- Email: [email protected]
Measurement of Michel parameters in leptonic τ decays at Belle
Available online at www.sciencedirect.com
Nuclear and Particle Physics Proceedings 287–288 (2017) 7–10 www.elsevier.com/locate/nppp
Measurement of Michel parameters in leptonic τ decays at Belle D.A. Epifanova,b,∗ a Budker
Institute of Nuclear Physics SB RAS, Novosibirsk 630090 State University, Novosibirsk 630090
b Novosibirsk
Abstract We present a study of Michel parameters in leptonic τ decays using experimental information collected at the Belle detector. Michel parameters are extracted in the unbinned maximum likelihood fit of the (τ∓ → ∓ νν; τ± → π± π0 ν) ( = e, μ) events in the full nine-dimensional phase space. We exploit the spin-spin correlation of tau leptons to extract ξρ ξ and ξρ ξδ in addition to the ρ and η parameters. Sensitivity of the method and systematic effects will be discussed. Keywords: tau lepton, charged weak interaction, Michel parameter
1. Introduction In the Standard Model (SM), the charged weak interaction is described by the exchange of a W ± boson with a pure vector coupling to only left-chirality fermions. Thus, in the low-energy four-fermion framework, the Lorentz structure of the matrix element is predicted to be of the “V-A⊗V-A” type. Deviations from this behavior would indicate new physics and might be caused either by changes in the W-boson couplings or through interactions mediated by new gauge bosons. Leptonic decays such as τ− → − ν¯ ντ ( = e, μ) (unless specified otherwise, charge-conjugated decays are implied throughout the paper) are the only ones in which the electroweak couplings can be probed without disturbance from the strong interaction. This makes them an ideal system to study the Lorentz structure of the charged weak current. The most general, Lorentz invariant, derivative-free and lepton-number-conserving four-lepton point interaction matrix element for this decay can be written as
∗ On
behalf of the Belle collaboration Email address: [email protected] (D.A. Epifanov)
http://dx.doi.org/10.1016/j.nuclphysbps.2017.03.033 2405-6014/© 2017 Elsevier B.V. All rights reserved.
[1]: 4G F M= √ 2
giNj u¯ i (l− )ΓN vn (¯νl ) u¯ m (ντ )ΓN u j (τ− ) ,
N=S ,V,T i, j=L,R
i √ (γμ γν − γν γμ ) (1) 2 2 The ΓN matrices define the properties of the two currents under a Lorentz transformation with N = S , V, T for scalar, vector and tensor interactions, respectively. The indices i and j label the right- or left-handedness (R, L) of the charged leptons. For a given i, j and N, the handedness of the neutrinos (n, m) is fixed. Ten nontrivial terms are characterized by ten complex coupling constants giNj ; those with gTRR and gTLL are identically zero. In the SM, the only non-zero coupling constant is gVLL = 1. As the couplings can be complex, with arbitrary overall phase, there are 19 independent parameters. The total strength of the weak interaction (charged weak current sector) is determined by the Fermi constant G F . In the case where neutrinos are not detected and the spin of the outgoing charged lepton is not determined, only four Michel parameters (MP) ρ, η, ξ and δ are experimentally accessible. They are bilinear combinations ΓS = 1, ΓV = γμ , ΓT =
D.A. Epifanov / Nuclear and Particle Physics Proceedings 287–288 (2017) 7–10
8
of the giNj coupling constants [2] and appear in the predicted energy spectrum of the charged lepton. In the τ rest frame, neglecting radiative corrections, this spectrum is given by [3]: 4 dΓ(τ∓ → ∓ νν) 4G2F Mτ Emax = x2 − x02 × dx dΩ (2π)4 2 × x(1 − x) + ρ(4x2 − 3x − x02 ) + ηx0 (1 − x) 9 1 2 ∓ Pτ cos θ ξ x2 − x02 1 − x + δ 4x − 4 + 1 − x02 , 3 3 m2 Mτ m E , Emax = , (2) x= 1 + 2 , x0 = Emax 2 Emax Mτ where Pτ is τ polarization, Ω is solid angle of the outgoing lepton, and θ is the angle between the τ spin and the lepton momentum. In the SM, the “V-A” charged weak current is characterized by ρ = 3/4, η = 0, ξ = 1 and δ = 3/4. 2. Method Measurement of ξ and δ requires knowledge of the τ spin direction. In experiments at e+ e− colliders with unpolarized e± beams, the average polarization of a single τ is zero. However, spin-spin correlations between the τ+ and τ− produced in the reaction e+ e− → τ+ τ− can be exploited [4]. The main idea of our method is to consider events where both taus decay to selected final states. One (signal) tau decays leptonically (τ− → − ντ ν¯ ) while the opposite tau, which decays via τ+ → π+ π0 ν¯ τ , serves as a spin analyser. We choose the τ+ → π+ π0 ν¯ τ decay mode because it has the largest branching fraction as well as properly studied dynamics (it is characterized by an additional parameter, ξρ , in the SM ξρ = 1)[5]. To write the total differential cross section for (τ− → − ντ ν¯ , τ+ → π+ π0 ν¯ τ ) (or, briefly, (− ; ρ+ )) events, we follow the approach developed in Refs. [6, 7]. The differential
