Search

We discuss the landscape of flavor physics at the Circular Electron-Positron Collider (CEPC), based on the nominal luminosity outlined in its Technical Design Report. The CEPC is designed to operate in multiple modes to address a variety of tasks. At the $Z$ pole, the expected production of 4 Tera $Z$ bosons will provide unique and highly precise measurements of $Z$ boson couplings, while the substantial number of boosted heavy-flavored quarks and leptons produced in clean $Z$ decays will facilitate investigations into their flavor physics with unprecedented precision. We investigate the prospects of measuring various physics benchmarks and discuss their implications for particle theories and phenomenological models. Our studies indicate that, with its highlighted advantages and anticipated excellent detector performance, the CEPC can explore beauty and $\tau$ physics in ways that are superior to or complementary with the Belle II and Large-Hadron-Collider-beauty experiments, potentially enabling the detection of new physics at energy scales of 10 TeV and above. This potential also extends to the observation of yet-to-be-discovered rare and exotic processes, as well as testing fundamental principles such as lepton flavor universality, lepton and baryon number conservation, etc., making the CEPC a vibrant platform for flavor physics research. The $WW$ threshold scan, Higgs-factory operation and top-pair productions of the CEPC further enhance its merits in this regard, especially for measuring the Cabibbo-Kobayashi-Maskawa matrix elements, and Flavor-Changing-Neutral-Current physics of Higgs boson and top quarks. We outline the requirements for detector performance and considerations for future development to achieve the anticipated scientific goals.

In this work, the soft rescattering parameters in the $B^\pm\rightarrow \pi^\pm\pi^+\pi^-$ and $B^\pm\rightarrow K^\pm\pi^+\pi^-$ decays with the light scalar meson $f_0(500)$ as the intermediate resonance are studied within the QCD factorization. Considering the interference effect between $\rho(770)^0$ and $f_0(500)$, we utilize the experimentally more direct event yields for fitting and get the soft rescattering parameters $|\rho_k^{SP}|=3.29\pm1.01$ and $|\rho_k^{PS}|=2.33\pm0.73$ in $B\rightarrow PS$ and $B\rightarrow SP$ decays ($P$ and $S$ denote pseudoscalar and scalar mesons, respectively), respectively. We also study the branching ratios and $CP$ asymmetries in the decay modes involving other scalar mesons, including $f_0(980)$, $a_0(980)$, $a_0(1450)$ and $K_0^*(1430)$, to test the rationality of the values of $|\rho_k^{SP}|$ and $|\rho_k^{PS}|$. Meanwhile, the wealth of experimental data facilitate the examination of the forward-backward asymmetry induced $CP$ asymmetries (FB-CPAs), and the localized $CP$ asymmetries (LACPs). We investigate these asymmetries resulting from the interference between $\rho(770)^0$ and $f_0(500)$ for $B^\pm\rightarrow \pi^\pm\pi^+\pi^-$ and $B^\pm\rightarrow K^\pm\pi^+\pi^-$ decays when the invariant mass of $\pi^+\pi^-$ locates in the low-energy region $0.445\mathrm{GeV}

The possible existence of nucleon-antinucleon bound states has been studied for decades. We investigate the $e^+e^-\to p\bar{p}$ and $e^+e^-\to n\bar{n}$ cross sections in the nonrelativistic effective field theory framework. The proton-antiproton and neutron-antineutron coupled-channel final state interactions are considered and found responsible for near-threshold enhancements. Both the proton-neutron mass difference and the Coulomb interaction between $p$ and $\bar{p}$ are considered, and the $N\bar{N}$ strong interactions are taken into account through a short-distance optical potential. By fitting the low energy constants in the amplitudes to the data for the near-threshold $e^+e^-\to N\bar{N}$ cross sections from the BESIII and SND Collaborations, a $N\bar{N}$ quasi-bound state is found just above the $p\bar{p}$ threshold, and another $N\bar{N}$ pole is found on the unphysical Riemann sheet, farther away from the threshold. The constructed coupled-channel amplitude with Coulomb effects also offers a framework that can be used directly in experimental analyses on fine structures near the $N\bar{N}$ thresholds., Comment: 17 pages, 9 figures, comments are welcome

The interference between amplitudes corresponding to different intermediate resonances plays an important role in generating large CP asymmetries in phase space in multi-body decays of bottom and charmed mesons. In this paper, we study the CP violation in the decay channel ${\overline{B}}^{0}\rightarrow K^{-}\pi^{+}\pi^{0}$ in phase space region where the intermediate resonances $\overline{K}^{*}(892)^{0}$ and ${\overline{K}^{*}_{0}(700)}$ dominate. The Forward-Backward Asymmetry (FBA) and the CP asymmetry induced by FBA (FB-CPA), which are closely related to the interference effects between the two aforementioned resonances, are especially investigated. The correlation of the behaviour of FBA and FB-CPA with the relative strong phase between the amplitude is analyzed., Comment: 16 pages, 5 figures

