Motivated by the large discrepancy of CP-violating phase in $\bar{B}_s-B_s$ mixing between the experimental data and the Standard Model prediction, we pursue possible solutions within a family non-universal $Z^{\prime}$ model. Within such a specific model, we find that both the $\bar{B}_s-B_s$ mixing anomaly and the well-known "$πK$ puzzle" could be moderated simultaneously with a nontrivial new weak phase, $ϕ^L_s\sim-72^{\circ}$ (S1) or $-82^{\circ}$ (S2). With the stringently constrained $Z^{\prime}$ coupling $B_{sb}^{L}$, we then study the $Z^{\prime}$ effects on the rare $B\to X_s μ^+μ^-$ and $B_s\to μ^+μ^-$ decays, which are also induced by the same $b\to s$ transition. The observables of $B\to X_s μ^+μ^-$, at both high and low $q^2$ regions, are found to be able to put strong constraints on the $μ-μ-Z^{\prime}$ coupling, $B_{μμ}^{L,R}\sim10^{-2}$. It is also shown that the combined constraints from $\bar{B}_s-B_s$ mixing, $B\to πK$ and $B\to X_s μ^+μ^-$ do not allow a large $Z^{\prime}$ contribution to the pure leptonic $B_s\toμ^+μ^-$ decay.
We enumerate various effective couplings that contribute to the mixings between an exotic vector boson $Z^{\prime}$ and the neutral electroweak vector bosons. The miscellaneous mixing patterns can be evaluated perturbatively. The effective oblique parameters $S^{\prime}$, $T^{\prime}$, and $U^{\prime}$ are calculated to compare with the electroweak precision test results. With the contributions to the non-negligible $U^{\prime}$ parameter from the $ε_{B,W}$ parameters and the aid of some other parameters to cancel the negative $T^{\prime}$, the recent CDF $W$-mass anomaly can therefore be expl…
In this work we study the interactions of the $Z$ and $Z^{\prime}$ generated by kinetic mixing in a class of theories for physics beyond the standard model motivated by the dark matter problem, containing a spontaneously broken extra $U(1)_{d}$ gauge factor group in a hidden scenario and a Higgs sector respecting custodial symmetry. It is shown that custodial symmetry allows us to write the $Z$ and $Z^{\prime}$ couplings to standard model fermions in terms of the measured values of $α$, $G_{F}$, $M_{Z}$ and $M_{Z^{\prime}}$. Working at the loop level, we calculate the ratio $ρ_{0}=M^{2}_{W}/\h…
In this work we consider the extension of the standard model by dark fields with an Abelian $U(1)_{d}$ spontaneously broken gauge symmetry in a hidden dark matter scenario. Considering all the dimension four gauge invariant terms we show that the tree-level relation $M^{2}_{W}=M^{2}_{\tilde Z} \cos^{2} \tilde θ_{w}$ holds and permits to write the mixing angle induced by the kinetic mixing in the neutral massive gauge boson sector, $θ_ζ$, in terms of the values of $M_{Z}$, the weak mixing angle and of the mass of the physical dark gauge $Z^{\prime}$ boson. At the loop level, a similar relation …
Assuming the existence of an eV or KeV scale sterile neutrino, we develop a 3+1 neutrino mass model using $A_4\times Z_4 \times Z_2$ symmetry group. Three Higgs $H, H^{\prime}$ and $H^{\prime\prime}$ are considered to give a desired neutrino mass matrix which generates non-zero $θ_{13}$. The model can give neutrino mixing parameters that are well within the experimental 3$σ$ bounds. We also calculate the $4\times 4$ active-sterile neutrino mixing matrix, and it is found to be consistent with experimental bounds.
