Superweak Theory Research Articles

Lepton asymmetry in B decays in the superweak and in the standard theory of CP violation

The predictions of the superweak theory of CP violation for semileptonic neutral B meson decays are considered. The charge asymmetry in conjunction with the measurements of f B is seen to be a promising way to distinguish the superweak from the standard theory.

Testing the superweak theory of CP violation in neutral B decays.

In order to rule out the superweak theory for $\mathrm{CP}$ violation, future experiments will try to find a difference between the $\mathrm{CP}$-violating asymmetries in the decays ${B}^{0}\ensuremath{\rightarrow}\ensuremath{\psi}{K}_{S}$ and ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. However, Winstein recently noted that, for some acceptable values of the Cabibbo-Kobayashi-Maskawa parameters, the standard model would give equal asymmetry parameters for these decays just as the superweak theory does. In this paper we show that, by considering both tree and penguin contributions to the decay amplitudes, the test can still be effective if a third asymmetry is measured with enough precision.

CP violation in the decays of neutral kaons into two photons

We compute the amplitudes for the decay into two photons of neutral kaons in the framework of the chiral effective Lagrangians. In particular we relate the ratios\(\eta _{||} = A(K_L \to 2\gamma _{||} )/A(K_S \to 2\gamma _{||} )\) and\(\eta _ \bot = A(K_S \to 2\gamma _ \bot )/A(K_L \to 2\gamma _ \bot ),\) which would vanish according toCP symmetry, to the prameters ɛ and ɛ′, appearing in the 2π decays ofKL. We find for\(\eta _{||} \) the value ɛ+i|ɛ′|. For the amplitudes into\(2\gamma _ \bot ,\), theCP-conserving amplitude\(A(K_2 \to 2\gamma _ \bot )\) depends very strongly on the parameterf, which gives the percentage of the amplitude\(A(K_2 \to 2\pi ^0 )\) arising from the «penguin» contributions. We predict two possible values for\(\eta _ \bot \): one is ≃ɛ. For the other =ɛ+i70|ɛ′|, which appears to us as more likely, the difference with respect to the superweak theory is larger than in the 2π decays. A distinction between the two theories requires a more precise measurement of γ(KS»γγ).

The anatomy of [formula omitted] in the standard model

We perform a detailed renormalization group analysis of the ratio ε′ ε for 50 GeV < m t < 250 GeV including the contributions from the gluon penguin, photon penguin, Z 0-penguin and neutral Higgs penguin diagrams as well as from π 0− η− η′ mixing and current-current operators. The final result for the Wilson coefficient functions with full O( α QED ) corrections taken into account can be written in a compact and transparent form. Using the constraints on m t and the phase δ coming from the data on ε and B 0− B 0 mixing, we investigate the dependence of the resulting ε′ ε ratio on the values of m t, Λ QCD, B K, m s(1 GeV), F B and the ratio Γ( b → u) Γ( b → c) . The presence of Z 0-diagrams suppresses strongly ε′ ε for large values of m t. For m t ≃ O(100 GeV) the standard model is milliweak wity typical values ε′ ε ≃ (1.0 ± 0.5) × 10 −3 . For m t ≃ O(220 GeV) it behaves like a superweak theory with | ε′ ε |≃0 and negative values for larger m t. These two distinct regions of m t, “milliweak” and “superweak” respectively, are the two regions of m t favoured by the data on ϵ and B 0− B 0 mixing.

Superweak contribution to B 0B̄ 0 mixing

A reasonable extension of the superweak theory for the K 0 system allows the possibility that the B 0B̄ 0 mass difference is primarily due to a superweak interaction. In contrast to the standard model this possibility does not require the B sB̄ s mass difference to be greater than B 0B̄ 0. With this explanation the CP violation associated with B 0B̄ 0 mixing is likely to be much smaller than in the standard model.

