Two-component Neutrino Theory Research Articles

CHIRAL ASYMMETRY AND GRAVITATION THOERY

In this letter we apply an alternative approach, recently developed, to the description of massless particles of arbitrary spin to the case of spin-two particles. This provides a non-geometrical approach to the theory of linearized gravitation. Within this method the chiral components of a spinor field are treated as independent field variables. The free field Lagrangian is built up from the requirement of chiral invariance. This formulation is parallel to the neutrino theory and leads to a formulation that generalizes, to particles of spin-two, the two-component neutrino theory. At the free field level the analog of curvature tensor, spin connection tensor, and metric tensor are independent quantities. By introducing left–right asymmetric linear interactions of these chiral components we get the linearized gravitation theory.

Left–right asymmetry and minimal coupling

In this paper we deal with an alternative approach to the description of massless particles of arbitrary spin. Within this scheme chiral components of a spinor field are regarded as fundamental quantities and treated as independent field variables. The free field Lagrangian is built up from the requirement of chiral invariance. This formulation is parallel to the neutrino theory and allows for a formulation that generalizes, to particles of arbitrary spin, the two-component neutrino theory. We achieve a spinor formulation of electrodynamics. In the case of the photon, the nonzero helicity components satisfy Weyl’s equations and are associated to observables (electromagnetic fields) whereas the zero helicity components are related to nonobservables (electromagnetic potentials). Within the spinor formulation of electrodynamics the minimal coupling substitution follows as a consequence of the linearity of the interaction and the preference of nature for chiral components, that is, of the left–right asymmetry of nature.

Orbits of Spin+(3,1), wave packets and asymptotic lepton symmetries

The Dirac equation is most easily formulated in terms of functions from space-time to the Clifford algebra R 3,1 and the gradient operator. In this setting we may construct wave packet solutions for all leptons by introducing a single operator which transforms a real valued function on the group Spin +(3,1) to a wave function by using integration on the group itself. Applying the operator to a certain space of real valued functions on the group, we produce Spin +(3,1)-invariant solution spaces which may then be classified. The results are one space each for electrons and positrons and two parameter families of spaces for neutrinos and antineutrinos. The electron and neutrino spaces display an asymptotic symmetry at high energies, as do the positron and antineutrino spaces. If we also insist that the solution spaces be translation invariant, then we get the familiar two-component neutrino theory and the asymptotic symmetry between leptons of the same handedness used in the theory of weak interactions. This symmetry is purely a result of the Dirac theory in the Clifford algebra setting.

Generalization of the Weak Charged V-A Current

In view of possible existence of the nucleonic sccond·class current, the weak charged urbaryonic and leptonic V-A currents are generalized so as to contain derivative currents by assuming two-component neutrino theory and baryon-lepton correspondence. Values of parameters associated with the derivative currents of lepton are determined from p-, 'i:- ·and K-decays. The generalized currents can explain ~ parameter of the p-decay. §I. Introduction Recently some experiments have been performed to study the possible existence of second-class currents. Measurements 11 of decay asymmetries in polarized nuclei showed that the coupling constants associated with the second-class 1 seem to be larger than the corresponding theoretical values expected from the SU (2) symmetry breaking. On the other hand, the latest experimental results in aligned nuclei are consistent with absence of the second-class current. 1 Although the experimental situation about the second-class current is in an unsettled state, it will be interesting to examine some consequences front the assumption of the existence of the second-class currents both in urbaryonic and leptonic levels. We generalize the weak charged V-A currents so as to involve derivative terms such as tensor (6' a,l (f§ +a) S), pseudo-tensor (u aS75 (fJ + 8) S), scalar (i (fJ +a) a) and pseudo-scalar (ir5 cf§ +a) a) as well as vector Cr a) and axial-vector Cr ar5) terms. We assume the following which gives further limitations on the form of the currents: i) The current is hermitian as well as T-in variant. ii) Neutrinos (v~, Ve) are massless with two components and the neutrinos and anti-neutrinos are left­ handed and right-handed, respectively. iii) Baryon-lepton (B-L) correspondence 41~61 is adopted. These assumptions imply that a P-type urbaryon appears as left-handed in the urbaryon current and that the coupling constant of the tensor term becomes equal to that of the pseudo-tensor one. \Ve show that the leptonic current involving derivative terms well reproduces the experimental value of e) parameter in the ,11-decay, while the com-entional V-A current theory with two-component neutrinos 81 shows some departure from experimental results. This conventional V-A current well reproduces experimental results except for the c; parameter. The theoretical value is c;v-A = 1, whereas the experimental value is slightly smaller; c;exp = 0.972 ± 0.013. 71 In a weak-intermedi

