- Email: [email protected]
Pythia 8: Simulating Tau-Lepton Decays
Available online at www.sciencedirect.com
Nuclear and Particle Physics Proceedings 260 (2015) 56–60 www.elsevier.com/locate/nppp
Pythia 8: Simulating Tau-Lepton Decays Philip Ilten Laboratory for Nuclear Science, Massachusetts Institute of Technology
Abstract As of version 8.150 of Pythia, the isotropic decays of τ-leptons have been replaced with a decay machinery that incorporates full spin correlations and more sophisticated decay models. Developments of the Pythia τ-lepton decay machinery from version 8.150 up to version 8.201 are summarized. The τ-lepton decay machinery in Pythia 8 is described, including the spin correlation algorithm, the available τ-lepton decay models, and the user interface. Keywords: Monte Carlo, tau decays, polarization, hadronic currents
1. Introduction The role of τ-leptons in Higgs boson measurements [1, 2] and beyond the Standard Model searches [3, 4, 5] is becoming increasingly important, due to the enhanced coupling of the τ-lepton in many of these physics models. Consequently, it is necessary for current Monte Carlo generators to ensure accurate modeling of τ-lepton decays. Prior to version 8.150 of Pythia [6, 7, 8], τ-lepton decays in Pythia were performed using a leptonic or generic hadronic current matrix element without including spin correlations, and more sophisticated τ-lepton modeling was only possible through external packages such as Tauola [9]. Now, from Pythia version 8.150 and above, fully modeled hadronic currents with spin correlations are available, based on prior τ-lepton modeling work in Tauola and Herwig++ [10]. Currently, all known τ-lepton decays with a branching fraction greater than 0.04% are modeled. In this update of a previous review [11], the spin correlation algorithm used in Pythia for τ-leptons is described, with an example given in Figure 1. The available τ-lepton decay matrix elements are also summarized and given in Table 1. An introduction to the user ∗ Email
address: [email protected] (Philip Ilten)
http://dx.doi.org/10.1016/j.nuclphysbps.2015.02.012 2405-6014/© 2015 Published by Elsevier B.V.
interface is also provided, including the flow chart of Figure 2 which describes the available options for handling spin correlations. Further documentation is also available in a more detailed write-up [12] and the Pythia HTML manual.
2. Developments Since its introduction, the τ-lepton decay machinery in Pythia has undergone extensive validation and development. A full list of the update history is available through the HTML manual distributed with Pythia, but a summary of the updates relevant to τ-lepton decays is given here. • 8.150: Sophisticated τ-lepton decay machinery was introduced. • 8.153: Forced τ-lepton polarization option was introduced and a minor technical code fix was included. • 8.157: A technical issue in forced τ-lepton polarization was fixed. • 8.160: Unnecessary warnings for τ-lepton decays using a forced polarization were removed.
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P. Ilten / Nuclear and Particle Physics Proceedings 260 (2015) 56–60
• 8.165: The ability to read the τ-lepton polarization from the SPINUP digit proved by Les Houches Accord (LHA) files was introduced. All τ-leptons produced from a W with an unknown production mechanism are assumed to be left-handed.
2. One of the outgoing particles is selected and its helicity density matrix is calculated, (2) ∗ ρ(λj)j λ j = ρ(1) κ1 κ1 ρκ2 κ2 Mκ1 κ2 ;λ1 ...λn Mκ1 κ2 ;λ1 ...λn (1) × D(k) λk λk k j
• 8.170: Additional decay matrix elements were added such that a non-isotropic model is available for all decay modes with a branching fraction greater than 0.1%. The decays of τ-lepton pairs from Z bosons with an unknown production mechanism was updated to assume production from an unpolarized Z boson. The spin correlation method applied to τ-leptons produced from mesons was extended to baryons. The momentum of massless photons from dipole shower evolution was updated to be the summed momenta of the produced τ-lepton pair. • 8.175: Lepton-number-violating production was introduced so the decays of τ-leptons in processes such as H → τμ are handled correctly, including correlations with the muon decay (if decayed). The branching fractions for τ-leptons were updated [13]. • 8.180: An option to overwrite the lifetime of τleptons from LHA files was introduced. A technical issue in the decay H 0 → A0 A0 → 4τ was fixed. • 8.200: A major update to the user options controlling how τ-lepton spins and correlations are handled, particularly for LHA input, was introduced. A new CP-mixing parameter for Higgs bosons was introduced, and the CP-mixing for Higgs bosons was extended to affect the correlations in τ-lepton decays, not just vector boson decays.
