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<jats:title>Abstract</jats:title> <jats:p>The deformation and associated optimum/uniquely fixed orientations play an important role in the synthesis of compound nuclei via cold and hot fusion reactions, respectively, at the lowest and highest barrier energies. The choice of optimum orientation ( <jats:inline-formula> <jats:tex-math><?CDATA $\theta_{\rm opt}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014102_M1.jpg" xlink:type="simple" /> </jats:inline-formula>) for the ‘cold or elongated’ and ‘hot or compact’ fusion configurations of quadrupole ( <jats:inline-formula> <jats:tex-math><?CDATA $\beta_2$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014102_M2.jpg" xlink:type="simple" /> </jats:inline-formula>) deformed nuclei depends only on the +/- signs of <jats:inline-formula> <jats:tex-math><?CDATA $\beta_2$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014102_M3.jpg" xlink:type="simple" /> </jats:inline-formula>-deformation [J. Phys. G: Nucl. Part. Phys. <jats:bold>31</jats:bold>, 631-644 (2005)]. In our recent study [Phys. Rev. C <jats:bold>101</jats:bold>, 051601(R) 2020], we proposed a new set of <jats:inline-formula> <jats:tex-math><?CDATA $\theta_{\rm opt}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014102_M4.jpg" xlink:type="simple" /> </jats:inline-formula> (different from the values reported for quadrupole deformed nuclei) after the inclusion of octupole deformation (up to <jats:inline-formula> <jats:tex-math><?CDATA $\beta_3$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014102_M5.jpg" xlink:type="simple" /> </jats:inline-formula>) effects. Using the respective <jats:inline-formula> <jats:tex-math><?CDATA $\theta_{\rm opt}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014102_M6.jpg" xlink:type="simple" /> </jats:inline-formula> of <jats:inline-formula> <jats:tex-math><?CDATA $\beta_3$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014102_M7.jpg" xlink:type="simple" /> </jats:inline-formula>-deformed nuclei for cold and hot optimum orientations, we analyzed the impact of the soft- and rigid-pear shapes of octupole deformed nuclei on the fusion barrier characteristics (barrier height <jats:inline-formula> <jats:tex-math><?CDATA $V_B$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014102_M8.jpg" xlink:type="simple" /> </jats:inline-formula> and barrier position <jats:inline-formula> <jats:tex-math><?CDATA $R_B$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014102_M9.jpg" xlink:type="simple" /> </jats:inline-formula>). This analysis is applied to approximately 200 spherical-plus- <jats:inline-formula> <jats:tex-math><?CDATA $\beta_3$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014102_M10.jpg" xlink:type="simple" /> </jats:inline-formula> deformed nuclear partners, that is, <jats:sup>16</jats:sup>O, <jats:sup>48</jats:sup>Ca+octupole deformed nuclei. Compared with the compact configuration, the elongated fusion configuration has a relatively larger impact on the fusion barrier and cross-sections owing to the inclusion of deformations up to <jats:inline-formula> <jats:tex-math><?CDATA $\beta_3$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014102_M11.jpg" xlink:type="simple" /> </jats:inline-formula>. Its agreement with available experimental data for the <jats:sup>16</jats:sup>O+<jats:sup>150</jats:sup>Sm reaction ( <jats:inline-formula> <jats:tex-math><?CDATA $\beta_{22}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014102_M12.jpg" xlink:type="simple" /> </jats:inline-formula>=0.205, <jats:inline-formula> <jats:tex-math><?CDATA $\beta_{32}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014102_M13.jpg" xlink:type="simple" /> </jats:inline-formula>=-0.055) also improves when the optimum orientation degree of freedom is fixed in view of octupole deformations. This reinforces the fact that nuclear structure effects play an important role in the nuclear fusion process. Thus, octupole deformed nuclei can be used for the synthesis of heavy and superheavy nuclei. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Within our aim to clarify some aspects of the breakup dynamics of loosely-bound neutron-halo projectiles on a heavy target, we apply the continuum discretized coupled-channel formalism to investigate the beryllium <jats:sup>11</jats:sup>Be breakup on a lead <jats:sup>208</jats:sup>Pb target at <jats:inline-formula> <jats:tex-math><?CDATA $E_{\rm lab}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014103_M1.jpg" xlink:type="simple" /> </jats:inline-formula>= 140 MeV incident energy. By evidencing that the continuum–continuum couplings are much stronger in the nuclear breakup than in the Coulomb breakup, we conclude that the strength of these couplings in the total breakup is dominated by the nuclear contribution, with the diagonal monopole nuclear potential in the projectile–target center-of-mass having negligible effect on the total and nuclear breakup cross-sections. For this kind of reaction, we show that the condition for the total breakup to approach its dominant component in the absorption region is strongly dependent on the continuum–continuum couplings and the diagonal monopole nuclear potential. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>It is known that elastic magnetic electron scattering can be used to study the magnetic properties of nuclei and determine the outermost-shell single-particle orbitals. In this study, the magnetic form factors <jats:inline-formula> <jats:tex-math><?CDATA $ |F_\mathrm{M}(q)|^{2} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014104_M1.jpg" xlink:type="simple" /> </jats:inline-formula> of odd-<jats:italic>A</jats:italic> nuclei calculated with relativistic and non-relativistic models are systematically compared. We use the relativistic mean-field (RMF) and Skyrme Hartree-Fock (SHF) models to generate single-particle wave functions and calculate the <jats:inline-formula> <jats:tex-math><?CDATA $ |F_\mathrm{M}(q)|^{2} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014104_M2.jpg" xlink:type="simple" /> </jats:inline-formula> values of selected nuclei under relativistic and non-relativistic frameworks, respectively. Geometric factors are introduced through the spherical limit method to consider the influences of deformation, which improves the agreement between the theoretical results and experimental data. It is shown that both the models have the capability to describe the magnetic form factors in the spherical and deformed cases, and the discrepancies in <jats:inline-formula> <jats:tex-math><?CDATA $ |F_\mathrm{M}(q)|^{2} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014104_M3.jpg" xlink:type="simple" /> </jats:inline-formula> reflect the differences in the descriptions of the single-particle orbital between the two models. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>In the contact interaction model, the quark propagator has only one solution, namely, the chiral symmetry breaking solution, at vanishing temperature and density in the case of physical quark mass. We generalize the condensate feedback onto the coupling strength from the 2 flavor case to the 2+1 flavor case, and find the Wigner solution appears in some regions, which enables us to tackle chiral phase transition as two-phase coexistences. At finite chemical potential, we analyze the chiral phase transition in the conditions of electric charge neutrality and <jats:inline-formula> <jats:tex-math><?CDATA $ \beta $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014105_M1.jpg" xlink:type="simple" /> </jats:inline-formula> equilibrium. The four chemical potentials, <jats:inline-formula> <jats:tex-math><?CDATA $ \mu_u $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014105_M2.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $ \mu_d $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014105_M3.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $ \mu_s $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014105_M4.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ \mu_e $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014105_M5.jpg" xlink:type="simple" /> </jats:inline-formula>, are constrained by three conditions, so that one independent variable remains: we choose the average quark chemical potential as the free variable. All quark masses and number densities suffer discontinuities at the phase transition point. The strange quarks appear after the phase transition since the system needs more energy to produce a <jats:inline-formula> <jats:tex-math><?CDATA $ d $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014105_M6.jpg" xlink:type="simple" /> </jats:inline-formula>-quark than an <jats:inline-formula> <jats:tex-math><?CDATA $ s $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014105_M7.jpg" xlink:type="simple" /> </jats:inline-formula>-quark. Taking the EOS as an input, the TOV equations are solved numerically, and we show that the mass–radius relation is sensitive to the EOS. The maximum mass of strange quark stars is not susceptible to the parameter <jats:inline-formula> <jats:tex-math><?CDATA $ \Lambda_q $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_014105_M8.jpg" xlink:type="simple" /> </jats:inline-formula> we introduced. