decays of b mesons to two - body final states containing a charmonium resonance such as a j/ or (2s ) offer a powerful way of studying electroweak transitions . such decays probe charmonium properties and play a role in the study of cp violation and mixing in the neutral b  system  . the relative branching fractions of b , b and \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s}$\end{document } mesons into j/ and (2s ) mesons have previously been studied by both the cdf and d0 collaborations  [ 24 ] . since the current experimental results for the study of cp violation in \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } $ \end{document } mixing using the \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } \rightarrow j/\psi \phi$\end{document } decay  [ 57 ] are statistically limited , it is important to establish other channels where this analysis can be done . one such channel is the \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } \rightarrow \psi ( 2s)\phi$\end{document } decay . in this paper , measurements of the ratios of the branching fractions of b mesons decaying to (2s)x and j/x are reported , where b denotes a b , b or \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s}$\end{document } meson ( charge conjugate decays are implicitly included ) and x denotes a k , k or  meson . the data were collected by the lhcb experiment in  pp  collisions at the centre - of - mass energy \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{s } = 7~\mathrm{tev}$\end{document } during 2011 and correspond to an integrated luminosity of 0.37  fb . the lhcb detector   is a single - arm forward spectrometer covering the pseudorapidity range 2<<5 , designed for the study of b- and c - hadrons . the detector includes a high precision tracking system consisting of a silicon - strip vertex detector surrounding the pp interaction region , a large - area silicon - strip detector located upstream of a dipole magnet with a bending power of about 4  tm , and three stations of silicon - strip detectors and straw drift - tubes placed downstream . the combined tracking system has a momentum resolution p / p that varies from 0.4  % at 5  gev / c to 0.6  % at 100  gev / c , and an impact parameter resolution of 20  m for tracks with high transverse momentum . data were taken with both magnet polarities to reduce systematic effects due to detector asymmetries . photon , electron and hadron candidates are identified by a calorimeter system consisting of scintillating - pad and pre - shower detectors , and electromagnetic and hadronic calorimeters . muons are identified by a muon system composed of alternating layers of iron and multiwire proportional chambers . the trigger consists of a hardware stage based on information from the calorimeter and muon systems , followed by a software stage which applies a full event reconstruction . events with a  j/ final state are triggered using two hardware trigger decisions : the single - muon decision , which requires one muon candidate with a transverse momentum pt larger than 1.5  gev / c , and the di - muon decision , which requires two muon candidates with transverse momenta \documentclass[12pt]{minimal } 
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				 \begin{document}$p_{\mathrm{t}_{1}}$\end{document } and \documentclass[12pt]{minimal } 
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				 \begin{document}$p_{\mathrm{t}_{2}}$\end{document } satisfying the relation \documentclass[12pt]{minimal } 
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				 \begin{document}$\sqrt{p_{\mathrm{t}_{1 } } \cdot p_{\mathrm{t}_{2 } } } > 1.3~\mathrm{gev}/c$\end{document}. the di - muon trigger decision in the software trigger requires muon pairs of opposite charge with pt>500  mev / c , forming a common vertex and with an invariant mass in excess of 2.9  gev / c . in this analysis , the decays \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{+}\rightarrow \psi k^{+}(b^{0}\rightarrow \psi k^{*0},\allowbreak b^{0}_{s}\rightarrow \psi\phi)$\end{document } are reconstructed , where  represents (2s ) or j/ , reconstructed in the  decay modes . a  k(k, ) candidate is added to the di - muon pair to form a \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{+}(b^{0 } , b^{0}_{s})$\end{document } candidate . the starting point of the analysis is the reconstruction of either a j/ or (2s ) meson decaying into a di - muon pair . candidates are formed from pairs of opposite sign tracks that both have a transverse momentum larger than 500  mev / c . good reconstruction quality is assured by requiring the  per degree of freedom of the track fit to satisfy /ndf<5 . this is achieved by requiring the muon identification variable , the difference in logarithm of the likelihood of the muon and hadron hypotheses   provided by the muon detection system , to satisfy \documentclass[12pt]{minimal } 
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				 \begin{document}$\delta\log\mathcal{l}^{\mu - h } > -5$\end{document}. the muons are required to form a common vertex of good quality ( \documentclass[12pt]{minimal } 
