Search

The compact tetraquark states with fully heavy quark contents $QQ\overline{Q}\overline{Q}$ are studied as the bound states of the diquark-antidiquark within the Bethe-Salpeter framework. The (anti)diquark masses and form factors used are the same as we calculated the doubly heavy baryons in a previous work. Under the instantaneous approximation, the three-dimensional (Bethe-)Salpeter equation of the tetraquarks is derived and solved numerically to obtain the corresponding mass spectra and wave functions of the tetraquarks with ${J}^{PC}={0}^{++}$, ${1}^{+\ensuremath{-}}$, and ${2}^{++}$. Our results show that the three ground states of $cc\overline{c}\overline{c}$ locate in the mass range of 6.4--6.5 GeV, and the $bb\overline{b}\overline{b}$ states in mass range of 19.2--19.3 GeV. The obtained relativistic wave functions naturally include the mixing effects from the possible $D$ (or $G$) partial waves, and then can be further used to do precise calculations of the tetraquark decays. Based on the obtained results, the LHCb's observation $X(6900)$ is less likely to be the ground states of compact $cc\overline{c}\overline{c}$ tetraquarks but might be the first or second excited states. In addition, a widely used propagatorlike form factor is also investigated and discussed.

The experimentally known $B_c$ states are all below open bottom-charm threshold, which experience three main decay modes, and all induced by weak interaction. In this work, we investigate the mass spectrum and strong decays of the $B_c(3S)$ states, which just above the threshold, in the Bethe-Salpeter formalism and $^3P_0$ model. The numerical estimation gives $M(B_c(3^1S_0))=7273\ {\rm MeV}$, $M(B_c^*(3^3S_1))=7304\ {\rm MeV}$, $\Gamma\left(B_c(3^1S_0)\to B^*D\right)=26.02^{+2.33}_{-2.21}\ {\rm MeV}$, $\Gamma\left(B_c^*(3^3S_1)\to BD\right)=3.39^{+0.27}_{-0.26}\ {\rm MeV}$, $\Gamma\left(B_c^*(3^3S_1)\to B^*D\right)=14.77^{+1.40}_{-1.33}\ {\rm MeV}$ and $\Gamma\left(B_c^*(3^3S_1)\to BD^*\right)=6.14^{+0.58}_{-0.54}\ {\rm MeV}$. Compared with previous studies in non-relativistic approximation, our results indicate that the relativistic effects are notable in $B_c(3S)$ exclusive strong decays. According to the results, we suggest to find the $B_c(3S)$ states in their hadronic decays to $B$ and $D$ mesons in experiment, like the LHCb., Comment: 10 pages, 1 figure, to appear in PLB

We study the CP violation in two-body nonleptonic decays of $B_c$ meson. We concentrate on the decay channels which contain at least one excited heavy meson in the final states. Specifically, the following channels are considered: $B_c\to c\bar c(2S, 2P)+\bar cq(1S, 1P)$, $B_c\to c\bar c(1S)+\bar cq(2S, 2P)$, $B_c\to c\bar c(1P)+\bar cq(2S)$, $B_c\to c\bar c(1D)+\bar cq(1S, 1P)$, and $B_c\to c\bar c(3S)+\bar cq(1S)$. The improved Bethe-Salpeter method is applied to calculate the hadronic transition matrix element. Our results show that some decay modes have large branching ratios, which is of the order of $10^{-3}$. The CP violation effect in $B_c \rightarrow \eta_c(1S)+D(2S)$, $B_c \rightarrow \eta_c(1S)+D_0^{*}(2P)$, and $B_c \rightarrow J/\psi+D^{*}(2S)$ are most likely to be found. If the detection precision of the CP asymmetry in such channels can reach the $3\sigma$ level, at least $10^7$ $B_c$ events are needed., Comment: 18 pages, 26 figures

We present the calibration strategy for the 20 kton liquid scintillator central detector of the Jiangmen Underground Neutrino Observatory (JUNO). By utilizing a comprehensive multiple-source and multiple-positional calibration program, in combination with a novel dual calorimetry technique exploiting two independent photosensors and readout systems, we demonstrate that the JUNO central detector can achieve a better than 1% energy linearity and a 3% effective energy resolution, required by the neutrino mass ordering determination. [Figure not available: see fulltext.], 0, info:eu-repo/semantics/published

In this paper, we study the FCNC decay processes of $B$ and $B_c$ meson, in which one invisible particle is emitted. Both the spin-0 and spin-1 cases are considered. The model-independent effective Lagrangian is introduced to describe the coupling between the light invisible boson and quarks. The constraints of the coupling coefficients are extracted by experimental upper limits of the missing energy in $B$ meson decays. The bounds are used to predict the upper limits of branching fractions of corresponding $B_c$ decays, which are of the order of $10^{-6}$ or $10^{-5}$ when final meson is pseudoscalar or vector, respectively. The maximum branch ratios are achieved when $m_\chi\approx3.5- 4$~GeV, where $m_\chi$ is the mass of the invisible particle., Comment: 17 pages, 27 figures

We propose a scheme to investigate the topological phase transition and the topological state transfer based on the small optomechanical lattice under the realistic parameters regime. We find that the optomechanical lattice can be equivalent to a topologically nontrivial Su-Schrieffer-Heeger (SSH) model via designing the effective optomechanical coupling. Especially, the optomechanical lattice experiences the phase transition between topologically nontrivial SSH phase and topologically trivial SSH phase by controlling the decay of the cavity field and the optomechanical coupling. We stress that the topological phase transition is mainly induced by the decay of the cavity field, which is counter-intuitive since the dissipation is usually detrimental to the system. Also, we investigate the photonic state transfer between the two cavity fields via the topologically protected edge channel based on the small optomechanical lattice. We find that the quantum state transfer assisted by the topological zero energy mode can be achieved via implying the external lasers with the periodical driving amplitudes into the cavity fields. Our scheme provides the fundamental and the insightful explanations toward the mapping of the photonic topological insulator based on the micro-nano optomechanical quantum optical platform., 11 pages, 10 figures, to appear in Frontiers of Physics

