Universality Of Weak Interactions Research Articles

Heavy + heavy and heavy + light pseudoscalar to vector semileptonic transitions

Using a symmetry-preserving regularisation of a vector times vector contact interaction (SCI), we complete a systematic treatment of twelve semileptonic transitions with vector meson final states: Drightarrow rho , D_{(s)}rightarrow K^*, D_srightarrow phi , Brightarrow rho , B_srightarrow K^*, B_{(s)}rightarrow D_{(s)}^*, B_c rightarrow B_{(s)}^*, J/psi , D^*; and thereby finalise a unified analysis of semileptonic decays of heavy + heavy and heavy + light pseudoscalar mesons to both pseudoscalar and vector meson final states. The analysis is marked by algebraic simplicity, few parameters, and the ability to consistently describe systems from Nambu-Goldstone modes to heavy + heavy mesons. Regarding the behaviour of the transition form factors, the SCI results compare well wherever sound experimental or independent theory analyses are available; hence, the SCI branching fraction predictions should be a reasonable guide. Considering the ratios R(D_{(s)}^{(*)}), R(J/psi ), R(eta _c), whose values are key tests of lepton universality in weak interactions, the SCI values agree with Standard Model predictions. The B_{(s)}rightarrow D_{(s)}^* transitions are used to predict the precursor functions that evolve into the universal Isgur–Wise function in the heavy-quark limit, with results that conform with those from other sources where such are available. The study also exposes effects on the transition form factors that flow from interference between emergent hadron mass from the strong interaction and Higgs boson couplings via current-quark masses, including flavour symmetry violation.

Status of Pion Decay Experiments

The branching ratio of pion decays, , has provided a sensitive test of electron-muon universality in weak interactions. The uncertainty of the Standard Model prediction is at a 0.01% level. Although a recent measurement, Re/μ = (1.2344 ± 0.0023(stat) ± 0.0019(syst)) × 10-4, reduced the experimental uncertainty by a factor of two, there is room for improvement by more than an order of magnitude. The status of two experiments at TRIUMF and PSI as well as related pion decay experiments is presented.

Status of the PIENU experiment

The branching ratio, Re/μ = Γ(π → eν + eνγ)/Γ(π → μν + μνγ), provides a sensitive test of muon-electron universality in weak interactions. The status of the PIENU experiment at TRIUMF, which aims to improve the precision of the Re/μ measurement by a factor of > 5, is presented.

The PIENU experiment at TRIUMF : a sensitive probe for new physics

Study of rare decays is an important approach for exploring physics beyond the Standard Model (SM). The branching ratio of the helicity suppressed pion decays, R = , is one of the most accurately calculated decay process involving hadrons and has so far provided the most stringent test of the hypothesis of electron-muon universality in weak interactions. The branching ratio has been calculated in the SM to better than 0.01% accuracy to be RSM = 1.2353(1) × 10 . The PIENU experiment at TRIUMF, which started taking physics data in September 2009, aims to reach an accuracy five times better than the previous experiments, so as to confront the theoretical calculation at the level of ±0.1%. If a deviation from the RSM is found, "new physics" beyond the SM, at potentially very high mass scales (up to 1000 TeV), could be revealed. Alternatively, sensitive constraints on hypotheses can be obtained for interactions involving pseudoscalar or scalar interactions. So far, 4 million π+ → e+ νe ue events have been accumulated by PIENU. This paper will outline the physics motivations, describe the apparatus and techniques designed to achieve high precision and present the latest results.

Precision Measurements with Pions—Review

The branching ratio of pion decays, R e / μ = Γ ( π + → e + ν + e + ν γ ) / Γ ( π + → μ + ν + μ + ν γ ) , has provided the best test of electron-muon universality in weak interactions. While the Standard Model prediction is R e / μ = ( 1.2353 ± 0.0001 ) × 10 − 4 , the existing experimental results, ( 1.2265 ± 0.0056 ) × 10 − 4 (TRIUMF) and ( 1.2346 ± 0.0050 ) × 10 − 4 (PSI), have still orders of magnitude worse uncertainties. Since the decay π + → e + ν is helicity-suppressed, it is extremely sensitive to a presence of pseudo-scalar couplings arising from a wide range of new physics up to a mass scale of 1000 TeV/c 2 . Two new experiments aiming at a precision level of < 0.1 % for R e / μ , as well as related precision measurements of other pion decays, are described.