SM = cross section, dσ Θ (Θ = {1, ρ, η, ξρ ξ, ξρ ξδ}, Θ d z {1, 3/4, 0, 1, 3/4}), is used to construct the probability density function (p.d.f.) for the measurement vector
z = {p , cos θ , φ , pρ , cos θρ , φρ , mππ , cos θ˜π , φ˜ π }:
= F ( z |Θ) , F ( z |Θ)
=
= dσ z |Θ Fi ( z)Θi , P( z |Θ)
d z N(Θ) i=0 4
= N(Θ)
F d z =
4 j=0
N jΘ j, N j =
F j ( z)d z,
(3)
where the form factors Fi ( z) (i = 0 ÷ 4) are calculated for each event and the five normalization constants Ni are evaluated using a Monte Carlo simulated sample. There are several corrections that must be incorporated in the procedure to take into account the real experimental situation. Physics corrections include electroweak higher-order corrections to the e+ e− → τ+ τ− cross section [8, 9], the effect of the radiative leptonic decay τ− → − ν¯ ντ γ [10], and the effect of the radiative hadronic decay τ− → π− π0 ντ γ [11]. Apparatus corrections include the effect of the finite detection efficiency and resolution, the effect of the external bremsstrahlung for (e± ; ρ∓ ) events, and the e± beam energy spread. The method described is used for a precise measurement of MP in (± ; ρ∓ ) events. This analysis is based on a 485 fb−1 data sample that contains 446 ×106 τ+ τ− pairs, collected with the Belle detector [12] at the KEKB energy-asymmetric e+ e− (3.5 on 8 GeV) collider [13] operating at the Υ(4S ) resonance. Two inner detector configurations are used in this analysis. A beampipe with a radius of 2.0 cm and a 3-layer silicon vertex detector are used for the first sample of 124 × 106 τ+ τ− pairs, while a 1.5 cm beampipe, a 4-layer silicon detector and a small-cell inner drift chamber are used to record the remaining 322 × 106 τ+ τ− pairs [14]. 3. Selection of (± ; ρ∓ ) events, background This analysis is based on events with one τ decaying to leptons τ− → − ν¯ ντ and the other decaying via the hadronic channel τ+ → π+ π0 ν¯ τ . The selection process, which is designed to suppress background while retaining a high efficiency for the decays under study, proceeds in two stages. The first-stage criteria suppress beam background to a negligible level and reject most of the background from other physical processes. In the second stage, the (± ; ρ∓ ) samples are selected from the remaining events. To select electrons, a likelihood ratio cut Pe = Le /(Le + L x ) > 0.8 is applied, where the electron likelihood function Le and the non-electron function L x include information on the specific ionization (dE/dx) measurement by the CDC, the ratio of the cluster energy in the ECL to the track momentum measured in the CDC, the transverse ECL shower shape and the light yield in the ACC. The efficiency of this cut for electrons is 93.1%. To select muons, the likelihood ratio cut Pμ = Lμ /(Lμ +Lπ +LK ) > 0.8 is applied. It has an 88.0% efficiency for muons. Each of the muon(Lμ ), pion(Lπ ) and kaon(LK ) likelihood functions is evaluated from two variables: the difference between the range calculated
D.A. Epifanov / Nuclear and Particle Physics Proceedings 287–288 (2017) 7–10
from the momentum of the particle and the range measured by KLM and the χ2 of the KLM hits with respect to the extrapolated track. To separate pions from kaons, we determine for each track the pion (Lπ ) and kaon (LK ) likelihoods from the ACC response, the dE/dx measurement in the CDC and the TOF flight-time measurement, and form a likelihood ratio PK/π = LK /(Lπ + LK ). For pions, we require PK/π < 0.6, which provides a pion identification efficiency of about 93% while keeping the pion fake rate at the 6% level. Finally, we select events with only one lepton ± , one charged pion π∓ and one π0 candidate. A π0 meson is reconstructed from a pair of gammas with an energy in the laboratory frame of EγLAB > 80 MeV and the γγ invariant mass in the range 115 MeV/c2 < Mγγ < 150 MeV/c2 . The absolute value of the π0 momentum in > the center-of-mass system (c.m.s.) must satisfy Pcms π0 0.3 GeV/c. The invariant mass of the π± π0 system must lie in the range 0.3 GeV/c2 < Mπ± π0 < 1.8 GeV/c2 . The