- Email: [email protected]
Search for lepton flavour violating decays τ−→ℓ−KS0 and τ−→ℓ−(ρ0,K∗0,K¯∗0,ϕ) at BaBar
Nuclear Physics B (Proc. Suppl.) 189 (2009) 154–159 www.elsevierphysics.com
Search for lepton flavour violating decays τ − → −KS0 and τ − → − (ρ0 , K ∗0, K ∗0, φ) at BABAR R. Cencia , and J. M. Roneyb (on behalf of BABAR Collaboration) a
SLAC National Accelerator Laboratory, 2575, Sand Hill Rd, Menlo Park, CA - 94025, USA b
Univ. of Victoria, Dept. of Physics & Astronomy, P.O. Box 3055, Victoria, BC, Canada V8W 3P6 We report on recent searches for lepton flavour violating decays of the τ lepton: τ − → − KS0 , τ − → − (ρ0 , K ∗0 , K ∗0 , φ). These preliminary results use data samples collected by the BABAR detector at the SLAC PEP-II B factory corresponding to integrated luminosities of 469 fb−1 for the τ − → − KS0 and 451 fb−1 for the τ − → − (ρ0 , K ∗0 , K ∗0 , φ) searches. No statistically significant signal has been observed in any of these channels and we set upper limits on their branching fractions between 0.8 − 18.2 × 10−8 at 90% confidence level.
1. THEORETICAL MOTIVATION Lepton flavour violation (LFV) is forbidden in the Standard Model (SM) if neutrinos are massless. Although the phenomenon of neutrino oscillations provide evidence of neutrino masses, their very small size makes LFV processes unobservably rare. Any occurrences of LFV decays with measurable branching fractions (BFs) would be a clear sign of new physics. No signal has been found in extensive searches for LFV in μ and τ decays (e.g. μ → eγ, τ → μγ [1]). However, within the bounds set by searches, some physics models that extend the SM include new sizable LFV processes. For a review, see Ref. [2]. Searching for LFV in all available τ decay channels will provide better limits on the parameters of these models. The τ − → − KS0 and τ − → − 0 ∗0 ∗0 (ρ , K , K , φ) BFs have been estimated in SM extensions with heavy singlet Dirac neutrinos [3] being below 10−6 for τ − → − (ρ0 , φ) decays and below 10−15 for τ − → − (KS0 , K ∗0 , K ∗0 ) decays. Recently, τ − → − ρ0 BF has been estimated to be below 10−7 and τ − → − φ below 10−8 using a constrained MSSM-seesaw model [4]. Alternatively in Ref. [5], the authors use experimental ULs on BFs to provide upper limits on couplings coefficients for R-parity violating 0920-5632/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2009.03.028
supersymmetric models. 2. ANALYSIS OVERVIEW The measurements reported here are performed using data collected by the BABAR detector at the PEP-II asymmetric energy storage ring. The detector is described in detail elsewhere [6,7]. The analyzed data sample corresponds to an integrated luminosity of 469 fb−1 for τ − → − KS0 and 451 fb−1 for τ − → − (ρ0 , K ∗0 , K ∗0 , φ) collected from e+ e− collisions at the Υ(4S) resonance (90%) and at center-of-mass (CM) energy 10.54 GeV (10%). τ pairs are produced back-toback in √ the CM system with a high momentum (Eτ = s/2). The total number of produced τ pairs Nτ τ is calculated using the average τ cross section of 0.919 ± 0.003 nb estimated with KK2f [8,9]. Although we conduct independent searches for the different modes, the analyses have common features which we discuss in this section. Features specific to τ − → − KS0 and τ − → − (ρ0 , K ∗0 , K ∗0 , φ) are presented in Sections 3 and 4 respectively. We search for the signal modes, with mesons decaying into two charged pions or kaons, by reconstructing τ candidates using three charged particles, each identified as
R. Cenci, J.M. Roney / Nuclear Physics B (Proc. Suppl.) 189 (2009) 154–159
the appropriate lepton or hadron, and having an invariant mass and energy consistent with that of the parent τ lepton. The lack of a neutrino in the LFV decay allows us to fully reconstruct the τ . The overall event charge must be zero. The thrust [10] is calculated using tracks and calorimeter energy deposits without an associated charged particle track. For each event, hemispheres are defined in the CM frame using the plane perpendicular to the thrust. The hemisphere that contains the reconstructed τ candidate is referred to as the signal side and the other hemisphere as the tag side. Candidate τ pair events are required to have three reconstructed charged particle tracks on the signal side and one track on the tag side. For τ − → e− KS0 channel events with three reconstructed tracks on the tag side are also retained. Electron, muons, pions and kaons are identified using selecors based on a combination of measurements from various subdetectors. The average efficiency for these selectors are detailed in Table 1. The particle identification (PID) is not sufficient to suppress certain backgrounds, and to reduce them, additional selection criteria are applied separately in the different search channels. We choose selection criteria that give the smallest expected upper limit (UL), or sensitivity, defined as the UL value obtained using the background events from MC assuming no signal. There are three main classes of background remaining after the selection criteria are applied: charm quark production (cc), combinatorial uds background from low-multiplicity continuum e+ e− → q q¯, where q = u, d, s quarks, and SM τ + τ − events. An irreducible background is D− → − M 0 ν, where M 0 = KS0 , ρ0 , K ∗0 , K ∗0 , φ. The signal τ candidates are examined in the two dimensional distribution of ΔEτ vs ΔMτ , where ΔMτ is the difference between the invariant mass of the reconstructed τ and the known τ mass, mτ [11], and ΔEτ is the difference between the energy of the reconstructed τ and the expected τ energy assuming no radiation, half the CM total energy. For τ − → − (ρ0 , K ∗0 , K ∗0 , φ) decays, instead of ΔMτ , we consider ΔMec , defined as mec − mτ , where mec is the beam-energyconstrained invariant mass of the three tracks.