ConsideringZ(3930) andX(4160) as$$\chi _{c2}(2P)$$χc2(2P)and$$\chi _{c2}(3P)$$χc2(3P)states, the semileptonic and nonleptonic of$$B_c$$Bcdecays toZ(3930) andX(4160) are studied by the improved Bethe–Salpeter (B–S) Method. The form factors of decay are calculated through the overlap integrals of the meson wave functions in the whole accessible kinematical range. The influence of relativistic corrections are considered in the exclusive decays. Branching ratios of$$B_c$$Bcweak decays toZ(3930) andX(4160) are predicted. Some of the branching ratios are:$$Br(B_c^+\rightarrow Z(3930)e^+\nu _e)=(3.03^{+0.09}_{-0.16})\times 10^{-4}$$Br(Bc+→Z(3930)e+νe)=(3.03-0.16+0.09)×10-4and$$Br(B_c^+\rightarrow X(4160)e^+\nu _e)=(3.55^{+0.83}_{-0.35})\times 10^{-6}$$Br(Bc+→X(4160)e+νe)=(3.55-0.35+0.83)×10-6. These results may provide useful information to discoverZ(3930) andX(4160) and the necessary information for the phenomenological study of$$B_c$$Bcphysics.

We solved the instantaneous Bethe-Salpeter equation for heavy pseudoscalars in different kernels, where the kernels are obtained using linear scalar potential plus one gluon exchange vector potentials in Feynman gauge, Landau gauge, Coulomb gauge and time-component Coulomb gauge. We obtained the mass spectra of heavy pseudoscalars, and compared the results between different kernels, found that using the same parameters we obtain the smallest mass splitting in time-component Coulomb gauge, the similar largest mass splitting in Feynman and Coulomb gauges, middle size splitting in Landau gauge., 13 pages, 2 figures

The typical velocity of a heavy quark in a quarkonium is a widely used quantity, in this paper, based on the relativistic Bethe-Salpeter equation method, we calculate the average values ${\overline{|\boldsymbol{q}|^n}}$ and $ \overline{|\boldsymbol{v}|^n}\equiv v^n$ of a heavy quark in a $S$ wave or $P$ wave quarkonium rest frame, where $\boldsymbol{q}$ and $\boldsymbol{v}$ are the three dimensional momentum and velocity, $n=1,2,3,4$. For a charm quark in $J/\psi$, we obtained $v_{J/\psi}=0.46$, $v^2_{J/\psi}=0.26$, $v^3_{J/\psi}=0.18$, and $v^4_{J/\psi}=0.14$, for a bottom quark in $\Upsilon(1S)$, $v_{\Upsilon(1S)}=0.24$, $v^2_{\Upsilon(1S)}=0.072$, $v^3_{\Upsilon(1S)}=0.025$, and $v^4_{\Upsilon(1S)}=0.010$. The values indicate that ${v^n} >{v^{n_1}}\cdot{v^{n_2}}$, where $n_1+n_2=n$, which is correct for all the charmonia and bottomonia. Our results also show the poor convergence if we make the {speed} expansion in charmonium system, but good for bottomonium. Based on the $v^n$ values and the following obtained relations $v^n_{4S} > v^n_{3S}> v^n_{2S}>v^n_{1S}$, $v^n_{4P} > v^n_{3P}> v^n_{2P}>v^n_{1P}$ and $v^n_{mP}>v^n_{mS}$ ($n,m=1,2,3,4$), we conclude that highly excited quarkonia have larger relativistic corrections than those of the corresponding low excited and ground states, and there are large relativistic corrections in charmonium system., Comment: 13 pages, 4 tables

We propose a scheme to achieve the analogous interface-state laser by dint of the interface between the two intermediate-resonator-coupled non-Hermitian resonator chains. We find that, after introducing the couplings between the two resonator chains and the intermediate resonator at the interface, the photons of the system mainly gather into the three resonators near the intermediate resonator. The phenomenon of the photon gathering towards the certain resonators is expected to construct the photon storage and even the laser generator. We reveal that the phenomenon is induced via the joint effect between the isolated intermediate resonator and two kinds of non-Hermitian skin effects. In particular, we investigate the interface-state laser in a topologically trivial non-Hermitian resonator array in detail. We find that the pulsed interface-state laser can be achieved accompanying with the intermittent proliferation of the photons at the intermediate resonator when an arbitrary resonator is excited. Also, we reveal that the pulsed interface-state laser in the topologically trivial non-Hermitian resonator array is immune to the on-site defects in some cases, whose mechanism is mainly induced by the nonreciprocal couplings instead of the protection of topology. Our scheme provides a promising and excellent platform to investigate interface-state laser in the microresonator array.

The flavor-changing neutral current decay processes of the $B$ and $B_c$ mesons with the final states involving spin-$1/2$ particles are investigated. By considering the background of the Standard Model where $\nu\bar\nu$ contributes the missing energy and the experimental upper bounds for the branching fractions, we get the constraints of the coupling constants of the quark-antiquark and the assumed invisible particles $\chi\bar\chi$. The constraints of the coupling constants are then used to study the similar processes of the $B_c$ meson. At some specific region of $m_\chi$, the upper limit of BR($B_c\to D_{(s)}\chi\bar\chi$) is of the order of $10^{-6}$, while for BR($B_c\to D^\ast_{(s)}\chi\bar\chi$), it is $10^{-5}$. The possibility of distinguishing $\chi$ to be a Majorana or Dirac fermion by the differential branching fractions is also discussed., Comment: 21 pages, 35 figures

We propose a scheme to achieve the photonic and the phononic state transfers via the topological protected edge channel based on a one-dimensional small optomechanical lattice. We find that the optomechanical lattice can be mapped into a Su–Schrieffer–Heeger model after eliminating the counter rotating wave terms. By dint of the edge channel of the Su–Schrieffer–Heeger model, we show that the quantum state transfer between the photonic left and the right edge states can be achieved with a high fidelity. Especially, our scheme can also achieve another phononic state transfer based on the same channel via controlling the next-nearest-neighboring interactions between the cavity fields; this is different from the previous investigations achieving only one kind of quantum state transfer. Our scheme provides a novel, to the best of our knowledge, path to switch two different kinds of quantum state transfers in a controllable way.

