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<jats:title>Abstract</jats:title> <jats:p>It is believed that there are more fundamental gauge symmetries beyond those described by the Standard Model of particle physics. The scales of these new gauge symmetries are usually too high to be reachable by particle colliders. Considering that the phase transition (PT) relating to the spontaneous breaking of new gauge symmetries to the electroweak symmetry might be strongly first order, we propose considering the stochastic gravitational waves (GW) arising from this phase transition as an indirect way of detecting these new fundamental gauge symmetries. As an illustration, we explore the possibility of detecting the stochastic GW generated from the PT of <jats:inline-formula> <jats:tex-math><?CDATA $ {\bf{B}}-{\bf{L}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123102_M1.jpg" xlink:type="simple" /> </jats:inline-formula> in the space-based interferometer detectors. Our study demonstrates that the GW energy spectrum is reachable by the LISA, Tianqin, Taiji, BBO, and DECIGO experiments only for the case where the spontaneous breaking of <jats:inline-formula> <jats:tex-math><?CDATA $ {\bf{B}}-{\bf{L}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123102_M2.jpg" xlink:type="simple" /> </jats:inline-formula> is triggered by at least two electroweak singlet scalars. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>In this work, we propose the possible assignment of the newly observed <jats:inline-formula> <jats:tex-math><?CDATA $X(2239)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M4.jpg" xlink:type="simple" /> </jats:inline-formula>, as well as <jats:inline-formula> <jats:tex-math><?CDATA $\eta(2225)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M5.jpg" xlink:type="simple" /> </jats:inline-formula>, as a molecular state from the interaction of a baryon <jats:inline-formula> <jats:tex-math><?CDATA $\Lambda$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M6.jpg" xlink:type="simple" /> </jats:inline-formula> and an antibaryon <jats:inline-formula> <jats:tex-math><?CDATA $\bar{\Lambda}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M7.jpg" xlink:type="simple" /> </jats:inline-formula>. With the help of effective Lagrangians, the <jats:inline-formula> <jats:tex-math><?CDATA $\Lambda\bar{\Lambda}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M8.jpg" xlink:type="simple" /> </jats:inline-formula> interaction is described within the one-boson-exchange model with <jats:inline-formula> <jats:tex-math><?CDATA $\eta$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M9.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $\eta'$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M10.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $\omega$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M11.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $\phi$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M12.jpg" xlink:type="simple" /> </jats:inline-formula>, and <jats:inline-formula> <jats:tex-math><?CDATA $\sigma$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M13.jpg" xlink:type="simple" /> </jats:inline-formula> exchanges considered. After inserting the potential kernel into the quasipotential Bethe-Salpeter equation, the bound states from the <jats:inline-formula> <jats:tex-math><?CDATA $\Lambda\bar{\Lambda}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M14.jpg" xlink:type="simple" /> </jats:inline-formula> interaction can be studied by searching for the pole of the scattering amplitude. Two loosely bound states with spin parities <jats:inline-formula> <jats:tex-math><?CDATA $I^G(J^{PC})=0^+(0^{-+})$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M15.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $0^-(1^{--})$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M16.jpg" xlink:type="simple" /> </jats:inline-formula> appear near the threshold with almost the same parameter. The <jats:inline-formula> <jats:tex-math><?CDATA $0^-(1^{--})$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M17.jpg" xlink:type="simple" /> </jats:inline-formula> state can be assigned to <jats:inline-formula> <jats:tex-math><?CDATA $X(2239)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M18.jpg" xlink:type="simple" /> </jats:inline-formula> observed at BESIII, which is very close to the <jats:inline-formula> <jats:tex-math><?CDATA $\Lambda\bar{\Lambda}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M19.jpg" xlink:type="simple" /> </jats:inline-formula> threshold. The scalar meson <jats:inline-formula> <jats:tex-math><?CDATA $\eta(2225)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M20.jpg" xlink:type="simple" /> </jats:inline-formula> can