Four-Leptonic Decays of Charged and Neutral <Emphasis Type="Italic">B</Emphasis> Mesons within the Standard Model

The branching ratios and differential distributions for the four-leptonic decays \({B^ - } \to {\mu ^ + }{\mu ^ - }{\bar v_e}{e^ - }\), \({B^ - } \to {e^ + }{e^ - }{\bar v_\mu }{\mu ^ - }\), and \({B^ - } \to {\mu ^ + }{\bar v_\mu }{\mu ^ - }{\mu ^ - }\) are calculated within the Standard Model. The branching ratios for the rare decays B_d,s → e⁺e^?μ⁺μ^? and B_d,s → μ⁺μ^?μ⁺μ^? are estimated. Methods for testing the lepton universality in rare multileptonic decays of charged and neutral B mesons are proposed.     

Studying the Fourth Generation Quark Contributions to the Double Charm Decays B(s)→D(s)(∗)Ds(∗)

Almost all branching ratios and longitudinal polarization fractions of the double charm decays \(B_{(s)} \to D_{(s)}^{(*)} D_{s}^{(*)}\) have been measured, and the experimental central value of \(f_{L}({B^{0}_{s}}\to D^{*+}_{s}D^{*-}_{s})\) is quite small comparing to its Standard Model prediction. We study the fourth generation quark contributions to the double charm decays \(B_{(s)} \to D_{(s)}^{(*)} D_{s}^{(*)}\). We find that the loop diagrams involving the fourth generation quark t′ have great effects on all branching ratios and CP asymmetries, which are very sensitive to the fourth generation parameter \(\lambda ^{s}_{t^{\prime }}\) and \(\phi _{t^{\prime }}\). Nevertheless, the experimental measurements of all branching ratios can not give effective constraints on relevant new physics parameters. In addition, they have no obvious effect on the relevant polarization fractions. These results could be used to search for the fourth heavy quark t′ via its indirect manifestations in loop diagrams.     

Recent results on kaon decays by the NA48/2 experiment at CERN

The NA48/2 experiment reports the first observation of the rare decay K^± → π^±π⁰e⁺e^?, based on about 2000 candidates from 2003 data. The preliminary branching ratio in the full kinematic region is \(\mathcal {B}(K^{\pm } \to \pi ^{\pm }\pi ^{0}e^{+}e^{-})=(4.06\pm 0.17)\cdot 10^{-6}\). A sample of 4.687 × 10⁶\(K^{\pm }\to \pi ^{\pm }{\pi ^{0}_{D}}\) events collected in 2003/4 is analyzed to search for the dark photon (\(A^{\prime }\)) via the decay chain K^± → π^±π⁰, \(\pi ^{0}\to \gamma A^{\prime }\), \(A^{\prime }\to e^{+}e^{-}\). No signal is observed, limits in the plane mixing parameter ε² versus its mass \(m_{A^{\prime }}\) are reported.     

Isotopic Symmetry Breaking in the η(1405) → f0(980)π0 → π+π–π0. Decay through a $$K\bar K$$ Loop Diagram and the Role of Anomalous Landau Thresholds

Anomalous isotopic symmetry breaking in the η(1405) → f₀(980)π⁰ → π+π–π⁰ decay through a mechanism featuring anomalous Landau thresholds in the form of logarithmic triangle singularities, i.e., through the \(\eta (1405) \to (K*\bar K + \bar K*K) \to ({K^ + }{K^ - } + {K^0}{\bar K^0}){\pi ^0} \to {f_0}(980){\pi ^0} \to {\pi ^ + }{\pi ^ - }{\pi ^0}\) transition, has been analyzed. It has been shown that this effect can be correctly quantified only by taking into account the nonzero K* width. Different scales of isotopic symmetry breaking associated with the K⁺–K⁰ mass difference are compared.     

The decays of $$\bar{B}^0$$, $$\bar{B}^0_s$$B¯s0 and $$B^-$$B- into $$\eta _c$$ηc plus a scalar or vector meson