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The whole decay tree is then fitted requiring that, within reconstruction uncertainties, the hadrons from the meson decay form a vertex, the meson mass is constrained to its nominal value, and the lepton and the meson trajectory form a vertex close to the beam interaction region. The ΔEτ vs ΔMτ distribution for signal MC is shown in Figure 1. The rectangle in Figure 1 defines the
Figure 1. Distribution of events in the (ΔEτ , ΔMτ ) plane for signal MC sample of τ − → e− KS0 mode. The rectangle corresponds to the signal box. The z-axis scale is logarithmic. final signal box (SB) used to calculate the UL. To avoid bias, a blinded analysis procedure was followed with the number of data events in the SB remaining unknown until the selection criteria were finalized, all crosschecks were performed and systematic uncertainties determined. The surrounding region, referred to as grand sideband (GS), is used to estimate the background in the SB. 3. τ − → − KS0 3.1. Events Selection For this decay mode, two different stages of selection are used. In the first, which we call the loose selection stage, we retain enough data to estimate background distribution shapes. The second, which we refer to as the tight selection, uses criteria that have been chosen to optimize the sensitivity. For each stage we use different PID selectors whose performances are given in Table 1. While for the τ − → μ− KS0 channel the loose selec-
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Table 1 Efficiency and misidentification rate for the PID selectors used for the various channels. ε % (Misid. %) Lepton ID Loose Lepton ID Tight π ID K ID
eKS0 98(10) 93(0.1) -
μKS0 92(6) 80(2) -
eρ0 92(0.15) 94(2.2) -
μρ0 60(0.8) 94(2.2) -
tion consists of the criteria described in Section 2, for the τ − → e− KS0 one it includes also further requirements on the reconstructed KS0 . Those requirements are applied later for muon channel during the tight selection. For both channels the tight selection includes also cuts on quantities related to the missing momentum of the event, e. g. on the transverse missing momentum and its polar angle in the CM system. Another requirement is applied on the squared invariant mass for the tag side m2TAG. This is calculated by taking the tag side τ direction to be opposite that of the fully reconstructed signal side τ and assigning the missing momentum in the event to the tag side neutrino momentum. As shown in Figure 2, the variable provides good discrimination for the events in which the tag side τ decays semileptonically so that there is only a single neutrino in the event. The variable m2TAG is required to be
eK ∗0 92(0.15) 94(2.2) 82(5)
μK ∗0 70(1) 94(2.2) 70(4)
∗0
eK 92(0.15) 94(2.2) 82(5)
∗0
μK 70(1) 94(2.2) 70(4)
eφ 92(0.15) 90(10)
μφ 70(1) 95(16)
For the final step of the analysis, we define another discriminating variable, χ2FULL , as the χ2 of the geometrical and kinematical fit for the whole decay tree, with additional constraints of ΔMτ and ΔEτ equal to 0. We require χ2FULL smaller than 50 and the event to fall within SB and the distribution of χ2FULL is shown in Figure 3 for data and signal MC. The background distribution, shown in the same figure, is obtained by fitting the product of a Landau function and a straight line to the MC background events after the loose selection. The overall efficiency ε in this
Figure 3. Distributions of χ2FULL after the selection for the τ − → e− KS0 channel. The signal and background MC distributions are normalized arbitrarily.
