lacroix-Violet [Arch. Ration. Mech. Anal. (233):975-1025, 2019] and Bresch, Gisclon, Lacroix-Violet, Vasseur [J. Math. Fluid Mech., 24(11):16, 2022], we prove that the weak solutions decay exponentially in time to equilibrium state. In order to prove the decay property of weak solutions, we obtain the relative entropy inequality of weak solutions and equilibrium solutions by defining the relative entropy functional. Considering that the structure of reduced gravity two-and-a-half layer model is more complicated than the compressible Navier-Stokes equations due to the presence of cross terms <inline-formula><tex-math id="M1">\begin{document}$ h_{1}\nabla h_{2} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ h_{2}\nabla h_{1} $\end{document}</tex-math></inline-formula>, we need to estimate the cross term in relative entropy.</p>