- Email: [email protected]
Measurement of the τ lifetime from Belle
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Nuclear Physics B (Proc. Suppl.) 253–255 (2014) 87–90 www.elsevier.com/locate/npbps
Measurement of the τ lifetime from Belle$ A.A. Sokolov IHEP, Protvino, Russia
Abstract The lifetime of the τ-lepton is measured using the process e+ e− → τ+ τ− , where both τ-leptons decay to 3πν. The preliminary result based on 711 fb−1 of data collected on the Υ(4S ) resonance and in the nearby continuum is ττ = (290.18 ± 0.54(stat.) ± 0.33(syst.)) × 10−15 s.
High precision measurements of the mass, lifetime and leptonic branching fractions of the τ-lepton can be used to test the lepton universality [1], which is assumed in the Standard Model. The present PDG value of the τ lifetime [2] is dominated by the results obtained by LEP experiments [3]. The BABAR experiment has also reported its preliminary result based on the data sample of 80 fb−1 [4] which is consistent with the PDG value and has the same level of precision as in the PDG. A high statistics data sample collected at Belle allows one to select τ+ τ− events where both τ-leptons decay to three charged pions and neutrino. The Belle τ-lepton lifetime precision measurement has systematic uncertainties quite different from the LEP experiments, that is why the combined result is useful for the test of the hypothesis of the lepton universality. In this paper we report a preliminary measurement of the τ-lepton lifetime in the Belle experiment. We use 711 fb−1 of data collected on the Υ(4S ) resonance and in the nearby continuum with the Belle detector [5] at the KEKB asymmetric-energy e+ e− collider [6]. We study e+ e− → τ+ τ− events where both τ-leptons decay to three charged pions and neutrino. In the Center-of-Mass (CM) frame τ+ and τ− leptons go back to back with the energy Eτ equal to the beam $ On
behalf of the Belle Collaboration. Email address: [email protected] (A.A. Sokolov)
http://dx.doi.org/10.1016/j.nuclphysbps.2014.09.021 0920-5632/© 2014 Elsevier B.V. All rights reserved.
energy Ebeam if we neglect the initial and final state radiation. For events under consideration the directions of the τ-leptons in the CM frame can be determined with two-fold ambiguity. Indeed, if we assume the neutrino mass to be zero for the hadronic decay τ → Xντ (X is the hadronic system), the angle θ between the momentum of the system X and the momentum of the τ-lepton is determined as cos(θ) = (2Eτ E X − m2τ − m2X )/(2PX Pτ ). Here Eτ , Pτ , mτ (E X , PX , mX ) are the energy, momentum and mass of the τ-lepton (hadronic system X), respectively. The requirement that τ-leptons go back to back in the CM frame may be written as a system of two linear and one quadratic equations. Two solutions of this system of equations are possible for τ-lepton flight directions. In the Laboratory frame τ-leptons should go along the straight lines which are defined by the directions, determined by the τ-momenta obtained after Lorentz boost and τ+ , τ− decay points. For the momentum direction of each τ-lepton we use the average direction of two solutions for this τ. For the decay point of each τ-lepton we take the 3D point of intersection of momenta of pions of the corresponding triplet. Due to the finite detector resolution the straight lines can not cross at a point of the 3-dimensional space. The separation between them is characterized by the minimal distance dl. The stability of this choice of τ-lepton momentum directions is supported by the Monte Carlo (MC) simulation of τ+ τ− events by the KKMC genera-
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A.A. Sokolov / Nuclear Physics B (Proc. Suppl.) 253–255 (2014) 87–90