3. Correlations The spin correlation algorithm used in Pythia for τ-lepton decays is based on the algorithm proposed by Collins [14] and Knowles [15], and expanded by Richardson [16]. The algorithm separates spin correlations from the hard process, parton shower, and hadronization phases of the Monte Carlo generator, while maintaining full correlations, and can be divided into the following steps. 1. The 2 → n hard process is generated according to its matrix element M.
and the trace is normalized. Here, ρ(1,2) are the helicity density matrices of the incoming particles with helicity κ1,2 , M is the matrix element with outgoing particle helicities λk , and D(k) are the decay matrices of the outgoing particles, initialized to the identity. If the particle is from a decay, the helicity density matrix is the same as above but without ρ(2) and κ2 . 3. The selected particle is decayed using the weight, D(k) W = ρλ0 λ0 Mλ0 ;λ1 ...λn M∗λ0 ;λ1 ...λn λk λk (2) k=1,n
where ρ is the helicity density matrix of the decaying particle with helicity λ0 and the decay matrix element M. 4. Steps 2 through 3 are performed until a decay is reached with no unstable particles. 5. The decay matrix of the last decayed particle is calculated, D(k) (3) Dλ0 λ0 = Mλ0 ;λ1 ...λn M∗λ0 ;λ1 ...λn λk λk k=1,n
and the trace is normalized. 6. An undecayed particle from the decay above is randomly selected and steps 2 through 5 are repeated. 7. Step 6 is repeated until all unstable particles are decayed. An example of the correlation algorithm used in Pythia is given in Figure 1 for a τ-lepton pair from γ∗ /Z production; the first τ-lepton is decayed into a ντ e¯νe final state and the second into a ντ μ¯νμ final state. The path of the algorithm is traced by the gray line with each step indicated by a colored box. In the red (left) box, the hard matrix element of step 1 is calculated and the 2 → 2 process is created. Next, in the blue (upper-middle) box the helicity density matrix for the τ− -lepton is calculated with Equation 1 from step 2. The τ− -lepton is then decayed via Equation 2 from step 3 in the green (upperright) box. Because all decay products are stable, the decay matrix for the τ− -lepton is calculated with Equation 3 from step 5 in the orange (small-middle-right) box. The helicity density matrix for the τ+ -lepton is then calculated using this new decay matrix in the second blue (lower-middle) box, and then decayed in the second green (lower-right) box.
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P. Ilten / Nuclear and Particle Physics Proceedings 260 (2015) 56–60
3. decay with Wτ→ντ e¯νe ∗ /Z→τ− τ+ 1. hard process with Mqq→γ ¯ − 2. calculate ρ(τ ) W− τ−
q¯ γ∗ /Z
q
ντ ν¯ e
5. calculate D(τ
−)
e− νμ
τ+ +)
2. calculate ρ(τ
μ+
W+ ν¯ τ
3. decay with Wτ→ντ μ¯νμ
Figure 1: An example of the spin correlation algorithm in Pythia for the decay of a τ-lepton pair from γ∗ /Z production where the first τ-lepton is decayed into a ντ e¯νe final state and the second τ-lepton is decayed into a ντ μ¯νμ final state.
4. Decays
3
M=
g2w Lμ J μ 8m2W
(4)
where gW is the SU(2) coupling, mW the W boson mass, Lμ the leptonic current of the τ-lepton, and Jμ a leptonic or hadronic current dependent upon the decay. The τlepton current Lμ is u¯ ντ γμ (1 − γ5 )uτ where uτ is the τlepton spinor, dependent upon momentum and helicity, and u¯ ντ is the τ-lepton neutrino spinor. A full list of the available Jμ currents modeled in Pythia is given in Table 1. For the two-body decays of the τ-lepton, Jμ is f q, where f is a constant and q is the momentum of the hadron. For the three-body leptonic decays, τ− → ντ e− ν¯ e and τ− → ντ μ− ν¯ μ , Jμ is of the same form as Lμ . Two hadronic three-body decay models are available, a decay via a vector resonance and a decay via a vector and scalar resonance. Four-body τ-lepton decays in Pythia are implemented in four different models. The primary four-body decays, τ− → ντ π0 π0 π− and τ− → ντ π− π− π+ , are modeled using the CLEO fit. These decays can also be performed using a generic hadronic four-body model from Decker, et al. The four-body decays with kaons in the final state are calculated using a model from Finkemeier and Mirkes. The five-body decays of the τ-lepton to pions are produced with the Novosibirsk model, a phenomenological fit of four pion production from electron-positron annihilation. The six-body decays of the τ-lepton are handled through a model proposed by K¨uhn and Wa¸s.