We investigate the decays of \(\bar{B}^0_s\), \(\bar{B}^0\) and \(B^-\) into \(\eta _c\) plus a scalar or vector meson in a theoretical framework by taking into account the dominant process for the weak decay of \(\bar{B}\) meson into \(\eta _c\) and a \(q\bar{q}\) pair. After hadronization of this \(q\bar{q}\) component into pairs of pseudoscalar mesons we obtain certain weights for the pseudoscalar meson-pseudoscalar meson components. In addition, the \(\bar{B}^0\) and \(\bar{B}^0_s\) decays into \(\eta _c\) and \(\rho ^0\), \(K^*\) are evaluated and compared to the \(\eta _c\) and \(\phi \) production. The calculation is based on the postulation that the scalar mesons \(f_0(500)\), \(f_0(980)\) and \(a_0(980)\) are dynamically generated states from the pseudoscalar meson-pseudoscalar meson interactions in S-wave. Up to a global normalization factor, the \(\pi \pi \), \(K \bar{K}\) and \(\pi \eta \) invariant mass distributions for the decays of \(\bar{B}^0_s \rightarrow \eta _c \pi ^+ \pi ^-\), \(\bar{B}^0_s \rightarrow \eta _c K^+ K^-\), \(\bar{B}^0 \rightarrow \eta _c \pi ^+ \pi ^-\), \(\bar{B}^0 \rightarrow \eta _c K^+ K^-\), \(\bar{B}^0 \rightarrow \eta _c \pi ^0 \eta \), \(B^- \rightarrow \eta _c K^0 K^-\) and \(B^- \rightarrow \eta _c \pi ^- \eta \) are predicted. Comparison is made with the limited experimental information available and other theoretical calcualtions. Further comparison of these results with coming LHCb measurements will be very valuable to make progress in our understanding of the nature of the low lying scalar mesons, \(f_0(500), f_0(980)\) and \(a_0(980)\).     

The S-wave resonance contributions in the $$B^{0}_{s}$$ decays into $$\psi (2S,3S)$$ψ(2S,3S) plus pion pair

The three-body decays \(B^0_s \rightarrow \psi (2S,3S) \pi ^+ \pi ^-\) are studied based on the perturbative QCD approach. With the help of the nonperturbative two-pion distribution amplitudes, the analysis is simplified into the quasi-two-body processes. Besides the traditional factorizable and nonfactorizable diagrams at the leading order, the next-to-leading order vertex corrections are also included to cancel the scale dependence. The \(f_0(980)\), \(f_0(1500)\) resonance contributions as well as the nonresonant contributions are taken into account using the presently known \(\pi \pi \) time-like scalar form factor for the \(s\bar{s}\) component. It is found that the predicted \(B^0_s \rightarrow \psi (2S) \pi ^+ \pi ^-\) decay spectra in the pion pair invariant mass shows a similar behavior as the experiment. The calculated S-wave contributions to the branching ratio of \(B^0_s \rightarrow \psi (2S) \pi ^+ \pi ^-\) is \(6.0\times 10^{-5}\), which is in agreement with the LHCb data \(\mathcal {B}(B^0_s \rightarrow \psi (2S) \pi ^+ \pi ^-)=(7.2\pm 1.2)\times 10^{-5} \) within errors. The estimate of \(\mathcal {B}(B^0_s \rightarrow \psi (3S) \pi ^+ \pi ^-)\) can reach the order of \(10^{-5}\), pending the corresponding measurements.     

Lightest scalar resonances and the dynamics of the γγ → ππ reactions

The high-statistics Belle data on the γγ → π⁺π^? and γγ → π⁰π⁰ reactions have been jointly analyzed. The main dynamical mechanisms of these reactions for energies below 1.5 GeV have been revealed. It has been shown that the direct coupling constants of the σ(600) and f ₀(980) resonances with a γγ pair are small and that the σ(600) → γγ and f ₀(980) → γγ decays are four-quark transitions due primarily to π⁺π^? and K ⁺ K ^?-loop mechanisms, respectively. The role of the chiral shielding of the σ(600) resonance is emphasized. The widths of the f ₀(980) → γγ and σ(600) → γγ decays averaged over the resonance mass distributions, as well as the width of the f ₂(1270) → γγ decay, are estimated as \(\langle \Gamma _{f_0 \to \gamma \gamma } \rangle _{\pi \pi } \approx 0.19 keV, \langle \Gamma _{\sigma \to \gamma \gamma } \rangle _{\pi \pi } \approx 0.45 keV\), and \(\Gamma _{f_2 \to \gamma \gamma } (m_{f_2 }^2 ) \approx 3.8 keV\).     