O(4) ⊗ U(1) gauge model

We propose an O(4) \ensuremath{\bigotimes} U(1) gauge model for weak and electromagnetic interactions, in which the Cabibbo angle is expressed as a free mixing angle between two charged vector bosons without rotating quarks. Four left-handed leptons (${\ensuremath{\nu}}_{e}$, $e$, ${\ensuremath{\nu}}_{\ensuremath{\mu}}$, $\ensuremath{\mu}$) and quarks ($u$, $d$, $c$, $s$) are, respectively, assumed to belong to quartets of O(4) whereas all the right-handed ones are assumed to belong to singlets. We use the representation (2,1) + (1,2) of O(4) \ensuremath{\simeq} SU(2) \ensuremath{\bigotimes} SU(2) for our quartets, different from that used by Pais, (2,2) of SU(2) \ensuremath{\bigotimes} SU(2). Our model naturally ensures the mechanism and respects quark-lepton universality. $\mathrm{CP}$ violation can be incorporated in the model to reproduce effectively results of the superweak theory by a small rotation of $d$ and $s$ quarks. The electric dipole moment ${D}_{n}$ of a neutron is shown to be small, $|\frac{D}{e}|\ensuremath{\lesssim}{10}^{\ensuremath{-}29}$ cm. The parity-violating asymmetry in the inelastic scattering of longitudinally polarized electrons from the deuterium recently measured at SLAC is reproduced in our model. A strangeness-changing neutral current also appears but is suppressed to the order ${G}_{F}\ensuremath{\alpha}$.

StrongPandTNoninvariances in a Superweak Theory

We show, by explicit construction of a highly convergent superweak theory of $\mathrm{CP}$ nonconservation, that the problem of natural suppression of strong $P$ and $T$ noninvariances---in the presence of instantons---may be resolved without invoking symmetries which imply massless quarks or nearly massless bosons.

Lepton-Quark Symmetry, CP-Violation and the Decay -&gt;e

If one attempts to understand a dynamical basis for fundamental properties such as the lepton-quark symmetry and parity violation, it appears that one needs in general several exotic gauge bosons. We discuss the phenomenological implications of those presumably massive bosons on CP-violation and the decay µ→e γ. We first consider the exotic gauge doublet (Y+, Y0) appearing in the vector-like SU(6) model discussed by Inoue et al., which realizes the ordinary 4-quarks and 4-leptons as 15-plet representatins of SU(6). As is shown, this SU(6) scheme allows a relatively simple model of sub-quarks and sub-leptons, and it is useful as a means to find relevant Feynman rules. We find that CP-violation induced by those exotic bosons (Y+, Y0) approximately reproduces the results of the superweak theory in the K0 sector, provided that the OZI rule and the ΔI = 1/2 enhancement are explained in the ordinary 4-quark model. The electric dipole moment D of the neutron is small D / e ≤10-27 cm. A reasonable estimate of the exotic decays of the muon is Γ(µ→e γ) / Γ(µ→all) ≲10-13 and Γ(µ→eee) / Γ(µ→all) ≲10-10. We also comment on the implications of the lepto-quark bosons appearing in the fractional charge version of the Pati-Salam model. In a light quark model with only four flavors, we estimate Γ(µ→e γ) / Γ(µ→all) ≤10-11.

CPviolation in gauge theory without charm

We show that the new gauge theory proposed by this author provides naturally a specific example of a superweak theory of CP violation. In this gauge theory, CP violation can arise in hadrons, but not in leptons, non can ..mu..-e transformation arise. However, K/sup 0//sub L/ ..-->.. 2..pi.. and the electric dipole moments of hadrons are due to independent parameters; thus the latter do not have to be as small as implied by superweak theory. (AIP)

CPviolation in the six-quark model

We construct a Weinberg-Salam-type gauge theory of a weak interaction with $\mathrm{CP}$ violation based on the six-quark model. Under the assumption of the validity of the Zweig-Iizuka rule and ${(\frac{\mathrm{quark}\mathrm{mass}}{W\ensuremath{-}\mathrm{meson}\mathrm{mass}})}^{2}\ensuremath{\ll}1$ this leads to the superweak theory of $\mathrm{CP}$ violation for both uncharmed and charmed hadrons. We also propose a new assignment for the $J$ and other $\ensuremath{\psi}$ particles, which predicts the existence of a 3.5-GeV ${0}^{\ensuremath{-}}$ meson using the 2.85-GeV ${0}^{\ensuremath{-}}$ state as input.

