- Email: [email protected]
Prospects for τ→3μ search at LHCb
Nuclear Physics B (Proc. Suppl.) 169 (2007) 363–367 www.elsevierphysics.com
Prospects for τ → 3μ search at LHCb M. Shapkina a
Institute for High Energy Physics, 142280, Pobeda 1, Protvino, Russia
A first look at the possibility of the search for the τ → 3μ decay shows that after one year of data taking LHCb can reach slightly better upper limit than the present one obtained at the e+ e− B-factories. Further improvement of this limit is quite possible. The detector performance was estimated using full Monte Carlo simulation.
1. INTRODUCTION
P(χ2)vertex(3μ) 5
Lepton flavour violating processes are clean signatures of physics beyond Standard Model. Since the discovery of the τ lepton, these processes were actively searched for at e+ e− colliders. The present upper limit for the branching fraction of τ → 3μ was obtained at the BaBar B-factory and is equal to ∼1.9 · 10−7 [1]. The 10−8 − 10−7 level of branching fractions for the τ decay into 3μ is predicted in some extensions of the Standard Model such as models with Higgs bosons with flavour violating couplings [2] or with nonuniversal additional Z’ bosons [3]. e+ e− colliders have important advantages for study τ physics compared to hadron colliders. In e+ e− collisions, τ leptons are produced in pairs with known energies and with low level of background. For some channels it is not so important. For example, in the lepton flavour violating channels τ → μμμ, τ → μμe, τ → μee and τ → eee all the decay products can be well reconstructed and secondary decay vertex is well separated from the primary one at hadronic collider. The advantage of the hadronic colliders for τ physics is a big statistics of the produced τ leptons in hadronic collisions. The main sources of τ at LHC are the decays of DS mesons into τ ντ (branching fraction is about 7.5%) and semileptonic decays of bhadrons b → τ ντ X (branching fraction is 2.5%). After one year of data taking, LHCb will record 2fb−1 of statistics, which corresponds to 70 billion τ leptons in the geometrical acceptance of the LHCb detector.
0920-5632/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2007.03.020
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Figure 1. Distribution of the probability of the vertex fit for the signal events.
2. DESCRIPTION OF THE ANALYSIS PROCEDURE The LHCb experiment [4] is designed to study rare decays and CP violation. The high precision measurements at LHCb will enable to probe physics beyond Standard Model. The LHCb detector is a single arm forward spectrometer, currently in its final construction phase. Its main characteristics are the precise vertexing, good tracking and particle identification. For the estimation of the detector performance we use full Monte Carlo simulation of the detec-
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Figure 2. Invariant mass spectra of the 3μ for the signal events (histogram with errors is for all 3μ combinations, the dark gray (blue) histogram is for good vertex fit, the gray (red) histogram is for good vertex fit for the events that fulfilled trigger conditions).
Figure 3. Invariant mass spectra of the 3μ for the background events (histogram with errors is for the all 3μ combinations, the dark gray (blue) histogram is for good vertex fit, the gray (red) histogram is for good vertex fit for the events that fulfilled trigger conditions).
√ tor. The pp collisions at s = 14 TeV are generated, including pileup. Generated particles are traced through the detector setup accounting for the detector’s response, material and spill-over effects. When the trigger requirements are fulfilled the events are passed through the LHCb reconstruction algorithms, which are supposed to be used for the real data. For the analysis we use about 100 thousand signal events with τ → 3μ decays where τ leptons are mainly produced from the decays of charm and beauty hadrons. We assume that the main source of background is the inclusive b-hadron events with the cross section 0.5 mb. We analysed for the background study about 30 million inclusive b-hadron events and about 3 million minimum bias events. The τ leptons at LHCb have visible flight distance and their decay products are well measured and identified. According to the mentioned above features, the event selection criteria for the τ → 3μ channel are the following:
• 3 standard identified muons, each one with momentum transverse to the beam axis greater than 0.4 GeV • Probability of the fit to the common vertex of the 3μ P (χ2 ) > 0.002 • Significance of the measured impact parameters of all three muons IP/σ(IP ) > 3 • Significance of the distance between secondary and primary vertexes in 3D space |V3μ − VP vtx |/σ > 3 • Distance between secondary and primary vertexes along the beam axis 4mm< (Z3μ − Zpr ) <37mm • Distance between secondary and primary vertexes in the plane transverse to the beam axis Rxy > 0.1 mm For the motivation of the choice of the selection criteria the following distributions are shown. In
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IPμ significance (IP/ σIP)
Significance of 3μ vertex
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Figure 4. Distributions of significance of impact parameters of the muons for the signal (blue histogram) and background (red histogram).
