Antineutrino science in KamLAND

The primary goal of KamLAND is a search for the oscillation of \({\bar{\nu }}_\mathrm{e}\) ’s emitted from distant power reactors. The long baseline, typically 180 km, enables KamLAND to address the oscillation solution of the “solar neutrino problem” with \({\bar{\nu }}_{e} \) ’s under laboratory conditions. KamLAND found fewer reactor \({\bar{\nu }}_{e} \) events than expected from standard assumptions about \(\overline{\nu }_e\) propagation at more than 9 \(\sigma \) confidence level (C.L.). The observed energy spectrum disagrees with the expected spectral shape at more than 5 \(\sigma \) C.L., and prefers the distortion from neutrino oscillation effects. A three-flavor oscillation analysis of the data from KamLAND and KamLAND + solar neutrino experiments with CPT invariance, yields \(\Delta m_{21}^2 \) = [ \(7.54_{-0.18}^{+0.19} \times \) 10 \(^{-5}\) eV \(^{2}\) , \(7.53_{-0.18}^{+0.19} \times \) 10 \(^{-5}\) eV \(^{2}\) ], tan \(^{2}\theta _{12}\) = [ \(0.481_{-0.080}^{+0.092} \) , \(0.437_{-0.026}^{+0.029} \) ], and sin \(^{2}\theta _{13}\) = [ \(0.010_{-0.034}^{+0.033} \) , \(0.023_{-0.015}^{+0.015} \) ]. All solutions to the solar neutrino problem except for the large mixing angle region are excluded. KamLAND also demonstrated almost two cycles of the periodic feature expected from neutrino oscillation effects. KamLAND performed the first experimental study of antineutrinos from the Earth’s interior so-called geoneutrinos (geo \({\bar{\nu }}_{e} \) ’s), and succeeded in detecting geo \({\bar{\nu }}_{e} \) ’s produced by the decays of \(^{238}\) U and \(^{232}\) Th within the Earth. Assuming a chondritic Th/U mass ratio, we obtain \(116_{-27}^{+28} {\bar{\nu }}_{e}\) events from \(^{238}\) U and \(^{232}\) Th, corresponding a geo \({\bar{\nu }}_{e}\) flux of \(3.4_{-0.8}^{+0.8}\times \) 10 \(^{6}\) cm \(^{-2}\)  s \(^{-1}\) at the KamLAND location. We evaluate various bulk silicate Earth composition models using the observed geo \({\bar{\nu }}_{e} \) rate.     

Split supersymmetry under GUT and current dark matter constraints

There are four types of two-Higgs doublet models under a discrete \(Z_2\) symmetry imposed to avoid tree-level flavor-changing neutral current, i.e. type-I, type-II, type-X, and type-Y models. We investigate the possibility to discriminate the four models in the light of the flavor physics data, including \(B_s\) – \(\bar{B}_s\) mixing, \(B_{s,d} \rightarrow \mu ^+ \mu ^-\) , \(B\rightarrow \tau \nu \) and \(\bar{B} \rightarrow X_s \gamma \) decays, the recent LHC Higgs data, the direct search for charged Higgs at LEP, and the constraints from perturbative unitarity and vacuum stability. After deriving the combined constraints on the Yukawa interaction parameters, we have shown that the correlation between the mass eigenstate rate asymmetry \(A_{\Delta \Gamma }\) of \(B_{s} \rightarrow \mu ^+ \mu ^-\) and the ratio \(R=\mathcal{B}(B_{s} \rightarrow \mu ^+ \mu ^-)_\mathrm{exp}/ \mathcal{B}(B_{s} \rightarrow \mu ^+ \mu ^-)_\mathrm{SM}\) could be a sensitive probe to discriminate the four models with future precise measurements of the observables in the \(B_{s} \rightarrow \mu ^+ \mu ^-\) decay at LHCb.     

