Final Report Summary - TAU DECAY (Physics of the tau lepton: from chiral dynamics to lepton flavour violation phenomena)
The main goal of the project is to study the hadronisation mechanism at low and intermediate energies through the hadronic decay modes of the tau lepton within resonance chiral theory (RChT), improve their description in the Monte Carlo (MC) generator TAUOLA and make thereby possible an adequate analysis of the large data samples collected at the B-factories. In the same spirit the hadronisation process of the electron-positron annihilation into hadrons was investigated.
Tau lepton is a fundamental particle of the Standard Model (SM) and knowledge of its properties with high accuracy is absolutely mandatory for precise SM tests. From the perspective of low energy physics, such as studied at superB- and B-factories (BaBar and Belle experiments), tau lepton decays provide an excellent laboratory for modeling hadronic interactions at the energy scale of about 1 - 2 GeV, where neither perturbative quantum chromodynamics (QCD) methods nor chiral lagrangians are expected to work to a good precision. Results of such analysis will allow one to perform sensitive tests of the SM and extract its fundamental parameters, such as the coupling constant of strong interactions, the Cabibbo-Kobayashi-Maskawa matrix element and other important parameters. Moreover, modelling of the hadronic form factors (FF) will help in the search for lepton flavour violating decays of the tau lepton with hadrons in the final state. In addition to this, study of the tau hadronic decay allows one to learn properties of the intermediate meson resonances that are exchanged in the decay and to get information about the hadronisation of QCD currents via the study of the participating FF. From the perspective of high-energy experiments such as those at Large Hadron Collider (LHC), good understanding of tau lepton properties is a prerequisite for finding new physics signatures. With the discovery of a new particle around the mass of 125 - 126 GeV (1), tau decays are an important ingredient for determining if this is the SM Higgs. This is especially pertinent since CMS Collaboration has reported a deficit in the number of fermion decays from the new particle relative to the SM Higgs prediction.
With the shut-down of both the B-factory collaborations Babar and Belle, this is a critical time to make the results arising from more than a decade of experimental research available in a useful manner to the high energy physics community before the opportunity is lost. To this purpose, interaction between experimentalists and theorists is required to determine the optimal way of comparing experimental data with theoretical prediction, e.g. by installation of the theoretical results in the MC event generator.
The MC generator TAUOLA, currently used by both Belle and BaBar, represents a long term project that started in the 90's (see Ref. (2)). At present, more than twenty modes, both leptonic and hadronic, are simulated by the code. Analysis of hadronic decay modes involves matrix elements that convey the hadronisation of the vector and axial-vector currents. At present there is no determination from first principles of these matrix elements as they involve strong interaction effects in a non-perturbative regime. Therefore one has to rely on models that parameterise the FFs arising from the hadronisation. Originally TAUOLA was based on hadronic FFs written as a weighted sum of products of Breit-Wigner (BW) functions, using lowest order Chiral Perturbation Theory (ChPT) to normalise them (3). Nevertheless this description is not consistent with the chiral behavior at the next-to-leading order. As an alternative to this approximation it was proposed to apply the methods of RChT (4). RChT is a natural continuation of ChPT to the region of several GeV and is theoretically better founded than the approach of the BW functions. This new approach requires comparison with both BaBar and Belle experimental data which, in turn, requires the implementation of the theoretical results into TAUOLA. During her Marie Curie fellowship, the researcher has partially upgraded TAUOLA using the expression for the hadronic currents calculated within RChT in the case of the two and three meson (kaons and pions) decay modes (5). These modes together with the one meson decay mode represent more than 85 % of the hadronic width of the tau. The addition of the four pion decay modes, already started, will increase this fraction up to ~ 97 %. This work will continue at the Institute Nuclear Physics (INP), Cracow under a new contract beginning the 1 January 2013. This upgrade of TAUOLA is compatible with the previous version and can be easily implemented in the software used by both collaborations BaBar and Belle, being compatible with the C++ software used in the experiments. Numerical tests have been carried out to check numerical stability of the generator and the precision of MC results is better than 0.05% for all upgraded channels. With the collaboration of Dr Ian M. Nugent, an experimentalist from Babar, the researcher has made the first comparison of the TAUOLA prediction for the three pion mode with the unfolded spectrum, showing the necessity to improve the theoretical calculation for the low energy region of the two pion invariant mass. This required the inclusion of the contribution from the scalar meson. This work has already started and extraction of the parameters for the scalar meson will be done. The same analysis will be done for all three pseudo-scalar channels. Also work on the multidimensional fit of the three pion data has been initiated with J. Zaremba, a student of Cracow University, using the method of re-weighting events. This latter activity will be continued at INP. To conclude the technical work on the current installation for two and three meson decay modes is complete and work on fits is in progress in collaboration with experimentalists from BaBar and Belle. Another part of the project, with a similar goal, was devoted to the calculation of the cross section of the process electron-positron into 1) electron-positron pair and pseudoscalar (pion, eta and eta-prime mesons) and 2) three pseudo-scalars (three pions, two pions and eta meson) in the framework of RChT. As in the case of the tau decays the knowledge of the cross section allows us to gather information about the hadronisation of currents in the non-perturbative regime of QCD.
