Charged Current Review

Transcription

1 SLAC-PUB-8943 July 2001 Chared Current Review S. H. Robertson Invited talk presented at the 6th International Workshop On Tau Lepton Physics (TAU 00), 9/18/2000 9/21/2000, Victoria, British Columbia, Canada Stanford Linear Accelerator Center, Stanford University, Stanford, CA Work supported by Department of Enery contract DE AC03 76SF00515.

2 1 Chared current review S. H. Robertson a a Stanford Linear Accelerator Center, M.S. 61, P.O. Box 4349, Stanford CA 94309, USA steven@slac.stanford.edu Experimental measurements of the lifetime and leptonic branchin ratios are combined to ive updated world averaes for these quantities. The results are then used to test the universality of the electroweak chared current couplins to the three lepton species and are found to be consistent with Standard Model predictions at the level of 0:2%, permittin limits to be derived on non-standard Model physics such as the mass of the neutrino. 1. INTRODUCTION Decays of leptons provide an excellent laboratory for precision testin of the chared currentweakinteraction. In particular, the Standard Model (SM) provides a robust prediction of the relationship between the lifetime and the leptonic branchin ratios under the assumption of a V ; A structure for the weak chared current and auniversal couplin strenth. The SM eective chared current Laranian is iven by n L cc = 2 p 2 W P`=e y ` (1 ; 5 )`+ (1) u (1 ; 5 )d + :::, where d = (cos c d + sin c s) and c is the Cabibbo anle. decays are mediated by a W boson, as shown in Fi. 1, which couples to the initial and nal state fermions with strenth. The leptonic branchin ratios, B e B( ;! e ; e ) and B B( ;! ; ), are iven by the expression B` = G2 `m f(m 2`=m2 ) r ew (2) where m and are the mass and lifetime respectively and ` =e. The quantity f(x) =1; 8x +8x 3 ; x 4 ; 12x ln x (3) is a phase space correction for the nal state chared lepton mass and has the values f(m 2 =m2 ) =0:97256 and f(m 2 e =m2 ) = 1:00000 for and e nal states respectively. The factor r ew = 1+ 3m2 5m 2 W 1+ (m ) ; 2 (4) τ - d θ cos θ c d + sin θ c s W ν τ e -, µ -, d θ ν e, ν µ, u Fiure 1. A decay via the weak chared current couplin with universal couplin strenth. contains radiative corrections and corrections for the non-local nature of the W propaator [1] and has the value r ew ' 0:9960. Under the SM assumption of universality ( e = = ) G ` = 1 p 2 ` 4m 2 W G F (5) is the Fermi constantobtainedfrommuon decays. This model of decays provides two aspects of the chared current interaction which can be tested experimentally: the Lorentz structure and the universality of the couplins. The Lorentz structure is accessible principally via measurements of the -decay Michel-type parameters. Measurements of these parameters are reviewed in a separate presentation at this workshop [2]. The universality of the couplins can be tested throuh measurements of the branchin ratios and lifetime. It is worth notin, however, that

3 2 even if the couplin strenth is universal there may be additional non-sm contributions to the leptonic decay widths, ;( ;! `;` )=(1+`);( ;! `;` ) SM (6) which may alter the relationship in Eq. 2 between the branchin ratios and the lifetime. For example, the existence of an additional contribution to the leptonic widths mediated by a scalar boson, such as a MSSM chared His boson, would manifest itself as a deviation from the SM expectation for the decay Michel parameter, but also as an apparent violation of - e universality [3,2] in leptonic decays. The various universality tests described in this work therefore are potentially sensitive to many dierent forms of non-sm physics. 2. MEASUREMENTS World averaes of the lifetime and leptonic branchin ratios are currently dominated by the measurements reported by and the four LEP experiments ALEPH, DELPHI, L3 and OPAL. All of the LEP experiments have now either published or reported preliminary results based on essentially the entire LEP1 dataset (up to and includin data from 1995). As such, it is unlikely that there will be substantial improvements in the current averaes due to new measurements from LEP. In the near future the asymmetric B-factory experiments, Babar and Belle, will likely report new measurements based on data sets with very hih statistics compared to LEP and with systematics which are similar to. It is therefore instructive