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The isospin dependence of spin-orbit (SO) splitting becomes increasingly important as <jats:italic>N/Z</jats:italic> increases in neutron-rich nuclei. Following the initial independent-particle strategy toward explaining the occurrence of magic numbers, we systematically investigated the isospin effect on the shell evolution in neutron-rich nuclei within the Woods-Saxon mean-field potential and the SO term. It is found that new magic numbers <jats:italic>N</jats:italic> = 14 and <jats:italic>N</jats:italic> =16 may emerge in neutron-rich nuclei if one changes the sign of the isospin-dependent term in the SO coupling, whereas the traditional magic number, <jats:italic>N</jats:italic> = 20, may disappear. The magic number <jats:italic>N</jats:italic> = 28 is expected to be destroyed despite the sign choice of the isospin part in the SO splitting, corresponding to the strength of the SO coupling term. Meanwhile, the <jats:italic>N</jats:italic> = 50 and 82 shells may persist within the single particle scheme, although there is a decreasing trend of their gaps toward extreme proton-deficient nuclei. Besides, an appreciable energy gap appears at <jats:italic>N</jats:italic> = 32 and 34 in neutron-rich Ca isotopes. All these results are more consistent with those of the interacting shell model when enhancing the strength of the SO potential in the independent particle model. The present study may provide a more reasonable starting point than the existing one for not only the interacting shell model but also other nuclear many-body calculations toward the neutron-dripline of the Segrè chart. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The energy content of the charged-Kerr (CK) spacetime surrounded by dark energy (DE) is investigated using approximate Lie symmetry methods for the differential equations. For this, we consider three different DE scenarios: cosmological constant with an equation of state parameter <jats:inline-formula> <jats:tex-math><?CDATA $ {\omega}_{c}=-1$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_015101_M1.jpg" xlink:type="simple" /> </jats:inline-formula>, quintessence DE with an equation of state parameter <jats:inline-formula> <jats:tex-math><?CDATA $ {\omega}_{q}=-{2}/{3}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_015101_M2.jpg" xlink:type="simple" /> </jats:inline-formula>, and a frustrated network of cosmic strings with an equation of state parameter <jats:inline-formula> <jats:tex-math><?CDATA $ {\omega}_{n}=- {1}/{3} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_1_015101_M3.jpg" xlink:type="simple" /> </jats:inline-formula>. To study the gravitational energy of the CK black hole surrounded by the DE, we explore the symmetries of the 2nd-order perturbed geodesic equations. It is noticed, for all the values of <jats:italic>ω</jats:italic>, the exact symmetries are recovered as 2nd-order approximate trivial symmetries. These trivial approximate symmetries give the rescaling of arc length parameter <jats:italic>s</jats:italic> in this spacetime which indicates that the energy in the underlying spacetime has to be rescaled by a factor that depends on the black hole parameters and the DE parameter. This rescaling factor is compared with the factor of the CK spacetime found in [Hussain <jats:italic>et al</jats:italic>. Gen. Relativ. Gravit. (2009)] and the effects of the DE on it are discussed. It is observed that for all the three values of the equation of state parameter <jats:italic>ω</jats:italic>, the effect of DE results in decreased energy content of the black hole spacetime, regardless of values of the charge <jats:italic>Q</jats:italic>, spin <jats:italic>a</jats:italic> and the DE parameter <jats:italic>α</jats:italic>. This reduction in the energy content due to the involvement of the DE favours the idea of mass reduction of black holes by accretion of DE given by [Babichev <jats:italic>et al</jats:italic>. Phys. Rev. Lett. (2004)]. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Owing to the special structure of a five-dimensional Elko spinor, its localization on a brane with codimension one becomes completely different from that of a Dirac spinor. By introducing the coupling between the Elko spinor and the scalar field that can generate the brane, we have two types of localization mechanism for the five-dimensional Elko spinor zero mode on a brane. One is the Yukawa-type coupling, and the other is the non-minimal coupling. In this study, we investigate the localization of the Elko zero mode on de Sitter and Anti-de Sitter thick branes with the two localization mechanisms, respectively. The results show that both the mechanisms can achieve localization. The forms of the scalar coupling function in both localization mechanisms have similar properties, and they play a similar role in localization.