Measurement of the absolute branching ratio of the K + → π + π − π + (γ) decay with the KLOE detector
aa r X i v : . [ h e p - e x ] S e p Measurement of the absolute branching ratioof the K + → π + π − π + ( γ ) decay with the KLOEdetector The KLOE/KLOE-2 CollaborationD. Babusci h , I. Balwierz-Pytko g , G. Bencivenni h , C. Bloise h ,F. Bossi h , P. Branchini r , A. Budano q , r ,L. Caldeira Balkest˚ahl u , F. Ceradini q , r , P. Ciambrone h ,F. Curciarello i , d , E. Czerwi´nski g , E. Dan`e h , V. De Leo i , d ,E. De Lucia h , G. De Robertis b , A. De Santis h ,P. De Simone h , ∗ , A. Di Cicco q , r , A. Di Domenico m , n ,R. Di Salvo p , D. Domenici h , O. Erriquez a , b , G. Fanizzi a , b ,A. Fantini o , p , G. Felici h , S. Fiore s , n , P. Franzini m , n , A. Gajos g ,P. Gauzzi m , n , G. Giardina i , d , S. Giovannella h , E. Graziani r ,F. Happacher h , L. Heijkenskj¨old u B. H¨oistad u , T. Johansson u ,D. Kami´nska g , W. Krzemien g , A. Kupsc u , J. Lee-Franzini h , t ,F. Loddo b , S. Loffredo q , r , G. Mandaglio i , d , c , M. Martemianov j ,M. Martini h ,ℓ , M. Mascolo o , p , R. Messi o , p , S. Miscetti h ,G. Morello h , D. Moricciani p , P. Moskal g , A. Palladino h ,A. Passeri r , V. Patera k , h , I. Prado Longhi q , r , A. Ranieri b ,P. Santangelo h , I. Sarra h , M. Schioppa e , f , B. Sciascia h ,M. Silarski g , L. Tortora r , G. Venanzoni h , W. Wi´slicki v ,M. Wolke u a Dipartimento di Fisica dell’Universit`a di Bari, Bari, Italy. b INFN Sezione di Bari, Bari, Italy. c Centro Siciliano di Fisica Nucleare e Struttura della Materia, Catania, Italy. d INFN Sezione di Catania, Catania, Italy. e Dipartimento di Fisica dell’Universit`a della Calabria, Cosenza, Italy. f INFN Gruppo collegato di Cosenza, Cosenza, Italy. g Institute of Physics, Jagiellonian University, Cracow, Poland. h Laboratori Nazionali di Frascati dell’INFN, Frascati, Italy. i Dipartimento di Fisica e Scienze della Terra dell’Universit`a di Messina, Messina,Italy.
Preprint submitted to Physics Letters B 10 August 2018
Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia. k Dipartimento di Scienze di Base ed Applicate per l’Ingegneria dell’Universit`a“Sapienza”, Roma, Italy. ℓ Dipartimento di Scienze e Tecnologie applicate, Universit`a “Guglielmo Marconi”,Roma, Italy. m Dipartimento di Fisica dell’Universit`a “Sapienza”, Roma, Italy. n INFN Sezione di Roma, Roma, Italy. o Dipartimento di Fisica dell’Universit`a “Tor Vergata”, Roma, Italy. p INFN Sezione di Roma Tor Vergata, Roma, Italy. q Dipartimento di Matematica e Fisica dell’Universit`a “Roma Tre”, Roma, Italy. r INFN Sezione di Roma Tre, Roma, Italy. s ENEA UTTMAT-IRR, Casaccia R.C., Roma, Italy t Physics Department, State University of New York at Stony Brook, USA. u Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden. v National Centre for Nuclear Research, Warsaw, Poland.
Abstract
The absolute branching ratio of the K + → π + π − π + ( γ ) decay, inclusive of final-stateradiation, has been measured using ∼
17 million tagged K + mesons collected withthe KLOE detector at DAΦNE, the Frascati φ -factory. The result is: BR ( K + → π + π − π + ( γ )) = 0 . ± . stat ± . syst a factor ≃ Key words: e + e − Experiments, Kaon decays
PACS:
The measurement of the branching ratio (BR) of K + → π + π − π + ( γ ) decaycompletes the KLOE program of precision measurements of the dominantkaon branching ratios, fully inclusive of radiation effects. We have alreadypublished an evaluation, from a fit to the KLOE measurements of the charged ∗ Corresponding author.