to consider the dierences between analyses performed at the Z 0 enery and those at the (4s) resonance. In e + e ; collisions at a centre of mass enery of 91 GeV, the decay products of -pair events are produced with a lare boost relative tothecentre of mass frame, resultin in a characteristic sinature of two hihly collimated, co-linear jets. The hih centre of mass enery additionally causes qq events to produce a relatively lare number of particles, permittin -pair events to be cleanly separated from the qq backround by requirin low particle multiplicity. In the LEP analyses, an inclusive sample of -pair events is typically obtained usin a selection based on event shapes, multiplicities and kinematic quantities such asthe total enery and momentum in the event. This sample is relatively unbiased with respect to decay modes and typically has a non- backround contamination of a few percent. This ability to cleanly and inclusively identify events has permitted lifetime and branchin ratio measurements to be made with relatively small systematic uncertainties. However, analyses based on the entire LEP1 dataset typically report statistics of pairs and consequently all LEP results reported here are statistically limited. At B-factory eneries ( 10:5 GeV) the particle multiplicity inqq events is considerably lower than at LEP, makin inclusive selection of - pair events much more dicult. In addition, the decay products possess a much smaller boost than at LEP and are consequently much less collimated. has relied on a method in which one of the two hemispheres, dened relative to the thrust axis of the event, is used to ta the event while the second hemisphere is used for the measurement [4]. Future branchin ratio measurements by Belle and Babar will likely use a similar approach. Lifetime measurements at the two asymmetric B-factories suer the additional disadvantae that the decay lenth is about an order of manitude smaller than the 2mm which is seen at LEP. In contrast to LEP, however, the B-factory datasets already consist of several million events and it is expected that Babar and Belle will have samples on the order of 10 8 events within a few years of runnin. Consequently, lifetime and leptonic branchin ratio results from the B-factories are expected to be limited by systematic uncertainties. Future measurements will depend critically on how well these systematics can be controlled. 3. BRANCHING RATIOS Since TAU'98, new preliminary leptonic branchin ratio measurements have been reported by L3 and ALEPH. Both of these results utilize the full LEP1 statistics and supersede previous analyses based on smaller datasets. The total

4 3 number of measurements included in the world averaes therefore remains the same. The L3 measurement is described in a separate presentation at this workshop [5] and other measurements which are included in the averaes have been described in previous workshops in this series. The preliminary ALEPH measurement [6] is the only result which has not been separately presented and it is therefore summarized in the followin section The ALEPH measurement The ALEPH measurement of the leptonic branchin ratios supersedes an earlier result based on the LEP data sets. Two distinct methods are used to evaluate the branchin ratios, followin which the two results are combined to obtain the nal measurements. The rst method closely follows the earlier ALEPH analysis and is similar to that which has been used by other LEP experiments. An inclusive -pair sample is selected based primarily on particle multiplicity and total enery in the event. Additional kinematic requirements are applied to further suppress Bhabha and dimuon events. Events within the -pair sample are then divided into two hemispheres. Candidate ;! `;` hemispheres are required to contain a sinle chared track which is identied as an electron or muon usin a likelihood-based particle ID alorithm. This method is applied to the data and the result is combined with the previously published measurement based on the data. The second method uses hemispheres which are selected without previously applyin a - pair selection. Electron and muon candidates are identied from the sample of hemispheres by requirin a sinle track with no associated hadronic activity and applyin particle ID requirements. Bhabha, dimuon and two-photon events are then rejected usin cuts based on