DSpace at VNU: Search for rare hadronic B decays

13 October 1994 PHYSICS LETTERS B ELSEVIER Physics Letters B 337 (1994) 393 404 Search for rare hadronic B decays OPAL Collaboration R Akers P, G Alexander w, j Allison P, K.J Anderson i, S Arcelli b, S Asai x, A Astbury ab, D Axen ac, G Azuelos r.l, A.H Ball q, E Barberio z, R.J Barlow P, R Bartoldus c, J.R Batley e, G Beaudoin r, A Beck w, G.A Beck m, j BeckerJ, C Beeston P, T Behnke aa, K.W Bell t, G Bella w, R Bentkowski r, S Bentvelsen h, R BerlichJ, S Bethke af, O Biebel af, I.J Bloodworth a, R Bock k, H.M Bosch k, M Boutemeur r, S Braibant e, E Bright-Thomas Y, R.M Brown t, A Buijs h, H.J Burckhart h, C Burgard aa, E Capiluppi b, R.K Carnegie f, A.A Carter m, J.R Carter e, C.Y Chang q, C Charlesworth f, D.G Charlton h, S.L Chu d, RE.L Clarke o, J.C Clayton a, S.G Clowes P, I Cohen w, J.E Conboy o, M Coupland n, M Cuffiani b, S Dado v, C Dallapiccolaq, G.M Dallavalle b, C Darling ~e, S De Jong m, H Deng q, M Dittmar d, M.S Dixit g, E Couto e Silva e, J.E Duboscq h, E Duchovni z, G Duckeck h, I.R Duerdoth P, U.C Dunwoody e, RA Elcombe e, RG Estabrooks f, E Etzion w, H.G Evans i, F Fabbri b, B Fabbro", M Fanti b, M Fierro b, M Fincke-Keeler ~b, H.M Fischer c, R Fischer c, R Folman z, D.G Fong q, M Foucher q, H Fukui x, A Ftirtjes h, R Gagnon f, A Gaidot u, J.W Gary d, j Gascon r, N.I Geddes t, C Geich-Gimbel c, S.W Gensler i, EX Gentit u, T Geralis t, G Giacomelli b, E Giacomelli d, R Giacomelli b, V Gibson ~, W.R Gibson m, J.D Gillies t, j Goldberg v, D.M Gingrich ad,1, M.J Goodrick e, W Gorn d, C Grandi b, E Grannis h, E Gross z, j Hagemann aa, G.G Hanson e, M Hansroul h, C.K Hargrove g, J Hart h, RA Hart i, M Hauschild h, C.M Hawkes h, E Heflin d, R.J Hemingway f, G Herten J, R.D Heuer h, J.C Hill e, S.J Hillier h, T Hilse J, D.A Hinshaw r, ER Hobson Y, D Hochrnan z, A Hfcker c, R.J Homer a, A.K Honma ab,l, R.E Hughes-Jones P, R Humber0, R Igo-Kemenes k, H Ihssen k, D.C Imrie Y, A Jawahery q, RW Jeffreys t, H Jeremie r, M Jimack a, M Jones f, R.W.L Jones h, p Jovanovic a, C Jui a, D Karlen f K Kawagoe x, T Kawamoto x, R.K Keeler ~b, R.G Kellogg q, B.W Kennedy t, B King h' J King m, S Kluth e, T Kobayashi x, M Kobel j, D.S Koetke h, T.P Kokott c, S Komamiya x, R Kowalewski h, R Howard ac, R Krieger f, J von Krogh k, R Kyberd m, G.D Lafferty P, H Lafoux h, R Lahmann q, J Lauber h, J.G Layter d, R Leblanc r, p Le Du u, A.M Lee ae, E Lefebvre r, M.H Lehto o, D Lellouch z, C Leroy r, j Letts d, L Levinson z, Z Li e, F Liu ac, S.L Lloyd m, F.K Loebinger P, G.D Long q, B Lorazo r, M.J Losty g, X.C Lou h, j Ludwig j, A LuigJ, M Mannelli h, S Marcellini b, C Markus c, A.J Martin m, j.p Martin r, T Mashimo x, R M~ittig c, U Maur c, j McKenna ac, T.J McMahon a, A.I McNab m, J.R McNutt Y, 0370-2693/94/$07.00 @ 1994 Elsevier Science B.V All rights reserved SSDI 0370-2693 (94) 01030-7 394 OPAL Collaboration/Physics Letters B 337 (1994) 393-404 E Meijers h, ES Merritt i, H Mes g, A Michelini h, R.E Middleton t, G Mikenberg z, J Mildenberger f, D.J Miller o, R Mir z, W MohrJ, C Moisan r, A Montanari b, T Mori x, M Morii x, U Miiller c, B Nellen c, B Nijjhar P, S.W O'Neale a, F.G Oakham g, F Odorici b, H.O Ogren e, C.J Oram ab,1, M.J Oreglia i, S Orito x, J.E Pansart u, G.N Patrick t, M.J Pearce a, E PfisterJ, ED Phillips P, J.E Pilcher i, J Pinfold ad, D Pitman ab, D.E Plane h, E Poffenberger ab, B Poli b, A Posthaus c, T.W Pritchard m, H Przysiezniak r, M.W Redmond h, D.L Rees h, D Rigby a, M Rison e, S.A Robins m, D Robinson e, J.M Roney ab, E Ros h, S Rossberg J, A.M Rossi b, M Rosvick ab, E Routenburg ad, Y Rozen h, K RungeJ, O Runolfsson h, D.R Rust e, M Sasaki x, C Sbarra b, A.D Schaile h, O Schaile j, F Scharf c, E Scharff-Hansen h, E Schenk d, B Schmitt c, H yon der Schmitt k, M Schr/Sder e, H.C Schultz-Coulon j, E Schfitz c, M Schulz h, C Schwick aa, j Schwiening c, W.G Scott t, M Settles e, T.G Shears e, B.C Shen d, C.H Shepherd-Themistocleous g, E Sherwood °, G.E Siroli b, A Skillman P, A Skuja q, A.M Smith h, T.J Smith ab, G.A Snow q, R Sobie ab, R.W Springer q, M Sproston t, A Stahl c, C StegmannJ, K Stephens p, J Steuerer ab, B Stockhausen c, R Strt~hmer k, D Strom s, E Szymanski t, H Takeda x, T Takeshita x, S Tarem z, M Tecchio i, E Teixeira-Dias k, N Tesch e, M.A Thomson o, S Towers f, T Tsukamoto x, M.F Turner-Watson h, D Van den plas r, R Van Kooten e, G Vasseur u, M Vincter ab, A Wagner aa, D.L Wagner i, C.E Ward e, D.R Ward e, j.j Ward o, P.M Watkins a, A.T Watson a, N.K Watson g, P Weber f, P.S Wells h, N Wermes c, B Wilkens J, G.W Wilson d, J.A Wilson a, V-H Winterer J, T Wlodek z, G Wolf z, S Wotton k, T.R Wyatt P, A Yeaman m, G Yekutieli z, M Yurko r, W Zeuner h, G.T Zorn q a School of Physics and Space Research, University of