We analyze the latest LHCb data on the $\pi^+\pi^-$ spectrum in the isospin-violating $X(3872)\to J/\psi \pi^+\pi^-$ decay, based on dispersion theory to deal with the $\pi\pi$ final state interactions. Additionally, the isospin breaking effects are properly introduced, allowing for a reliable and accurate extraction of the ratio, $R_X$, between the $X(3872)$ couplings to the $J/\psi \rho$ and $J/\psi \omega$ channels from the data. We find very good agreement with the LHCb data for the whole range of the $\pi^+\pi^-$ invariant mass, and $R_X$ is determined to be {$0.26\pm 0.03$}. Using this value, we make predictions for the $\pi^+\pi^0\pi^-$ mass distribution in the $X(3872)\to J/\psi \pi^+\pi^0\pi^-$ process, which is currently accessible by the BESIII Collaboration, and update a prediction for the pole positions of the isovector partner states of the $X(3872)$, $W_{c1}$, with $I(J^{PC})=1(1^{++})$., Comment: 9 pages, 1 table and 2 figures. Version to be published in Phys. Rev. D; results updated with a mistake on the rho-omega mixing corrected and a new appendix explaining how the mixing was obtained

In this work, we systematically study the heavy baryonium and heavy dibaryon systems using the Bethe-Salpeter equation in the ladder and instantaneous approximations for the kernel. Our results indicate that all the heavy baryonium systems, specifically $\Lambda_Q\bar{\Lambda}_Q$, $\Xi_Q\bar{\Xi}_Q$, $\Sigma_Q\bar{\Sigma}_Q$, $\Xi'_Q\bar{\Xi}'_Q$, and $\Omega_Q\bar{\Omega}_Q$ ($Q=c, b$), can form bound states. Among the heavy dibaryon systems, only the $\Xi_Q\Xi_Q$ system with $I=0$ and the $\Sigma_Q\Sigma_Q$ systems with $I=0$ and $I=1$ can exist as bound states. Additionally, the $\Sigma_Q\bar{\Sigma}_Q$ system with $I=2$ and the $\Sigma_Q\Sigma_Q$ system with $I=1$ are not deeply bound.

A mechanism of generating CP violation through the imaginary part of the interference of two amplitudes is proposed. This mechanism has shown clear evidence in decays such as $B^\pm\to \pi^\pm\pi^+\pi^-$. The proposed mechanism is helpful in searching for CP violation in bottom and charmed baryon decay processes., Comment: 12 pages,1 figure

Since 2003, plenty of resonant structures have been observed in the heavy quarkonium regime. Many of them are close to the thresholds of a few pairs of heavy hadrons. They are candidates of exotic hadrons and have attracted immense attentions. Based on a coupled-channel nonrelativistic effective field theory, we classify the near-threshold structures of a symmetry-related two-channel system according to the scattering length and channel coupling strength. We show that the evolution of the scattering amplitude line shapes can be understood from the pole trajectories in the complex energy plane, and the pole evolution can be traced back to the renormalization group fixed points. We provide a dictionary of correspondence between the evolution of line shapes and pole trajectories, which can be used to understand the experimental observations of the near-threshold structures., Comment: 8 pages, 2 figures, 2 tables. Comments are welcome

With a clean environment and high collision energy, the Circular Electron Positron Collider (CEPC) would be an excellent facility for heavy flavor physics. Using the Monte Carlo event generator Pythia, we simulate the production of the charmed (bottom) hadron pairs in the electron-positron collisions at the $Z$ factory of CEPC, and the inclusive production rates for typical candidates of the hidden/double-charm and hidden/double-bottom $S$-wave hadronic molecules are estimated at an order-of-magnitude level with the final state interactions after the hadron pair production. The predicted cross sections for the hidden-charm meson-meson molecules $X(3872)$ and $Z_c(3900)$ are at $\rm{pb}$ level, which are about two to three orders of magnitude larger than the production cross sections for the double-charm meson-meson molecules $T_{cc}$ and $T_{cc}^{*}$, as the double-charmed ones require the production of two pairs of $c\bar{c}$ from the $Z$ boson decay. The production cross sections for the hidden-charm pentaquark states $P_{c}$ and $P_{cs}$ as meson-baryon molecules are a few to tens of fb, which are about one magnitude larger than those of the possible hidden-charm baryon-antibaryon and double-charm meson-baryon molecules. In the bottom sector, the production cross sections for the $Z_b$ states as $B^{(*)}\bar{B}^{*}$ molecules are about tens to hundreds of fb, indicating $10^6$ - $10^7$ events from a two-year operation of CEPC, and the expected events from the double-bottom molecules are about 2 - 5 orders of magnitude smaller than the $Z_b$ states. Our results shows great prospects of probing heavy exotic hadrons at CEPC., Comment: 24 pages, 10 figures, published version

The extended kernel ridge regression (EKRR) method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models. These are: (i) the isospin dependent $A^{1/3}$ formula, (ii) relativistic continuum Hartree-Bogoliubov (RCHB) theory, (iii) Hartree-Fock-Bogoliubov (HFB) model HFB25, (iv) the Weizs\"acker-Skyrme (WS) model WS$^\ast$, and (v) HFB25$^\ast$ model. In the last two models, the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models, respectively. For each model, the resultant root-mean-square deviation for the 1014 nuclei with proton number $Z \geq 8$ can be significantly reduced to 0.009-0.013~fm after considering the modification with the EKRR method. The best among them was the RCHB model, with a root-mean-square deviation of 0.0092~fm. The extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined and it was found that after considering the odd-even effects, the extrapolation power was improved compared with that of the original KRR method. The strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron $N=126$ and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method., Comment: 8 pages, 5 figures, 1 table