tor [7] which were the input of the full detector simulation based on the GEANT 3 [8]. These events were passed through the same reconstruction procedures as for the data. The points of the minimal distance at the τ momentum straight lines are considered as the production points of the correponding τ-leptons. Thus, for each τ+ τ− event, where both τ-leptons decay into a 3π hadronic system and neutrino, we can determine the proper decay time parameters ct for both τ-leptons. The reconstructed value of ct (product of the speed of light and the τ lifetime) for each τ-lepton is evaluated from the distance between the production and decay points l as ct = l/(βγ). Here βγ is the relativistic kinematic factor. Some limitations were applied for the selection of the τ+ τ− events where both τ-leptons decay into three charged pions and neutrino: 1. there are exactly 6 charged tracks compatible with the pion hypothesis with zero net charge; 2. there are no KS , Λ and π0 in the event; 3. the number of photons which are not assigned to be from π0 should be smaller than 6, their total energy should be less than 0.7 GeV; 4. the thrust value of the event in the CM frame is greater than 0.9; 5. the square of the transverse momentum of the 6π system is greater than 0.25 (GeV/c)2 ; 6. the mass m(6π) of the 6π system obeys 4 GeV/c2 < m(6π) < 10.25 GeV/c2 ; 7. the event is divided into two hemispheres by the plane perpendicular to the thrust axis; in each hemisphere there should be 3 pions with the net charge equal to ±1; 8. pseudomass (Mmin =
m2X
+ 2(Ebeam − E X )(E X − PX )) of each
triplet of pions is less than 1.8 GeV/c2 ; 9. each pion triplet should be fitted to a common vertex with the χ2 < 20; 10. dl < 0.02 cm. The selection rules listed above were applied to the data and MC events for the signal τ+ τ− events and different sorts of background. The generated proper time distribution for the MC τ+ τ− events after the application of the listed above selection rules is well described by the exponential function. The shift of the coresponding exponential slope from the original value 87.11 μm is 0.56 ± 0.06 μm. The resolution function can be extracted from the signal MC τ+ τ− events which is the distribution of the difference of the reconstructed ct of the τ-lepton and true ct
Figure 1: The difference between the reconstructed and true ct values for τ-leptons (KKMC generator). The line is the result of the fit by the function (1).
value with which the τ-lepton was generated by KKMC (see Fig. 1). This distribution was fitted by the function (1) R(x) = P1 · R(x, P2 , ..., P6 ) = P1 · (1 − 2.5x)· (x − P2 )2 , exp − 2 · σ2
(1)
where σ = P3 + P4 |x − P2 |1/2 + P5 |x − P2 | + P6 |x − P2 |3/2 , Pi (i =1,...6) are free parameters. The ct distribution for the MC τ+ τ− events is parameterized with a convolution of the exponential function with the resolution function R(x) Y(x) = P1 e−t/P2 R((x − t), P3 , ..., P7 )dt (2) with free parameters P1 -P7 . The parameter P2 corresponds to the cτ where τ is the τ-lepton lifetime. To fit the data ct distribution we should take into account the background contamination. This contamination amounts to a few percent. The main source of background are light quark qq-events. ¯ For these events, all six pions come mainly from the same primary vertex and they are similar to the τ+ τ− events with a zero lifetime; the reconstructed ct distribution can be described with (1). The similar behavior is expected for γγ events. Other sources of the background comig from the events
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A.A. Sokolov / Nuclear Physics B (Proc. Suppl.) 253–255 (2014) 87–90
Table 1: Generated and fitted cτ values for MC events after all selections.
Generated cτ μm 87.11 84 90
Figure 2: The reconstructed ct values for the data (filled circles with errors). The black line is the result of the fit by (3). The red histogram is the MC prediction for the sum of qq¯ and γγ background contribution. The magenta line is the contribution for (qq¯ + γγ) obtained in the fit. The blue histogram is the MC prediction for the sum of charm and beauty background contributions. The blue line is the approximation of charm and beauty contribution which is used in the fit.
