arXiv subjects

Y. K. Hsiao

Publications and source records attributed to Y. K. Hsiao.

At least 37 records · Page 2Linked to original sources

arXiv2017

Determinations of $|V_{cb}|$ and $|V_{ub}|$ from baryonic $Λ_b$ decays

We extract the Cabibbo-Kobayashi-Maskawa matrix element $V_{cb}$ from the exclusive decays of $Λ_b\to Λ_c\ell\bar ν_\ell$ and $Λ_b\to Λ_c M_{(c)}$ with $M=(π^-,K^-)$ and $M_c=(D^-,D^-_s)$, where the branching ratios of $Λ_b\to ΛM_{(c)}$ measured with high precisions have not been used in the previous studies. Explicitly, we find $|V_{cb}|=(44.0\pm 3.5)\times 10^{-3}$, which agrees with the value of $(42.11\pm 0.74)\times 10^{-3}$ from the inclusive $B\to X_c\ell\bar ν_\ell$ decays. Furthermore, based on the most recent ratio of $|V_{ub}|/|V_{cb}|$ from the exclusive $Λ_b$ decays, we obtain $|V_{ub}|=(4.2\pm 0.4)\times 10^{-3}$, which is close to the value of $(4.49\pm 0.24)\times 10^{-3}$ from the inclusive $B\to X_u\ell\bar ν_\ell$ decays. We conclude that our determinations of $|V_{cb}|$ and $|V_{ub}|$ from the exclusive $Λ_b$ decays favor the inclusive extractions in the $B$ decays.

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arXiv2017

Charmless two-body anti-triplet $b$-baryon decays

We study the charmless two-body decays of $b$-baryons $(Λ_b$, $Ξ_b^-$, $Ξ_b^0)$. We find that ${\cal B}(Ξ_b^-\to Λρ^-)=(2.08^{+0.69}_{-0.51})\times 10^{-6}$ and ${\cal B}(Ξ_b^0\to Σ^+ M^-)=(4.45^{+1.46}_{-1.09},11.49^{+3.8}_{-2.9},4.69^{+1.11}_{-0.79},2.98^{+0.76}_{-0.51})\times 10^{-6}$ for $M^-=(π^-,ρ^-,K^-,K^{*-})$, which are compatible to ${\cal B}(Λ_b\to p π^-,p K^-)$. We also obtain that ${\cal B}(Λ_b\to Λω)=(2.30\pm0.10)\times 10^{-6}$, ${\cal B}(Ξ_b^-\toΞ^- ϕ,Ξ^- ω)\simeq {\cal B}(Ξ_b^0\toΞ^0 ϕ,Ξ^0 ω)=(5.35\pm0.41,3.65\pm0.16)\times 10^{-6}$ and ${\cal B}(Ξ^-_b\toΞ^{-} η^{(\prime)})\simeq {\cal B}(Ξ^0_b\to Ξ^0 η^{(\prime)})=(2.51^{+0.70}_{-0.46},2.99^{+1.16}_{-0.57})\times 10^{-6}$. For the CP violating asymmetries, we show that ${\cal A}_{CP}(Λ_b\to p K^{*-})={\cal A}_{CP}(Ξ_b^-\to Σ^0(Λ)K^{*-})={\cal A}_{CP}(Ξ_b^0\to Σ^+K^{*-})=(19.7\pm 1.4)\%$. Similar to the charmless two-body $Λ_b$ decays, the $Ξ_b$ decays are accessible to the LHCb detector.

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arXiv2017

Four-body baryonic decays of $B\to p \bar{p} π^+π^-(π^+K^-)$ and $Λ\bar{p} π^+π^-(K^+K^-)$

We study the four-body baryonic $B\to {\bf B_1 \bar B_2}M_1 M_2$ decays with $\bf B_{1,2}$ ($M_{1,2}$) being charmless baryons (mesons). In accordance with the recent LHCb observations, each decay is considered to proceed through the $B\to M_1 M_2$ transition together with the production of a baryon pair. We obtain that ${\cal B}(B^-\to Λ\bar p π^+π^-)=(3.7^{+1.5}_{-1.0} )\times 10^{-6}$ and ${\cal B}(\bar B^0\to p\bar p π^+π^-,p\bar p π^+ K^-)=(3.0\pm 0.9,6.6\pm 2.4)\times 10^{-6}$, in agreement with the data. We also predict ${\cal B}(B^-\toΛ\bar p K^+ K^-)=(3.0^{+1.3}_{-0.9})\times 10^{-6}$, which is accessible to the LHCb and BELLE experiments.

