Charged Current Lepton Universality and |Vus| using τ Lepton Decays at BaBar

Nuclear Physics B (Proc. Suppl.) 189 (2009) 9–14 www.elsevierphysics.com

Charged Current Lepton Universality and |Vus | using τ Lepton Decays at BABAR I. M. Nugent

a∗

(representing the BABAR Collaboration )

a

Department of Physics and Astronomy, University of Victoria, PO Box 3055, STN CSC, Victoria, BC, V8W 3P6 Canada Using a data sample corresponding to an integrated luminosity of L = 467 fb−1 , collected with the BABAR →μνν) detector at the SLAC PEP-II e+ e− storage ring, we present preliminary measurements of B(τ =(0.9796 ± B(τ →eνν)

B(τ →πν) B(τ →Kν) →Kν) =(0.5945 ± 0.0014 ± 0.0061), B(τ =(0.03882 ± 0.00032 ± 0.00056), and B(τ 0.0016 ± 0.0035), B(τ →eνν) →eνν) B(τ →πν) =(0.06531 ± 0.00056 ± 0.00093), where the uncertainties are statistical and systematic, respectively. From the →Kν) →μνν) , |Vus | is determined to be 0.2255 ± 0.0023. The branching ratio B(τ enables a branching ratio B(τ B(τ →πν) B(τ →eνν) gμ precision test of the Standard Model assumption of charged current lepton universality, | ge | =1.0036 ± 0.0020. B(τ →Kν) B(τ →πν) The branching ratios B(τ , and B(τ provide additional tests of charged current lepton universality, →eνν) →eνν) gτ gτ | gμ | = 0.9859 ± 0.0057 in non-strange and | gμ | = 0.9836 ± 0.0087 in strange decays.

1. Introduction τ decays into a single charge particle and neutrinos can be used to measure the relative coupling strength of the weak interaction between the first and second generation[1] of quarks, |Vus |, and tests the assumption that all the lepton have ∗ We are grateful for the extraordinary contributions of our PEP-II colleagues in achieving the excellent luminosity and machine conditions that have made this work possible. The success of this project also relies critically on the expertise and dedication of the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and the kind hospitality extended to them. This work is supported by the US Department of Energy and National Science Foundation, the Natural Sciences and Engineering Research Council (Canada), Institute of High Energy Physics (China), the Commissariat ` a l’Energie Atomique and Institut National de Physique Nucl´eaire et de Physique des Particules (France), the Bundesministerium f¨ ur Bildung und Forschung and Deutsche Forschungsgemeinschaft (Germany), the Istituto Nazionale di Fisica Nucleare (Italy), the Foundation for Fundamental Research on Matter (The Netherlands), the Research Council of Norway, the Ministry of Science and Technology of the Russian Federation, and the Particle Physics and Astronomy Research Council (United Kingdom). Individuals have received support from CONACyT (Mexico), the A. P. Sloan Foundation, the Research Corporation, and the Alexander von Humboldt Foundation.

0920-5632/$ – see front matter © 2009 Published by Elsevier B.V. doi:10.1016/j.nuclphysbps.2009.03.003

the same coupling strength to the gauge bosons, charged lepton universality[2–5]. Recent measurements of the strange branching fractions, interpreted in the framework of Operator Product Expansion (OPE) and finite energy sum rules, suggest a value of |Vus | that is ∼ 3 standard deviations lower than the expectation from CKM unitarity [6], as well as from measurements of |Vus | from Kl2 and Kl3 decays [7]. Measuring B(τ →Kν) B(τ →πν) , and using the meson decay constants from lattice QCD [8], provides a measurement of |Vus | from τ decays which is independent of the convergence of the OPE series. A precision mea→μνν) surement of the ratio B(τ B(τ →eνν) tests μ−e charged current lepton universality, while measurements B(τ →πν) B(τ →Kν) of the branching ratios B(τ →eνν) and B(τ →eνν) tests τ − μ charged current lepton universality in non-strange and strange mesons respectively. 2. The BABAR Detector, Monte Carlo Samples