Figure 2. Distributions of m2TAG after the loose selection for the τ − → e− KS0 channel. The signal MC distribution is normalized arbitrarily, while the background MC to the data luminosity. The arrow indicates the applied requirement. smaller than 2.6 ( GeV/c2 )2 for both channels.
range of χ2FULL , after the final step of the analysis is 9.4% for the τ − → e− KS0 mode and 7.0% for the τ − → μ− KS0 mode. We estimate the number of background events in the signal region using the background MC: MC Nloose is the number of events after the loose selection with no χ2FULL cut; nMC loose is the number of events after the loose selection but with MC is the number of events χ2FULL < 50, and Ntight
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where s90 is the limit for the signal yield at 90% confidence level, and ε and Nτ τ are already defined above. The dominant systematic uncertainties on the signal efficiency for the electron (muon) channel come from possible data/MC differences in the efficiency of the PID requirements, 0.4% (5.1%) and of the tracking reconstruction, 1.7% (1.6%). Other sources of systematic uncertainty for the efficiency are: data/MC differences in KS0 reconstruction efficiency (1.0%), the
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3.2. Modified Frequentist Analysis The numbers of events is consistent with background expectations and we set a 90% confidence level UL using the modified frequentist analysis (CLS method) [12,13] using χ2FULL as the discriminating variable. For the observed distribution of χ2FULL after the selection, the test-statistic is the the likelihood of observing this distribution under the hypothesis of background plus signal for a particular signal branching fraction to the likelihood of the same observation for a background only hypothesis. The confidence level CLS is defined as the ratio CLS+B /CLB , where CLS+B and CLB are the probabilities that the test-statistic is less than the value observed in the data under the respective hypotheses. Signal hypotheses corresponding to CLS < α are rejected at the 1 − α confidence level. This method avoids setting ULs which exceed the sensitivity of the experiment, which can happen when downward background fluctuations occur. The method also enables us to include uncertainties on the signal and background distributions. The ULs on BFs at 90% confidence level are calculated as s90 (1) B(τ − → − KS0 ) < 2εNτ τ
beam energy scale and the energy spread (less than 0.2%). The efficiency errors from MC statistics are negligible compared with the systematics ones. The uncertainty for the total number of τ pairs comes from the error on the luminosity and on the τ cross section values (0.7%). We assume these uncertainties are uncorrelated and combine them in quadrature to give a total signal uncertainty of 2.1% and 5.5% respectively for the electron and muon channels. For each bin of the signal χ2FULL distribution, we consider the total uncertainties on the signal yield, and for the background distributions the uncertainties on the expected background levels. The uncertainties are treated as fully correlated between the bins as they are mainly due to normalization uncertainties. The analysis results are summarized in Figure 4 presenting CLS for the observed events versus the BFs, with the horizontal line defining the UL at 90% confidence level. From Figure 4, CLS
after the tight selection with no χ2FULL cut. The number of background events in the signal region MC MC is estimated to be nMC loose ×Ntight /Nloose . We apply a 10% correction to normalize the MC to the levels of background seen in data outside the blinded box after the tight selection. Total backgrounds of 1.0 ± 0.4 and 5.3 ± 2.2 events are expected for τ − → e− KS0 and τ − → μ− KS0 respectively. In the signal region we find 1 and 2 events for the electron and muon modes, respectively.
0.6
0.5
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0.3
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0.1
0
1 2 3 4 5 6 7 Branching Fraction (10-8)
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1 2 3 4 5 6 7 Branching Fraction (10-8)
Figure 4. Observed CLS as a function of the BFs (10−8 ) for the decays τ − → e− KS0 and τ − → μ− KS0 . the ULs on the BFs at 90% confidence level are determined to be: B(τ − → e− KS0 ) < 3.3 × 10−8 and B(τ − → μ− KS0 ) < 4.0 × 10−8 . 3.3. Cross-check method The search is also performed using another technique that has a similar but lower sensitivity and therefore is used only as a cross-check. For this method, selection criteria on the same quantities were slightly tightened to reduce the background as much as possible, and signal candidates are counted inside the elliptical region shown in Figure 5. The final signal efficiencies
