EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-PH-EP-2014-163 LHCb-PAPER-2014-025 8 July 2014

Measurement of the ratio of branching fractions

to and final states

The LHCb collaboration^{†}^{†}†Authors are listed at the end of this paper.

The first measurement that relates semileptonic and hadronic decay rates of the meson is performed using proton-proton collision data corresponding to of integrated luminosity collected with the LHCb detector. The measured value of the ratio of branching fractions, , is at the lower end of available theoretical predictions.

Submitted to Physical Review D

© CERN on behalf of the LHCb collaboration, license CC-BY-4.0.

## 1 Introduction

The meson is the ground state of the quark-pair
system and is the only meson in which weak-interaction decays of both constituents
compete with each other.^{1}^{1}1Charge-conjugate states are implied in this article.
About 70% of the decay width
is expected to be due to the transition,
favored by the Cabibbo-Kobayashi-Maskawa quark-coupling hierarchy [1].
This decay process has recently been observed in the mode [2].
The complementary transition, which is predicted to account for 20% of the decay width,
is more straightforward to observe experimentally,
having a substantial probability to produce a meson.
Among such decays, semileptonic
and hadronic channels have played
a special role in many measurements.
The semileptonic decays were used in the discovery of the meson [3],
the measurements of its
lifetime [3, 4, 5, 6]
and the measurement of the production cross-section at the Tevatron [3].
The decays were used to measure its lifetime [7],
mass [8, 9, 10],
production cross-section at the LHC [10]
and as a reference for other hadronic branching fraction
measurements [11, 12, 13, 14, 15, 16].
However, there is no experimental determination of the relative size of semileptonic and hadronic decay rates.
The goal of this work is a measurement of the ratio of branching fractions,

(1) |

and to test various theoretical models of meson decays, for which predictions of vary over a wide range, 0.050–0.091 [17, 18, 20, 21, 22, 23, 24, 25].

## 2 Analysis outline

Final states containing a muon offer a distinctive
experimental signature and can be triggered and reconstructed
with high efficiency at LHCb. Therefore, this analysis relies on decays to .
Since the neutrino is not detected, both of the studied decay modes
are reconstructed using a candidate plus a charged track (), referred to as the bachelor track.
The mass of signal candidates peaks at the mass within the experimental resolution,
allowing a straightforward signal yield extraction
in the presence of relatively small backgrounds under the signal peak.
The main challenge in this analysis is the signal yield extraction for the
decay mode, as the mass () distribution is broad due to the undetected neutrino.
To suppress the dominant backgrounds, the analysis is restricted
to the endpoint
region and uses the mass-shape difference
between the signal and the remaining background to extract the signal
yield.^{2}^{2}2Units in which are used.
In this mass region the neutrino has low energy, thus
the candidates are kinematically
similar to the candidates.
Therefore, many reconstruction uncertainties cancel in the ratio of their rates,
allowing a precise measurement of .
This endpoint value is then extrapolated to the full phase space
using theoretical predictions.
Since the and are both heavy quarkonia states,
the form factors involved in predicting the extrapolation factor and
the shape of the mass distribution at the endpoint
have only modest model dependence.

## 3 Detector and data sample

The analysis is performed on a data sample of collisions at a center-of-mass energy of 7 TeV, collected during 2011 by the LHCb experiment and corresponding to an integrated luminosity of 1.0 fb. The LHCb detector [26] is a single-arm forward spectrometer covering the pseudorapidity range , designed for the study of particles containing or quarks. The detector includes a high-precision tracking system consisting of a silicon-strip vertex detector surrounding the interaction region [27], a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about , and three stations of silicon-strip detectors and straw drift tubes [28] placed downstream of the magnet. The tracking system provides a measurement of momentum, , with a relative uncertainty that varies from 0.4% at low momentum to 0.6% at 100. The minimum distance of a track to a primary vertex, the impact parameter (IP), is measured with a resolution of m, where is the component of transverse to the beam, in . Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors [29]. Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers [30].