Email address: [email protected] K ± → π ± π + π − ) = (5 . ± . K ± → π ± π + π − ) measurement, based on 2330 events from a sample of ∼ kaondecays, dates back to 1972 and gives no information on the radiation cut-off : BR( K ± → π ± π + π − ) = (5 . ± . K ± → π ± π + π − ) = (5 . ± . K ± → π ± π + π − ) measurements but the ratemeasurement Γ( π + π + π − ) = (4 . ± . × s − published in 1970 [8].Furthermore the BR( K ± → π ± π + π − ) value enters in the evaluation of thedifference a − a between the I = 0 and I = 2 S -wave ππ scattering lengths[16] [19]; this will be discussed in section 5.In the following we report the measurement of the absolute branching ratioBR( K + → π + π − π + ( γ )) performed with the KLOE detector using data corre-sponding to an integrated luminosity R L dt ≃
174 pb − collected at DAΦNE,the Frascati φ -factory[9]. DAΦNE is an e + e − collider operated at the energyof 1020 MeV, the mass of the φ -meson. The beams collide at the interactionpoint (IP) with a crossing angle θ x ≃
25 mrad , producing φ -mesons with asmall momentum of ∼ . φ -mesons decayin anti-collinear and monochromatic neutral (34%) and charged (49%) kaonpairs. The unique feature of a φ -factory is the tagging: detection of a K ± (the tagging kaon) tags the presence of a K ∓ (the tagged kaon) with knownmomentum and direction. The availability of tagged kaons enables the preci-sion measurement of absolute BRs providing the normalization sample. Thedecay products of the K + K − pair define two spatially well separated regionscalled in the following the tag and the signal hemispheres. The KLOE detector consists of a large cylindrical drift chamber (DC) [10],surrounded by a lead scintillating fiber electromagnetic calorimeter (EMC) [11]both immersed in an axial 0.52 T magnetic field produced by a supercondu-cting coil. At the beams IP the spherical beam pipe of 10 cm radius is madeof a beryllium-aluminum alloy of 0.5 mm thickness.The DC tracking system has 25 cm internal radius, 4 m diameter and 3.3m length, with a total of ∼ ∼ K L regeneration, and to maximize the detection efficiency for low energyphotons, the DC works with a helium-based gas mixture and its walls are We use left-handed coordinates system with the z -axis defined as the bisectrix ofthe e + e − beams and the y -axis vertical. σ xy ≃ µ m and σ z ≃ σ ( p T ) /p T ≤ . σ E /E = 5.7% / q E (GeV) , σ z = 1.2 cm/ q E (GeV) , σ φ = 1.2 cm, and σ t =57 ps / q E (GeV) ⊕
100 ps. Energy clusters not associated with reconstructedtracks in the DC (neutral clusters) identify neutral particles. The definitionof energy clusters associated with reconstructed tracks is related to the track-to-cluster association procedure described in Ref. [12].The trigger [13] is based on energy deposits in the calorimeter and on hitmultiplicity in the drift chamber. Only events triggered by the calorimeter havebeen used in the present analysis. The trigger system includes a second-levelveto for cosmic-ray muons (cosmic-ray veto or CRV) based on energy depositsin the outermost layers of the calorimeter and followed by a third-level softwaretrigger. A software filter (SF), based on the topology and multiplicity of energyclusters and drift chamber hits, is applied to filter out machine background.Both CRV and SF may be sources of events loss. Their effect on the BRmeasurement has been studied on control data samples acquired respectivelywithout the CRV and the SF filters.The data sample used for this analysis has been processed and filtered with theKLOE standard reconstruction software and the event classification procedure[12]. The KLOE monte carlo (MC) simulation package, GEANFI, has beenused to produce a sample equivalent to data, accounting for the detector statusand the machine operation on a run-by-run basis.