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Table 2 Efficiency, number of expected background events (nbgd ), number of observed events (Nobs ), and observed UL at 90% CL for each decay mode. Mode eρ0 μρ0 eK ∗0 μK ∗0 ∗0 eK ∗0 μK eφ μφ
Figure 5. Candidate distribution in the (ΔEτ , ΔMτ ) plane after the selection for cross-check method. The gray bands and the ellipse indicate the sidebands used for extrapolating the background and the signal region. with this selection are 9.1% for the τ − → e− KS0 mode and 6.1% for the τ − → μ− KS0 mode. The level of background in the signal ellipse is estimated by extrapolating the event densities found in two sideband regions of ΔMτ defined in Figure 5. The ΔMτ background distribution is modeled as a linear function plus a Gaussian function to account for the peak related to the decay mode D− → KS0 π − . The final estimated number of background events in the signal region is 0.6 ± 0.3 and 0.3 ± 0.2 for the electron and muon channels respectively. When the signal region is unblinded, we find only one event inside the elliptical signal region for each channel. ULs on the BFs at 90% confidence level for this cross-check are calculated including the uncertainties with the POLE program [14]: B(τ − → e− KS0 ) < 4.8 × 10−8 and B(τ − → μ− KS0 ) < 7.6 × 10−8 . 4. τ − → − (ρ0 , K ∗0 , K ∗0 , φ) 4.1. Events Selection The PID requirements are again not sufficient to suppress certain backgrounds, particularly those from charm and light quark pair production and SM τ pairs. The additional criteria applied to reject background involve quantities related to the topology and the missing momentum of the event, the invariant mass of the hadrons on the signal side, the number of photons in the signal and in the tag side, and the acolin-
(%) 7.31 ± 0.18 4.52 ± 0.41 8.00 ± 0.18 4.57 ± 0.36 7.76 ± 0.17 4.11 ± 0.31 6.43 ± 0.18 5.18 ± 0.26
nbkg 1.32 ± 0.19 2.04 ± 0.21 1.64 ± 0.29 1.79 ± 0.25 2.76 ± 0.30 1.72 ± 0.18 0.68 ± 0.14 2.76 ± 0.21
Nobs 1 0 2 4 2 1 0 6
UL(10−8 ) 4.3 0.8 5.6 16.7 4.0 6.4 3.1 18.2
earity angle between the tag and signal side momentum vectors in the CM frame. The efficiency of the selection for signal events is estimated with a MC simulation of lepton-flavour violating τ decays. The total efficiency for signal events to be found in the signal region is shown in Table 2 for each decay mode and ranges from 4.1% to 8.0%. This efficiency includes the branching fraction for the vector meson decay to charged daughters, as well as the branching fraction for 1-prong τ decays. In Figure 6 we show the final distributions of events after the selection for each decay channel and the blinded regions. The expected background rates for each decay mode are determined by fitting a probability density function (PDF) for each class of background to the observed data in the GS region of the ΔEτ /ΔMτ plane. The shapes of these PDFs are determinded from background MC samples. With the shapes of the three background PDFs determined, an unbinned extended maximum likelihood fit to the data in the GS region is used to find the expected background rate in the signal region, shown in Table 2. 4.2. Upper Limits The numbers of events observed and the background expectations are shown in Table 2, with no significant excess found in any decay mode. Upper limits on the branching fractions are calculated according to Eq. 1. The dominant systematic uncertainties on the signal efficiency for the various channels are the same as τ − → − KS0 ones. For the τ − → − φ channels, the uncertainty on the branching fraction B(φ → K + K − ) give an additional 1.2% contribute. The total sys-
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5. SUMMARY These preliminary results yield more stringent constraints on the LFV modes considered than previous experiments [17] in almost all channels. REFERENCES
Figure 6. Observed data shown as dots in the (ΔEτ , ΔMec ) plane, The rectangles indicate the signal region for each mode and the dark and light shading indicates contours containing 50% and 90% of the selected MC signal events, respectively.
tematic uncertainties range from 1.7% to 9.0%. We consider uncertainties on the background estimation from the background normalizations, from the background shape parameters and from the finite data available in the GS region. The total uncertainties on the signal efficiences and background estimates are reported in Table 2. The uncertainty on Nτ τ is 1.0%. The branching fraction upper limits are calculated including all uncertainties using the technique of Cousins and Highland [15] following the implementation of Barlow [16]. The 90% CL upper limits on the τ − → − (ρ0 , K ∗0 , K ∗0 , φ) branching fractions are in the range (0.76 − 18) × 10−8 .