Simulated event samples are generated for the signal decays and the decay modes contributing to the background. In the simulation, collisions are generated using Pythia [31] with a specific LHCb configuration [32]. The production of mesons, which is not adequately simulated in Pythia, is performed by the dedicated generator Bcvegpy[33]. Several dynamical models are used to simulate decays. Decays of hadronic particles are described by EvtGen [34], in which final-state radiation is generated using Photos [35]. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [36] as described in Ref. [38].

## 4 Data selection

This analysis relies on candidates satisfying the trigger [39], which consists of a hardware stage, based on information from the muon system, followed by a two-level software stage, which applies a full event reconstruction. At the hardware stage, a muon with , or a pair of muons with , is required. The subsequent lower-level software triggers require a charged-particle track with ( if identified as muon) and with an IP relative to any primary -interaction vertex (PV) larger than m. A dimuon trigger, which requires a large dimuon mass, , and each muon to have , complements the single track triggers. The final software trigger stage requires either a candidate with a decay vertex separation from the nearest PV of at least three standard deviations, or that a two- or three-track combination, which includes a muon, is identified as a secondary vertex using a multivariate selection [39].

In the offline analysis, candidates are selected with the following criteria: ; ; per degree of freedom (ndf) for the two muons to form a common vertex ; and a mass consistent with the meson. The separation of the decay vertex from the nearest PV must be at least five standard deviations. The bachelor track, and at least one of the muons from the decay of the meson, must not point to any PV, through the requirement . The quantity is defined as the difference between the of the PV fitted with and without the considered particle. The bachelor track must not be collinear within 0.8 with either of the muons from the meson decay and must satisfy ( for ). A loose kaon veto is applied to the pion candidates, , where is the particle identification likelihood [40]. The candidates are combined with the bachelor tracks in a kinematic fit to form candidates with the known mass and the vertex used as constraints. The candidate must satisfy and have a pseudo-proper decay time greater than ps. The pseudo-proper decay time is determined as , where is the projection of the distance between the production and decay vertices onto the direction of the momentum and is the mass.

Four discriminating variables () are used in a likelihood ratio to improve the background suppression. Three of the variables are common between the two channels: , , and the cosine of the angle between the meson and the bachelor track transverse momenta. The latter quantity peaks at positive values for the signal as the meson has a high transverse momentum. Background events in which particles are combined from two different decays usually peak at negative values, whilst those due to random combinations of particles are more uniformly distributed. The variable is small for decays since the momentum points back to the PV. For candidates, the pointing is only approximate since the neutrino is not reconstructed. However, is often smaller than for the background events because the neutrino has low momentum. The fourth variable for the mode is , while for the mode it is the pseudo-proper decay time, as is found to be ineffective for this channel. The four one-dimensional signal probability density functions (PDFs), , are obtained from a simulated sample of signal events. The background PDFs, , are obtained from the data in the mass sidebands (5.35–5.80 and 6.80–8.50 ) and from the simulation of inclusive backgrounds from decays ( denotes one or more particles) for the candidates. The requirement preserves about 93% (87%) of signal events for ( with ) and efficiently suppresses the backgrounds. These requirements minimize the expected average statistical uncertainty on the signal yields, given the observed background levels in each channel.

## 5 Extraction of the signal

An extended maximum likelihood fit to the unbinned distribution of observed values yields signal events and is shown in Fig. 1.

The signal is represented in the fit by a double-sided Crystal Ball (CB) function[41]. The peak position, the Gaussian mass resolution and the peak amplitude are free parameters in the fit, while the parameters describing small non-Gaussian tails are fixed by a fit to the simulated signal distribution. Using a Gaussian function to model the signal results in a 2.3% relative change in value, and this is assigned as the systematic uncertainty. The background is smoothly distributed and modeled by an exponential function. Varying the background parameterization and the fit range results in up to a 0.6% relative change in . A small background from decays, peaking below the signal peak, is also included in the fit with all shape parameters fixed from the simulation. Its normalization is constrained to be 1% of the fitted signal amplitude, as predicted by the measured ratio of the branching fractions [14] scaled by an efficiency ratio of 15% obtained from the simulation. The relative systematic uncertainty on related to this fit component is 0.1%.