event kinematics which are specic to the ;! e ; e and ;! ; samples. The branchin ratios are computed from the number of selected candidates, corrected for backrounds and selection eciencies, divided by the estimated number of decays in the data sample, which isderived from the interated luminosity of the sample and an ALEPH measurement ofthe + ; cross section. The two methods produce consistent results with comparable uncertainties. The measurement are combined, takin into account correlations between the two selected samples to ive the (preliminary) ALEPH branchin ratios B e = (17:783 0:072 0:032)% B = (17:290 0:069 0:029)% (7) where the rst uncertainty is statistical in oriin and the second is due to systematics. These are the most precise measurements of B e and B reported to date by a sinle experiment World averaes The TAU2000 averaes for the leptonic branchin ratios are obtained by combinin the ALEPH and L3 preliminary results with an older preliminary B measurement by OPAL [7] and with published measurements by other experiments [8]. Measurements contributin to the world averaes are plotted in Fi. 2 and 3. Combinin these results yield B e = (17:804 0:051)% B = (17:336 0:051)%. (8) The relative precision of these averaes is now better than 0:3% and they are clearly dominated by the measurements by and the four LEP experiments. All other measurements combined contribute less than 3% to the total weiht. Unfortunately, the most precise measurements also possess a much hiher consistency than would be expected for uncorrelated measurements, suestin that they suer from experimenter bias or other correlated systematic eects. The ve + LEP results for B e can be combined to ive a 2 of 0.35, yieldin a probability of less than 2%. Similarly, the ve most precise B measurements ive a 2 of 1.41 for a probability of 15%, however in this case includin the older measurements in the averae reduces the probability even further. The excessively hih internal consistencies of these measurements cannot be attributed entirely to conservative overestimation of systematic uncertainties, since the LEP results are all statistically limited.

5 4 HRS ± ± 0.72 ALEPH ± 0.64 ARGUS ± ± 0.18 DELPHI ± 0.15 OPAL ± 0.11 ALEPH (prel) ± 0.08 L (prel) ± 0.13 MARK-J ± 1.00 CELLO ± 0.89 ALEPH ± 0.55 ARGUS ± ± 0.20 OPAL (prel) ± 0.14 DELPHI ± 0.12 ALEPH (prel) ± 0.07 L (prel) ± 0.13 TAU2000 averae ± B(τ eνν ) (%) Fiure 2. Measurements of B e contributin to the world averae. The hatched reion represents the uncertainty on the TAU2000 averae. TAU2000 averae ± B(τ µνν ) (%) Fiure 3. Measurements of B contributin to the world averae. The hatched reion represents the uncertainty on the TAU2000 averae euniversality A test of - e universality can be obtained from these averaes by comparin the ratio of the leptonic branchin ratios and correctin for phase space eects: 2 = f(m2 e =m2 ) e f(m 2 =m2 ) B. (9) B e Possible non-sm contributions to the partial decay widths, as expressed in Eq. 6, would contribute an additional term of (1+ )=(1+ e )to the left hand side of Eq. 9. This test therefore has sensitivity to non-sm physics which contributes dierently to the ;! e ; e and ;! ; widths, such as for example the mass-dependent couplin of a chared His boson. The four LEP experiments and have independently reported values for the ratio = e determined from B e and B measurements by each collaboration [4{7,9]. These results are plotted in Fi. 4. The world averae for the ratio = e is obtained by combinin = e values reported by individual experiments when available, with the value obtained usin the averae of branchin ratio measurements plotted in Fi. 2 and 3 for analyses which do not report a value of = e. This approach allows correlated systematic uncertainties in B e and B measurements to be properly taken into account by the individual experiments, resultin in an increased precision in the = e averae. Since the combined LEP and measurements contribute almost all of the weiht, the world averae is numerically equal to that obtained with only these ve results. The averae, = 1:0010 0:0020, (10) e is consistent with - e universality. Some caution must be exercised in the interpretation of limits derived usin Eq. 10, since the hih consistency of the experimental results could be evidence for an experimental bias toward the SM prediction, which would potentially mask non-sm eects.

