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Hadronic R Decays and QCD

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Hadronic R Decays and QCD FR0005562 LAL 99-78 December 1999 Hadronic r decays and QCD M. Davier Laboratoire de l'Accelerateur Lineaire IN2P3-CNRS et Universite de Paris-Sud, BP 34, F-91898 Orsay Cedex Invited talk given at the &h International Symposium on Heavy Flavour Physics University of Southampton, England, 25-29 July 1999 U.E.R Institut National de de Physique Nucleaire PUniversite Paris-Sud et de Physique des Particules 32/ 05 B.P. 34 ~ Bailment 200 - 91898 ORSAY CEDEX Gestion IH\S Doc. Enreg. I© .iU4/. N* TRN &&.O.O.OSS LAL 99-78 December 1999 Hadronic r decays and QCD Michel Davier Laboratoire de VAccel6rateur Lineaire IN2P3/CNRS et University de Paris-Sud 91898 Orsay, France E-mail: davierQlal.in2p3.fr ABSTRACT: Hadronic decays of the r lepton provide a clean source to study hadron dynamics in an energy regime dominated by resonances, with the interesting information captured in the spectral functions. Recent results on exclusive channels are reviewed. Inclusive spectral functions are the basis for QCD analyses, delivering an accurate determination of the strong coupling constant and quantitative information on nonperturbative contributions. Strange decays yield a determination of the strange quark mass. 1. Introduction Radiative corrections violate CVC, as contained in the SEW factor which is dominated by short- Hadrons produced in T decays are borne out of distance effects and thus expected to be essen- the charged weak current, i.e. out of the QCD tially final-state independent. vacuum. This property garantees that hadronic Hadronic r decays are then a clean probe of physics factorizes in these processes which are hadron dynamics in an interesting energy region then completely characterized for each decay chan- dominated by resonances. However, perturbative nel by spectral functions as far as the total rate is QCD can be seriously considered due to the rel- concerned . Furthermore, the produced hadronic atively large r mass. Many hadronic modes have systems have 1 = 1 and spin-parity Jp = 0+, 1~ p + been measured and studied, while some earlier (V) and J = 0-, 1 (A). The spectral functions discrepancies (before 1990) have been resolved are directly related to the invariant mass spectra with high-statistics and low-systematics exper- of the hadronic final states, normalized to their iments. Samples of ~ 4 x 105 measured decays respective branching ratios and corrected for the are available in each LEP experiment and CLEO. r decay kinematics. For a given spin-1 vector Conditions for low systematic uncertainties are decay, one has particularly well met at LEP: measured samples have small non-r backgrounds (< 1%) and large mt B(T~ -> V- uT) vi(s) = 2 selection efficiency (92%), for example in ALEPH. 61Vud\ SEW B{T Recent results in the field are discussed in . dN v (1.1) this report. ' Nyds where Vud denotes the CKM weak mixing matrix 2. Specific final states element and SEW = 1-0194 ± 0.0040 accounts for electroweak radiative corrections [1]. 2.1 Vector states Isospin symmetry (CVC) connects the r and + The decay r -» vTir~Tr° is now studied with large e e~ annihilation spectral functions, the latter statistics of ~ 105 events. Data from ALEPH being proportional to the R ratio. For example, have been published [2]. New results from CLEO Aira? are now available [3] with the mass spectrum T/=i (S) = vi,x-(s) (1.2) given in figure 1 dominated by the p(770) res- Michel Davier onance. Good agreement is observed between (24.65±0.35)% [9]. This 1.8<7 discrepancy should the ALEPH and CLEO data and the lineshape be further investigated with a detailed examina- fits show strong evidence for the contribution of tion of the respective possible systematic effects, p(1400) through interference with the dominant such as radiative corrections in e+e~ data and amplitude. Fits also include a p(1700) contribu- 7T° reconstruction in t data. CVC violations are tion, taken from e+e~ data as the value of the r of course expected at some point: hadronic vio- 2 mass does not allow r data alone to tie down the lation should be very small (~ {mu - md) /m*), corresponding resonance parameters. Thanks to while significant effects could arise from long- the high precision of the data, fits are sensitive to distance radiative processes. Estimates show that the exact form of the p lineshape, with a prefer- the difference between the charged and neutral ence given to the Gounaris-Sakurai parametriza- p widths should only be at the level of (0.3 ± tion [4] over that of Kiihn-Santamaria [5]. 