1. W. J. Marciano, T. Mori, and J. M. Roney. Annual Review of Nuclear and Particle Systems, 58:315–341, 2008. 2. M. Raidal et al. Eur. Phys. J., C57:13–182, 2008. 3. A. Ilakovac. Phys. Rev. D, 62:036010, 2000. 4. E. Arganda, M. J. Herrero, and J. Portoles. JHEP, 06:079, 2008. 5. Jyoti Prasad Saha and Anirban Kundu. Phys. Rev. D, 66:054021, 2002. 6. B. Aubert et al. Nucl. Instrum. Meth. A, 479:1–116, 2002. 7. W. Menges. IEEE Nucl. Sci. Symp. Conf. Rec., 5:1470–1474, 2006. 8. S. Jadach, B. F. L. Ward, and Z. Was. Comput. Phys. Commun., 130:260–325, 2000. 9. Swagato Banerjee, Bolek Pietrzyk, J. Michael Roney, and Zbigniew Was. Phys. Rev. D, 77:054012, 2008. 10. S. Brandt, C. Peyrou, R. Sosnowski, and A. Wroblewski. Phys. Lett., 12:57–61, 1964. 11. W. M. Yao et al. J. Phys. G, 33:1–1232, 2006. 12. Thomas Junk. Nucl. Instrum. Meth. A, 434:435–443, 1999. 13. Workshop on confidence limits, CERN, Geneva, Switzerland, 17-18 Jan 2000: Proceedings, 2000. CERN-2000-005. 14. Jan Conrad, O. Botner, A. Hallgren, and Carlos Perez de los Heros. Phys. Rev. D, 67:012002, 2003. 15. Robert D. Cousins and Virgil L. Highland. Nucl. Instrum. Meth., A320:331–335, 1992. 16. Roger Barlow. Comput. Phys. Commun., 149:97–102, 2002. 17. Y. Nishio et al. Phys. Lett., B664:35–40, 2008.
Search for lepton flavour violating decays τ − → −KS0 and τ − → − (ρ0 , K ∗0, K ∗0, φ) at BABAR R. Cencia , and J. M. Roneyb (on behalf of BABAR Collaboration) a
SLAC National Accelerator Laboratory, 2575, Sand Hill Rd, Menlo Park, CA - 94025, USA b
Univ. of Victoria, Dept. of Physics & Astronomy, P.O. Box 3055, Victoria, BC, Canada V8W 3P6 We report on recent searches for lepton flavour violating decays of the τ lepton: τ − → − KS0 , τ − → − (ρ0 , K ∗0 , K ∗0 , φ). These preliminary results use data samples collected by the BABAR detector at the SLAC PEP-II B factory corresponding to integrated luminosities of 469 fb−1 for the τ − → − KS0 and 451 fb−1 for the τ − → − (ρ0 , K ∗0 , K ∗0 , φ) searches. No statistically significant signal has been observed in any of these channels and we set upper limits on their branching fractions between 0.8 − 18.2 × 10−8 at 90% confidence level.
1. THEORETICAL MOTIVATION Lepton flavour violation (LFV) is forbidden in the Standard Model (SM) if neutrinos are massless. Although the phenomenon of neutrino oscillations provide evidence of neutrino masses, their very small size makes LFV processes unobservably rare. Any occurrences of LFV decays with measurable branching fractions (BFs) would be a clear sign of new physics. No signal has been found in extensive searches for LFV in μ and τ decays (e.g. μ → eγ, τ → μγ [1]). However, within the bounds set by searches, some physics models that extend the SM include new sizable LFV processes. For a review, see Ref. [2]. Searching for LFV in all available τ decay channels will provide better limits on the parameters of these models. The τ − → − KS0 and τ − → − 0 ∗0 ∗0 (ρ , K , K , φ) BFs have been estimated in SM extensions with heavy singlet Dirac neutrinos [3] being below 10−6 for τ − → − (ρ0 , φ) decays and below 10−15 for τ − → − (KS0 , K ∗0 , K ∗0 ) decays. Recently, τ − → − ρ0 BF has been estimated to be below 10−7 and τ − → − φ below 10−8 using a constrained MSSM-seesaw model [4]. Alternatively in Ref. [5], the authors use experimental ULs on BFs to provide upper limits on couplings coefficients for R-parity violating 0920-5632/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2009.03.028
supersymmetric models. 2. ANALYSIS OVERVIEW The measurements reported here are performed using data collected by the BABAR detector at the PEP-II asymmetric energy storage ring. The detector is described in detail elsewhere [6,7]. The analyzed data sample corresponds to an integrated luminosity of 469 fb−1 for τ − → − KS0 and 451 fb−1 for τ − → − (ρ0 , K ∗0 , K ∗0 , φ) collected from e+ e− collisions at the Υ(4S) resonance (90%) and at center-of-mass (CM) energy 10.54 GeV (10%). τ pairs are produced back-toback in √ the CM system with a high momentum (Eτ = s/2). The total number of produced τ pairs Nτ τ is calculated using the average τ cross section of 0.919 ± 0.003 nb estimated with KK2f [8,9]. Although we conduct independent searches for the different modes, the analyses have common features which we discuss in this section. Features specific to τ − → − KS0 and τ − → − (ρ0 , K ∗0 , K ∗0 , φ) are presented in Sections 3 and 4 respectively. We search for the signal modes, with mesons decaying into two charged pions or kaons, by reconstructing τ candidates using three charged particles, each identified as
