arXiv subjects

J. Kahn

Publications and source records attributed to J. Kahn.

At least 19 recordsLinked to original sources

arXiv2023

Search for the double-charmonium state with $\eta_c J/\psi$ at Belle

We measure the cross section of $e^+e^-\rightarrow\eta_c J/\psi$ at the $\Upsilon(nS) (n=1$ -- $5)$ on-resonance and 10.52 GeV off-resonance energy points using the full data sample collected by the Belle detector with an integrated luminosity of $955~\rm fb^{-1}$. We also search for double charmonium production in $e^+e^-\rightarrow\eta_c J/\psi$ via initial state radiation near the $\eta_c J/\psi$ threshold. No evident signal of the double charmonium state is found, but evidence for the $e^+e^-\rightarrow\eta_c J/\psi$ process is found with a statistical significance greater than $3.3\sigma$ near the $\eta_c J/\psi$ threshold. The average cross section near the threshold is measured and upper limits of cross sections are set for other regions.

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arXiv2023

Search for $C\!P$ violation using $T$-odd correlations in $D_{(s)}^{+}\to K^{+} K^{-}\pi^{+}\pi^{0}$, $D_{(s)}^{+}\to K^{+} \pi^{-}\pi^{+}\pi^{0}$, and $D^{+}\to K^{-}\pi^{+}\pi^{+}\pi^{0}$ decays

We search for $C\!P$ violation using $T$-odd correlations in five $D_{(s)}^{+}$ and $D_{(s)}^{-}$ four-body decays. Our analysis is based on 980 $\rm fb^{-1}$ of data collected by the Belle detector at the KEKB energy-asymmetric $e^+e^-$ collider. Our results for the $T$-odd $C\!P$-violating parameter $a^{T\text{-odd}}_{C\!P}$ are: $a^{T\text{-odd}}_{C\!P}({D^{+}\to K^{-}K^{+}\pi^{+}\pi^{0}}) = (+2.6\pm 6.6\pm 1.3 )\times10^{-3}$, $a^{T\text{-odd}}_{C\!P}({D^{+}\to K^{+}\pi^{-}\pi^{+}\pi^{0}}) = (-1.3\pm 4.2\pm 0.1 )\times10^{-2}$, $a^{T\text{-odd}}_{C\!P}({D^{+}\to K^{-}\pi^{+}\pi^{+}\pi^{0}}) = (+0.2\pm 1.5\pm 0.8 )\times10^{-3}$, $a^{T\text{-odd}}_{C\!P}({D_s^{+}\to K^{+}\pi^{-}\pi^{+}\pi^{0}}) = (-1.1\pm 2.2\pm 0.1 )\times10^{-2}$, and $a^{T\text{-odd}}_{C\!P}({D_s^{+}\to K^{-}K^{+}\pi^{+}\pi^{0}}) = (+2.2\pm 3.3\pm 4.3 )\times10^{-3}$, where the uncertainties are statistical and systematic, respectively. These results are the first such measurements and are all consistent with zero. They include the first measurement for a $D^+_s$ singly Cabibbo-suppressed decay, and the first measurement for a $D$ meson doubly Cabibbo-suppressed decay. We also measure $a^{T\text{-odd}}_{C\!P}$ in different subregions of phase space, where the decays are dominated by different intermediate resonance states such as $D^+\to\phi\rho^+$, $\bar{K}^{*0}K^{*+}$, and $\bar{K}^{*0}\rho^+$; and $D_s^+\to K^{*+}\rho^{0}$, $K^{*0}\rho^{+}$, $\phi\rho^+$, and $\bar{K}^{*0}K^{*+}$. No evidence for $C\!P$ violation is found.