the Figure 1 we show probability of the χ2 of the fit P (χ2 ) distribution for the signal events. This distribution is expected to have flat distribution for the τ → 3μ decays and peaks near zero for accidental combinatorics. In Figure 2 it is shown the invariant mass of 3μ distributions for all triplets of muons and after cut on the P (χ2) > 0.002. We see that the combinatoric background is significantly suppressed by this cut. We can also see in Figure 2 the influence of the trigger conditions on signal efficiency. The efficiency drops by a factor about 0.7 due to trigger (see the gray/red and dark gray/blue histograms at Figure 2). The influence of the P (χ2 ) cut on the background is shown in Figure 3. We see that the level of background is high for search of the rare τ decays. For the further background suppression we apply a cut on the significance of impact parameters IP/σ(IP ) > 3 of each identified muons. The muons coming from the secondary vertex should all have non-zero impact parameters. Figure 4 shows the distributions of the significance of the muons impact parameters for signal and background events.
0 0
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14 16 18 20 |V -Vprimary |/σ 3μ
Figure 5. Distributions of significance of the distance in 3D space between secondary and primary vertexes for signal (dark gray/blue histogram) and for the background (gray/red histogram).
After the cut on impact parameters significance we see that the distributions of the significance of the distance between secondary and primary vertexes |V3μ − Vpr |/σ are still different for the signal and background events as it is seen at Figure 4. We require that the significance be greater than 3. For the further background suppression we looked separately at the distance between secondary and primary vertexes along the beam axis and in the plane transverse to the beam axis. The distributions of the distance along the beam axis for the signal and background events are shown in Figure 6. We require this variable to be between 4 and 37 mm. After applying the above cuts, the distributions of the distance between secondary and primary vertexes in the plane transverse to the beam axis for the signal and background are shown in Figure 7. We require this distance to be greater than 0.1 mm. The influence of the listed set of cuts on the invariant mass spectrum of the 3μ for the signal and background events is shown in Figure 8 and
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Figure 6. Distributions of the distance along the beam axis between the secondary and primary vertexes for signal (dark gray/blue histogram) and background (gray/red histogram).
Figure 9 respectively. The histograms with error bars on these figures are the invariant mass of 3μ distributions after trigger conditions and quality of the vertex fit are fulfilled. The final light gray/green histograms are after all set of cuts. The suppression of the efficiency by the cuts followed after the vertex fit is about 0.6 while the background suppression is about 200. The final signal efficiency depends on the cut on the invariant mass of the 3μ. For the mass range corresponding to ±10 MeV with respect to the maximum of the peak, the signal efficiency is equal to 4.7%. For the background, the expected number of 3μ combinations in a given mass range is 4.6 × 10−7 per inclusive b-hadron event. Using these numbers we can estimate the upper limit for the τ → 3μ decay branching fraction. For an integrated luminosity of 2 fb−1 , the reconstructed number of τ → 3μ events is equal to 7 · 1010 · × Br. The number of background combinations in the taken 3μ invariant mass range is 0.5 ·1012 f b ·2f b−1 ·0.35 ·4.6 ·10−7 = 1.6 · 105 , where 0.5 · 1012 fb is the inclusive bhadron events cross section and 0.35 is the geo-
0 0
0.5
1
1.5
2
2.5 3 ΔXY (mm)
Figure 7. Distributions of the distance in the plane transverse to the beam axis between the secondary and primary vertexes for signal (dark gray/blue histogram) and background (gray/red histogram).