A recently observed spectrum of ${P}_{c}$ states exhibits a strong link to ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{(*)}$ thresholds. In spite of successful molecular interpretations, we still push forward to wonder whether there exist finer structures. Utilizing the effecitve Lagrangians respecting heavy quark symmetry and chiral symmetry, as well as instantaneous Bethe-Salpeter equations, we investigate the ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{(*)}$ interactions and three ${P}_{c}$ states. We confirm that ${P}_{c}(4312)$ and ${P}_{c}(4440)$ are good candidates of ${\mathrm{\ensuremath{\Sigma}}}_{c}\overline{D}$ and ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}$ molecules with spin-$\frac{1}{2}$, respectively. Unlike other molecular calculations, our results indicate the ${P}_{c}(4457)$ signal might be a mixture of spin-$\frac{3}{2}$ and spin-$\frac{1}{2}$ ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}$ molecules, where the latter one appears to be an excitation of ${P}_{c}(4440)$. Therefore we conclude that, confronting three LHCb ${P}_{c}$ signals, there may exist not three, but four molecular states.

We calculate the two-body strong decays of the orbitally excited scalar mesons $$D_0^*(2400)$$ and $$D_J^*(3000)$$ by using the relativistic Bethe–Salpeter (BS) method. $$D_J^*(3000)$$ was observed recently by the LHCb Collaboration, the quantum number of which has not been determined yet. In this paper, we assume that it is the $$0^+(2P)$$ state and obtain the transition amplitude by using the PCAC relation, low-energy theorem and effective Lagrangian method. For the 1P state, the total widths of $$D_0^*(2400)^{0}$$ and $$ D_0^*(2400)^+$$ are 226 and 246 MeV, respectively. With the assumption of $$0^+(2P)$$ state, the widths of $$D_J^*(3000)^0$$ and $$D_J^*(3000)^+$$ are both about 131 MeV, which is close to the present experimental data. Therefore, $$D_J^*(3000)$$ is a strong candidate for the $$2^3P_0$$ state.

In this work, we study the lepton-number-violating processes of $K^\pm$ and $D^\pm$ mesons. Two quasi-degenerate sterile neutrinos are assumed to induce such processes. Different with the case where only one sterile neutrino involves, here, the CP phases of the mixing parameters could give sizable contribution. This, in turn, would affect the absolute values of the mixing parameters determined by the experimental upper limits of the branching fractions. A general function which express the difference of the mixing parameters for two-generation and one-generation is presented. Special cases with specific relations of the parameters are discussed. Besides, we also thoroughly investigate the CP violation effect of such processes. It is shown that generally $\mathcal A_{CP}$ is a function of the sterile neutrino mass., Comment: 14 pages, 10 figures

The bosonic system possessing the identical real-space form as a fermionic Kitaev model usually exhibits the trivial topology since bosonic operators conform to the bosonic commutation relation. However, a nontrivial bosonic Kitaev phase can also emerge under some certain conditions. Here we propose a scheme to induce a topologically nontrivial bosonic Kitaev phase based on a frequency-modulated one-dimensional optomechanical array. We find that the bosonic Kitaev model with pure imaginary tunneling amplitudes induced by effective optomechanical coupling can be mapped into a subspace expanded by two Hermitian quadrature operators in which the bosonic system possesses two isolated analogous Majorana modes. The isolated analogous modes imply that the proposed bosonic Kitaev system possesses a topologically nontrivial phase. Furthermore, we investigate the effects of the modulated partial next-nearest-neighbor (NNN) hopping on the topology of the system, in which the system exhibits distinct topological behavior under different parameter regimes. In particular, the bosonic Kitaev system experiences completely different phase-transition processes with the change of real partial NNN hopping corresponding to an even and odd number of lattice sites. Our scheme provides a flexible and controllable platform to investigate bosonic Kitaev phases and phase transitions both in theory and experiment.

The mass spectra, mixing angle, and decay constants of the ${J}^{P}={1}^{+}$ heavy-light mesons are systematically studied within the framework of the Bethe-Salpeter equation (BSE). The full ${1}^{+}$ Salpeter wave function is given for the first time. The mixing between the ${1}^{+\ensuremath{-}}$ and ${1}^{++}$ in the ${1}^{+}$ heavy-light systems are automatically determined by the dynamics in the equation without any man-made mixing. The results indicate that in a rigorous study there exists the phenomenon of mixing angle inversion or mass inversion within ${1}^{+}$ heavy-light doublet, which is sensitive to the $s$-quark mass for the charmed mesons and $u$- or $d$-quark masses for the bottomed mesons. This inversion phenomenon can answer the question of why we have confused mixing angles in the literature and partly explain the lower mass of ${D}_{s1}(2460)$ compared to that of ${D}_{s1}(2536)$. The decay constants are also presented and can behave as a good quantity to distinguish the ${1}^{+}$ doublet in heavy-light mesons. This study indicates that the light-quark mass may play an important role in deciding the mass order, mixing angle, and decay constant relation between the $|{j}_{l}=\frac{3}{2}⟩$ and $|{j}_{l}=\frac{1}{2}⟩$ heavy-light mesons.

