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Study of the lineshape of the $chi_{c1}(3872)$ state

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 Publication date 2020
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A study of the lineshape of the $chi_{c1}(3872)$ state is made using a data sample corresponding to an integrated luminosity of $3,$fb$^{-1}$ collected in $pp$ collisions at centre-of-mass energies of 7 and 8,TeV with the LHCb detector. Candidate $chi_{c1}(3872)$ and $psi(2S)$ mesons from b-hadron decays are selected in the $ J/psi pi^+ pi^-$ decay mode. Describing the {mbox{lineshape}} with a Breit--Wigner function, the mass splitting between the $chi_{c1}(3872)$ and $psi(2S)$ states, $Delta m$, and the width of the $chi_{c1}(3872)$ state, $Gamma_{mathrm{BW}}$, are determined to be begin{eqnarray*} Delta m & = & 185.598 pm 0.067 pm 0.068, mathrm{MeV} ,, Gamma_{mathrm{BW}} & = & phantom{00}1.39phantom{0} pm 0.24phantom{0} pm 0.10phantom{0} mathrm{MeV} ,, end{eqnarray*} where the first uncertainty is statistical and the second systematic. Using a Flatte-inspired model, the mode and full width at half maximum of the lineshape are determined to be begin{eqnarray*} mathrm{mode} & = 3871.69^{,+,0.00,+,0.05}_{,-,0.04,-,0.13} &mathrm{MeV} mathrm{FWHM} & = 0.22^{,+,0.07,+,0.11}_{,-,0.06,-,0.13}& mathrm{MeV} . end{eqnarray*} An investigation of the analytic structure of the Flatte amplitude reveals a pole structure, which is compatible with a quasi-bound $D^0bar{D}^{*0}$ state but a quasi-virtual state is still allowed at the level of $2$ standard deviations.



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Using proton-proton collision data, collected with the LHCb detector and corresponding to 1.0, 2.0 and 1.9fb$^{-1}$ of integrated luminosity at the centre-of-mass energies of 7, 8, and 13 TeV, respectively, the decay $Lambda_b^0to chi_{c1}(3872)pK^-$ with $chi_{c1}to J/psipi^+pi^-$ is observed for the first time. The significance of the observed signal is in excess of seven standard deviations. It is found that $(58pm15)%$ of the decays proceed via the two-body intermediate state $chi_{c1}(3872)Lambda(1520)$. The~branching fraction with respect to that of the $Lambda_brightarrowpsi(2S)p K^{-}$ decay mode, where the $psi(2S)$~meson is reconstructed in the $J/psi pi^+pi^-$ final state, is measured to be: begin{equation*} frac{Lambda_b^0tochi_{c1}(3872)pK^-}{Lambda_btopsi(2S)p K^-} times frac{mathcal{B}(chi_{c1} to J/psi pi^+pi^-)}{mathcal{B}(psi(2S)to J/psi pi^+pi^-)} = left(5.4 pm 1.1 pm 0.2right)times 10^{-2},, end{equation*} where the first uncertainty is statistical and the second is systematic.
Using a total of $9.0~mathrm{fb}^{-1}$ of $e^+e^-$ collision data with center-of-mass energies between 4.15 and 4.30 GeV collected by the BESIII detector, we search for the processes $e^+e^-to gamma X(3872)$ with $X(3872)topi^0chi_{cJ}$ for $J=0,1,2$. We report the first observation of $X(3872)topi^{0}chi_{c1}$, a new decay mode of the $X(3872)$, with a statistical significance of more than 5$sigma$. Normalizing to the previously established process $e^+e^-to gamma X(3872)$ with $X(3872)topi^+pi^-J/psi$, we find ${cal B}(X(3872) to pi^0 chi_{c1})/{cal B}(X(3872) to pi^+pi^- J/psi) = 0.88^{+0.33}_{-0.27}pm0.10$, where the first error is statistical and the second is systematic. We set 90% confidence level upper limits on the corresponding ratios for the decays to $pi^0chi_{c0}$ and $pi^0chi_{c2}$ of 19 and 1.1, respectively.
The decays $B^+rightarrow J/psi pi^+ pi^- K^+$ are studied using a data set corresponding to an integrated luminosity of 9fb$^{-1}$ collected with the LHCb detector in proton-proton collisions between 2011 and 2018. Precise measurements of the ratios of branching fractions with the intermediate $psi_2(3823)$, $chi_{c1}(3872)$ and $psi(2S)$ states are reported. The decay of $B^+rightarrow psi_2(3872)K^+$ with $psi_2(3823)rightarrow Jpsipi^+pi^-$ is observed for the first time with a significance of 5.1 standard deviations. The mass differences between the $psi_2(3823)$, $chi_{c1}(3872)$ and $psi(2S)$ states are measured to be $$ begin{array}{rcl} m_{chi_{c1(3872)}} - m_{psi_2(3823)} &= & 47.50 pm 0.53 pm 0.13,mathrm{MeV/}c^2,, m_{psi_2(3823)} - m_{psi(2S)} &= & 137.98 pm 0.53 pm 0.14,mathrm{MeV/}c^2,, m_{chi_{c1}(3872)} - m_{psi(2S)} &= & 185.49 pm 0.06 pm 0.03,mathrm{MeV/}c^2,, end{array} $$ resulting in the most precise determination of the $chi_{c1}(3782)$ mass. The width of the $psi_2(3823)$ state is found to be below 5.2MeV at 90% confidence level. The Breit-Wigner width of the $chi_{c1}(3872)$ state is measured to be $$ Gamma^{mathrm{BW}}_{chi_{c1}(3872)} = 0.96^{+0.19}_{-0.18}pm0.21 mathrm{MeV},$$ which is inconsistent with zero by 5.5 standard deviations.
The decays $chi_{c1} rightarrow J/psi mu^+ mu^-$ and $chi_{c2} rightarrow J/psi mu^+ mu^-$ are observed and used to study the resonance parameters of the $chi_{c1}$ and $chi_{c2}$ mesons. The masses of these states are measured to be m(chi_{c1}) = 3510.71 pm 0.04(stat) pm 0.09(syst)MeV,, m(chi_{c2}) = 3556.10 pm 0.06(stat) pm 0.11(syst)MeV,, where the knowledge of the momentum scale for charged particles dominates the systematic uncertainty. The momentum-scale uncertainties largely cancel in the mass difference m(chi_{c2}) - m(chi_{c1}) = 45.39 pm 0.07(stat) pm 0.03(syst)MeV,. The natural width of the $chi_{c2}$ meson is measured to be $$Gamma(chi_{c2}) = 2.10 pm 0.20(stat) pm 0.02(syst)MeV,.$$ These results are in good agreement with and have comparable precision to the current world averages.
The production of $chi_{c1}(3872)$ and $psi(2S)$ hadrons is studied as a function of charged particle multiplicity in $pp$ collisions at a center-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 2 fb$^{-1}$. For both states, the fraction that is produced promptly at the collision vertex is found to decrease as charged particle multiplicity increases. The ratio of $chi_{c1}(3872)$ to $psi(2S)$ cross-sections for promptly produced particles is also found to decrease with multiplicity, while no significant dependence on multiplicity is observed for the equivalent ratio of particles produced away from the collision vertex in $b$-hadron decays. This behavior is consistent with a calculation that models the $chi_{c1}(3872)$ structure as a compact tetraquark. Comparisons with model calculations and implications for the binding energy of the $chi_{c1}(3872)$ state are discussed.
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