1
5
x→τy
←x x→ external = externalMode tauMother
ρ(τ) =
←yτ
4
internal f f¯ → γ∗ /Z, W → f f¯ H, h0 , A0 , H 0 , H ± → f f¯ B/D-mesons, baryons
y=τ→
P=0
The matrix element for the decay of the τ-lepton can be written as,
P = tauPolarization
2
1−P 0 0 1+P
/2
Z, W → f f¯
γ → f f¯
Figure 2: Flow chart of how spin correlations are handled for a τlepton decay from the process x → τy, given the mode option of 1 through 5. The colored circles indicate the option, the lines the flow of the algorithm, and the gray boxes possible methods for determining the τ-lepton spin and correlation. If a method cannot determine the τ-lepton spin and correlation, then the algorithm continues along its path.
5. Interface Documentation for τ-lepton decays in Pythia can be found under the Tau Decays subsection of Particle Decays in the Pythia HTML manual. The CP-mixing of the Higgs boson also affects the decays of τ-leptons produced from Higgs bosons and can be set by the parameters Higgsx:parity, Higgsx:etaParity, and Higgsx:phiParity where x is H1, H2, or A3. Further details on these parameters can be found in the Higgs subsection of Process Selection. All τ-lepton decay options begin with TauDecays separated from the option with a colon. The τ-lepton spin and correlation is determined either using internal matrix elements or the external SPINUP information from an LHA file. Six options, set by mode, are available, which determine the τ-lepton decay mechanism. Option 0 reverts to the old isotropic decays, while the remaining options use the more sophisticated machinery. The options 1 though 5 are described in
P. Ilten / Nuclear and Particle Physics Proceedings 260 (2015) 56–60
Multiplicity
M
Model
Decay Products
1521
π− , K −
[17] [18]
1531 1532 1533
e− ν¯ e , μ− ν¯ μ π0 π− , K 0 K − , ηK − π− K¯ 0 , π0 K −
CLEO
[19]
1541
Finkemeier and Mirkes
[20]
1542
Decker, et al.
[21]
1543
Jadach, et al.
[22]
1544
π0 π0 π− , π− π− π+ K − π− K + , K 0 π− K¯ 0 , KS0 π− KS0 , KL0 π− KL0 , KS0 π− KL0 , K − π0 K 0 , π0 π0 K − , K − π− π+ , π− K¯ 0 π0 π0 π0 π+ , π− π− π+ , K − π− K + , K 0 π− K¯ 0 , K − π0 K 0 , π0 π0 K − , K − π− π+ , π− K¯ 0 π0 , π− π0 η γπ0 π−
5-body
Novosibirsk
[23]
1551
π0 π− π− π+ , π0 π0 π0 π−
6-body
K¨uhn and Wa¸s
[24]
1561
π0 π0 π− π− π+ , π0 π0 π0 π0 π− , π− π− π− π+ π+
2-body
single hadron
3-body
leptonic K¨uhn and Santamaria Finkemeier and Mirkes
4-body
59
Table 1: Summary of available τ-lepton decay models in Pythia, grouped by multiplicity. For each model the internal Pythia matrix element mode identifier (M) is given, as well as the decays available through the model and the reference of the model. The implicit ντ is omitted for brevity.