Using chiral effective field theory, we predict that there must be isovector charmonium-like $D\bar D^*$ hadronic molecules with $J^{PC}=1^{++}$ denoted as $W_{c1}$. The inputs are the properties of the $X(3872)$, including its mass and the ratio of its branching fractions of decays into $J/\psi\rho^0$ and $J/\psi\omega$. The predicted states are virtual state poles of the scattering matrix, pointing at a molecular nature of the $X(3872)$ as well as its spin partners. They should show up as either a mild cusp or dip at the $D\bar D^*$ thresholds, explaining why they are elusive in experiments. The so far negative observation also indicates that the $X(3872)$ is either a bound state with non-vanishing binding energy or a virtual state, only in these cases the $X(3872)$ signal dominates over that from the $W_{c1}^0$. The pole positions are $3881.2^{+0.8}_{-0.0}- i 1.6^{+0.7}_{-0.9}$ MeV for $W_{c1}^0$ on the fourth Riemann sheet of the $D^0\bar D^{*0}$-$D^+D^{*-}$ coupled-channel system, and $3866.9^{+4.6}_{-7.7}- i (0.07\pm0.01)$ MeV for $W_{c1}^\pm$ on the second Riemann sheet of the $(D\bar D^*)^\pm$ single-channel system. The findings imply that the peak in the $J/\psi\pi^+\pi^-$ invariant mass distribution is not purely from the $X(3872)$ but contains contributions from $W_{c1}^0$ predicted here. The states should have isovector heavy quark spin partners with $J^{PC}=0^{++}$, $2^{++}$ and $1^{+-}$, with the last one corresponding to $Z_c$. We suggest to search for the charged $0^{++}$, $1^{++}$ and $2^{++}$ states in $J/\psi\pi^\pm \pi^0$., Comment: 26 pages, 8 figures; version to be published in JHEP

$C\!P$ violation in baryon decay processes is still undiscovered to date. We present a general analysis of the decay-angular-distributions and the corresponding $C\!P$ asymmetries in cascade decays of the type $\mathbb{H}\to R(\to ab) c$, where $\mathbb{H}$ is a heavy hadron that decays through weak interactions $\mathbb{H}\to R c$, and the resonance $R$ decays strongly via $R\to ab$. Based on the analysis, we propose to search for $C\!P$ violation in the decay-angular-distributions in the cascade decay processes ${\mathbb{B}}\to \mathcal{B} M$, with $\mathcal{B}$ or $M$ subsequently decaying through strong interactions, where ${\mathbb{B}}$ is the mother baryon, $\mathcal{B}$ or $M$ are the daughter baryon and meson, respectively, and $M$ has to be spin-nonzero. We also present some typical decay channels in which the search for such kinds of $C\!P$ asymmetries can be performed., Comment: 16 pages

In this work, we investigate the isospin breaking decay $X_b \to \pi^0\chi_{bJ}$ and the isospin conserved decay $X_b \to \pi\pi\chi_{bJ}$, where $X_b$ is taken to be the heavy quark flavor symmetry counterpart of $X(3872)$ in the bottomonium sector as a $B^*\bar B$ molecule candidate. Since the mass of this state may be far below the $B {\bar B}^*$ threshold and the mass difference between the neutral and charged bottom meson is small compared to the binding energy of the $X_b$, the isospin-violating decay channel $X_b \to \pi^0 \chi_{bJ}$ would be highly suppressed. The calculated partial width of $X_b \to \pi\pi\chi_{b1}$ is found to be about tens of $\rm{keVs}$, $1\sim 2$ order(s) of magnitude larger than those of $X_b \to \pi\pi\chi_{b2}$ and $X_b \to \pi\pi\chi_{b0}$. Taking into account the fact that the total width of $X_b$ may be smaller than a few MeV like $X(3872)$, the calculated branching ratios $X_b\to \pi\pi \chi_{b1}$ may reach to orders of $10^{-2}$, which makes it a possible channel for the experimental searching of the $X_b$., Comment: 14 pages, 5 figures, published in Phys.Rev.D

In this paper, some subtleties in the measurement of the transverse polarization of the produced hadrons on symmetric colliders -- such as the Large Hadron Collider when conducting the $pp$ collisions -- are revealed. It can be proved that the transverse polarization of the produced particles with opposite pseudorapidity takes exactly opposite values if the normal vector of the production plane is defined in a convention-dependent way, regardless of whether parity is conserved or not in the production process. The analysis shows that, due to the symmetry of the initial state, the $\Lambda_b$ transverse polarization measured by the CMS collaboration in Phys. Rev. D 97, 072010 (2018) should be exactly equal to zero. A modified measurement of the $\Lambda_b$ polarization for CMS and ATLAS is proposed, the result of which can be compared to the LHCb measurement., Comment: Accepted by Phys. Rev. D, 4 pages, 1 figure (with 2 subfigures)

With the assumptions that the $T_{cc}^+$ discovered at LHCb is a $D^{*}D$ hadronic molecule, using a nonrelativistic effective field theory we calculate the radiative partial widths of $T_{cc}^* \to D^*D\gamma$ with $T_{cc}^*$ being a $D^{*}D^{*}$ shallow bound state and the heavy-quark-spin partner of $T_{cc}^+$. The $I=0$ $D^*D$ rescattering effect with the $T_{cc}$ pole is taken into account. The results show that the isoscalar $D^{\ast} D$ rescattering can increase the tree-level decay width of $T_{cc}^{\ast +}\rightarrow D^{*+}D^0\gamma$ by about $50\%$, while decrease that of $T_{cc}^{\ast +}\rightarrow D^{*0}D^+\gamma$ by a similar amount. The two-body partial decay widths of the $T_{cc}^{*+}$ into $T_{cc}^+\gamma$ and $T_{cc}^+\pi^0$ are also calculated, and the results are about $6~\rm{keV}$ and $3~\rm{keV}$, respectively. Considering that the $D^*$ needs to be reconstructed from the $D\pi$ or $D\gamma$ final state in an experimental measurement, the four-body partial widths of the $T_{cc}^{*+}$ into $DD\gamma\gamma$ and $DD\pi\gamma$ are explicitly calculated, and we find that the interference effect between different intermediate $D^*D\gamma$ states is small. The total radiative decay width of the $T_{cc}^*$ is predicted to be about $24~\rm{keV}$. Adding the hadronic decay widths of $T_{cc}^* \to D^*D\pi$, the total width of the $T_{cc}^*$ is finally predicted to be $(65\pm2)$ keV., Comment: 27 pages, 13 figures. arXiv admin note: text overlap with arXiv:2211.02479