Birmingham, Birmingham B15 2T1], UK b Dipartimento di Fisica deU'Universitg~ di Bologna and INFN, 1-40126 Bologna, Italy c Physikalisches Institut, Universitdt Bonn, D-53115 Bonn Germany d Department of Physics, University of California, Riverside CA 92521, USA e Cavendish Laboratory, Cambridge CB30HE, UK f Carleton University Department of Physics, Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada g Centre for Research in Particle Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canada h CERN, European Organisationfor Particle Physics, CH-1211 Geneva 23, Switzerland i Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago IL 60637, USA J Fakultgitfiir Physik, Albert Ludwigs Universitiit, D-79104 Freiburg Germany k Physikalisches Institut, Universitgit Heidelberg, D-69120 Heidelberg, Germany e Indiana University, Department of Physics, Swain Hall West 117, Bloomington IN 47405, USA m Queen Mary and Wes~qeld College, University of London London E1 4NS, UK n Birkbeck College, London WCIE 7HV, UK o University College London, London WC1E 6BT, UK P Department of Physics, Schuster Laboratory The University, Manchester M13 9PL, UK q Department of Physics, University of Maryland, College Park, MD 20742, USA r Laboratoire de Physique Nucl~aire, Universitd de Montreal, Montrial, Quebec H3C 3J7, Canada s University of Oregon, Department of Physics, Eugene OR 97403, USA t Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OXI10QX, UK u CEA, DAPNIA/SPP, CE-Saclay, F-91191 Gif-sur-Yvette, France v Department of Physics, Technion-lsrael Institute of Technology, Haifa 32000, Israel w Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978 Israel x International Centre for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo 113, and Kobe University, Kobe 657, Japan Y Brunel University, Uxbridge, Middlesex UB8 3PH, UK z Particle Physics Department, Weizmann Institute of Science, Rehovot 76100, Israel OPAL Collaboration/Physics Letters B 337 (1994) 393-404 395 aa Universitgit Hamburg/DESY, 11 lnstitut fiir Experimental Physik, Notkestrasse 85, D-22607 Hamburg, Germany ab University of Victoria, Department of Physics, P Box 3055, Victoria BC VSW 3t>6, Canada ac University of British Columbia, Department of Physics, Vancouver BC V6T 1Z1, Canada ad University of Alberta, Department of Physics, Edmonton AB TrG 2J1, Canada ae Duke University, Department of Physics, Durham, NC 27708-0305, USA af Technische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D-52056 Aachen, Germany Received July 1994 Editor: K Winter Abstract A search for rare decays of B hadrons has been performed using approximately two million hadronic Z° decays collected by the OPAL experiment between 1990 and 1993 The exclusive decay channels B~° ~ lr+~r- , B ° ~ K+cr- , B ° ~ 7r+K and B ° ~ K+K - have been studied Such decays include contributions from flavour changing neutral current processes such as hadronic penguin decays No significant excess of events has been observed in the 7r+~r- , ~r+K - and K+K - invariant mass distributions Consequently, upper limits on the B ° branching ratios, Br (B° -~r+~ - ) < 4.7 × 10 -5 and Br (B° -~K+~r-) < 8.1 × 10 -5, and on the B° branching ratios, Br (Bs° *~'+K- ) < 2.6 x - ' and Br (B° -+K+K- ) < 1.4 x 10 -4, have been set at the 90% confidence level These limits assume that the ratio of the partial decay widths of the Z °, F(Z° -~ b b ) / F (Z ° ~ hadrons), is 0.217 and that the fractions of B° and B ° mesons produced during fragmentation are 39.5% and 12% respectively The B° branching ratio limits are the first such limits obtained I n t r o d u c t i o n Searches for rare decays o f B hadrons at LEE with branching ratios o f O ( - - - ) , are now becoming feasible with the large statistics available Such rare processes include decays o f B hadrons into final states which not contain a charmed quark In the Standard Model [ ], these decays can occur through Cabibbo suppressed b ~ u transitions [2] or through one loop diagrams, such as penguin diagrams, which involve a virtual W ± boson and a heavy quark [3] In addition, penguin decays offer a unique window to probe new physics beyond the Standard Model For example, theories with two Higgs doublets contain new diagrams with a charged Higgs boson that add constructively to the W + boson loop diagram [3,4] Also, in the minimal supersymmetric extension o f the Standard Model there could be contributions from superpartners that affect the decay rates [ 3,5 ] l Also at TRIUME Vancouver, Canada V6T 2A3 This paper describes the search for rare hadronic decays of the B ° and Bs° mesons in the exclusive decay channels B o ~ ~'+¢r-, B ~ K+Tr - , B ~ ~ + K and B ° ~ K + K - using approximately two million hadronic Z ° decays collected by the OPAL experiment between 