metrical acceptance of the LHCb detector. We suppose that the signal is seen over the background if its level is higher than the background fluctuations. So smallest branching fraction at which we can √ see the signal over the background is Brmin = 1.6 · 105 /7·1010/4.7·10−2 = 1.2·10−7. 3. CONCLUSION A first look at possibility of search of τ → 3μ decay shows that after one year of data taking LHCb can reach the sensitivity to τ decays at branching fraction of about 1.2 · 10−7 . Further improvement of this limit is quite possible. REFERENCES 1. B.Aubert et al, Phys. Rev. Lett. 92, 121801 (2004) B.Aubert, et al, hep-ex/0312027. 2. Andrea Brignole and Anna Rossi, hepph/0304081. Ernest Ma, hep-ph/0209170.
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Figure 8. Invariant mass spectra of the 3μ for the signal events (histogram with errors is for the 3μ combinations that fulfilled the trigger conditions and with good vertex fit, the blue (non filled) histogram is after adding the cut on significance of the impact parameters of the muons, the gray/red histogram is after adding the cuts on the distances between secondary and primary vertexes, the light gray/green histogram is after adding cut 0.4 GeV on the Pt of the muons).
3. Chongxing Yue, Yanming Zhang and Lanjun Liu, Phys. Lett. B 547 (2002) 252. 4. Technical design report CERN/LHCC 2003030 (2003).
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Figure 9. Invariant mass spectra of the 3μ for the background events (histogram with errors is for the 3μ combinations that fulfilled the trigger conditions and with good vertex fit, the blue (non filled) histogram is after adding the cut on significance of the impact parameters of the muons, the gray/red histogram is after adding the cuts on the distances between secondary and primary vertexes, the light gray/green histogram is after adding cut 0.4 GeV on the Pt of the muons).
Prospects for τ → 3μ search at LHCb M. Shapkina a
Institute for High Energy Physics, 142280, Pobeda 1, Protvino, Russia
A first look at the possibility of the search for the τ → 3μ decay shows that after one year of data taking LHCb can reach slightly better upper limit than the present one obtained at the e+ e− B-factories. Further improvement of this limit is quite possible. The detector performance was estimated using full Monte Carlo simulation.
1. INTRODUCTION
P(χ2)vertex(3μ) 5
Lepton flavour violating processes are clean signatures of physics beyond Standard Model. Since the discovery of the τ lepton, these processes were actively searched for at e+ e− colliders. The present upper limit for the branching fraction of τ → 3μ was obtained at the BaBar B-factory and is equal to ∼1.9 · 10−7 [1]. The 10−8 − 10−7 level of branching fractions for the τ decay into 3μ is predicted in some extensions of the Standard Model such as models with Higgs bosons with flavour violating couplings [2] or with nonuniversal additional Z’ bosons [3]. e+ e− colliders have important advantages for study τ physics compared to hadron colliders. In e+ e− collisions, τ leptons are produced in pairs with known energies and with low level of background. For some channels it is not so important. For example, in the lepton flavour violating channels τ → μμμ, τ → μμe, τ → μee and τ → eee all the decay products can be well reconstructed and secondary decay vertex is well separated from the primary one at hadronic collider. The advantage of the hadronic colliders for τ physics is a big statistics of the produced τ leptons in hadronic collisions. The main sources of τ at LHC are the decays of DS mesons into τ ντ (branching fraction is about 7.5%) and semileptonic decays of bhadrons b → τ ντ X (branching fraction is 2.5%). After one year of data taking, LHCb will record 2fb−1 of statistics, which corresponds to 70 billion τ leptons in the geometrical acceptance of the LHCb detector.
0920-5632/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2007.03.020
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Figure 1. Distribution of the probability of the vertex fit for the signal events.