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the appropriate lepton or hadron, and having an invariant mass and energy consistent with that of the parent τ lepton. The lack of a neutrino in the LFV decay allows us to fully reconstruct the τ . The overall event charge must be zero. The thrust [10] is calculated using tracks and calorimeter energy deposits without an associated charged particle track. For each event, hemispheres are defined in the CM frame using the plane perpendicular to the thrust. The hemisphere that contains the reconstructed τ candidate is referred to as the signal side and the other hemisphere as the tag side. Candidate τ pair events are required to have three reconstructed charged particle tracks on the signal side and one track on the tag side. For τ − → e− KS0 channel events with three reconstructed tracks on the tag side are also retained. Electron, muons, pions and kaons are identified using selecors based on a combination of measurements from various subdetectors. The average efficiency for these selectors are detailed in Table 1. The particle identification (PID) is not sufficient to suppress certain backgrounds, and to reduce them, additional selection criteria are applied separately in the different search channels. We choose selection criteria that give the smallest expected upper limit (UL), or sensitivity, defined as the UL value obtained using the background events from MC assuming no signal. There are three main classes of background remaining after the selection criteria are applied: charm quark production (cc), combinatorial uds background from low-multiplicity continuum e+ e− → q q¯, where q = u, d, s quarks, and SM τ + τ − events. An irreducible background is D− → − M 0 ν, where M 0 = KS0 , ρ0 , K ∗0 , K ∗0 , φ. The signal τ candidates are examined in the two dimensional distribution of ΔEτ vs ΔMτ , where ΔMτ is the difference between the invariant mass of the reconstructed τ and the known τ mass, mτ [11], and ΔEτ is the difference between the energy of the reconstructed τ and the expected τ energy assuming no radiation, half the CM total energy. For τ − → − (ρ0 , K ∗0 , K ∗0 , φ) decays, instead of ΔMτ , we consider ΔMec , defined as mec − mτ , where mec is the beam-energyconstrained invariant mass of the three tracks.
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The whole decay tree is then fitted requiring that, within reconstruction uncertainties, the hadrons from the meson decay form a vertex, the meson mass is constrained to its nominal value, and the lepton and the meson trajectory form a vertex close to the beam interaction region. The ΔEτ vs ΔMτ distribution for signal MC is shown in Figure 1. The rectangle in Figure 1 defines the
Figure 1. Distribution of events in the (ΔEτ , ΔMτ ) plane for signal MC sample of τ − → e− KS0 mode. The rectangle corresponds to the signal box. The z-axis scale is logarithmic. final signal box (SB) used to calculate the UL. To avoid bias, a blinded analysis procedure was followed with the number of data events in the SB remaining unknown until the selection criteria were finalized, all crosschecks were performed and systematic uncertainties determined. The surrounding region, referred to as grand sideband (GS), is used to estimate the background in the SB. 3. τ − → − KS0 3.1. Events Selection For this decay mode, two different stages of selection are used. In the first, which we call the loose selection stage, we retain enough data to estimate background distribution shapes. The second, which we refer to as the tight selection, uses criteria that have been chosen to optimize the sensitivity. For each stage we use different PID selectors whose performances are given in Table 1. While for the τ − → μ− KS0 channel the loose selec-
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Table 1 Efficiency and misidentification rate for the PID selectors used for the various channels. ε % (Misid. %) Lepton ID Loose Lepton ID Tight π ID K ID
eKS0 98(10) 93(0.1) -
μKS0 92(6) 80(2) -
eρ0 92(0.15) 94(2.2) -
μρ0 60(0.8) 94(2.2) -
tion consists of the criteria described in Section 2, for the τ − → e− KS0 one it includes also further requirements on the reconstructed KS0 . Those requirements are applied later for muon channel during the tight selection. For both channels the tight selection includes also cuts on quantities related to the missing momentum of the event, e. g. on the transverse missing momentum and its polar angle in the CM system. Another requirement is applied on the squared invariant mass for the tag side m2TAG. This is calculated by taking the tag side τ direction to be opposite that of the fully reconstructed signal side τ and assigning the missing momentum in the event to the tag side neutrino momentum. As shown in Figure 2, the variable provides good discrimination for the events in which the tag side τ decays semileptonically so that there is only a single neutrino in the event. The variable m2TAG is required to be
eK ∗0 92(0.15) 94(2.2) 82(5)
μK ∗0 70(1) 94(2.2) 70(4)
∗0
eK 92(0.15) 94(2.2) 82(5)
∗0
μK 70(1) 94(2.2) 70(4)
eφ 92(0.15) 90(10)
μφ 70(1) 95(16)
For the final step of the analysis, we define another discriminating variable, χ2FULL , as the χ2 of the geometrical and kinematical fit for the whole decay tree, with additional constraints of ΔMτ and ΔEτ equal to 0. We require χ2FULL smaller than 50 and the event to fall within SB and the distribution of χ2FULL is shown in Figure 3 for data and signal MC. The background distribution, shown in the same figure, is obtained by fitting the product of a Landau function and a straight line to the MC background events after the loose selection. The overall efficiency ε in this
Figure 3. Distributions of χ2FULL after the selection for the τ − → e− KS0 channel. The signal and background MC distributions are normalized arbitrarily.