opening angles between a lepton and charged pion and between a lepton and π0 should exceed 90◦ . To avoid the uncertainty due to the simulation of low energy fake ECL clusters, we allow additional photons in an event with the total energy in the laboratory frame of LAB Erestγ < 0.2 GeV. To evaluate the background and calculate efficiencies, a Monte Carlo sample of 2.87 × 109 τ+ τ− pairs is produced with the KKMC/TAUOLA generators [15, 16]. The detector response is simulated by a GEANT3-based program [17]. The detection efficiencies for signal events are ε(e ¯ ± ; ρ∓ ) = (11.53 ± 0.01)% and ε(μ ¯ ± ; ρ∓ ) = (12.43 ± 0.01)%. It is found that the dominant background comes from other τ decays; a contribution from non-ττ processes is very small – less than 0.1%. The dominant background arises from (τ− → − ν¯ ντ , τ+ → π+ π0 π0 ν¯ τ ) (or, briefly, (− ; (3π)+ )) events, where the second π0 is lost, and (τ− → π− ντ , τ+ → π+ π0 ν¯ τ ) (or, briefly, (π− ; ρ+ )) events, where a pion is misidentified as an electron or muon. Their contributions are: λ3π (± ; (3π)∓ ) = 9.8%/8.0% and λπ (π± ; ρ∓ ) = 0.1%/1.3% for the (e± ; ρ∓ )/(μ± ; ρ∓ ) events. For the (μ± ; ρ∓ ) events, an additional background at the level of λρ = 0.4% originates from (τ− → π− π0 ντ , τ+ → π+ π0 ν¯ τ ) (or, briefly, (ρ− ; ρ+ )) events, where a pion is misidentified as a muon, and π0 on the signal side is lost. The remaining background comes from the other τ decays; its contribution is λother = 2.0%/2.1% for the (e± ; ρ∓ )/(μ± ; ρ∓ ) events. The main background processes, (± ; (3π)∓ ), (π± ; ρ∓ ) and (ρ− ; ρ+ ) are included
9
in the p.d.f. analytically while the remaining background is taken into account using the MC-based approach [18]. The total p.d.f. is written as: P( z) =
ε( z) (1 − λ3π − λπ − λρ − λother ) ε¯
+λρ
B3π ( z | Θ) ε( z) ˜
z z | Θ)d ε¯ B3π ( ˜
+λ3π
+ λπ
B˜ ρ ( z) + λother ε( z) ˜ Bρ ( z)d z ε¯
S ( z | Θ) ε( z)
z z | Θ)d ε¯ S (
+
˜
Bπ ( z) + ε( z) ˜ z)d z ε¯ Bπ ( MC Bother ( z)
ε( z) MC z)d z ε¯ Bother (
,
(4)
B˜ π ( z) and B˜ ρ ( z) are the cross
B˜ 3π ( z | Θ), where S ( z | Θ), ± sections for the ( ; ρ∓ ), (± ; (3π)∓ ), (π± ; ρ∓ ) and (ρ− ; ρ+ ) events, respectively; ε( z) is the detection efficiency for signal phase events in the nine-dimensional
SM )d z/ S ( z | Θ
SM )d z is the space; and ε¯ = ε( z)S ( z | Θ average signal detection efficiency. 4. Analysis of experimental data After all selections, about 5.5 million events in all four configurations ((e+ ; ρ− ), (e− ; ρ+ ), (μ+ ; ρ− ), (μ− ; ρ+ )) are selected for the fit. A special procedure has been developed to evaluate the experimental trigtrg trg trg ger efficiency correction, corr = εEXP /εMC . The trigger efficiency correction as well as the lepton identiID , are incorporated in fication efficiency correction, corr the fitter by modifying the detection efficiency in Eq. 4: trg ID ε( z) → ε( z)corr corr . The result of the fit of the (e+ , ρ− ) experimental data is illustrated in Fig. 1. Reasonable agreement can be observed for the whole energy range, although the relative difference between experimental and optimal spectra indicates a remaining systematic effect of about a few percent. It is confirmed that the uncertainties arising from the physical and apparatus corrections to the p.d.f. as well as from the normalization are well below 1%; see Table 1. However, we still observe a systematic bias of the order of a few percent, especially in the ξρ ξ and ξρ ξδ MP. This bias originates from the remaining inaccuracies in the description of the experimental trigger efficiency correction. 5. Summary We present a study of Michel parameters in leptonic τ decays using a 485 fb−1 data sample collected at Belle. They are extracted in the unbinned maximum likelihood
D.A. Epifanov / Nuclear and Particle Physics Proceedings 287–288 (2017) 7–10
10
hetot
+
-
(e νν ; ρ ν)
14000
0.1 0.08 MC NEXP events/N events-1
Nevents/(50 MeV)
12000 10000 8000
(e+νν ; 3πν)
6000
0.02 0
−0.04
other
−0.06 −0.08
2000
0
0.06 0.04
−0.02
4000
0
(e+νν ; ρ-ν)
0.5
1
1.5
2
2.5
ECMS e
3
3.5
(GeV)
4
4.5
5
5.5
−0.1 0
0.5
1
1.5
2
2.5
3
3.5
ECMS (GeV) e
4
4.5
5
5.5
6
Figure 1: Result of the fit of (e+ ; ρ− ) experimental events. e+ energy spectrum in c.m.s. (left), relative difference between experimental energy spectrum and fit result (right). Points with errors show experimental data, histogram - result of the fit. Open histograms show signal events, shaded histograms - background contributions.