Nature's natural numbers: relativistic quantum theory over the ring of complex quaternions

The 2×2 complex matrix formulation of relativity and the two-component spin-1/2 formalism are merged with the complex quaternion algebra to yield a concise, manifestly covariant formalism of relativistic quantum mechanics. Along with reproducing all the old results of quantum theory, this complex quaternion formulation extends naturally the concept of scalar mass by adding to it orientation- and velocity-dependent parts giving a hyper-mass. The hyper-mass spin-1/2 equation, with the scalar part of the mass set equal to zero, gives a subtle variation on the two-component neutrino theory with very unsubtle consequences, such as an invariant mass parameter which could distinguishv eandv μ and elimination of the superposition principle.

Capture of ??-mesons by polarized proton target

Differential capture sections are calculated of longitudinally polarized or unpoiarizedμ −-mesons by polarized proton target of low order in weak (V, A, P)-interaction. It is shown that the presence of pseudoscalar interaction in the effective Hamiltonian results in the appearance in the angular distribution of neutrons emitted in the longitudinal capture of polarized muons polarized by proton target; the latter is characteristic for the interference term ∼cos2 θ but for high-energy right-polarizedμ −-mesons the capture section by unpolarzed or polarized protons is only proportional to G p 2 and may be used to determine the strength and the sign of the pseudoscalar interaction. It is also shown that in the (V-λA)-variant of the interaction between muon and nucleon currents the predictions of two-component and fourcomponent neutrino theory diverse.

Measurement of the Velocity Dependence of the Helicity of Beta Particles fromCo60

A series of experiments has been carried out to study the velocity dependence of the helicity $\mathcal{H}$ of $\ensuremath{\beta}$ particles from the allowed Gamow-Teller decay in ${\mathrm{Co}}^{60}$. The energies examined were varied from 205 keV ($\frac{v}{c}=0.7$) to 50 keV ($\frac{v}{c}=0.41$), a region where the velocity is changing rapidly with energy, and where several other measurements have reported deviations from $\mathcal{H}=\ensuremath{-}\frac{v}{c}$. We have not observed any discrepancy with a $\ensuremath{-}\frac{v}{c}$ dependence for the helicity within a measurement accuracy of a few percent at the highest velocities and 9% at the lowest velocity. The weighted mean of the helicity measurements is $\ensuremath{-}\frac{\mathcal{H}}{(\frac{v}{c})}=1.014\ifmmode\pm\else\textpm\fi{}0.018$. Assuming, in turn, either the two-component neutrino theory with predominantly axialvector interaction or the absence of any tensor interaction admixture, this result limits the ratio $\frac{{C}_{T}}{{C}_{A}}$ to 0.0029, and the ratio $\frac{{C}_{A}^{\ensuremath{'}}}{{C}_{A}}$ to values between 0.90 and 1.11. The helicity was analyzed by Mott scattering after transformation of the polarization from longitudinal to transverse. A screened Mott scattering function $S(\ensuremath{\theta})$ was used in the analysis. The behavior of depolarization effects and the other systematic errors associated with the technique as a function of $\ensuremath{\beta}$-particle energy was investigated extensively, and the influence of these effects on the results is reported.

Measurement of the Muon Decay Spectrum with a Wire Spark-Chamber Spectrometer

The decay spectrum of the positive muon has been studied in a wire spark-chamber spectrometer of wide momentum acceptance. Both the parameters $\ensuremath{\delta}$ and $\ensuremath{\rho}$ were determined. On the basis of 4.9\ifmmode\times\else\texttimes\fi{}${10}^{5}$ events, obtained in runs with different fields and targets, we find for the parameter governing the energy dependence of the asymmetry, the value $\ensuremath{\delta}=0.752\ifmmode\pm\else\textpm\fi{}0.009$. From a spectrum of 1.7\ifmmode\times\else\texttimes\fi{}${10}^{5}$ events we find for the shape parameters of the isotropic spectrum $\ensuremath{\rho}=0.762\ifmmode\pm\else\textpm\fi{}0.008$ (assuming $\ensuremath{\eta}\ensuremath{\equiv}0$), or $\ensuremath{\eta}=\ensuremath{-}0.7\ifmmode\pm\else\textpm\fi{}0.5$ (assuming $\ensuremath{\rho}\ensuremath{\equiv}\frac{3}{4}$). These values for $\ensuremath{\rho}$ and $\ensuremath{\delta}$ are in agreement with two-component neutrino theory. Using our value of $\ensuremath{\delta}$ and averages of the most accurate published values of the other muon decay parameters, we find that the scalar and tensor couplings (in charge retention ordering) can still account for as much as 30% of the interaction.

