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Michel Parameters Averages and Interpretation

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Michel Parameters Averages and Interpretation 1 Michel Parameters BONN-HE-98-04 Averages and Interpretation a A. Stahl a Physikalisches Institut, Nussallee 12, 53115 Bonn, Germany e-mail: [email protected] onn.de The new measurements of Michel parameters in decays are combined to world averages. From these mea- (26-October-1998) surements mo del indep endent limits on non-standard mo del couplings are derived and interpretations in the Preprint - Server framework of sp eci c mo dels are given. Alower limit of 2:5 tan GeV on the mass of a charged Higgs b oson in mo dels with two Higgs doublets can b e set and a 229 GeV limit on a right-handed W -b oson in left-right symmetric mo dels (95 % c.l.). the two sections following these are dedicated to 1. INTRODUCTION an interpretation of the results in terms of two Now that you have seen several presentations sp eci c mo dels. I will not giveanintro duction to of new exp erimental results on the Lorentz struc- Michel Parameters in decays. There are excel- ture of the charged current mediating decays, lent reviews in the literature [1]. it is my task to present up dated world averages and interpretations. The question b eing what we 2. LEPTONIC DECAYS can learn from these numb ers in terms of new physics, what can we exclude or are there hints In the most general case the matrix elementof ab out where to go. This motivation is quite dif- the leptonic decays ! e and ! e ferent from what was driving p eople to study the can b e describ ed by the following Lorentz invari- Lorentz structure of muon decays. There the pure ant, lo cal, derivative free, lepton numb er conserv- V-A character of the standard mo del currentwas ing, 4-fermion p oint-interaction established and nowwe are asking the question is X G F there anything else. p 4 (`) j j ( )i g h ` " " 2 There are two approaches to this question: The =S;V ;T ";=R;L rst will be to make as few assumptions ab out h ( ) j j ( ) i: (1) new physics as p ossible, lo ok at the data and see ! which extensions of the standard mo del current However even the so-called most general ansatz can be excluded on these general grounds. The is based on non-trivial assumptions and I wantto second approach has a guess (a mo del) ab out how discuss some of them, b efore I giveaverages and the new physics might lo ok like at its starting limits on the couplings g . p oint. The mo del is tted to the data and the parameter space of the mo del is then insp ected Lorentz invariance and lo cality should hold for preferred/excluded regions. These two ap- for any kind of new physics. proaches are quite di erent. The rst approach will give weaker limits in general, however with Neglecting the propagators of the b osons the second approach there is the risk, that if mediating b etween the two currents leads to there are signs of new physics in the data and a p ointinteraction. This is a go o d approx- one guesses wrong, one might miss them. imation for the standard mo del W-b oson I will try to cover b oth approaches: In the next and should be an even b etter approxima- three sections I will talk ab out general limits and tion for new heavier b osons. 2 ν Equation 1 assumes conservation of lepton τ numb ers. It has b een extented to lepton - umber non-conserving currents [2]. The n τ - χ- e result is a sp ectrum indistinguishable from the one following from eq. 1, however the ν meaning of the couplings g changes. Each e coupling is replaced by the original coupling plus a sum of several lepton numb er violat- ing new couplings. If such new physics ex- Figure 1. A feynman diagram of the decayof a ists, it will still show up in a deviation of in a SUSY mo del. The dashed lines represent the Michel parameters from their standard SUSY particles. mo del values, except for some pathological cases. The argument for assuming derivative free and they might not even b e lighter than the couplings is an argument of simplicity. The . case of derivatives in connection with a Apart from these assumptions on the decay of the vector current can be approximately sub- 's built into the Michel sp ectrum an actual mea- stituted