The results for the first process have been published in (6). Lately the two-photon transition FF's of the pseudo-scalar mesons have received a great attention both from the experimental and the theoretical side. The BaBar data (7) revealed unexpectedly large values in the range of Q2 = 10 - 35 GeV2 resulting in an excess of the pQCD predicted limit. This striking result attracted a lot of interest and motivated extensive theoretical investigations. Soon after, the Belle collaboration (8) published their data analysis that did not confirm the high-Q2 behaviour seen by BaBar. The two photon FF of the pseudo-scalars has been calculated within RChT and its has been applied to the process of the two photon electron-positron annihilation. Reasonable agreement with experimental data (CLEO, BaBar) for the FF's has been achieved. The only data sample which is not consistent with the model is the BaBar data for the pion (however, for the eta and eta-prime transition FFs are in perfect agreement) (7). The results obtained for the FF have been implemented in the MC EKHARA that simulates the process of the two photon electron-positron annihilation. The differential cross-section for the process of two-photon electron-positron annihilation into scalars has been compared with data from CLEO and BaBar. In order to investigate the impact of the event selection on the error estimate of the FF's, the simulation has been done with the direct cut on the untagged invariant and separately with the cut on the phase space of the untagged lepton (following the experimental cuts). It was shown that the error estimate and its Q2 dependence are very sensitive to the event selection in contrast to the estimate of BaBar (7). The future improvement of experimental data expected from the Belle and BES-III collaborations, will allow to get new information about the high energy behaviour of the FF's.
The previous theoretical calculation of the cross section of the electron-positron annihilation into three pions carried out in the framework of vector meson dominance in (9) did not take into account the anomalous structure of the production of three mesons from a vector current, as given by QCD. The calculation done within RChT includes both contributions, QCD anomalous and non-anomalous, consistently with our present knowledge of QCD. The amplitude for three meson production in e+ e- collisions has been calculated including the chiral, one-resonance and two-resonance contributions. The results for both three pion and (eta and two pions) currents within RChT has been implemented in MC generator PHOKHARA7.0. The numerical tests to check the implementation of the currents has been done. Fit to experimental data is in progress (10).
The web-page of the project is http://ific.uv.es/~shekhovt/taudecay.html where the tar-ball version of the updated generator TAUOLA and manual for it can be found. As soon as the fit procedure to data of the electron-positron annihilation into three pseudo-scalars is finished, the updated version of the code PHOKHARA will be added.
Reference
(1) G. Aad et al., Phys. Lett. B716 (2012) 1, arXiv: 1207.7214 (hep-ex); S. Chatrchyan, et al., Phys. Lett. B716 (2012) 30, arXiv:1207.7235 (hep-ex)
(2) S. Jadach, Z. Was, R. Decker and J. H. Kuhn Comput. Phys. Comm 76 (1993) 361
(3) J.H. Kuhn, E. Mirkes, Z. Phys. C56 (1992) 661; J.H. Kuhn, A. Santamaria, Z. Phys. C48 (1990) 445
(4) G. Ecker, J. Gasser, H. Leutwyler, A. Pich, E. de Rafael, Phys. Lett. B223 (1989) 425; G. Ecker, J. Gasser, H. Leutwyler, A. Pich, E. de Rafael, Nucl. Phys. B321 (1989) 311
(5) O. Shekhovtsova, T. Przedzinski, P. Roig and Z. Was Phys.Rev D86(2012) 113008
(6) H. Czyz, S. Ivashyn, A. Korchin, O. Shekhovtsova Phys.Rev. D85 (2012) 094010
(7) BABAR Collaboration, B. Aubert et al., Phys. Rev. D80, 052002 (2009), arXiv:0905.4778. BABAR Collaboration, P. del Amo Sanchez et al., Phys.Rev. D84, 052001 (2011), arXiv:1101.1142
(8) S. Uehara et al. (Belle Collaboration), arXiv:1205.3249 (hep-ex)
(9) H. Czyz, A. Grzelinska, J. H. Kuhn, and G. Rodrigo Eur.Phys.J. C47 (2006) 617
(10) CMD-2 Collaboration Collaboration, R. Akhmetshin et al. Phys.Lett. B578 (2004) 285; BABAR Collaboration, B. Aubert et al. Phys. Rev. D76 (2007) 092005
Tau lepton is a fundamental particle of the Standard Model (SM) and knowledge of its properties with high accuracy is absolutely mandatory for precise SM tests. From the perspective of low energy physics, such as studied at superB- and B-factories (BaBar and Belle experiments), tau lepton decays provide an excellent laboratory for modeling hadronic interactions at the energy scale of about 1 - 2 GeV, where neither perturbative quantum chromodynamics (QCD) methods nor chiral lagrangians are expected to work to a good precision. Results of such analysis will allow one to perform sensitive tests of the SM and extract its fundamental parameters, such as the coupling constant of strong interactions, the Cabibbo-Kobayashi-Maskawa matrix element and other important parameters. Moreover, modelling of the hadronic form factors (FF) will