Dataset,

and

This paper presents preliminary measurements →μνν) B(τ →πν) B(τ →Kν) B(τ →Kν) of B(τ B(τ →eνν) , B(τ →eνν) , B(τ →eνν) and B(τ →πν) , where charge conjugate decays are implied. The data set employed in this analysis has a luminos-

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ity of 467 fb−1 and was collected with the BABAR detector at the PEP-II storage ring at a centre√ of-mass (cm) energy near s = 10.58GeV where the cross section is σ(τ + τ − ) = 0.919 ± 0.003[9]. τ -pair event production is simulated with higher-order radiative corrections using the KK2f Monte Carlo (MC) generator [10]The τ decays are simulated with Tauola [11] & Photos [12] using measured rates [6]. The detector response is simulated with GEANT4 [13]. Simulated events for signal as well as background processes [14,15,12,16, 17] are reconstructed in the same manner as data. The MC samples are used for selection optimization, control sample studies, and systematic error studies. The number of simulated non-signal events is comparable to the number expected in the data, with the exception of Bhabha and twophoton events, which are not simulated. Data studies demonstrate that these backgrounds are negligible and we set an upper limit on their contributions. The BABAR detector is described in detail elsewhere [18]. Charged-particle (track) momenta are measured with a 5-layer double-sided silicon vertex tracker and a 40-layer drift chamber inside a 1.5-T superconducting solenoidal magnet. An electromagnetic calorimeter consisting of 6580 CsI(Tl) crystals is used to identify electrons and photons, a ring-imaging Cherenkov detector is used to identify charged hadrons, and the instrumented magnetic flux return (IFR) is used to identify muons. Particle attributes are reconstructed in the laboratory frame and then boosted to the e+ e− cm frame using the measured asymmetric beam energies. 3. Analysis The approach for this analysis is to select a pure sample of one prong τ − decays with no neutrals using a three prong τ + → π + π + π − ν tag. After selection, the true number of events are calculated for each channel separately using the efficiencies determined from MC simulations. The efficiency, Ei , of each channel is modified using data control samples for each channel to account for small differences between MC and data. The number of decay mode i signal events measured

in the sample, NSig i , is then:   Bkg −1 Data N = (E ) − N NSig i i i i

(1)

is the number of data events sewhere NData i lected in decay channel i and NBkg is the esi timated number of background events in decay channel i. From this, the branching ratio relative to τ → eνν,

Bi Bτ →eνν

=

NSig i , NSig τ →eνν

can be com-

puted for each decay mode i. The data distributions are scaled with a reproducible random number to blind the signal branching fractions, until all selection criteria and systematic error evaluations have been finalized. Once unblinded, the values of the three branching ratios are used to calculate updated world averages of the branching fractions, which are then subsequently input into the background cross-contamination determination in an iterative manner to obtain final results. Events that have a total net charge of zero and four well reconstructed tracks, which are inconsistent with originating from the conversion of a photon in the material of the detector, are selected. The four tracks are required to be within the angular acceptance of the DIRC and EMC and to reach the DIRC, pt > 250M eV /c2 thus insuring good particle identification from the EMC, DIRC and DCH. The plane orthogonal to the thrust axis[19,20] is used to divide the event into hemispheres in the cm, where each hemisphere is associated with one of the τ decays. The “signal” hemisphere is required to have a single track and the other tracks are in the “3 prong” hemisphere. To remove two photon and Bhabha background, the event must have a missing energy in √ the cm between 10% and 70% of s. The angle of cm , is conthe missing momentum in the cm, θmiss cm strained to satisfy the relation |cos(θmiss )| < 0.7. To further reduce the two photon contamination, the thrust[19,20] of the event is required to be above 0.9, and the net missing transverse √ momentum in the cm is greater than 0.009 s. The three prong tracks have an electron veto applied to them to further reduce the Bhabha contamination. This results in less than 0.03% contamination from two photon events and less than 0.01%

