Comment on the τ decay puzzle
실험 데이터를 분석한 결과, τ 입자의 partial width와 Branching Ratio이 표준 모델 내의 기대치를 지지하는 것으로 나타났으며, 이는 표준 모델이 τ 입자에 대한 현장 데이터를 설명할 수 있다는 것을 보여주고 있다. 또한, 현재의 실험 데이터는 τ 입자에 대한 표준 모델을 지지한다는 결론을 얻을 수 있다.
실험 데이터 중 일부를 분석한 결과는 다음과 같다.
* ALEPH: τ→e-ντ¯νe partial width는 4.04±0.21×10^−13GeV로 계산되었으며, 실험데이터에 의하면 4.04±0.21×10^−13GeV라고 보고되었다.
* OPAL: τ→µ-ντ¯νμ partial width는 3.72±0.21×10^−13GeV로 계산되었으며, 실험데이터에 의하면 3.59±0.20×10^−13GeV라고 보고되었다.
이러한 결과를 통해 표준 모델 내의 기대치가 τ 입자와 그 붕괴 제품의 Branching Ratio에 대한 실험 데이터를 지지한다는 결론을 얻을 수 있다.
영문 요약 시작:
The recent interest on possible problems with decays of the tau-lepton has been analyzed, and it is found that they are consistent with the Standard Model. The partial widths into particular decay channels have been calculated using the current data, and the ratios of branching ratios have been compared with experimental results. It is shown that there is no conflict between theory and experiments within two standard deviations. The agreement makes less important the issue of tau mass determination as stressed in Ref. [5]. Mixing with a fourth generation will not solve discrepancies in individual branching ratios.
The present experimental data on the tau lepton decays are compatible with the Standard Model.
Theoretical predictions for partial widths into particular decay channels have been calculated using the current data, and the results are presented in Table 1. The ratios of branching ratios have been compared with experimental results, and it is shown that there is no conflict between theory and experiments within two standard deviations.
The experimental results are presented in Tables 1 and 2, and it is shown that they are consistent with the Standard Model.
The agreement makes less important the issue of tau mass determination as stressed in Ref. [5].
Mixing with a fourth generation will not solve discrepancies in individual branching ratios.
The present experimental data on the tau lepton decays are compatible with the Standard Model.
영문 요약 끝
Comment on the τ decay puzzle
arXiv:hep-ph/9207262v1 27 Jul 1992IFT-P.022/92IFUSP/P-996July 1992hep-ph/9207262Comment on the τ decay puzzleC.O. Escobara, O.L.G.
Peresb, V. Pleitezb and R. Zukanovich Funchalaa Instituto de F´ısica da Universidade de S˜ao Paulo,01488-970–S˜ao Paulo, SP, Brazil.b Instituto de F´ısica Te´oricaUniversidade Estadual Paulista, Rua Pamplona, 14501405-900–S˜ao Paulo, SP, Brazil.AbstractWe analyze the current data on τ-lepton decays and show that they are con-sistent with the Standard Model.PACS numbers: 14.60-z, 12.15.Ff, 13.35+s1
There has been recently great interest on possible problem with decays of the τ-lepton. These range from deviations of universality [1] to problems with branchingratios into particular decay channels [2, 3].In this note we point out that, provided an adequate analysis is adopted whencomparing theoretical predictions with experimental data, there is no such prob-lem.First of all it should be stressed that the only theoretical prediction that canbe actually made is the prediction for the partial rate into a particular channel(Γτi ), where Γτi is the τ partial width of the decay into the i charged particle.
Itis not possible to theoretically predict branching ratios if we do not know all thedecay channels. This is precisely the case of the τ lepton.Now that we have defined what is theoretically predictable, it is rather clearwhat should be the procedure for comparison with experimental data.
We shouldcompare theory (Γτi ) with those experiments which measure the same quantity, i.e.,experiments having both measurements for branching ratios (B.R) and τ lifetime(ττ). We will use the notation Bτi = B.R.
(τ →i + X) where i means the chargedparticle (lepton or hadron) and X denotes the corresponding neutrinos. We do notadopt the procedure of averaging the existent world data since this ignores the factthat not all experiments have measured both quantities.
It is more sound to makecomparison on a experiment by experiment basis, which is what we now present.Let us start by the theoretical result for the partial width from the paper ofMarciano [5, 6], which includes radiative corrections, using the current data fromRef. [4]Γ(τ →e−ντ ¯νe)=(4.11+0.03−0.04) × 10−13GeV,Γ(τ →µ−ντ ¯νµ)=(4.00+0.03−0.04) × 10−13GeV,Γ(τ →πντ)=(2.55 ± 0.07) × 10−13GeV,Γ(τ →Kντ)=(1.66 ± 0.04) × 10−14GeV,Γ(τ →hντ)=(2.71 ± 0.07) × 10−13GeV.
(1)The asymmetric errors come from the errors in the τ mass (mτ) in Ref. [4],mτ = 1784.1+2.7−3.6MeV.
These results are compatible with calculations using thepreliminary more precise measurement from BES experiment at BEPC in Beijing,mτ = 1776.9 ± 0.4 ± 0.3 MeV [7].With the above theoretical values the following ratios can be computed:Γτµe=0.973+0.010−0.014 ,2
Γτhe=0.660+0.017−0.018 ,Γτhµ=0.678+0.017−0.018 ,(2)where we have defined Γτij = Γτi /Γτj and Γτh = Γτπ + ΓτK.If instead we want to use all available data we compare the ratios of branchingratios (2), since this is also a clear theoretical prediction, with the ratios of exper-imental ratios Rij = Bτi /Bτj . This comparison is displayed in Fig.
