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Test of lepton universality with $B^{0} \rightarrow K^{*0}\ell^{+}\ell^{-}$ decays

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Abstract

A test of lepton universality, performed by measuring the ratio of the branching fractions of the $B^{0} \rightarrow K^{*0}\mu^{+}\mu^{-}$ and $B^{0} \rightarrow K^{*0}e^{+}e^{-}$ decays, $R_{K^{*0}}$, is presented. The $K^{*0}$ meson is reconstructed in the final state $K^{+}\pi^{-}$, which is required to have an invariant mass within 100$\mathrm{\,MeV}c^2$ of the known $K^{*}(892)^{0}$ mass. The analysis is performed using proton-proton collision data, corresponding to an integrated luminosity of about 3$\mathrm{\,fb}^{-1}$, collected by the LHCb experiment at centre-of-mass energies of 7 and 8$\mathrm{\,TeV}$. The ratio is measured in two regions of the dilepton invariant mass squared, $q^{2}$, to be \begin{eqnarray*} R_{K^{*0}} = \begin{cases} 0.66 ^{+ 0.11}_{- 0.07}\mathrm{\,(stat)} \pm 0.03\mathrm{\,(syst)} & \textrm{for } 0.045 < q^{2} < 1.1 \mathrm{\,GeV^2}c^4 \, , \\ 0.69 ^{+ 0.11}_{- 0.07}\mathrm{\,(stat)} \pm 0.05\mathrm{\,(syst)} & \textrm{for } 1.1\phantom{00} < q^{2} < 6.0 \mathrm{\,GeV^2}c^4 \, . \end{cases} \end{eqnarray*} The corresponding 95.4% confidence level intervals are $[0.52, 0.89]$ and $[0.53, 0.94]$. The results, which represent the most precise measurements of $R_{K^{*0}}$ to date, are compatible with the Standard Model expectations at the level of 2.1--2.3 and 2.4--2.5 standard deviations in the two $q^{2}$ regions, respectively.

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Feynman diagrams in the SM of the $ B ^0 \!\rightarrow K ^{*0} \ell^+ \ell^- $ decay for the (top left) electroweak penguin and (top right) box diagram. Possible NP contributions violating LU: (bottom left) a tree-level diagram mediated by a new gauge boson $ Z ^{\prime}$ and (bottom right) a tree-level diagram involving a leptoquark $LQ$.

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Number of candidates for $ B ^0 \!\rightarrow K ^{*0} \ell^+ \ell^- $ final states with (left) muons and (right) electrons as a function of the dilepton invariant mass squared, $ q^2$ , and the four-body invariant mass of the $ B ^0$ .

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Sketch of the topology of a $ B ^0 \!\rightarrow K ^{*0} e ^+ e ^- $ decay. The transverse momentum lost via bremsstrahlung is evaluated as the difference between the $p_{\rm T}$ of the $ K ^{*0}$ meson and that of the dielectron system, where both are calculated with respect to the $ B ^0$ meson direction of flight. Bremsstrahlung photons that are not recovered by the reconstruction are assumed to follow the dielectron momentum direction.

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Fraction of (left) $ B ^0 \!\rightarrow K ^{*0} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} (\rightarrow e ^+ e ^- )$ and (right) $ B ^0 \!\rightarrow K ^{*0} \gamma(\rightarrow e ^+ e ^- )$ candidates (in percent) with zero, one, and two or more recovered clusters per trigger category. The numbers are from (darker colour) data and (lighter colour) simulation. Due to the very low opening angle of the two electrons in $ B ^0 \!\rightarrow K ^{*0} \gamma(\rightarrow e ^+ e ^- )$ decays, the bremsstrahlung photon energy deposits overlap and only one bremsstrahlung cluster at most is resolved.

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Fit to the $ m( K ^+ \pi ^- \mu ^+\mu ^- )$ invariant mass of (top) $ B ^0 \!\rightarrow K ^{*0} \mu ^+\mu ^- $ in the low- and central- $ q^2$ bins and (bottom) $ B ^0 \!\rightarrow K ^{*0} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} (\!\rightarrow \mu ^+\mu ^- )$ candidates. The dashed line is the signal PDF, the shaded shapes are the background PDFs and the solid line is the total PDF. The fit residuals normalised to the data uncertainty are shown at the bottom of each distribution.

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Fit to the $ m( K ^+ \pi ^- e ^+ e ^- )$ invariant mass of (top) $ B ^0 \!\rightarrow K ^{*0} e ^+ e ^- $ in the low- and central- $ q^2$ bins and (bottom) $ B ^0 \!\rightarrow K ^{*0} { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} (\rightarrow e ^+ e ^- )$ candidates. The dashed line is the signal PDF, the shaded shapes are the background PDFs and the solid line is the total PDF. The fit residuals normalised to the data uncertainty are shown at the bottom of each distribution.

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(hatched) Background-subtracted distributions for (darker colour) $ B ^0 \!\rightarrow K ^{*0} \mu ^+\mu ^- $ and (lighter colour) $ B ^0 \!\rightarrow K ^{*0} e ^+ e ^- $ candidates, compared to (full line) simulation. From top to bottom: $ q^2$ , $ K ^+ \pi ^- $ invariant mass, $ m( K ^+ \pi ^- )$ , opening angle between the two leptons, $\theta_{\textrm{lepton}}$, and projection along the beam axis of the distance between the $ K ^+ \pi ^- $ and $\ell^+ \ell^- $ vertices, $\Delta z_{\textrm{vertex}}$. The distributions are normalised to unity. The hatched areas correspond to the statistical uncertainties only. The data are not efficiency corrected.

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Distributions of the $ R_{ K ^{*0} }$ delta log-likelihood for the three trigger categories separately and combined.

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(left) Comparison of the LHCb $ R_{ K ^{*0} }$ measurements with the SM theoretical predictions: BIP [26] CDHMV [27,28,29], \texttt{EOS} [30,31], \texttt{flav.io} [33,34,35] and JC [36]. The predictions are displaced horizontally for presentation. (right) Comparison of the LHCb $ R_{ K ^{*0} }$ measurements with previous experimental results from the $ B $ factories [4,5]. In the case of the $ B $ factories the specific vetoes for charmonium resonances are not represented.

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Tables and captions

Recent SM predictions for $ R_{ K ^{*0} }$ .

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Yields obtained from the mass fits to the muon and electron (in the three trigger categories) channels. The uncertainties are statistical only.

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Efficiency ratios between the nonresonant and resonant modes, $\varepsilon_{\ell^+ \ell^- } / \varepsilon_{ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} (\ell^+ \ell^- ) }$, for the muon and electron (in the three trigger categories) channels. The uncertainties are statistical only.

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Systematic uncertainties on the $ R_{ K ^{*0} }$ ratio for the three trigger categories separately (in percent). The total uncertainty is the sum in quadrature of all the contributions.

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Measured $ R_{ K ^{*0} }$ ratios in the two $ q^2$ regions. The first uncertainties are statistical and the second are systematic. About 50% of the systematic uncertainty is correlated between the two $ q^2$ bins. The 95.4% and 99.7% confidence level (CL) intervals include both the statistical and systematic uncertainties.

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Created on 09 December 2018.Citation count from INSPIRE on 18 December 2018.