New physics effects in charm meson decays involving $$c \rightarrow u l^+ l^- (l_i^{\mp } l_j^{\,\pm \,})$$ transitions

We study the effect of the scalar leptoquark and \(Z^\prime \) boson on the rare decays of the D mesons involving flavour changing transitions \(c \rightarrow u l^+ l^- (l^{\mp }_i l^{\,\pm \,}_j)\). We constrain the new physics parameter space using the branching ratio of the rare decay mode \(D^0 \rightarrow \mu ^+ \mu ^-\) and the \(D^0 - {\bar{D}}^0\) oscillation data. We compute the branching ratios, forward–backward asymmetry parameters and flat terms in \(D^{+(0)} \rightarrow \pi ^{+(0)} \mu ^+ \mu ^-\) processes using the constrained parameters. The branching ratios of the lepton flavour violating D meson decays, such as \(D^0 \rightarrow \mu e, ~\tau e\) and \(D^{+(0)} \rightarrow \pi ^{+(0)} \mu ^- e^+\) are also investigated.     

Determinations of $$|V_{cb}|$$ and $$|V_{ub}|$$|Vub| from baryonic $$\Lambda _b$$Λb decays

We present the first attempt to extract \(|V_{cb}|\) from the \(\Lambda _b\rightarrow \Lambda _c^+\ell \bar{\nu }_\ell \) decay without relying on \(|V_{ub}|\) inputs from the B meson decays. Meanwhile, the hadronic \(\Lambda _b\rightarrow \Lambda _c M_{(c)}\) decays with \(M=(\pi ^-,K^-)\) and \(M_c=(D^-,D^-_s)\) measured with high precisions are involved in the extraction. Explicitly, we find that \(|V_{cb}|=(44.6\pm 3.2)\times 10^{-3}\), agreeing with the value of \((42.11\pm 0.74)\times 10^{-3}\) from the inclusive \(B\rightarrow X_c\ell \bar{\nu }_\ell \) decays. Furthermore, based on the most recent ratio of \(|V_{ub}|/|V_{cb}|\) from the exclusive modes, we obtain \(|V_{ub}|=(4.3\pm 0.4)\times 10^{-3}\), which is close to the value of \((4.49\pm 0.24)\times 10^{-3}\) from the inclusive \(B\rightarrow X_u\ell \bar{\nu }_\ell \) decays. We conclude that our determinations of \(|V_{cb}|\) and \(|V_{ub}|\) favor the corresponding inclusive extractions in the B decays.     

Study of the weak annihilation contributions in charmless $$\varvec{B_s\rightarrow VV}$$ decays

In this paper, in order to probe the spectator-scattering and weak annihilation contributions in charmless \(B_s\rightarrow VV\) (where V stands for a light vector meson) decays, we perform the \(\chi ^2\)-analyses for the endpoint parameters within the QCD factorization framework, under the constraints from the measured \(\bar{B}_{s}\rightarrow \) \(\rho ^0\phi \), \(\phi K^{*0}\), \(\phi \phi \) and \(K^{*0}\bar{K}^{*0}\) decays. The fitted results indicate that the endpoint parameters in the factorizable and nonfactorizable annihilation topologies are non-universal, which is also favored by the charmless \(B\rightarrow PP\) and PV (where P stands for a light pseudo-scalar meson) decays observed in previous work. Moreover, the abnormal polarization fractions \(f_{L,\bot }(\bar{B}_{s}\rightarrow K^{*0}\bar{K}^{*0})=(20.1\pm 7.0)\%,(58.4\pm 8.5)\%\) measured by the LHCb collaboration can be reconciled through the weak annihilation corrections. However, the branching ratio of \(\bar{B}_{s}\rightarrow \phi K^{*0}\) decay exhibits a tension between the data and theoretical result, which dominates the contributions to \(\chi _\mathrm{min}^2\) in the fits. Using the fitted endpoint parameters, we update the theoretical results for the charmless \(B_s\rightarrow VV\) decays, which will be further tested by the LHCb and Belle-II experiments in the near future.     

Analysis of charmless two-body <Emphasis Type="Italic">B</Emphasis> decays in factorization-assisted topological-amplitude approach

We analyze charmless two-body non-leptonic B decays \(B \rightarrow PP, PV\) under the framework of a factorization-assisted topological-amplitude approach, where P(V) denotes a light pseudoscalar (vector) meson. Compared with the conventional flavor diagram approach, we consider the flavor SU(3) breaking effect assisted by a factorization hypothesis for topological diagram amplitudes of different decay modes, factorizing out the corresponding decay constants and form factors. The non-perturbative parameters of topology diagram magnitudes \(\chi \) and the strong phase \(\phi \) are universal; they can be extracted by \(\chi ^2\) fit from current abundant experimental data of charmless Bdecays. The number of free parameters and the \(\chi ^2\) per degree of freedom are both reduced compared with previous analyses. With these best fitted parameters, we predict branching fractions and CP asymmetry parameters of nearly 100 \(B_{u,d}\) and \(B_s\) decay modes. The long-standing \(\pi \pi \) and \(\pi K\)-CP puzzles are solved simultaneously.     