In this paper, the dilepton electromagnetic decays $$\chi _{cJ}(1P) \rightarrow J/\psi e^+e^-$$χcJ(1P)→J/ψe+e- and $$\chi _{cJ}(1P) \rightarrow J\psi \mu ^+\mu ^-$$χcJ(1P)→Jψμ+μ-, where $$\chi _{cJ}$$χcJ denotes $$\chi _{c0}$$χc0, $$\chi _{c1}$$χc1 and $$\chi _{c2}$$χc2, are calculated systematically in the improved Bethe–Salpeter method. The numerical results of decay widths and the invariant mass distributions of the final lepton pairs are given. The comparison is made with the recently measured experimental data of BESIII. It is shown that for the cases including $$e^+e^-$$e+e-, the gauge invariance is decisive and should be considered carefully. For the processes of $$\chi _{cJ}(1P) \rightarrow J/\psi e^+e^-$$χcJ(1P)→J/ψe+e-, the branching fraction are: $$\mathcal {B}[\chi _{c0}(1P) \rightarrow J/\psi e^+e^-]=1.06^{+0.16}_{-0.18} \times 10^{-4}$$B[χc0(1P)→J/ψe+e-]=1.06-0.18+0.16×10-4, $$\mathcal {B}[\chi _{c1}(1P) \rightarrow J/\psi e^+e^-]=2.88^{+0.50}_{-0.53} \times 10^{-3}$$B[χc1(1P)→J/ψe+e-]=2.88-0.53+0.50×10-3, and $$\mathcal {B}[\chi _{c2}(1P) \rightarrow J/\psi e^+e^-]=1.74^{+0.22}_{-0.21} \times 10^{-3}$$B[χc2(1P)→J/ψe+e-]=1.74-0.21+0.22×10-3. The calculated branching fractions of $$\chi _{cJ}(1P)\rightarrow J/\psi \mu ^+\mu ^-$$χcJ(1P)→J/ψμ+μ- channels are: $$\mathcal {B}[\chi _{c0}(1P) \rightarrow J/\psi \mu ^+\mu ^-]=3.80^{+0.59}_{-0.64} \times 10^{-6}$$B[χc0(1P)→J/ψμ+μ-]=3.80-0.64+0.59×10-6, $$\mathcal {B}[\chi _{c1}(1P) \rightarrow J/\psi \mu ^+\mu ^-]=2.04^{+0.36}_{-0.38} \times 10^{-4}$$B[χc1(1P)→J/ψμ+μ-]=2.04-0.38+0.36×10-4, and $$\mathcal {B}[\chi _{c2}(1P) \rightarrow J/\psi \mu ^+\mu ^-]=1.66^{+0.19}_{-0.19} \times 10^{-4}$$B[χc2(1P)→J/ψμ+μ-]=1.66-0.19+0.19×10-4.

In this paper, we use the instantaneous Bethe-Salpeter method to calculate the semi-leptonic and non-leptonic production of the orbitally excited scalar $ D_0^* $ in $ B $ meson decays. When the final state is $ 1P $ state $ D_0^*(2400) $, our theoretical decay rate is consistent with experimental data. For $ D_J^*(3000) $ final state, which was observed by LHCb collaboration recently and here treated as the orbitally excited scalar $D^{*}_{0}(2P)$, its rate is in the order of $ 10^{-4} \sim 10^{-6}$. We find the special node structure of $D^{*}_{0}(2P)$ wave function possibly results in the suppression of its branching ratio and the abnormal uncertainty. The $3P$ states production rate is in the order of $ 10^{-5}$., 17 pages, 26 figures

In this paper, we study the light scalar and pseudoscalar invisible particles in the flavor changing neutral current processes of the $B_c$ meson. Effective operators are introduced to describe the couplings between quarks and light invisible particles. The Wilson coefficients are extracted from the experimental results of the $B$ and $D$ mesons, which are used to predict the upper limits of the branching fractions of the similar decay processes for the $B_c$ meson. The hadronic transition matrix element is calculated with the instantaneously approximated Bethe-Salpeter method. The upper limits of the branching fractions when $m_\chi$ taking different values are presented. It is found that at some region of $m_\chi$, the channel $B_c\to D_s^{(\ast)}\chi\chi$ has the largest upper limit which is of the order of $10^{-6}$, and for $B_c\to D_s^\ast\chi\chi^\dagger$, the largest value of the upper limits can achieve the order of $10^{-5}$. Other decay modes, such as $B_c\to D^{(*)}\chi\chi^{(\dagger)}$ and $B_c\to B^{(*)}\chi\chi^{(\dagger)}$, are also considered., Comment: 24 pages, 35 figures

Recently, many new excited states of heavy mesons, especially the radially excited states, are discovered. The study of the production processes of these states from the ground b-flavored mesons is of interest. In this paper, we use the improved Bethe-Salpeter method to study the semi-leptonic and non-leptonic decays of $B$, $B_s$, and $B_c$ mesons, where the final states are focused on the radial excited $2S$ and $3S$ states. We find that many channels have branching ratios up to $10^{-4}$, which are within the detection accuracy of current experiments., Comment: 17 pages,1 figures

The heavy quark effective theory vastly reduces the weak-decay form factors of hadrons containing one heavy quark. Many works attempt to directly apply this theory to hadrons with multiple heavy quarks. In this paper, we examine this confusing application by the instantaneous Bethe-Salpeter method from a phenomenological perspective, and give the numerical results for decays to charmonium where the final states include , , , and . Our results indicate that the form factors parameterized by a single Isgur-Wise function deviate substantially from the full ones, especially when excited states are involved. The relativistic corrections ( corrections) require the introduction of more non-perturbative universal functions, similar to the Isgur-Wise function, which are the overlapping integrals of the wave functions with the relative momentum between the quark and antiquark.

Recently, the deviation of the ratios $R(D)$, $R(D^{*})$ and $R(J/\psi)$ have been found between experimental data and the Standard Model predictions, which may be the hint of New Physics. In this work, we calculate these ratios within the Standard Model by using the improved instantaneous Bethe-Salpeter method. The emphasis is pad to the relativistic correction of the form factors. The results are $R(D)=0.312 ^{+0.006}_{-0.007}$, $R(D^*)= 0.249^{+0.001}_{-0.002}$, $R(D_s)=0.320 ^{+0.009}_{-0.009}$, $R(D^*_s)=0.251 ^{+0.002}_{-0.003}$, $R(\eta_c)=0.384 ^{+0.032}_{-0.042}$, and $R(J/\psi)=0.267 ^{+0.009}_{-0.011}$, which are consistent with predictions of other models and the experimental data. The semileptonic decay rates and corresponding form factors at zero recoil are also given., Comment: 19 pages, 15 figures