Many $P-$wave mixing heavy-light $1^+$ states have not been discovered by experiment, some of them have been discovered but without the information of width, or with large uncertainty widths. In this paper, we study the strong decays of $P-$wave mixing heavy-light $1^+$ states $D^0$, $D^\pm$, $D_s^\pm$, $B^0$, $B^\pm$ and $B_s$ by the improved Bethe-Salpeter(B-S) method in two conditions of mixing angle $θ$: one is $θ=35.3^\circ$; another is considering the correction to mixing angle $θ=35.3^\circ+θ_1$. And we get some valuable predictions of the strong decay widths: $Γ(D_1^{\prime0})=232$ MeV…
The $η-η^{\prime}$ mixing mass term due to the derivative coupling $SU(3)\times SU(3)$ symmetry breaking term, produces an additional momentum-dependent pole term for processes with $η^{\prime}$, but is suppressed in the $η$ amplitude by a factor $m_η^{2}/m_{η^{\prime}}^{2}$. This seems to be the origin of the two-angle description of the pseudo-scalar decay constants used in the literature. In this paper, by diagonalizing both the mixing mass term and the momentum-dependent mixing term, we show that the $η-η^{\prime}$ system could be described by a meson field renormalization and a new mixing…
This article provides the calculation of an effective vertex function between a nucleon and a $Z^\prime$ boson that couples preferentially to either the top quark or the third generation of fermions, for the purpose of calculating vector-portal dark matter nuclear recoil cross sections. Mixing effects between the new gauge group $U(1)^\prime$ and the Standard Model hypercharge group $U(1)_Y$ are taken into account. Contributions to the $U(1)^\prime$ nucleon current from heavy quarks are quantified using the heavy quark expansion. Also taken into account are contributions from the 1-loop $Z^\pr…
The full CMS Run 2 datasets with time-integrated luminosity of 137 fb$^{-1}$ in the diboson channels are used to probe benchmark models with extended gauge sectors such as $E_6$, left-right symmetric (LR) and the sequential standard model (extended gauge model, EGM), that predict the existence of neutral $Z'$- and charged $W'$-bosons decaying to a pair of bosons $WW$, $ZH$, $WZ$ and $WH$ in the semileptonic final state. These benchmark models are used to interpret the results. Exclusion limits at the 95% C.L. on the $Z'$ and $W'$ resonance production cross section times branching ratio to elec…
Very recently, the LHCb Collaboration observed distinct structures with the $cc\bar{c}\bar{c}$ in the $J/Ψ$-pair mass spectrum. In this work, we construct four scalar ($J^{PC} = 0^{++}$) $[8_c]_{Q\bar{Q^\prime}}\otimes [8_c]_{Q^\prime \bar{Q}}$ type currents to investigate the fully-heavy tetraquark state $Q Q^\prime \bar{Q} \bar{Q^\prime}$ in the framework of QCD sum rules, where $Q=c, b$ and $Q^\prime = c, b$. Our results suggest that the broad structure around 6.2-6.8 GeV can be interpreted as the $0^{++}$ octet-octet tetraquark states with masses $6.44\pm 0.11$ GeV and $6.52\pm 0.10$ GeV, …
$QQ^{\prime} \bar u \bar d$ bound state in the Bethe-Salpeter equation approach
在重夸克极限下，我们建立了含有一个重双夸克$QQ^{\prime}$（$Q, Q^{\prime}=b$或$c$）和一个轻反双夸克$\bar u \bar d$的基态$QQ^{\prime} \bar u \bar d$的Bethe-Salpeter方程.我们在协变瞬时近似下数值求解了Bethe-Salpeter方程，其核包含一个标量禁闭项和一个胶子交换项。数值解的Bethe-Salpeter波函数。结果表明，$bb \bar u \bar d$、$bc \bar u \bar d$和$cc \bar u \bar d$束缚态的质量分别低于$\bar{B}^{*0}\,B^-$或$B^0\,{B^*}^-$、$B^-D^+$或$\bar{B}^{0} D^0$、$D^+\,{D^*}^0$或${D^*}^+\,D^0$介子的阈值.基态$QQ^{\prime} \bar u \bar d$可能存在，我们预计即将到来的实验数据将证实它们。
An enhanced phenomenological model that includes isospin-symmetry breaking is presented in this letter. The model is then used in a number of statistical fits to the most recent experimental data for the radiative transitions $V\!Pγ$ ($V=ρ$, $K^*$, $ω$, $ϕ$ and $P=π$, $K$, $η$, $η^{\prime}$) and estimations for the mixing angles amongst the three pseudoscalar states with vanishing third-component of isospin are obtained. The quality of the performed fits is good, e.g. $χ^2_{\textrm{min}}/\textrm{d.o.f} = 1.9$. The current experimental uncertainties allow for isospin symmetry violations with a …
Angular and invariant-mass observables in the four-body Higgs decay $h\to\ell\barν_\ell\bar{\ell}^\primeν_{\ell^\prime}$
Zhengzhou University（郑州大学）；Chongqing University of Posts & Telecommunications（重庆邮电大学）；Chongqing University（重庆大学）；Chongqing University of Science and Technology（重庆科技大学）
Motivated by the first search for the rare charged-current $B$ decay to four leptons, $\ell \barν_\ell \ell^{(\prime)} \bar{\ell}^{(\prime)}$, we calculate the decay amplitude with factorization methods. We obtain the $B\to γ^*$ form factors, which depend on the invariant masses of the two lepton pairs, at leading power in an expansion in $Λ_{\rm QCD}/m_b$ to next-to-leading order in $α_s$, and at $\mathcal{O}(α_s^0)$ at next-to-leading power. Our calculations predict branching fractions of a few times $10^{-8}$ in the $\ell^{(\prime)} \bar{\ell}^{(\prime)}$ mass-squared bin up to $q^2=1~\text…
We identify a class of $U(1)_X$ models which can explain the $R_K$ anomaly and the neutrino mixing pattern, by using a bottom-up approach. The different $X$-charges of lepton generations account for the lepton universality violation required to explain $R_K$. In addition to the three right-handed neutrinos needed for the Type-I seesaw mechanism, these minimal models only introduce an additional doublet Higgs and a singlet scalar. While the former helps in reproducing the quark mixing structure, the latter gives masses to neutrinos and the new gauge boson $Z^\prime$. Our bottom-up approach dete…