Starting from the hypothesis that the $T_{cc}^+$ discovered at LHCb is a $D^{\ast+} D^0/D^{\ast 0}D^+$ hadronic molecule, we consider the partial width of its heavy quark spin partner, the $T_{cc}^{\ast +}$ as a $D^{\ast +} D^{\ast 0}$ shallow bound state, decaying into the $D^{\ast}D\pi$ final states including the contributions of the $D^{\ast} D$ and $D^{\ast} \pi$ final state interaction by using a nonrelativistic effective field theory. Because of the existence of the $T_{cc}^+$ pole, the $I=0$ $D^{\ast} D$ rescattering can give a sizeable correction up to about $40\%$ to the decay widths considering only the tree diagrams, and the $D^{\ast} \pi$ rescattering correction is about $10\%$. The four-body partial widths of the $T_{cc}^{*+}$ into $D D\pi\pi$ are also explicitly calculated, and we find that the interference effect between different intermediate $D^*D\pi$ states is small. The total width of the $T_{cc}^{*+}$ is predicted to be about 41 keV., Comment: 31 pages, 10 figues. Results updated and extended, version to be published in Phys. Rev. D

It is proposed to search for $C\!P$ violation through the two-fold angular distributions in the four-body decays of bottom and charmed hadrons. The two polar angles in the two-fold angular distributions are correlated, to which the interferences of intermediate resonances are one important origin. These interferences will leave tracks in the two-fold angular distributions, with which the $C\!P$ violation can be studied. Special attention is paid to the case when all the intermediate resonances are different, which is unique to four-body decays. It is suggested to look for $C\!P$ violation in four-body decays such as $\Lambda_b^0\to p \pi^-\pi^+\pi^-$ through the analysis of the two-fold angular distributions. The method proposed in this paper is also widely applicable to other four-body decays processes., Comment: 8 pages, 3 figures, accepted by PRD

$CP$ violation of the decay $B^{\pm}\rightarrow \pi^{\pm}\pi^{+}\pi^{-}$ in the $f_{0}(500)-\rho(770)^{0}$ interfering region is analyzed. The forward-backward asymmetries (FBAs) and the corresponding $CP$ asymmetries FB-$CP$As are particularly investigated. To isolate the $CP$V caused by the interference of different partial wave more cleanly, we also introduce the direct-$CP$V-subtracted FB-$CP$A. Based on the LHCb data, we extract the FBAs, FB-$CP$As, direct-$CP$V-subtracted FB-$CP$A, as well as the regional $CP$As with invariant mass of the $\pi^{+}\pi^{-}$ pair in the range 0.2 GeV/$c^{2}<\sqrt{s_{\text{low}}}<1.8$ GeV/$c^{2}$. It is found that the (direct-$CP$V-subtracted) FB-$CP$As are quite large in the $f_{0}(500)-\rho(770)^{0}$ interfering region, which confirms that the interference of the intermediate resonances $f_{0}(500)$ and $\rho(770)^{0}$ plays an important role for the $CP$ violation of the three-body decay channel $B^{\pm}\rightarrow \pi^{\pm}\pi^{+}\pi^{-}$., Comment: 14 pages, 5 figures, 3 tables, version accepted by PRD

We introduce a set of observables representing angular distribution asymmetries, which can be viewed as a generalization of the forward-backward asymmetry of angular distributions, and can be used as an effective tool to search for $C\!P$ violation in three-body decays of bottom and charmed baryons. We propose to search for such $C\!P$ asymmetries (1) in decays with $\Lambda^0$, $\Sigma^\pm$, or $\Lambda_c^+$ involved, such as $\Lambda_b\to \Lambda^0 D$ and $\Lambda_b\to\Lambda^0\rho(770)^0$; and (2) in three-body decays of bottom baryons with opposite parity intermediate resonances involved. Typical examples include $\Xi_b^-\to p K^- K^-$, $\Lambda_b^0\to p K_S\pi^-$ and $\Lambda_b^0\to p \pi^0\pi^-$, in which the last decay channel is used as a toy model to illustrate of the basic idea., Comment: 13 pages, 1 figure, discussion on a toy model added with contribution from J.-J. Qi

The kernel ridge regression (KRR) method with Gaussian kernel is used to improve the description of the nuclear charge radius by several phenomenological formulae. The widely used $A^{1/3}$, $N^{1/3}$ and $Z^{1/3}$ formulae, and their improved versions by considering the isospin dependence are adopted as examples. The parameters in these six formulae are refitted using the Levenberg-Marquardt method, which give better results than the previous ones. The radius for each nucleus is predicted with the KRR network, which is trained with the deviations between experimental and calculated nuclear charge radii. For each formula, the resultant root-mean-square deviations of 884 nuclei with proton number $Z \geq 8$ and neutron number $N \geq 8$ can be reduced to about 0.017~fm after considering the modification of the KRR method. The extrapolation ability of the KRR method for the neutron-rich region is examined carefully and compared with the radial basis function method. It is found that the improved nuclear charge radius formulae by KRR method can avoid the risk of overfitting and have a good extrapolation ability. The influence of the ridge penalty term on the extrapolation ability of the KRR method is also discussed. At last, the nuclear charge radii of several recently observed K and Ca isotopes have been analyzed., Comment: 9 pages, 5 figures, 2 tables

