International Journal of Modern Physics A

Inspired by recent anomalies associated with the $b$ hadron decays, a theoretical investigation on $B_{d(s)}^{\ast }\to D_d^{+}(D_s^{+}){\tau }^{-}{\bar{v}}_{\tau }$ decays has been performed in $W^{\prime }$ model and scalar leptoquark model. To implicate these models, new coupling parameters are fixed by ${\chi }^2$ fitting using recent experimental results from $b\to c\tau {\bar{v}}_{\tau }$ transition as constraints. We have estimated branching fraction, lepton flavor universality (LFU) parameter, forward–backward asymmetry and lepton-spin asymmetry in the standard model (SM) as well as above two new physics (NP) models. Except lepton-spin asymmetry, significant deviations from the SM predictions are observed in $W^{\prime }$ model for both channels. In comparison to other observables, lepton-spin asymmetry shifts slightly from the SM in scalar leptoquark model. Our results may be helpful to the experimental communities to explore these decays and $W^{\prime }$ boson and leptoquark at the colliders.

In this paper, I investigate the effect of a magnetic field on the Casimir effect due to a massless and charged fermion field that violates Lorentz invariance according to the Horava-Lifshitz theory. I focus on the case of a fermion field that obeys MIT bag boundary conditions on a pair of parallel plates. I carry out this investigation using the $\zeta$-function technique that allows me to obtain Casimir energy and pressure in the presence of a uniform magnetic field orthogonal to the plates. I investigate the cases of the parameter associated with the violation of Lorentz invariance being even or odd and the cases of weak and strong magnetic field, examining all possible combinations of the above quantities. In all cases I obtain simple and very accurate analytic expressions of the magnetic field-dependent Casimir energy and pressure.

Recently, the BESIII Collaboration reported that there exist two explicit enhancement structures near 2.25GeV, one has the mass of $M=2232\pm 19\pm 27$MeV and the width of $\mathrm{\Gamma }=93\pm 53\pm 20$MeV and another structure has the mass of $M=2200\pm 11\pm 17$MeV and the width of $\mathrm{\Gamma }=74\pm 20\pm 24$MeV when analyzing the cross section of subprocesses. Earlier, the BESIII Collaboration reported the existence of the $X(2220)$, with a mass of $2222\pm 7\pm 2$MeV and width of $59\pm 30\pm 6$MeV. Based on these experimental results, we carried out a study. We present the comparison of the mass spectrum between theoretical and experimental masses and examine the two-body strong decays of these states within two different approaches to the ${}^3{P}_0$ model. We find that the newly discovered states are most likely to be an $\omega (3\mathrm{\text{D}})$ state. This discovery could be useful in establishing entire $\omega$ mesons.

We investigate the weak leptonic and semileptonic decay widths of pseudoscalar light and heavy mesons in a Dirac formalism. We take relativistic-independent quark model of the form $V_q(r)=\frac{1}{2}(1+{\gamma }^0)(a^{2}r+V_0)$, where $a>0$. This is computed using the binding quark eigenfunction and taking the assumptions of a significant relationship between the quark and antiquark momenta inside the decaying meson in the rest frame. To calculate the decay constant $(f_M)$, decay width and branching fractions of pseudoscalar mesons, we employ the model parameters that we used earlier. The experimental findings and various similar models are in good agreement with our predictions such as $“f_{B_C}>f_{B_S}>f_B,f_{D_S}>f_D,f_D>f_B$ and $f_B>f_{\pi }$”. Finally, we calculate the form factors and branching fractions for the semileptonic $D(D^0)$ decays $“D^{+}\to K_S^0{e}^{+}{\nu }_e$, $D^{+}\to K_L^0{e}^{+}{\nu }_e$, $D^{+}\to {\pi }^0{e}^{+}{\nu }_e$, $D^0\to K^{-}{e}^{+}{\nu }_e$ and $D^0\to {\pi }^{-}{e}^{+}{\nu }_e$” and find reasonable agreement with the experimental results.

