Study of the tau meson decay modes with Monte Carlo generator TAUOLA. Status and perspectives
NNuclear Physics B Proceedings Supplement 00 (2018) 1–5
Nuclear Physics BProceedingsSupplement / locate / procedia IFJPAN-IV-2014-15
Study of the tau meson decay modes with Monte Carlogenerator TAUOLA. Status and perspectives.
Olga Shekhovtsova
Institute of Nuclear Physics PAN ul. Radzikowskiego 152 31-342 Krakow, PolandKharkov Institute of Physics and Technology 61108, Akademicheskaya,1, Kharkov, Ukraine
Abstract
In the last two years substantial progress for the simulation of the process: τ − → π − π + π − ν τ by the Monte Carlogenerator TAUOLA was achieved. It is related to a new parametrization of the corresponding hadronic current basedon the Resonance Chiral Lagrangian and the recent availability of the unfolded distributions from the BaBar Collabo-ration analysis for all invariant hadronic masses. The theoretical model parameters were fitted to the one-dimensionaldistributions provided by the BaBar Collaboration and results of the fit are discussed. A set of the hadronic currents forother final states with two and three pseudoscalars is also installed in TAUOLA and the preliminary results for fitting K + K − π − and π π − to BaBar and Belle data are presented.c (cid:13) Keywords:
Tau physics, Monte Carlo generator, TAUOLA, Resonance Chiral Lagrangian, Data analysis
1. Introduction
TAUOLA [1] is a Monte Carlo (MC) generatordedicated to the generation of τ -lepton decays andit is used in the analysis of experimental data bothat B-factories, BaBar [2] and Belle [3] Collabora-tions, and LHC [4]. The generator simulates morethan twenty decay modes, including both leptonicand hadronic modes. The leptonic decay modes ofthe τ lepton allow to test the universality of the lep-ton couplings to the gauge bosons. The hadronicdecays (in fact, the τ lepton due to its high mass isthe only one that can decay into hadrons) give in-formation about the hadronization mechanism andresonance dynamics in the energy region where the Email address: [email protected] (Olga Shekhovtsova) methods of perturbative QCD cannot be applied.Also hadronic flavour- and CP-violating decays ofthe τ lepton allow to search for new physics scenar-ios. In addition, the tau lepton decay data allows usto measure the Standard Model parameters, suchas the strong coupling constant, the quark-mixingmatrix, the strange quark mass etc.The main problem in description of the hadronicdecay modes of the τ lepton is the lack of a the-ory coming from the first principle in the energyregion populated by the resonances (i.e. in the re-gion of 1-2 GeV). The hadronic currents imple-mented in the first version of TAUOLA [1] as wellas in the internal versions of the code used byBaBar and Belle are based on Vector Meson Dom-inance (VMD) approach. As shown in [5], Figs.20.6.3 and 20.6.4, the current version of TAUOLA,used by Belle collaboration does not give a sat- a r X i v : . [ h e p - ph ] N ov / Nuclear Physics B Proceedings Supplement 00 (2018) 1–5 ) )] / N ) / ( M e V / c + π - π - π ([ d N / d M ( ) (GeV) + π - π - π M(0.5 1 1.5 ) )] / N ) / ( M e V / c - π - π ([ d N / d M ( ) (GeV) - π - π M(0.5 1 1.5 ) )] / N ) / ( M e V / c + π - π ([ d N / d M ( ) (GeV) + π - π M(0.5 1 1.5 Fig. 1. The τ − → π − π − π + ν τ decay invariant mass distribution of the three-pion system (left panel) and two-pion pairs (central andright panels). The BaBar measurements [7] are represented by the data points, with the results from the R χ L current as described inthe text (blue line) and the old fit from CLEO as detailed in Refs. [4] (red-dashed line) overlaid. At the bottom of the figures the ratioof the new R χ L prediction to the data is given. The parameters used in our model are collected in Table 1 of [9]. isfactory description of the data. This indicatesthat the model in the generator code should be up-dated. In last three years we have been working onthe partial upgrade of the generator TAUOLA byusing the results for the hadronic currents calcu-lated within Resonance Chiral Lagrangian (R χ L)formalism and fitting the model parameters to theavailable experimental data from B-factories. TheR χ L approach succeeds in reproducing low energyresults, predicted by Chiral Perturbation Theory, atleast, at the next-to-leading order and also com-plies with QCD high energy constraints. Alter-native ad-hoc models, as VMD mentioned above,lack a link with QCD and thus can, at most, re-produce the leading order properties. Presently theR χ L currents for the main two-meson (final stateswith two pion, pion-kaon, two kaons) and three-pseudoscalar (three pion, two kaon-one pion) de-cay modes