We report the status of the Heavy Flavour Averaging Group (HFLAV) averages of
the $\tau$ lepton measurements We then update the latest published HFLAV global
fit of the $\tau$ lepton branching fractions (Spring 2017) with recent results
by BABAR. We use the fit results to update the Cabibbo-Kobayashi-Maskawa (CKM)
matrix element Vus measurements with the $\tau$ branching fractions. We combine
the direct $\tau$ branching fraction measurements with indirect predictions
using kaon branching fractions measurements to improve the determination of Vus
using $\tau$ branching fractions. The Vus determinations based on the inclusive
branching fraction of $\tau$ to strange final states are about $3\sigma$ lower
than the Vus determination from the CKM matrix unitarity.Comment: Proceedings of the 15th International Workshop on Tau Lepton Physics
  (Tau 2018). SciPost editorial revisions applied. Fixed radiative correction
  that was erroneously including an isospin-breaking correction, fixed one
  formula, corrected a few typo

Lusiani, Alberto

English

arXiv

We report the status of the Heavy Flavour Averaging Group (HFLAV) averages
of the $\tau$ lepton measurements We then update the latest published
HFLAV global fit of the $\tau$ lepton branching fractions (Spring 2017)
with recent results by BABAR. We use the fit results to update the
Cabibbo-Kobayashi-Maskawa (CKM) matrix element Vus measurements with the
$\tau$ branching fractions. We combine the direct $\tau$ branching
fraction measurements with indirect predictions using kaon branching
fractions measurements to improve the determination of Vus using $\tau$
branching fractions. The Vus determinations based on the inclusive
branching fraction of $\tau$ to strange final states are about $3\sigma$
lower than the Vus determination from the CKM matrix unitarity