Table 1: Systematic uncertainties of MP related to: physical and apparatus corrections to p.d.f., finite accuracy of the normalization coefficients. Values are shown in units of percent (i.e. absolute deviation of the MP is multiplied by 100%).
MP σ(ρ), % σ(η), % σ(ξρ ξ), % σ(ξρ ξδ), %
ISR+O(α3 ) 0.10 0.30 0.20 0.15
τ → ννγ 0.03 0.10 0.09 0.08
τ → ρνγ 0.06 0.16 0.11 0.02
fit of the (± ; ρ∓ ) events in the full nine-dimensional phase space. We exploit the spin-spin correlation of tau leptons to extract ξρ ξ and ξρ ξδ in addition to the ρ and η Michel parameters. Although systematic uncertainties coming from the physical and apparatus corrections as well as from the normalization are below 1%, currently we still have a relatively large systematic bias in the ξρ ξ and ξρ ξδ parameters, which originates from the inaccurate description of the experimental trigger efficiency correction. 6. Acknowledgments This work was supported by Russian Foundation for Basic Research (grant 15-02-05674). References [1] W. Fetscher, H. J. Gerber and K. F. Johnson, Phys. Lett. B 173 (1986) 102. [2] W. Fetscher and H. J. Gerber, Adv. Ser. Direct. High Energy Phys. 14 (1995) 657. [3] C. Patrignani et al. (Particle Data Group), Chin. Phys. C 40 (2016) 100001.
Res. ⊕ brem. 0.10 0.33 0.11 0.19
σ(Ebeam ) 0.07 0.25 0.03 0.15
Norm. 0.21 0.60 0.38 0.26
trg
corr 1 2 3 3
[4] Y. -S. Tsai, Phys. Rev. D 4 (1971) 2821 [Erratum-ibid. D 13 (1976) 771]. [5] M. Fujikawa et al. [Belle Collaboration], Phys. Rev. D 78 (2008) 072006. [6] W. Fetscher, Phys. Rev. D 42 (1990) 1544. [7] K. Tamai, Nucl. Phys. B 668 (2003) 385. [8] E. A. Kuraev and V. S. Fadin, Sov. J. Nucl. Phys. 41 (1985) 466 [Yad. Fiz. 41 (1985) 733]. [9] S. Jadach and Z. Was, Acta Phys. Polon. B 15 (1984) 1151 [Erratum-ibid. B 16 (1985) 483]. [10] A. B. Arbuzov, Phys. Lett. B 524 (2002) 99. [11] F. Flores-Baez et al, Phys. Rev. Lett. D 74 (2006) 071301(R). [12] A. Abashian et al. (Belle Collaboration), Nucl. Instrum. Methods Phys. Res. Sect. A 479 (2002) 117; also see detector section in J.Brodzicka et al., Prog. Theor. Exp. Phys. 2012 (2012) 04D001. [13] S. Kurokawa and E. Kikutani, Nucl. Instrum. Methods Phys. Res. Sect. A 499 (2003) 1, and other papers included in this volume; T.Abe et al., Prog. Theor. Exp. Phys. 2013 (2013) 03A001 and following articles up to 03A011. [14] Z. Natkaniec et al. (Belle SVD2 Group), Nucl. Instr. Meth. A 560 (2006) 1. [15] S. Jadach, B. F. L. Ward and Z. Was, Comput. Phys. Commun. 130 (2000) 260. [16] Z. Was, Nucl. Phys. Proc. Suppl. 98 (2001) 96. [17] R. Brun et al, GEANT 3.21, CERN Report No. DD/EE/84-1 (1984). [18] D. M. Schmidt, R. J. Morrison and M. S. Witherell, Nucl. Instrum. Meth. A 328 (1993) 547.