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>In this study, we investigate the Kotzinian-Mulders effect under semi-inclusive deep inelastic scattering (SIDIS) within the framework of transverse momentum dependent (TMD) factorization. The asymmetry is contributed by the convolution of the Kotzinian-Mulders function <jats:inline-formula> <jats:tex-math><?CDATA $ g_{1T}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023102_M1.jpg" xlink:type="simple" /> </jats:inline-formula> and the unpolarized fragmentation function <jats:inline-formula> <jats:tex-math><?CDATA $ D_1$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023102_M2.jpg" xlink:type="simple" /> </jats:inline-formula>. As a TMD distribution, the Kotzinian-Mulders function in the coordinate space in the perturbative region can be represented as the convolution of the <jats:italic>C</jats:italic>-coefficients and the corresponding collinear correlation function. The Wandzura-Wilczek approximation is used to obtain this correlation function. We perform a detailed phenomenological numerical analysis of the Kotzinian-Mulders effect in the SIDIS process within TMD factorization at the kinematics of the HERMES and COMPASS experiments. We observe that the obtained <jats:inline-formula> <jats:tex-math><?CDATA $ x_B$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023102_M3.jpg" xlink:type="simple" /> </jats:inline-formula>-, <jats:inline-formula> <jats:tex-math><?CDATA $ z_h$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023102_M4.jpg" xlink:type="simple" /> </jats:inline-formula>-, and <jats:inline-formula> <jats:tex-math><?CDATA $ P_{h\perp}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023102_M5.jpg" xlink:type="simple" /> </jats:inline-formula>-dependent Kotzinian-Mulders effects are basically consistent with the HERMES and COMPASS measurements. We also make predictions at EIC and EicC kinematics. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>In this study, by combining the equal spacing rule with recent observations of <jats:inline-formula> <jats:tex-math><?CDATA $ \Omega_c(X) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M1.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ \Xi_c(X) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M2.jpg" xlink:type="simple" /> </jats:inline-formula> baryons, we predict the spectrum of the low-lying <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_46_2_023103_M3.jpg" xlink:type="simple" /> </jats:inline-formula>-mode <jats:inline-formula> <jats:tex-math><?CDATA $ 1P $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M4.jpg" xlink:type="simple" /> </jats:inline-formula>-wave excited <jats:inline-formula> <jats:tex-math><?CDATA $ \Sigma_c $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M5.jpg" xlink:type="simple" /> </jats:inline-formula> states. Furthermore, their strong decay properties are predicted using the chiral quark model and the nature of <jats:inline-formula> <jats:tex-math><?CDATA $ \Sigma_c(2800) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M6.jpg" xlink:type="simple" /> </jats:inline-formula> is investigated by analyzing the <jats:inline-formula> <jats:tex-math><?CDATA $ \Lambda_c\pi $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M7.jpg" xlink:type="simple" /> </jats:inline-formula> invariant mass spectrum. The <jats:inline-formula> <jats:tex-math><?CDATA $ \Sigma_c(2800) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M8.jpg" xlink:type="simple" /> </jats:inline-formula> structure observed in the <jats:inline-formula> <jats:tex-math><?CDATA $ \Lambda_c \pi $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M9.jpg" xlink:type="simple" /> </jats:inline-formula> mass spectrum was found to potentially arise from two overlapping <jats:inline-formula> <jats:tex-math><?CDATA $ P $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M10.jpg" xlink:type="simple" /> </jats:inline-formula>-wave <jats:inline-formula> <jats:tex-math><?CDATA $ \Sigma_c $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M11.jpg" xlink:type="simple" /> </jats:inline-formula> resonances, <jats:inline-formula> <jats:tex-math><?CDATA $ \Sigma_c(2813)3/2^- $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M12.