## 6 Extraction of the signal

To measure the rate, feeddown from other , decays must be accounted for. Decays to excited charmonium states (, with or ) and states containing leptons () are the dominant contributions. Since the rates for such decays have not been measured, we rely on theoretical predictions for

(2) |

Although the spread in predictions is large, the related systematic uncertainty is minimized by restricting the analysis to the high mass region. Unreconstructed decay products in the transitions (, , , , ) or decays carry energy away, lowering the mass relative to that from direct decays, as illustrated in Fig. 2. The selection requirement in is chosen to eliminate the backgrounds from decays to mesons associated with hadrons, with one of the hadrons misidentified as a muon. These backgrounds are large because the production rates are orders of magnitude higher than for . Since many exclusive decay modes with various hadron multiplicities and unknown branching ratios contribute, the shape of such backgrounds is difficult to predict. The lower limit on is above the kinematic limit for decays, with denoting a charged kaon or pion, as illustrated in Fig. 2.

The backgrounds in the selected region are much smaller, and are from decays paired with a bachelor originating from a semileptonic decay of the companion quark in the produced pair. Simulation of -baryon decays to final states involving a meson shows that they also contribute via this mechanism. The shape of such combinatorial backgrounds is less sensitive to the details of the composition of -hadron decay modes, and thus is easier to predict. Since the combinatorial backgrounds are dominated by genuine muons, the analysis is not sensitive to the estimation of muon misidentification rates and associated systematic uncertainties.

The signal shape is dominated by the endpoint kinematics, whereas the combinatorial background is smooth and extends beyond the kinematic limit for the decays. The signal yield is determined by a fit to the distribution. The feeddown background is small as discussed in detail below. Its shape is constrained by simulation, while its normalization is related to the signal yield via theoretical predictions. The unbinned maximum likelihood fit is performed simultaneously to the distribution in data and the signal and background distributions from simulation, in the range of to , and gives signal events. The distributions and the fit results are displayed in Fig. 3. The fit is described in detail below.

The total PDF used in the fit is the sum of the signal PDF (), the feeddown background PDF () and the combinatorial background PDF (),

(3) |

where is the feeddown-to-signal yield ratio and is the combinatorial background yield. The signal shape is dominated by the endpoint kinematics, thus it is modeled as

(4) |

where and corresponds to the uniform distribution in the three-body phase-space,

(5) |

with the and masses ( and ) set to their known values [42], and set to an effective value, which is slightly higher than the mass to account for detector resolution effects. Setting to the known mass [42] changes the signal yield by a negligible amount. Deviations from the uniform distribution are allowed by the linear term, with the coefficient determined by the simultaneous fit to the simulated signal distribution and the data. The simulation based on the Kiselev et al. QCD sum rules model [22] is used in the default fit. The models of Ebert et al. [23], based on a relativistic quasipotential Schrödinger approach, and ISGW2 [43], based on a nonrelativistic constituent quark model with relativistic corrections, alter the determined signal yield by and , respectively. Relying on the data themselves to determine the signal shape changes the signal yield by . The latter value is taken as a systematic error.

The feeddown includes contributions from the following decay modes , and . Feeddown from and plus hadrons is also investigated and found negligible. Their individual proportions with respect to the signal yield are determined as

(6) |

and then added, ,
where is
the sum of the measured branching fractions [42] for the state to
decay to a meson by emission of unreconstructed photons or light hadrons,
and is the ratio of the feeddown and the signal reconstruction
efficiencies.^{3}^{3}3For ,
.
This quantity is small because of the requirement.
For states the sum extends over the three values,
.
The values of the parameters affecting the estimate of the feeddown fraction are summarized
in Table 1.
Theoretical predictions
for for the feeddown mode
vary over a wide range,
0.009–0.185 [44, 23, 17, 22, 21, 25, 43].
An average of the highest and the lowest prediction is taken for the nominal estimate,
and half of the difference is taken for the systematic error.
The theoretical uncertainties in the values
for the dominant feeddown mode are smaller,
0.032–0.038 [24, 45, 46].
The spread is also limited for theoretical predictions of
for the decay,
0.237–0.283 [24, 22, 46, 18].
The simulated distributions for the
individual feeddown modes are mixed
according to the proportions resulting from the values
and then parameterized as

(7) |

where and are parameters determined by the fit. The effect of the unreconstructed decay products is to lower the effective value in Eq. (5). Varying the feeddown fraction within its uncertainty changes the signal yield by up to .