6 ± OPAL (prel) ± DELPHI ± ALEPH (prel) ± L3 (prel) ± χ 2 /ν = 0.90 / 4 (CL = 92%) TAU2000 averae ± µ / e Fiure 4. = e universality results reported by and the four LEP experiments. The hatched reion represents the uncertainty onthe TAU2000 averae and the vertical line is the SM expectation. However, it is worth notin that this result is becomin competitive with the most precise - e universality test currently available. This test compares the branchin ratios of the helicitysuppressed decays ;! ; and ;! e ; e. The current experimental data yield [10] e L = 1:0020 0:0016. (11) This test should not be thouht of as equivalent to that of Eq. 10 thouh, since the decay ofthe spinless pion requires that the W be in a lonitudinal state. It therefore has a dierent sensitivity to new physics than the test from Eq. 10 usin leptonic decays. 4. TAU LIFETIME Since TAU'98, there have been updated lifetime measurements reported by the L3 and SLD ± ± 4.9 OPAL ± 2.1 ALEPH ± 1.9 L ± 2.5 DELPHI (prel) ± 1.9 χ 2 /ν = 2.5 / 5 (CL = 78%) TAU2000 averae ± τ lifetime (fs) Fiure 5. lifetime measurementscontributin to the world averae. The hatched reion represents the uncertainty on the TAU2000 averae. DELPHI experiments usin both the impact parameter and decay lenth methods. Both of the new measurements are based on essentially the entire LEP1 dataset and supersede earlier measurements by these experiments. The L3 measurement has recently been published [11], while the DELPHI result remains preliminary. Both of these analyses are described in separate presentations at this workshop [5,12]. The TAU2000 averae is formed usin the six measurements [8,13] shown in Fi. 5. Several earlier measurements with larer measurement uncertainties are not included since their inclusion has a neliible eect on the averae. As is the case with the leptonic branchin ratios, the consistency of the lifetime measurements is hiher than should be expected, with only a 12% 2 probability 1. 1 The DELPHI lifetime result reported by [12]is1:2 fs lower than the value from [13] which was used in the averae. Usin the value from [12] results in a world averae of =290:57 0:98 with 2 = =2:1=5

7 eand - universality The lifetime can be combined with the leptonic branchin ratios to test ; e and ; universality. Usin Eq. 2 and an analoous expression for the decay ;! e ; e, the followin expressions can be derived: 2 =0:9996 m 5 m 5 B e (12) τ lifetime (fs) τ lifetime (fs) τ / µ = ± τ / e = ± =0:9996 m 5 B e m 5 f(m 2 =m2 ) B(τ eνν ) (%) B(τ µνν ) (%) (13) where the numerical factor accounts for electroweak propaator and radiative corrections in the and decays. Usin PDG [8] values for the mass (m ) and lifetime ( ), the BES measurement of the mass [14] and TAU2000 averaes for the lifetime and leptonic branchin ratios yields the results = 0:9994 0:0023 (14) and e = 1:0000 0:0023. (15) Both ratios are consistent with the SM expectation to a precision of better than a quarter of a percent. The relationship iven by Eq. 2 between the lifetime and leptonic branchin ratios is plotted in Fi. 6, with the SM prediction indicated by the diaonal band. The width of the band, representin the uncertainty introduced by the experimental uncertainty in the mass, is not neliible compared to the current precision of the lifetime and branchin ratio world averaes. Since the is sinicantly more massive than the other two chared leptons, it is reasonable to postulate that new physics will couple more stronly to the than to the other lepton enerations. Under the assumption of ; e universality, the two leptonic branchin ratios can be combined, correctin for phase space, to ive the effective branchin ratio for a decayin into massless leptons. The result, B` =(17:814 0:036)%, (16) τ lifetime (fs) τ / e,µ = ± B(τ lνν ) (%) Fiure 6. The lifetime plotted versus the leptonic branchin ratios B e, B and the eective branchin ratio for a massless lepton, B`. The