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ \Sigma_c(2840)5/2^- $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M13.jpg" xlink:type="simple" /> </jats:inline-formula>. These resonances have similar decay widths of <jats:inline-formula> <jats:tex-math><?CDATA $ \Gamma\sim 40 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M14.jpg" xlink:type="simple" /> </jats:inline-formula> MeV and predominantly decay into the <jats:inline-formula> <jats:tex-math><?CDATA $ \Lambda_c \pi $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M15.jpg" xlink:type="simple" /> </jats:inline-formula> channel. The <jats:inline-formula> <jats:tex-math><?CDATA $ \Sigma_c(2755)1/2^- $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M16.jpg" xlink:type="simple" /> </jats:inline-formula> state is likely to be a very narrow state with a width of <jats:inline-formula> <jats:tex-math><?CDATA $ \Gamma\sim 15 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M17.jpg" xlink:type="simple" /> </jats:inline-formula> MeV, with its decays almost saturated by the <jats:inline-formula> <jats:tex-math><?CDATA $ \Lambda_c \pi $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M18.jpg" xlink:type="simple" /> </jats:inline-formula> channel. Additionally, evidence of the <jats:inline-formula> <jats:tex-math><?CDATA $\Sigma_c(2755) {1}/{2}^-$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M19.jpg" xlink:type="simple" /> </jats:inline-formula> resonance as a very narrow peak may be seen in the <jats:inline-formula> <jats:tex-math><?CDATA $ \Lambda_c\pi $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M20.jpg" xlink:type="simple" /> </jats:inline-formula> invariant mass spectrum. The other two <jats:inline-formula> <jats:tex-math><?CDATA $ P $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M21.jpg" xlink:type="simple" /> </jats:inline-formula>-wave states, <jats:inline-formula> <jats:tex-math><?CDATA $\Sigma_c(2746) {1}/{2}^-$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M22.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $\Sigma_c(2796) {3}/{2}^-$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M23.jpg" xlink:type="simple" /> </jats:inline-formula>, are relatively narrow states with similar widths of <jats:inline-formula> <jats:tex-math><?CDATA $ \Gamma\sim 30 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M24.jpg" xlink:type="simple" /> </jats:inline-formula> MeV and predominantly decay into <jats:inline-formula> <jats:tex-math><?CDATA $ \Sigma_c\pi $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M25.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ \Sigma^{*}_c\pi $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M26.jpg" xlink:type="simple" /> </jats:inline-formula>, respectively. This study can provide useful references for discovering these low-lying <jats:inline-formula> <jats:tex-math><?CDATA $ P $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023103_M27.jpg" xlink:type="simple" /> </jats:inline-formula>-wave states in forthcoming experiments. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>Extensive dynamical <jats:inline-formula> <jats:tex-math><?CDATA $N/D$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023104_M1.jpg" xlink:type="simple" /> </jats:inline-formula> calculations are conducted in the study of <jats:inline-formula> <jats:tex-math><?CDATA $S_{11}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023104_M2.jpg" xlink:type="simple" /> </jats:inline-formula> channel low energy <jats:inline-formula> <jats:tex-math><?CDATA $\pi N$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023104_M3.jpg" xlink:type="simple" /> </jats:inline-formula> scatterings, based on various phenomenological model inputs of left cuts at the tree level. The subtleties of the singular behavior of the partial wave amplitude, at the origin of the complex <jats:inline-formula> <jats:tex-math><?CDATA $s$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023104_M4.jpg" xlink:type="simple" /> </jats:inline-formula> plane, are analysed in detail. Furthermore, it is found that the dispersion representation for the phase shift, <jats:inline-formula> <jats:tex-math><?CDATA $\delta$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023104_M5.jpg" xlink:type="simple" /> </jats:inline-formula>, must be modified in the case of <jats:inline-formula> <jats:tex-math><?CDATA $\pi N$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023104_M6.jpg" xlink:type="simple" /> </jats:inline-formula> scatterings. An additional contribution from the dispersion integral exists, which approximately cancels the contribution of the two virtual poles located near the end points of the segment cut, induced by <jats:inline-formula> <jats:tex-math><?CDATA $u$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023104_M7.jpg" xlink:type="simple" /> </jats:inline-formula> channel nucleon exchanges. With limited reliance on the details of the dynamical inputs, the subthreshold resonance <jats:inline-formula> <jats:tex-math><?CDATA $N^*(890)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_46_2_023104_M8.jpg" xlink:type="simple" /> </jats:inline-formula> survives. </jats:p>