The open-charm radiative and pionic decays of molecular charmonium <Emphasis Type="Italic">Y</Emphasis>(4274)

In this work, we investigate the decay widths and the line shapes of the open-charm radiative and pionic decays of Y(4274) with the \(D_{s}\bar{D}_{s0}(2317)\) molecular charmonium assignment. Our calculation indicates that the decay widths of \(Y(4274)\to D^{+}_{s}D^{*-}_{s}\gamma\) and \(Y(4274)\to D^{+}_{s}D^{-}_{s}\pi^{0}\) can reach up to 0.05 keV and 0.75 keV, respectively. In addition, the result of the line shape of the photon spectrum of \(Y(4274)\to D_{s}^{+} {D}_{s}^{*-} \gamma\) shows that there exists a very sharp peak near the large end point of photon energy. The line shape of the pion spectrum of \(Y(4274)\to D_{s}^{+} {D}_{s}^{*-} \pi^{0}\) is similar to that of the pion spectrum of \(Y(4274)\to D_{s}^{+} {D}_{s}^{*-} \gamma\), where we also find a very sharp peak near the large end point of pion energy. According to our calculation, we suggest further experiments to carry out the search for the open-charm radiative and pionic decays of Y(4274).     

<Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> meson rare decays in the light-cone quark model

We investigate the rare decays \(B_{c} \rightarrow D_{s}(1968)\ell \overline{\ell}\) and \(B_{c}\rightarrow D_{s}^{*}(2317) \ell \overline{\ell}\) in the framework of the light-cone quark model (LCQM). The transition form factors are calculated in the space-like region and then analytically continued to the time-like region via exponential parametrization. The branching ratios and longitudinal lepton polarization asymmetries (LPAs) for the two decays are given and compared with each other. The results are helpful for investigating the structure of B _c meson and for testing the unitarity of CKM quark mixing matrix. All these results can be tested in the future experiments at the LHC.     

Spin-label Order Parameter Calibrations for Slow Motion

Calibrations are given to extract orientation order parameters from pseudo-powder electron paramagnetic resonance line shapes of ¹⁴N-nitroxide spin labels undergoing slow rotational diffusion. The nitroxide z-axis is assumed parallel to the long molecular axis. Stochastic-Liouville simulations of slow-motion 9.4-GHz spectra for molecular ordering with a Maier–Saupe orientation potential reveal a linear dependence of the splittings, \(2A_{\hbox{max} }\) and \(2A_{\hbox{min} }\), of the outer and inner peaks on order parameter \(S_{zz}\) that depends on the diffusion coefficient \(D_{{{\text{R}} \bot }}\) which characterizes fluctuations of the long molecular axis. This results in empirical expressions for order parameter and isotropic hyperfine coupling: \(S_{zz} = s_{1} \times \left( {A_{\hbox{max} } - A_{\hbox{min} } } \right) - s_{o}\) and \(a_{o}^{{}} = \tfrac{1}{3}\left( {f_{\hbox{max} } A_{\hbox{max} } + f_{\hbox{min} } A_{\hbox{min} } } \right) + \delta a_{o}\), respectively. Values of the calibration constants \(s_{1}\), \(s_{\text{o}}\), \(f_{\hbox{max} }\), \(f_{\hbox{min} }\) and \(\delta a_{o}\) are given for different values of \(D_{{{\text{R}} \bot }}\) in fast and slow motional regimes. The calibrations are relatively insensitive to anisotropy of rotational diffusion \((D_{{{\text{R}}//}} \ge D_{{{\text{R}} \bot }} )\), and corrections are less significant for the isotropic hyperfine coupling than for the order parameter.     