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				 \begin{document}$\chi^{2}_{\mathrm{vtx}}<20$\end{document } ) . the resulting di - muon candidate is required to have decay length significance from its associated primary vertex greater than 5 and have an invariant mass between 3020 and 3135  mev / c in the case of a j/ candidate or between 3597 and 3730  mev / c for a (2s ) candidate . the selected j/ and (2s ) candidates are then combined with a k , k or  to create b meson candidates . pion - kaon separation is provided by the ring - imaging cherenkov detectors . to identify kaons the difference in logarithm of the likelihood of the kaon and pion hypotheses   is required to satisfy \documentclass[12pt]{minimal } 
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				 \begin{document}$\delta\log\mathcal{l}^ { k- \pi } > -5$\end{document}. in the case of pions the difference in logarithm of the likelihood of the pion and kaon hypotheses is required to satisfy \documentclass[12pt]{minimal } 
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				 \begin{document}$\delta\log\mathcal{l}^ { \pi - k } > -5$\end{document}. as in the case of muons , a cut is applied on the track /ndf provided by the track fit at  5 . the kaons and pions are required to have a transverse momentum larger than 250  mev / c and to have an impact parameter significance with respect to any primary vertex larger than  2 . in the b channel , the mass of the kaon and pion system is required to be \documentclass[12pt]{minimal } 
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				 \begin{document}$842<\mathrm{m } _ { k^{+ } \pi^{-}}<942~\mathrm{mev}/c^{2}$\end{document } and in the \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s}$\end{document } channel the mass of the kaon pair is required to be \documentclass[12pt]{minimal } 
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				 \begin{document}$1010<\mathrm{m } _ { k^{+ } k^{- } } < 1030~\mathrm{mev}/c^{2}$\end{document}. in addition , we require the decay time of the b candidate ( c ) to be larger than 100  m to reduce the large combinatorial background from particles produced in the primary pp interaction . a  global refit of the three - prong ( four - prong ) combination is performed with a primary vertex constraint and with the di - muon pair mass constrained to the nominal value   using the decay tree fit ( dtf ) procedure  . the reduced  of this fit ( \documentclass[12pt]{minimal } 
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				 \begin{document}$\chi^{2}_{\mathrm{dtf}}/\mathrm{ndf}$\end{document } ) is required to be less than  5 , where the dtf algorithm takes into account the number of decay products to determine the number of degrees of freedom . the b candidates , where a muon from the (2s) decay is reconstructed as both muon and kaon , are removed by requiring the angle between the same sign muon and kaon to be greater than 3  mrad . the number of the bk candidates is estimated by performing an unbinned maximum likelihood fit . the same procedure is used to determine the number of the bk candidates in a \documentclass[12pt]{minimal } 
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				 \begin{document}$842<\mathrm{m } _ { k^{+ } \pi^{-}}<942~\mathrm{mev}/c^{2}$\end{document } mass window and the number of the \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } \rightarrow \psi k^{+ } k^{-}$\end{document } candidates in a \documentclass[12pt]{minimal } 
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				 \begin{document}$1010<\mathrm{m } _ { k^{+ } k^{-}}<1030~\mathrm{mev}/c^{2}$\end{document } mass window . the number of signal candidates is determined by fitting a double - sided crystal ball function [ 12 , 13 ] for signal together with an exponential function to model the background . the tail parameters of the crystal ball function are fixed to values determined from simulation . 1mass distributions of ( a )  b 
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				 \begin{document}$b^{0}_{s } \rightarrow \psi(2s ) k^{+ } k^{-}$\end{document}. the total fitted function ( solid ) and the combinatorial background ( dashed ) are shown . the variation in resolution of the different modes is fully consistent with the energy released in the decays and in agreement with simulation mass distributions of ( a )  b 
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				 \begin{document}$b^{0}_{s } \rightarrow \psi(2s ) k^{+ } k^{-}$\end{document}. the total fitted function ( solid ) and the combinatorial background ( dashed ) are shown . the variation in resolution of the different modes is fully consistent with the energy released in the decays and in agreement with simulation to estimate the contribution from non - resonant decays bk and \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } \rightarrow \psi k^{+ } k^{-}$\end{document } , the k and kk invariant mass distributions have been studied after relaxing requirements on the k and kk invariant masses , see fig .  2 . the k and kk invariant mass distributions are then fitted with the sum of a relativistic breit - wigner function convolved with a gaussian , to describe the resonant contribution from the k or  , two - body phase space function multiplied by a second order polynomial , to describe the non - resonant k or kk contribution . the splot technique   is used to unfold the k or kk invariant mass of the non - resonant ( in k and kk ) candidates . this unfolded distribution contains a mixture of combinatorial background and non - resonant bk or \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } \rightarrow \psi k^{+ } k^{-}$\end{document } decays . is then used to estimate the contribution from the non - resonant b decays , which is subtracted from the total yield to estimate the contribution from resonant bk or \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } \rightarrow \psi\phi$\end{document } decays . the contribution of the resonant decays can also be extracted by unfolding the contribution of resonant k or kk decays to the k or kk invariant mass distribution . 2mass distributions of k 
  