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arXiv2016

Three-body charmless baryonic $\bar B^0_s$ decays

We study for the first time the three-body charmless baryonic decays $\bar B^0_s\to \bar p ΛM^+ (p \bar ΛM^-)$, with $M=π, K$. We find that the branching ratios of $\bar B^0_s\to (\bar p ΛK^+$ and $p\bar ΛK^-)$ and $\bar B^0_s\to p\bar Λπ^-$ are $(5.1\pm 1.1)\times 10^{-6}$ and $(2.8\pm 1.5)\times 10^{-7}$, respectively, which agree with recent experimental results reported by the LHCb collaboration. In addition, we derive the relations \mbox{${\cal B}(\bar B^0_s\to \bar p ΛK^+)\simeq (f_K/f_π)^2(τ_{B^0_s}/τ_{B^0}) {\cal B}(\bar B^0\to \bar p Λπ^+)$} and ${\cal B}(\bar B^0_s\to p\bar Λπ^-)/{\cal B}(\bar B^0_s\to p\bar ΛK^-)\simeq {\cal B}(B^-\to p\bar p π^-)/{\cal B}(B^-\to p\bar p K^-)$ to be confronted to future experimental measurements. The fact that all four processes $B^0_s, \bar B^0_s \to p\bar ΛK^-, \bar p ΛK^+$ can occur opens the possibility of decay-time-dependent CP violation measurements in baryonic $B$ decays, something that had not been realised before.

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arXiv2016

Exploring the simplest purely baryonic decay processes

Though not considered in general, purely baryonic decays could shed light on the puzzle of the baryon number asymmetry in the universe by means of a better understanding of the baryonic nature of our matter world. As such, they constitute a yet unexplored class of decay processes worth investigating. We propose to search for purely baryonic decay processes at the LHCb experiment. No such type of decay has ever been observed. In particular, we concentrate on the decay $Λ_b^0\to p\bar pn$, which is the simplest purely baryonic decay mode, with solely spin-1/2 baryons involved. We predict its decay branching ratio to be ${\cal B}(Λ_b^0\to p\bar pn)=(2.0^{+0.3}_{-0.2})\times 10^{-6}$, which is sufficiently large to make the decay mode accessible to LHCb. Our study can be extended to other purely baryonic decays such as $Λ_b^0\to p\bar p Λ$ and $Λ_b^0\to Λ\bar ΛΛ$, as well as to similar decays of anti-triplet $b$-baryons such as $Ξ_b^{0,-}$.

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arXiv2016

Branching fractions of $B_{(c)}$ decays involving $J/ψ$ and $X(3872)$

We study two-body $B_{(c)}\to M_c(π,K)$ and semileptonic $B_{c}\to M_c\ell^-\bar ν_\ell$ decays with $M_c=(J/ψ,X_c^0)$, where $X_c^0\equiv X^0(3872)$ is regarded as the tetraquark state of $c\bar cu\bar u(d\bar d)$. With the decay constant $f_{X_c^0}=(234\pm 52)$~MeV determined from the data, we predict that ${\cal B}(B^-\to X_c^0π^-)=(11.5\pm 5.7)\times 10^{-6}$, ${\cal B}(\bar B^0\to X_c^0\bar K^0)=(2.1\pm 1.0)\times 10^{-4}$, and ${\cal B}(\bar B^0_s\to X_c^0\bar K^0)=(11.4\pm 5.6)\times 10^{-6}$. With the form factors in QCD models, we calculate that ${\cal B}(B_c^-\to X_c^0π^-,X_c^0 K^-)=(6.0\pm 2.6)\times 10^{-5}$ and $(4.7\pm 2.0)\times 10^{-6}$, and ${\cal B}(B_c^-\to J/ψμ^-\bar ν_μ, X_c^0 μ^-\bar ν_μ)=(2.3\pm0.6)\times 10^{-2}$ and $(1.35\pm 0.18)\times 10^{-3}$, respectively, and extract the ratio of the fragmentation fractions to be $f_c/f_u=(6.4\pm 1.9)\times 10^{-3}$.