Nuclear and Particle Physics Proceedings 287–288 (2017) 7–10 www.elsevier.com/locate/nppp
Measurement of Michel parameters in leptonic τ decays at Belle D.A. Epifanova,b,∗ a Budker
Institute of Nuclear Physics SB RAS, Novosibirsk 630090 State University, Novosibirsk 630090
b Novosibirsk
Abstract We present a study of Michel parameters in leptonic τ decays using experimental information collected at the Belle detector. Michel parameters are extracted in the unbinned maximum likelihood fit of the (τ∓ → ∓ νν; τ± → π± π0 ν) ( = e, μ) events in the full nine-dimensional phase space. We exploit the spin-spin correlation of tau leptons to extract ξρ ξ and ξρ ξδ in addition to the ρ and η parameters. Sensitivity of the method and systematic effects will be discussed. Keywords: tau lepton, charged weak interaction, Michel parameter
1. Introduction In the Standard Model (SM), the charged weak interaction is described by the exchange of a W ± boson with a pure vector coupling to only left-chirality fermions. Thus, in the low-energy four-fermion framework, the Lorentz structure of the matrix element is predicted to be of the “V-A⊗V-A” type. Deviations from this behavior would indicate new physics and might be caused either by changes in the W-boson couplings or through interactions mediated by new gauge bosons. Leptonic decays such as τ− → − ν¯ ντ ( = e, μ) (unless specified otherwise, charge-conjugated decays are implied throughout the paper) are the only ones in which the electroweak couplings can be probed without disturbance from the strong interaction. This makes them an ideal system to study the Lorentz structure of the charged weak current. The most general, Lorentz invariant, derivative-free and lepton-number-conserving four-lepton point interaction matrix element for this decay can be written as
∗ On
behalf of the Belle collaboration Email address: [email protected] (D.A. Epifanov)
http://dx.doi.org/10.1016/j.nuclphysbps.2017.03.033 2405-6014/© 2017 Elsevier B.V. All rights reserved.
[1]: 4G F M= √ 2
giNj u¯ i (l− )ΓN vn (¯νl ) u¯ m (ντ )ΓN u j (τ− ) ,
N=S ,V,T i, j=L,R
i √ (γμ γν − γν γμ ) (1) 2 2 The ΓN matrices define the properties of the two currents under a Lorentz transformation with N = S , V, T for scalar, vector and tensor interactions, respectively. The indices i and j label the right- or left-handedness (R, L) of the charged leptons. For a given i, j and N, the handedness of the neutrinos (n, m) is fixed. Ten nontrivial terms are characterized by ten complex coupling constants giNj ; those with gTRR and gTLL are identically zero. In the SM, the only non-zero coupling constant is gVLL = 1. As the couplings can be complex, with arbitrary overall phase, there are 19 independent parameters. The total strength of the weak interaction (charged weak current sector) is determined by the Fermi constant G F . In the case where neutrinos are not detected and the spin of the outgoing charged lepton is not determined, only four Michel parameters (MP) ρ, η, ξ and δ are experimentally accessible. They are bilinear combinations ΓS = 1, ΓV = γμ , ΓT =
D.A. Epifanov / Nuclear and Particle Physics Proceedings 287–288 (2017) 7–10
8
of the giNj coupling constants [2] and appear in the predicted energy spectrum of the charged lepton. In the τ rest frame, neglecting radiative corrections, this spectrum is given by [3]: 4 dΓ(τ∓ → ∓ νν) 4G2F Mτ Emax = x2 − x02 × dx dΩ (2π)4 2 × x(1 − x) + ρ(4x2 − 3x − x02 ) + ηx0 (1 − x) 9 1 2 ∓ Pτ cos θ ξ x2 − x02 1 − x + δ 4x − 4 + 1 − x02 , 3 3 m2 Mτ m E , Emax = , (2) x= 1 + 2 , x0 = Emax 2 Emax Mτ where Pτ is τ polarization, Ω is solid angle of the outgoing lepton, and θ is the angle between the τ spin and the lepton momentum. In the SM, the “V-A” charged weak current is characterized by ρ = 3/4, η = 0, ξ = 1 and δ = 3/4. 2. Method Measurement of ξ and δ requires knowledge of the τ spin direction. In experiments at e+ e− colliders with unpolarized e± beams, the average polarization of a single τ is zero. However, spin-spin correlations between the τ+ and τ− produced in the reaction e+ e− → τ+ τ− can be exploited [4]. The main idea of our method is to consider events where both taus decay to selected final states. One (signal) tau decays leptonically (τ− → − ντ ν¯ ) while the opposite tau, which decays via τ+ → π+ π0 ν¯ τ , serves as a spin analyser. We choose the τ+ → π+ π0 ν¯ τ decay mode because it has the largest branching fraction as well as properly studied dynamics (it is characterized by an additional parameter, ξρ , in the SM ξρ = 1)[5]. To write the total differential cross section for (τ− → − ντ ν¯ , τ+ → π+ π0 ν¯ τ ) (or, briefly, (− ; ρ+ )) events, we follow the approach developed in Refs. [6, 7]. The differential