Tagging with K ± → µ ± ν ( γ ) ( K µ tags) and K ± → π ± π ( γ ) ( K π tags)provides two indipendent samples of pure kaons for the signal selection usefulfor systematic uncertainties evaluation and cross-checks [3]. These decays areeasily identified as clear peaks in the distribution of p ∗ m π , the momentum ofthe charged secondary track in the kaon rest frame evaluated using the pionmass . The selection efficiency of the two tagging normalization samples The contribution to the p ∗ m π distribution from K µ decays is slightly broadeneddue to the pion mass hypothesis [3]. φ → K + K − and archived in dedicated data summary tapes, as described in Ref. [12]. MCstudies show that the contamination due to φ -meson decays other than K + K − is negligible.To minimize the impact of the trigger efficiency on the signal side, we chooseas normalization sample K µ or K π tags providing the trigger of the event(self-triggering two-body decays). After this request the K µ sample is reducedby a factor of ∼ K π sample by a factor of ∼ K − asthe tagging kaon ( K µ or K π ) and K + as the tagged kaon (signal), since thenuclear cross section for positive kaons with momenta ≃
100 MeV is lower bya factor of ∼ with respect to that of negative kaons [14].The track of the tagging kaon is backward extrapolated from its first hit inthe DC to the IP. We use the momentum of the tagging kaon at the IP, p IPK − , and the momentum of the φ -meson measured run by run with Bhabhascattering events, p φ , to evaluate the momentum of the tagged kaon at theIP, p IPK + = p φ − p IPK − . Finally we extrapolate p IPK + inside the DC (signal kaonpath).The kaon and the three charged pions from its decay have low momenta, lessthan ∼
200 MeV, and curl up in the KLOE magnetic field; this increasesthe probability to have poorly reconstructed tracks broken in more segments(the track reconstruction procedure in KLOE is described in Ref. [12]). Wesignificantly improve the quality of the reconstruction requiring the K + decayto occur before it reaches the DC sensitive volume, i.e. inside a cylindricalfiducial volume centered at the IP and with a transverse radius ρ xy close tothe DC inner wall (detector acceptance ∼ K + → π + π − π + ( γ ) we fit the missing mass spectrum m miss = E miss − ( p K + − p − p ) where p and p are the momenta of theselected tracks, with MC-predicted shapes for the signal and the background.The branching ratio is given by: BR ( K + → π + π − π + ( γ )) = N K → π N tag × ǫ sel C T B C SF C CRV (1)where N K → π is the number of signal events, N tag is the number of taggedevents and ǫ sel is the overall signal selection efficiency, including the detectoracceptance and the reconstruction efficiency. C SF and C CRV are the correctionsfor the machine background filter and the cosmic-ray veto. C T B accounts for5he tag bias effect. K − µ normalization sample The normalization sample is given by N tag = 12065087 K − µ tagging events.The K + → π + π − π + ( γ ) signal selection uses DC information only.Any reconstructed track identified as a K + (and therefore corresponding to a K + outside the fiducial volume) is rejected. More specifically we reject trackswith the point of closest approach (PCA) to the IP satisfying the conditions q x P CA + y P CA <
10 cm, and | z P CA | <
20 cm, with the momentum within70 < p K <
130 MeV, and with a good matching with the position and themomentum extrapolated from the tagging kaon.To select the decay vertex K + → π + π − π + ( γ ) we require at least two recon-structed tracks that have:(1) momentum in the kaon rest frame, p ∗ m π <
190 MeV, this cut removes thebackground from two-body decays;(2) distance of closest approach (DCA) between each extrapolated track andthe signal kaon path, DCA < < | cos( θ ) | < ρ xy ≤
26 cm.Fig 1 shows the comparison between MC and data missing mass distributionsfor the selected K + decays. We count the number of signal events in themissing mass window 10000 < m miss < , where the signal overbackground ratio is S/B ≃
88 . The background composition is given by K + intwo-body µ + ν and π + π ≃ . π e + ν and π µ + ν ≃ . π + π π ≃ .