be interpreted as a <jats:inline-formula> <jats:tex-math><?CDATA $0^+(0^{-+})$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M21.jpg" xlink:type="simple" /> </jats:inline-formula> state from the <jats:inline-formula> <jats:tex-math><?CDATA $\Lambda\bar{\Lambda}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M22.jpg" xlink:type="simple" /> </jats:inline-formula> interaction. The annihilation effect is also discussed through a coupled-channel calculation plus a phenomenological optical potential. It provides large widths to two bound states produced from the <jats:inline-formula> <jats:tex-math><?CDATA $\Lambda\bar{\Lambda}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M23.jpg" xlink:type="simple" /> </jats:inline-formula> interaction. The mass of the <jats:inline-formula> <jats:tex-math><?CDATA $1^-$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M24.jpg" xlink:type="simple" /> </jats:inline-formula> state is slightly larger than the mass of the <jats:inline-formula> <jats:tex-math><?CDATA $0^-$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M25.jpg" xlink:type="simple" /> </jats:inline-formula> state after including the annihilation effect, which is consistent with our assignment of these two states as <jats:inline-formula> <jats:tex-math><?CDATA $X(2239)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M26.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $\eta(2225)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M27.jpg" xlink:type="simple" /> </jats:inline-formula>, respectively. The results suggest that further investigation is required to understand the structures near the <jats:inline-formula> <jats:tex-math><?CDATA $\Lambda\bar{\Lambda}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M28.jpg" xlink:type="simple" /> </jats:inline-formula> threshold, such as <jats:inline-formula> <jats:tex-math><?CDATA $X(2239)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M29.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $\eta(2225)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M30.jpg" xlink:type="simple" /> </jats:inline-formula>, and <jats:inline-formula> <jats:tex-math><?CDATA $X(2175)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123103_M31.jpg" xlink:type="simple" /> </jats:inline-formula>. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Motivated by the problem of expanding the single-trace tree-level amplitude of Einstein-Yang-Mills theory to the BCJ basis of Yang-Mills amplitudes, we present an alternative expansion formula in gauge invariant vector space. Starting from a generic vector space consisting of polynomials of momenta and polarization vectors, we define a new sub-space as a gauge invariant vector space by imposing constraints on the gauge invariant conditions. To characterize this sub-space, we compute its dimension and construct an explicit gauge invariant basis from it. We propose an expansion formula in this gauge invariant basis with expansion coefficients being linear combinations of the Yang-Mills amplitude, manifesting the gauge invariance of both the expansion basis and coefficients. With the help of quivers, we compute the expansion coefficients via differential operators and demonstrate the general expansion algorithm using several examples.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Vector boson scattering at the Large Hadron Collider (LHC) is sensitive to anomalous quartic gauge couplings (aQGCs). In this study, we investigate the aQGC contribution to <jats:italic>Wγjj</jats:italic> production at the LHC with <jats:inline-formula> <jats:tex-math><?CDATA $\sqrt{s}=13$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123105_M2.jpg" xlink:type="simple" /> </jats:inline-formula> TeV in the context of an effective field theory (EFT). The unitarity bound is applied as a cut on the energy scale of this production process, which is found to have significant suppressive effects on signals. To enhance the statistical significance, we analyze the kinematic and polarization features of the aQGC signals in detail. We find that the polarization effects induced by aQGCs are unique and can discriminate the signals from the SM backgrounds well. With the proposed event selection strategy, we obtain the constraints on the coefficients of dimension-8 operators with current luminosity. The results indicate that the process <jats:inline-formula> <jats:tex-math><?CDATA $pp \to W \gamma jj$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123105_M3.jpg" xlink:type="simple" /> </jats:inline-formula> is powerful for searching for the <jats:inline-formula> <jats:tex-math><?CDATA $O_{M_{2,3,4,5}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123105_M4.