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arXiv2022

Measurements of the branching fractions $\mathcal{B} (\bar{B}{}^0 \to D^{+} \pi^-)$ and $\mathcal{B} (\bar{B}{}^0 \to D^{+} K^-)$ and tests of QCD factorization

Using $(771.6 \pm 10.6) \times 10^6$ $B\bar{B}$ meson pairs recorded by the Belle experiment at the KEKB $e^+ e^-$ collider, we report the branching fractions $\mathcal{B}(\bar{B}^0 \to D^{*+} \pi^-) = (2.62 \pm 0.02 \pm 0.09)\times 10^{-3}$ and $\mathcal{B}(\bar{B}^0 \to D^{*+} K^-) = (2.22 \pm 0.06 \pm 0.08)\times 10^{-4}$; the quoted uncertainties are statistical and systematic, respectively. A measurement of the ratio of these branching fractions is also presented, $\mathcal{R}_{K/\pi}=\mathcal{B}(\bar{B} \to D^{*+}K^-) /\mathcal{B}( \bar{B} \to D^{*+}\pi^-) = (8.41 \pm 0.24 \pm 0.13)\times 10^{-2}$, where systematic uncertainties due to the $D^{*+}$ meson reconstruction cancel out. Furthermore, we report a new QCD factorization test based on the measured ratios for $\bar{B} \to D^{*+}h^-$ and $\bar{B} \to D^{*+}\ell^-\nu$ decays at squared momentum transfer values equivalent to the mass of the $h = \pi$ or $K$ hadron. The parameters $|a_1(h)|$ are measured to be $|a_1(\pi)|= 0.884 \pm 0.004 \pm 0.003 \pm 0.016$ and $|a_1(K)|=0.913 \pm 0.019 \pm 0.008 \pm 0.013$, where the last uncertainties account for all external inputs. These values are approximately $15\%$ lower than those expected from theoretical predictions. Subsequently, flavor $SU(3)$ symmetry is tested by measuring the ratios for pions and kaons, $|a_1(K)|^2/ |a_1(\pi)|^2=1.066 \pm 0.042 \pm 0.018 \pm 0.023$, as well as for different particle species. The ratio is consistent with unity and therefore no evidence for $SU(3)$ symmetry breaking effects is found at the $5\%$ precision level.

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arXiv2022

Search for $B^{0} \to K_S^{0}K_S^{0}\gamma$ decays at Belle

We report the first search for the penguin-dominated process $B^0 \rightarrow K_S^0 K_S^0 \gamma$ using the full data sample of $772\times 10^6$ $B\bar{B}$ pairs collected with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We do not observe any statistically significant signal yield in the $K_S^0$-pair invariant mass range 1 GeV/$c^2 < M_{K_S^0 K_S^0} < $ 3 GeV/$c^2$, and set the following upper limits at 90% confidence level: $\mathcal{B}(B^0 \to K_S^0 K_S^0 \gamma) < 5.8\times10^{-7}$, $\mathcal{B}(B^0 \to f_2 \gamma)\times \mathcal{B}(f_2 (1270) \to K_S^0 K_S^0 ) < 3.1\times10^{-7}$, and $\mathcal{B}(B^0 \to f_2^{\prime} \gamma)\times \mathcal{B}(f_2^{\prime} (1525) \to K_S^0 K_S^0 ) < 2.1\times10^{-7}$. Further, 90% confidence upper limits have also been set in the range of [0.7-2.9]$\times10^{-7}$ on the $B^0 \rightarrow K_S^0 K_S^0 \gamma$ branching fraction in bins of $M_{K_S^0 K_S^0}$.

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arXiv2022

Search for charged lepton flavor violating decays of $\Upsilon(1S)$

We present a search for the charged lepton-flavor-violating decays $\Upsilon(1S)\rightarrow\ell\ell^\prime$ and radiative charged lepton-flavour-violating decays $\Upsilon(1S)\rightarrow\gamma\ell\ell^\prime$ [$\ell,\ell^\prime = e, \mu, \tau$] using the 158 million $\Upsilon(2S)$ sample collected by the Belle detector at the KEKB collider. This search uses $\Upsilon(1S)$ mesons produced in $\pi^+\pi^-\Upsilon(1S)$ transitions. We do not find any significant signal, so we provide upper limits on the branching fractions at the 90% confidence level.

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arXiv2022

Search for the decay $B_s^0 \to \eta^\prime K_S^0$

We report the results of the first search for the decay $B_s^0 \to \eta^\prime K_S^0$ using $121.4\,{\rm fb}^{-1}$ of data collected at the $\Upsilon(5S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We observe no signal and set a 90\% confidence-level upper limit of $8.16 \times 10^{-6}$ on the $B_s^0 \to \eta^\prime K_S^0$ branching fraction.