Feeddown mode | ||||
---|---|---|---|---|

Total |

The combinatorial background is parameterized with an exponential function. The tail of the distribution, with the light hadron misidentified as a muon, may enter the signal region because of detector resolution. We parameterize it with a Gaussian function, , with a mean value and width fixed to the results of the fit to the simulated distribution. The exponential and functions together define ,

where normalizes the exponential function to one. The combinatorial background fraction and the polynomial coefficients and are free parameters in the simultaneous fit to the simulated distribution and to the distribution in the data. To avoid relying on simulation for the absolute values of the muon misidentification rates, is allowed to vary independently in the fit to the simulated and the observed distributions. A systematic uncertainty of 1.8% is assigned to this background parameterization based on fit results in which either the Gaussian term is neglected or the exponential function is replaced by a sum of two exponential functions.

Varying the upper limit of the mass range used in the fit from down to , results in a signal yield change of up to . Varying the corresponding lower limit from its default value of to , thus including the peak of the component (see Fig. 2), or to , thus avoiding the tail of that component, results in a relative change in the value of up to .

The default method of the signal-yield determination relies on simulation to predict the signal and background shapes in the distribution. An alternative approach relies on simulation to predict the signal and background shapes of the distribution. Correlations between and variables are small. The requirement on the value is removed. The range is restricted to 5.3–6.1 to exclude the backgrounds above the kinematic limit. The signal and combinatorial background yields are determined by a fit to the distribution in the data. The feeddown simulation predicts a similar shape as for the signal. Therefore, this contribution is not represented explicitly in the fit to the distribution, but is subtracted from the fitted signal yield according to the feeddown fraction . Taking into account the differences in signal efficiency, the signal yield is consistent with that resulting from the fit method within , which is included as an additional systematic uncertainty due to the requirement in the nominal approach.

## 7 Results

The ratio of the reconstruction efficiencies between the two signal modes, as determined from simulation, is (statistical error) for events generated in the endpoint region. Using different form factor models changes this efficiency ratio by up to . Efficiencies of the pion and muon particle identification (PID) requirements have systematic uncertainties of and , respectively. The efficiency-ratio systematic uncertainties from the lifetime assumed in the simulation is due to the cancelations between the two decay modes. The fraction of multiple signal candidates per event is for and for decays. To check for possible biases due to the neglected correlations between multiple candidates, one candidate is randomly chosen, which changes the result by . The systematic uncertainty associated with the limited knowledge of the efficiency of the requirement for decays is included using the results of the fit. To study the corresponding uncertainty for decays, the requirement is varied, resulting in a variation. The systematic uncertainty associated with the trigger simulation is , as estimated by modifying the trigger requirements. The systematic errors are summarized in Table 2. The total relative systematic uncertainty on is .

Contribution | Relative |
---|---|

error | |

signal shape | |

background shape | |

component | |

signal shape | |

background shape | |

feeddown | |

Lower fit range limit | |

Upper fit range limit | |

model dependence of efficiency | |

Pion PID | |

Muon PID | |

Lifetime | |

Multiple candidates | |

requirement for | |

requirement for | |

Trigger simulation | |

Total within selected range | |

extrapolation | |

Total |

The result for the ratio of the branching fractions restricted to decays with is

(8) |

where the first uncertainty is statistical and the second is systematic. This ratio is extrapolated to the full phase-space as follows. The model of Kiselev et al. [22] predicts the fraction of the rate with above to be , which is close to an average over six different models [47, 25, 48, 23, 43]. The largest deviation from this prediction is , which is taken as an estimate of the extrapolation systematic error. This increases the systematic uncertainty on , when extrapolated to the full mass range, to yielding