SU(3) symmetry breaking in charmed baryon decays

We explore the breaking effects of the SU(3) flavor symmetry in the singly Cabibbo-suppressed anti-triplet charmed baryon decays of \(\mathbf{B}_c\rightarrow \mathbf{B}_n M\), with \(\mathbf{B}_c=(\Xi _c^0,\Xi _c^+,\Lambda _c^+)\) and \(\mathbf{B}_n(M)\) the baryon (pseudo-scalar) octets. We find that these breaking effects can be used to account for the experimental data on the decay branching ratios of \({\mathcal {B}}(\Lambda _c^+\rightarrow \Sigma ^{0} K^{+},\Lambda ^{0} K^{+})\) and \(R'_{K/\pi }={\mathcal {B}}(\Xi ^0_c \rightarrow \Xi ^- K^+)\)/\({\mathcal {B}}(\Xi ^0_c \rightarrow \Xi ^- \pi ^+)\). In addition, we obtain that \({\mathcal {B}}(\Xi _{c}^{0} \rightarrow \Xi ^{-} K^{+},\Sigma ^{-} \pi ^{+})=(4.6 \pm 1.7,12.8 \pm 3.1)\times 10^{-4}\), \({\mathcal {B}}(\Xi _c^0\rightarrow pK^-,\Sigma ^+\pi ^-)=(3.0 \pm 1.0, 5.2 \pm 1.6)\times 10^{-4}\) and \({\mathcal {B}}(\Xi _c^+\rightarrow \Sigma ^{0(+)} \pi ^{+(0)})=(10.3 \pm 1.7)\times 10^{-4}\), which all receive significant contributions from the breaking effects, and can be tested by the BESIII and LHCb experiments.     

Heuristic Relative Entropy Principles with Complex Measures: Large-Degree Asymptotics of a Family of Multi-variate Normal Random Polynomials

Let \(z\in \mathbb {C}\), let \(\sigma ^2>0\) be a variance, and for \(N\in \mathbb {N}\) define the integrals

$$\begin{aligned} E_N^{}(z;\sigma ) := \left\{ \begin{array}{ll} {\frac{1}{\sigma }} \!\!\!\displaystyle \int _{\mathbb {R}}\! (x^2+z^2) \frac{e^{-\frac{1}{2\sigma ^2} x^2}}{\sqrt{2\pi }}dx&{}\quad \text{ if }\, N=1,\\ {\frac{1}{\sigma }} \!\!\!\displaystyle \int _{\mathbb {R}^N}\! \prod \prod \limits _{1\le k<l\le N}\!\! e^{-\frac{1}{2N}(1-\sigma ^{-2}) (x_k-x_l)^2} \prod _{1\le n\le N}\!\!\!\!(x_n^2+z^2) \frac{e^{-\frac{1}{2\sigma ^2} x_n^2}}{\sqrt{2\pi }}dx_n &{}\quad \text{ if }\, N>1. \end{array}\right. \!\!\! \end{aligned}$$

These are expected values of the polynomials \(P_N^{}(z)=\prod _{1\le n\le N}(X_n^2+z^2)\) whose 2N zeros \(\{\pm i X_k\}^{}_{k=1,\ldots ,N}\) are generated by N identically distributed multi-variate mean-zero normal random variables \(\{X_k\}^{N}_{k=1}\) with co-variance \(\mathrm{{Cov}}_N^{}(X_k,X_l)=(1+\frac{\sigma ^2-1}{N})\delta _{k,l}+\frac{\sigma ^2-1}{N}(1-\delta _{k,l})\). The \(E_N^{}(z;\sigma )\) are polynomials in \(z^2\), explicitly computable for arbitrary N, yet a list of the first three \(E_N^{}(z;\sigma )\) shows that the expressions become unwieldy already for moderate N—unless \(\sigma = 1\), in which case \(E_N^{}(z;1) = (1+z^2)^N\) for all \(z\in \mathbb {C}\) and \(N\in \mathbb {N}\). (Incidentally, commonly available computer algebra evaluates the integrals \(E_N^{}(z;\sigma )\) only for N up to a dozen, due to memory constraints). Asymptotic evaluations are needed for the large-N regime. For general complex z these have traditionally been limited to analytic expansion techniques; several rigorous results are proved for complex z near 0. Yet if \(z\in \mathbb {R}\) one can also compute this “infinite-degree” limit with the help of the familiar relative entropy principle for probability measures; a rigorous proof of this fact is supplied. Computer algebra-generated evidence is presented in support of a conjecture that a generalization of the relative entropy principle to signed or complex measures governs the \(N\rightarrow \infty \) asymptotics of the regime \(iz\in \mathbb {R}\). Potential generalizations, in particular to point vortex ensembles and the prescribed Gauss curvature problem, and to random matrix ensembles, are emphasized.