CP violation in purely lefthanded weak interactions

In a model with six quarks and pure V-A weak interactions CP violation can be introduced in weak currents by spontaneous breaking. The resulting milliweak model is shown to lead uniquely, with good approximation, to the results of the superweak theory both for K decays and for the neutron electric dipole moment.

Particle-antiparticle symmetry and irreversibility

A statistical theory of neutral kaon decay is presented, in which the violation of combined CP parity arises through non-equilibrium interaction with a heat bath, and not through a microscopic CP-violating term in the Hamiltonian. The theory is set up in the language of the Takahashi-Umezawa 'thermo-field theory', generalized to admit non-equilibrium processes. The usual 'superweak' theory emerges as a special case, but the theory also permits other solutions, which for a pure K0 meson beam are identical with superweak theory, but which restore K0-K0 symmetry.

The neutron electric dipole moment as a test of the superweak interaction theory

Theoretical calculations of the neutron electric dipole moment D n are reviewed for various theories of CP violation. It is shown that for the superweak interaction theory D n is less than 10 −29 e · cm in contrast to values of 10 −23 to 10 −24 predicted by many but not all milliweak theories. It is concluded that prospective measurements of D n may provide decisive evidence against or significant evidence in favour of the superweak theory.

Phenomenological Dynamics forCPViolation

A fairly general current-current form for the $\mathrm{CP}$-violating interaction is investigated in the phenomenological Lagrangian framework. Special attention is given to the computation of both the $\mathrm{CP}$-conserving and $\mathrm{CP}$-violating self-masses in the ${K}_{L}\ensuremath{-}{K}_{S}$ system. In addition the relevant amplitudes appearing in the neutral-kaon decay matrix are calculated. We find that several kinds of models naturally give the same results as the superweak theory, within present experimental accuracy.

CPTViolation and theKL→μ+μ−Puzzle

The effects of possible $\mathrm{CPT}$ violation on the ${K}_{L}\ensuremath{\rightarrow}2\ensuremath{\mu}$ amplitude are found to be concentrated at the right place to suppress the experimentally violated "conventional" unitarity bound, irrespective of ${K}_{S}\ensuremath{\rightarrow}2\ensuremath{\mu}$. $\mathrm{CPT}$ nonconservation may, therefore, resolve the ${K}_{L}\ensuremath{\rightarrow}2\ensuremath{\mu}$ puzzle, even if $\mathrm{CP}$ violation or the recently proposed new interactions will fail to do this. The possible breaking of $\mathrm{CPT}$ invariance is studied systematically and bounds are given on the violating part of the related amplitudes. Only nonconservation of $\mathrm{CPT}$ in the absorptive part of the ${K}_{L}\ensuremath{\rightarrow}2\ensuremath{\mu}$ amplitude (e.g., in ${K}_{L}\ensuremath{\rightarrow}2\ensuremath{\gamma}$) may be accessible to experiment in the near future. Superweak theory is inconsistent with experiment, under the "conventional" assumptions, even in its $\mathrm{CPT}$-violating version.

CP violation and the K → μ+μ− puzzle

The unitarity relations for K → μ + μ − are studied under the assumption of CPT alone, and including γγ, ππ, and the CP even π π γ states in the absorptive parts for both K S and K L. A new bound for K S → μ μ is obtained and it is shown explicitly that superweak theory contradicts present experimental data under these assumptions.

CP-Violation Experiments: Superweak Theory is Out

Since a Princeton group (James Christenson, James Cronin, Val Fitch and Rene Turlay) found the first violation of CP in 1964, high-energy physicists have been eagerly looking for the source of the violation. Of the four classes of theories proposed, at least one and a half classes seem to be ruled out by recent experiments at CERN (by Jean-Marc Gaillard, F. Krienen, W. Galbraith, A. Hussri, M. R. Jane, N. H. Lipman, G. Manning, T. Ratcliffe, P. Day, A. G. Parham, B. T. Payne, A. C. Sherwood, H. Faissner and H. Teithler) and at the Princeton-Pennsylvania Accelerator (by James Cronin, Paul Kunz, Winthrop Risk and Paul Wheeler).