Archivio istituzionale della Ricerca - Scuola Normale Superiore

SciPost Phys. Proc. 1, 001 (2019)HFLAV τ branching fractions fit and measurementsof |Vus| with τ lepton dataAlberto Lusiani1?1 Scuola Normale Superiore and INFN sezione di Pisa, Italy? alberto.lusiani@pi.infn.itProceedings for the 15th International Workshop on Tau Lepton Physics,Amsterdam, The Netherlands, 24-28 September 2018doi:10.21468/SciPostPhysProc.1AbstractWe report the status of the Heavy Flavour Averaging Group (HFLAV) averages of the τ lep-ton measurements We then update the latest published HFLAV global fit of the τ leptonbranching fractions (Spring 2017) with recent results by BABAR. We use the fit results toupdate the Cabibbo-Kobayashi-Maskawa (CKM) matrix element |Vus|measurements withthe τ branching fractions. We combine the direct τ branching fraction measurementswith indirect predictions using kaon branching fractions measurements to improve thedetermination of |Vus| using τ branching fractions. The |Vus| determinations based on theinclusive branching fraction of τ to strange final states are about 3σ lower than the |Vus|determination from the CKM matrix unitarity.Copyright A. Lusiani.This work is licensed under the Creative CommonsAttribution 4.0 International License.Published by the SciPost Foundation.Received 16-11-2018Accepted 17-01-2019Published 18-02-2019Check forupdatesdoi:10.21468/SciPostPhysProc.1.0011 IntroductionThe τ subgroup of the Heavy Flavour Averaging Group (HFLAV) provides a global fit of theτ branching fractions, the lepton universality tests and the |Vus| determination based on τmeasurements. The latest published report for the τ lepton is labelled “Spring 2017” [1]. Aversion of the HFLAV τ branching fractions fit with unitarity constraint is published on theReview of Particle Physics [2] (RPP). There are additional minor differences between the twofits [1,3]. The fit results are used to test lepton universality and to compute |Vus| [1].The HFLAV-Tau group collects and combines also a list of upper limits set by searches oflepton-flavour-violating τ decays [1].In the following, we update the HFLAV-Tau global fit inputs with two BABAR measurementsthat became public in 2018 [4, 5] and we update the |Vus| determinations based on τ data.The new results have a negligible effect on the lepton universality tests.Finally, we add to the fit input measurements of three τ branching fractions that are in-directly determined using measurements of kaon branching fractions [6], in order to improvethe precision on |Vus|.1.1SciPost Phys. Proc. 1, 001 (2019)2 New τ branching fraction measurementsSince the last HFLAV report, BABAR published [4] a measurement ofB(τ−→ K−K0ντ) = (14.78± 0.22± 0.40)10−4and presented [5] preliminary measurements ofB(τ−→ K−ντ) = (7.174± 0.033± 0.213)10−3 ,B(τ−→ K−π0ντ) = (5.054± 0.021± 0.148)10−3 ,B(τ−→ K−2π0ντ(ex .K0)) = (6.151± 0.117± 0.338)10−4 ,B(τ−→ K−3π0ντ(ex .K0,η)) = (1.246± 0.164± 0.238)10−4 ,B(τ−→ K−3π0ντ(ex .K0,η)) = (1.168± 0.006± 0.038)10−2 ,B(τ−→ K−4π0ντ(ex .K0,η)) = (9.020± 0.400± 0.652)10−4 .3 |Vus| determination including the 2018 BABAR resultsWe add the measurements listed in the previous section to the HFLAV-Tau global fit, removinga former BABAR measurement of B(τ−→ K−π0ντ) [7] that has been superseded [5]. The newmeasurements of the branching fractions τ decaying to a kaon and 0, 1, 2, 3 π0’s improve theexperimental resolution on several modes that most contribute to the uncertainty on |Vus|.We compute |Vus|τs using the total branching fraction of the τ to strange final states fol-lowing Ref. [8]:|Vus|τs =√√√Rs/RVA|Vud |2 −δRtheory= 0.2195± 0.0019 ,where |Vud |= 0.97420±0.00021 [9], Rs and RVA are the τ hadronic partial widths to strangeand to non-strange hadronic final states (Γs and