have been installed into TAUOLA. Thisset covers more than 88% of the hadronic τ decaywidth. The implementation of the currents, the re-lated technical tests as well as the necessary theo-retical concepts are documented in [6].Studies of the one-dimensional three-prong de-cay modes by BaBar [7] allowed us to compareR χ L predictions with the measured data. Westarted with the π − π − π + mode. The choice ofthis channel was motivated by its relatively largebranching ratio and the already non-trivial dynam-ics of three-pion final state. The first comparison tothe BaBar preliminary data demonstrated satisfac-tory agreement with the three pion invariant massspectrum and a mismatch in the low energy tail intwo pion invariant distributions [8]. This mismatchindicates that the lack of the scalar f (500) reso-nance, so called σ meson, in the R χ L formalism may be responsible for this discrepency. A modifi-cation to the R χ L approach to include the σ mesonwas proposed in [9] and as a result the agreementwith the data was improved by a factor of abouteight.The paper is organized as follows. In Sec-tion 2 the theoretical framework for π − π − π + cur-rent as well as numerical results of the fit to datafrom BaBar is presented. Section 3 contains thefirst results of the fit for π π − and K + K − π − todata from BaBar and Belle experiments, corre-spodningly. The summary of Section 4 closes thepaper.
2. Decay mode τ − → π − π − π + ν τ . Fit to BaBardata: numerical results and tests For the final state π − π − π + the following mecha-nisms of production have been taken into account: • double resonance mechanism of production τ − → a − ν τ → π − ( ρ ; σ ) ν τ → π − π − π + ν τ , • single resonance mechanism of production τ − → π − ( ρ ; σ ) ν τ → π − π − π + ν τ , • a chiral contribution (a direct decay, withoutproduction of any intermediate resonance) .The exact form of the hadronic current can befound in [9], Section II.A resonance mechanism for the production ofthe π + π − via the lightest scalar resonance, f (500),not present in the previous version of TAUOLA[6, 8], has been included in the simulation. Thenature of the σ resonance, is still unclear and vari-ous descriptions are proposed by di ff erent groups: Nuclear Physics B Proceedings Supplement 00 (2018) 1–5 meson-meson molecular, tetraquark etc. [10]. Asa result of this behavior the σ resonance cannot beeasily included in the R χ L formalism. In view ofthis we have decided to incorporate the interme-diate σ meson state in a form that reproduces theR χ L current structure (i.e. contains single and dou-ble resonance contributions, see above), and repre-sent the σ meson by an s-wave Breit-Wigner func-tion following a phenomelogical approximation.To obtain the numerical values of the model pa-rameters (the mass of resonances, vertex couplingsetc, for details, see [9]) the three one-dimensionaldistributions, namely d Γ / dm π − π − π + , d Γ / dm π − π − and d Γ / dm π − π + , have been fitted to the BaBar prelim-inary data [7]. The partial width of the τ − → π − π − π + ν τ decay is normalized to that measured byBaBar Γ = (2 . ± . · − GeV [2].The first problem related with the fit is the cal-culation of the width in the a (1260) propagator.The a width can be written down as the imaginarypart of the two-loop axial-vector-axial-vector cor-relation function with suitable flavour indices andis a double integral of the same hadronic form fac-tors that fill in the hadronic currents (for details,see [6], Section 3). Calculating this integral ateach point in the parameter space would degradethe performance of the MC generator by a factor ofa thousand (taking into account all decays rejectedin the MC process). To avoid this, TAUOLA usesa 1000-point precalculated table of the resonancewidth which is later interpolated to obtain precisevalue for each point in phase space. Our first at-tempt was to calculate the width only at the startingpoint of the fitting procedure and not to recalculateit during the fit. However, the lack of proper re-calculation of this resonance turned out to greatlyinfluence the results. A fitting procedure that relieson the width calculated only once ends up in a min-imum completely o ff the global minimum foundwhen this width is properly recalculated for eachpoint in the parameter space. Another approxima-tion used in the a width calculation was based onan estimate of the g -function, as detailed in [9]. Fi-nally, after the introduction of the parallelized cal-culation, we were able to incorporate the precisecalculations of the a width table into the project.To fit the data we used the MINUIT packagethrough the ROOT framework and the fit result