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $O_{T_{5,6,7}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123105_M5.jpg" xlink:type="simple" /> </jats:inline-formula> operators. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>In this paper, we summarize the existing methods of solving the evolution equation of the leading-twist <jats:italic>B</jats:italic>-meson LCDA. Then, in the Mellin space, we derive a factorization formula with next-to-leading-logarithmic (NLL) resummation for the form factors <jats:inline-formula> <jats:tex-math><?CDATA $F_{A,V}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123106_M2.jpg" xlink:type="simple" /> </jats:inline-formula> in the <jats:inline-formula> <jats:tex-math><?CDATA $B \to \gamma \ell\nu$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123106_M3.jpg" xlink:type="simple" /> </jats:inline-formula> decay at leading power in <jats:inline-formula> <jats:tex-math><?CDATA $\Lambda/m_b$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123106_M4.jpg" xlink:type="simple" /> </jats:inline-formula>. Furthermore, we investigate the power suppressed local contributions, factorizable non-local contributions (which are suppressed by <jats:inline-formula> <jats:tex-math><?CDATA $1/E_\gamma$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123106_M5.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $1/m_b$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_123106_M6.jpg" xlink:type="simple" /> </jats:inline-formula>), and soft contributions to the form factors. In the numerical analysis, which employs the two-loop-level hard function and the jet function, we find that both the resummation effect and the power corrections can sizably decrease the form factors. Finally, the integrated branching ratios are also calculated for comparison with future experimental data. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The cross sections for the <jats:sup>94</jats:sup>Zr(<jats:italic>n</jats:italic>,<jats:italic>d</jats:italic>*)<jats:sup>93m+g</jats:sup>Y, <jats:sup>96</jats:sup>Zr(<jats:italic>n</jats:italic>,γ)<jats:sup>97</jats:sup>Z, <jats:sup>96</jats:sup>Zr(<jats:italic>n</jats:italic>,2<jats:italic>n</jats:italic>)<jats:sup>95</jats:sup>Zr, <jats:sup>90</jats:sup>Zr(<jats:italic>n</jats:italic>,α)<jats:sup>87m</jats:sup>Sr, <jats:sup>94</jats:sup>Zr(<jats:italic>n</jats:italic>,α)<jats:sup>91</jats:sup>Sr,<jats:sup>90</jats:sup>Zr(<jats:italic>n</jats:italic>,<jats:italic>p</jats:italic>)<jats:sup>90m</jats:sup>Y, <jats:sup>92</jats:sup>Zr(<jats:italic>n</jats:italic>,<jats:italic>p</jats:italic>)<jats:sup>92</jats:sup>Y, and <jats:sup>94</jats:sup>Zr(<jats:italic>n</jats:italic>,<jats:italic>p</jats:italic>)<jats:sup>94</jats:sup>Y reactions have been measured in the neutron energy range of 13.5-14.8 MeV by means of the activation technique. The neutrons were produced via the D-T reaction. A high-purity germanium detector with high energy resolution was used to measure the induced γ activities. In combination with the nuclear reaction theoretical models, the excitation curves of the above-mentioned eight nuclear reactions within the incident neutron energy range from the threshold to 20 MeV were obtained by adopting the nuclear theoretical model program system Talys-1.9. The resulting experimental cross sections were analyzed and compared with the experimental data from published studies. Calculations were performed using Talys-1.9 and are in agreement with our experimental results, previous experimental values, as well as results of the theoretical excitation curves at the corresponding energies. The theoretical excitation curves generally match the experimental data well. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The atomic mass table presents zones where the structure of the states changes rapidly as a function of the neutron or proton number. Among them, notable examples are the <jats:italic>A</jats:italic> ≈ 100 Zr region, the Pb region around the neutron midshell (N = 104), and the <jats:italic>N</jats:italic> ≈ 90 rare-earth region. The observed phenomena can be understood in terms of either shape coexistence or quantum phase transitions. The objective of this study is to find an observable that can distinguish between both shape coexistence and quantum phase transitions. As an observable to be analyzed, we selected the two-neutron transfer intensity between the 0<jats:sup>+</jats:sup> states in the parent and daughter nuclei. The framework used for this study is the Interacting Boson Model (IBM), including its version with configuration mixing (IBM-CM). To generate wave functions of isotope chains of interest needed for calculating transfer intensities, previous systematic studies using IBM and IBM-CM were used without changing the parameters. The results