SM = cross section, dσ Θ (Θ = {1, ρ, η, ξρ ξ, ξρ ξδ}, Θ d z {1, 3/4, 0, 1, 3/4}), is used to construct the probability density function (p.d.f.) for the measurement vector
z = {p , cos θ , φ , pρ , cos θρ , φρ , mππ , cos θ˜π , φ˜ π }:
= F ( z |Θ) , F ( z |Θ)
=
= dσ z |Θ Fi ( z)Θi , P( z |Θ)
d z N(Θ) i=0 4
= N(Θ)
F d z =
4 j=0
N jΘ j, N j =
F j ( z)d z,
(3)
where the form factors Fi ( z) (i = 0 ÷ 4) are calculated for each event and the five normalization constants Ni are evaluated using a Monte Carlo simulated sample. There are several corrections that must be incorporated in the procedure to take into account the real experimental situation. Physics corrections include electroweak higher-order corrections to the e+ e− → τ+ τ− cross section [8, 9], the effect of the radiative leptonic decay τ− → − ν¯ ντ γ [10], and the effect of the radiative hadronic decay τ− → π− π0 ντ γ [11]. Apparatus corrections include the effect of the finite detection efficiency and resolution, the effect of the external bremsstrahlung for (e± ; ρ∓ ) events, and the e± beam energy spread. The method described is used for a precise measurement of MP in (± ; ρ∓ ) events. This analysis is based on a 485 fb−1 data sample that contains 446 ×106 τ+ τ− pairs, collected with the Belle detector [12] at the KEKB energy-asymmetric e+ e− (3.5 on 8 GeV) collider [13] operating at the Υ(4S ) resonance. Two inner detector configurations are used in this analysis. A beampipe with a radius of 2.0 cm and a 3-layer silicon vertex detector are used for the first sample of 124 × 106 τ+ τ− pairs, while a 1.5 cm beampipe, a 4-layer silicon detector and a small-cell inner drift chamber are used to record the remaining 322 × 106 τ+ τ− pairs [14]. 3. Selection of (± ; ρ∓ ) events, background This analysis is based on events with one τ decaying to leptons τ− → − ν¯ ντ and the other decaying via the hadronic channel τ+ → π+ π0 ν¯ τ . The selection process, which is designed to suppress background while retaining a high efficiency for the decays under study, proceeds in two stages. The first-stage criteria suppress beam background to a negligible level and reject most of the background from other physical processes. In the second stage, the (± ; ρ∓ ) samples are selected from the remaining events. To select electrons, a likelihood ratio cut Pe = Le /(Le + L x ) > 0.8 is applied, where the electron likelihood function Le and the non-electron function L x include information on the specific ionization (dE/dx) measurement by the CDC, the ratio of the cluster energy in the ECL to the track momentum measured in the CDC, the transverse ECL shower shape and the light yield in the ACC. The efficiency of this cut for electrons is 93.1%. To select muons, the likelihood ratio cut Pμ = Lμ /(Lμ +Lπ +LK ) > 0.8 is applied. It has an 88.0% efficiency for muons. Each of the muon(Lμ ), pion(Lπ ) and kaon(LK ) likelihood functions is evaluated from two variables: the difference between the range calculated
D.A. Epifanov / Nuclear and Particle Physics Proceedings 287–288 (2017) 7–10
from the momentum of the particle and the range measured by KLM and the χ2 of the KLM hits with respect to the extrapolated track. To separate pions from kaons, we determine for each track the pion (Lπ ) and kaon (LK ) likelihoods from the ACC response, the dE/dx measurement in the CDC and the TOF flight-time measurement, and form a likelihood ratio PK/π = LK /(Lπ + LK ). For pions, we require PK/π < 0.6, which provides a pion identification efficiency of about 93% while keeping the pion fake rate at the 6% level. Finally, we select events with only one lepton ± , one charged pion π∓ and one π0 candidate. A π0 meson is reconstructed from a pair of gammas with an energy in the laboratory frame of EγLAB > 80 MeV and the γγ invariant mass in the range 115 MeV/c2 < Mγγ < 150 MeV/c2 . The absolute value of the π0 momentum in > the center-of-mass system (c.m.s.) must satisfy Pcms π0 0.3 GeV/c. The invariant mass of the π± π0 system must lie in the range 0.3 GeV/c2 < Mπ± π0 < 1.8 GeV/c2 . The opening angles between a lepton and charged