     

Electrical conductivity in single crystals of GaSe<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Te<Subscript>1 – <Emphasis Type="Italic">x</Emphasis></Subscript> solid solutions in strong electrical fields

This paper presents some results of studying the Poole–Frenkel effect with allowance for shielding in layered GaSe and GaTe single crystals and their solid solutions in strong electrical fields of up to 10⁵ V/cm at temperatures of 103–250 K. According to the relationship \(\left(\frac{\sigma}{\sigma(0)}\right)^{1/2}\) log\(\frac{\sigma}{\sigma(0)} = E\sqrt{\frac{\varepsilon}{4\pi n(0)kT}}\), there exists a linear dependence between \(\left(\frac{\sigma}{\sigma(0)}\right)^{1/2}\) log\(\frac{\sigma}{\sigma(0)}\) and the electrical field E (σ is the electrical conductivity in strong electrical fields, and σ(0) is the electrical conductivity in the ohmic region). The slopes of these lines have been determined at different temperatures (103–250 K) by estimating the concentration of current carriers n(0) = 3 × 10¹³–5 × 10¹⁵ cm^–3 in the ohmic region of the electrical conductivity of solid solutions of layered GaSe _x Te_1–x single crystals (x = 1.00, 0.95, 0.90, 0.80, 0.70, 0.30, 0.20, 0.10, 0).     

Two Phases of the Non-Commutative Quantum Mechanics with the Generalized Uncertainty Relations

We consider the quantum mechanics on the noncommutative plane with the generalized uncertainty relations \({\Delta } x_{1} {\Delta } x_{2} \ge \frac {\theta }{2}, {\Delta } p_{1} {\Delta } p_{2} \ge \frac {\bar {\theta }}{2}, {\Delta } x_{i} {\Delta } p_{i} \ge \frac {\hbar }{2}, {\Delta } x_{1} {\Delta } p_{2} \ge \frac {\eta }{2}\). We show that the model has two essentially different phases which is determined by \(\kappa = 1 + \frac {1}{\hbar ^{2} } (\eta ^{2} - \theta \bar {\theta })\). We construct a operator \(\hat {\pi }_{i}\) commuting with \(\hat {x}_{j} \) and discuss the harmonic oscillator model in two dimensional non-commutative space for three case κ > 0, κ = 0, κ < 0. Finally, we discuss the thermodynamics of a particle whose hamiltonian is related to the harmonic oscillator model in two dimensional non-commutative space.     

Effect of FCNC mediated <Emphasis Type="Italic">Z</Emphasis> boson on lepton flavor violating decays

We study the three body lepton flavor violating (LFV) decays μ ^?→e ^? e ⁺ e ^?, \(\tau^{-} \to l_{i}^{-} l_{j}^{+} l_{j}^{-}\) and the semileptonic decay τ→μφ in the flavor changing neutral current (FCNC) mediated Z boson model. We also calculate the branching ratios for LFV leptonic B decays, B _d,s →μe, B _d,s →τe, B _d,s →τμ and the conversion of muon to electron in Ti nucleus. The new physics parameter space is constrained by using the experimental limits on μ ^?→e ^? e ⁺ e ^? and τ ^?→μ ^? μ ⁺ μ ^?. We find that the branching ratios for τ→eee and τ→μφ processes could be as large as \({\sim}{\mathcal{O}}(10^{-8})\) and \(\mathrm{Br}(B_{d,s} \to \tau \mu,~ \tau e) \sim {\mathcal{O}}(10^{-10})\). For other LFV B decays the branching ratios are found to be too small to be observed in the near future.     

Kinetically modified non-minimal inflation with exponential frame function

We consider supersymmetric (SUSY) and non-SUSY models of chaotic inflation based on the \(\phi ^n\) potential with \(n=2\) or 4. We show that the coexistence of an exponential non-minimal coupling to gravity \(f_\mathcal{R}=\mathrm{e}^{c_\mathcal{R}\phi ^{p}}\) with a kinetic mixing of the form \(f_{\mathrm{K}}=c_{\mathrm{K}}f_\mathcal{R}^m\) can accommodate inflationary observables favored by the Planck and Bicep2/Keck Array results for \(p=1\) and 2, \(1\le m\le 15\) and \(2.6\times 10^{-3}\le r_{\mathcal {R}\mathrm{K}}=c_\mathcal{R}/c_{\mathrm{K}}^{p/2}\le 1,\) where the upper limit is not imposed for \(p=1\). Inflation is of hilltop type and it can be attained for subplanckian inflaton values with the corresponding effective theories retaining the perturbative unitarity up to the Planck scale. The supergravity embedding of these models is achieved employing two chiral gauge singlet supefields, a monomial superpotential and several (semi)logarithmic or semi-polynomial Kähler potentials.