Figure 2. The default option 1 should provide sensible behavior for τ-leptons produced internally from Pythia and from LHA files. When attempting to determine the spin and correlation of a τ-lepton using the external method, the case for an uncorrelated τ-lepton is well defined; the τ-lepton polarization is set to SPINUP and ρ is calculated. However, for correlated τ-lepton pairs, this procedure will destroy the correlations between the two τ-lepton decays. Consequently, the option externalMode allows the user to choose how this is handled. Option 0 forces all decays to be uncorrelated. Option 1 tries to calculate the process internally. If this fails then an attempt is made to use the SPINUP information for the τ-lepton mother. The default option 2 skips correlated decays and hands them off to the next method set by mode. Consequently, the default behavior for correlated decays when reading an LHA file is to handle them internally and provide full correlations. The models used to decay the τ-leptons for each channel can be changed by switching the matrix element mode of the channel. The syntax takes the form 15:channel:meMode = mode where 15 is the τlepton particle identification code, channel specifies the decay channel number as listed under the Particle Data section, and mode is the new matrix element mode. For example, the default CLEO model used for the τ− → ντ π0 π0 π− decay can switched to the Decker, et al. model using 15:9:meMode = 1543.
6. Conclusion Fully modeled τ-lepton decays with spin correlations are available in Pythia, and have been tested extensively. Further development is underway, and feedback on requested features is always welcome. References [1] The ATLAS collaboration, Evidence for Higgs boson Yukawa couplings in the H → ττ decay mode with the ATLAS detector, Tech. rep. (2014). [2] S. Chatrchyan, et al., Evidence for the 125 GeV Higgs boson decaying to a pair of τ leptons, JHEP 1405 (2014) 104. arXiv:1401.5041. [3] G. Aad, et al., Search for neutral Higgs bosons of the min√ imal supersymmetric standard model in pp collisions at s = 8 TeV with the ATLAS detector, JHEP 1411 (2014) 056. arXiv:1409.6064. [4] V. Khachatryan, et al., Search for neutral MSSM Higgs bosons decaying to a pair of tau leptons in pp collisions, JHEP 1410 (2014) 160. arXiv:1408.3316. [5] R. Aaij, et al., Limits on neutral Higgs √ boson production in the forward region in pp collisions at s = 7 TeV, JHEP 1305 (2013) 132. arXiv:1304.2591. [6] T. Sj¨ostrand, S. Mrenna, P. Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 0605 (2006) 026. arXiv:hep-ph/0603175. [7] T. Sj¨ostrand, S. Mrenna, P. Z. Skands, et al., A Brief Introduction to PYTHIA 8.1, Comput.Phys.Commun. 178 (2008) 852– 867. arXiv:0710.3820. [8] T. Sj¨ostrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, et al., An Introduction to PYTHIA 8.2arXiv:1410.3012. [9] P. Golonka, B. Kersevan, T. Pierzchala, E. Richter-Was, Z. Was, et al., The Tauola photos F environment for the TAUOLA and PHOTOS packages: Release. 2., Comput.Phys.Commun. 174 (2006) 818–835. arXiv:hep-ph/0312240. [10] D. Grellscheid, P. Richardson, Simulation of Tau Decays in the Herwig++ Event GeneratorarXiv:0710.1951.
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[11] P. Ilten, Tau Decays in Pythia 8, Nucl.Phys.Proc.Suppl. 253-255 (2014) 77–80. arXiv:1211.6730. [12] P. Ilten, Electroweak and Higgs Measurements Using Tau Final States with the LHCb DetectorarXiv:1401.4902. [13] J. Beringer, et al., Review of Particle Physics (RPP), Phys.Rev. D86 (2012) 010001. [14] J. C. Collins, Spin Correlations in Monte Carlo Event Generators, Nucl.Phys. B304 (1988) 794. [15] I. Knowles, A Linear Algorithm for Calculating Spin Correlations in Hadronic Collisions, Comput.Phys.Commun. 58 (1990) 271–284. [16] P. Richardson, Spin correlations in Monte Carlo simulations, JHEP 0111 (2001) 029. arXiv:hep-ph/0110108. [17] J. H. K¨uhn, A. Santamaria, Tau decays to pions, Z.Phys. C48 (1990) 445–452. [18] M. Finkemeier, E. Mirkes, The Scalar contribution to τ → kπντ , Z.Phys. C72 (1996) 619–626. arXiv:hep-ph/9601275. [19] D. Asner, et al., Hadronic structure in the decay τ− → ντ π− π0 π0 and the sign of the ντ helicity, Phys.Rev. D61 (2000) 012002. arXiv:hep-ex/9902022. [20] M. Finkemeier, E. Mirkes, Tau decays into kaons, Z.Phys. C69 (1996) 243–252. arXiv:hep-ph/9503474. [21] R. Decker, E. Mirkes, R. Sauer, Z. Was, Tau decays into three pseudoscalar mesons, Z.Phys. C58 (1993) 445–452. [22] S. Jadach, Z. Was, R. Decker, J. H. Kuhn, The τ decay library TAUOLA: Version 2.4, Comput.Phys.Commun. 76 (1993) 361– 380. [23] A. Bondar, S. Eidelman, A. Milstein, T. Pierzchala, N. Root, et al., Novosibirsk hadronic currents for τ → 4π channels of τ decay library TAUOLA, Comput.Phys.Commun. 146 (2002) 139–153. arXiv:hep-ph/0201149. [24] J. H. K¨uhn, Z. Wa¸s, τ decays to five mesons in TAUOLA, Acta Phys.Polon. B39 (2008) 147–158. arXiv:hep-ph/0602162.