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contamination from Bhabha events with an electron as the 1-prong. To increase the purity of the τ + τ − pair sample, the tracks in the 3 prong hemisphere are required to be consistent with being pions. Events that contain track pairs consistent with coming from a KS0 are vetoed. Large unassociated net neutral energy > 0.200MeV in the 3 prong hemisphere is also removed to reduce the non-τ backgrounds. Once a sample of 1-vs-3 prong τ events has been selected, the 1-prong decays are then classified as τ → eνν, τ → μνν, τ → πν or τ → Kν, using a likelihood approach to identify the τ → eνν, τ → πν and τ → Kν decays, and a neural network to identify τ → μνν decays. To improve the separation between signal channels and minimize systematic uncertainties, the 1-prong tracks are required to have a lab mometum of 1 to 4 GeV/c. The particle identification employs information from all five subdetectors of BABAR and is calibrated using control samples in the data and MC. To reduce contamination from Bhabha events and cross-feed from τ → eνν events into the τ → πν and τ → Kν channels, the ratio of deposited electromagnetic energy to the particle momentum in the lab frame of the kaon and pion tracks is required to be less than 0.85. Contamination from τ → μνν is reduced by vetoing muons with momentum in the lab frame from 1 to 4 GeV/c in the τ → πν channel, and above 3 GeV/c in the τ → Kν channel. The pion and kaon control samples from D∗+ → π + D0 , D0 → π + K − decays are used to study and correct for small differences between MC and data. These are crosschecked with independent π + (K − ) control samples from τ − → π − π − π + ντ (τ − → K − π − K + ντ ) decays using particle identification of two of the oppositely charged particles and the fact that τ − → π − π − K + ντ decays are essentially forbidden. Samples of radiative Bhabha and radiative μ-pair events provide control samples of electrons and muons. The systematic uncertainties associated with the charge particle identification is assessed from the control sample statistical errors, consistency between control samples, and the sensitivity of the control sample corrections to the density of particles in the event. The statisti-

cal errors in the more limited cross-check control samples dominate these errors. Channel specific selection criteria suppress cross-contamination and backgrounds from both other 1-prong τ -decays and non-τ events. For τ → eνν and τ → μνν events, the remaining Bhabha and μ-pair background is reduced by requiring the signal √ track to have a momentum less than 80% of s/2. Events with an unassociated EMC energy > 1.0 GeV (> 0.5 GeV) in the 1prong hemisphere are removed from the τ → eνν (τ → μνν) channels to further reduce the non-τ backgrounds. Events with > 0.2 GeV EMC energy in signal hemisphere unassociated with the 1-prong track are rejected for the τ → πν and τ → Kν channels. In the τ → Kν and τ → πν channels the largest remaining backgrounds come from τ decays with undetected neutral particles. To suppress these events, an algorithm that uses an approximation of the τ directions to determine the “pseudo-mass” of the neutrino, Mνpseudo , is employed. The cm direction of the τ that produced the signal track is approximated from the 3 prong system by assuming the τ + τ − pairs are back-to-back. The angle between the τ that decayed to the 3-prong system and direction of the 3-prong system in the cm is √ α = arccos

cm − m2 − m2 sEπππ τ πππ cm 2Pτcm Pπππ

 (2)

cm , m where Eπππ πππ , and Pπππ are the energy, mass, and momentum of the 3 prong hadronic system in CM, Pτcm is the momentum of the τ particle in the cm, and mτ is the mass of the τ [21]. The projection angle of the τ out of the plane of the signal track and 3 prong hadronic system, δ, is fixed to an optimized value. From this approximate τ direction and the cm direction of the signal track, the invariant mass of the neutrino, Mνpseudo , is evaluated. The angle δ and the cut on the Mνpseudo are optimized to minimize the statistical and background systematic uncertainties. Figure 1 show the Mνpseudo distribution. Events with Mνpseudo > 0.56 GeV are rejected. This reduces the sensitivity to the modelling of the angular resolution of the detector and initialand final-state radiation.