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				 \begin{document}$b^{0}_{s } \rightarrow \psi(2s ) k^{+ } k^{-}$\end{document } decays . the total fitted function ( solid ) and the combination of the non - resonant component and the combinatorial background ( dashed ) 3mass distributions of a ( a )  b 
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				 \begin{document}$b^{0}_{s } \rightarrow \psi(2s ) k^{+ } k^{-}$\end{document } for resonant component ( full circles ) and non - resonant component ( open circles ) . the total fitted function ( solid ) and the combinatorial background ( dashed ) are shown . the fit is described in the texttable  1summary of the signal yields for the six b modes considered and the ratios of the number of j/ and (2s ) decays : n 
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				 \begin{document}$n^{\mathrm{res}}_{\psi x}$\end{document } is the signal yield for resonant decays ( through k 
  or  ) . the uncertainties are statistical only 
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				 \begin{document}$n^{\mathrm{res}}_{\psi(2s)x}/n^{\mathrm{res}}_{j/\psi x}$\end{document } 

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				 \begin{document}$b^{0}_{s } \rightarrow j/\psi k^{+ } k^{-}$\end{document } 
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				 \begin{document}$0^{+1}_{-0}$\end{document } 
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				 \begin{document}$b^{0}_{s } \rightarrow \psi(2s ) k^{+ } k^{-}$\end{document } decays . the total fitted function ( solid ) and the combination of the non - resonant component and the combinatorial background ( dashed ) the fit is described in the text mass distributions of a ( a )  b 
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				 \begin{document}$b^{0}_{s } \rightarrow \psi(2s ) k^{+ } k^{-}$\end{document } for resonant component ( full circles ) and non - resonant component ( open circles ) . the total fitted function ( solid ) and the combinatorial background ( dashed ) the fit is described in the text summary of the signal yields for the six b modes considered and the ratios of the number of j/ and (2s ) decays : n 
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				 \begin{document}$n^{\mathrm{res}}_{\psi x}$\end{document } is the signal yield for resonant decays ( through k 
  or  ) . the branching fraction ratio is calculated using 
 1 where n is the number of signal candidates and  is the overall efficiency . the overall efficiency is the product of the geometrical acceptance of the detector , the combined reconstruction and selection efficiency , and the trigger efficiency . the simulation samples used are based on the pythia  6.4 generator   configured with the parameters detailed in ref .  . the evtgen   and geant4   packages are used to generate hadron decays and simulate interactions in the detector , respectively . the digitized output is passed through a full simulation of both the hardware and software trigger and then reconstructed in the same way as the data . the overall efficiency ratio is 0.9010.016 , 1.0110.014 and 0.9940.014 for the b , the b and the \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } $ \end{document } channels respectively . since the selection criteria for bj/x and b(2s)x decays are identical , the ratio of efficiencies is expected to be close to unity . the deviation of the overall efficiency ratio from unity in the case of the bk decays is due to the difference between the pt spectra of muons for the j/ and (2s ) decays . for the b and \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } $ \end{document } channels this difference is small . it has been checked that the behaviour of the efficiencies of all selection criteria is consistent in the data and simulation . since the decay products in each of the pairs of channels considered have similar kinematics , most uncertainties cancel in the ratio . the different contributions to the systematic uncertainties affecting this analysis are discussed in the following and summarized in table  2 . table  2systematic uncertainties ( in % ) on the relative branching fractionssource 