Nuclear and Particle Physics Proceedings 260 (2015) 56–60 www.elsevier.com/locate/nppp
Pythia 8: Simulating Tau-Lepton Decays Philip Ilten Laboratory for Nuclear Science, Massachusetts Institute of Technology
Abstract As of version 8.150 of Pythia, the isotropic decays of τ-leptons have been replaced with a decay machinery that incorporates full spin correlations and more sophisticated decay models. Developments of the Pythia τ-lepton decay machinery from version 8.150 up to version 8.201 are summarized. The τ-lepton decay machinery in Pythia 8 is described, including the spin correlation algorithm, the available τ-lepton decay models, and the user interface. Keywords: Monte Carlo, tau decays, polarization, hadronic currents
1. Introduction The role of τ-leptons in Higgs boson measurements [1, 2] and beyond the Standard Model searches [3, 4, 5] is becoming increasingly important, due to the enhanced coupling of the τ-lepton in many of these physics models. Consequently, it is necessary for current Monte Carlo generators to ensure accurate modeling of τ-lepton decays. Prior to version 8.150 of Pythia [6, 7, 8], τ-lepton decays in Pythia were performed using a leptonic or generic hadronic current matrix element without including spin correlations, and more sophisticated τ-lepton modeling was only possible through external packages such as Tauola [9]. Now, from Pythia version 8.150 and above, fully modeled hadronic currents with spin correlations are available, based on prior τ-lepton modeling work in Tauola and Herwig++ [10]. Currently, all known τ-lepton decays with a branching fraction greater than 0.04% are modeled. In this update of a previous review [11], the spin correlation algorithm used in Pythia for τ-leptons is described, with an example given in Figure 1. The available τ-lepton decay matrix elements are also summarized and given in Table 1. An introduction to the user ∗ Email
address: [email protected] (Philip Ilten)
http://dx.doi.org/10.1016/j.nuclphysbps.2015.02.012 2405-6014/© 2015 Published by Elsevier B.V.
interface is also provided, including the flow chart of Figure 2 which describes the available options for handling spin correlations. Further documentation is also available in a more detailed write-up [12] and the Pythia HTML manual.
2. Developments Since its introduction, the τ-lepton decay machinery in Pythia has undergone extensive validation and development. A full list of the update history is available through the HTML manual distributed with Pythia, but a summary of the updates relevant to τ-lepton decays is given here. • 8.150: Sophisticated τ-lepton decay machinery was introduced. • 8.153: Forced τ-lepton polarization option was introduced and a minor technical code fix was included. • 8.157: A technical issue in forced τ-lepton polarization was fixed. • 8.160: Unnecessary warnings for τ-lepton decays using a forced polarization were removed.
57
P. Ilten / Nuclear and Particle Physics Proceedings 260 (2015) 56–60
• 8.165: The ability to read the τ-lepton polarization from the SPINUP digit proved by Les Houches Accord (LHA) files was introduced. All τ-leptons produced from a W with an unknown production mechanism are assumed to be left-handed.
