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<jats:title>Abstract</jats:title> <jats:p>It is well-known that direct analytic continuation of the DGLAP evolution kernel (splitting functions) from space-like to time-like kinematics breaks down at three loops. We identify the origin of this breakdown as due to splitting functions not being analytic functions of external momenta. However, splitting functions can be constructed from the squares of (generalized) splitting amplitudes. We establish the rules of analytic continuation for splitting amplitudes, and use them to determine the analytic continuation of certain holomorphic and anti-holomorphic part of splitting functions and transverse-momentum dependent distributions. In this way we derive the time-like splitting functions at three loops without ambiguity. We also propose a reciprocity relation for singlet splitting functions, and provide non-trivial evidence that it holds in QCD at least through three loops.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We calculate the masses of the <jats:inline-formula> <jats:tex-math><?CDATA $QQ\bar{q}\bar{q}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M1.jpg" xlink:type="simple" /> </jats:inline-formula> ( <jats:inline-formula> <jats:tex-math><?CDATA $Q=c,b$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M2.jpg" xlink:type="simple" /> </jats:inline-formula>; <jats:inline-formula> <jats:tex-math><?CDATA $q=u,d,s$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M3.jpg" xlink:type="simple" /> </jats:inline-formula>) tetraquark states with the aid of heavy diquark-antiquark symmetry (HDAS) and the chromomagnetic interaction (CMI) model. The masses of the highest-spin ( <jats:inline-formula> <jats:tex-math><?CDATA $J=2$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M4.jpg" xlink:type="simple" /> </jats:inline-formula>) tetraquarks that have only the <jats:inline-formula> <jats:tex-math><?CDATA $(QQ)_{\bar{3}_c}(\bar{q}\bar{q})_{3_c}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M5.jpg" xlink:type="simple" /> </jats:inline-formula>color structure are related with those of conventional hadrons using HDAS. Thereafter, the masses of their partner states are determined with the mass splittings in the CMI model. Our numerical results reveal that (i) the lightest <jats:inline-formula> <jats:tex-math><?CDATA $cc\bar{n}\bar{n}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M6.jpg" xlink:type="simple" /> </jats:inline-formula> ( <jats:inline-formula> <jats:tex-math><?CDATA $n=u,d$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M7.jpg" xlink:type="simple" /> </jats:inline-formula>) is an <jats:inline-formula> <jats:tex-math><?CDATA $I(J^P)=0(1^+)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M8.jpg" xlink:type="simple" /> </jats:inline-formula> state around 3929 MeV (53 MeV above the <jats:inline-formula> <jats:tex-math><?CDATA $DD^*$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M9.jpg" xlink:type="simple" /> </jats:inline-formula> threshold), and none of the double-charm tetraquarks are stable; (ii) the stable double-bottom tetraquarks are the lowest <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_45_4_043102_M10.jpg" xlink:type="simple" /> </jats:inline-formula> <jats:inline-formula> <jats:tex-math><?CDATA $bb\bar{n}\bar{n}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M11.jpg" xlink:type="simple" /> </jats:inline-formula> around 10488 MeV ( <jats:inline-formula> <jats:tex-math><?CDATA $\approx116$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M12.jpg" xlink:type="simple" /> </jats:inline-formula> MeV below the <jats:inline-formula> <jats:tex-math><?CDATA $\bar{B}\bar{B}^*$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M13.jpg" xlink:type="simple" /> </jats:inline-formula> threshold) and the lowest <jats:inline-formula> <jats:tex-math><?CDATA $1/2(1^+)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M14.jpg" xlink:type="simple" /> </jats:inline-formula> <jats:inline-formula> <jats:tex-math><?CDATA $bb\bar{n}\bar{s}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M15.jpg" xlink:type="simple" /> </jats:inline-formula> around 10671 MeV ( <jats:inline-formula> <jats:tex-math><?CDATA $\approx20$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M16.jpg" xlink:type="simple" /> </jats:inline-formula> MeV below the <jats:inline-formula> <jats:tex-math><?CDATA $\bar{B}\bar{B}_s^*/\bar{B}_s\bar{B}^*$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M17.jpg" xlink:type="simple" /> </jats:inline-formula> threshold); and (iii) the two lowest <jats:inline-formula> <jats:tex-math><?CDATA $bc\bar{n}\bar{n}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M18.jpg" xlink:type="simple" /> </jats:inline-formula> tetraquarks, namely the lowest <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_45_4_043102_M19.jpg" xlink:type="simple" /> </jats:inline-formula> around 7167 MeV and the lowest <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_45_4_043102_M20.jpg" xlink:type="simple" /> </jats:inline-formula> around 7223 MeV, are in the near-threshold states. Moreover, we discuss the constraints on the masses of double-heavy hadrons. Specifically, for the lowest nonstrange tetraquarks, we obtain <jats:inline-formula> <jats:tex-math><?CDATA $T_{cc} &lt; 3965$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M21.jpg" xlink:type="simple" /> </jats:inline-formula> MeV, <jats:inline-formula> <jats:tex-math><?CDATA $T_{bb} &lt; 10627$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M22.jpg" xlink:type="simple" /> </jats:inline-formula> MeV, and <jats:inline-formula> <jats:tex-math><?CDATA $T_{bc} &lt; 7199$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043102_M23.jpg" xlink:type="simple" /> </jats:inline-formula> MeV. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>In this paper, we consider a set of new symmetries in the SM: <jats:italic>diagonal reflection</jats:italic> symmetries <jats:inline-formula> <jats:tex-math><?CDATA $R \, m_{u,\nu}^{*} \, R = m_{u,\nu}, m_{d,e}^{*} = m_{d,e}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M1.jpg" xlink:type="simple" /> </jats:inline-formula> with <jats:inline-formula> <jats:tex-math><?CDATA $R =$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M2.jpg" xlink:type="simple" /> </jats:inline-formula> diag <jats:inline-formula> <jats:tex-math><?CDATA $(-1,1,1)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M3.jpg" xlink:type="simple" /> </jats:inline-formula>. These generalized <jats:inline-formula> <jats:tex-math><?CDATA $CP$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M4.jpg" xlink:type="simple" /> </jats:inline-formula> symmetries predict the Majorana phases to be <jats:inline-formula> <jats:tex-math><?CDATA $\alpha_{2,3} /2 \sim 0$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M5.jpg" xlink:type="simple" /> </jats:inline-formula> or <jats:inline-formula> <jats:tex-math><?CDATA $\pi /2$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M6.jpg" xlink:type="simple" /> </jats:inline-formula>. Realization of diagonal reflection symmetries implies a broken chiral <jats:inline-formula> <jats:tex-math><?CDATA $U(1)_{\rm{PQ}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M7.jpg" xlink:type="simple" /> </jats:inline-formula> symmetry only for the first generation. The axion scale is suggested to be <jats:inline-formula> <jats:tex-math><?CDATA $\langle {\theta_{u,d}} \rangle \sim \Lambda_{\rm{GUT}} \, \sqrt{m_{u,d} \, m_{c,s}} / v \sim 10^{12} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M8.jpg" xlink:type="simple" /> </jats:inline-formula> [GeV]. By combining the symmetries with the four-zero texture, the mass eigenvalues and mixing matrices of quarks and leptons are reproduced well. This scheme predicts the normal hierarchy, the Dirac phase <jats:inline-formula> <jats:tex-math><?CDATA $\delta _{CP} \simeq 203^{\circ},$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M9.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $|m_{1}| \simeq 2.5$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M10.jpg" xlink:type="simple" /> </jats:inline-formula> or <jats:inline-formula> <jats:tex-math><?CDATA $6.2 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M11.jpg" xlink:type="simple" /> </jats:inline-formula> [meV]. In this scheme, the type-I seesaw mechanism and a given neutrino Yukawa matrix <jats:inline-formula> <jats:tex-math><?CDATA $Y_{\nu}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M12.jpg" xlink:type="simple" /> </jats:inline-formula> completely determine the structure of the right-handed neutrino mass <jats:inline-formula> <jats:tex-math><?CDATA $M_{R}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M13.jpg" xlink:type="simple" /> </jats:inline-formula>. A <jats:inline-formula> <jats:tex-math><?CDATA $u-\nu$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M14.jpg" xlink:type="simple" /> </jats:inline-formula> unification predicts the mass eigenvalues to be <jats:inline-formula> <jats:tex-math><?CDATA $ (M_{R1} \, , M_{R2} \, , M_{R3}) = (O (10^{5}) \, , O (10^{9}) \, , O (10^{14})) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M15.jpg" xlink:type="simple" /> </jats:inline-formula> [GeV]. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We investigate the dynamics of a strong first-order quark-hadron transition driven by cubic interactions via homogeneous bubble nucleation in the Friedberg-Lee model. The one-loop effective thermodynamic potential of the model and the critical bubble profiles have been calculated at different temperatures and chemical potentials. By taking the temperature and the chemical potential as variables, the evolutions of the surface tension, the typical radius of the critical bubble, and the shift in the coarse-grained free energy in the presence of a nucleation bubble are obtained, and the limit on the reliability of the thin-wall approximation is also addressed accordingly. Our results are compared to those obtained for a weak first-order quark-hadron phase transition; in particular, the spinodal decomposition is relevant.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>Electro-production of several pentaquark states is investigated in this study. The eSTARlight package is adapted to study the electro-production of <jats:inline-formula> <jats:tex-math><?CDATA $J/\psi$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043105_M1.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $\Upsilon (1S)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043105_M2.jpg" xlink:type="simple" /> </jats:inline-formula> via pentaquark <jats:inline-formula> <jats:tex-math><?CDATA $P_c$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043105_M3.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $P_b$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043105_M4.jpg" xlink:type="simple" /> </jats:inline-formula> resonance channels in <jats:inline-formula> <jats:tex-math><?CDATA $e p \to e J/\psi p$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043105_M5.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $e p \to e \Upsilon(1S) p$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043105_M6.jpg" xlink:type="simple" /> </jats:inline-formula> scattering processes at the proposed electron-ion colliders (EICs). The results obtained in this study are compared to those of non-resonance <jats:italic>t</jats:italic>-channels, which are described in the pomeron exchange model developed in our studies. Some pseudo-rapidity and rapidity distributions of <jats:inline-formula> <jats:tex-math><?CDATA $J/\psi$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043105_M7.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $\Upsilon(1S)$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043105_M8.jpg" xlink:type="simple" /> </jats:inline-formula> are presented for the proposed EICs, including EicC and EIC-US. It is found that EicC is a good platform to identify <jats:inline-formula> <jats:tex-math><?CDATA $P_b$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043105_M9.jpg" xlink:type="simple" /> </jats:inline-formula> states in the future. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We investigate the thermodynamics and stability of the horizons in warped anti-de Sitter black holes of the new massive gravity under the scattering of a massive scalar field. Under scattering, conserved quantities can be transferred from the scalar field to the black hole, thereby changing the state of the black hole. We determine that the changes in the black hole are well coincident with the laws of thermodynamics. In particular, the Hawking temperature of the black hole cannot be zero in the process as per the third law of thermodynamics. Furthermore, the black hole cannot be overspun beyond the extremal condition under the scattering of any mode of the scalar field.</jats:p>

<jats:title>Abstract</jats:title> <jats:p>We studied the condensate mass of QCD vacuum through the duality approach via dilaton wall background in the presence of the parameter <jats:inline-formula> <jats:tex-math><?CDATA $ c $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043107_M1.jpg" xlink:type="simple" /> </jats:inline-formula>, which represents the condensation in a holographic set up. First, from Wilson line calculation, we found <jats:inline-formula> <jats:tex-math><?CDATA $ m_0^2 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043107_M2.jpg" xlink:type="simple" /> </jats:inline-formula> (i.e., the condensate parameter in mixed non-local condensation), whose behavior mimics that of QCD. The