ispresented in Fig. 1, for the numerical values of themodel parameters see Table 1 in [9]. The good-ness of the fit is quantified by χ / nd f = / ) )] / N ) / ( M e V / c - π π ([ d N / d M ( ) (GeV) - π π M(0.5 1 1.5 Fig. 2. The τ − → π π − ν τ decay invariant mass distribution estimated the χ value using the combined statisti-cal and systematic uncertainties since only the to-tal covariance matrix was publicly available at thattime. For the present results we obtain χ / nd f = / HESSE routine from MINUITunder the assumption that the correlations betweendistributions and the correlations related to havingtwo entries per event in the π − π + distribution canbe neglected. The fit results with estimated sys-tematical and statistical errors, the statistical andthe systematic correlation matrices are collected intables 3, 4 and 5 of [9], correspondingly.The following test has been done to checkwhether the obtained minimum is a global one anddoes not depend on the starting parameter values.We start from a random scan of 2 . ∗ pointsand select 1000 events with the best χ , out ofwhich 20 points with maximum distance betweenthen are retained and then these points are usedas a start point for the full fit. We find that morethan a half converges to the minimum (Table 1 in[9]), the rest either reach the limits of the para-metric range or converge to local minimum withhigher χ . Therefore, we conclude that the ob-tained result is stable and does not depend on theinitial value of the fitting parameters. As an addi-tional cross check we calculated the partial widthresulting from the phase space integration of thematrix element Γ τ − → π − π − π + ν τ = . · − GeVwhich agrees with the one measured by BaBar Γ τ − → π − π − π + ν τ = (2 . ± . · − GeV [2].In addition, based on the fitted values of the R χ Lparameters we estimated the π π π − partial width: Γ = (2 . ± . · − GeV that is 1% higher / Nuclear Physics B Proceedings Supplement 00 (2018) 1–5 ) )] / N ) / ( M e V / c + K - π - ([ d N / d M ( K ) (GeV) + K - π - M(K1.2 1.4 1.6 ) )] / N ) / ( M e V / c - π - ([ d N / d M ( K ) (GeV) - π - M(K1 1.5 ) )] / N ) / ( M e V / c + K - ([ d N / d M ( K ) (GeV) + K - M(K1 1.2 1.4 ) )] / N ) / ( M e V / c + K - π ([ d N / d M ( ) (GeV) + K - π M(0.8 1 1.2 Fig. 3. The τ − → K + K − π − ν τ decay invariant mass distributionof three and two meson system. For the description of the plotssee Fig. 1. than the central PDG value and within the errorscited by PDG.
3. Decay modes τ − → π π − ν τ and τ − → K + K − π − ν τ . Preliminary results The first preliminary results for the π π − and K + K − π − modes are presented in Figs. 2 and 3. Forthe former, we have fitted the absolute value of thepion form factor calculated within the dispersiverepresentation [11] and to the Belle parametriza-tion for the pion form factor, Eqs. (11)-(14) in [12](at present the experimental errors are not includedin the fit). The latter was carried out in the gen-eralized version of the fitting strategy used for the π − π − π + mode presented above. In our approach weused the a width calculated only at the beginningof the fitting and did not change it during the fit.An improved procedure might require a commonfit of both π − π − π + and K + K − π − modes.
4. Conclusion
In this paper we have discussed the status ofthe TAUOLA project. The main attention was de-voted to the results of the one-dimensional fit forthe τ − → π − π + π − ν τ decay mode to the preliminaryBaBar data. The theoretical approach was based on the Resonance Chiral Lagrangian with an ad-ditional modification to the current to include thesigma meson. As a result, we improved agreementwith the data by a factor of about eight comparedwith the previous results [8]. We tested that the ob-tained result corresponds to a global minimum andthat the fitting procedure does not depend on theinitial values of the model parameters.Nonetheless, the model shows discrepancies inthe high energy tail of the three pion invariant massspectrum, that may be related with missing reso-nances, e.g. a (1640), in the corresponding theo-retical approach. We will come again to this pointin future multidimensional analysis.We presented the first results of the generaliza-tion of the fitting strategy to the case of an arbitrarythree meson tau decay, specializing to the K + K − π − decay mode. In addition we fitted the two pionform factor [11] to the Belle parametrization forit. The technical study of the fit stability and thecorrelation of the parameters is in progress.
5. Acknowledgements
This research was supported in part by Foun-dation of Polish Science grant POMOST / /
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