In the usual Su-Schrieffer-Heeger (SSH) chain, the topology of the energy spectrum is divided into two categories in different parameter regions. Here we study the topological and nontopological edge states induced by qubit-assisted coupling potentials in circuit quantum electrodynamics (QED) lattice system modelled as a SSH chain. We find that, when the coupling potential added on only one end of the system raises to a certain extent, the strong coupling potential will induce a new topologically nontrivial phase accompanied with the appearance of a nontopological edge state in the whole parameter region, and the novel phase transition leads to the inversion of odd-even effect in the system directly. Furthermore, we also study the topological properties as well as phase transitions when two unbalanced coupling potentials are injected into both the ends of the circuit QED lattice system, and find that the system exhibits three distinguishing phases in the process of multiple flips of energy bands. These phases are significantly different from the previous phase induced via unilateral coupling potential, which is reflected by the existence of a pair of nontopological edge states under strong coupling potential regime. Our scheme provides a feasible and visible method to induce a variety of different kinds of topological and nontopological edge states through controlling the qubit-assisted coupling potentials in circuit QED lattice system both in experiment and theory., Comment: 10 pages,9 figures

We revisit the heavy quarkonium leptonic decays $\psi(nS) \to \ell^+\ell^-$ and $\Upsilon(nS) \to \ell^+\ell^-$ using the Bethe-Salpeter method. The emphasis is on the relativistic correction. For the $\psi(1S-5S)$ decays, the relativistic effects are $22^{+3}_{-2}\%$, $34^{+5}_{-5}\%$, $41^{+6}_{-6}\%$, $52^{+11}_{-13}\%$ and $62^{+14}_{-12}\%$, respectively. For the $\Upsilon(1S-5S)$ decays, the relativistic effects are $14^{+1}_{-2}\%$, $23^{+0}_{-3}\%$, $20^{+8}_{-2}\%$, $21^{+6}_{-7}\%$ and $28^{+2}_{-7}\%$, respectively. Thus, the relativistic corrections are large and important in heavy quarkonium leptonic decays, especially for the highly excited charmonium. Our results for $\Upsilon(nS) \to \ell^+\ell^-$ are consistent with the experimental data., Comment: 22 pages, 3 figures, 6 tables

The mass spectra and wave functions for the doubly heavy baryons are computed under the picture that the two heavy quarks inside a doubly heavy baryon, such as two $c$-quarks in $\Xi_{cc}$, combine into a heavy `diquark core' in color anti-triplet firstly, then the diquark core turns into a color-less doubly heavy baryon via combining the light $q$-quark inside the baryon. Namely both of the combinations, the two heavy quarks inside the baryon into a diquark core in color anti-triplet and the heavy diquark core with the light quark into the baryon, are depicted by relativistic Bethe-Salpeter equations (BSEs) with an accordingly QCD inspired kernel respectively, although in the paper only the heavy diquark cores with the quantum numbers $J^P=1^+$ are considered. Since the `second combination' is of the heavy diquark core and the light quark, so the structure effect of the diquark core to the relevant kernel of the BSE is specially considered in terms of the diquark-core wave functions. The mass spectra and wave functions for the `low-laying' doubly heavy baryons in the flavors $(ccq)$, $(bcq)$ and $(bbq)$ and in the quantum numbers $J^P=\frac{1}{2}^+$, $J^P=\frac{3}{2}^+$, achieved by solving the equations under the so-called instantaneous approximation, are presented properly and some comparisons with the others' results under different approaches in the literature are made., Comment: 21 pages, 17 figures; To be published in Chinese Physics C

Relativistic effects are important in the rigorous study of heavy quarks. In this paper, we study the relativistic corrections of semileptonic $B_c$ decays to charmonium with the instantaneous Bethe-Salpeter method. Within the Bethe-Salpeter framework, we use two methods to study the relativistic effects. One of them is to expand the transition amplitude in powers of $\vec{q}$ which is the relative momentum between the quark and antiquark, and the other is to expand the amplitude base on the wave functions. In the level of decay width, the results show that, for the transition of $B_c\to \eta_c$, the relativistic correction is about $22\%$; for $B_c\to J/\psi$, it is about $19\%$; the relativistic effects of $1P$ final states are about $14\sim46\%$ larger than those of $1S$ final states; for $2S$ final states, they are about $19\sim 28\%$ larger than those of $1S$ final states; for $3S$ final states, they are about $12\sim13\%$ larger than those of $2S$ final states; for $2P$ final states, they are about $10\sim14\%$ larger than those of $1P$ final states; for $3P$ final states, they are about $7\sim12\%$ larger than those of $2P$ final states. We conclude that the relativistic corrections of the $B_c$ decays to the orbitally or radially excited charmonium (2S, 3S, 1P, 2P, 3P) are quite large., Comment: 25 pages, 32 figures

In this paper, we study the four-body decay processes of neutral flavored mesons, including $\bar K^0$, $D^0$, $\bar B^0$, and $\bar B_s^0$. These processes, which induced by a hypothetical doubly-charged scalar particle, violate the lepton number. The quantity $Br\times\left(\frac{s_\Delta h_{ij}}{m_\Delta^2}\right)^{-2}$ of different channels are calculated, where $s_\Delta$, $h_{ij}$, and $M_\Delta$ are parameters related to the doubly-charged scalar. For $\bar K^0\rightarrow h_1^+h_2^+l_1^-l_2^-$, $D^0\rightarrow h_1^-h_2^-l_1^+l_2^+$, and $\bar B_{d,s}^0\rightarrow h_1^+h_2^+l_1^-l_2^-$, it is of the order of $10^{-13}\sim 10^{-11}$ ${\rm GeV^4}$, $10^{-17}\sim 10^{-10}$ ${\rm GeV^4}$, and $10^{-17}\sim 10^{-10}$ ${\rm GeV^4}$, respectively. Based on the experimental results for the $D^0\rightarrow h_1^-h_2^-l_1^+l_2^+$ channels, we also set the upper limit for $\frac{s_\Delta h_{ij}}{M_\Delta^2}$., Comment: 15 pages, 2 figures

In this paper, we systematically calculate two-body strong decays of newly observed ${D}_{J}(3000)$ and ${D}_{sJ}(3040)$ with $2\mathrm{P}({1}^{+})$ and $2\mathrm{P}({1}^{+\ensuremath{'}})$ assignments in an instantaneous approximation of the Bethe-Salpeter equation method. Our results show that both resonances can be explained as the $2\mathrm{P}({1}^{{+}^{\ensuremath{'}}})$ with broad width via $^{3}{P}_{1}$ and $^{1}{P}_{1}$ mixing in $D$ and ${D}_{s}$ families. For ${D}_{J}(3000)$, the total width is 229.6 MeV in our calculation, close to the upper limit of experimental data, and the dominant decay channels are ${D}_{2}^{*}\ensuremath{\pi}$, ${D}^{*}\ensuremath{\pi}$, and ${D}^{*}(2600)\ensuremath{\pi}$. For ${D}_{sJ}(3040)$, the total width is 157.4 MeV in our calculation, close to the lower limit of experimental data, and the dominant channels are ${D}^{*}K$ and ${D}^{*}{K}^{*}$. These results are consistent with observed channels in experiments. Given the very little information that has been obtained from experiments and the large error bars of the total decay widths, we recommend the detection of dominant channels in our calculation.