Optimal N-Point Configurations on the Sphere: “Magic” Numbers and Smale’s 7th Problem

This paper inquires into the concavity of the map \(N\mapsto v_s(N)\) from the integers \(N\ge 2\) into the minimal average standardized Riesz pair-energies \(v_s(N)\) of \(N\) -point configurations on the sphere \(\mathbb {S}^2\) for various \(s\in \mathbb {R}\) . The standardized Riesz pair-energy of a pair of points on \(\mathbb {S}^2\) a chordal distance \(r\) apart is \(V_s(r)= s^{-1}\left( r^{-s}-1 \right) \) , \(s \ne 0\) , which becomes \(V_0(r) = \ln \frac{1}{r}\) in the limit \(s\rightarrow 0\) . Averaging it over the \(\left( \begin{array}{c} N\\ 2\end{array}\right) \) distinct pairs in a configuration and minimizing over all possible \(N\) -point configurations defines \(v_s(N)\) . It is known that \(N\mapsto v_s(N)\) is strictly increasing for each \(s\in \mathbb {R}\) , and for \(s<2\) also bounded above, thus “overall concave.” It is (easily) proved that \(N\mapsto v_{-2}^{}(N)\) is even locally strictly concave, and that so is the map \(2n\mapsto v_s(2n)\) for \(s<-2\) . By analyzing computer-experimental data of putatively minimal average Riesz pair-energies \(v_s^x(N)\) for \(s\in \{-1,0,1,2,3\}\) and \(N\in \{2,\ldots ,200\}\) , it is found that the map \(N\mapsto {v}_{-1}^x(N)\) is locally strictly concave, while \(N\mapsto {v}_s^x(N)\) is not always locally strictly concave for \(s\in \{0,1,2,3\}\) : concavity defects occur whenever \(N\in {\mathcal {C}}^{x}_+(s)\) (an \(s\) -specific empirical set of integers). It is found that the empirical map \(s\mapsto {\mathcal {C}}^{x}_+(s),\ s\in \{-2,-1,0,1,2,3\}\) , is set-theoretically increasing; moreover, the percentage of odd numbers in \({\mathcal {C}}^{x}_+(s),\ s\in \{0,1,2,3\}\) is found to increase with \(s\) . The integers in \({\mathcal {C}}^{x}_+(0)\) are few and far between, forming a curious sequence of numbers, reminiscent of the “magic numbers” in nuclear physics. It is conjectured that these new “magic numbers” are associated with optimally symmetric optimal-log-energy \(N\) -point configurations on \(\mathbb {S}^2\) . A list of interesting open problems is extracted from the empirical findings, and some rigorous first steps toward their solutions are presented. It is emphasized how concavity can assist in the solution to Smale’s \(7\) th Problem, which asks for an efficient algorithm to find near-optimal \(N\) -point configurations on \(\mathbb {S}^2\) and higher-dimensional spheres.     

Blow Up Dynamics for Equivariant Critical Schrödinger Maps

For the Schrödinger map equation \({u_t = u \times \triangle u \, {\rm in} \, \mathbb{R}^{2+1}}\) , with values in S ², we prove for any \({\nu > 1}\) the existence of equivariant finite time blow up solutions of the form \({u(x, t) = \phi(\lambda(t) x) + \zeta(x, t)}\) , where \({\phi}\) is a lowest energy steady state, \({\lambda(t) = t^{-1/2-\nu}}\) and \({\zeta(t)}\) is arbitrary small in \({\dot H^1 \cap \dot H^2}\) .     

Is the CNMSSM more credible than the CMSSM?

“Post-sphaleron baryogenesis”, a fresh and profound mechanism of baryogenesis accounts for the matter–antimatter asymmetry of our present universe in a framework of Pati–Salam symmetry. We attempt here to embed this mechanism in a non-SUSY SO(10) grand unified theory by reviving a novel symmetry breaking chain with Pati–Salam symmetry as an intermediate symmetry breaking step and as well to address post-sphaleron baryogenesis and neutron–antineutron oscillation in a rational manner. The Pati–Salam symmetry based on the gauge group \(\mathrm{SU}(2)_L \times \mathrm{SU}(2)_{R} \times \mathrm{SU}(4)_C\) is realized in our model at \(10^{5}\) – \(10^{6}\)  GeV and the mixing time for the neutron–antineutron oscillation process having \(\Delta B=2\) is found to be \(\tau _{n-\bar{n}} \simeq 10^{8}\) – \(10^{10}\)  s with the model parameters, which is within the reach of forthcoming experiments. Other novel features of the model include low scale right-handed \(W^{\pm }_R\) , \(Z_R\) gauge bosons, explanation for neutrino oscillation data via the gauged inverse (or extended) seesaw mechanism and most importantly TeV scale color sextet scalar particles responsible for an observable \(n\) – \(\bar{n}\) oscillation which may be accessible to LHC. We also look after gauge coupling unification and an estimation of the proton lifetime with and without the addition of color sextet scalars.     