help in the search for lepton flavour violating decays of the tau lepton with hadrons in the final state. In addition to this, study of the tau hadronic decay allows one to learn properties of the intermediate meson resonances that are exchanged in the decay and to get information about the hadronisation of QCD currents via the study of the participating FF. From the perspective of high-energy experiments such as those at Large Hadron Collider (LHC), good understanding of tau lepton properties is a prerequisite for finding new physics signatures. With the discovery of a new particle around the mass of 125 - 126 GeV (1), tau decays are an important ingredient for determining if this is the SM Higgs. This is especially pertinent since CMS Collaboration has reported a deficit in the number of fermion decays from the new particle relative to the SM Higgs prediction.
With the shut-down of both the B-factory collaborations Babar and Belle, this is a critical time to make the results arising from more than a decade of experimental research available in a useful manner to the high energy physics community before the opportunity is lost. To this purpose, interaction between experimentalists and theorists is required to determine the optimal way of comparing experimental data with theoretical prediction, e.g. by installation of the theoretical results in the MC event generator.
The MC generator TAUOLA, currently used by both Belle and BaBar, represents a long term project that started in the 90's (see Ref. (2)). At present, more than twenty modes, both leptonic and hadronic, are simulated by the code. Analysis of hadronic decay modes involves matrix elements that convey the hadronisation of the vector and axial-vector currents. At present there is no determination from first principles of these matrix elements as they involve strong interaction effects in a non-perturbative regime. Therefore one has to rely on models that parameterise the FFs arising from the hadronisation. Originally TAUOLA was based on hadronic FFs written as a weighted sum of products of Breit-Wigner (BW) functions, using lowest order Chiral Perturbation Theory (ChPT) to normalise them (3). Nevertheless this description is not consistent with the chiral behavior at the next-to-leading order. As an alternative to this approximation it was proposed to apply the methods of RChT (4). RChT is a natural continuation of ChPT to the region of several GeV and is theoretically better founded than the approach of the BW functions. This new approach requires comparison with both BaBar and Belle experimental data which, in turn, requires the implementation of the theoretical results into TAUOLA. During her Marie Curie fellowship, the researcher has partially upgraded TAUOLA using the expression for the hadronic currents calculated within RChT in the case of the two and three meson (kaons and pions) decay modes (5). These modes together with the one meson decay mode represent more than 85 % of the hadronic width of the tau. The addition of the four pion decay modes, already started, will increase this fraction up to ~ 97 %. This work will continue at the Institute Nuclear Physics (INP), Cracow under a new contract beginning the 1 January 2013. This upgrade of TAUOLA is compatible with the previous version and can be easily implemented in the software used by both collaborations BaBar and Belle, being compatible with the C++ software used in the experiments. Numerical tests have been carried out to check numerical stability of the generator and the precision of MC results is better than 0.05% for all upgraded channels. With the collaboration of Dr Ian M. Nugent, an experimentalist from Babar, the researcher has made the first comparison of the TAUOLA prediction for the three pion mode with the unfolded spectrum, showing the necessity to improve the theoretical calculation for the low energy region of the two pion invariant mass. This required the inclusion of the contribution from the scalar meson. This work has already started and extraction of the parameters for the scalar meson will be done. The same analysis will be done for all three pseudo-scalar channels. Also work on the multidimensional fit of the three pion data has been initiated with J. Zaremba, a student of Cracow University, using the method of re-weighting events. This latter activity will be continued at INP. To conclude the technical work on the current installation for two and three meson decay modes is complete and work on fits is in progress in collaboration with experimentalists from BaBar and Belle. Another part of the project, with a similar goal, was devoted to the calculation of the cross section of the process electron-positron into 1) electron-positron pair and pseudoscalar (pion, eta and eta-prime mesons) and 2) three pseudo-scalars (three pions, two pions and eta meson) in the framework of RChT. As in the case of the tau decays the knowledge of the cross section allows us to gather information about the hadronisation of currents in the non-perturbative regime of QCD.