4% decays. These single track events pass the selection criteriabecause a secondary charged track is wrongly reconstructed as two separatetracks. The top panel of Fig 2 shows the result of the fit of the missing massdistribution compared to data. The fit gives N K → π = 48032 ±
286 signal events(the error accounting for data and MC statistics), with χ /ndf = 44.8/46(P( χ ) = 0.52). The bottom panel of Fig 2 shows the fit normalized residuals.The signal selection efficiency, ǫ sel , is related to the track reconstruction effi-ciency of two charged secondaries from K + decays. We evaluate the selectionefficiency from MC, and then we correct it to take into account data-MC dif-ferences in the track reconstruction. To this aim we select, both on data andMC, a control sample of K + → π − X decays (for signal events X correspondsto π + π + ). The first requirement is the presence of a self-triggering K − µ in6 ata- - - - MC signal + background. . . . . MC background Fig. 1. MC (dashed) and data (points) missing mass spectrum of the selected events.The arrows show the missing mass window for signal counting. -50 -40 -30 -20 -10 0 10 20 30 40 50 data_____ fit outputnormalized residuals -6-4-20246 -50 -40 -30 -20 -10 0 10 20 30 40 50 Fig. 2. Top plot: fit of the missing mass spectrum superimposed with data points.Bottom plot: residuals between the output of the fit and data distribution norma-lized to their errors. the tag hemisphere. Then the track of the π − candidate is selected with thefollowing requirements:(1) the number of neutral clusters with an energy E γ ≥
30 MeV must be,N clusters ≤
1; 7 able 1Corrections to BR( K + → π + π + π − ( γ )) measurement. The events selected by thetwo tags have different topologies in the KLOE detector determining different cor-rections factors. Table of corrections K − µ tags K − π tagscosmic ray veto correction C CRV ± ± C SF ± ± C T B ± ± (2) the momentum of the selected track in the kaon rest frame must be,p ∗ m π ≤
130 MeV;(3) the distance of closest approach between the extrapolated track and thesignal kaon path must be, DCA π − < θ Kπ ) ≤ -0.85.The control sample K + → π − X , selected with a background contaminationof ≃ p TX , and of the total longitudinal momentum p LX of the π + π + pair (the average efficiency correction is ∼ ǫ sel = 0.0842 ± C CRV and C SF have been measured with data taken withoutthe cosmic-ray veto and the software filter, respectively. The correction for thetag bias, C T B , has been evaluated using MC. All correction values are reportedin Table 1.
Table 2Summary table of the fractional statistical uncertainties.
Source of statistical uncertainties K − µ tags (%) K − π tags (%)signal counting 0.45 0.70selection efficiency 0.38 0.60tag bias 0.11 0.18software filter 0.13 0.05cosmic ray veto 0.002 0.0005Total fractional statistical uncertainty 0.62 0.95 The summary of the fractional statistical uncertainties is reported in Table 2.The total statistical fractional uncertainty on the branching ratio measurementis 0 . .2 BR measurement with the K − π normalization sample The normalization sample is given by N tag = 5171239 K − π tagging events.The signal selection described in sub-section is also applied to the sam-ple tagged by K − π decays. The fit to the missing mass spectrum of the se-lected events gives N K → π = 20,063 ±
186 signal events with χ /ndf = 42.9/45(P( χ ) = 0.56). The signal over background ratio in the missing mass window10000 < m miss < is evaluated with MC: S/B ≃ K + → π − X tagged by K − µ events. The selection efficiency forsignal events tagged by K − π events, is: ǫ sel = 0 . ± . K − π tagging sample is 0 . The following sources of systematic uncertainties on the branching ratios mea-sured using both tags, K − µ and K − π , have been considered:(1) the cuts used to select the signal sample;(2) the fiducial volume;(3) the cuts used to select the control sample K + → π − X ;(4) the cuts used to select the tagging samples K − µ and K − π ;(5) the charged kaon lifetime.The corresponding systematic uncertainties are listed in Table 3.The contributions to the systematic error due to points (1), (2), and (3) havebeen evaluated varying the selection cuts. The DCA, DCA variables and thefiducial volume ρ xy have been varied within few sigmas, the cuts on cos( θ ),p ∗ m π and m miss have been varied to decrease the S/B ratio to ≃
64. The cutsused to select the control sample K + → π − X have been varied to increase thebackground contamination up to ≃ C T B variation on the BR measurements. This hasbeen done modifying the selection of the data and MC normalization sam-ples adding a cut on the opening angle between the K − track and the se-condary track retaining events with cos( θ Kt ) ≥
0, where t is the µ − ( π − )9 able 3Summary table of the fractional systematic uncertainties. Source of systematic uncertainties K − µ tags (%) K − π tags (%)DCA, DCA , cos( θ ) cuts 0.52 0.41p ∗ m π cut 0.08 0.11m miss cut 0.05 0.14fiducial volume 0.11 0.10selection efficiency estimate 0.16 0.16tag bias 0.16 0.32 K ± lifetime 0.12 0.12Total fractional systematic uncertainty 0.60 0.59 track in case of the K − µ ( K − π ) sample. Using MC we found that the fractio-nal variations of the tag bias corrections are δC T B /C T B ( K − µ ) = 0 .