An analysis of the Forward-Backward Asymmetry (FBA) in the decay $B^\pm \to K^\pm K^\mp K^\pm$ is carried out based on the LHCb data. It is found that the large FBA observed for the invariant mass of the $K^+ K^-$ pair around 1.5 GeV can be explained by the interference of the amplitudes between the resonances with even and odd spins, where the former can be the spin-0 $f_0(1500)$ resonance plus a non-resonance $s$-wave, while the latter is a spin-1 resonance which is probably $\rho^0 (1450)$. The analysis shows the existence of the decay channel $B^\pm\to \rho^0(1450) K^\pm$, with $C\!P$ asymmetry of $A_{CP}(B^\pm\to \rho^0(1450) K^\pm)=(-3.4\pm3.0)\%$. This is in contradiction with the conclusion of BaBar in Phys. Rev. D 85, 112010, according to which the analysis showed no signal of the spin-1 resonance $\rho^0(1450)$. We suggest our experimental colleagues to perform a closer analysis to this channel. We also suggest to perform the measurements of the FBAs (as well as the FB-$C\!P$As) in other three-body decay channels of beauty and charmed mesons, as it is helpful for resonance analysis., Comment: 14 pages, 5 figures, 3 tables

The influence of the isospin-breaking $\pi^0\!\!-\!\eta\!-\!\eta'$ mixing effect on the $CP$-asymmetries of $B\to K\pi$ processes is examined for the first time. It is found that this mixing effect brings a large uncertainty both to the $CP$-asymmetry sum rule of $B\to K\pi$ processes and the $CP$-asymmetry difference of the $B^+\to K^+\pi^0$ and $B^0\to K^+\pi^-$, obscuring the significance of the $K\pi$-puzzle. This uncertainty can be so large that it is even possible to explain the $K\pi$-puzzle by the $\pi^0\!\!-\!\eta\!-\!\eta'$ mixing effect {\it alone}., Comment: 7 pages, with no figure

There must be Coulomb bound states of a pair of hadrons, which are stable against the strong interaction, with opposite electric charges. Such bound states are hadronic atoms. We study the properties and the production of the ground-state $D^+D^-$ hadronic atom $A_{D^+D^-}$, called dionium, with quantum numbers $J^{PC}=0^{++}$. Using a nonrelativistic effective field theory for the $D^0\bar{D}^0$-$D^+D^-$ coupled-channel system, the mass of the ground-state dionium is predicted to be $(3739.3 \pm 0.1)~\text{MeV}$, with the binding energy reduced by about 10% compared to the Coulomb binding energy due to the strong interaction. Its width for the decay into the neutral $D^0\bar D^0$ channel is predicted to be $1.8^{+1.4}_{-0.6}$ keV using lattice inputs for the $D\bar D$ strong interaction. The cross section for the inclusive prompt production of the dionium at CMS and LHCb and that for the direct production $p\bar p\to A_{D^+D^-}$ at PANDA are estimated at an order-of-magnitude level. In particular, we expect that $\mathcal{O}(10^3\sim 10^5)$ events of the reaction chain $p\bar p\to A_{D^+D^-}\to D^0\bar D^0 \to K^-\pi^+K^+\pi^-$ can be collected at PANDA, and valuable information on the charmed meson interaction and on understanding charmoniumlike states will be obtained., Comment: 25 pages, 5 figures. Version to appear in Phys. Rev. D

The particle-number conserving method based on the cranked shell model is adopted to investigate the possible antimagnetic rotation bands in $^{100}$Pd. The experimental kinematic and dynamic moments of inertia, together with the $B(E2)$ values are reproduced quite well. The occupation probability of each neutron and proton orbital in the observed antimagnetic rotation band is analyzed and its configuration is confirmed. The contribution of each major shell to the total angular momentum alignment with rotational frequency in the lowest-lying positive and negative parity bands is analyzed. The level crossing mechanism of these bands is understood clearly. The possible antimagnetic rotation in the negative parity $\alpha=0$ branch is predicted, which sensitively depends on the alignment of the neutron ($1g_{7/2}$, $2d_{5/2}$) pseudo-spin partners. The two-shears-like mechanism for this antimagnetic rotation is investigated by examining the closing of the proton hole angular momentum vector towards the neutron angular momentum vector., Comment: 17 pages, 7 figures

The recently observed two and four-quasiparticle high-spin rotational bands in the odd-odd nuclei $^{166, 168, 170, 172}$Re are investigated using the cranked shell model with pairing correlations treated by a particle-number conserving method. The experimental moments of inertia and alignments can be reproduced well by the present calculation if appropriate bandhead spins and configurations are assigned for these bands, which in turn confirms their spin and configuration assignments. It is found that the bandhead spins of those two rotational bands observed in $^{166}$Re~[Li {\it et al.}, Phys. Rev. C 92 014310 (2015)] should be both increased by $2\hbar$ to get in consistent with the systematics of the experimental and calculated moments of inertia for the same configurations in $^{168, 170, 172}$Re. The variations of the backbendings/upbendings with increasing neutron number in these nuclei are investigated. The level crossing mechanism is well understood by analysing the variations of the occupation probabilities of the single-particle states close to the Fermi surface and their contributions to the angular momentum alignment with rotational frequency. In addition, the influence of the deformation driving effects of the proton $1/2^-[541]$ ($h_{9/2}$) orbtial on the level crossing in $^{172}$Re is also discussed., Comment: 29 pages, 14 figures, 3 tables