In this paper, we study the lepton number violation processes of $B_c$ meson induced by possible doubly-charged scalars. Both the three-body decay channels and the four-body decay channels are considered. For the former, $Br\times\left(\frac{s_\Delta h_{ij}}{M_\Delta^2}\right)^{-2}$ is of the order of $10^{-7}\sim 10^{-9}$, and for the later channels, $Br\times\left(\frac{s_\Delta h_{ij}}{M_\Delta^2}\right)^{-2}$ is of the order of $10^{-12}\sim 10^{-20}$, where $s_\Delta$, $h_{ij}$, $M_\Delta$ are the constants related to the doubly-charged boson., Comment: 15 pages, 2 figures

The semileptonic decays \(B_c^ + \to P(V) + \ell ^ + + \bar \nu _\ell \) and the nonleptonic decays Bc+ → P(V) + L, where P(V) denotes a pseudoscalar (vector) charmonium or \((\bar bs)\)-meson, and L denotes a light meson, are studied in the framework of improved instantaneous Bethe-Salpeter (BS) equation and the Mandelstam formula. The numerical results (width and branching ratio of the decays) are presented in tables, and in order to compare conveniently, those obtained by other approaches are also put in the relevant tables. Based on the fact that the ratio \(\frac{{\mathcal{B}\mathcal{R}(B_c^ + \to \psi (2S)\pi ^ + )}} {{\mathcal{B}\mathcal{R}(B_c^ + \to J/\psi \pi ^ + )}} = 0.24_{ - 0.040}^{ + 0.023} \) estimated here is in good agreement with the observation by LHCb \(\frac{{\mathcal{B}\mathcal{R}(B_c^ + \to \psi (2S)\pi ^ + )}} {{\mathcal{B}\mathcal{R}(B_c^ + \to J/\psi \pi ^ + )}} = 0.250 \pm 0.068(stat) \pm 0.014(syst) \pm 0.006(\mathcal{B}) \), one may conclude that with respect to the decays the present framework works quite well.

We study the weak decays of $\bar{B}_{(s)}$ and $B_c$ into $D$-wave heavy-light mesons, including $J^P=2^-$ ($D_{(s)2},D'_{(s)2},B_{(s)2}, B'_{(s)2}$) and $3^-$~($D^*_{(s)3}, B^*_{(s)3}$) states. The weak decay hadronic matrix elements are achieved based on the instantaneous Bethe-Salpeter method. The branching ratios for $\bar{B}$ decays are $\mathcal{B}[\bar{B}\to D_{2}e\bar{\nu}_e] = 1.1^{-0.3}_{+0.3} \times 10^{-3}$, $\mathcal{B}[\bar{B}\to D'_2e\bar{\nu}_e]=4.1^{-0.8}_{+0.9} \times 10^{-4}$, and $\mathcal{B}[\bar{B}\to D^*_3e\bar{\nu}_e]=1.0^{-0.2}_{+0.2} \times 10^{-3}$, respectively. For semi-electronic decays of $\bar B_s$ to $D_{s2}$, $D'_{s2}$, and $D^*_{s3}$, the corresponding branching ratios are $1.7^{-0.5}_{+0.5}\times 10^{-3}$, $5.2^{-1.5}_{+1.6}\times 10^{-4}$, and $1.5^{-0.4}_{+0.4}\times 10^{-3}$, respectively. The branching ratios of semi-electronic decays of $B_c$ to $D$-wave $D$ mesons are in the order of $10^{-5}$. We also achieved the forward-backward asymmetry, angular spectra, and lepton momentum spectra. In particular the distribution of decay widths for $2^-$ states $D_2$ and $D'_2$ varying along with mixing angle are presented.

In this paper, we study the OZI-allowed two-body strong decays of $$3^-$$ heavy–light mesons. Experimentally the charmed $$D_{3}^{*}(2760)$$ and the charm–strange $$D_{s3}^{*}(2860)$$ states with these quantum numbers have been discovered. For the bottomed B(5970) state, which was found by the CDF Collaboration recently, its quantum number has not been decided yet and we assume it is a $$3^-$$ meson in this paper. The theoretical prediction for the strong decays of bottom–strange state $$B_{s3}^*$$ is also given. The relativistic wave functions of $$3^-$$ heavy mesons are constructed and their numerical values are obtained by solving the corresponding Bethe–Salpeter equation with instantaneous approximation. The transition matrix is calculated by using the PCAC and low energy theorem, following which the decay widths are obtained. For $$D_{3}^*(2760)$$ and $$D_{s3}^*(2860)$$ , the total strong decay widths are 72.6 and 47.6 MeV, respectively. For $$B_3^*$$ with $$M=5978$$ MeV and $$B_{s3}^*$$ with $$M=6178$$ MeV, their strong decay widths are 22.9 and 40.8 MeV, respectively.

