Volume 95B, number 1 PttYSICS LETTERS 8 September 1980 UNIQUE SOLUTION FOR THE WEAK NEUTRAL CURRENT COUPLING CONSTANTS IN PURELY LEPTONIC INTERACTIONS D.P. BARBER, U. BECKER, G. BERGHOFF, A. BOHM, J.G. BRANSON, J. BRON, D. BUIKMAN, J.D. BURGER, C.C. CHANG, H.S. CHEN, M. CHEN, C.P. CHENG, Y.S. CHU, R. CLARE, P. DUINKER, G.Y. FANG, H. FESEFELDT, D. FONG, M. FUKUSHIMA, J.C. GUO, A. ttARIRI, G. HERTEN, M.C. ttO, H.K. HSU, T.T. HSU, R.W. KADEL, W. KRENZ, J. LI, Q.Z. LI, M. LU, D. LUCKEY, C.M. MA, D.A. MA, G.G.G. MASSARO, T. MATSUDA, H. NEWMAN, M. POHL, E.P. POSCHMANN, J.P. REVOL, M. ROHDE, H. RYKACZEWSKI, K. SINRAM, H.W. TANG, L.G. TANG, D. TEUCHERT, Samuel C.C. TING, K.L. TUNG, F. VANNUCCI, X.R. WANG, J. WARNOCK, P.S. WEI, M. WHITE, G.H. WU, T.W. WU, J.P. XI, P.C. YANG, C.C. YU, X.H. YU, N.L. ZHANG and R.Y. ZHU IlL Physikalisches Institut, Teetmisehe Hochschule Aachen, West Germany Deutsehes Elektronen-Synchrotron (DES Y], Hamburg, West Germany Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA, USA Nationaal Instituut voor Kernfysiea en IIoge-Energiefysica (NIKHEF), Amsterdam, The Netherlands Institute of High Ener~ Physics, Ch&ese Academy of Science, Peking, People's Republic of China Received 14 July 1980 By combining results from the MARK-J at PETRA on Bhabha scattering, ~z+/~-and r+r - production with recent world data from neutrino-electron scattering experiments, we determine unique values for the leptonic weak neutral current coupling constants gv and gA in the framework of electroweak models containing a single Z° . In contrast to previous anal- yses, we only use data from purely leptonic interactions, and therefore avoid the inherent uncertainties resulting from the use of hadronic targets. From the MARK-J data alone in the context of the standard SU(2) ® U(I) model of Glashow, Weinberg and Salam, we find sin20w = 0.24 + 0.11. Since the first experimental observation of the weak neutral current interaction [1] in t7 + e- -+ ~u + e- several neutrino-electron scattering experi- ments [2] have obtained important constraints on the structure of the weak neutral currents. A unique de- termination of the leptonic coupling constants gv and gA, however, was only possible in a more general framework incorporating lepton-lepton an d lepton- quark neutral current interactions, as defined by Sehgal [3] or by Hung and Sakurai [4]. The analysis involved the use of data from neutrino-nucleon scat- tering [5] and the scattering of polarized electrons on deuterium [6], as well as the neutrino-electron scattering results, and depended on factorization rela- tions [4] to relate the lepton-quark to the purely leptonic couplings. By combining the recent results on e+e - elastic scattering,/~+/J- and 7+r - production obtained by the MARK-J experiment at PETRA over the center of mass energy range 12 ~<x/~-~< 36 GeV with the neu- trino-electron scattering data, we are now able to de- termine gv and gA uniquely without the complica- tions which arise from the use of hadronic targets. In the general framework of SU(2)® U(1), with a single Z ° mediating the weak neutral current the sole as- sumptions required for this determination are: (1) e, t~, T universality, (2) an effective interaction hamiltonian which is a sum of products of vector and axial-vector currents, and (3) the point-like nature of leptons. The MARK-J data which is used to test electroweak 149