Despite the large baryon-anti-baryon asymmetry in the observable Universe, the closely related phenomenon -- the violation of the combined charge and parity symmetry ($C\!P$V) -- has not been observed in the baryon sector in laboratories. In this paper, a new strategy for searching for $C\!P$V in heavy hadron multi-body decays is proposed, in which a set of novel observables measuring $C\!P$V in such decays -- the partial wave $C\!P$ asymmetries (PW$C\!P$As) -- are introduced. This strategy is model-independent and applicable to multi-body decays of heavy hadrons with arbitrary spin configurations in both initial and final states, and with any number of particles in the final state. It is especially applicable for $C\!P$V investigations in multi-body decays of heavy baryons. As applications of this strategy, we suggest to measure the PW$C\!P$As in some decay channels of bottom baryons such as $\Lambda_b^0\to p \pi^-\pi^+\pi^-$, $\Lambda_b\to p K^- \pi^+\pi^-$, $\Lambda^0_b\to p\pi^-K^+K^-$, $\Lambda_b^0\to\Lambda K^+\pi^-$, and $\Lambda_b^0\to p \pi^- K_s$.}, Comment: 15 pages, 4 figures, 2 tables, accepted for publication in JHEP

A novel observable measuring the $C\!P$ asymmetry in multi-body decays of heavy mesons, which is called the forward-backward asymmetry induced $C\!P$ asymmetry (FBI-$C\!P$A), $A_{CP}^{FB}$, is introduced. This observable has the dual advantages that 1) it can isolate the $C\!P$ asymmetry associated with the interference of the $S$- and $P$-wave amplitude from that associated with the $S$- or $P$-wave amplitude alone; 2) it can effectively almost double the statistics comparing to the conventionally defined regional $C\!P$ asymmetry. We also suggest to perform the measurements of FBI-$C\!P$A in some three-body decay channels of charm and beauty mesons., Comment: 13 pages, accepted for publication in PLB, title changed

In the framework of the QCD factorization approach, we study the localized $CP$ violations of the $B^-\rightarrow K^- \pi^+\pi^-$ decay with and without $a_0^0(980)-f_0(980)$ mixing mechanism, respectively, and find that the localized $CP$ violation can be enhanced by this mixing effect when the mass of the $\pi^+\pi^-$ pair is in the vicinity of the $f_0(980)$ resonance. The corresponding theoretical prediction results are $\mathcal{A}_{CP}(B^-\rightarrow K f_0 \rightarrow K^-\pi^+\pi^-)=[0.24, 0.36]$ and $\mathcal{A}_{CP}(B^-\rightarrow K^- f_0(a_0) \rightarrow K^-\pi^+\pi^-)=[0.33, 0.52]$, respectively. Meanwhile, we also calculate the branching fraction of the $B^-\rightarrow K^-f_0(980)\rightarrow K^-\pi^+\pi^-$ decay, which is consistent with the experimental results. We suggest that $a_0^0(980)-f_0(980)$ mixing mechanism should be considered when studying the $CP$ violation of the $B$ or $D$ mesons decays theoretically and experimentally., Comment: 11 pages, 3 figures

The $X(3872)$, whose mass coincides with the $D^0\bar D^{*0}$ threshold, is the most extended hadron object. Since its discovery in 2003, debates have never stopped regarding its internal structure. We propose a new object, the $X$ atom, which is the $D^\pm D^{*\mp}$ composite system with positive charge parity and a mass of $(3879.89\pm0.07)$ MeV, formed mainly due to the Coulomb force. We show that a null signal of the $X$ atom can be used to put a lower limit on the binding energy of the $X(3872)$. From the current knowledge of the $X(3872)$ properties, the production rate for the $X$ atom relative to the $X(3872)$ in $B$ decays and at hadron colliders should be at least $1\times10^{-3}$. New insights into the $X(3872)$ will be obtained through studying the $X$ atom., Comment: 6 pages, 3 figures

We study the $CP$ asymmetry of $B^\pm\to \omega K^\pm$ with the inclusion of the $\rho-\omega$ mixing mechanism. It is shown that the $CP$ asymmetry of $B^\pm\to\omega K^\pm$ experimentally measured ($A_{CP}^{\text{exp}}$) and conventionally defined ($A_{CP}^{\text{con}}$) are in fact different, which relation can be illustrated as $A_{CP}^{\text{exp}}=A_{CP}^{\text{con}}+\Delta A_{CP}^{\rho\omega}$, with $\Delta A_{CP}^{\rho\omega}$ the $\rho-\omega$ mixing contribution to $A_{CP}^{\text{exp}}$. $A_{CP}^{\text{exp}}$ is in fact the regional $CP$ asymmetry of $B^\pm\to\pi^+\pi^-\pi^0 K^\pm$ when the invariant mass of the three pions lies in the vicinity of the $\omega$ resonance. The numerical value of $\Delta A_{CP}^{\rho\omega}$ is extracted from the experimental data of $B^\pm\to\pi^+\pi^-K^\pm$ and is found to be comparable with $A_{CP}^{\text{exp}}$, hence, nonnegligible. The conventionally defined $CP$ asymmetry, $A_{CP}^{\text{con}}$, is obtained from the values of $A_{CP}^{\text{exp}}$ and $\Delta A_{CP}^{\rho\omega}$, and is compared with the theoretical calculations in the literature., Comment: 8 pages, version accepted by JHEP