12

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Mν

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(GeV/c )

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Figure 1. The Mνpseudo distribution used to reject events with additional unmeasured particles for (left) the τ → πν and (right) the τ → Kν selected samples for the optimized value of δ = 58.5◦ . Data are points, the histogram is MC.

Table 1 The selection efficiency, purity, and number of selected events for each decay mode. N Data  Purity

τ → eνν 884426 0.589% 0.9969

τ → μνν 731102 0.485% 0.9729

τ → πν 369091 0.324% 0.7868

τ → Kν 25123 0.330% 0.7661

4. Results The selected number of events, the efficiency, and the purity for selected τ events can be seen in Table 1 while the branching ratios, along with their uncertainties, are presented in Table 2. Figures 2 and 3 show the momentum distributions in the cm for each of the four decay modes for data and MC. Systematic uncertainties are calculated for both the branching fractions and branching ratios, and include: contributions from efficiency; MC statistical and systematic uncertainties associated with particle identification; the sensitivity of the measurement to the hadronic and electromagnetic showers in the EMC; modelling of the EMC and DCH responses including scale and resolution; the modelling of backgrounds; modelling

0.9 0.2 1.0 0.1 0.2 < 0.1 < 0.1 1.4 0.9 0.5 0.9 0.1 0.3 0.4 0.20 1.4

0 0

0.5 0.6 0.4 0.1 0.1 0.4 0.20 1.0

-0.5

0.32 0.08 0.08 0.10 0.01 0.01 0.02 0.35

-1 -1

(0.06531 ± 0.00056 ± 0.00093) (0.0623 ± 0.0022)

-2

-1.5

(0.03882 ± 0.00032 ± 0.00056) (0.0384 ± 0.0013)

100

1000 -2

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(0.5945 ± 0.0014 ± 0.0061) (0.6076 ± 0.0061)

3000 2000 2000

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(0.9796 ± 0.0016 ± 0.0035) (0.9725 ± 0.0039)

4000 4000

B(τ →Kν) B(τ →πν)

5000

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6000 6000

BABAR Preliminary

700 600 600

B(τ →πν) B(τ →eνν)

7000

800 800

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BABAR Preliminary

9000 8000 8000

Branching Ratios This work PDG Sys. Uncert. (%) Particle ID &  EMC & DCH response backgrounds trigger π − π − π + modelling B(τ → π − π − π + ντ ) Lσe+ e− →τ + τ − Total Sys. Uncert.

Data τ- →K ντ τ- →π-ντ, π-π0ντ τ- → K K0L ντ, K π0ντ other τ non-τ

Events/(20MeV/c)

Events/(20MeV/c)

Data τ-→π-ντ τ-→μ-νμντ τ→π-π0ντ other τ non-τ

Table 2: The results of the branching ratios are presented where the first error is statistical and the second systematic. The contribution to the systematic uncertainty on each ratio is also presented. Note that efficiency includes a factor from the world average B(τ → π − π − π + ντ ) = (8.85 ± 0.13) × 10−2 [6].

I.M. Nugent / Nuclear Physics B (Proc. Suppl.) 189 (2009) 9–14

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I.M. Nugent / Nuclear Physics B (Proc. Suppl.) 189 (2009) 9–14

40000 40000 30000 20000 20000 10000

BABAR Preliminary

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Data τ- →K ντ τ- →π-ντ, π-π0ντ τ- → K K0L ντ, K π0ντ other τ non-τ

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BABAR Preliminary

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Data τ- →μ-νμ ντ τ→π-ντ, π-π0ντ τ- → K ντ,K K 0L ντ, K π0ντ other τ non-τ

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BABAR Preliminary

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Figure 2. Distribution of cm momentum for (left) the τ → eνν and (right) the τ → μνν selected samples. Data are points, the histogram is MC. The linear plot is on the top and the logarithmic plot is shown on the bottom.