2. One of the outgoing particles is selected and its helicity density matrix is calculated, (2) ∗ ρ(λj)j λ j = ρ(1) κ1 κ1 ρκ2 κ2 Mκ1 κ2 ;λ1 ...λn Mκ1 κ2 ;λ1 ...λn (1) × D(k) λk λk k j
• 8.170: Additional decay matrix elements were added such that a non-isotropic model is available for all decay modes with a branching fraction greater than 0.1%. The decays of τ-lepton pairs from Z bosons with an unknown production mechanism was updated to assume production from an unpolarized Z boson. The spin correlation method applied to τ-leptons produced from mesons was extended to baryons. The momentum of massless photons from dipole shower evolution was updated to be the summed momenta of the produced τ-lepton pair. • 8.175: Lepton-number-violating production was introduced so the decays of τ-leptons in processes such as H → τμ are handled correctly, including correlations with the muon decay (if decayed). The branching fractions for τ-leptons were updated [13]. • 8.180: An option to overwrite the lifetime of τleptons from LHA files was introduced. A technical issue in the decay H 0 → A0 A0 → 4τ was fixed. • 8.200: A major update to the user options controlling how τ-lepton spins and correlations are handled, particularly for LHA input, was introduced. A new CP-mixing parameter for Higgs bosons was introduced, and the CP-mixing for Higgs bosons was extended to affect the correlations in τ-lepton decays, not just vector boson decays.
3. Correlations The spin correlation algorithm used in Pythia for τ-lepton decays is based on the algorithm proposed by Collins [14] and Knowles [15], and expanded by Richardson [16]. The algorithm separates spin correlations from the hard process, parton shower, and hadronization phases of the Monte Carlo generator, while maintaining full correlations, and can be divided into the following steps. 1. The 2 → n hard process is generated according to its matrix element M.
and the trace is normalized. Here, ρ(1,2) are the helicity density matrices of the incoming particles with helicity κ1,2 , M is the matrix element with outgoing particle helicities λk , and D(k) are the decay matrices of the outgoing particles, initialized to the identity. If the particle is from a decay, the helicity density matrix is the same as above but without ρ(2) and κ2 . 3. The selected particle is decayed using the weight, D(k) W = ρλ0 λ0 Mλ0 ;λ1 ...λn M∗λ0 ;λ1 ...λn λk λk (2) k=1,n
where ρ is the helicity density matrix of the decaying particle with helicity λ0 and the decay matrix element M. 4. Steps 2 through 3 are performed until a decay is reached with no unstable particles. 5. The decay matrix of the last decayed particle is calculated, D(k) (3) Dλ0 λ0 = Mλ0 ;λ1 ...λn M∗λ0 ;λ1 ...λn λk λk k=1,n
and the trace is normalized. 6. An undecayed particle from the decay above is randomly selected and steps 2 through 5 are repeated. 7. Step 6 is repeated until all unstable particles are decayed. An example of the correlation algorithm used in Pythia is given in Figure 1 for a τ-lepton pair from γ∗ /Z production; the first τ-lepton is decayed into a ντ e¯νe final state and the second into a ντ μ¯νμ final state. The path of the algorithm is traced by the gray line with each step indicated by a colored box. In the red (left) box, the hard matrix element of step 1 is calculated and the 2 → 2 process is created. Next, in the blue (upper-middle) box the helicity density matrix for the τ− -lepton is calculated with Equation 1 from step 2. The τ− -lepton is then decayed via Equation 2 from step 3 in the green (upperright) box. Because all decay products are stable, the decay matrix for the τ− -lepton is calculated with Equation 3 from step 5 in the orange (small-middle-right) box. The helicity density matrix for the τ+ -lepton is then calculated using this new decay matrix in the second blue (lower-middle) box, and then decayed in the second green (lower-right) box.
58
P. Ilten / Nuclear and Particle Physics Proceedings 260 (2015) 56–60
3. decay with Wτ→ντ e¯νe ∗ /Z→τ− τ+ 1. hard process with Mqq→γ ¯ − 2. calculate ρ(τ ) W− τ−
q¯ γ∗ /Z
q
ντ ν¯ e
5. calculate D(τ
−)
e− νμ
τ+ +)
2. calculate ρ(τ
μ+
W+ ν¯ τ
3. decay with Wτ→ντ μ¯νμ
Figure 1: An example of the spin correlation algorithm in Pythia for the decay of a τ-lepton pair from γ∗ /Z production where the first τ-lepton is decayed into a ντ e¯νe final state and the second τ-lepton is decayed into a ντ μ¯νμ final state.