Misalignment tolerance analysis and fabrication for highly efficient parallel optical-electrical convertor module

A compact, highly efficient, and passively assembled parallel optical-electrical convertor module (POECM) for active optical cable application is proposed. This paper presents our POECM structure, optical design simulation results, fabrication process, and data transmission test results, in sequence. The POECM has a compact size of \(18.5\hbox {mm} \times 10\hbox {mm} \times 2.8\hbox {mm}\) . We confirm a data rate of total throughput at 21.6 Gbps ( \(5.4\hbox {Gbps} \times 4\) channels) with a bit error rate of less than \(10^{-12}\) .     

A flexible scintillation light apparatus for rare event searches

Compelling experimental evidences of neutrino oscillations and their implication that neutrinos are massive particles have given neutrinoless double beta decay ( \(\beta \beta 0\nu \) ) a central role in astroparticle physics. In fact, the discovery of this elusive decay would be a major breakthrough, unveiling that neutrino and antineutrino are the same particle and that the lepton number is not conserved. It would also impact our efforts to establish the absolute neutrino mass scale and, ultimately, understand elementary particle interaction unification. All current experimental programs to search for \(\beta \beta 0\nu \) are facing with the technical and financial challenge of increasing the experimental mass while maintaining incredibly low levels of spurious background. The new concept described in this paper could be the answer which combines all the features of an ideal experiment: energy resolution, low cost mass scalability, isotope choice flexibility and many powerful handles to make the background negligible. The proposed technology is based on the use of arrays of silicon detectors cooled to 120 K to optimize the collection of the scintillation light emitted by ultra-pure crystals. It is shown that with a 54 kg array of natural CaMoO \(_4\) scintillation detectors of this type it is possible to yield a competitive sensitivity on the half-life of the \(\beta \beta 0\nu \) of \(^{100}\) Mo as high as \(\sim \) \(10^{24}\)  years in only 1 year of data taking. The same array made of \(^{40}\) Ca \(^{\mathrm {nat}}\) MoO \(_4\) scintillation detectors (to get rid of the continuous background coming from the two neutrino double beta decay of \(^{48}\) Ca) will instead be capable of achieving the remarkable sensitivity of \(\sim \) \(10^{25}\)  years on the half-life of \(^{100}\) Mo \(\beta \beta 0\nu \) in only 1 year of measurement.     

Investigation of conductivity of adhesive layer including indium tin oxide particles for multi-junction solar cells

We report connection conductivity ( \(C_{\rm c}\) ) of adhesive which including \(\hbox {In}_2\hbox {O}_3\) – \(\hbox {SnO}_2\) (ITO) particles developed for fabrication of stacked-type-multi-junction solar cells. The commercial 20- \(\upmu \) m sized ITO particles were heated in vacuum at temperature ranging from 800 to 1,300  \(^{\circ }{\rm C}\) for 10 min to increase \(C_{\rm c}\) . 6.2 wt% ITO particles were dispersed in commercial Cemedine adhesive gel to form 100 samples structured with n-type Si/adhesive/n-type Si (n-Si sample) and p-type Si/adhesive/p-type Si (p-Si sample). Current density as a function of voltage (J–V) characteristics gave \(C_{\rm c}\) . It ranged from 4.3 to 1.0 S/cm \(^2\) for the n-Si sample with 800 \(^{\circ }{\rm C}\) heat-treated ITO particles. Its standard deviation was 0.59 S/cm \(^2\) . On the other hand, it ranged from 2.0 to 0.6 S/cm \(^2\) for the p-Si sample with 800  \(^{\circ }{\rm C}\) heat-treated ITO particles. Its standard deviation was 0.22 S/cm \(^2\) . The distribution of \(C_{\rm c}\) mainly resulted from contact efficiency of ITO particles to substrate. We theoretically estimated that present \(C_{\rm c}\) achieved a low loss of the power conversion efficiency ( \(E_{\rm ff}\) ) lower than 0.3 % in the application of fabrication of multi-junction solar cell with an intrinsic \(E_{\rm ff}\) of 30 % and an open circuit voltage above 1.9 V.     