High-spin rotational bands in rare-earth Er ($Z=68$), Tm ($Z=69$) and Yb ($Z=70$) isotopes are investigated by three different nuclear models. These are (i) the cranked relativistic Hartree-Bogoliubov (CRHB) approach with approximate particle number projection by means of the Lipkin-Nogami (LN) method, (ii) the cranking covariant density functional theory (CDFT) with pairing correlations treated by a shell-model-like approach (SLAP) or the so called particle-number conserving (PNC) method, and (iii) cranked shell model (CSM) based on the Nilsson potential with pairing correlations treated by the PNC method. A detailed comparison between these three models in the description of the ground state rotational bands of even-even Er and Yb isotopes is performed. The similarities and differences between these models in the description of the moments of inertia, the features of band crossings, equilibrium deformations and pairing energies of even-even nuclei under study are discussed. These quantities are considered as a function of rotational frequency and proton and neutron numbers. The changes in the properties of the first band crossings with increasing neutron number in this mass region are investigated. On average, a comparable accuracy of the description of available experimental data is achieved in these models. However, the differences between model predictions become larger above the first band crossings. Because of time-consuming nature of numerical calculations in the CDFT-based models, a systematic study of the rotational properties of both ground state and excited state bands in odd-mass Tm nuclei is carried out only by the PNC-SCM. With few exceptions, the rotational properties of experimental 1-quasiparticle and 3-quasiparticle bands in $^{165,167,169,171}$Tm are reproduced reasonably well., Comment: 29 pages, 18 figures. submitted to Physical Review C, revised version with takes into account the suggestions of referee

The rotational bands in the neutron-rich nuclei $^{153-157}$Pm are investigated by a particle-number conserving method. The kinematic moments of inertia for the 1-quasiparticle bands in odd-$A$ Pm isotopes $^{153, 155, 157}$Pm are reproduced quite well by the present calculation. By comparison between the experimental and calculated moments of inertia for the three 2-quasiparticle bands in the odd-odd nuclei $^{154, 156}$Pm, their configurations and bandhead spins have been assigned properly. For the 2-quasiparticle band in $^{154}$Pm, the configuration is assigned as $\pi5/2^-[532]\otimes \nu3/2^-[521]$ ($K^\pi=4^+$) with the bandhead spin $I_0=4\hbar$. In $^{156}$Pm, the same configuration and bandhead spin assignments have been made for the 2-quasiparticle band with lower excitation energy. The configuration $\pi5/2^+[413]\otimes \nu5/2^+[642]$ ($K^\pi=5^+$) with the bandhead spin $I_0=5\hbar$ is assigned for that with higher excitation energy., Comment: 6 figures, 2 tables

The particle-number-conserving method based on the cranked shell model is used to investigate the antimagnetic rotation band in $^{104}$Pd. The experimental moments of inertia and reduced $B(E2)$ transition probabilities are reproduced well. The $J^{(2)}/B(E2)$ ratios are also discussed. The occupation probability of each orbital close to the Fermi surface and the contribution of each major shell to the total angular momentum alignment with rotational frequency are analyzed. The backbending mechanism of the ground state band in $^{104}$Pd is understood clearly and the configuration of the antimagnetic rotation after backbending is clarified. In addition, the crossing of a four quasiparticle states with this antimagnetic rotation band is also predicted. By examining the the closing of the four proton hole angular momenta towards the neutron angular momenta, the "two-shears-like" mechanism for this antimagnetic rotation is investigated and two stages of antimagnetic rotation in $^{104}$Pd are seen clearly., Comment: 7 figures

The $\theta_K$ has been re-evaluated via mass relations and latest experimental results, meanwhile, the $M_{K_{1B}}$ also be obtained. Based on the singlet-octet mixing model and quark-flavor mixing model, the $\theta_{h_1}$ has been recalculated with a modified formula, by inputting $M_{K_{1B}}$ instead of $\theta_K$. The values are calculated to be $|{\theta _K}| = {(42.6 \pm 2.2)^ \circ }$, $M_{K_{1B}} = 1333.9 \pm 4.6\ {\rm{MeV}}/c^{2}$ and $\theta _{h_1} = 29.5\pm 2.0^\circ$. Using these calculations as input, we predict that the branching fraction of $J/\psi \to \eta'(\eta)h_1(1170)$ is about one order higher than that of $J/\psi \to \eta'(\eta)h_1(1415)$, which can be measured in future experiments to test the validity of these two models., Comment: 6 pages, with no figure

The multi-particle states and rotational properties of two-particle bands in $^{254}$No are investigated by the cranked shell model (CSM) with pairing correlations treated by a particle-number conserving (PNC) method. For the first time, the rotational bands on top of two-particle $K^{\pi}=3^+,8^-$ and $10^+$ states and the pairing reduction are studied theoretically in $^{254}$No. The experimental excitation energies and moments of inertia for the multi-particle state are reproduced well by the calculation. Better agreement with the data are achieved by including the high-order deformation $\varepsilon_{6}$ which leads to enlarged $Z=100$ and $N=152$ deformed shell gaps. The rise of the $J^{(1)}$ in these two-particle bands compared with the ground-state band is attributed to the pairing reduction due to the Pauli blocking effects.