(9) |

A comparison between the measured and the predicted values of is shown in Fig. 4. The measured value is slightly below the lowest predicted value. The predictions by the relativistic quasipotential Schrödinger model of Ebert et al. [23] and the model of El-Hady et al., based on a nonrelativistic reduction of the Bethe-Salpeter equation [20], are in good agreement with the experimental value. The model of Ke et al. [25], based on the modified harmonic oscillator wave function in light-front quark model, is also consistent with the data. The other models [17, 18, 21, 22, 24] significantly overestimate .

## 8 Summary

The ratio of hadronic and semileptonic decay branching fractions of the meson is measured for the first time. Within the observed mass range, , the measured value of is found to be . Extrapolating to the full mass range, we obtain a value of , which is in good agreement with the theoretical predictions by Ebert et al. [23] and El-Hady et al. [20], and consistent with the prediction by Ke et al. [25]. All other currently available models [17, 18, 21, 22, 24] overestimate this ratio.

## Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MinES and FANO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). The Tier1 computing centres are supported by IN2P3 (France), KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom). We are indebted to the communities behind the multiple open source software packages on which we depend. We are also thankful for the computing resources and the access to software R&D tools provided by Yandex LLC (Russia). Individual groups or members have received support from EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union), Conseil général de Haute-Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR (Russia), XuntaGal and GENCAT (Spain), Royal Society and Royal Commission for the Exhibition of 1851 (United Kingdom).