The Isospin Mixing in the X(3872) Decay Spectrum

The large isospin symmetry breaking found in the X(3872) decay is investigated by looking into the transfer strength from the \({{c}\bar{c}}\) quarkonium to the two-meson states: \({c\bar{c} \rightarrow D^{0}\overline{D}^{*0}, D^{+} D^{*-} , J /\psi\omega, {\rm and} \, J /\psi\rho}\) . The widths of the \({\rho}\) and \({\omega}\) mesons are taken into account in the calculation. It is found that very narrow \({J /\psi\omega}\) and \({J /\psi\rho}\) peaks appear at the \({D^{0}\overline{D}^{*0}}\) threshold. These narrow peaks appear provided that the strength of the \({D^{0}\overline{D}^{*0}}\) component is large around the threshold. The large width of the \({\rho}\) meson enhances the isospin-one component in the transfer strength considerably, which reduces the ratio \({{\rm Br}(X \rightarrow J /\psi\omega)/{\rm Br}(X \rightarrow J /\psi\rho)}\) down to 2.5.     

Phase Transitions in Layered Systems

We consider the Ising model on \(\mathbb Z\times \mathbb Z\) where on each horizontal line \(\{(x,i), x\in \mathbb Z\}\) , called “layer”, the interaction is given by a ferromagnetic Kac potential with coupling strength \(J_{ \gamma }(x,y)={ \gamma }J({ \gamma }(x-y))\) , where \(J(\cdot )\) is smooth and has compact support; we then add a nearest neighbor ferromagnetic vertical interaction of strength \({ \gamma }^{A}\) , where \(A\ge 2\) is fixed, and prove that for any \(\beta \) larger than the mean field critical value there is a phase transition for all \({ \gamma }\) small enough.     

Dirac quasinormal modes of two-dimensional charged dilatonic black holes

Following some recent unexpected hints of neutron production in high-voltage atmospheric discharges, we present a measurement of the neutron flux in plasma discharges in electrolytic cells. We use two different types of neutron detectors, polyallyl diglycol carbonate (PADC, aka CR-39) tracers and indium disks. At 95 % C.L. we provide an upper limit of 1.5 neutrons cm \(^{-2}\)  s \(^{-1}\) for the thermal neutron flux at \({\approx } 5\) cm from the center of the cell. Allowing for a higher energy neutron component, the largest allowed flux is 64 neutrons cm \(^{-2}\)  s \(^{-1}\) . This upper limit is two orders of magnitude smaller than the signal previously claimed in an electrolytic cell plasma discharge experiment. Furthermore the behavior of the CR-39 is discussed to point out possible sources of spurious signals.     

Analysis of the \frac{1} {2}^ - and \frac{3} {2}^ - heavy and doubly heavy baryon states with QCD sum rules

In this article, we study the $\frac{1} {2}^ -$ and $\frac{3} {2}^ -$ heavy and doubly heavy baryon states $\Sigma _Q \left( {\frac{1} {2}^ - } \right)$ , $\Xi '_Q \left( {\frac{1} {2}^ - } \right)$ , $\Omega _Q \left( {\frac{1} {2}^ - } \right)$ , $\Xi _{QQ} \left( {\frac{1} {2}^ - } \right)$ , $\Omega _{QQ} \left( {\frac{1} {2}^ - } \right)$ , $\Sigma _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Xi _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Omega _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Xi _{QQ}^* \left( {\frac{3} {2}^ - } \right)$ and $\Omega _{QQ}^* \left( {\frac{3} {2}^ - } \right)$ by subtracting the contributions from the corresponding $\frac{1} {2}^ +$ and $\frac{3} {2}^ +$ heavy and doubly heavy baryon states with the QCD sum rules in a systematic way, and make reasonable predictions for their masses.     