1990 and 1993, The exclusive decays B ~ ~r+~ - , B ° ~ K+Tr - , B ° -* 7r+K - and B ° K + K - are illustrated in Fig The hadronic penguin contribution to the decay rates, which is proportional to the mass o f the heaviest quark in the loop, is expected to be significant [6] and should dominate for the decays B ° ~ K+Tr - and B ° ~ K + K - where the tree level contribution is strongly Cabibbo suppressed The current theoretical prediction for the exclusive decay rates, Br (B ° ~ 7r+Tr-), Br (B ° ~ K + o r - ) , Br (B° *Tr+K - ) and Br (Bs° -~K+K- ) is ,-~ ( 2) x 10 -5 for a top quark mass in the range ,,~ 100200 G e V / c [7] Throughout this paper the charge conjugate processes are also implied OPAL Collaboration/Physics Letters B 337 (1994) 393-404 396 U B3 d , U ~+'K+ /,d,~ 7r + , K + • B° - d s fi p It K_ S b) W+ d • W+ u rr+, K+ d ~r c) u S P • 7r+, K+ d) Fig Diagrams contributing to a) the tree level B~ *~r+cr- and B° -~K+~r- decays, b) the tree level Bs° *Ir+K- and Bs° -,K+Kdecays, c) the badronic penguin B° *lr+Ir - and B~ -*K+~r- decays and d) the hadronic penguin Bs° -,~r+K- and B° -*K+K - decays The C L E O experiment at the e+e - collider CESR, running at the Y ( S ) centre-of-mass energy, has recently reported results from a search for the exclusive decays B ° ~ ~r+cr - and B ° -~K+vr - [8] The 90% confidence level upper limits obtained for the branching ratios are Br (B° *~r+~r - ) < 2.9 x 10 -5 and Br (B° *K+cr - ) < 2.6 x 10 -5 They have also reported an observation o f charmless hadronic B decays in the combined decay channels and have measured the branching ratio Br (B° -, ~ r + r r - ) + Br (B° ~ K+Tr - ) +0.8 = (2.4_o dz 0.2) x 10 -5 The result they obtain indicates that the decay rate is at the level predicted by the Standard Model The mixture o f B hadrons available at the centreof-mass energy x f i ~ Mz provides an opportunity to study rare decays o f B hadrons, in particular those of the B ° meson, not available at the Y (4S) centreof-mass energy A search for the rare decays B ° -, ~ + ~ - - , B ° + K + ~ ' - , Bs° -+~r+ K - and Bs° + K + K at LEP is important for several reasons Observations o f this type would provide supporting evidence that the C K M matrix element IVub[ is non zero [9] In addition, a measurement of the exclusive branching ratios would provide a method to extract the relative amount of penguin decays and constrain the angle y in the C K M unitarity triangle [7,10] Moreover, it has been proposed to use the decay B ° ~ ¢r+~- - , at future colliders such as the L H C and the SLAC B factory, in order to measure the CP violation asymmetry and to extract the angle ot in the C K M unitarity triangle [ 11,12] A thorough understanding o f the effects of penguin diagrams is important here because the penguin contributions could dilute the measured asymmetry and reduce the 'CP reach' o f these experiments Event selection The OPAL detector has been described in detail elsewhere [13] Charged particles are tracked in central detector situated inside a solenoidal coil witt a uniform magnetic field of 0.435 T The central de tector elements used in this analysis consist o f a sil icon microvertex detector [ 14], a vertex drift cham ber, a large volume jet drift chamber, and drift cham OPAL Collaboration/Physics Letters B 337 (1994) 393-404 bers that measure the z coordinate of tracks as they leave the jet chamber The coil is surrounded by an array of time-of-flight counters and a lead glass electromagnetic calorimeter and presampler, divided into a cylindrical barrel and endcaps Outside the electromagnetic calorimeter is the return yoke of the magnet which forms the hadron calorimeter and beyond this are the muon chambers Multihadronic Z ° decays are selected using the criteria described in Ref [ 15] In order to reduce background from Z° decays to tau pairs to a negligible level, events are also required to contain at least seven charged tracks passing minimal quality requirements The total number of multihadronic Z ° decays used in this analysis is 1.92 million events, for which a selection efficiency of 98.2% has been determined The thrust axis direction of each event is computed using good charged tracks and neutral clusters that are reconstructed in the electromagnetic calorimeter but not associated to charged tracks The event is divided into two hemispheres perpendicular to the thrust axis direction The average intersection point, or beam spot, of the LEP beams in the x - y plane is determined for each LEP fill and, statistics allowing, several times within a fill, using charged tracks from both multihadronic and leptonic decays of the Z ° [ 16 ] The average beam spot precision in the x coordinate is 15/zm and in the y coordinate is 10/~m The intrinsic width of the beam