of two-neutron transfer intensities are presented for Zr, Hg, and Pt isotopic chains using IBM-CM. Moreover, for Zr, Pt, and Sm isotopic chains, the results are presented using IBM with only a single configuration, i.e., without using configuration mixing. For Zr, the two-neutron transfer intensities between the ground states provide a clear observable, indicating that normal and intruder configurations coexist in the low-lying spectrum and cross at <jats:italic>A</jats:italic> = 98 → 100. This can help clarify whether shape coexistence induces a given quantum phase transition. For Pt, in which shape coexistence is present and the regular and intruder configurations cross for the ground state, there is almost no impact on the value of the two-neutron transfer intensity. Similar is the situation with Hg, where the ground state always has a regular nature. For the Sm isotope chain, which is one of the quantum phase transition paradigms, the value of the two-neutron transfer intensity is affected strongly. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Half-lives of <jats:italic>α</jats:italic> decay for <jats:italic>Z</jats:italic>≥ 84 nuclei are calculated based on the WKB theory applied for a phenomenological potential barrier composed of a centrifugal contribution and a screened electrostatic interaction represented by a Hulthen potential. For favored decays, the model has a single adjustable parameter associated with the screening of the electrostatic potential. The description of half lives for unfavored decays requires an additional hindrance term. A good agreement with experimental data is obtained in all considered cases. The evolution of the screening parameter for each nucleus revealed its dependence on shell filling. The model is also used for theoretical predictions on a few nuclei with uncertain or incomplete decay information. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We construct a new global optical model potential to describe the elastic scattering of <jats:sup>12</jats:sup>C. The experimental data of elastic-scattering angular distributions and total reaction cross sections for targets from <jats:sup>24</jats:sup>Mg to <jats:sup>209</jats:sup>Bi are considered below 200 MeV within the framework of the optical model. The results calculated using the derived global optical potential are then compared with the existing experimental data. The reliability of the global optical potential is further tested by predicting the elastic scattering data out of the mass and energy ranges, within which the global potential parameters are determined, and reasonable results are also obtained. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Using bare Argonne V4' (AV4'), V6' (AV6'), and V8' (AV8') nucleon–nucleon (NN) interactions, the nuclear equations of state (EOSs) for neutron matter are calculated with the unitary correlation operator and high-momentum pair methods. Neutron matter is described using a finite particle number approach with magic number <jats:inline-formula> <jats:tex-math><?CDATA $N=66$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_124104_M2.jpg" xlink:type="simple" /> </jats:inline-formula> under a periodic boundary condition. The central short-range correlation originating from the short-range repulsion in the <jats:inline-formula> <jats:tex-math><?CDATA $NN$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_124104_M3.jpg" xlink:type="simple" /> </jats:inline-formula> interaction is treated by the unitary correlation operator method (UCOM), and the tensor correlation and spin-orbit effects are described by the two-particle two-hole (2<jats:italic>p</jats:italic>2<jats:italic>h</jats:italic>) excitations of nucleon pairs, where the two nucleons with a large relative momentum are regarded as a high-momentum (HM) pair. With increasing 2<jats:italic>p</jats:italic>2<jats:italic>h</jats:italic> configurations, the total energy per particle of the neutron matter is well-converged under this UCOM+HM framework. Comparing the results calculated with AV4', AV6', and AV8' <jats:inline-formula> <jats:tex-math><?CDATA $NN$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_44_12_124104_M4.jpg" xlink:type="simple" /> </jats:inline-formula> interactions, we demonstrate the effects of the short-range correlation, tensor correlation, and spin-orbit coupling on the density dependence of the total energy per particle of neutron matter. Moreover, the contribution of each Hamiltonian component to the total energy per particle is discussed. The EOSs of neutron matter calculated within the present UCOM+HM framework agree with the calculations of six microscopic many-body theories, especially the auxiliary field-diffusion Monte Carlo calculations. </jats:p>