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arXiv2016

Study of $Λ_b\to Λ(ϕ,η^{(\prime)})$ and $Λ_b\to ΛK^+K^-$ decays

We study the charmless two-body $Λ_b\to Λ(ϕ,η^{(\prime)})$ and three-body $Λ_b\to ΛK^+K^- $ decays. We obtain ${\cal B}(Λ_b\to Λϕ)=(3.53\pm 0.24)\times 10^{-6}$ to agree with the recent LHCb measurement. However, we find that ${\cal B}(Λ_b\to Λ(ϕ\to)K^+ K^-)=(1.71\pm 0.12)\times 10^{-6}$ is unable to explain the LHCb observation of ${\cal B}(Λ_b\toΛK^+ K^-)=(15.9\pm 1.2\pm 1.2\pm 2.0)\times 10^{-6}$, which implies the possibility for other contributions, such as that from the resonant $Λ_b\to K^- N^*,\,N^*\toΛK^+$ decay with $N^*$ as a higher-wave baryon state. For $Λ_b\to Λη^{(\prime)}$, we show that ${\cal B}(Λ_b\to Λη,\,Λη^\prime)= (1.47\pm 0.35,1.83\pm 0.58)\times 10^{-6}$, which are consistent with the current data of $(9.3^{+7.3}_{-5.3},<3.1)\times 10^{-6}$, respectively. Our results also support the relation of ${\cal B}(Λ_b\to Λη) \simeq {\cal B}(Λ_b\toΛη^\prime)$, given by the previous study.

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arXiv2016

Roles of scalar mesons in charmless $Λ_b$ decays

We first study the charmless two-body $Λ_b$ decays with the scalar mesons as the final states and predict that ${\cal B}(Λ_b\to Λf_0(980,1500))=(2.9\pm 0.7,12.4\pm 3.8)\times 10^{-6}$ and ${\cal B}(Λ_b\to p K^{*-}_0(800,1430))=(1.9\pm 0.5,14.1\pm 4.5)\times 10^{-6}$. With the resonant $f_0(980,1500)\to (π^+π^-,K^+K^-)$ and $K^{*-}_0\to \bar K^0 π^-$ decays, we then obtain ${\cal B}(Λ_b\to Λ(π^+π^-,K^+K^-))=(4.2\pm 1.0,3.5\pm0.7)\times 10^{-6}$ and ${\cal B}(Λ_b\to p\bar K^0 π^-)=(10.4\pm2.9)\times 10^{-6}$, in comparison with the data of $(4.6\pm 1.9,15.9\pm2.6)\times 10^{-6}$ and $(12.6\pm 4.0)\times 10^{-6}$ from LHCb, respectively. Our results for $Λ_b\to Λπ^+π^-$ and $Λ_b\to p\bar K^0 π^-$ would be regarded as the first evidences of the scalar meson productions in the anti-triplet $b$-baryon decays. The smaller predicted value of ${\cal B}(Λ_b\to ΛK^+K^-)$ indicates the existences of other resonant contributions to the decay, such as $Λ_b\to K^-(N^{*+}\to)ΛK^+$.

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arXiv2016

Determination of $|V_{ub}|$ from exclusive baryonic $B$ decays

We use the exclusive baryonic $B$ decays to determine the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $V_{ub}$. From the relation $|V_{ub}|^2/|V_{cb}|^2=({\cal B}_π/{\cal B}_D){\cal R}_{ff}$ based on $B^-\to p\bar p π^-$ and $\bar B^0\to p\bar p D^0$ decays, where $|V_{cb}|$ and ${\cal B}_π/{\cal B}_D\equiv{\cal B}(B^-\to p\bar p π^-)/{\cal B}(\bar B^0\to p\bar p D^0)$ are the data input parameters, while ${\cal R}_{ff}$ is the one fixed by the $B\to p\bar p$ transition matrix elements, we find $|V_{ub}|=(3.48^{+0.87}_{-0.63}\pm 0.40\pm 0.07)\times 10^{-3}$ with the errors corresponding to the uncertainties from ${\cal R}_{ff}$, ${\cal B}_π/{\cal B}_D$ and $|V_{cb}|$, respectively. Being independent of the previous results, our determination of $|V_{ub}|$ has the central value close to those from the exclusive $\bar B\to π\ell\bar ν_\ell$ and $Λ_b\to pμ^-\bar ν_μ$ decays, but overlaps the one from the inclusive $\bar B\to X_u \ell\bar ν_\ell$ with the current uncertainties. The extraction of $|V_{ub}|$ in the baryonic $B$ decays is clearly very useful for the complete determination of the CKM matrix elements as well as the exploration of new physics.