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LHCb collaboration

R. Aaij, B. Adeva, M. Adinolfi, A. Affolder, Z. Ajaltouni, S. Akar, J. Albrecht, F. Alessio, M. Alexander, S. Ali, G. Alkhazov, P. Alvarez Cartelle, A.A. Alves Jr, S. Amato, S. Amerio, Y. Amhis, L. An, L. Anderlini, J. Anderson, R. Andreassen, M. Andreotti, J.E. Andrews, R.B. Appleby, O. Aquines Gutierrez, F. Archilli, A. Artamonov, M. Artuso, E. Aslanides, G. Auriemma, M. Baalouch, S. Bachmann, J.J. Back, A. Badalov, V. Balagura, W. Baldini, R.J. Barlow, C. Barschel, S. Barsuk, W. Barter, V. Batozskaya, V. Battista, A. Bay, L. Beaucourt, J. Beddow, F. Bedeschi, I. Bediaga, S. Belogurov, K. Belous, I. Belyaev, E. Ben-Haim, G. Bencivenni, S. Benson, J. Benton, A. Berezhnoy, R. Bernet, M.-O. Bettler, M. van Beuzekom, A. Bien, S. Bifani, T. Bird, A. Bizzeti, P.M. Bjørnstad, T. Blake, F. Blanc, J. Blouw, S. Blusk, V. Bocci, A. Bondar, N. Bondar, W. Bonivento, S. Borghi, A. Borgia, M. Borsato, T.J.V. Bowcock, E. Bowen, C. Bozzi, T. Brambach, J. van den Brand, J. Bressieux, D. Brett, M. Britsch, T. Britton, J. Brodzicka, N.H. Brook, H. Brown, A. Bursche, G. Busetto, J. Buytaert, S. Cadeddu, R. Calabrese, M. Calvi, M. Calvo Gomez, P. Campana, D. Campora Perez, A. Carbone, G. Carboni, R. Cardinale, A. Cardini, L. Carson, K. Carvalho Akiba, G. Casse, L. Cassina, L. Castillo Garcia, M. Cattaneo, Ch. Cauet, R. Cenci, M. Charles, Ph. Charpentier, S. Chen, S.-F. Cheung, N. Chiapolini, M. Chrzaszcz, K. Ciba, X. Cid Vidal, G. Ciezarek, P.E.L. Clarke, M. Clemencic, H.V. Cliff, J. Closier, V. Coco, J. Cogan, E. Cogneras, P. Collins, A. Comerma-Montells, A. Contu, A. Cook, M. Coombes, S. Coquereau, G. Corti, M. Corvo, I. Counts, B. Couturier, G.A. Cowan, D.C. Craik, M. Cruz Torres, S. Cunliffe, R. Currie, C. D’Ambrosio, J. Dalseno, P. David, P.N.Y. David, A. Davis, K. De Bruyn, S. De Capua, M. De Cian, J.M. De Miranda, L. De Paula, W. De Silva, P. De Simone, D. Decamp, M. Deckenhoff, L. Del Buono, N. Déléage, D. Derkach, O. Deschamps, F. Dettori, A. Di Canto, H. Dijkstra, S. Donleavy, F. Dordei, M. Dorigo, A. Dosil Suárez, D. Dossett, A. Dovbnya, K. Dreimanis, G. Dujany, F. Dupertuis, P. Durante, R. Dzhelyadin, A. Dziurda, A. Dzyuba, S. Easo, U. Egede, V. Egorychev, S. Eidelman, S. Eisenhardt, U. Eitschberger, R. Ekelhof, L. Eklund, I. El Rifai, Ch. Elsasser, S. Ely, S. Esen, H.-M. Evans, T. Evans, A. Falabella, C. Färber, C. Farinelli, N. Farley, S. Farry, RF Fay, D. Ferguson, V. Fernandez Albor, F. Ferreira Rodrigues, M. Ferro-Luzzi, S. Filippov, M. Fiore, M. Fiorini, M. Firlej, C. Fitzpatrick, T. Fiutowski, M. Fontana, F. Fontanelli, R. Forty, O. Francisco, M. Frank, C. Frei, M. Frosini, J. Fu, E. Furfaro, A. Gallas Torreira, D. Galli, S. Gallorini, S. Gambetta, M. Gandelman, P. Gandini, Y. Gao, J. García Pardiñas, J. Garofoli, J. Garra Tico, L. Garrido, C. Gaspar, R. Gauld, L. Gavardi, G. Gavrilov, E. Gersabeck, M. Gersabeck, T. Gershon, Ph. Ghez, A. Gianelle, S. Giani’, V. Gibson, L. Giubega, V.V. Gligorov, C. Göbel, D. Golubkov, A. Golutvin, A. Gomes, H. Gordon, C. Gotti, M. Grabalosa Gándara, R. Graciani Diaz, L.A. Granado Cardoso, E. Graugés, G. Graziani, A. Grecu, E. Greening, S. Gregson, P. Griffith, L. Grillo, O. Grünberg, B. Gui, E. Gushchin, Yu. Guz, T. Gys, C. Hadjivasiliou, G. Haefeli, C. Haen, S.C. Haines, S. Hall, B. Hamilton, T. Hampson, X. Han, S. Hansmann-Menzemer, N. Harnew, S.T. Harnew, J. Harrison, J. He, T. Head, V. Heijne, K. Hennessy, P. Henrard, L. Henry, J.A. Hernando Morata, E. van Herwijnen, M. Heß, A. Hicheur, D. Hill, M. Hoballah, C. Hombach, W. Hulsbergen, P. Hunt, N. Hussain, D. Hutchcroft, D. Hynds, M. Idzik, P. Ilten, R. Jacobsson, A. Jaeger, J. Jalocha, E. Jans, P. Jaton, A. Jawahery, F. Jing, M. John, D. Johnson, C.R. Jones, C. Joram, B. Jost, N. Jurik, M. Kaballo, S. Kandybei, W. Kanso, M. Karacson, T.M. Karbach, S. Karodia, M. Kelsey, I.R. Kenyon, T. Ketel, B. Khanji, C. Khurewathanakul, S. Klaver, K. Klimaszewski, O. Kochebina, M. Kolpin, I. Komarov, R.F. Koopman, P. Koppenburg, M. Korolev, A. Kozlinskiy, L. Kravchuk, K. Kreplin, M. Kreps, G. Krocker, P. Krokovny, F. Kruse, W. Kucewicz, M. Kucharczyk