Within the context of a six-quark model combined with quantum chromodynamics we study the asymmetry in the decay of heavy charged mesons into a definite final state as compared with the charge-conjugated mode. We find that, in decays of mesons involving the b quark, measurable asymmetries may arise. This would present the first evidence for CP noninvariance in charged systems.
The K L -K S mass difference provides a stringent constraint on the mass (Md of the charged right-handed gauge field occurring in a "manifest" left-right-symmetric electroweak theory, yielding M R £1.6 TeV. Taken in the context of a grand-unifying gauge theory, e.g., O(10), such a large bound on M Ri along with the measured value of sin 2 0 w , implies that ^^10 9 GeV.The standard model of electroweak interactions is currently enjoying great success in being able to account for the existing experimental data. 1 However, the purely left-handed nature of that model is widely considered to be highly asymmetrical and unaesthetic leading to the suggestion that the standard model may be only an effective theory valid at current energies and that at higher energies an underlying left-right-symmetric (LRS) theory may make its presence felt. 2 It is therefore important to seek an understanding of the energy scales at which one may hope to see some evidence of such a symmetric theory.A comprehensive study of the experimental constraints on a LRS theory from the low-energy charged-current sector was first conducted by Bdg et al., 3 leading them to conclude (among other things) that of a LRS theory deduced from the precisely determined mass difference, Am A , between K L and K s . 4 We find that, even allowing for the theoretical uncertainties in the calculation of Am A , the constraints on (3 are by far the most stringent to date, surpassing not only the existing constraints derived from /3 decay, muon decay, and neutral currents, but also projected improvements from forthcoming precision experiments.We consider a six-quark model based on G w = SU(2) L 0 SU(2) E (S) U(l) with the charged-current eigenstates placed in left-and right-handed doublets. 5 To calculate Am^, we first calculate the free-quark amplitude A (ds~ ds) and then, taking that amplitude to be the effective Lagrangian, £ eff , we evaluate the matrix element (K 0 |3e eff |K 0 ),where M L and M R are the masses of the charged left-and right-handed gauge bosons. In this work we present constraints imposed on the mass scale where 3C eff = -£ e ffThe leading correction to the result obtained in the standard model 6 arises from the box graph in Fig. 1, A LR , plus its equivalent L+-R exchange. In the limit where the external quark momenta are assumed to be negligible compared to the loop momenta, we obtain, in the 't Hooft-Feynman gauge
The internal 0(4) symmetry group of the nonrelativistic hydrogen atom is discussed and used to relate the various approaches to the bound-state problems. A more general group 0(1, 4) of transformations is shown to connect the various levels, which appear as basis vectors for a continuous set of unitary representations of this noncompact group. Several recent lectures given at Stanford by Professor Y. Ne eman were the inspiration for this work. It is a pleasure to thank him for his stimulation. It is clear that many of the results were known to him and certainly to many other physicists. We apologize in advance for giving only a very sketchy bibliography.
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