2. DESCRIPTION OF THE ANALYSIS PROCEDURE The LHCb experiment [4] is designed to study rare decays and CP violation. The high precision measurements at LHCb will enable to probe physics beyond Standard Model. The LHCb detector is a single arm forward spectrometer, currently in its final construction phase. Its main characteristics are the precise vertexing, good tracking and particle identification. For the estimation of the detector performance we use full Monte Carlo simulation of the detec-
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Figure 2. Invariant mass spectra of the 3μ for the signal events (histogram with errors is for all 3μ combinations, the dark gray (blue) histogram is for good vertex fit, the gray (red) histogram is for good vertex fit for the events that fulfilled trigger conditions).
Figure 3. Invariant mass spectra of the 3μ for the background events (histogram with errors is for the all 3μ combinations, the dark gray (blue) histogram is for good vertex fit, the gray (red) histogram is for good vertex fit for the events that fulfilled trigger conditions).
√ tor. The pp collisions at s = 14 TeV are generated, including pileup. Generated particles are traced through the detector setup accounting for the detector’s response, material and spill-over effects. When the trigger requirements are fulfilled the events are passed through the LHCb reconstruction algorithms, which are supposed to be used for the real data. For the analysis we use about 100 thousand signal events with τ → 3μ decays where τ leptons are mainly produced from the decays of charm and beauty hadrons. We assume that the main source of background is the inclusive b-hadron events with the cross section 0.5 mb. We analysed for the background study about 30 million inclusive b-hadron events and about 3 million minimum bias events. The τ leptons at LHCb have visible flight distance and their decay products are well measured and identified. According to the mentioned above features, the event selection criteria for the τ → 3μ channel are the following:
• 3 standard identified muons, each one with momentum transverse to the beam axis greater than 0.4 GeV • Probability of the fit to the common vertex of the 3μ P (χ2 ) > 0.002 • Significance of the measured impact parameters of all three muons IP/σ(IP ) > 3 • Significance of the distance between secondary and primary vertexes in 3D space |V3μ − VP vtx |/σ > 3 • Distance between secondary and primary vertexes along the beam axis 4mm< (Z3μ − Zpr ) <37mm • Distance between secondary and primary vertexes in the plane transverse to the beam axis Rxy > 0.1 mm For the motivation of the choice of the selection criteria the following distributions are shown. In
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M. Shapkin / Nuclear Physics B (Proc. Suppl.) 169 (2007) 363–367
IPμ significance (IP/ σIP)
Significance of 3μ vertex
0.1 0.014
Cut
Background
0.08
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Figure 4. Distributions of significance of impact parameters of the muons for the signal (blue histogram) and background (red histogram).
the Figure 1 we show probability of the χ2 of the fit P (χ2 ) distribution for the signal events. This distribution is expected to have flat distribution for the τ → 3μ decays and peaks near zero for accidental combinatorics. In Figure 2 it is shown the invariant mass of 3μ distributions for all triplets of muons and after cut on the P (χ2) > 0.002. We see that the combinatoric background is significantly suppressed by this cut. We can also see in Figure 2 the influence of the trigger conditions on signal efficiency. The efficiency drops by a factor about 0.7 due to trigger (see the gray/red and dark gray/blue histograms at Figure 2). The influence of the P (χ2 ) cut on the background is shown in Figure 3. We see that the level of background is high for search of the rare τ decays. For the further background suppression we apply a cut on the significance of impact parameters IP/σ(IP ) > 3 of each identified muons. The muons coming from the secondary vertex should all have non-zero impact parameters. Figure 4 shows the distributions of the significance of the muons impact parameters for signal and background events.
0 0
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4
6
8
10
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14 16 18 20 |V -Vprimary |/σ 3μ
Figure 5. Distributions of significance of the distance in 3D space between secondary and primary vertexes for signal (dark gray/blue histogram) and for the background (gray/red histogram).