¯ production contribute with a charm (c¯c) and beauty (bb) to the selected data sample at the per mille level. The reconstructed ct distribution for the sum of charm and beauty MC events can be fitted by the function Bkgcb (x) which is the sum of two Gaussians with six free parameters. The data ct distribution is fitted by the sum of functions for the signal contribution Y(x) (2) and background contributions, which are fixed at the level predicted by MC: F(x) = P1 e−t/P2 R((x − t), P3 , ..., P7 )dt +Aqq¯ · R(x, P3 , ..., P7 ) + Bkgcb (x),
(3)
with seven free parameters P1 -P7 , the coefficient Aqq¯ gives the level of qq-events. ¯ The variation of the levels of the background contributions in the data fit was taken into account in the estimation of the systematic uncertainty. The experimental ct distribution together with the result of the fit and estimated sources of background contributions are shown in Fig. 2. The value of the P2 parameter obtained from the fit of the data ct distribution is 86.53 ± 0.16 μm. The relation of the parameter P2 value to the true cτ value was analyzed using three KKMC τ+ τ− samples with the τlepton cτ value 84.00, 87.11 and 90.00 μm, respectively. To check that the fitting procedure gives the correct es-
Generated cτ after all selections 86.550 ± 0.064 83.528 ± 0.070 89.518 ± 0.080
P2 value from the fit 86.57 ± 0.12 83.61 ± 0.12 89.46 ± 0.13
timation of the input lifetime value we fit the ct distributions for these MC samples of events selected by rules (1.-10.). Comparison of the generated cτ values after all selections and the parameter P2 values obtained from the fit shows that they are compatible within errors (see Table 1), that is the fitting procedure well reproduces the lifetime value of the selected events. From Table 1 we see that the selection criteria introduce a certain shift to the measured cτ value which is about 0.5 μm. This shift does not depend on the τ-lepton lifetime. To correct this shift we use the following procedure. For the used MC samples we constructed a plot of the obtained P2 values as a function of the cτ values which was used in a generation of the corresponding MC samples. The corresponding dependence can be fitted by the straight line. The values of parameters A and B obtained from the fit of this dependence by the function (P2 − 87) = A + B · (cτ − 87) are: A = −0.465 ± 0.067, B = 0.982 ± 0.027. We use this parametrization for the correction of the fitted P2 value in the measured cτ value. This correction gives: cτmeasured = (86.99±0.16(stat.)±0.07(MC)) μm.(4) The first error is statistical and the second one is due to the correction procedure. The following sources of systematic uncertainties have been analyzed: fitting procedure (choice of the fit range of the reconstructed ct distribution); accuracy of the description of the initial and final state radiation in MC; beam energy accuracy; alignment of the vertex detector SVD; accuracy of the estimation of the background contribution; accuracy of a knowledge of the τlepton mass; accuracy of the measured cτ value shift estimation from a dl cut. An additional source of a systematic uncertainty comes from the limited statistics of the τ+ τ− MC samples which introduce an uncertainty to the correction of the lifetime parameter obtained from the fit. The summary of systematic uncertainties is shown in Table 2 In summary, the τ-lepton lifetime has been measured using the technique of the direct lifetime measurement in fully kinematically reconstructed e+ e− → τ+ τ− →
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A.A. Sokolov / Nuclear Physics B (Proc. Suppl.) 253–255 (2014) 87–90
Table 2: Systematic uncertainties.
Source of Systematics MC correction Fit range ISR & FSR description Beam energy SVD alignement Background contribution Error of the τ-lepton mass dl cut Total
Δcτ in μm 0.068 0.020 0.018 0.016 0.050 0.003 0.009 0.050 0.103
3πν 3πν events. The preliminary result is τ = (290.18 ± 0.54(stat.) ± 0.33(syst.) × 10−15 s. cτ = 86.99 ± 0.16(stat.) ± 0.10(syst.) μm. References [1] Y.S. Tsai, Phys.Rev. D 4, 2821 (1971); H.B. Thacker and J.J. Sakurai, Phys. Lett. B 36, 103 (1971). [2] J. Beringer et al. (Particle Data Group), Phys. Rev. D86, 010001 (2012). [3] P. Abreu et al. (DELPHI Collaboration), Phys. Lett. B 365, 448 (1996); G. Alexander et al. (OPAL Collaboration), Phys. Lett. B 374, 341 (1996); R. Barate et al. (ALEPH Collaboration), Phys. Lett. B 414, 362 (1997); M. Acciarri et al. (L3 Collaboration), Phys. Lett. B 479, 67 (2000). [4] A. Lusiani, Nucl. Phys. B (Proc. Suppl.) 144, 105 (2005). [5] A. Abashian et al. (Belle Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 479, 117 (2002). [6] S. Kurokawa and E. Kikutani, Nucl. Instrum. Methods Phys. Res., Sect. A 499, 1 (2003), and other papers included in this volume. [7] S.Jadach, B.F.L.Ward, Z.Wa¸s, Comp. Phys. Commun. 130, 260 (2000). [8] R. Brun et al. GEANT 3.21. Report No. CERN DD/EE/84-1 (1984).