\mathrm{CO}_{2}^{*} chemiluminescence study at low and elevated pressures

Chemiluminescence experiments have been performed to assess the state of current $\mathrm{CO}_{2}^{*}$ kinetics modeling. The difficulty with modeling $\mathrm{CO}_{2}^{*}$ lies in its broad emission spectrum, making it a challenge to isolate it from background emission of species such as CH^? and CH₂O^?. Experiments were performed in a mixture of 0.0005H₂+0.01N₂O+0.03CO+0.9595Ar in an attempt to isolate $\mathrm{CO}_{2}^{*}$ emission. Temperatures ranged from 1654 K to 2221 K at two average pressures, 1.4 and 10.4 atm. The unique time histories of the various chemiluminescence species in the unconventional mixture employed at these conditions allow for easy identification of the $\mathrm{CO}_{2}^{*}$ concentration. Two different wavelengths to capture $\mathrm{CO}_{2}^{*}$ were used; one optical filter was centered at 415 nm and the other at 458 nm. The use of these two different wavelengths was done to verify that broadband $\mathrm{CO}_{2}^{*}$ was in fact being captured, and not emission from other species such as CH^? and CH₂O^?. As a baseline for time history and peak magnitude comparison, OH^? emission was captured at 307 nm simultaneously with the two $\mathrm{CO}_{2}^{*}$ filters. The results from the two $\mathrm{CO}_{2}^{*}$ filters were consistent with each other, implying that indeed the same species (i.e., $\mathrm{CO}_{2}^{*}$ ) was being measured at both wavelengths. A first-generation kinetics model for $\mathrm{CO}_{2}^{*}$ and CH₂O^? was developed, since no comprehensively validated one exists to date. CH₂O^? and CH^? were ruled out as being present in the experiments at any measurable level, based on calculations and comparisons with the data. Agreement with the $\mathrm{CO}_{2}^{*}$ model was only fair, which necessitates future improvements for a better understanding of $\mathrm{CO}_{2}^{*}$ chemiluminescence as well as the kinetics of the ground state species.     

Analysis of the {3\over 2}^{+} heavy and doubly heavy baryon states with QCD sum rules

In this article, we study the ${3\over 2}^{+}$ heavy and doubly heavy baryon states $\varXi^{*}_{cc}$ , $\varOmega^{*}_{cc}$ , $\varXi^{*}_{bb}$ , $\varOmega^{*}_{bb}$ , $\varSigma_{c}^{*}$ , $\varXi_{c}^{*}$ , $\varOmega_{c}^{*}$ , $\varSigma_{b}^{*}$ , $\varXi_{b}^{*}$ and $\varOmega_{b}^{*}$ by subtracting the contributions from the corresponding ${3\over 2}^{-}$ heavy and doubly heavy baryon states with the QCD sum rules, and we make reasonable predictions for their masses.     

Line intensity measurements of methane’s \nu _3-band using a cw-OPO

We report on absolute line strength measurements of P(1), R(0) and R(1) singlet lines in the \(3.3\,\upmu\hbox {m}\,\nu _{3}\) (C–H stretching) band of methane \(^{12}\hbox {CH}_4\) at reference temperature \(T=296\)  K. Line strength measurements are performed at low pressure \((P \le 1\hbox { Torr})\) using direct absorption spectroscopy technique based on a widely tunable continuous-wave singly resonant optical parametric oscillator. The \(1\sigma \) overall accuracy in line strength determinations ranges between 7 and 8 % mostly limited by pressure and frequency measurements. A comparison with previous reported values is made. Our results show good agreement with the HITRAN 2012 database.     

Reunion Probabilities of N One-Dimensional Random Walkers with Mixed Boundary Conditions

In this work we extend the results of the reunion probability of \(N\) one-dimensional random walkers to include mixed boundary conditions between their trajectories. The level of the mixture is controlled by a parameter \(c\) , which can be varied from \(c=0\) (independent walkers) to \(c\rightarrow \infty \) (vicious walkers). The expressions are derived by using Quantum Mechanics formalism (QMf) which allows us to map this problem into a Lieb-Liniger gas (LLg) of \(N\) one-dimensional particles. We use Bethe ansatz and Gaudin’s conjecture to obtain the normalized wave-functions and use this information to construct the propagator. As it is well-known, depending on the boundary conditions imposed at the endpoints of a line segment, the statistics of the maximum heights of the reunited trajectories have some connections with different ensembles in Random Matrix Theory. Here we seek to extend those results and consider four models: absorbing, periodic, reflecting, and mixed. In all four cases, the probability that the maximum height is less or equal than \(L\) takes the form \(F_N(L)=A_N\sum _{\varvec{k}\in \Omega _{\text {B}}} \mathrm{e}^{-\sum _{j=1}^Nk_j^2}\mathcal {V}_N(\varvec{k})\) , where \(A_N\) is a normalization constant, \(\mathcal {V}_N(\varvec{k})\) contains a deformed and weighted Vandermonde determinant, and \(\Omega _{\text {B}}\) is the solution set of quasi-momenta \(\varvec{k}\) obeying the Bethe equations for that particular boundary condition.     