Γhad) divided by the universality-improvedbranching fraction B(τ → eνν̄) = Bunie = (17.814 ± 0.022)% [1, 3], and the SU(3)-breakingterm δRtheory = 0.242 ± 0.033 is computed using inputs from Ref. [8] andms = (95.00± 6.70)MeV [2] (the uncertainties on ms have been symmetrized).We compute also|Vus|τK/π = |Vud |fπ±fK±m2τ −m2πm2τ −m2K√√√B(τ−→ K−ντ)B(τ→ π−ντ)Rτ/πRτ/K1RτK/τπ= 0.2236± 0.0016 ,where fK±/ fπ± = 1.193±0.003 from the FLAG 2016 Lattice averages with N f = 2+1+1 [10–13] (the same value persists in the FLAG 2017 web update). The radiative correction terms areRτ/K = 1+(0.90±0.22)%, Rτ/π = 1+(0.16±0.14)% [14–17], RτK/τπ = 1+(−0.69±0.17)%[18–20]. The third value differs from the one quoted in the Spring 2017 HFLAV-Tau report [1],which incorrectly included a strong isospin-breaking correction that is not needed when usingfK±/ fπ± rather than its isospin-limit variant. The other parameters are taken from the Reviewof Particle Physics (RPP) 2018 [2].Averaging the two above |Vus| determinations, we obtain |Vus|τ = 0.2220± 0.0014.1.2SciPost Phys. Proc. 1, 001 (2019)Table 1: Deviations of |Vus| computed with τ data with respect to |Vus| obtained withCKM unitarity. The second and third row use the |Vus| determinations performedabove.∆ |Vus|τs ∆ |Vus|τK/π ∆ |Vus|τ[σ] [σ] [σ]HFLAV Spring 2017 -3.0 -1.0 -2.3HFLAV + BABAR 2018 -2.9 -1.1 -2.3HFLAV + BABAR + kaon predictions -2.7 -0.1 -0.94 τ branching fraction predictions from kaon measurementsAssuming the validity of the Standard Model (SM), three τ branching fractions have beencomputed using the precisely measured K`2 and K`3 branching fractions and the measuredτ−→ (Kπ)−ντ spectra [6]:B(τ−→ K−ντ) = (0.713± 0.003)% ,B(τ−→ K−π0ντ) = (0.471± 0.018)% ,B(τ−→ K0π−ντ) = (0.857± 0.030)% .The uncertainties on the last two results are fully correlated. It has been observed [6,18] thatall the above indirect values are higher than the corresponding directly measured τ branchingfractions. If the indirect values replace the direct ones, |Vus|= 0.2207± 0.027 [6].We add the kaon-indirect determinations of the three above τ branching fractions to thedata set used in the previous section in order to obtain improved calculations of|Vus|τs = 0.2202± 0.0018, |Vus|τK/π = 0.22546± 0.00097 , |Vus|τ = 0.22439± 0.00088.5 Consistency of |Vus| with the CKM matrix unitarityAssuming the CKM matrix unitarity,|Vus|uni =q1− |Vud |2 − |Vub|2 = 0.22565± 0.00089 ,using |Vud |= 0.97420± 0.00021 [9] and |Vub|= (0.3940± 0.0360)10−2 [2]. Table 1 summa-rizes the residuals, expressed as numbers of standard deviations, of the above mentioned |Vus|determinations with respect to the |Vus| computation from the CKM matrix unitarity. |Vus| com-puted with the τ-inclusive method is significantly lower, but the significance of the discrepancyis mildly reduced alongside a mild progress in the experimental resolution.6 ConclusionsFigure 1 reports the |Vus|τs determinations described above, a determination of |Vus|τs obtainedreplacing some τ branching fractions measurements with the indirect predictions based onkaon branching fractions [6], and other more complex determinations that use the τ spectralfunctions [21] and Lattice QCD techniques [22]. Updates on the last two determinations havebeen presented at the Tau 2018 workshop [23]. The last four determinations use an older andin some cases partial set of experimental τ branching fractions measurements.1.3SciPost Phys. Proc. 1, 001 (2019)-2-20.22 0.225|us|VCKM unitarity, PDG 2018 0.0009±0.2256  s incl., HFLAV Spring 2017→ τ 0.0021±0.2186  s incl., HFLAV + BABAR 2018→ τ 0.0019±0.2195  s incl., HFLAV + BABAR + kaons→ τ 0.0018±0.2202  s incl., Antonelli 2013→ τ 0.0027±0.2207  s incl., Hudspith 2018→ τ 0.0004± 0.0027 ±0.2231  s incl., Boyle 2018a→ τ 0.0013± 0.0015 ±0.2228  s incl., Boyle 2018b→ τ 0.0013± 0.0011 ±0.2245 A.L. elab.Tau 2018Figure 1: |Vus|τs determinations obtained in this document, from the top: |Vus|uni ,|Vus|τs with the HFLAV Spring 2017 fit, after adding the BABAR 2018 data, after addingboth the BABAR 2018 and the kaon indirect predictions, from Ref. [6], from Ref. [21],and two determinations from Ref. [22].