0.4)% [10]. ' • ' ' 1 ' ' • ' i > >i ' ' [••i i • v-f • . • i j T ,"\-r-rx- II . - Mj I C V -» 7t* It' Sr T I A ALEI'll t • CMD-2 1 ? I « NA7 - I o OLVA ii " l01'' i It 4 CMD ft, n DM1 - JI r* we Invariant Mass Figure 1: Mass distribution in CLEO r ->• VTK TT° s (CJcV) events. The solid curve overlaid is the result of the Kiihn-Santamaria fit, while the dashed curve has the Figure 2: Cross section for e+e~ - p(1400) contribution turned off. pared to the ALEPH r data using CVC with p — w interference built in (shaded band). + The quality of data on e e~ -> TT+TT" has also recently improved with the release of the The 4TT final states have also been studied [2, CMD-2 results from Novosibirsk [6]. A compar- 11]. Tests of CVC are severely hampered by ison of the mass spectrum as measured in e+e~ large deviations between different e+e~ experi- and r data is given in figure 2 (for this exercise ments which disagree well beyond their quoted the p — w interference has to be artificially intro- systematic uncertainties. A new CLEO analy- duced in the r data). Although the agreement sis studies the resonant structure in the STTTT0 looks impressive, it is possible to quantify it by channel which is shown to be dominated by unr computing a single number, integrating over the and aiTr contributions. The ton spectral func- complete spectrum. It is convenient for this to tion shown in figure 3 is in good agreement with use the branching ratio B(r -* vT%~ir°) as di- CMD-2 results and it is interpreted by a sum of rectly measured in r decays and computed from p-like amplitudes. The mass of the second state the e+e~ spectral function under the assump- is however found at (1523 ± 10)MeV, in contrast tion of CVC. Using B(T -> Vyh'-rr0) = (25.79 ± with the value (1406± 14)MeV from the fit of the 0.15)% [7] and subtracting out B(T -* i/TK~ir°) = 2TT spectral function. This point has to be clar- (0.45 ± 0.02)% [8], one gets B{T -» uTic-ir°) = ified. Following a limit of 8.6% obtained earlier (25.34 ± 0.15)%, somewhat larger than the CVC by ALEPH [12], CLEO sets anew 95% CL limit value using all available e+e~ data, of 6.4% for the relative contribution of second- Michel Davier class currents in the decay r -> vr-K LJ from the (a) : hadronic angular decay distribution. - T 1°3 8 / i a 3 V(q) i.A(1523),,o-(17OO) / 10 0.050 : <p(770).A(1523) -If- ^ 101 i .p(770),/>-(1700) -< P('7O) z 1 1.3 1.4 1.S ;: . , I ... I ... : 1.0 1.4 1.8 m, (GeV) 0.8 1.2 16 q(om) [GeV/c2] Figure 3U).: Fits of the CLEO spectral function for 2.2 Axial-vector states The decay r -> I/T3TT is the cleanest place to Figure 4: (a) 3TT mass spectrum from CLEO in the study axial-vector resonance structure. The spec- TT~ 2TT° channel with the lineshape from the resonance + trum is dominated by the 1 a\ state, known to fit (zoom on the K*K threshold). In (b), the -y/s- decay essentially through fm. A comprehensive dependent a\ width is plotted with the different con- analysis of the ir~2ir° channel has been presented tributions considered. by CLEO. First, a model-independent determi- nation of the hadronic structure functions gave procedure requires a careful separation of vector no evidence for non-axial-vector contributions (< (V) and axial-vector (A) states involving the re- 17% at 90% CL) [13]. Second, a partial-wave am- construction of multi-7r0 decays and the proper plitude analysis was performed [14]: while the treatment of final states with a KK pair. The dominant (m mode was of course confirmed, it V and A spectral functions are given in figures 5 came as a surprize that an important contribu- and 6, respectively. They show a strong resonant tion (~ 20%) from scalars {a, /0(1470), /2(1270)) behaviour, dominated by the lowest p and ai was found in the 2TT system. states, with a tendancy to converge at large mass The a\ —> 7r~27r° lineshape is displayed in toward a value near the parton model expecta- figure 4 where the opening of the K*K decay tion. Yet, the vector part stays clearly above mode in the total a\ width is clearly seen. The while the axial-vector one lies below. Thus, the derived branching ratio, B(a\ -> K*K) = (3.3 ± two spectral functions are clearly not 'asymp- 0.5)% is in good agreement with ALEPH results totic' at the r mass scale. on the KKir modes which were indeed shown The V + A spectral function, shown in fig- + (with the help of e e~ data and CVC) to be ure 7 has a clear converging pattern toward a axial-vector (ai) dominated with B(a\ ->• K*K) ~ value above the parton level as expected in QCD.
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