We study the semileptonic and nonleptonic decays of $$B_c$$ meson to D-wave charmonia, namely, $$\eta _{c2}(1^1\!D_2)$$ , $$\psi _2(1^3\!D_2)$$ , and $$\psi _3(1^3\!D_3)$$ . In our calculations, the instantaneous Bethe–Salpeter method is applied to obtain the hadronic matrix elements. This method includes relativistic corrections which are important especially for the higher orbital excited states. For the semileptonic decay channels with electron as the final lepton, we get the branching ratios $$\mathcal {B}[B_c \rightarrow \eta _{c2}e\bar{\nu }_e] = 5.9^{-0.8}_{+1.0}\times 10^{-4}$$ , $$\mathcal {B}[B_c \rightarrow \psi _2e\bar{\nu }_e]=1.5^{-0.2}_{+0.3}\times 10^{-4}$$ , and $$\mathcal {B}[B_c \rightarrow \psi _3e\bar{\nu }_e]=3.5^{-0.6}_{+0.8}\times 10^{-4}$$ . The transition form factors, forward–backward asymmetries, and lepton spectra in these processes are also presented. For the nonleptonic decay channels, those with $$\rho $$ as the lighter meson have the largest branching ratios, $$\mathcal {B}[B_c \rightarrow \eta _{c2}\rho ] = 8.1^{-1.0}_{+1.0}\times 10^{-4}$$ , $$\mathcal {B}[B_c \rightarrow \psi _2\rho ]=9.6^{-1.0}_{+1.0}\times 10^{-5}$$ , and $$\mathcal {B}[B_c \rightarrow \psi _3\rho ]=4.1^{-0.7}_{+0.8}\times 10^{-4}$$ .

The Jiangmen Underground Neutrino Observatory (JUNO), a 20 kton multi-purpose underground liquid scintillator detector, was proposed with the determination of the neutrino mass hierarchy as a primary physics goal. It is also capable of observing neutrinos from terrestrial and extra-terrestrial sources, including supernova burst neutrinos, diffuse supernova neutrino background, geoneutrinos, atmospheric neutrinos, solar neutrinos, as well as exotic searches such as nucleon decays, dark matter, sterile neutrinos, etc. We present the physics motivations and the anticipated performance of the JUNO detector for various proposed measurements. By detecting reactor antineutrinos from two power plants at 53-km distance, JUNO will determine the neutrino mass hierarchy at a 3-4 sigma significance with six years of running. The measurement of antineutrino spectrum will also lead to the precise determination of three out of the six oscillation parameters to an accuracy of better than 1\%. Neutrino burst from a typical core-collapse supernova at 10 kpc would lead to ~5000 inverse-beta-decay events and ~2000 all-flavor neutrino-proton elastic scattering events in JUNO. Detection of DSNB would provide valuable information on the cosmic star-formation rate and the average core-collapsed neutrino energy spectrum. Geo-neutrinos can be detected in JUNO with a rate of ~400 events per year, significantly improving the statistics of existing geoneutrino samples. The JUNO detector is sensitive to several exotic searches, e.g. proton decay via the $p\to K^++\bar\nu$ decay channel. The JUNO detector will provide a unique facility to address many outstanding crucial questions in particle and astrophysics. It holds the great potential for further advancing our quest to understanding the fundamental properties of neutrinos, one of the building blocks of our Universe., Comment: Version submitted to Journal of Physics G, with minor typo corrections. 222 Pages, 147 figures

We calculate the masses and the strong decays of orbitally excited states B s 0 , B s 1 ′ , B s 1 and B s 2 by the improved Bethe–Salpeter method. The predicted masses of B s 0 and B s 1 ′ are M B s 0 = 5.723 ± 0.280 GeV , M B s 1 ′ = 5.774 ± 0.330 GeV . We calculate the isospin symmetry violating decay processes B s 0 → B s π and B s 1 ′ → B s ⁎ π through π 0 – η mixing and get small widths. Considering the uncertainties of the masses, for B s 0 and B s 1 ′ , we also calculate the OZI allowed decay channels: B s 0 → B K ¯ and B s 1 ′ → B ⁎ K ¯ . For B s 1 and B s 2 , the OZI allowed decay channels B s 1 → B ⁎ K ¯ , B s 2 → B K ¯ and B s 2 → B ⁎ K ¯ are studied. In all the decay channels, the reduction formula, PCAC relation and low energy theorem are used to estimate the decay widths. We also obtain the strong coupling constants G B s 0 B s π , G B s 0 B K ¯ , G B s 1 ′ B s ⁎ π , F B s 1 ′ B s ⁎ π , G B s 1 ′ B ⁎ K ¯ , F B s 1 ′ B ⁎ K ¯ , G B s 1 B ⁎ K ¯ , F B s 1 B ⁎ K ¯ , G B s 2 B K ¯ and G B s 2 B ⁎ K ¯ .

Many P-wave mixing heavy-light 1+ states have not yet been discovered by experiment, while others have been discovered but without width information, or with large uncertainties on the widths. In this paper, the strong decays of the P-wave mixing heavy-light 1+ states D 0, , , B 0, and B s are studied by the improved Bethe-Salpeter (B-S) method with two conditions of mixing angle θ: one is θ = 35.3°; the other is considering a correction to the mixing angle . Valuable predictions for the strong decay widths are obtained: , , , , , , , , and . It is found that the decay widths of and are very sensitive to the mixing angle. The results will provide theoretical assistance to future experiments.

The magnetic dipole transitions between the vector mesons $B_c^*$ and their relevant pseudoscalar mesons $B_c$ ($B_c$, $B_c^*$, $B_c(2S)$, $B_c^*(2S)$, $B_c(3S)$ and $B_c^*(3S)$ etc, the binding states of $(c\bar{b})$ system) of the $B_c$ family are interesting. To see the `hyperfine' splitting due to spin-spin interaction is an important topic for understanding the spin-spin interaction and the spectrum of the the $(c\bar{b})$ binding system. The knowledge about the magnetic dipole transitions is also very useful for identifying the vector boson $B_c^*$ mesons experimentally, whose masses are just slightly above the masses of their relevant pseudoscalar mesons $B_c$ accordingly. Considering the possibility to observe the vector mesons via the transitions at $Z^0$ factory and the potentially usages of the theoretical estimate on the transitions, we fucus our efforts on calculating the magnetic dipole transitions, i.e. precisely to calculate the rates for the transitions such as decays $B_c^*\to B_c\gamma$ and $B_c^*\to B_c e^+e^-$, and particularly work in the Behte-Salpeter framework. In the estimate, as a typical example, we carefully investigate the dependance of the rate $\Gamma(B_c^*\to B_c\gamma)$ on the mass difference $\Delta M=M_{B_c^*}-M_{B_c}$ as well.