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				 \begin{document}$b^{0}_{s } $ \end{document } channelnon - resonant decays1.53.4data - simulation agreement1.70.52.0magnet polarity1.40.60.7finite simulation sample size0.30.50.6trigger1.11.11.1background shape0.60.20.2signal shape0.70.80.5angular distribution<0.10.6particle misidentification0.4<0.1<0.1sum in quadrature2.72.24.3 systematic uncertainties ( in % ) on the relative branching fractions the dominant source of systematic uncertainty arises from the subtraction of the non - resonant components in the b and the \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{(s)}$\end{document } mass distribution of candidates containing genuine k( ) resonances . second , using the \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{(s)}$\end{document } mass distribution as the discriminating variable to unfold the k(kk ) mass distribution of genuine \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{(s)}$\end{document } candidates and fitting this distribution to determine the number of non - resonant decays . the corresponding uncertainties are found to be 1.5  % in the b channel and 3.4  % in the \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } $ \end{document } channel . the other important source of uncertainty arises from the estimation of the efficiencies due to the potential disagreement between data and simulation . the corresponding uncertainties are found to be 1.7  % in the b channel , 0.5  % in the b channel and 2.0  % in the \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } $ \end{document } channel . the observed difference in the efficiency ratios for the two magnet polarities is conservatively taken as an estimate of the systematic uncertainty . this is 1.4  % in the b channel , 0.6  % in the b channel and 0.7  % in the \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } $ \end{document } channel . the trigger is highly efficient in selecting b meson decays with two muons in the final state . for this analysis the di - muon pair is required to trigger the event . differences in the trigger efficiency between data and simulation are studied in the data using events which were triggered independently on the di - muon pair . a further uncertainty arises from the imperfect knowledge of the shape of the signal and background in the b meson mass distribution . to estimate this effect , a linear and a quadratic function are considered as alternative models for the background mass distribution . in addition , a double gaussian shape and a sum of double - sided crystal ball and gaussian shapes are used as alternative models for the signal shape . the maximum observed change in the ratio of yields in the (2s ) and j/ modes is taken as systematic uncertainty . the central value of the relative efficiency is determined by assuming that the angular distribution of the b(2s)x decay is the same as that of the bj/x . the systematic uncertainty due to the unknown polarization of the (2s ) in the b meson decays is estimated as follows . the simulation samples were re - weighted to match the angular distributions found from the data and the relative efficiency was recalculated . the difference between the baseline analysis and the re - weighted simulation is taken as the systematic uncertainty , as shown in table  2 . finally , the uncertainty due to potential contribution from the cabibbo - suppressed mode with a  misidentified as k is found to be 0.4  % in the b channel and negligible in the b and \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } $ \end{document } channels . the uncertainty due to the cross - feed between b and \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } $ \end{document } channels with a  misidentified as k ( or a k misidentified as  ) is negligible . since the di - electron branching fractions are measured more precisely than those of the di - muon decay modes , we assume lepton universality and take \documentclass[12pt]{minimal } 
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				 \begin{document}$r_{\psi}=\mathcal{b } ( j/\psi \rightarrow \mu ^{+}\mu ^{-})/\mathcal { b } ( \psi(2s)\rightarrow \mu ^{+}\mu ^{- } ) = \mathcal{b } ( j/\psi \rightarrow e^{+}e^{-})/ \mathcal{b } ( \psi(2s)\rightarrow e^{+}e^{- } ) = 7.69\pm0.19$\end{document }  . the results are combined using eq . ( 1 ) to give 
  where the first uncertainty is statistical , the second is systematic and the third is the uncertainty on the r  value  . the resulting branching fraction ratios are compatible with , but significantly more precise than , the current world averages of \documentclass[12pt]{minimal } 
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				 \begin{document}$\mathcal{b } ( b^{+}\rightarrow \psi ( 2s ) k^{+})/\mathcal{b } ( b^{+}\rightarrow j/\psi k^{+})=0.60\pm0.07$\end{document } and \documentclass[12pt]{minimal } 
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				 \begin{document}$\mathcal{b } ( b^{0}_{s } \rightarrow \psi ( 2s)\phi)/\mathcal{b } ( b^{0}_{s } \rightarrow j/\psi \phi)=0.53\pm 0.10$\end{document }   and the cdf result of \documentclass[12pt]{minimal } 
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				 \begin{document}$\mathcal{b } ( b^{0}\rightarrow \psi ( 2s ) k^{*0})/\mathcal{b } ( b^{0}\rightarrow j/\psi k^{*0 } ) = 0.515\pm0.113\pm0.052$\end{document } . the \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } \rightarrow \psi(2s)\phi$\end{document } decay is particularly interesting since , with more data , it can be used for the measurement of cp violation in \documentclass[12pt]{minimal } 
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				 \begin{document}$b^{0}_{s } $ \end{document } mixing .