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arXiv2021

First Measurement of the $\Lambda_c^+ \to p \eta'$ decay

We present the first measurement of the branching fraction of the singly Cabibbo-suppressed (SCS) decay $\Lambda_c^+ \to p \eta'$ with $\eta' \to \eta\pi^+\pi^-$, using a data sample corresponding to an integrated luminosity of 981 $\rm fb^{-1}$, collected by the Belle detector at the KEKB $e^{+}$$e^{-}$ asymmetric-energy collider. A significant $\Lambda_c^+$ signal is observed for the first time with a signal significance of 5.4$\sigma$. The relative branching fraction with respect to the normalization mode $\Lambda_c^+ \to pK^-\pi^+$ is measured to be \begin{equation*} \frac{{\cal B}(\Lambda_c^+ \to p \eta')}{{\cal B}(\Lambda_c^+ \to p K^-\pi^+)} = (7.54 \pm 1.32 \pm 0.75) \times 10^{-3}, \end{equation*} where the uncertainties are statistical and systematic, respectively. Using the world-average value of ${\cal B}(\Lambda_c^+ \to p K^-\pi^+) = (6.28\pm0.32)\times10^{-2}$, we obtain \begin{equation*} {\cal B}(\Lambda_c^+ \to p \eta') = (4.73 \pm 0.82 \pm 0.47 \pm 0.24)\times 10^{-4}, \end{equation*} where the uncertainties are statistical, systematic, and from ${\cal B}(\Lambda_c^+ \to pK^-\pi^+)$, respectively.

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arXiv2021

Search for a light Higgs boson in single-photon decays of $\Upsilon(1S)$ using $\Upsilon(2S) \to \pi^+ \pi^- \Upsilon(1S)$ tagging method

We search for a light Higgs boson ($A^0$) decaying into a $\tau^+\tau^-$ or $\mu^+\mu^-$ pair in the radiative decays of $\Upsilon(1S)$. The production of $\Upsilon(1S)$ mesons is tagged by $\Upsilon(2S)\to \pi^+ \pi^- \Upsilon(1S)$ transitions, using 158 million $\Upsilon(2S)$ events accumulated with the Belle detector at the KEKB asymmetric energy electron-positron collider. No significant $A^0$ signals in the mass range from the $\tau^+\tau^-$ or $\mu^+\mu^-$ threshold to 9.2 GeV/$c^2$ are observed. We set the upper limits at 90\% credibility level (C.L.) on the product branching fractions for $\Upsilon(1S)\to \gamma A^0$ and $A^0\to \tau^+\tau^-$ varying from $3.8\times10^{-6}$ to $1.5\times10^{-4}$. Our results represent an approximately twofold improvement on the current world best upper limits for the $\Upsilon(1S)\to \gamma A^0(\to \tau^+\tau^-)$ production. For $A^0\to \mu^+\mu^-$, the upper limits on the product branching fractions for $\Upsilon(1S)\to \gamma A^0$ and $A^0\to \mu^+\mu^-$ are at the same level as the world average limits, and vary from $3.1\times10^{-7}$ to $1.6\times10^{-5}$. The upper limits at 90\% C.L. on the Yukawa coupling $f_{\Upsilon(1S)}$ and mixing angle ${\rm sin}\theta_{A^0}$ are also given.

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arXiv2021

First test of Lepton Flavor Universality in the charmed baryon decays $\Omega^{0}_{c} \to \Omega^{-} \ell^{+} \nu_{\ell}$ using data of the Belle experiment