In this paper we study the semileptonic decays of B*, , and by using the Bethe–Salpeter method with instantaneous approximation. Both the and cases are considered. The largest partial width of these channels is of the order of 10−14 GeV. The branching ratios of these semileptonic decays are also estimated by using the partial width of the one photon decay channel to approximate the total width. For and , the branching ratios are of the order of 10−8 and 10−7, respectively. For , the and channels have the largest branching ratio, which is of the order of 10−6.

Annihilation rates of vector 1 − − charmonium and bottomonium S 1 3 states V → e + e − and V → 3 γ , V → γ g g and V → 3 g are estimated in the relativistic Salpeter method. In our calculations, special attention is paid to the relativistic correction, which is important and cannot be ignored for excited 2 S , 3 S and higher excited states. We obtain Γ ( J / ψ → 3 γ ) = 6.8 × 10 − 4 keV , Γ ( ψ ( 2 S ) → 3 γ ) = 2.5 × 10 − 4 keV , Γ ( ψ ( 3 S ) → 3 γ ) = 1.7 × 10 − 4 keV , Γ ( ϒ ( 1 S ) → 3 γ ) = 1.5 × 10 − 5 keV , Γ ( ϒ ( 2 S ) → 3 γ ) = 5.7 × 10 − 6 keV , Γ ( ϒ ( 3 S ) → 3 γ ) = 3.5 × 10 − 6 keV and Γ ( ϒ ( 4 S ) → 3 γ ) = 2.6 × 10 − 6 keV .

This paper is designed to calculate the branching ratio of four-body decays of $B$ meson with lepton number changed by 2. With the new experimental data limit to lepton-number violation processes, we update the upper limits of mixing parameters between heavy Majorana neutrino and charged leptons. Afterwards, we calculate the branching ratio of $B^0(P)\rightarrow D^{*-}(P_1)\ell^+_1(P_2)\ell^+_2(P_3)M_2^-(P_4)$ using the updated parameters. It is found that the most hopeful decay channel is $B^0(P)\rightarrow D^{*-}(P_1)e^+_1(P_2)e^+_2(P_3)\rho^-(P_4)$ or $B^0(P)\rightarrow D^{*-}(P_1)e(\mu)^+_1(P_2)\mu(e)^+_2(P_3)\rho^-(P_4)$, whose branching ratio can reach about $10^{-4}$ with heavy Majorana neutrino mass range around $2~\mathrm{GeV}$., Comment: 19 pages,10 figures

We analyzed the decays of B + → D ¯ 0 + D s J + ( 2 S ) and B + → D ¯ 0 + D s J + ( 1 D ) by naive factorization method and model dependent calculation based on the Bethe–Salpeter method, the branching ratios are Br ( D ¯ 0 D s J + ( 2 S ) ) = ( 0.72 ± 0.12 ) % and Br ( D ¯ 0 D s J + ( 1 D ) ) = ( 0.027 ± 0.007 ) % . The branching ratio of decay B + → D ¯ 0 D s J + ( 2 S ) → D ¯ 0 D 0 K + consists with the data of Belle Collaboration, so we conclude that the new state D s J + ( 2700 ) is the first excited state D s J + ( 2 S ) .

The decay constants of S wave and P wave heavy mesons are computed by means of the relativistic (instantaneous) Salpeter equation.

We present a quantitative analysis of the D-sJ(+) (2632) observed by SELEX mainly focusing on the assumption that D-sJ(+) (2632) is the first radial excitation of the 1(-) ground state D-s(*)(2112). By solving the instantaneous Bethe-Salpeter equation, we obtain the mass 2658 +/- 15 MeV for the first excited state, which is about 26 MeV heavier than the experimental value 2632 +/- 1.7 MeV. By means of PCAC and low-energy theorem we calculate the transition matrix elements and obtain the decay widths: Gamma(D-sJ(+) -> D(s)(+)eta) = 4.07 +/- 0.34 MeV, Gamma(D-sJ(+), (DK+)-K-0) similar or equal to Gamma(Gamma(D-sJ(+) -> (D+K0)) = 8.9 +/- 1.2 MeV, and the ratio Gamma(D-sJ(+) -> (DK+)-K-0)/Gamma(D-sJ(+) -> D(s)(+)eta) = 2.2 +/- 0.2 as well. This ratio is quite different from the SELEX data 0.14 +/- 0.06. The summed decay width of those three channels is approximately 21.7 MeV, already larger than the observed bound for the full width (

Two-photon and two-gluon annihilation rates of η c , η c ′ , η b and η b ′ are estimated in the relativistic Salpeter method. By solving the full Salpeter equation with a well defined relativistic wave function, we estimate M η c = 2.979 ± 0.432 GeV , M η c ′ = 3.566 ± 0.437 GeV , M η b = 9.364 ± 1.120 GeV and M η b ′ = 9.941 ± 1.112 GeV . We calculated the transition amplitude using the Mandelstam formalism and estimate the decay widths: Γ ( η c → 2 γ ) = 7.14 ± 0.95 keV , Γ ( η c ′ → 2 γ ) = 4.44 ± 0.48 keV , Γ ( η b → 2 γ ) = 0.384 ± 0.047 keV and Γ ( η b ′ → 2 γ ) = 0.191 ± 0.025 keV . We also give estimates of total widths by the two-gluon decay rates: Γ tot ( η c ) = 19.6 ± 2.6 MeV , Γ tot ( η c ′ ) = 12.1 ± 1.3 MeV , Γ tot ( η b ) = 6.98 ± 0.85 MeV and Γ tot ( η b ) = 3.47 ± 0.45 MeV .

Whether the $\sigma-meson$ ($f_0(600)$) exists as a real particle is a long-standing problem in both particle physics and nuclear physics. In this work, we analyze the deuteron binding energy in the linear $\sigma$ model and by fitting the data, we are able to determine the range of $m_{\sigma}$ and also investigate applicability of the linear $\sigma$ model for the interaction between hadrons in the energy region of MeV's. Our result shows that the best fit to the data of the deuteron binding energy and other experimental data about deuteron advocates a narrow range for the $\sigma-$meson mass as $520\leq m_{\sigma}\leq 580$ MeV and the concrete values depend on the input parameters such as the couplings. Inversely fitting the experimental data, our results set constraints on the couplings. The other relevant phenomenological parameters in the model are simultaneously obtained.