The wave equation for zero rest-mass particles

It is shown that (γ · ∂ ∂x ) + 1 2 χ (1 ± γ 5) Ψ ± = 0 may also be taken as the wave equation for zero rest mass, spin 1 2 particles. The new parameter is a measure of the degree of chirality. The investigations of the invariance properties of the equation lead to the same as those of the usual two-component neutrino theory with the exceptions of γ 5 invariance. It seems plausible that at least one of the neutrinos satisfies this kind of wave equation.

Precise Measurement of the ParameterδGoverning the Decay Spectrum of Polarized Muons

A precision measurement of the energy dependence of the asymmetry of the decay of the positive muon has been made with a wire spark-chamber spectrometer of large momentum acceptance. We find, as an average of runs at different fields and with different targets, $\ensuremath{\delta}=0.758\ifmmode\pm\else\textpm\fi{}0.010$, in agreement with the two-component neutrino theory.

Precise Measurement of the ParameterδGoverning the Decay Spectrum of Polarized Muons

A precision measurement of the energy dependence of the asymmetry of the decay of the positive muon has been made with a wire spark-chamber spectrometer of large momentum acceptance. We find, as an average of runs at different fields and with different targets, $\ensuremath{\delta}=0.758\ifmmode\pm\else\textpm\fi{}0.010$, in agreement with the two-component neutrino theory.

Two neutrinos or one?

We discuss the value, in the light of recent «two-neutrino» experiments (1), of giving meaning to the neutrino charge or lepton number independent of helicity;i.e., of giving up the two-component neutrino theory and reverting to a single four-component neutrino whose left- and right-helicity states are coupled to e− and μ+, respectively. It is shown that, in fact,only by such experiments, involving muonsand electrons or their neutrinos, can a nontrivial meaning be given to lepton conservation. This Dirac neutrino theory is compared with the conventional theory of two two-component neutrinos from the conceptual and experimental points of view. Some remarks are made about the possibility of explaining the μ—e mass difference.

A precision measurement of the longitudinal polarization of betas following P 32 decay

The method of Mott scattering has been used to determine the longitudinal polarization of 616 keV betas from the allowed Gamow-Teller decay of P 32. After rotation of the spin from longitudinal to transverse by a spherical electrostatic analyser, the up-down asymmetry was measured over a wide range of gold target thickness. Source depolarization, plate scattering depolarization, multiple and plural scattering in gold and aluminium targets and instrumental asymmetry effects were carefully investigated experimentally. Corrections were made for various backgrounds, wall scattering, finite geometry and fringing fields. The final value of P = (−0.990±0.009)υ/c for υ/ c = 0.891 depends upon a calculated value of the Most-scattering function S( θ), which has not been corrected for screening, inelastic scattering, Schwinger radiative loss, or finite nuclear size effects. These are estimated to be the order of 2 % or less. Neglecting these effects and small theoretical corrections to the polarization which result from such effects as Δl-forbiddenness and finite nuclear size, this experimental result can be interpreted in terms of the beta-decay coupling constants. If time reversal invariance and the two-component neutrino theory are assumed, the ratio C T C A = 0.011±0.010 is computed from the measured polarization. On the other hand, assuming time reversal invariance and C T = C′ T = O, then the ratio C′ A C A is limited to the range +0.82 to +1.22 by the result reported here.