In this work, within the QCD factorization approach, we study the localized integrated $CP$ violation in the $B^-\rightarrow \pi^-\pi^+\pi^-$ decay and the branching fraction of the $B^-\rightarrow\sigma\pi^-$ decay. Both the resonance and nonresonance contributions are included when we study the localized $CP$ asymmetry in the $B^-\rightarrow \pi^-\pi^+\pi^-$ decay. The resonance contributions from the scalar $\sigma(600)$ and vector $\rho^0(770)$ mesons are included. For the $\sigma(600)$ meson, we apply both the Breit-Wigner and Bugg models to deal with its propagator, and obtain $\mathcal{B}(B^-\rightarrow \sigma(600)\pi^-)<1.67\times10^{-6}$ and $\mathcal{B}(B^-\rightarrow \sigma(600) \pi^-)<1.946\times10^{-5}$ in these two models, respectively. We find that there is no allowed divergence parameters $\rho_S$ and $\phi_S$ to satisfy the experimental data $\mathcal{A_{CP}}(\pi^-\pi^+\pi^-)=0.584\pm0.082\pm0.027\pm0.007$ in the region $m_{\pi^+\pi^- \mathrm{high}}^2>15$ $\mathrm{GeV}^2$ and $m_{\pi^+\pi^-\mathrm{low}}^2<0.4$ $\mathrm{GeV}^2$ and the upper limit of $\mathcal{B}(B^-\rightarrow \sigma(600)\pi^-)$ in the Breit-Wigner model, however, there exists the region $\rho_S\in[1.70,3.34]$ and $\phi_S \in [0.50,4.50]$ satisfying the data for $\mathcal{A_{CP}}(\pi^-\pi^+\pi^-)$ and the upper limit of $\mathcal{B}(B^-\rightarrow \sigma(600)\pi^-)$ in the Bugg model. This reveals that the Bugg model is more plausible than the Breit-Wigner model to describe the propagator of the $\sigma(600)$ meson even though the finite width effects are considered in both models. The large values of $\rho_S$ indicate that the contributions from weak annihilation and hard spectator scattering processes are both large, especially, the weak annihilation contribution should not be negleted for $B$ decays to final states including a scalar meson., Comment: arXiv admin note: substantial text overlap with arXiv:1811.02167

We study the $\mathit{CP}$ violation induced by the interference between two intermediate resonances $K^*(892)^+$ and $K^*(892)^-$ in the phase space of singly-Cabibbo-suppressed decay $D^0 \to K^+K^-\pi^0$. We adopt the factorization-assisted topological approach in dealing with the decay amplitudes of $D^0 \to K^\pm K^*(892)^\mp$. The $\mathit{CP}$ asymmetries of two-body decays are predicted to be very tiny, which are $(-1.27 \pm 0.25) \times 10^{-5}$ and $(3.86 \pm 0.26) \times 10^{-5}$ respectively for $D^0 \to K^+ K^*(892)^-$ and $D^0 \to K^- K^*(892)^+$. While the differential $\mathit{CP}$ asymmetry of $D^0 \to K^+K^-\pi^0$ is enhanced because of the interference between the two intermediate resonances, which can reach as large as $3\times10^{-4}$. For some NPs which have considerable impacts on the chromomagnetic dipole operator $O_{8g}$, the global $\mathit{CP}$ asymmetries of $D^0 \to K^+ K^*(892)^- $ and $D^0 \to K^- K^*(892)^+ $ can be then increased to $(0.56\pm0.08)\times10^{-3}$ and $(-0.50\pm0.04)\times10^{-3}$, respectively. The regional $\mathit{CP}$ asymmetry in the overlapped region of the phase space can be as large as $( 1.3\pm 0.3)\times10^{-3}$., Comment: 24 pages

The structures of two observed high-spin rotational bands in the doubly-odd nucleus ${}^{168}$Ta are investigated using the cranked shell model with pairing correlations treated by a particle-number conserving method, in which the blocking effects are taken into account exactly. The experimental moments of inertia and alignments are reproduced very well by the calculations, which confirms the configuration assignments for these two bands in previous works. The backbending and upbending mechanisms in these two bands are analyzed in detail by calculating the occupation probabilities of each orbital close to the Fermi surface and the contributions of each orbital to the total angular momentum alignments. The investigation shows that the level crossings in the first backbending is the neutron $i_{13/2}$ crossing and the in second upbending is the proton $h_{11/2}$ crossing., Comment: 12 pages, 5 figures. arXiv admin note: text overlap with arXiv:1810.06086 and substantial text overlap with arXiv:1606.00573

In this work, we study the localized $CP$ violation in $B^-\rightarrow K^-\pi^+\pi^-$ and $B^-\rightarrow K^- \sigma(600)$ decays by employing the quasi two-body QCD factorization approach. Both the resonance and the nonresonance contributions are studied for the $B^-\rightarrow K^-\pi^+\pi^-$ decay. The resonance contributions include those not only from $[\pi\pi]$ channels including $\sigma(600)$, $\rho^0(770)$ and $\omega(782)$ but also from $[K\pi]$ channels including $K^*(892)$, $K_0^*(1430)$, $K^*(1410)$, $K^*(1680)$ and $K_2^*(1430)$. By fitting the experimental data $\mathcal{A_{CP}}(K^-\pi^+\pi^-)=0.678\pm0.078\pm0.0323\pm0.007$ for $m_{K^-\pi^+}^2<15$ $\mathrm{GeV}^2$ and $0.08