26% and δC T B /C T B ( K − π ) = 0 . δBR/BR ( K − µ ) = 0 .
32% and δBR/BR ( K − π ) = 0 . K + → π + π + π − ( γ )) depends on the charged kaon lifetime τ K ± throughthe detector acceptance, that is evaluated with MC simulation (point (5)). Thesystematic effect has been obtained varying τ K ± within the uncertainty of theKLOE result τ K ± = 12 . ± .
030 ns [1]. This has been done re-weighting theMC events with a hit-or-miss procedure, both for the signal and the controlsample selection procedures. The corresponding sistematic errors are listed inTable 3.The analysis is fully inclusive of radiative decays. Only the efficiency evaluationcould be affected by a systematic uncertanty due to the cut N clusters ≤ . ). We have used PHOTOS [15] to evaluate such an effect andwe obtained a negligible contribution, being O (10 − ) the fraction of decaysremoved by the cut N clusters ≤ K + undergoing nuclear interactions is negligible, ∼ − , asevaluated using the MC simulation, based on data available in literature [14].Therefore the related systematic uncertainty is negligible.Furthermore we have checked on two independent sub-samples of about 88pb − and 86 pb − that the efficiency corrections and the BR evaluations arenot correlated. 10inally the stability of the measurements with respect to different data takingperiods and conditions has been checked. With a sample of K − → µ − ¯ ν ( γ ) tagging events N tag = 12065087 we found N K → π = 48032 ±
286 signal events. Using equation 1, we obtain the branchingratio: BR ( K + → π + π − π + ( γ )) | T agK µ = 0 . ± . stat ± . syst . (2)With a sample of K − → π − π ( γ ) tagging events N tag = 5171239 we found N K → π = 20063 ±
186 signal events, corresponding to: BR ( K + → π + π − π + ( γ )) | T agK π = 0 . ± . stat ± . syst . (3)Averaging these two results, accounting for correlations, we obtain: BR ( K + → π + π − π + ( γ )) = 0 . ± . stat ± . syst . (4)This absolute branching ratio measurement is fully inclusive of final-state ra-diation and has a 0.72% accuracy, a factor ≃ Table 4Results of the fit: K ± BRs and correlation coefficients.Parameter Value Correlation coefficientsBR( K ± µ ) 0.6372(11)BR( K ± π ) 0.2070(9) 0.55BR( π ± π − π + ) 0.0558(4) -0.23 -0.05BR( K ± e ) 0.0498(5) 0.42 -0.15 0.06BR( K ± µ ) 0.0324(4) -0.39 0.14 -0.05 -0.58BR( π ± π π ) 0.01764(25) -0.13 0.05 -0.02 0.04 -0.04 τ K ± (ns) 12.344(29) 0.20 0.19 -0.14 0.05 -0.04 0.02
11e fit the six largest K ± BRs and the lifetime τ ± K using the KLOE measure-ments of τ K ± [1], BR( K + µ ) [2], BR( K + π ) [5], BR( K + → π + π − π + ( γ )) (eq. 4),BR( K ± l ) [3], and BR( K ± → π ± π π ) [4], with their dependence on τ ± K , andimposing the constraint P BR( K ± → f ) = 1. The fit results, with χ /ndf =0.24/1 (CL = 0.63), show a coherent set of measurements (see Table 4).The NA48 experiment observed in the π π invariant mass distribution a cusp-like anomaly at M = 2 m π + [16], which has been interpreted as mainly dueto the final state charge-exchange reaction π + π − → π π in K ± → π ± π + π − decay [17], [18]. The fit to the M distribution [19] with two different models[20] and [21] [22] determines a − a , the difference between the S-wave ππ scat-tering lengths in the isospin I =0 and I =2 states. In this calculation the mainsource of uncertainty is the ratio of the weak amplitudes of K ± → π ± π − π + and K ± → π ± π π decay, that is obtained from the ratio R of the branch-ing ratio values. Using the BR( π ± π − π + ), BR( π ± π π ) and their correlationshown in Table 4 we evaluate R = 3 . ± . R = 3 . ± .