Search for pseudoscalar interaction in [formula omitted] transitions : (II) On the calculation of the longitudinal polarization of β−-particles emitted in [formula omitted] and the relative contribution of the pseudoscalar interaction

A relation between the longitudinal polarization of the β −-particles emitted in 1 2 + → 1 2 − transitions and the relative contribution of the pseudoscalar interaction to β decay is obtained. Lepton conservation, time reversal invariance, C S = C T = 0 and the validity of the two-component neutrino theory with a left-handed neutrino were assumed. The non-relativistic nuclear matrix elements as well as the relativistic ones were taken into account and the importance of the latter mentioned. The combinations of electron radial wave functions were calculated by taking into account the finite size of the nucleus and carried out using a surface as well as a uniform distributed nuclear charge. Some considerations on the sensitivity of other ΔJ = 0, yes, transitions to the detection of the pseudoscalar interaction are also made.

Search for pseudoscalar interaction in [formula omitted] β-decay transitions : (I) Measurement of the longitudinal polarization of the β −-particles emitted in the transition 81Tl 207 → 82Pb 207

The longitudinal polarization of β-rays emitted in the transition 81Tl 207 → 82Pb 207 ( 1 2 + → 1 2 − ) was measured by double Coulomb scattering. The result obtained was P 0 { 81Tl 207} = (1.04±0.25) ( − v c ). Assuming two-component neutrino theory with a left-handed neutrino and C s = C T = 0, this result indicates that pseudoscalar interaction gives only a small contribution, if any, to β-decay.

Determination of the Fierz Interference Term From the K-Capture/ +Ratio for the Pure Gamow-Teller Decay of58Co

A direct determination has been made of the Fierz interference term b for the pure Gamow-Teller decay of 58Co. The K/β+ ratio has been determined by an internal source scintillation counter coincidence method. The value obtained was 4.92 ± 0.09. This may be compared with the recent predicted value of 4.87. Allowing for the variation in the theoretical value arising from β+ end point uncertainty this yields a value for b of (+0.6 ± 2.3)%. Two interpretations of the result are possible on the basis of two-component neutrino theory. If, as is customarily assumed, CA = CA', CT = -CT', then b should vanish identically; and the small experimental value for b confirms the theory. If alternatively, CA = CA', CT = +CT' then the experimental result requires that CT, CT' be very small.

Polarization of Cosmic-Ray Muons at Sea Level

Cosmic-ray muons at sea level are known to be partially longitudinally polarized. The object of this experiment was to measure the positive muon polarization by stopping the muons in a copper absorber and observing the up: down asymmetry in the decay electrons. Measurements were also made with iron and sulfur as control absorbers to test the symmetry of the apparatus. Since this experiment is performed in zero magnetic field, it has been possible to verify that unmagnetized iron depolarizes positive muons by precessing their magnetic moments in the strong, randomly oriented magnetic fields of the domains. The up: down ratio of decay electrons was 1.14\ifmmode\pm\else\textpm\fi{}0.02 for copper, 0.98\ifmmode\pm\else\textpm\fi{}0.02 for iron, and 1.02\ifmmode\pm\else\textpm\fi{}0.03 for sulfur. On the basis of the two-component neutrino theory, the muon polarization is found to be \ensuremath{\ge}(21\ifmmode\pm\else\textpm\fi{}3)%, where the inequality is due to depolarization effects. On the basis of cosmic-ray data on the muon energy spectrum as a function of altitude, the polarization is expected to be about 30%. The data of the present experiment suggest that in the absence of external magnetic fields copper depolarizes positive muons, as there appears to be a decrease in the up: down ratio with time lived before decay.

Some remarks on the two-component neutrino theory of Lee and Yang

Some remarks on the two-component neutrino theory of Lee and Yang

Preliminary Results on the Momentum Dependence of the Asymmetry in Muon Decay

Positive muons from the Berkeley 184-in. synchrocyclotron were stopped in various materials and the asymmetry of positrons from their decay was determined by using a magnetic spectrometer method. The measurements of the polarization are in agreement with that predicted by the two-component neutrino theory.The product of the muon beam polarization and of $\ensuremath{\xi}$, the parameter of the two-component neutrino theory, was measured as 0.89\ifmmode\pm\else\textpm\fi{}0.09.

Helicity of the Electron and Positron in Muon Decay

The helicity of the electron and positron from muon decay has been measured by determining the sense of circular polarization of their bremsstrahlung by the method of absorption in iron magnetized against or along the direction of motion of the particles. The positron is found to be right-handed and the electron left-handed.The results are consistent with the two-component neutrino theory, which assumes ($V, A$) interaction, conservation of leptons, and left-handed neutrinos.