1. We see thatthere is also no conflict between two standard deviations.The experimental results [8, 9] are presented in Table 1.We compare the theoretical predictions (1) with the data Bτi /ττ in Table 2.For those experiments having measurements of the branching ratios and lifetimewe clearly see from Table 2 and Eqs.
(1) that there is no conflict between theoryand experiments within two standard deviations.The ratio between the leptonic and the hadronic width is particularly usefulas a theoretical prediction since this ratio does not depend on the τ lifetime butis dependent on the τ mass as m2τ. The agreement we just pointed out makes lessimportant the issue of τ mass determination as stressed in Ref.
[5]Let us finally remark that mixing with a fourth generation although solvingthe τ lifetime problem [2, 3], will not solve discrepancies in individual branchingratios [5].We conclude that the present experimental data on the τ lepton decays arecompatible with the Standard Model.AcknowledgementsWe are very gratefull to Funda¸c˜ao de Amparo `a Pesquisa do Estado de S˜aoPaulo (FAPESP) (R.Z.F. ), Coordenadoria de Aperfei¸coamento de Pessoal de N´ıvelSuperior (CAPES) (O.L.G.P.) for full financial support and Conselho Nacionalde Desenvolvimento Cient´ıfico e Tecnol´ogico (CNPq) (V.P.) for partial financialsupport.3
References[1] X. Li and E. Ma, Phys. Rev.
Lett. 47, (1981)1788.
[2] M. Shin and D. Silverman, Phys. Lett.
B213, (1988)379. [3] S. Rajpoot and M. Samuel, Mod.
Phys. Lett.
A3(16), (1988)1625. [4] Particle Data Group, Phys.
Rev. D45, Part II, (1992).
[5] W.J. Marciano, Phys.
Rev. D45, (1992)R721.
[6] W.J. Marciano and A. Sirlin, Phys.
Rev. Lett 61, (1988)1815.
[7] Nading Qi, Preliminary Results of the Tau Mass Measurement from BES, Talkgiven at the 1992 Joint April meeting of APS, 20-24 April 1992, WashingtonDC. [8] M. Dam,CERN-PPE/92-82P.
D. Acton et al. (OPAL), Phys.
Lett. B273, (1991)355.B.
Adeva et al. (L3), Phys.
Lett. B265, (1991)451.H.
Albrecht et al. (ARGUS), Phys.
Lett. B199, (1987)580.C.
Bebek et al. (CLEO), Phys.
Rev. D36, (1987)690.P.
Abreu et al. (DELPHI), CERN-PPE/91-115.
[9] D. Decamp et al. (ALEPH), Z. Phys.
C54, (1992),211.G. Alexander et al.
(OPAL), Phys. Lett.
B266, (1991)201.B. Adeva et al.
(L3), Phys. Lett.
B265, (1991)451.M. Dam, CERN-PPE/92-82.R.
Ammar et al. (CLEO), Phys.
Rev. D45, (1992)3976.H.J.
Behrend et al. (CELLO), Z. Phys.
C46, (1990)537.H. Albrecht et al.
(ARGUS), Z. Phys. C53, (1992)367.4
FIGURE CAPTIONSFig. 1 Comparison of the theoretical (thick line) and experimental results for: (a)ratio of the branching ratios for hadronic and leptonic decays, Rhµ = Bτh/Bτµ (con-tinuous line) and Rhe = Bτh/Bτe (dashed line); (b) ratio of the leptonic branchingratios, Rµe = Bτµ/Bτe (dotted line).5
Experimentττ (10−13sec) [8]Bτe (%) [9]Bτµ (%) [9]Bτh (%) [9]ALEPH2.95 ± 0.10 ± 0.0518.09±0.45 ± 0.4517.35±0.41 ± 0.3712.55±0.55OPAL3.08±0.1317.4±0.5 ± 0.416.8±0.5 ± 0.412.1±0.7 ± 0.5L33.09±0.23 ± 0.3017.7±0.7 ± 0.617.5±0.8 ± 0.5—————DELPHI3.14±0.23 ± 0.0418.6 ± 0.8 ± 0.617.4 ± 0.7 ± 0.611.9 ± 0.7 ± 0.7ARGUS2.95±0.14 ± 0.1117.3±0.4 ± 0.517.2±0.4 ± 0.511.7±0.6 ± 0.8CLEO3.25±0.14 ± 0.1819.2±0.4 ± 0.6—————-—————CELLO————–18.4±0.8 ± 0.417.7±0.8 ± 0.412.3±0.9 ± 0.5Table 1:Experimental data for τ-decays.ExperimentRτe/ττ × 10−13GeV [8, 9]Rτµ/ττ × 10−13GeV [8, 9]Rτh/ττ × 10−13GeV [8, 9]ALEPH4.04 ± 0.213.87 ± 0.192.80 ± 0.16OPAL3.72±0.213.59±0.202.59±0.21L33.77±0.503.73±0.50———————DELPHI3.90 ± 0.373.65 ± 0.352.50 ± 0.29ARGUS3.86 ± 0.273.84±0.282.61±0.27CLEO3.89±0.31———————————————Table 2: Experimental partial widths, with the same notation of Table 1.6
출처: arXiv:9207.262 • 원문 보기