After the cut on impact parameters significance we see that the distributions of the significance of the distance between secondary and primary vertexes |V3μ − Vpr |/σ are still different for the signal and background events as it is seen at Figure 4. We require that the significance be greater than 3. For the further background suppression we looked separately at the distance between secondary and primary vertexes along the beam axis and in the plane transverse to the beam axis. The distributions of the distance along the beam axis for the signal and background events are shown in Figure 6. We require this variable to be between 4 and 37 mm. After applying the above cuts, the distributions of the distance between secondary and primary vertexes in the plane transverse to the beam axis for the signal and background are shown in Figure 7. We require this distance to be greater than 0.1 mm. The influence of the listed set of cuts on the invariant mass spectrum of the 3μ for the signal and background events is shown in Figure 8 and
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Figure 6. Distributions of the distance along the beam axis between the secondary and primary vertexes for signal (dark gray/blue histogram) and background (gray/red histogram).
Figure 9 respectively. The histograms with error bars on these figures are the invariant mass of 3μ distributions after trigger conditions and quality of the vertex fit are fulfilled. The final light gray/green histograms are after all set of cuts. The suppression of the efficiency by the cuts followed after the vertex fit is about 0.6 while the background suppression is about 200. The final signal efficiency depends on the cut on the invariant mass of the 3μ. For the mass range corresponding to ±10 MeV with respect to the maximum of the peak, the signal efficiency is equal to 4.7%. For the background, the expected number of 3μ combinations in a given mass range is 4.6 × 10−7 per inclusive b-hadron event. Using these numbers we can estimate the upper limit for the τ → 3μ decay branching fraction. For an integrated luminosity of 2 fb−1 , the reconstructed number of τ → 3μ events is equal to 7 · 1010 · × Br. The number of background combinations in the taken 3μ invariant mass range is 0.5 ·1012 f b ·2f b−1 ·0.35 ·4.6 ·10−7 = 1.6 · 105 , where 0.5 · 1012 fb is the inclusive bhadron events cross section and 0.35 is the geo-
0 0
0.5
1
1.5
2
2.5 3 ΔXY (mm)
Figure 7. Distributions of the distance in the plane transverse to the beam axis between the secondary and primary vertexes for signal (dark gray/blue histogram) and background (gray/red histogram).
metrical acceptance of the LHCb detector. We suppose that the signal is seen over the background if its level is higher than the background fluctuations. So smallest branching fraction at which we can √ see the signal over the background is Brmin = 1.6 · 105 /7·1010/4.7·10−2 = 1.2·10−7. 3. CONCLUSION A first look at possibility of search of τ → 3μ decay shows that after one year of data taking LHCb can reach the sensitivity to τ decays at branching fraction of about 1.2 · 10−7 . Further improvement of this limit is quite possible. REFERENCES 1. B.Aubert et al, Phys. Rev. Lett. 92, 121801 (2004) B.Aubert, et al, hep-ex/0312027. 2. Andrea Brignole and Anna Rossi, hepph/0304081. Ernest Ma, hep-ph/0209170.
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Figure 8. Invariant mass spectra of the 3μ for the signal events (histogram with errors is for the 3μ combinations that fulfilled the trigger conditions and with good vertex fit, the blue (non filled) histogram is after adding the cut on significance of the impact parameters of the muons, the gray/red histogram is after adding the cuts on the distances between secondary and primary vertexes, the light gray/green histogram is after adding cut 0.4 GeV on the Pt of the muons).
3. Chongxing Yue, Yanming Zhang and Lanjun Liu, Phys. Lett. B 547 (2002) 252. 4. Technical design report CERN/LHCC 2003030 (2003).
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Figure 9. Invariant mass spectra of the 3μ for the background events (histogram with errors is for the 3μ combinations that fulfilled the trigger conditions and with good vertex fit, the blue (non filled) histogram is after adding the cut on significance of the impact parameters of the muons, the gray/red histogram is after adding the cuts on the distances between secondary and primary vertexes, the light gray/green histogram is after adding cut 0.4 GeV on the Pt of the muons).