spot in the vertical direction is taken to be 8/~m, from considerations of the LEP beam optics The width in the horizontal direction, which is measured directly, is between 100/zm and 160/xm, depending on the beam optics A primary vertex for each event is reconstructed using a X minimization method and incorporates the average beam spot position as a constraint in the vertex fit The impact parameter resolution in the x - y plane achieved for 45 GeV/c muon pairs is ,,~ 18/~m for tracks with associated hits in both layers of the silicon microvertex detector Due to the effects of multiple scattering, the impact parameter resolution degrades to ,,~ 40/zm for tracks with momenta of 3The coordinate system is defined so that the z axis is in the direction of the electron beam, the x axis is horizontal and points approximately towards the centre of the LEP ring, and the y axis is nearly vertical The polar and azimuthal angles, and ~b, are defined with respect to the z and x axes, respectively 397 GeV/c Event simulation The Lund parton shower Monte Carlo JETSET 7.3 [17], interfaced to the EURODEC [18] decay package, was used to generate 20 000 Z° ~ bl~ events in which just one of the B hadrons produced was required to decay via one of the exclusive decay modes B ° - 7r+~ - , B ° ~ K+Tr- , Bs° ~ ¢r+K - or B ° ~ K+K - The other B hadron was allowed to decay into any of the default final states defined by EURODEC The events were then passed through the full detector simulation of OPAL [ 19] and the same reconstruction program as used for the data themselves These Monte Carlo events are used to calculate the efficiency of the rare decay selection criteria The fragmentation in the Monte Carlo was performed according to the Peterson scheme [20] where the shape of the fragmentation function depends on a single parameter % The value used in the generation was eb = 0.0057, corresponding to the LEP average measurement for the fraction of energy carried by a B hadron [21 ] In order to simulate various shapes of the fragmentation function, the Monte Carlo events were reweighted according to the z of the parent b quark, where z = Ehadron/EavaJlableand Eavailable is the energy available for fragmentation after the parton shower The mass of the BoO meson generated in the Monte Carlo was 5.279 GeV/c [22] The mass oftheBs° meson generated in the Monte Carlo was 5.480 GeV/c 2, consistent with theoretical predictions [ 23 ], but differing from the best available measurement of the B ° meson mass (5.3686 + 0.0056 4- 0.0015) GeV/c [24] The difference between the measured and generated B ° mass is taken into account in the analysis The lifetime of B hadrons generated in the Monte Carlo was 1.4 ps The events were then reweighted to model a neutral B meson lifetime of 1.5 ps which is consistent with the current experimental measurement of the average lifetime from exclusive decays of neutral B mesons [25] An example of an event generated using JETSET 7.3 and containing a rare B hadron decay is shown in Fig On one side of the event a Bs° meson decays at Vertex via the rare decay channel B ° ~ 7r+K - A I ~ is produced in association with the B ° and decays to OPAL Collaboration/Physics Letters B 337 (1994) 393-404 398 7-r+ [,Vertex rtex Vertex I~ ~~+ z 020 I Fig An example of a Monte Carlo event containing a rare Bs° ~ ~r+K - decay at Vertex The average decay length is mm for rare B ° mesons and the typical decay length error is 180/~m The Bs° is produced in association with a K° which decays at Vertex to two charged pions On the other side of the event, a B° decays at Vertex via the decay channel B° -~D*+e-Te, D *+ -,D%r +, and D O -*K*°~r°~r° two charged pions at Vertex On the other side of the event, a B ° decays at Vertex via the decay channel B ° * D*+e-~e, D *+ ~ D°Tr+, and D O~ K*%'°~"° In addition, a total of 0.98 million multihadronic Monte Carlo events, generated using JETSET 7.3 and with a full detector simulation, are used for background studies and to check the analysis method The fraction of hadronic Z° decays to bb, F(Z ° b b ) / F ( Z ° ~ hadrons), used in the generation of the multihadronic Monte Carlo was the Standard Model value of 0.217 [26] and the Lund symmetric fragmentation function [17] was used to describe the hadronization properties of the light quark flavours (u,d and s) while the fragmentation of the c and b quarks was described by the Peterson fragmentation function with input parameters ec = 0.046 and eb = 0.0057 [21,27] The impact parameter, vertex decay length and mass resolutions predicted by the Monte Carlo are known to be better than those actually observed in the data The resolution of the Monte Carlo events was therefore degraded by increasing the difference between the true and the reconstructed