050 obtained by NA48 [19] with BRs from the PDG fit [7].
We have measured the absolute branching ratio of the K + → π + π − π + ( γ )decay, inclusive of final-state radiation, using two indipendent normalizationsamples from K − µ and K − π tags: BR ( K + → π + π − π + ( γ )) = 0 . ± . stat ± . syst with an overall accuracy of 0.72%. This measurement completes the KLOEprogram of precision measurements of the dominant kaon branching ratios. We warmly thank our former KLOE colleagues for the access to the data col-lected during the KLOE data taking campaign. We thank the DAΦNE teamfor their efforts in maintaining low background running conditions and theircollaboration during all data taking. We want to thank our technical staff:G.F. Fortugno and F. Sborzacchi for their dedication in ensuring efficientoperation of the KLOE computing facilities; M. Anelli for his continuous at-tention to the gas system and detector safety; A. Balla, M. Gatta, G. Corradiand G. Papalino for electronics maintenance; M. Santoni, G. Paoluzzi and R.Rosellini for general detector support; C. Piscitelli for his help during major12aintenance periods. This work was supported in part by the EU IntegratedInfrastructure Initiative Hadron Physics Project under contract number RII3-CT- 2004-506078; by the European Commission under the 7th FrameworkProgramme through the ‘Research Infrastructures’ action of the ‘Capacities’Programme, Call: FP7-INFRASTRUCTURES-2008-1, Grant Agreement No.227431; by the Polish National Science Centre through the Grants No. DEC-2011/03/N/ST2/02641, 2011/01/D/ST2/00748,2011/03/N/ST2/02652, 2013/08/M/ST2/00323, and by the Foundation forPolish Science through the MPD programme and the project HOMING PLUSBIS/2011-4/3.
References [1] KLOE coll., F. Ambrosino, et al. , JHEP (2008) 73.[2] KLOE coll., F. Ambrosino, et al. , Phys. Lett. B (2006) 76.[3] KLOE coll., F. Ambrosino, et al. , JHEP (2008) 98.[4] KLOE coll., A. Aloisio, et al. , Phys. Lett. B (2004) 139.[5] KLOE coll., F.Ambrosino, et al. , Phys. Lett. B (2008) 15.[6] I.H. Chiang, et al. , Phys. Rev. D (1972) 1254.[7] PDG, Phys. Rev. D (2012) 010001.[8] W.T. Ford, et al. , Phys. Rev. Lett. (1970) 1370.[9] A. Drago, et al. LNF -03/012 (2003).[10] KLOE coll., M. Adinolfi et al. , Nucl. Inst. and Meth. A (2002) 51.[11] KLOE coll., M. Adinolfi et al. , Nucl. Inst. and Meth. A (2002) 364.[12] KLOE coll., F. Ambrosino, et al. , Nucl. Inst. and Meth. A (2004) 403.[13] KLOE coll., M. Adinolfi et al. , Nucl. Inst. and Meth. A (2002) 134.[14] C.B. Dover and G.E. Walker,
The interaction of kaons with nucleons and nuclei ,Physics Report, (1991) 115.[16] NA48 coll., J.R. Batley, et al. , Phys. Lett. B (2006) 173.[17] P. Budini, L. Fonda, Phys. Rev. Lett. (1961) 419.[18] N. Cabibbo, Phys. Rev. Lett. (2004) 121801.[19] NA48 coll., J.R. Batley, et al. , EPJ B (2009) 589.
20] N. Cabibbo and G. Isidori, JHEP 0503 (2005) 21.[21] G. Colangelo, J. Gasser, B. Kubis, A. Rusetsky, Phys. Lett. B (2006) 187.[22] M. Bissegger, A. Fuhrer, J. Gasser, B. Kubis, A. Rusetsky, Nucl. Phys. B (2009) 178.(2009) 178.