Nuclear Physics B (Proc. Suppl.) 253–255 (2014) 87–90 www.elsevier.com/locate/npbps
Measurement of the τ lifetime from Belle$ A.A. Sokolov IHEP, Protvino, Russia
Abstract The lifetime of the τ-lepton is measured using the process e+ e− → τ+ τ− , where both τ-leptons decay to 3πν. The preliminary result based on 711 fb−1 of data collected on the Υ(4S ) resonance and in the nearby continuum is ττ = (290.18 ± 0.54(stat.) ± 0.33(syst.)) × 10−15 s.
High precision measurements of the mass, lifetime and leptonic branching fractions of the τ-lepton can be used to test the lepton universality [1], which is assumed in the Standard Model. The present PDG value of the τ lifetime [2] is dominated by the results obtained by LEP experiments [3]. The BABAR experiment has also reported its preliminary result based on the data sample of 80 fb−1 [4] which is consistent with the PDG value and has the same level of precision as in the PDG. A high statistics data sample collected at Belle allows one to select τ+ τ− events where both τ-leptons decay to three charged pions and neutrino. The Belle τ-lepton lifetime precision measurement has systematic uncertainties quite different from the LEP experiments, that is why the combined result is useful for the test of the hypothesis of the lepton universality. In this paper we report a preliminary measurement of the τ-lepton lifetime in the Belle experiment. We use 711 fb−1 of data collected on the Υ(4S ) resonance and in the nearby continuum with the Belle detector [5] at the KEKB asymmetric-energy e+ e− collider [6]. We study e+ e− → τ+ τ− events where both τ-leptons decay to three charged pions and neutrino. In the Center-of-Mass (CM) frame τ+ and τ− leptons go back to back with the energy Eτ equal to the beam $ On
behalf of the Belle Collaboration. Email address: [email protected] (A.A. Sokolov)
http://dx.doi.org/10.1016/j.nuclphysbps.2014.09.021 0920-5632/© 2014 Elsevier B.V. All rights reserved.
energy Ebeam if we neglect the initial and final state radiation. For events under consideration the directions of the τ-leptons in the CM frame can be determined with two-fold ambiguity. Indeed, if we assume the neutrino mass to be zero for the hadronic decay τ → Xντ (X is the hadronic system), the angle θ between the momentum of the system X and the momentum of the τ-lepton is determined as cos(θ) = (2Eτ E X − m2τ − m2X )/(2PX Pτ ). Here Eτ , Pτ , mτ (E X , PX , mX ) are the energy, momentum and mass of the τ-lepton (hadronic system X), respectively. The requirement that τ-leptons go back to back in the CM frame may be written as a system of two linear and one quadratic equations. Two solutions of this system of equations are possible for τ-lepton flight directions. In the Laboratory frame τ-leptons should go along the straight lines which are defined by the directions, determined by the τ-momenta obtained after Lorentz boost and τ+ , τ− decay points. For the momentum direction of each τ-lepton we use the average direction of two solutions for this τ. For the decay point of each τ-lepton we take the 3D point of intersection of momenta of pions of the corresponding triplet. Due to the finite detector resolution the straight lines can not cross at a point of the 3-dimensional space. The separation between them is characterized by the minimal distance dl. The stability of this choice of τ-lepton momentum directions is supported by the Monte Carlo (MC) simulation of τ+ τ− events by the KKMC genera-
88
A.A. Sokolov / Nuclear Physics B (Proc. Suppl.) 253–255 (2014) 87–90