value of <jats:inline-formula> <jats:tex-math><?CDATA $ m_0^2 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043107_M3.jpg" xlink:type="simple" /> </jats:inline-formula> that we found by this approach is in agreement with QCD data. Second, we considered the produced mass <jats:inline-formula> <jats:tex-math><?CDATA $ m $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043107_M4.jpg" xlink:type="simple" /> </jats:inline-formula> via the Schwinger effect mechanism in the presence of the parameter <jats:inline-formula> <jats:tex-math><?CDATA $ c $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043107_M5.jpg" xlink:type="simple" /> </jats:inline-formula>. We show that vacuum condensation generally contributes the mass dominantly and that the produced mass via Schwinger effect is suppressed by <jats:inline-formula> <jats:tex-math><?CDATA $ m_0 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043107_M6.jpg" xlink:type="simple" /> </jats:inline-formula>. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>The discovery of <jats:inline-formula> <jats:tex-math><?CDATA $ \Xi_{cc}^{++} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043108_M2.jpg" xlink:type="simple" /> </jats:inline-formula> has inspired new interest in studying doubly heavy baryons. In this study, the weak decays of a doubly charmed baryon <jats:inline-formula> <jats:tex-math><?CDATA $ {\cal B}_{cc} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043108_M3.jpg" xlink:type="simple" /> </jats:inline-formula> to a light baryon <jats:inline-formula> <jats:tex-math><?CDATA $ {\cal B} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043108_M4.jpg" xlink:type="simple" /> </jats:inline-formula> and a charm meson <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_45_4_043108_M5.jpg" xlink:type="simple" /> </jats:inline-formula> (either a pseudoscalar or a vector one) are calculated. Following our previous work, we calculate the short distance contributions under the factorization hypothesis, whereas the long distance contributions are modeled as the final state interactions, which are calculated with the one particle exchange model. We find that the <jats:inline-formula> <jats:tex-math><?CDATA $ {\cal B}_{cc}\to {\cal B} D^{*} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043108_M6.jpg" xlink:type="simple" /> </jats:inline-formula> decays' branching ratios are obviously larger, as they receive contributions of more polarization states. Among the decays that we investigate, the following have the largest branching fractions: <jats:inline-formula> <jats:tex-math><?CDATA $ {\cal BR}(\Xi_{cc}^{++}\rightarrow\Sigma^{+}D^{*+}) \in [0.46 \%, 3.33 \%] $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043108_M7.jpg" xlink:type="simple" /> </jats:inline-formula> estimated with <jats:inline-formula> <jats:tex-math><?CDATA $ \tau_{\Xi_{cc}^{++}} = 256 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043108_M8.jpg" xlink:type="simple" /> </jats:inline-formula> fs; <jats:inline-formula> <jats:tex-math><?CDATA $ {\cal BR}(\Xi_{cc}^{+}\rightarrow\Lambda D^{*+}) \in [0.38 \%, 2.63 \%] $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043108_M9.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ {\cal BR}(\Xi_{cc}^{+}\rightarrow\Sigma^{0} D^{*+}) \in [0.45 \%, 3.16 \%] $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043108_M10.jpg" xlink:type="simple" /> </jats:inline-formula> with <jats:inline-formula> <jats:tex-math><?CDATA $ \tau_{\Xi_{cc}^+} = 45 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043108_M11.jpg" xlink:type="simple" /> </jats:inline-formula> fs; and <jats:inline-formula> <jats:tex-math><?CDATA ${\cal BR}(\Omega_{cc}^{+}\rightarrow \Xi^{0} D^{*+}) \in [0.27 \%, 1.03 \%]$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043108_M12.jpg" xlink:type="simple" /> </jats:inline-formula>, <jats:inline-formula> <jats:tex-math><?CDATA $ {\cal BR}(\Omega_{cc}^{+}\rightarrow\Xi^{0} D^{+}) \in [0.07 \%, 0.44 \%] $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043108_M13.jpg" xlink:type="simple" /> </jats:inline-formula>, and <jats:inline-formula> <jats:tex-math><?CDATA $ {\cal BR}(\Omega_{cc}^{+}\rightarrow\Sigma^{0} D^{*+}) \in [0.06 \%, 0.45 \%] $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043108_M14.jpg" xlink:type="simple" /> </jats:inline-formula> with <jats:inline-formula> <jats:tex-math><?CDATA $ \tau_{\Omega_{cc}^+} = 75 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043108_M15.jpg" xlink:type="simple" /> </jats:inline-formula> fs. By comparing the decay widths of pure color commensurate channels with those of pure bow-tie ones, we find that the bow-tie mechanism plays an important role in charm decays. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>In this study, light-by-light (LBL) scattering with initial polarized Compton backscattered photons at the CLIC, induced by axion-like particles (ALPs), is investigated. The total cross sections are calculated assuming <jats:italic>CP</jats:italic>-even coupling of the pseudoscalar ALP to photons. The 95% C.L. exclusion region for the ALP mass <jats:inline-formula> <jats:tex-math><?CDATA $m_a$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043109_M1.jpg" xlink:type="simple" /> </jats:inline-formula> and its coupling constant <jats:italic>f</jats:italic> is presented. The results are compared with CLIC bounds previously obtained for the unpolarized case. It is shown that the bounds on <jats:italic>f</jats:italic> for the polarized beams in the region <jats:inline-formula> <jats:tex-math><?CDATA $m_a = 1000 - 2000 \;{\rm{GeV}}$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043109_M2.jpg" xlink:type="simple" /> </jats:inline-formula> with collision energy of 3000 GeV and integrated luminosity of 4000 fb <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_45_4_043109_M3.jpg" xlink:type="simple" /> </jats:inline-formula> are on average 1.5 times stronger than the bounds for the unpolarized beams. Moreover, our CLIC bounds are stronger than those for all current exclusion regions for <jats:inline-formula> <jats:tex-math><?CDATA $m_a &gt; 80$?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043109_M4.jpg" xlink:type="simple" /> </jats:inline-formula> GeV. In particular, they are more restrictive than the limits that follow from the ALP-mediated LBL scattering at the LHC. </jats:p>

<jats:title>Abstract</jats:title> <jats:p>We investigate the prospect of discovering the Flavour Changing Neutral Current (FCNC) <jats:inline-formula> <jats:tex-math><?CDATA $ tqZ $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043110_M1.jpg" xlink:type="simple" /> </jats:inline-formula> couplings via two production processes yielding trilepton signals: top quark pair production <jats:inline-formula> <jats:tex-math><?CDATA $ pp\to t\bar{t} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043110_M2.jpg" xlink:type="simple" /> </jats:inline-formula> with one top quark decaying to the <jats:italic>Z</jats:italic> boson and one light jet and the anomalous single top quark plus <jats:italic>Z</jats:italic> boson production process <jats:inline-formula> <jats:tex-math><?CDATA $ pp\to tZ $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043110_M3.jpg" xlink:type="simple" /> </jats:inline-formula>. We study these channels at various successors of the Large Hadron Collider (LHC), i.e., the approved High-Luminosity LHC (HL-LHC) as well as the proposed High-Energy LHC (HE-LHC) and Future Circular Collider in hadron-hadron mode (FCC-hh). We perform a full simulation for the signals and the relevant Standard Model (SM) backgrounds and obtain limits on the Branching Ratios (BRs) of <jats:inline-formula> <jats:tex-math><?CDATA $ t\to qZ\; (q = u,c) $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043110_M4.jpg" xlink:type="simple" /> </jats:inline-formula>, eventually yielding a trilepton final state through the decay modes <jats:inline-formula> <jats:tex-math><?CDATA $ t\to b W^{+}\to b\ell^{+}\nu_{\ell} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043110_M5.jpg" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA $ Z\to \ell^{+}\ell^{-} $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043110_M6.jpg" xlink:type="simple" /> </jats:inline-formula>. The upper limits on these FCNC BRs at 95% Confidence Level (CL) are obtained at the HL-LHC with <jats:inline-formula> <jats:tex-math><?CDATA $ \sqrt s = 14 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043110_M7.jpg" xlink:type="simple" /> </jats:inline-formula> TeV and 3 ab<jats:sup>−1</jats:sup>, at the HE-LHC with <jats:inline-formula> <jats:tex-math><?CDATA $ \sqrt s = 27 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043110_M8.jpg" xlink:type="simple" /> </jats:inline-formula> TeV and 15 ab<jats:sup>−1</jats:sup>, and at the FCC-hh with <jats:inline-formula> <jats:tex-math><?CDATA $ \sqrt s = 100 $?></jats:tex-math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043110_M9.jpg" xlink:type="simple" /> </jats:inline-formula> TeV and 30 ab<jats:sup>−1</jats:sup>. </jats:p>