HADRON POLARIZATION IN HEAVY LEPTON DECAYS*

Transcription

1 SLAC-PUB-2766 June 1981 (T/E) HADRON POLARZATON N HEAVY LEPTON DECAYS* James E. Brau and Giora J. Tarnopolsky Stanford Linear Accelerator Center Stanford University, Stanford, California ABSTRACT n the decay of the -c lepton into a spin one meson and a neutrino, the meson state with helicity opposite its charge is forbidden by angular momentum conservation if the decay is mediated by the con- ventional V - A current. The laboratory momentum distribution of pions in the decay chain T -f PV, P -+ ~TT reflects the polarization of the P meson and provides an experimental check of the nature of the decay current. This method requires the identification of the decay mode pv but does not depend on finding the T laboratory direction. The nature of the current mediating the heavy lepton [ll decay has been convincingly established for the leptonic modes for which the v - A theory fits the electron and muon spectra [2,3]. Of the identified semileptonic modes the TV decay distributions are sensitive to the coupling structure only for polarized r which have not been obtained so far. However, the decays of the r into a spin one meson and a neutrino offer the possibility of observing effects reflecting the nature of the current. Weak decays involving vector mesons have * Work supported by the Department of Energy, contract DE-AC03-76SF (Submitted to Physical Review D)

2 -2- been discussed previously in another context [4]. As shown in Fig...l, if the 'c neutrino is massless and the decay proceeds via the V - A current, the helicity state of the meson opposite the sign of its charge is forbidden by angular momentum conservation. This polarization of the meson is independent of the polarization state of the T, and is present in the observed events in existing electron-positron colliding beam rings. Further, for the decay T + pv [5],the decay of the p into two pions is a good analyzer of the P polarization. While the measurement of the p density matrix seems too ambitious experimentally 161, noticeable effects persist in the laboratory energy distribution of pions and these can be readily measured.._ Many features of the T -t pv process have been discussed before [7,8]. The angular distribution of the p in the T rest frame is given by dn xi P M2 = p '(1 + XQ). (1 + n (2. d>/jzl> 4$M2 T + 2Mp2) (1) for helicities X = +l, and by -f for helicity h = 0. Here, T- is the charge of the T, s is a unit vector directed along its spin and g is the rest-frarep momentum. (2)

3 -3- When both orientations of the 'c spin are equally probable, the P distribution becomes isotropic, but the state with X =- n is nevertheless forbidden, while the zero-helicity state is favoured in the ratio Mt/(2Mz) with respect to the A =n state. Thus, in the p rest frame, the angular distribution of pions with respect to the line of flight of the p in the T rest frame is given by -= dn 3 dqtr 4r(M2 T + 2M2p) _-. (MLp + (ML T -ML,) cosl fj) (3) and appears in Figure 2. The marked anisotropy in Eq.(3)is due to both the angular momentum selection rule and the relative probability that the V - A inter- action ascribes to the allowed helicity states.of the -p. The labora- tory energy distribution of pions is obtained by applying the appro- priate Lorentz boosts. We evaluated it at electron-positron energies of 2.5 and 14.5 GeV/beam and compared it in Figure 3 with that obtained neglecting the p polarization. The p resonance was described by a Breit-Wigner function around the mass M = GeV P with width r P = GeV.. Radiative effects have been neglected. The difference between the energy distributions in Figures 3a and 3b can be expressed by the second moment (variance) of each distribution. At 2.5 GeV the energy distribution has a variance of while if polarization is neglected it drops to An experiment with 2000 events would measure this parameter to better than.ool. Likewise,

4 -4- at 14.5 GeV a 2000 event experiment easily distinguishes the two distributions as the second moment is 0.051, while it drops to when the polarization is neglected. The 2000 event experiment would have an uncertainty of slightly more than n conclusion, we have stressed that the decay of a heavy lepton into a spin one particle and a neutrino results in a polarization of the meson if the decay proceeds via the conventional V - A current. Furthermore, the laboratory energy distribution of pions carries through the polarization information even though the r leptons themselves are not polarized. This experimental verification of the nature of the decay current does not require knowledge of the r laboratory direction. We acknowledge useful discussions with our. colleagues at SLAC.

5 -5- REFERENCES AND FOOTNOTES 1. Perl, M. L., in Proc. Summer nstitute Part. Phys., SLAC-191, ed. M. C. Zipf, p Stanford, Perl, M. L. et al., Phys. Rev. Letters35, 1489 (1975). See also Perl, M. L., in Ann. Rev. Nucl. Sci. 30, 299 (1980). 2. Perl, M. L. et al., Phys. Letters 63B,466 (1976) 3. Kirkby, J., Proc nt. Symp. Lepton Photon nteract. High Energies, ed. T. B. W. Kirk, H. D.. Abarbanel, p. 107,Batavia,ll. 4. Tarnopolsky, G. J., Phys. Lett. x, 451 (1978). 5. Dorfan, J. M., contributed to the KVth Rencontre de Moriond, Les Arcs, France, March 1981, Dorfan, J. M., et al., Phys. Rev. Lett. 45,.215 (1981).._ 6. The non-vanishing elements of the rho density matrix are P 00 = C M2r/M2p(l - np(:.g)/l& PAX = c (1 + AT-) (1 + np (X) / $1) where C is a normalization function,and p is the polarization of the T. f the direction of r spin and the neutrino were known, as foreseen in the future linear colliders, the angular distributions of pions in the rho rest-frame would show the azimuthal anisotropy expected from the finite off-diagonal density matrix elements.

6 -6-7. Thacker, H. B. and Sakurai, J. J., Phys. Lett. 36B, 103 (1971). -. Y. S. Tsai, Phys. Rev. a 2821 (1971). a. K. J. F. Gaemers and Risto Raitio, Phys. Rev. z, 1262 (1976).

7 -7- Figure Captions 1. Schematic of the tau decay to a rho meson and a left-handed neutrino, with arrows representing the indicated helicities. The V-A weak coupling forbids one rho helicity state and favors one of the two allowed. 2. The angular distribution of the pions in the rho rest frame relative to the rho direction of flight in the tau rest frame. The marked anisotropy results from preference for helicity 0 over helicity The pion energy distributions in the laboratory where the full p polarization effects have been compared to the absence of such effects. The second moment calculations described in the text quantify the differences.

8 Al x=-l X=0 X=+l Forbidden Fig. 1

9 0.2 L fn 0.1 g d u 0-0 G 81 case, 4 lrtoa2 Fig. 2

10 3.2 E,,,,=2.5GeV (a) Full treatment of p polarization _ - - p polarization neglected o 6-6 x~ (=WEBEAM) 414oc3 Fig. 3