Comprehensive Bayesian analysis of rare (semi)leptonic and radiative \varvec{B} decays

The available data on \(|\Delta B| = |\Delta S| = 1\) decays are in good agreement with the Standard Model when permitting subleading power corrections of about \(15\,\%\) at large hadronic recoil. Constraining new-physics effects in \(\mathcal {C}_{7}^{\mathrm {}}\) , \(\mathcal {C}_{9}^{\mathrm {}}\) , \(\mathcal {C}_{10}^{\mathrm {}}\) , the data still demand the same size of power corrections as in the Standard Model. In the presence of chirality-flipped operators, all but one of the power corrections reduce substantially. The Bayes factors are in favor of the Standard Model. Using new lattice inputs for \(B\rightarrow K^*\) form factors and under our minimal prior assumption for the power corrections, the favor shifts toward models with chirality-flipped operators. We use the data to further constrain the hadronic form factors in \(B\rightarrow K\) and \(B\rightarrow K^*\) transitions.     

Functional Properties of Hörmander’s Space of Distributions Having a Specified Wavefront Set

The space \({\mathcal{D}_\Gamma^\prime}\) of distributions having their wavefront sets in a closed cone \({\Gamma}\) has become important in physics because of its role in the formulation of quantum field theory in curved spacetime. In this paper, the topological and bornological properties of \({\mathcal{D}_\Gamma^\prime}\) and its dual \({\mathcal{E}_\Lambda^\prime}\) are investigated. It is found that \({\mathcal{D}_\Gamma^\prime}\) is a nuclear, semi-reflexive and semi-Montel complete normal space of distributions. Its strong dual \({\mathcal{E}_\Lambda^\prime}\) is a nuclear, barrelled and (ultra)bornological normal space of distributions which, however, is not even sequentially complete. Concrete rules are given to determine whether a distribution belongs to \({\mathcal{D}_\Gamma^\prime}\) , whether a sequence converges in \({\mathcal{D}_\Gamma^\prime}\) and whether a set of distributions is bounded in \({\mathcal{D}_\Gamma^\prime}\) .     

Flavour models with three Higgs generations

A search for axioelectric absorption of solar axions produced in the \(p + d \rightarrow {^3\mathrm {He}}+\gamma (5.5~\mathrm {MeV})\) reaction has been performed with a BGO detector placed in a low-background setup. A model-independent limit on the combination of axion–nucleon and axion–electron coupling constants has been obtained: \(| g_{Ae}\times g_{AN}^3|< 1.9\times 10^{-10}\) for 90 % confidence level. The constraint of the axion–electron coupling constant has been obtained for hadronic axion with masses of (0.1–1) MeV: \(|g_{Ae}| \le (0.96 - 8.2)\times 10^{-8}\) .     

Radiative and semileptonic B decays involving higher K-resonances in the final states

We study the radiative and semileptonic B decays involving a spin-J resonant $K_{J}^{(*)}$ with parity (?1) ^J for $K_{J}^{*}$ and (?1) ^J+1 for K _J in the final state. Using large energy effective theory (LEET) techniques, we formulate $B\to K_{J}^{(*)}$ transition form factors in the large recoil region in terms of two independent LEET functions $\zeta_{\perp}^{K_{J}^{(*)}}$ and $\zeta_{\parallel}^{K_{J}^{(*)}}$ , the values of which at zero momentum transfer are estimated in the BSW model. According to the QCD counting rules, $\zeta_{\perp,\parallel}^{K_{J}^{(*)}}$ exhibit a dipole dependence in q ². We predict the decay rates for $B\to K_{J}^{(*)}\gamma$ , $B\to K_{J}^{(*)}\ell^{+}\ell^{-}$ and $B\to K_{J}^{(*)}\nu \bar{\nu}$ . The branching fractions for these decays with higher K-resonances in the final state are suppressed due to the smaller phase spaces and the smaller values of $\zeta^{K_{J}^{(*)}}_{\perp,\parallel}$ . Furthermore, if the spin of $K_{J}^{(*)}$ becomes larger, the branching fractions will be further suppressed due to the smaller Clebsch–Gordan coefficients defined by the polarization tensors of the $K_{J}^{(*)}$ . We also calculate the forward–backward asymmetry of the $B\to K_{J}^{(*)}\ell^{+}\ell^{-}$ decay, for which the zero is highly insensitive to the K-resonances in the LEET parametrization.