by a scalar current through the surement of the parameters has to make also some Dirac equation. Therefore such kind of new assumptions ab out their pro duction. One would physics would not b e missed. However the like to treat the pro duction with the same gener- extension to couplings involving derivatives ality as the decay (see [4]), as new physics in the of a tensor current create non-trivial exten- charged current decay might go along with new sions of the sp ectrum and are not included physics in the neutral current pro duction. How- in the ansatz of eq. 1. DELPHI has investi- ever this increases the number of parameters to gated such kind of couplings and I wantto an unmanageable amount. Therefore all exp eri- refer the reader to their presentation [3]. ments assume the pairs to b e pro duced purely by spin 1 b osons. Most exp eriments re t the The assumption of 4 fermions participating p olarization, i.e. they allow for an arbitrary cou- in the decay might sound obvious at rst pling of the pairs to this vector current. The sight, but there are p ossible extensions of coupling of the current to the initial electrons is the standard mo del, where the two unob- xed to the standard mo del value and has proba- served particles in the decay are no longer bly little impact on the measurement. Pro duction neutrinos. For example g. 1 shows a feyn- of pairs through scalar or tensor b osons would man diagram of a decaying through SUSY however drasticly change the picture. particles. The two unobserved particles are Now with these restrictions in mind we can take sneutrinos which don't have spin 1/2. the averages. They are presented in g. 2 for ! e and g. 3 for ! [5{12]. The e Although not mentioned in the list of prep o- average takes into account the correlations be- sitions to the most general ansatz, there is 1 tween the parameters within each exp eriment , a serious assumption entering the calcula- but treats the di erent exp eriments indep endent tion of the sp ectra from eq. 1. In inte- of each other. There is no sensitivity to the - grating over the phase-space of the unob- parameter in ! e decays. The measure- e served neutrinos, it is assumed that their ments havenow reached a precision of a few p er- masses are small compared to m . This is certainly ful lled for the standard mo del, 1 For SLD I assume the correlation matrix elements not though new physics might come with new including to b e the same as in the t assuming lepton universality. neutrinos (right-handed ones for example) 3 ALEPH ALEPH ALEPH 0.747+/-0.024 0.776+/-0.049 0.16+/-0.16 DELPHI DELPHI DELPHI 0.764+/-0.044 0.905+/-0.081 0.38+/-0.25 OPAL OPAL 0.779+/-0.055 0.777+/-0.047 SLD SLD SLD 0.71+/-0.15 0.54+/-0.31 -0.59+/-0.94 CLEO CLEO CLEO 0.747+/-0.013 0.750+/-0.048 0.01+/-0.23 ARGUS ARGUS 0.68+/-0.08 0.69+/-0.08 ρ 0.748+/-0.010 η ρ 0.771+/-0.018 η 0.127+/-0.066 ALEPH ALEPH ALEPH ALEPH 1.01+/-0.10 0.788+/-0.070 1.03+/-0.13 0.786+/-0.072 DELPHI DELPHI DELPHI DELPHI 0.951+/-0.091 0.727+/-0.069 1.16+/-0.14 0.721+/-0.092 OPAL OPAL OPAL OPAL 1.13+/-0.41 0.72+/-0.34 0.79+/-0.41 0.63+/-0.25 SLD SLD SLD SLD 1.16+/-0.52 0.85+/-0.44 0.75+/-0.52 0.82+/-0.33 CLEO CLEO CLEO CLEO 0.979+/-0.051 0.720+/-0.034 1.050+/-0.083 0.786+/-0.052 ARGUS ARGUS ARGUS ARGUS 1.11+/-0.22 0.56+/-0.15 1.26+/-0.30 0.73+/-0.21 ξ 0.986+/-0.039 ξδ 0.726+/-0.026 ξ 1.110+/-0.045 ξδ 0.756+/-0.035 Figure 2. New world averages of the Michel pa- Figure 3. New world averages of the Michel pa- rameters of the decay ! e . The average is rameters of the decay ! . See g. 2 for e indicated by the number at the b ottom and the details. shaded band. The solid line is the standard mo del 3 3 exp ectation ( ; 0; 1; ). Errors are statistical and 4 4 systematic added in quadrature [5{11]. Some old measurements of are also included. B ( ! ) = (17:36 0:06) %) and the life- time [14] ( = (290:5 1:0) fsec) give cent. There is very go o d agreement with the stan- A = 1:000 0:005 e dard mo del for ! e and a reasonable agree- e A = 0:972 0:016 ment in case of ! . The rst step towards mo del indep endent lim- One can now use the relations presented in a pre- its on the couplings g is the determination of vious talk [15] to set limits on the g .
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