We present the first observation of the $\Omega_{c}^{0} \to \Omega^{-} \mu^{+} \nu_{\mu}$ decay and present measurements of the branching fraction ratios of the $\Omega_{c}^{0} \to \Omega^{-} \ell^{+} \nu_{\ell}$ decays compared to the reference mode $\Omega_{c}^{0} \to \Omega^{-} \pi^+$, ($\ell = e$ or $\mu$). This analysis is based on 89.5 fb$^{-1}$, 711 fb$^{-1}$, and 121.1 fb$^{-1}$ data samples collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider at the center-of-mass energies of 10.52 GeV, 10.58 GeV, and 10.86 GeV, respectively. The $\Omega_{c}^{0}$ signal yields are extracted by fitting $M_{\Omega^{-} \ell^{+}}$ and $M_{\Omega^{-}\pi^+}$ spectra. The branching fraction ratios ${\cal B}(\Omega_{c}^{0} \to \Omega^{-} e^{+} \nu_{e})/{\cal B}(\Omega_{c}^{0} \to \Omega^{-} \pi^+)$ and ${\cal B}(\Omega_{c}^{0} \to \Omega^{-} \mu^{+} \nu_{\mu})/{\cal B}(\Omega_{c}^{0} \to \Omega^{-} \pi^+)$ are measured to be $1.98 \pm0.13~({\rm stat.}) \pm 0.08~({\rm syst.})$ and $ 1.94 \pm 0.18~({\rm stat.}) \pm 0.10~({\rm syst.})$, respectively. The ratio of ${\cal B}(\Omega_{c}^{0} \to \Omega^{-} e^{+} \nu_{e})/{\cal B}(\Omega_{c}^{0} \to \Omega^{-} \mu^{+} \nu_{\mu})$ is measured to be $1.02 \pm 0.10~({\rm stat.}) \pm 0.02~({\rm syst.})$, which is consistent with the expectation of lepton flavor universality.

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arXiv2021

Search for tetraquark states $X_{cc\bar{s}\bar{s}}$ in $D_{s}^{+}D_{s}^{+}~(D_{s}^{+}D_{s}^{+})$ final states at Belle

A search for double-heavy tetraquark state candidates $X_{cc\bar{s}\bar{s}}$ decaying to $D_{s}^{+}D_{s}^{+}$ and $D_{s}^{*+} D_{s}^{*+}$ is presented for the first time using the data samples of 102 million $\Upsilon(1S)$ and 158 million $\Upsilon(2S)$ events, and the data samples at $\sqrt{s}$ = 10.52~GeV, 10.58~GeV, and 10.867~GeV corresponding to integrated luminosities of 89.5~fb$^{-1}$, 711.0~fb$^{-1}$, and 121.4~fb$^{-1}$, respectively, accumulated with the Belle detector at the KEKB asymmetric energy electron-positron collider. The invariant-mass spectra of the $D_{s}^{+}D_{s}^{+}$ and $D_{s}^{*+} D_{s}^{*+}$ are studied to search for possible resonances. No significant signals are observed, and the 90\% confidence level upper limits on the product branching fractions [${\cal B}(\Upsilon(1S,2S) \to X_{cc\bar{s}\bar{s}} + anything) \times {\cal B}(X_{cc\bar{s}\bar{s}} \to D_{s}^{+}D_{s}^{+}(D_{s}^{*+} D_{s}^{*+}))$] in $\Upsilon(1S,2S)$ inclusive decays and the product values of Born cross section and branching fraction [$\sigma(e^+e^- \to X_{cc\bar{s}\bar{s}} + anything ) \times {\cal B}(X_{cc\bar{s}\bar{s}} \to D_{s}^{+}D_{s}^{+}(D_{s}^{*+} D_{s}^{*+}))$] in $e^+e^-$ collisions at $\sqrt{s}$ = 10.52~GeV, 10.58~GeV, and 10.867~GeV under different assumptions of $X_{cc\bar{s}\bar{s}}$ masses and widths are obtained.

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arXiv2021

Measurements of the branching fractions of $\Xi_c^0 \to \Lambda K_S^0$, $\Xi_c^0 \to \Sigma^0 K_S^0$, and $\Xi_c^0 \to \Sigma^+ K^-$ decays at Belle

Using the entire data sample of $980\mathrm{~fb}^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider, we present measurements of the branching fractions of the Cabibbo-favored decays $\Xi_c^0 \to \Lambda K_S^0$, $\Xi_c^0 \to \Sigma^0 K_S^0$, and $\Xi_c^0 \to \Sigma^+ K^-$. Taking the decay $\Xi_c^0 \to \Xi^- \pip$ as the normalization mode, we measure the branching fraction ratio ${\cal B}(\Xi_c^0 \to \Lambda K_S^0)/{\cal B}(\Xi_c^0 \to \Xi^- \pi^+) = 0.229\pm0.008\pm0.012$ with improved precision, and measure the branching fraction ratios ${\cal B}(\Xi_c^0 \to \Sigma^0 K_S^0)/{\cal B}(\Xi_c^0 \to \Xi^- \pi^+) = 0.038\pm0.006\pm0.004$ and ${\cal B}(\Xi_c^0 \to \Sigma^+ K^-)/{\cal B}(\Xi_c^0 \to \Xi^- \pi^+) = 0.123\pm0.007\pm0.010$ for the first time. Taking into account the branching fraction of the normalization mode, the absolute branching fractions are determined to be ${\cal B}(\Xi_c^0 \to \Lambda K_S^0) = (3.27\pm0.11\pm0.17\pm0.73) \times 10^{-3}$, ${\cal B}(\Xi_c^0 \to \Sigma^0 K_S^0) = (0.54\pm 0.09\pm 0.06\pm 0.12) \times 10^{-3}$, and ${\cal B}(\Xi_c^0 \to \Sigma^+ K^-) = (1.76\pm 0.10\pm0.14\pm 0.39) \times 10^{-3}$. The first and second uncertainties above are statistical and systematic, respectively, while the third ones arise from the uncertainty of the branching fraction of $\Xi_c^0 \to \Xi^- \pi^+$.