pion and between a lepton and π0 should exceed 90◦ . To avoid the uncertainty due to the simulation of low energy fake ECL clusters, we allow additional photons in an event with the total energy in the laboratory frame of LAB Erestγ < 0.2 GeV. To evaluate the background and calculate efficiencies, a Monte Carlo sample of 2.87 × 109 τ+ τ− pairs is produced with the KKMC/TAUOLA generators [15, 16]. The detector response is simulated by a GEANT3-based program [17]. The detection efficiencies for signal events are ε(e ¯ ± ; ρ∓ ) = (11.53 ± 0.01)% and ε(μ ¯ ± ; ρ∓ ) = (12.43 ± 0.01)%. It is found that the dominant background comes from other τ decays; a contribution from non-ττ processes is very small – less than 0.1%. The dominant background arises from (τ− → − ν¯ ντ , τ+ → π+ π0 π0 ν¯ τ ) (or, briefly, (− ; (3π)+ )) events, where the second π0 is lost, and (τ− → π− ντ , τ+ → π+ π0 ν¯ τ ) (or, briefly, (π− ; ρ+ )) events, where a pion is misidentified as an electron or muon. Their contributions are: λ3π (± ; (3π)∓ ) = 9.8%/8.0% and λπ (π± ; ρ∓ ) = 0.1%/1.3% for the (e± ; ρ∓ )/(μ± ; ρ∓ ) events. For the (μ± ; ρ∓ ) events, an additional background at the level of λρ = 0.4% originates from (τ− → π− π0 ντ , τ+ → π+ π0 ν¯ τ ) (or, briefly, (ρ− ; ρ+ )) events, where a pion is misidentified as a muon, and π0 on the signal side is lost. The remaining background comes from the other τ decays; its contribution is λother = 2.0%/2.1% for the (e± ; ρ∓ )/(μ± ; ρ∓ ) events. The main background processes, (± ; (3π)∓ ), (π± ; ρ∓ ) and (ρ− ; ρ+ ) are included
9
in the p.d.f. analytically while the remaining background is taken into account using the MC-based approach [18]. The total p.d.f. is written as: P( z) =
ε( z) (1 − λ3π − λπ − λρ − λother ) ε¯
+λρ
B3π ( z | Θ) ε( z) ˜
z z | Θ)d ε¯ B3π ( ˜
+λ3π
+ λπ
B˜ ρ ( z) + λother ε( z) ˜ Bρ ( z)d z ε¯
S ( z | Θ) ε( z)
z z | Θ)d ε¯ S (
+
˜
Bπ ( z) + ε( z) ˜ z)d z ε¯ Bπ ( MC Bother ( z)
ε( z) MC z)d z ε¯ Bother (
,
(4)
B˜ π ( z) and B˜ ρ ( z) are the cross
B˜ 3π ( z | Θ), where S ( z | Θ), ± sections for the ( ; ρ∓ ), (± ; (3π)∓ ), (π± ; ρ∓ ) and (ρ− ; ρ+ ) events, respectively; ε( z) is the detection efficiency for signal phase events in the nine-dimensional
SM )d z/ S ( z | Θ
SM )d z is the space; and ε¯ = ε( z)S ( z | Θ average signal detection efficiency. 4. Analysis of experimental data After all selections, about 5.5 million events in all four configurations ((e+ ; ρ− ), (e− ; ρ+ ), (μ+ ; ρ− ), (μ− ; ρ+ )) are selected for the fit. A special procedure has been developed to evaluate the experimental trigtrg trg trg ger efficiency correction, corr = εEXP /εMC . The trigger efficiency correction as well as the lepton identiID , are incorporated in fication efficiency correction, corr the fitter by modifying the detection efficiency in Eq. 4: trg ID ε( z) → ε( z)corr corr . The result of the fit of the (e+ , ρ− ) experimental data is illustrated in Fig. 1. Reasonable agreement can be observed for the whole energy range, although the relative difference between experimental and optimal spectra indicates a remaining systematic effect of about a few percent. It is confirmed that the uncertainties arising from the physical and apparatus corrections to the p.d.f. as well as from the normalization are well below 1%; see Table 1. However, we still observe a systematic bias of the order of a few percent, especially in the ξρ ξ and ξρ ξδ MP. This bias originates from the remaining inaccuracies in the description of the experimental trigger efficiency correction. 5. Summary We present a study of Michel parameters in leptonic τ decays using a 485 fb−1 data sample collected at Belle. They are extracted in the unbinned maximum likelihood
D.A. Epifanov / Nuclear and Particle Physics Proceedings 287–288 (2017) 7–10
10
hetot
+
-
(e νν ; ρ ν)
14000
0.1 0.08 MC NEXP events/N events-1
Nevents/(50 MeV)
12000 10000 8000
(e+νν ; 3πν)
6000
0.02 0
−0.04
other
−0.06 −0.08
2000
0
0.06 0.04
−0.02
4000
0
(e+νν ; ρ-ν)
0.5
1
1.5
2
2.5
ECMS e
3
3.5
(GeV)
4
4.5
5
5.5
−0.1 0
0.5
1
1.5
2
2.5
3
3.5
ECMS (GeV) e
4
4.5
5
5.5
6
Figure 1: Result of the fit of (e+ ; ρ− ) experimental events. e+ energy spectrum in c.m.s. (left), relative difference between experimental energy spectrum and fit result (right). Points with errors show experimental data, histogram - result of the fit. Open histograms show signal events, shaded histograms - background contributions.