tor [7] which were the input of the full detector simulation based on the GEANT 3 [8]. These events were passed through the same reconstruction procedures as for the data. The points of the minimal distance at the τ momentum straight lines are considered as the production points of the correponding τ-leptons. Thus, for each τ+ τ− event, where both τ-leptons decay into a 3π hadronic system and neutrino, we can determine the proper decay time parameters ct for both τ-leptons. The reconstructed value of ct (product of the speed of light and the τ lifetime) for each τ-lepton is evaluated from the distance between the production and decay points l as ct = l/(βγ). Here βγ is the relativistic kinematic factor. Some limitations were applied for the selection of the τ+ τ− events where both τ-leptons decay into three charged pions and neutrino: 1. there are exactly 6 charged tracks compatible with the pion hypothesis with zero net charge; 2. there are no KS , Λ and π0 in the event; 3. the number of photons which are not assigned to be from π0 should be smaller than 6, their total energy should be less than 0.7 GeV; 4. the thrust value of the event in the CM frame is greater than 0.9; 5. the square of the transverse momentum of the 6π system is greater than 0.25 (GeV/c)2 ; 6. the mass m(6π) of the 6π system obeys 4 GeV/c2 < m(6π) < 10.25 GeV/c2 ; 7. the event is divided into two hemispheres by the plane perpendicular to the thrust axis; in each hemisphere there should be 3 pions with the net charge equal to ±1; 8. pseudomass (Mmin =
m2X
+ 2(Ebeam − E X )(E X − PX )) of each
triplet of pions is less than 1.8 GeV/c2 ; 9. each pion triplet should be fitted to a common vertex with the χ2 < 20; 10. dl < 0.02 cm. The selection rules listed above were applied to the data and MC events for the signal τ+ τ− events and different sorts of background. The generated proper time distribution for the MC τ+ τ− events after the application of the listed above selection rules is well described by the exponential function. The shift of the coresponding exponential slope from the original value 87.11 μm is 0.56 ± 0.06 μm. The resolution function can be extracted from the signal MC τ+ τ− events which is the distribution of the difference of the reconstructed ct of the τ-lepton and true ct
Figure 1: The difference between the reconstructed and true ct values for τ-leptons (KKMC generator). The line is the result of the fit by the function (1).
value with which the τ-lepton was generated by KKMC (see Fig. 1). This distribution was fitted by the function (1) R(x) = P1 · R(x, P2 , ..., P6 ) = P1 · (1 − 2.5x)· (x − P2 )2 , exp − 2 · σ2
(1)
where σ = P3 + P4 |x − P2 |1/2 + P5 |x − P2 | + P6 |x − P2 |3/2 , Pi (i =1,...6) are free parameters. The ct distribution for the MC τ+ τ− events is parameterized with a convolution of the exponential function with the resolution function R(x) Y(x) = P1 e−t/P2 R((x − t), P3 , ..., P7 )dt (2) with free parameters P1 -P7 . The parameter P2 corresponds to the cτ where τ is the τ-lepton lifetime. To fit the data ct distribution we should take into account the background contamination. This contamination amounts to a few percent. The main source of background are light quark qq-events. ¯ For these events, all six pions come mainly from the same primary vertex and they are similar to the τ+ τ− events with a zero lifetime; the reconstructed ct distribution can be described with (1). The similar behavior is expected for γγ events. Other sources of the background comig from the events
89
A.A. Sokolov / Nuclear Physics B (Proc. Suppl.) 253–255 (2014) 87–90
Table 1: Generated and fitted cτ values for MC events after all selections.
Generated cτ μm 87.11 84 90
Figure 2: The reconstructed ct values for the data (filled circles with errors). The black line is the result of the fit by (3). The red histogram is the MC prediction for the sum of qq¯ and γγ background contribution. The magenta line is the contribution for (qq¯ + γγ) obtained in the fit. The blue histogram is the MC prediction for the sum of charm and beauty background contributions. The blue line is the approximation of charm and beauty contribution which is used in the fit.