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arXiv2016

Factorization and angular distribution asymmetries in charmful baryonic B decays

We examine the validity of the generalized factorization method and calculate the angular correlations in the charmful three-body baryonic decays of $\bar B^0\to Λ\bar p D^{(*)+}$. With the timelike baryonic form factors newly extracted from the measured baryonic $B$ decays, we obtain ${\cal B}(\bar B^0\to Λ\bar p D^+,Λ\bar p D^{*+})=(1.85\pm 0.30,2.75\pm 0.24)\times 10^{-5}$ to agree with the recent data from the BELLE Collaboration, which demonstrates that the theoretical approach based on the factorization still works well. For the angular distribution asymmetries, we find ${\cal A}_θ(\bar B^0\to Λ\bar p D^+,Λ\bar p D^{*+})=(-0.030\pm 0.002\,,+0.150\pm 0.000)$, which are consistent with the current measurements. Moreover, we predict that ${\cal A}_θ(\bar B^0\to p\bar p D^{0},p\bar p D^{*0})=+0.04\pm 0.01$. Future precise explorations of these angular correlations at BELLE and LHCb as well as super-BELLE are important to justify the present factorization approach in the charmful three-body baryonic decays.

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arXiv2016

Search for $XYZ$ states in $Λ_b$ decays at the LHCb

We consider $X(3872)$ and $Y(4140)$ as the vector tetraquark states of $X_c^0\equiv c\bar c u\bar u(d\bar d)$ and $c\bar c s\bar s$, respectively. By connecting $Λ_b\to X_c^0Λ$ to $B^-\to X_c^0 K^-$, we predict that the branching ratios of $Λ_b\to Λ(X(3872)^0\to) J/ψπ^+π^-$ and $Λ_b\to Λ(Y(4140)\to) J/ψϕ$ are $(5.2\pm 1.8)\times 10^{-6}$ and $(4.7\pm 2.6)\times 10^{-6}$, which are accessible to the experiments at the LHCb, respectively. The measurements of these $Λ_b$ modes would be the first experimental evidences for the $XYZ$ states in baryonic decays.

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arXiv2015

Charmful two-body anti-triplet $b$-baryon decays

We study the charmful decays of the two-body ${\cal B}_b\to {\cal B}_n M_c$ decays, where ${\cal B}_b$ represents the anti-triplet of $(Λ_b,Ξ_b^0,Ξ_b^-)$, ${\cal B}_n$ stands for the baryon octet and $M_c$ denotes as the charmed meson of $D^{(*)}_{(s)}$, $η_c$ and $J/ψ$. Explicitly, we predict that ${\cal B}(Λ_b\to D_s^- p)=(1.8\pm 0.3)\times 10^{-5}$, which is within the measured upper bound of ${\cal B}(Λ_b\to D_s^- p)<4.8(5.3)\times 10^{-4}$ at 90\%\,(95\%) C.L., and reproduce ${\cal B}(Λ_b\to J/ψΛ)=(3.3\pm 2.0)\times 10^{-4}$ and ${\cal B}(Ξ_b^-\to J/ψΞ^-)=(5.1\pm 3.2)\times 10^{-4}$ in agreement with the data. Moreover, we find that ${\cal B}(Λ_b \to Λη_c)=(1.5 \pm 0.9) \times 10^{-4}$, ${\cal B}(Ξ_b^-\toΞ^-η_c)=(2.4\pm1.5) \times 10^{-4}$ and ${\cal B}(Ξ_b^0\toΞ^0η_c,Ξ^0 J/ψ)=(2.3\pm1.4,4.9\pm3.0)\times 10^{-4}$, which are accessible to the experiments at the LHCb.