Table 1: Systematic uncertainties of MP related to: physical and apparatus corrections to p.d.f., finite accuracy of the normalization coefficients. Values are shown in units of percent (i.e. absolute deviation of the MP is multiplied by 100%).
MP σ(ρ), % σ(η), % σ(ξρ ξ), % σ(ξρ ξδ), %
ISR+O(α3 ) 0.10 0.30 0.20 0.15
τ → ννγ 0.03 0.10 0.09 0.08
τ → ρνγ 0.06 0.16 0.11 0.02
fit of the (± ; ρ∓ ) events in the full nine-dimensional phase space. We exploit the spin-spin correlation of tau leptons to extract ξρ ξ and ξρ ξδ in addition to the ρ and η Michel parameters. Although systematic uncertainties coming from the physical and apparatus corrections as well as from the normalization are below 1%, currently we still have a relatively large systematic bias in the ξρ ξ and ξρ ξδ parameters, which originates from the inaccurate description of the experimental trigger efficiency correction. 6. Acknowledgments This work was supported by Russian Foundation for Basic Research (grant 15-02-05674). References [1] W. Fetscher, H. J. Gerber and K. F. Johnson, Phys. Lett. B 173 (1986) 102. [2] W. Fetscher and H. J. Gerber, Adv. Ser. Direct. High Energy Phys. 14 (1995) 657. [3] C. Patrignani et al. (Particle Data Group), Chin. Phys. C 40 (2016) 100001.
Res. ⊕ brem. 0.10 0.33 0.11 0.19
σ(Ebeam ) 0.07 0.25 0.03 0.15
Norm. 0.21 0.60 0.38 0.26
trg
corr 1 2 3 3
[4] Y. -S. Tsai, Phys. Rev. D 4 (1971) 2821 [Erratum-ibid. D 13 (1976) 771]. [5] M. Fujikawa et al. [Belle Collaboration], Phys. Rev. D 78 (2008) 072006. [6] W. Fetscher, Phys. Rev. D 42 (1990) 1544. [7] K. Tamai, Nucl. Phys. B 668 (2003) 385. [8] E. A. Kuraev and V. S. Fadin, Sov. J. Nucl. Phys. 41 (1985) 466 [Yad. Fiz. 41 (1985) 733]. [9] S. Jadach and Z. Was, Acta Phys. Polon. B 15 (1984) 1151 [Erratum-ibid. B 16 (1985) 483]. [10] A. B. Arbuzov, Phys. Lett. B 524 (2002) 99. [11] F. Flores-Baez et al, Phys. Rev. Lett. D 74 (2006) 071301(R). [12] A. Abashian et al. (Belle Collaboration), Nucl. Instrum. Methods Phys. Res. Sect. A 479 (2002) 117; also see detector section in J.Brodzicka et al., Prog. Theor. Exp. Phys. 2012 (2012) 04D001. [13] S. Kurokawa and E. Kikutani, Nucl. Instrum. Methods Phys. Res. Sect. A 499 (2003) 1, and other papers included in this volume; T.Abe et al., Prog. Theor. Exp. Phys. 2013 (2013) 03A001 and following articles up to 03A011. [14] Z. Natkaniec et al. (Belle SVD2 Group), Nucl. Instr. Meth. A 560 (2006) 1. [15] S. Jadach, B. F. L. Ward and Z. Was, Comput. Phys. Commun. 130 (2000) 260. [16] Z. Was, Nucl. Phys. Proc. Suppl. 98 (2001) 96. [17] R. Brun et al, GEANT 3.21, CERN Report No. DD/EE/84-1 (1984). [18] D. M. Schmidt, R. J. Morrison and M. S. Witherell, Nucl. Instrum. Meth. A 328 (1993) 547.