values of the transverse track parameters, K, and ~b0 Here, K is the track curvature, is the distance of closest approach of the track to the coordinate origin and q~0 is the azimuthal angle made by the track at the point of closest approach A degredation factor of 1.4 was found appropriate fo] this analysis OPAL Collaboration/Physics Letters 13337 (1994) 393-404 Rare decay selection The rare decay selection criteria are optimized, using the rare decay and multihadronic Monte Carlo event samples, to provide the highest possible significance for the decay channels B ° ~ rr+rr - , B ° , K+rr - , Bs° -+ rr+K - and B ° -+ K+K - The background is mainly combinatorial where one or more tracks come from the fragmentation o f primary quarks All pairs of tracks with opposite charges and in the same thrust hemisphere o f an event are considered as rare decay candidates Each track is required to have a minimum transverse momentum with respect to the beam direction of 150 M e V / c and a polar angle such that [ cos 01 < 0.9 If the tracks traverse the barrel section o f the jet chamber, such that [ cos 0[ < 0.73, they are required to have at least 120 jet chamber hits out of a maximum of 159 This requirement falls linearly with I cos0[, due to the geometry of the jet chamber, from at least 120 hits at I cos01 = 0.73 to at least 40 hits at I cos01 = 0.9 In addition, the impact parameter of each track to the average beam spot, in the transverse plane, is required to be less than mm The radial intersection points of the two tracks are calculated and the distance from the primary vertex to the closest intersection point is required to be less than cm in order to reduce K ° + rr+rr - and A ~ per- decays In order to improve the determination of the polar angle and hence the mass resolution, the two tracks are then refitted using the constraint that they originate from a common three dimensional vertex In order to reduce the combinatorial background, a selection of cuts is chosen that exploits the characteristic decay of the B hadron These cuts are illustrated in Fig 3, for all two track combinations, in which both tracks pass the track quality criteria described above, have a momentum greater than G e V / c and a ¢r+rr - invariant mass greater than G e V / c Due to the hard fragmentation of the b quark, the B hadron carries on average 70% of the beam energy (Fig 3a) Since the B°s meson is pseudo-scalar, its decay products are isotropically distributed in its rest frame, in contrast to the combinatorial background which is observed to peak in the forward and backward directions (Fig 3b) The decay products o f the B hadron tend to have smaller opening angles than the background (Fig 3c) The long lifetime of B hadrons provides a further selection criterion to reduce the combinato- 0.12 ' ' a) ' I ' ' ' I 399 ' • ' ,~ o.o8 ~- 0.1 b) ,~ 0.07 ~ ~0.~ -o II\ / ~" 0.05 ~ - I r 0.06 0.03 0.02 H! : ~~ 0.04 0.02 ~ o.ol 0.4 0.6 0.8 t~, •/ ~ , , -1 , r , ,i -0,5 i I i ,I ~oa~ 0.25 F c) , , ~ ~ 7~ , , 0.5 cos(O*) X E ~,,, 1:: d) , 0.15 10" 0.1 10 , 0.05 0 (radians) 10" -20 -10 10 20 L/~L Fig A comparison of a) xE, where xe = Ehadron/Ebeam, b) cos(8*), where 0* is the angle between the B hadron direction and the positively charged track in the centre-of-massof the d e c a y i n g B hadron, c) ¢,, the three dimensional o p e n i n g a n g l e between the two tracks, and, d) L/O-L, where L is the two dimensional decay length and o-L is its error; for data (points) and multihadronic Monte Carlo (solid lines) for all two track combinations The distributions for the rare decay Monte Carlo (dotted lines) are for tracks which originate from the rare decay of a B hadron The arrows indicate the values of the selection cuts rial background (Fig 3d) Therefore, candidates are required to have - XE > 0.6, where xe = Ehadron/Ebeam and Ehadron is the energy of the candidate B hadron assuming the two tracks are pions and Ebeam is the beam energy, - [cos(0*) I < 0.75, where 0* is the angle between the B hadron direction and the positively charged track in the centre-of-mass o f the decaying B hadron, - ~p < 0.5, where ~p is the three dimensional opening angle in radians between the two tracks, and, L / o ' c > 2.0, where L is the two dimensional decay length and o'L is its error L is calculated from the distance between the average beam spot and the intersection point of the two tracks and is signed such that it is positive if the angle between the B hadron momentum vector and the vector from the beam spot to the intersection point is less than 90 ° , otherwise it is negative The background rejection factors and efficiencies o f - 400 O P A L C o l l a b o r a t i o n / P h y s i c s Letters B 337 (1994) 393 404 Table The background rejection factors and efficiencies of the individual xE, ] c o s ( * ) ] , ff and L/O'L cuts The total corresponds to the effect of applying the cuts simultaneously Errors are statistical only Cut Background rejection factor Efficiency (%) xe > 0.6 I cos(0*)l < 0.75 ~b < 0.5 L/O'L > 2.0 2.5 4- 0.l 1.44-0.1 1.5 4- 0,1 4.0-[-0.2 89,5 q- 0.4 91.94-0.3 98.6 4- 0.2 83.64-0.1 ~ 1400 7ai ' ' ~ ~ 1200 -M=S.282.