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arXiv2015

Pentaquarks from intrinsic charms in $Λ_b$ decays

We study the three-body $Λ_b$ decays of $Λ_b\to J/ψpM$ with $M=K^-$ and $π^-$. The two new states ${\cal P}_{c1}\equiv {\cal P}_c(4380)^+$ and ${\cal P}_{c2}\equiv {\cal P}_c(4450)^+$ observed recently as the resonances in the $J/ψp$ invariant mass spectrum of $Λ_b\to J/ψp K^-$ can be identified to consist of five quarks, $uudc\bar c$, being consistent with the existence of the pentaquark states. We argue that, in the doubly charmful $Λ_b$ decays of $Λ_b\to J/ψpK^-$ through $b\to c\bar c s$, apart from those through the non-resonant $Λ_b\to pK^-$ and resonant $Λ_b\to Λ^*\to pK^-$ transitions, the third contribution with the non-factorizable effects is not the dominant part for the resonant $Λ_b\to K^-{\cal P}_{c1,c2}, {\cal P}_{c1,c2}\to J/ψp$ processes, such that we propose that the ${\cal P}_{c1,c2}$ productions are mainly from the charmless $Λ_b$ decays through $b\to \bar u u s$, in which the $c\bar c$ content in ${\cal P}_{c1,c2}$ arises from the intrinsic charms within the $Λ_b$ baryon. We hence predict the observables related to the branching ratios and the direct CP violating asymmetries to be ${\cal B}(Λ_b\to π^-({\cal P}_{c1,c2}\to) J/ψp)/{\cal B}(Λ_b\to K^-({\cal P}_{c1,c2}\to) J/ψp)=0.8\pm 0.1$, ${\cal A}_{CP}(Λ_b\to π^-({\cal P}_{c1,c2}\to)J/ψp)=(-3.9\pm 0.2)\%$, and ${\cal A}_{CP}(Λ_b\to K^-({\cal P}_{c1,c2}\to)J/ψp)=(5.8\pm 0.2)\%$, which can alleviate the inconsistency between the theoretical expectations from the three contributions in the doubly charmful $Λ_b$ decays and the observed data.

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arXiv2015

Fragmentation fractions of two-body b-baryon decays

We study the fragmentation fractions $(f_{{\bf B}_b})$ of the $b$-quark to b-baryons (${\bf B}_b$). By the assumption of $f_{Λ_b}/(f_u+f_d)=0.25\pm 0.15$ in accordance with the measurements by LEP, CDF and LHCb Collaborations, we estimate that $f_{Λ_b}=0.175\pm 0.106$ and $f_{Ξ_b^{-,0}}=0.019\pm 0.013$. From these fragmentation fractions, we derive ${\cal B}(Λ_b\to J/ψΛ)=(3.3\pm 2.1)\times 10^{-4}$, ${\cal B}(Ξ_b^-\to J/ψΞ^-)=(5.3\pm 3.9)\times 10^{-4}$ and ${\cal B}(Ω_b^-\to J/ψΩ^-)>1.9\times 10^{-5}$. The predictions of ${\cal B}(Λ_b\to J/ψΛ)$ and ${\cal B}(Ξ_b^-\to J/ψΞ^-)$ clearly enable us to test the theoretical models, such as the QCD factorization approach in the $b$-baryon decays.

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arXiv2015

Violation of PCAC and two-body baryonic $B$ and $D_s$ decays

We study the two-body baryonic $B$ and $D_s$ decays based on the annihilation mechanism without the partial conservation of axial-vector current (PCAC) at the GeV scale. We demonstrate that the contributions of $B^-\to Λ\bar p$, $B^-\to Σ^0 \bar p$ and $\bar B^0_s\to Λ\bar Λ$ are mainly from the scalar and pseudoscalar currents with their branching ratios predicted to be around $(3.5,\,5.3,\,5.3)\times 10^{-8}$, respectively, exactly the sizes of ${\cal B}(B\to {\bf B\bar B'})$ established by the data. We also apply the annihilation mechanism to all of the charmless two-body baryonic $B$ and $D_s$ decays. In particular, we can explain ${\cal B}(\bar B^0_{(s)}\to p\bar p)$ of order $10^{-8}$ and ${\cal B}(D_s^+\to p\bar n)$ of order $10^{-3}$, which are from the axial-vector currents. In addition, the branching ratios of $\bar B^0\to Λ\bar Λ$, $B^-\to n\bar p$, and $B^-\to Σ^- \barΣ^0$ are predicted to be $(0.3,\,3.2,\,9.6)\times 10^{-8}$, which can be measured by LHCb and viewed as tests for the violation of PCAC at the GeV scale.