¯ production contribute with a charm (c¯c) and beauty (bb) to the selected data sample at the per mille level. The reconstructed ct distribution for the sum of charm and beauty MC events can be fitted by the function Bkgcb (x) which is the sum of two Gaussians with six free parameters. The data ct distribution is fitted by the sum of functions for the signal contribution Y(x) (2) and background contributions, which are fixed at the level predicted by MC: F(x) = P1 e−t/P2 R((x − t), P3 , ..., P7 )dt +Aqq¯ · R(x, P3 , ..., P7 ) + Bkgcb (x),
(3)
with seven free parameters P1 -P7 , the coefficient Aqq¯ gives the level of qq-events. ¯ The variation of the levels of the background contributions in the data fit was taken into account in the estimation of the systematic uncertainty. The experimental ct distribution together with the result of the fit and estimated sources of background contributions are shown in Fig. 2. The value of the P2 parameter obtained from the fit of the data ct distribution is 86.53 ± 0.16 μm. The relation of the parameter P2 value to the true cτ value was analyzed using three KKMC τ+ τ− samples with the τlepton cτ value 84.00, 87.11 and 90.00 μm, respectively. To check that the fitting procedure gives the correct es-
Generated cτ after all selections 86.550 ± 0.064 83.528 ± 0.070 89.518 ± 0.080
P2 value from the fit 86.57 ± 0.12 83.61 ± 0.12 89.46 ± 0.13
timation of the input lifetime value we fit the ct distributions for these MC samples of events selected by rules (1.-10.). Comparison of the generated cτ values after all selections and the parameter P2 values obtained from the fit shows that they are compatible within errors (see Table 1), that is the fitting procedure well reproduces the lifetime value of the selected events. From Table 1 we see that the selection criteria introduce a certain shift to the measured cτ value which is about 0.5 μm. This shift does not depend on the τ-lepton lifetime. To correct this shift we use the following procedure. For the used MC samples we constructed a plot of the obtained P2 values as a function of the cτ values which was used in a generation of the corresponding MC samples. The corresponding dependence can be fitted by the straight line. The values of parameters A and B obtained from the fit of this dependence by the function (P2 − 87) = A + B · (cτ − 87) are: A = −0.465 ± 0.067, B = 0.982 ± 0.027. We use this parametrization for the correction of the fitted P2 value in the measured cτ value. This correction gives: cτmeasured = (86.99±0.16(stat.)±0.07(MC)) μm.(4) The first error is statistical and the second one is due to the correction procedure. The following sources of systematic uncertainties have been analyzed: fitting procedure (choice of the fit range of the reconstructed ct distribution); accuracy of the description of the initial and final state radiation in MC; beam energy accuracy; alignment of the vertex detector SVD; accuracy of the estimation of the background contribution; accuracy of a knowledge of the τlepton mass; accuracy of the measured cτ value shift estimation from a dl cut. An additional source of a systematic uncertainty comes from the limited statistics of the τ+ τ− MC samples which introduce an uncertainty to the correction of the lifetime parameter obtained from the fit. The summary of systematic uncertainties is shown in Table 2 In summary, the τ-lepton lifetime has been measured using the technique of the direct lifetime measurement in fully kinematically reconstructed e+ e− → τ+ τ− →
90
A.A. Sokolov / Nuclear Physics B (Proc. Suppl.) 253–255 (2014) 87–90
Table 2: Systematic uncertainties.
Source of Systematics MC correction Fit range ISR & FSR description Beam energy SVD alignement Background contribution Error of the τ-lepton mass dl cut Total
Δcτ in μm 0.068 0.020 0.018 0.016 0.050 0.003 0.009 0.050 0.103
3πν 3πν events. The preliminary result is τ = (290.18 ± 0.54(stat.) ± 0.33(syst.) × 10−15 s. cτ = 86.99 ± 0.16(stat.) ± 0.10(syst.) μm. References [1] Y.S. Tsai, Phys.Rev. D 4, 2821 (1971); H.B. Thacker and J.J. Sakurai, Phys. Lett. B 36, 103 (1971). [2] J. Beringer et al. (Particle Data Group), Phys. Rev. D86, 010001 (2012). [3] P. Abreu et al. (DELPHI Collaboration), Phys. Lett. B 365, 448 (1996); G. Alexander et al. (OPAL Collaboration), Phys. Lett. B 374, 341 (1996); R. Barate et al. (ALEPH Collaboration), Phys. Lett. B 414, 362 (1997); M. Acciarri et al. (L3 Collaboration), Phys. Lett. B 479, 67 (2000). [4] A. Lusiani, Nucl. Phys. B (Proc. Suppl.) 144, 105 (2005). [5] A. Abashian et al. (Belle Collaboration), Nucl. Instrum. Methods Phys. Res., Sect. A 479, 117 (2002). [6] S. Kurokawa and E. Kikutani, Nucl. Instrum. Methods Phys. Res., Sect. A 499, 1 (2003), and other papers included in this volume. [7] S.Jadach, B.F.L.Ward, Z.Wa¸s, Comp. Phys. Commun. 130, 260 (2000). [8] R. Brun et al. GEANT 3.21. Report No. CERN DD/EE/84-1 (1984).