diaonal band represents the SM prediction, with the width reectin the uncertainty in the mass. Note that the displayed reion represents a rane of 1% of the central value of each axis, illustratin that the measurement uncertainty on is comparable to that of B e and B, but is much lare than that of B`. can then be compared to usin Eq. 12 to ive a more precise test of - ` universality: e =0:9997 0:0020, (17) which also shows no evidence for non-sm eects. It is clear from Fi. 6 that the uncertainty in = e is dominated by the uncertainty in the lifetime world averae. Future improvements in the sensitivity of this universality test will therefore be due primarily to improvements in the determination of the lifetime rather than in the leptonic branchin ratios neutrino mass An hypothetical non-zero neutrino mass would introduce an additional phase space cor-

8 7 rection to Eq. 2, alterin the relation between the lifetime and branchin ratios. Assumin that the neutrino is sinicantly more massive than the other two neutrino enerations, then there is no correspondin phase space correction to ;! e ; e decays. In this scenario the relationships in Eq. 12 and 13 are modied by a factor ` (` = e) iven by [15] ` = ;8 (m 2 =m 2 ) (1 ; m 2`=m2 ) 3 + :::, (18) permittin a limit to be placed on m usin this universality test. Assumin that the W couplin is in fact universal, the result iven in Eq. 17 implies a limit of m < 37 MeV at the 95% condence level. This result is not competitive with direct limits from endpoint measurements [16] but it is an independent and complementary limit Semi-hadronic decays An additional test of - universality canbe obtained by comparin the branchin ratios for! and! K with leptonic decays of and K mesons. The ratio of the couplin constants is iven by 2 = ( ) 2m 2 m 2 where h = Kand B( ;! h ; ) H + H K (19) H h = h i (1 + h ) m 1;(mh =m ) 2 2 h m h 1;(m =m h ) 2 B(h ;! ; ) (20) where h and m h are the pion and kaon lifetimes and masses respectively and h accounts for radiative corrections [17]. In formin this ratio, the CKM matrix elements and decay constants f K associated with the meson production and decay vertices cancel, enablin a comparatively clean test of - universality to be obtained. Usin the TAU2000 averae for,thetau'98 averae [18] for B( ;! h ; ) = (11:710:09)% and PDG values for the other quantities, yields L = 1:0029 0:0042. (21) The precision of this universality test is currently about a factor of two worse than the tests from leptonic decays, but aain it should be noted that this test is complementary since it has dierent sensitivity to potential forms of new physics. 5. HADRONIC WIDTH The leptonic branchin ratios and lifetime have sensitivity to the total hadronic width throuh the quantity R, dened as R ;( ;! hadrons ) ;( ;! e ; e ) ' 3 (1 + QCD ) (22) where QCD ' 0:2 are QCD corrections to the parton-level prediction. The inclusive branchin ratio to hadronic nal states is simply unity minus the leptonic branchin ratios, allowin R to be obtained directly from B e and B. Assumin - e universality, 2 R can be expressed as R = 1 B` ; 1:97256 (23) or alternatively, it can be expressed in terms of the lifetime as R =0:9996 m 5 m 5 ; 1: (24) Substitutin the TAU2000 averaes into these equations yield 8 < R = : 3:641 0:011 (branchin ratios) 3:636 0:019 ( lifetime) 3:640 0:010 (combined) (25) resultin in a combined experimental precision on R of 0:25%. From the theoretical perspective, R can be expressed as an operator product expansion R = 3 ; n jv ud j 2 + jv us j 2 S EW 1+ EW + (0) + P D=2 4 ::: (D)o (26) where S EW and EW are electroweak corrections and (D) are non-perturbative and quark mass corrections [19]. The perturbative expansion, (0),isknowtoO( 3 s ) and the O( 4 s ) term has been estimated: (0) = ; s ; +5:2023 s 2 ; +26:366 s 3 +(78:00 + d 3 ) ; s 4 (27) 2 A similar but less precise result may be obtained without this assumption.