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arXiv2021

Search for $B^0$ meson decays into $\Lambda$ and missing energy with a hadronic tagging method at Belle

We present a search for the decays of $B^0$ mesons into a final state containing a $\Lambda$ baryon and missing energy. These results are obtained from a $711\text{fb}^{-1}$ data sample that contains $772 \times 10^6$ $B{\kern 0.18em}\overline{\kern -0.18em B}$ pairs and was collected near the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. We use events in which one $B$ meson is fully reconstructed in a hadronic decay mode and require the remainder of the event to consist of only a single $\Lambda$. No evidence for these decays is found and we set $90\%$ confidence level upper limits on the branching fractions in the range $2.1$-$3.8\times 10^{-5}$. This measurement provides the world's most restrictive limits, with implications for baryogenesis and dark matter production.

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arXiv2021

Search for the decay $B^{0}\rightarrow K^{\ast 0}\tau^{+}\tau^{-}$ at the Belle experiment

This letter presents a search for the rare flavor-changing neutral current process $B^{0}\rightarrow K^{\ast 0}\tau^{+}\tau^{-}$ using data taken with the Belle detector at the KEKB asymmetric energy $e^{+}e^{-}$ collider. The analysis is based on the entire $\Upsilon(4S)$ resonance data sample of 711 $\rm fb^{-1}$, corresponding to $772\times 10^{6} B \bar{B}$ pairs. In our search we fully reconstruct the companion $B$ meson produced in the process $e^{+}e^{-}\rightarrow\Upsilon(4S)\rightarrow B\bar{B}$ from its hadronic decay modes, and look for the decay $B^{0}\rightarrow K^{\ast 0}\tau^{+}\tau^{-}$ in the rest of the event. No evidence for a signal is found. We report an upper limit on the branching fraction $\mathcal{B}({B^{0}\rightarrow K^{\ast 0}\tau^{+}\tau^{-}})<3.1\times 10^{-3}$ at 90\% confidence level. This is the first direct limit on $\mathcal{B}({B^{0}\rightarrow K^{\ast 0}\tau^{+}\tau^{-}})$.

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arXiv2021

Punzi-loss: A non-differentiable metric approximation for sensitivity optimisation in the search for new particles

We present the novel implementation of a non-differentiable metric approximation and a corresponding loss-scheduling aimed at the search for new particles of unknown mass in high energy physics experiments. We call the loss-scheduling, based on the minimisation of a figure-of-merit related function typical of particle physics, a Punzi-loss function, and the neural network that utilises this loss function a Punzi-net. We show that the Punzi-net outperforms standard multivariate analysis techniques and generalises well to mass hypotheses for which it was not trained. This is achieved by training a single classifier that provides a coherent and optimal classification of all signal hypotheses over the whole search space. Our result constitutes a complementary approach to fully differentiable analyses in particle physics. We implemented this work using PyTorch and provide users full access to a public repository containing all the codes and a training example.