4. Decays
3
M=
g2w Lμ J μ 8m2W
(4)
where gW is the SU(2) coupling, mW the W boson mass, Lμ the leptonic current of the τ-lepton, and Jμ a leptonic or hadronic current dependent upon the decay. The τlepton current Lμ is u¯ ντ γμ (1 − γ5 )uτ where uτ is the τlepton spinor, dependent upon momentum and helicity, and u¯ ντ is the τ-lepton neutrino spinor. A full list of the available Jμ currents modeled in Pythia is given in Table 1. For the two-body decays of the τ-lepton, Jμ is f q, where f is a constant and q is the momentum of the hadron. For the three-body leptonic decays, τ− → ντ e− ν¯ e and τ− → ντ μ− ν¯ μ , Jμ is of the same form as Lμ . Two hadronic three-body decay models are available, a decay via a vector resonance and a decay via a vector and scalar resonance. Four-body τ-lepton decays in Pythia are implemented in four different models. The primary four-body decays, τ− → ντ π0 π0 π− and τ− → ντ π− π− π+ , are modeled using the CLEO fit. These decays can also be performed using a generic hadronic four-body model from Decker, et al. The four-body decays with kaons in the final state are calculated using a model from Finkemeier and Mirkes. The five-body decays of the τ-lepton to pions are produced with the Novosibirsk model, a phenomenological fit of four pion production from electron-positron annihilation. The six-body decays of the τ-lepton are handled through a model proposed by K¨uhn and Wa¸s.
1
5
x→τy
←x x→ external = externalMode tauMother
ρ(τ) =
←yτ
4
internal f f¯ → γ∗ /Z, W → f f¯ H, h0 , A0 , H 0 , H ± → f f¯ B/D-mesons, baryons
y=τ→
P=0
The matrix element for the decay of the τ-lepton can be written as,
P = tauPolarization
2
1−P 0 0 1+P
/2
Z, W → f f¯
γ → f f¯
Figure 2: Flow chart of how spin correlations are handled for a τlepton decay from the process x → τy, given the mode option of 1 through 5. The colored circles indicate the option, the lines the flow of the algorithm, and the gray boxes possible methods for determining the τ-lepton spin and correlation. If a method cannot determine the τ-lepton spin and correlation, then the algorithm continues along its path.
5. Interface Documentation for τ-lepton decays in Pythia can be found under the Tau Decays subsection of Particle Decays in the Pythia HTML manual. The CP-mixing of the Higgs boson also affects the decays of τ-leptons produced from Higgs bosons and can be set by the parameters Higgsx:parity, Higgsx:etaParity, and Higgsx:phiParity where x is H1, H2, or A3. Further details on these parameters can be found in the Higgs subsection of Process Selection. All τ-lepton decay options begin with TauDecays separated from the option with a colon. The τ-lepton spin and correlation is determined either using internal matrix elements or the external SPINUP information from an LHA file. Six options, set by mode, are available, which determine the τ-lepton decay mechanism. Option 0 reverts to the old isotropic decays, while the remaining options use the more sophisticated machinery. The options 1 though 5 are described in
P. Ilten / Nuclear and Particle Physics Proceedings 260 (2015) 56–60
Multiplicity
M
Model
Decay Products
1521
π− , K −
[17] [18]
1531 1532 1533
e− ν¯ e , μ− ν¯ μ π0 π− , K 0 K − , ηK − π− K¯ 0 , π0 K −
CLEO
[19]
1541
Finkemeier and Mirkes
[20]
1542
Decker, et al.
[21]
1543
Jadach, et al.