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arXiv2015

$f_J(2220)$ and Hadronic $\bar B^0_s$ Decays

We study the hadronic $\bar B^0_s$ decays based on the existence of the resonant state $f_J(2220)$. In particular, we are able to explain the unexpected large experimental result of ${\cal B}(\bar B^0_s\to J/ψp\bar p) =(3.0^{+1.2}_{-1.1}\pm 0.52\pm 0.03)\times 10^{-6}$ measured recently by the LHCb collaboration due to the resonant contribution in $\bar B^0_s\to J/ψf_J(2220)$ with $f_J(2220) \to p\bar p$, while it is estimated to be at most of order $10^{-9}$ in terms of the OZI rule without the resonance. In addition, we find that ${\cal B}(\bar B^0_s\to D^{*0}(f_J\to) p\bar p)=(4.05\pm 2.46)\times 10^{-7}$, ${\cal B}(\bar B^0_s\to J/ψ(f_J\to)ππ)=(15.6\pm 15.2)\times 10^{-6}$ and ${\cal B}(\bar B^0_s\to D^{*0}(f_J\to)ππ)=(21.2\pm 20.9)\times 10^{-7}$, while ${\cal B}(\bar B^0_s\to J/ψ(f_J\to)K\bar K)<1.6\times 10^{-5}$ and ${\cal B}(\bar B^0_s\to D^{*0}(f_J\to)K\bar K)<2.2\times 10^{-6}$. Moreover, we predict that the decay branching ratios of $\bar B^0_s\to (J/ψ\,,D^{*0})Λ\bar Λ$ are $(2.68\pm1.23)\times 10^{-7}$ and $(2.25\pm0.80)\times 10^{-6}$. Some of the predicted $\bar B^0_s$ decays are accessible to the experiments at the LHCb.

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arXiv2014

Direct CP violation in $Λ_b$ decays

We study direct CP violating asymmetries (CPAs) in the two-body $Λ_b$ decays of $Λ_b\to pM(V)$ with $M(V)=K^-(K^{*-})$ and $π^-(ρ^-)$ based on the generalized factorization method. After simultaneously explaining the observed decay branching ratios of $Λ_b\to (p K^-\,,\; p π^-)$ with ${\cal R}_{πK}\equiv {\cal B}(Λ_b\to p π^-)/{\cal B}(Λ_b\to p K^-)$ being $0.84\pm 0.09$, we find that their corresponding direct CPAs are $(5.8\pm 0.2,\,-3.9\pm 0.2)\%$ in the standard model (SM), in comparison with $(-5^{+26}_{-~5},\, -31^{+43}_{-~1})\%$ and $(-10\pm8\pm4,\, 6\pm7\pm3)\%$ from the perturbative QCD calculation and the CDF experiment, respectively. For $Λ_b\to ( p K^{*-},\, pρ^-)$, the decay branching ratios and CPVs in the SM are predicted to be $(2.5\pm0.5,\,11.4\pm2.1)\times 10^{-6}$ with ${\cal R}_{ρK^*}=4.6\pm0.5$ and $(19.6\pm1.6,\, -3.7\pm0.3)\%$, respectively. The uncertainties for the CPAs in these decay modes as well as ${\cal R}_{πK,\,ρK^{*-}}$ mainly arise from the quark mixing elements and non-factorizable effects, whereas those from the hadronic matrix elements are either totally eliminated or small. We point out that the large CPA for $Λ_b\to p K^{*-}$ is promising to be measured by the CDF and LHCb experiments, which is a clean test of the SM.

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arXiv2014

Semileptonic $B^-\to f_0(1710\,,1500\,,1370) e^-\bar ν_e$ decays

We study the semileptonic decays of $B^-\to f_0(1710\,,1500\,,1370) e^-\bar ν_e$, in which the three $f_0$ states mix with glueball, $\bar s s$ and $(\bar u u+\bar d d)/\sqrt 2$ states, respectively. By averaging the mixings fitted in the literature, we find that the branching ratios of $B^-\to f_0 e^-\bar ν_e$ are $O(10^{-6})$, $O(10^{-6})$ and $O(10^{-5})$, respectively, which can be simultaneously observed in experiments at $B$ factories. The large predicted branching rate for $B^-\to f_0(1370) e^-\bar ν_e$ would provide a clean mode to directly observe the $f_0(1370)$ state.

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