~.O02 : ~ = 0.137"20.002 £ ~ ~ t~ 141.9 4- 8.8 56.7 4- 0.5 the xzr, I cos(0*) I, ~/' and L/trL cuts are summarized in Table The background rejection factor is estimated from the data and the efficiency is calculated from the rare decay Monte Carlo for each o f the cuts in question and after all other cuts described above have been applied Particle identification is achieved using measurements o f dE/dx in the jet chamber [28] Both tracks are required to have at least 20 separate dE/dx measurement points and to have a momentum greater than G e V / c in order to avoid the region where the mean dE/dx values for kaons and pions coincide It is hypothesized that each pair of tracks is a 7r+~r - , 7r+K or K + K - combination For each track, the measured dE/dx is compared to that expected for all possible mass assignments and a probability assigned to each Tracks are considered as pion candidates if the probability for the pion mass assignment exceeds 1% and as kaon candidates if the probability for the kaon mass assignment exceeds 7% The invariant mass of each pair of tracks is then calculated, for each decay channel, using the relevant pion and kaon mass assignments Each pair of tracks is selected as a Bd° ~ • r+rr - (K+~r - ) candidate if the ~ + ¢ r - (K+rr - ) invariant mass lies between 5.1 G e V / c and 5.5 G e V / c and as a Bs° ~ ~ r + K - ( K + K - ) candidate if the rr+K - ( K + K - ) invariant mass lies between 5.2 G e V / c and 5.6 G e V / c Fig shows the invariant mass distributions for the B ° ~ ar+~r - , B ° ~ K+Tr - , Bs° -, ~r+K - and Bs° -, K + K - Monte Carlo events Shown on the figure are the results of Gaussian fits to the invariant mass distributions The mass resolutions obtained are ,~140150 M e V / c In order to calculate the Bs° + ~r+K - m 350 ,,,1~11 5.5 xữrt"Mass (GeV/Âz) ,, Âi i i 04 4.5 $ 5.5 ~6 x*K"Mass (GeV/c) ~ 400 % , , , 350 7M = 5.479~.003 30O : o = 0.137:i'0.004 ~ 2"~ 3oo :"M= 5.472_+0.004 "o = 0.152~.004 ~ : M = 5.280-20.002 -o = 0.151-20.003 ~ 200 2OO Total 1200 150 50 4.5 5.5 n*IC Mass (GeVIc2) 50 4.5 5.5 26 K+K" Mass (GeV/c) Fig The ~ ' + ~ r - , 7r+K - and K + K - invariant mass distributions for pairs of tracks originating from Monte Carlo rare decays of B hadrons and satisfying all selection criteria in the exclusive decay channels a) B ° ~ ÷ ~ , - , b) B° .K÷~r - , c) 8° .~+K - and d) Bs° -,K+K - The curves are the result of a Gaussian fit and Bs° , K + K - efficiencies, the B ° meson mass window is centered around the Bs° meson mass generated in the Monte Carlo The number of rare decay Monte Carlo events generated in each exclusive decay channel, the number accepted after all the above cuts have been applied and the corresponding efficiencies are given in Table 4.1 Efficiency systematic error The evaluation of the possible systematic uncertainties on the calculation of the rare decay selection efficiencies is described in this section, and the resulting systematic errors are given in Table The systematic error due to the uncertainty in the dE/dx calibration has been checked using pions from Ks° ~ ~r+~r - decays and kaons from dp~K+K - decays, resulting in an error of 4-1.1% For the other systematic errors, the efficiency is recalculated when the source of uncertainty is varied by the amount described below The systematic error due to the modelling of the b quark fragmentation is estimated by varying the mean xE ot the b quark in the range (XE)b = 0.704-0.02 and corresponds to varying eb between 0.0025 and 0.0095 [ I ] OPAL Collaboration ~PhysicsLettersB 337 (1994) 393-404 401 Table Efficiency of the rare decay selection criteria The B° and Bs° decay channels include the charge conjugate B° and Bs° decays respectively The first error is the statistical error and the second error is the systematic error Decay channel Number of events generated Number of events accepted Efficiency (%) B° -*~r+Tr - 7669 7706 2298 2327 1867 1774 526 456 24.3 4- 0.5-4- 1.8 23.0 4- 0.5 4- 1.6 22.9 4- 0.9 4- 1.9 19.6 4- 0.8 4- 1.4 Bd0 ~ K+~"B° *~+K B° -*K+K- Table Systematic errors on the determination of the B° *Tr+~- - , B° ~K+~"-, Bs° -*~+K- and BsO -~K+K- efficiencies Effect on efficiency (%) Source s Bo .K+x- dE/dx Fragmentation B Hadron Lifetime Resolution Beam spot -4-1.1 4-0.8 :t:0.2 4-1.1 -0.3 4-1.1 4-0.6 4-0.2 4-1.0 -0.2 4-1.1 4-0.8 4-0.3 4-1.2 -0.2 4-1.1 4-0.4 4-0.1 4-0.7 -0.I Total (Added in