The results for the first process have been published in (6). Lately the two-photon transition FF's of the pseudo-scalar mesons have received a great attention both from the experimental and the theoretical side. The BaBar data (7) revealed unexpectedly large values in the range of Q2 = 10 - 35 GeV2 resulting in an excess of the pQCD predicted limit. This striking result attracted a lot of interest and motivated extensive theoretical investigations. Soon after, the Belle collaboration (8) published their data analysis that did not confirm the high-Q2 behaviour seen by BaBar. The two photon FF of the pseudo-scalars has been calculated within RChT and its has been applied to the process of the two photon electron-positron annihilation. Reasonable agreement with experimental data (CLEO, BaBar) for the FF's has been achieved. The only data sample which is not consistent with the model is the BaBar data for the pion (however, for the eta and eta-prime transition FFs are in perfect agreement) (7). The results obtained for the FF have been implemented in the MC EKHARA that simulates the process of the two photon electron-positron annihilation. The differential cross-section for the process of two-photon electron-positron annihilation into scalars has been compared with data from CLEO and BaBar. In order to investigate the impact of the event selection on the error estimate of the FF's, the simulation has been done with the direct cut on the untagged invariant and separately with the cut on the phase space of the untagged lepton (following the experimental cuts). It was shown that the error estimate and its Q2 dependence are very sensitive to the event selection in contrast to the estimate of BaBar (7). The future improvement of experimental data expected from the Belle and BES-III collaborations, will allow to get new information about the high energy behaviour of the FF's.
The previous theoretical calculation of the cross section of the electron-positron annihilation into three pions carried out in the framework of vector meson dominance in (9) did not take into account the anomalous structure of the production of three mesons from a vector current, as given by QCD. The calculation done within RChT includes both contributions, QCD anomalous and non-anomalous, consistently with our present knowledge of QCD. The amplitude for three meson production in e+ e- collisions has been calculated including the chiral, one-resonance and two-resonance contributions. The results for both three pion and (eta and two pions) currents within RChT has been implemented in MC generator PHOKHARA7.0. The numerical tests to check the implementation of the currents has been done. Fit to experimental data is in progress (10).
The web-page of the project is http://ific.uv.es/~shekhovt/taudecay.html where the tar-ball version of the updated generator TAUOLA and manual for it can be found. As soon as the fit procedure to data of the electron-positron annihilation into three pseudo-scalars is finished, the updated version of the code PHOKHARA will be added.
Reference
(1) G. Aad et al., Phys. Lett. B716 (2012) 1, arXiv: 1207.7214 (hep-ex); S. Chatrchyan, et al., Phys. Lett. B716 (2012) 30, arXiv:1207.7235 (hep-ex)
(2) S. Jadach, Z. Was, R. Decker and J. H. Kuhn Comput. Phys. Comm 76 (1993) 361
(3) J.H. Kuhn, E. Mirkes, Z. Phys. C56 (1992) 661; J.H. Kuhn, A. Santamaria, Z. Phys. C48 (1990) 445
(4) G. Ecker, J. Gasser, H. Leutwyler, A. Pich, E. de Rafael, Phys. Lett. B223 (1989) 425; G. Ecker, J. Gasser, H. Leutwyler, A. Pich, E. de Rafael, Nucl. Phys. B321 (1989) 311
(5) O. Shekhovtsova, T. Przedzinski, P. Roig and Z. Was Phys.Rev D86(2012) 113008
(6) H. Czyz, S. Ivashyn, A. Korchin, O. Shekhovtsova Phys.Rev. D85 (2012) 094010
(7) BABAR Collaboration, B. Aubert et al., Phys. Rev. D80, 052002 (2009), arXiv:0905.4778. BABAR Collaboration, P. del Amo Sanchez et al., Phys.Rev. D84, 052001 (2011), arXiv:1101.1142
(8) S. Uehara et al. (Belle Collaboration), arXiv:1205.3249 (hep-ex)
(9) H. Czyz, A. Grzelinska, J. H. Kuhn, and G. Rodrigo Eur.Phys.J. C47 (2006) 617
(10) CMD-2 Collaboration Collaboration, R. Akhmetshin et al. Phys.Lett. B578 (2004) 285; BABAR Collaboration, B. Aubert et al. Phys. Rev. D76 (2007) 092005