of initial-final state radiation in τ + τ − decays; modelling of τ − → π − π − π + ντ decays; modelling of the trigger and estimation of the luminosity and cross-section. The various contributions to the systematic errors are shown in Table 2. Using the world average value of B(τ → eνν) = (17.82 ± 0.05) × 10−2 [22], the branching fractions B(τ → μνν) = (17.46 ± 0.09) × 10−2 , B(τ → πν) = (10.59 ± 0.11) × 10−2 , and B(τ → Kν) = (6.92 ± 0.12) × 10−3 were determined from the branching ratios relative to τ → eνν. The B(τ → Kν) branching fraction is consistent with and two times more precise than the current world average. The B(τ → μνν) branching fraction is both consistent with and competitive with the previous measurements, which are used in the world averages, and the B(τ → πν) branching ratio is consistent within 1.5 standard devi-

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Figure 3. Distribution of cm momentum for (left) the τ → πν and (right) the τ → Kν selected samples. Data are points, the histogram is MC. The linear plot is on the top and the logarithmic plot is shown on the bottom.

ations and competitive with the only previous measurements used in the world average[23]. Us→Kν) ing B(τ B(τ →πν) =(0.06531 ± 0.00056 ± 0.00093) and fK /fπ = 1.189 ± 0.007 [8] in  2 m2K 2 fK |Vus |2 1 − m2τ B(τ → Kν) = 2  2 B(τ → πν) fπ |Vud |2 m2 1 − mπ2

(3)

τ

we obtain |Vus | =0.2255 ± 0.0023, which is consistent with the value of (0.2262 ± 0.0011) predicted by CKM unitarity from |Vud | = (0.97408 ± 0.00026) [24]. If one includes the long distance electromagnetic corrections[25–28] in the determination of |Vus |, one obtains |Vus | =0.2254 ± 0.0023. Tests of μ − e universality can be ex-

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pressed as: gμ2 B(τ → μνν) f (m2e /m2τ ) = ge2 B(τ → eνν) f (m2μ /m2τ )

(4)

where f (x) = 1−8x+8x3 −x4 −12x2 log x, assuming that the neutrino masses are negligible. This g yields | gμe | = 1.0036 ± 0.0020. μ − τ universality can be expressed as:  2 m2μ 2 1 − 2 2 m τ 2m B(τ → Kν) gτ mK k μ K = (5)   m2 2 gμ2 B(K − → μ− ν μ ) δτ /K m3τ ττ 1 − mK2 τ  2 m2μ 2 1 − 2 2 m τ 2m mπ B(τ → πν) gτ π μ π =  2 (6) gμ2 B(π − → μ− ν μ ) δτ /π m3τ ττ m2 1 − mπ2 τ

where the radiative corrections are δτ /K = (1.0090 ± 0.0022), δτ /π = (1.0016 ± 0.0014) [29]. Using the world averaged mass and lifetime values [6], this yields | ggμτ | = 0.9836 ± 0.0087 using kaons and | ggμτ | = 0.9859 ± 0.0057 using pions. 5. Summary ¿From the preliminary results presented here, →Kν) it is seen that |Vus | obtained from B(τ B(τ →πν) is consistent with unitarity prediction, but individually both the branching fractions are lower slightly than the universality predictions. This makes both re-measuring the strange and non-strange spectral density function to extract |Vus | from τ decays with QCD Sum Rules, and obtaining improved measurements for testing charged lepton universality very interesting. REFERENCES 1. Cabibbo, N. Phys. Rev. Lett. 10, 531–532 (1963). 2. Klein, O. Nature 161, 897 (1948). 3. Puppi, G. Nuovo Cim. 5, 587–588 (1948). 4. Tiomno, J. and Wheeler, J. Rev. Mod. Phys. 21, 144 (1949). 5. Lee, T., Rosenbluth, M., and Yang, C. Phys. Rev. 75, 905 (1949). 6. Particle Data Group, W.-M. Y. et al.. J. Phys. G 33, 1 (2006).

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