quadrature) 4-1.8 4-1.6 4-1.9 4-1.4 A multi-parameter fit to the OPAL single and dilepton data yielded a value o f (XE)b = 0.697 4- 0.01 40.006 [ ] , and includes a systematic error arising from different choices o f fragmentation model Since xE is calculated assuming both tracks are pions, the systematic error due to the modelling o f the b quark fragmentation varies among decay channels The lifetime o f the B ° meson is varied by ± I ps and the lifetime o f the Bs° meson is varied by 4-0.2 ps, the variations corresponding to the current experimental uncertainties [25] In order to estimate the effect o f the difference between the impact parameter, vertex decay length and mass resolutions predicted by the Monte Carlo and those observed in the data, the degradation factor used for the Monte Carlo track parameters is varied between 1.2 and 1.6 In addition, to check for any bias in the decay length, the efficiency is recalculated using the primary event vertex instead o f the average beam spot position The systematic error due to the experimental uncertainty o f the B ° meson mass is negligible Results After all selection criteria 15 events remain in the data sample Since the d E / d x criteria are not exclusive, each o f these events can fall into more than one rare decay category The number o f rare decay candidates in each channel is given in Table The combinatorial background is estimated from the shape o f the invariant mass distributions in the data These are shown in Figs and A function o f the form f ( M ) = exp ( a + b × M ) , where M is the invariant mass for a particular decay channel and a and b are free parameters, is fitted to the invariant mass distributions in the mass range 4.4 G e V / c to G e V / c and excluding the chosen mass windows The results o f the fits are shown in Figs and 6, where the dotted lines correspond to the standard deviation errors on the fit parameterization The results are insensitive to the exact form of parameterization chosen, provided a reasonable fit to the data is obtained As a consistency check, the total number o f background events is estimated using the multihadronic Monte Carlo event OPAL Collaboration / Physics Letters B 337 (1994) 393 404 402 ,= 20 ' ' I ' ' ' I ' ' ' ] ' ' ' I ' ' ' I ' a) 18 ' i ' ' ' I ' Table Number of rare decay candidates and background events predicted from the fit after all cuts, The number of candidates in the B ° and ' f(M)=exp(a+b*M) ~ z6 ~ ' a = 10~ _+1.9 b = -1.8-+0.4 Bs° rare decay channels include the charge conjugate B ° and Bs° decays respectively 12 ~ ~ ~ Decay channel 4., 4.6 20 ~_b-), "~ 18 , 4.8 , , , $ 5.2 , , , 5.4 , , , , ' 16 _ [., [ "',, 5.6 5.8 rt+x"Mass (GeV/cz) , ' ' I ' ' ' , ' f(M)=exp(a+b*M) a = 9.9-+1.5 b ffi-1 6:=0.3 ' Number of rare decay candidates Number of b a c k g r o u n d events B] ~ 7r+~r - 10.7 4- 2.5 B0d -+K + q r - 13 14.44-2.6 B0 -+7r+K - 11 12.44-2.7 B~ -~K + K - - 1.9 14 " 12 i g ? - ",, - -"" " , t 4.6 4.4 4.8 5.2 5.4 5.6 5.8 26 n+K" Mass (GeV/c) Fig The invariant mass distributions for the OPAL data in the decay channels a) B * 7r+~r - and b) B * cr+K - The solid lines are the result of the fit to the combinatorial background, the arrows indicate the mass range 5.1 G e V / c to 5,5 G e V / c which is excluded from the fit, and the dotted lines are the standard deviation errors on the background %"~ 18 16 ~ ~ "12:: ~ 10 " j I I ' ~ I l ' I [ l I I l I [ I l I [ ' l I I -a) f(M)=exp(a+b*M) " a = 9.9 ~'I', [ ~" ",, [ ~1.6 b=-1.6:~-0.3 "-, L l ~ l sample After all selection criteria, 19.6 + 6.2 events are expected which is consistent with the 15 events observed in the data The products of the fractions of B ° and B ° mesons produced during fragmentation and the exclusive branching ratios are calculated assuming the Standard Model value of F(Z ° ~ b b ) / F ( Z ° ~ hadrons) = 0.217 [26] Upper limits are obtained by subtracting the number of background events from the number of candidates and adding all errors in quadrature before calculating the 90% confidence level limit In the case that the background estimation exceeds the number of rare decay candidates, the upper limits are estimated by normalizing the probability distribution inside the physical region [22] The 90% confidence level limits obtained are °) • B r 4.4 4.6 10 ' '~ ' i 4.8 ' ' ' i , , , i 5.2 , ' , i 5.4 , , ' t b) 5.6 5.8 7t÷K"Mass (GeV/ez) , , , t , , , i ' 4.