The triviality of four-dimensional scalar quantum field theories poses challenging problems to the usually adopted perturbative implementation of the Higgs mechanism. In the first part of the paper, we compare the triviality scenario and the renormalized two-loop perturbation theory to precise and extensive results from nonperturbative numerical simulations of the real scalar field theory on the lattice. The proposal of triviality and spontaneous symmetry breaking turns out to be in good agreement with numerical simulations, while the renormalized perturbative approach seems to suffer significant deviations from the numerical simulation results. In the second part of the paper, we try to illustrate how the triviality of four-dimensional scalar field theory leads, nevertheless, to the spontaneous symmetry breaking in the scalar sector of the Standard Model. We show how triviality allows us to develop a physical picture of the Higgs mechanism in the Standard Model. We suggest that the Higgs condensate behaves like a relativistic quantum liquid leading to the prevision of two Higgs bosons. The light Higgs boson resembles closely the new LHC narrow resonance at 125 GeV. The heavy Higgs boson is a rather broad resonance with mass of about 730 GeV. We critically compare our proposal to the complete LHC Run 2 data collected by the ATLAS and CMS Collaborations. We do not find convincingly evidences of the heavy Higgs boson in the ATLAS datasets. On the other hand, the CMS full Run 2 data display evidences of a heavy Higgs boson in the main decay modes $H\to WW$, while in the preliminary Run 2 data there are hints of the decays $H\to ZZ$ in the golden channel. We also critically discuss plausible reasons for the discrepancies between the two LHC experiments.

In this paper, we consider the soft-wall holographic model with the linear dilaton background. The model leads to a Hydrogen-like meson spectrum which can be interpreted as the static limit with very large quark masses when the Coulomb interaction dominates. The mass scale introduced by the linear dilaton is matched to the quark mass. The resulting model is analyzed for the scalar, vector and tensor cases. The electromagnetic coupling constants predicted by the model are decreasing with the radial number in contrast to the soft-wall model with quadratic dilaton where these couplings represent a universal constant. The given prediction is qualitatively consistent with the corresponding experimental data in vector quarkonia. The proposed model can thus be used as a constituent part of more elaborated holographic models for heavy quarkonia. A particular example of such a model is put forward.

In this work, we systematically investigate the singly charmed pentaquark molecular states $D^{(\ast )}N$, $D^{(\ast )}{\mathrm{\Xi }}^{(\ast )}$ and $D_s^{(\ast )}{\mathrm{\Xi }}^{(\ast )}$ with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension 13 and taking fully account of the light-flavor $SU(3)$ breaking effects. The numerical results favor assigning the ${\mathrm{\Omega }}_c(3185)$ as the $D\mathrm{\Xi }$ molecular state with the $J^P={\frac{1}{2}}^{-}$ and $|I,I_3〉=|0,0〉$, assigning the ${\mathrm{\Omega }}_c(3327)$ as the $D^{\ast }\mathrm{\Xi }$ molecular state with the $J^P={\frac{3}{2}}^{-}$ and $|I,I_3〉=|0,0〉$, assigning the ${\mathrm{\Sigma }}_c(2800)$ as the $DN$ molecular state with the $J^P={\frac{1}{2}}^{-}$ and $|I,I_3〉=|1,0〉$, and assigning the ${\mathrm{\Lambda }}_c(2940)/{\mathrm{\Lambda }}_c(2910)$ as the $D^{\ast }N$ molecular state with the $J^P={\frac{3}{2}}^{-}$ and $|I,I_3〉=|0,0〉$. Other potential molecule candidates are also predicted, which may be observed in future experiments. For example, we can search for the $D\mathrm{\Xi }$ and $D^{\ast }\mathrm{\Xi }$ molecular states with the isospin $|I,I_3〉=|1,\pm 1〉$ in the ${\mathrm{\Xi }}_c^{+}{\bar{K}}^0$ and ${\mathrm{\Xi }}_c^0{\bar{K}}^{-}$ mass spectrum, respectively, in the future, which could shed light on the nature of the ${\mathrm{\Omega }}_c(3185/3327)$.

Recently, a novel measure for the complexity of operator growth is proposed based on Lanczos algorithm and Krylov recursion method. We study this Krylov complexity in quantum mechanical systems derived from some well-known local toric Calabi–Yau geometries, as well as some nonrelativistic models. We find that for the Calabi–Yau models, the Lanczos coefficients grow slower than linearly for small $n$’s, consistent with the behavior of integrable models. On the other hand, for the nonrelativistic models, the Lanczos coefficients initially grow linearly for small $n$’s, then reach a plateau. Although this looks like the behavior of a chaotic system, it is mostly likely due to saddle-dominated scrambling effects instead, as argued in the literature. In our cases, the slopes of linearly growing Lanczos coefficients almost saturate a bound by the temperature. During our study, we also provide an alternative general derivation of the bound for the slope.

Using the Schwinger proper time method I calculate exactly the bubble diagram contribution to the thermal neutrino self-energy, obtaining exact results that cannot be achieved using the contact approximation. These results allow me to obtain the dispersion relation for neutrino in a medium under several different conditions.