[22]
1544
π0 π0 π− , π− π− π+ K − π− K + , K 0 π− K¯ 0 , KS0 π− KS0 , KL0 π− KL0 , KS0 π− KL0 , K − π0 K 0 , π0 π0 K − , K − π− π+ , π− K¯ 0 π0 π0 π0 π+ , π− π− π+ , K − π− K + , K 0 π− K¯ 0 , K − π0 K 0 , π0 π0 K − , K − π− π+ , π− K¯ 0 π0 , π− π0 η γπ0 π−
5-body
Novosibirsk
[23]
1551
π0 π− π− π+ , π0 π0 π0 π−
6-body
K¨uhn and Wa¸s
[24]
1561
π0 π0 π− π− π+ , π0 π0 π0 π0 π− , π− π− π− π+ π+
2-body
single hadron
3-body
leptonic K¨uhn and Santamaria Finkemeier and Mirkes
4-body
59
Table 1: Summary of available τ-lepton decay models in Pythia, grouped by multiplicity. For each model the internal Pythia matrix element mode identifier (M) is given, as well as the decays available through the model and the reference of the model. The implicit ντ is omitted for brevity.
Figure 2. The default option 1 should provide sensible behavior for τ-leptons produced internally from Pythia and from LHA files. When attempting to determine the spin and correlation of a τ-lepton using the external method, the case for an uncorrelated τ-lepton is well defined; the τ-lepton polarization is set to SPINUP and ρ is calculated. However, for correlated τ-lepton pairs, this procedure will destroy the correlations between the two τ-lepton decays. Consequently, the option externalMode allows the user to choose how this is handled. Option 0 forces all decays to be uncorrelated. Option 1 tries to calculate the process internally. If this fails then an attempt is made to use the SPINUP information for the τ-lepton mother. The default option 2 skips correlated decays and hands them off to the next method set by mode. Consequently, the default behavior for correlated decays when reading an LHA file is to handle them internally and provide full correlations. The models used to decay the τ-leptons for each channel can be changed by switching the matrix element mode of the channel. The syntax takes the form 15:channel:meMode = mode where 15 is the τlepton particle identification code, channel specifies the decay channel number as listed under the Particle Data section, and mode is the new matrix element mode. For example, the default CLEO model used for the τ− → ντ π0 π0 π− decay can switched to the Decker, et al. model using 15:9:meMode = 1543.
6. Conclusion Fully modeled τ-lepton decays with spin correlations are available in Pythia, and have been tested extensively. Further development is underway, and feedback on requested features is always welcome. References [1] The ATLAS collaboration, Evidence for Higgs boson Yukawa couplings in the H → ττ decay mode with the ATLAS detector, Tech. rep. (2014). [2] S. Chatrchyan, et al., Evidence for the 125 GeV Higgs boson decaying to a pair of τ leptons, JHEP 1405 (2014) 104. arXiv:1401.5041. [3] G. Aad, et al., Search for neutral Higgs bosons of the min√ imal supersymmetric standard model in pp collisions at s = 8 TeV with the ATLAS detector, JHEP 1411 (2014) 056. arXiv:1409.6064. [4] V. Khachatryan, et al., Search for neutral MSSM Higgs bosons decaying to a pair of tau leptons in pp collisions, JHEP 1410 (2014) 160. arXiv:1408.3316. [5] R. Aaij, et al., Limits on neutral Higgs √ boson production in the forward region in pp collisions at s = 7 TeV, JHEP 1305 (2013) 132. arXiv:1304.2591. [6] T. Sj¨ostrand, S. Mrenna, P. Z. Skands, PYTHIA 6.4 Physics and Manual, JHEP 0605 (2006) 026. arXiv:hep-ph/0603175. [7] T. Sj¨ostrand, S. Mrenna, P. Z. Skands, et al., A Brief Introduction to PYTHIA 8.1, Comput.Phys.Commun. 178 (2008) 852– 867. arXiv:0710.3820. [8] T. Sj¨ostrand, S. Ask, J. R. Christiansen, R. Corke, N. Desai, et al., An Introduction to PYTHIA 8.2arXiv:1410.3012. [9] P. Golonka, B. Kersevan, T. Pierzchala, E. Richter-Was, Z. Was, et al., The Tauola photos F environment for the TAUOLA and PHOTOS packages: Release. 2., Comput.Phys.Commun. 174 (2006) 818–835. arXiv:hep-ph/0312240. [10] D. Grellscheid, P. Richardson, Simulation of Tau Decays in the Herwig++ Event GeneratorarXiv:0710.1951.
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