Figure 2. Distributions of m2TAG after the loose selection for the τ − → e− KS0 channel. The signal MC distribution is normalized arbitrarily, while the background MC to the data luminosity. The arrow indicates the applied requirement. smaller than 2.6 ( GeV/c2 )2 for both channels.
range of χ2FULL , after the final step of the analysis is 9.4% for the τ − → e− KS0 mode and 7.0% for the τ − → μ− KS0 mode. We estimate the number of background events in the signal region using the background MC: MC Nloose is the number of events after the loose selection with no χ2FULL cut; nMC loose is the number of events after the loose selection but with MC is the number of events χ2FULL < 50, and Ntight
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where s90 is the limit for the signal yield at 90% confidence level, and ε and Nτ τ are already defined above. The dominant systematic uncertainties on the signal efficiency for the electron (muon) channel come from possible data/MC differences in the efficiency of the PID requirements, 0.4% (5.1%) and of the tracking reconstruction, 1.7% (1.6%). Other sources of systematic uncertainty for the efficiency are: data/MC differences in KS0 reconstruction efficiency (1.0%), the
0.6
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CLS
3.2. Modified Frequentist Analysis The numbers of events is consistent with background expectations and we set a 90% confidence level UL using the modified frequentist analysis (CLS method) [12,13] using χ2FULL as the discriminating variable. For the observed distribution of χ2FULL after the selection, the test-statistic is the the likelihood of observing this distribution under the hypothesis of background plus signal for a particular signal branching fraction to the likelihood of the same observation for a background only hypothesis. The confidence level CLS is defined as the ratio CLS+B /CLB , where CLS+B and CLB are the probabilities that the test-statistic is less than the value observed in the data under the respective hypotheses. Signal hypotheses corresponding to CLS < α are rejected at the 1 − α confidence level. This method avoids setting ULs which exceed the sensitivity of the experiment, which can happen when downward background fluctuations occur. The method also enables us to include uncertainties on the signal and background distributions. The ULs on BFs at 90% confidence level are calculated as s90 (1) B(τ − → − KS0 ) < 2εNτ τ
beam energy scale and the energy spread (less than 0.2%). The efficiency errors from MC statistics are negligible compared with the systematics ones. The uncertainty for the total number of τ pairs comes from the error on the luminosity and on the τ cross section values (0.7%). We assume these uncertainties are uncorrelated and combine them in quadrature to give a total signal uncertainty of 2.1% and 5.5% respectively for the electron and muon channels. For each bin of the signal χ2FULL distribution, we consider the total uncertainties on the signal yield, and for the background distributions the uncertainties on the expected background levels. The uncertainties are treated as fully correlated between the bins as they are mainly due to normalization uncertainties. The analysis results are summarized in Figure 4 presenting CLS for the observed events versus the BFs, with the horizontal line defining the UL at 90% confidence level. From Figure 4, CLS
after the tight selection with no χ2FULL cut. The number of background events in the signal region MC MC is estimated to be nMC loose ×Ntight /Nloose . We apply a 10% correction to normalize the MC to the levels of background seen in data outside the blinded box after the tight selection. Total backgrounds of 1.0 ± 0.4 and 5.3 ± 2.2 events are expected for τ − → e− KS0 and τ − → μ− KS0 respectively. In the signal region we find 1 and 2 events for the electron and muon modes, respectively.