9 8 where d 3 = 27:5 27:5 [20]. The perturbative contribution completely dominates QCD, ivin R sinicant sensitivity to the stron couplin s (m 2 ). The current experimental precision on R from Eq. 25 translates into an uncertainty of approximately 0:003 on the extracted value of s (m 2 ), compared with theoretical uncertainties of 0:015. Recent papers describin leptonic branchin ratio and lifetime measurements have quoted values of s (m 2 Z ) with uncertainties of 0:002, which are obtained by extractin s (m 2 ) usin this method and then evolvin it to the Z 0 scale. Althouh the consistency of these results with measurements of s (m 2 Z ) obtained at hiher enery scales is a remarkable test of the runnin of s, it is clear that such measurements will not benet from future improvements in the experimental precision of branchin ratio or lifetime measurements unless there are correspondin improvements in the theoretical uncertainties. 6. CONCLUSIONS World averaes of measurements of the lifetime and leptonic branchin ratios currently have a relative precision of 0:3%, enablin the universality of the chared current couplins to be veried to an impressive precision of better than 0:2%. Unfortunately, the existin experimental measurements suest of a deree of experimental bias which could reduce the sensitivity ofthese universality tests and thus potentially obscure evidence for non-sm physics. With all LEP experiments reportin statistically limited measurements based on essentially the entire LEP1 data set, it is not likely that there will be sinicant improvements in the world averaes in the future due to new LEP results. Instead, future measurements will come from B-factory experiments and will most likely be limited by systematic, rather than statistical, uncertainties. Consequently, these measurements will potentially be even more susceptible to experimental bias. In order to maintain the interity of these measurements it will be essential that appropriate steps be taken to reduce these biases. REFERENCES 1. W. J. Marciano and A. Sirlin, Phys. Rev. Lett. 61 (1988) I. Boyko, these proceedins. 3. A. Stahl, Phys. Lett. B324(1994) A. Anastassov et al. ( Collaboration), Phys. Rev. D55 (1997) 2559 Erratum-ibid. D58 (1998) P. Garcia-Abia, these proceedins. 6. H. Videau, CERN-OPEN (ALEPH ), (March 1999) and references therein. 7. S. H. Robertson, Proceedins of the 1999 Lake Louise Winter Institute, Lake Louise, Alberta, Canada, February 14-20, 1999 (World Scientic, 2000) D. E. Groom et al. (Particle Data Group), Eur. Phys. J. C15(2000) P. Abreu et al. (DELPHI Collaboration), Eur. Phys. J. C10(1999) D. I. Britton et al., Phys. Rev. Lett. 68 (1992) 3000 G. Czapek et al., Phys. Rev. Lett. 70 (1993) M. Acciarri et al. (L3 Collaboration), Phys. Lett. B479(2000) R. McNulty, these proceedins. 13. DELPHI Collaboration, An updated measurement of the tau lifetime, contribution to the HEP-99 Conference, Tampere Finland, July 15-21, (DELPHI CONF 320). 14. J. Z. Bai et al. (BES Collaboration), Phys. Rev. D53, (1996) M. T. Dova, J. Swain and L. Taylor, Proceedins of the 5th Workshop on Tau Lepton Physics, Santander, Spain, Sept , Nucl. Phys. B (Proc. Suppl.) 76 (1999) J. Duboscq, these proceedins. 17. R. Decker and M. Finkemeier, Phys. Lett. B316 (1993) 403 R. Decker and M. Finkemeier, Phys. Lett. B334 (1994) B. K. Heltsley, Proceedins of the 5th Workshop on Tau Lepton Physics, Santander, Spain, Sept , Nucl. Phys.B(Proc. Suppl.) 76 (1999) E. Braaten, S. Narison and A. Pich, Nucl. Phys. B373 (1992) A. L. Kataev and V. V. Starshenko, Mod. Phys. Lett. A10 (1995) 235.