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arXiv2021

Measurement of Differential Branching Fractions of Inclusive ${B \to X_u \, \ell^+\, \nu_{\ell}}$ Decays

The first measurements of differential branching fractions of inclusive semileptonic ${B \to X_u \, \ell^+\, \nu_{\ell}}$ decays are performed using the full Belle data set of 711 fb$^{-1}$ of integrated luminosity at the $\Upsilon(4S)$ resonance and for $\ell = e, \mu$. Differential branching fractions are reported as a function of the lepton momentum, the four-momentum-transfer squared, light-cone momenta, the hadronic mass, and the hadronic mass squared. They are obtained by subtracting the backgrounds from semileptonic ${B \to X_c \, \ell^+\, \nu_{\ell}}$ decays and other processes, and corrected for resolution and acceptance effects. The measured distributions are compared to predictions from inclusive and hybrid ${B \to X_u \, \ell^+\, \nu_{\ell}}$ calculations.

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arXiv2021

Search for the Decay $B_s^0 \rightarrow \eta^\prime \eta$

We report the results of the first search for the decay $B_s^0 \rightarrow \eta^\prime \eta$ using $121.4~\textrm{fb}^{-1}$ of data collected at the $\Upsilon(5S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. We observe no significant signal and set a 90\% confidence-level upper limit of %$7.1 \times 10^{-5}$ $6.5 \times 10^{-5}$ on the branching fraction of this decay.

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arXiv2021

The study of $\gamma\gamma\to\gamma\psi(2S)$ at Belle

Using $980~\rm fb^{-1}$ of data on and around the $\Upsilon(nS)(n=1,2,3,4,5)$ resonances collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider, the two-photon process $\gamma\gamma\to \gamma\psi(2S)$ is studied from the threshold to $4.2~{\rm GeV}$ for the first time. Two structures are seen in the invariant mass distribution of $\gamma\psi(2S)$: one at $M_{R_1} = 3922.4\pm 6.5 \pm 2.0~{\rm MeV}/c^2$ with a width of $\Gamma_{R_1} = 22\pm 17\pm 4~{\rm MeV}$, and another at $M_{R_2} = 4014.3\pm 4.0 \pm 1.5~{\rm MeV}/c^2$ with a width of $\Gamma_{R_2} = 4\pm 11 \pm 6~{\rm MeV}$; the signals are parametrized with the incoherent sum of two Breit-Wigner functions. The first structure is consistent with the $X(3915)$ or the $\chi_{c2}(3930)$, and the local statistical significance is determined to be $3.1\sigma$ with the systematic uncertainties included. The second matches none of the known charmonium or charmoniumlike states, and its global significance is determined to be $2.8\sigma$ including the look-elsewhere effect. The production rates are $\Gamma_{\gamma\gamma}{\cal B}(R_1\to\gamma\psi(2S)) = 9.8\pm 3.6\pm 1.2~{\rm eV}$ assuming $(J^{PC}, |\lambda|) =(0^{++}, 0)$ or $2.0\pm 0.7\pm 0.2~{\rm eV}$ with $(2^{++}, 2)$ for the first structure and $\Gamma_{\gamma\gamma}{\cal B}(R_2\to\gamma\psi(2S)) = 6.2\pm 2.2\pm 0.8~{\rm eV}$ with $(0^{++}, 0)$ or $1.2\pm 0.4\pm 0.2~{\rm eV}$ with $(2^{++}, 2)$ for the second one. Here, the first errors are statistical and the second systematic, and $\lambda$ is the helicity.

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arXiv2021

Measurement of the branching fractions of the $B^+ \to \eta \ell^+ \nu_{\ell} $ and $B^+ \to \eta^{\prime} \ell^+ \nu_{\ell} $ decays with signal-side only reconstruction in the full $q^2$ range

The branching fractions of the decays $B^{+} \to \eta \ell^{+} \nu_{\ell}$ and $B^{+} \to \eta^{\prime} \ell^{+} \nu_{\ell}$ are measured, where $\ell$ is either an electron or a muon, using a data sample of $711\,{\rm fb}^{-1}$ containing $772 \times 10^6 B\bar{B}$ pairs collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. To reduce the dependence of the result on the form factor model, the measurement is performed over the entire $q^2$ range. The resulting branching fractions are ${\cal B}(B^{+} \rightarrow \eta \ell^{+} \nu_{\ell}) = (2.83 \pm 0.55_{\rm (stat.)} \pm 0.34_{\rm (syst.)}) \times 10^{-5}$ and ${\cal B}(B^{+} \rightarrow \eta' \ell^{+} \nu_{\ell}) = (2.79 \pm 1.29_{\rm (stat.)} \pm 0.30_{\rm (syst.)}) \times 10^{-5}$.

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