~ 4.6 4.8 5.2 5.4 5.6 5.8 , f ( I ~ B ° ) • Br (B° ~ K + T r - ) < 3.2 × 10 -s, f (6 +B °) • Br (Bs° + K+K - ) < 1.6 x 10 -5, 10 f (13 -+B°) Br (Bs° -~Tr+K- ) < x 10 -5, , f(M)ffiexp(a+b*M) a = 4.7 :rr.2A b = -0.8-+0.5 t5 ~ - ) < 1.9× 26 K+K" Mass (GeV/c) Fig 6, The invariant mass distributions for the OPAL data in the decay channels a) B ~ ~r+K - and b) B ~ K + K - The solid lines are the result o f the fit to the combinatorial background, the arrows indicate the mass range G e V / c to G e V / c which is excluded from the fit, and the dotted lines are the standard deviation errors on the background where f (b ~ B °) and f (b + B °) are the fraction of B ° and Bs° mesons produced during fragmentation In order to extract the exclusive branching ratios for the B ° and B ° mesons separately, estimates are needed for the B ° and Bs° production rates during fragmentation Therefore, assuming relative production rates during fragmentation for ufi : dd : sg : diquarks of 1.0 : 1.0 : 0.3 : 0.23 [ 17], consistent with the measured yield of hadrons of various flavours in e+e annihilation at lower energies and at LEP [ 30], gives f (b ~B °) = 39.5% and f (13 -*B°) = 12% Hence, OPAL Collaboration /Physics Letters B 337 (1994) 393 404 the 90% confidence level upper limits on the B ° branching ratios are Br (B° -~Tr+¢r - ) < x I0 -5, Br(B°d -~K+~- - ) < 8.1 x 10 -5 , and on the Bs° branching ratios are, Br (B° -~zr+K- ) < 2.6 x 10 - , Br (Bs° ~K+K - ) < 1.4 x l -4 Conclusions A search has been made for the rare decays of B ° and Bs° mesons to two charged particles in the exclusive decay channels B ° -,¢r+or-, B ° ~ K + zr-, B ° ¢r+K - and Bs° 7-4 K+K - No excess of events has been seen after all selection cuts in the invariant mass distributions and upper limits on the B ] branching ratios, Br (B° -*'rr+zr- ) < 4.7 × - ' , 403 National Science Foundation, USA, Texas National Research Laboratory Commission, USA, Particle Physics and Astronomy Research Council, UK, Natural Sciences and Engineering Research Council, Canada, Fussefeld Foundation, Israeli Ministry of Energy and Ministry of Science, Minerva Gesellschaft, Japanese Ministry of Education, Science and Culture (the Monbusho) and a grant under the Monbusho International Science Research Program, German Israeli Bi-national Science Foundation (GIF), Direction des Sciences de la Mati~re du Commissariat l'Energie Atomique, France, Bundesministerium fiir Forschung und Technologie, Germany, National Research Council of Canada, A.E Sloan Foundation and Junta Nacional de Investigaq~o Cientffica e Tecnol6gica, Portugal Br (B° -~K+zr- ) < 8.1 x 10 -5, and on the B ° branching ratios, References Br (B° -~'n'+K- ) < 2.6 x 10 -4, B r ( B ° - - , K + K - ) < 1.4 × 10 -4 , have been set at the 90% confidence level These limits assume that the ratio of the partial decay widths of the Z °, F ( Z ° ~ b b ) / F ( Z ° ~ hadrons), is 0.217 and that the fractions of B ° and B ° mesons produced during fragmentation are 39.5% and 12% respectively These are the first limits set on the above branching ratios for the rare decay of the B ° meson Acknowledgements Useful comments from D Wyler are gratefully acknowledged It is a pleasure to thank the SL Division for the efficient operation of the LEP accelerator, the precise information on the absolute energy, and their continuing close cooperation with our experimental group In addition to the support staff at our own institutions we are pleased to acknowledge the Department of Energy, USA, [1] S.L Glashow, Nucl Phys B 22 (1961) 579; S Weinberg, Phys Rev Lett 19 (1967) 1264; A Salam, in Proc of the 8th Nobel Symp 367, ed N Svartholm, Almqvist and Wiksell, Stockholm, 1968; S.L Glashow, I lliopoulos, L 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University, Ithaca, August 1993 [26] D Bardin et al., ZFI'Iq'ER, An Analytical Program for Fermion Pair Production in e+e - Annihilation, CERNTH.6443/92 For this prediction, the Z°, top quark and Higgs masses are Mz = 91.18GeV/c 2, Mtop = 150GeV/c and Mltiggs = 300GeV/c 2, and as = 0.12 [27] OPAL Collaboration, Phys Lett B 262 (1991) 341 [28] M Hauschild et al., Nucl Inst and Meth A 314 (1992) 74 [29] OPAL Collaboration, Z Phys C 60 (1993) 199 [30] For the s~ fraction at LEP see: OPAL Collaboration, Phys Lett B 264 (1991) 467; DELPHI Collaboration, Phys Lett B 275 (1992) 231 For reviews see: T Sjtstrand et al., in Z physics at LEP 1, ed G Altarelli et al., CERN 89-08, Vol (1989) 143; D.H Saxon, Quark and Gluon Fragmentation in High Energy e+e - Annihilation, RAL-86-057  ... limits obtained I n t r o d u c t i o n Searches for rare decays o f B hadrons at LEE with branching ratios o f O ( - - - ) , are now becoming feasible with the large statistics available Such rare. .. level B~ *~r+cr- and B -~K+~r- decays, b) the tree level Bs° *Ir+K- and Bs° -,K+Kdecays, c) the badronic penguin B *lr+Ir - and B~ -*K+~r- decays and d) the hadronic penguin Bs° -,~r+K- and B ... for the B ° and B ° mesons separately, estimates are needed for the B ° and Bs° production rates during fragmentation Therefore, assuming relative production rates during fragmentation for ufi