-2-2●|Vus|(τ → K τ → π)|Vus|(τ → s)|Vud|CKMunitarityfit0.2150.2200.2250.2300.973 0.974 0.975 0.976|Vud||Vus|Figure 2: Results of a |Vud |-|Vus| simultaneous fit. The bands describe the constraintscorresponding to the |Vud |measurement, the |Vus|τs and the |Vus|τK/π determinationsthat use the τ measurements. The oblique line corresponds to the CKM matrix uni-tarity constraint. The ellipse corresponds to 1σ uncertainty on the |Vud | and |Vus| fitresults.1.4SciPost Phys. Proc. 1, 001 (2019)The τ based |Vus| determinations use the |Vud | measurements as input. The dependenceon |Vud | is however very small, and there is in first approximation negligible correlation be-tween |Vus| and |Vud | when doing a simultaneous fit. Figure 2 shows the results of a |Vud |-|Vus|simultaneous fit on the τ measurements corresponding to the HFLAV Spring 2017 fit and theBABAR 2018 results. The fit results are:|Vud |= 0.97420± 0.00021,|Vus|= 0.2223 ± 0.0014,|Vud | - |Vus| correlation= 0.035.Tables 2 and 3 report the contributions to the |Vus|τs uncertainty before and after the BABAR2018 results. The largest contributions come from the τ branching fractions to strange fi-nal states and from the theory. The BABAR 2018 measurements reduced significantly severallarge contributions. High multiplicity τ decays to strange final states dominate the |Vus|τsuncertainty. The Belle II super flavour factory will offer the opportunity to improve the exper-imental precision on the τ strange branching fractions. More precise τ branching fractionsand spectral function measurements will help improving also the theory uncertainty.Table 2: Contributions to the |Vus|τs uncertainty in percent before the BABAR 2018results.π−K̄0π0π0ντ (ex. K0) 0.3963K−2π0ντ (ex. K0) 0.3789K−3π0ντ (ex. K0,η) 0.3714K̄0h−h−h+ντ 0.3478K−π0ντ 0.2561K−π−π+π0ντ (ex. K0,ω,η) 0.2456π−K̄0ντ 0.2424π−K̄0π0ντ 0.2219K−ντ 0.1646K−ωντ 0.1585K−π−π+ντ (ex. K0,ω) 0.1157π−K̄0ηντ 0.0256K−π0ηντ 0.0200K−ηντ 0.0138K−φντ (φ→ K+K−) 0.0138K−φντ (φ→ K0S K0L ) 0.0096K−2π−2π+ντ (ex. K0) 0.0021K−2π−2π+π0ντ (ex. K0) 0.0010τ→ non-strange 0.0896Bunive 0.0045theory 0.48611.5SciPost Phys. Proc. 1, 001 (2019)Table 3: Contributions to the |Vus|τs uncertainty in percent after the BABAR 2018 re-sults.π−K̄0π0π0ντ (ex. K0) 0.3931K̄0h−h−h+ντ 0.3450K−π−π+π0ντ (ex. K0,ω,η) 0.2436π−K̄0ντ 0.2372π−K̄0π0ντ 0.2200K−ωντ 0.1572K−π0ντ 0.1554K−ντ 0.1459K−π−π+ντ (ex. K0,ω) 0.1147K−2π0ντ (ex. K0) 0.0460K−3π0ντ (ex. K0,η) 0.0449π−K̄0ηντ 0.0254K−π0ηντ 0.0198K−ηντ 0.0137K−φντ (φ→ K+K−) 0.0136K−φντ (φ→ K0S K0L ) 0.0095K−2π−2π+ντ (ex. K0) 0.0021K−2π−2π+π0ντ (ex. K0) 0.0010τ→ non-strange 0.0855Bunive 0.0045theory 0.4863References[1] Y. Amhis et al., Averages of b-hadron, c-hadron, and τ -lepton properties as of summer2016, Eur. Phys. J. C 77, 895 (2017), doi:10.1140/epjc/s10052-017-5058-4.[2] M. Tanabashi et al., Review of particle physics, Phys. Rev. D 98, 030001 (2018),doi:10.1103/PhysRevD.98.030001.[3] A. Lusiani, HFAG 2016 and PDG 2016 τ lepton averages and |Vus| de-termination from τ data, Nucl. Part. Phys. 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HFLAV $\tau$ branching fractions fit and measurements of Vus with $\tau$ lepton data

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HFLAV τ\tauτ branching fractions fit and measurements of Vus with τ\tauτ lepton data

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HFLAV $\tau$ branching fractions fit and measurements of Vus with $\tau$ lepton data