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Figure 4. Observed CLS as a function of the BFs (10−8 ) for the decays τ − → e− KS0 and τ − → μ− KS0 . the ULs on the BFs at 90% confidence level are determined to be: B(τ − → e− KS0 ) < 3.3 × 10−8 and B(τ − → μ− KS0 ) < 4.0 × 10−8 . 3.3. Cross-check method The search is also performed using another technique that has a similar but lower sensitivity and therefore is used only as a cross-check. For this method, selection criteria on the same quantities were slightly tightened to reduce the background as much as possible, and signal candidates are counted inside the elliptical region shown in Figure 5. The final signal efficiencies
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Table 2 Efficiency, number of expected background events (nbgd ), number of observed events (Nobs ), and observed UL at 90% CL for each decay mode. Mode eρ0 μρ0 eK ∗0 μK ∗0 ∗0 eK ∗0 μK eφ μφ
Figure 5. Candidate distribution in the (ΔEτ , ΔMτ ) plane after the selection for cross-check method. The gray bands and the ellipse indicate the sidebands used for extrapolating the background and the signal region. with this selection are 9.1% for the τ − → e− KS0 mode and 6.1% for the τ − → μ− KS0 mode. The level of background in the signal ellipse is estimated by extrapolating the event densities found in two sideband regions of ΔMτ defined in Figure 5. The ΔMτ background distribution is modeled as a linear function plus a Gaussian function to account for the peak related to the decay mode D− → KS0 π − . The final estimated number of background events in the signal region is 0.6 ± 0.3 and 0.3 ± 0.2 for the electron and muon channels respectively. When the signal region is unblinded, we find only one event inside the elliptical signal region for each channel. ULs on the BFs at 90% confidence level for this cross-check are calculated including the uncertainties with the POLE program [14]: B(τ − → e− KS0 ) < 4.8 × 10−8 and B(τ − → μ− KS0 ) < 7.6 × 10−8 . 4. τ − → − (ρ0 , K ∗0 , K ∗0 , φ) 4.1. Events Selection The PID requirements are again not sufficient to suppress certain backgrounds, particularly those from charm and light quark pair production and SM τ pairs. The additional criteria applied to reject background involve quantities related to the topology and the missing momentum of the event, the invariant mass of the hadrons on the signal side, the number of photons in the signal and in the tag side, and the acolin-
(%) 7.31 ± 0.18 4.52 ± 0.41 8.00 ± 0.18 4.57 ± 0.36 7.76 ± 0.17 4.11 ± 0.31 6.43 ± 0.18 5.18 ± 0.26
nbkg 1.32 ± 0.19 2.04 ± 0.21 1.64 ± 0.29 1.79 ± 0.25 2.76 ± 0.30 1.72 ± 0.18 0.68 ± 0.14 2.76 ± 0.21
Nobs 1 0 2 4 2 1 0 6
UL(10−8 ) 4.3 0.8 5.6 16.7 4.0 6.4 3.1 18.2
earity angle between the tag and signal side momentum vectors in the CM frame. The efficiency of the selection for signal events is estimated with a MC simulation of lepton-flavour violating τ decays. The total efficiency for signal events to be found in the signal region is shown in Table 2 for each decay mode and ranges from 4.1% to 8.0%. This efficiency includes the branching fraction for the vector meson decay to charged daughters, as well as the branching fraction for 1-prong τ decays. In Figure 6 we show the final distributions of events after the selection for each decay channel and the blinded regions. The expected background rates for each decay mode are determined by fitting a probability density function (PDF) for each class of background to the observed data in the GS region of the ΔEτ /ΔMτ plane. The shapes of these PDFs are determinded from background MC samples. With the shapes of the three background PDFs determined, an unbinned extended maximum likelihood fit to the data in the GS region is used to find the expected background rate in the signal region, shown in Table 2. 4.2. Upper Limits The numbers of events observed and the background expectations are shown in Table 2, with no significant excess found in any decay mode. Upper limits on the branching fractions are calculated according to Eq. 1. The dominant systematic uncertainties on the signal efficiency for the various channels are the same as τ − → − KS0 ones. For the τ − → − φ channels, the uncertainty on the branching fraction B(φ → K + K − ) give an additional 1.2% contribute. The total sys-
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5. SUMMARY These preliminary results yield more stringent constraints on the LFV modes considered than previous experiments [17] in almost all channels. REFERENCES
Figure 6. Observed data shown as dots in the (ΔEτ , ΔMec ) plane, The rectangles indicate the signal region for each mode and the dark and light shading indicates contours containing 50% and 90% of the selected MC signal events, respectively.
tematic uncertainties range from 1.7% to 9.0%. We consider uncertainties on the background estimation from the background normalizations, from the background shape parameters and from the finite data available in the GS region. The total uncertainties on the signal efficiences and background estimates are reported in Table 2. The uncertainty on Nτ τ is 1.0%. The branching fraction upper limits are calculated including all uncertainties using the technique of Cousins and Highland [15] following the implementation of Barlow [16]. The 90% CL upper limits on the τ − → − (ρ0 , K ∗0 , K ∗0 , φ) branching fractions are in the range (0.76 − 18) × 10−8 .
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