Gauge-Higgs unification and quark-lepton phenomenology in the warped spacetime

In the dynamical gauge-Higgs unification of electroweak interactions in the Randall-Sundrum warped spacetime the Higgs boson mass is predicted in the range 120 GeV -- 290 GeV, provided that the spacetime structure is determined at the Planck scale. Couplings of quarks and leptons to gauge bosons and their Kaluza-Klein (KK) excited states are determined by the masses of quarks and leptons. All quarks and leptons other than top quarks have very small couplings to the KK excited states of gauge bosons. The universality of weak interactions is slightly broken by magnitudes of $10^{-8}$, $10^{-6}$ and $10^{-2}$ for $\mu$-$e$, $\tau$-$e$ and $t$-$e$, respectively. Yukawa couplings become substantially smaller than those in the standard model, by a factor $|\cos \onehalf \theta_W|$ where $\theta_W$ is the non-Abelian Aharonov-Bohm phase (the Wilson line phase) associated with dynamical electroweak symmetry breaking.

Asymmetry in scattering of leptons and protons

On the assumption of differences among the constants of weak interactions of electron, muon and tau-leptons the asymmetry of interactions has been considered in the processes e + +e - ->mu + +mu - , e + +e - ->tau + +tau - , being in qualitative agreement with new experimental data at s 1/2 >50 GeV. On the consideration of asymmetry of these processes, the lepton multiplets are choosen such that the mue-, taue- universality of weak interactions is broken.

PRECISE TESTS OF e-μ UNIVERSALITY

The status of experimental tests of electron-muon universality in weak interactions is reviewed. The average of the new measurements of the π+→e+ν branching ratio, R ave =Γ(π→eν+π→eνγ)/Γ(π→μν+π→μνγ)=(1.2312±0.0037)×10−4, is consistent with standard model calculations R th =(1.234±0.001)×10−4 and confirms the hypothesis of electron-muon universality at the 0.2% level.

EVIDENCE FOR THE FOURTH GENERATION?

In a recent experiment, the measured lifetime of the tau lepton suggests that the e-µ universality may not hold in the case of the third-generation leptons. It is shown here that the universality of weak interactions can be restored by invoking the existence of a fourth generation of quarks and leptons, and by mixing the τ-lepton with the charged lepton of the fourth generation by a Cabibbo-like mixing angle. Agreement between the experimentally measured lifetime and the theoretical value as predicted by the standard SU (2) L × U (1) model on the basis of universality of weak interactions requires the cosine of the Cabbibo-like mixing angle (ϕ) to be | cos ϕ|=0.96±0.02.

EVIDENCE FOR A TAU-NEUTRINO MASS?

In a recent experiment, the measured lifetime of the tau lepton indicates that the e–μ universality may not hold in the case of the third-generation leptons. It is shown here that the universality of weak interactions can be restored if the tau-neutrino has a non-zero mass. Our result is [Formula: see text].

Effective lagrangian analysis of new interactions and flavour conservation

New interactions with a scale Λ larger than the Fermi scale G F − 1 2 will manifest themselves at energies below Λ through small deviations from the standard model, which can be described by an effective lagrangian containing non-renormalizable SU(3) × SU(2) × U(1) invariant operators. We construct the first two terms of this lagrangian in an expansion in powers of 1/Λ and study systematically possible effects of new interactions such as anomalous magnetic moments, deviations from universality in weak interactions and rare processes. Among the flavour conserving processes the universality of the charged current weak interactions yields the strongest bound on the new interaction scale, Λ > 5 TeV, whereas flavour non-conserving processes imply the bound Λ > 3000 TeV. We derive conditions for natural flavour conservation. Although it cannot be excluded that all flavour changing operators are dynamically suppressed, this appears difficult to understand without a symmetry for which the standard electroweak theory seems to provide no hint. We emphasize the importance of searching for rare decays of D-mesons.

BETA DECAY OPENS THE WAY TO WEAK INTERACTIONS

After a short introduction with some personal recollection, the author summarizes, in Sect 2, the main points of Fermi's theory of beta decay and of the neutrino hypothesis first proposed by Pauli. The successive Sections refer to : a few extensions and modifications of this theory (Sect 3), various experimental investigations carried out in the 30s for testing Pauli's hypothesis and Fermi's approach (Sect 4), further attempts, refinements and proposals (Sect 5) and a few fundamental step forward such as the discovery of the universality of weak interactions, of parity violation by weak interactions, the 2-component theory of the neutrino and the (V-A) theory of weak interactions (Sect 6). Finally Section 7 refers to a few contributions given in the period 1930-1960 to the problem of double beta decay.

New Universality of Weak Interactions and "Ur-Citon Scheme"

A new form of universality for weak interactions is proposed, based on the "ur-citon scheme." It enables us, by following simple rules, to derive an effective Hamiltonian for arbitrary weak processes without any parameter except for a universal coupling strength, the Cabibbo angle, and a constant inherent to the "ur-citon scheme." By applying our method to the decay widths of the typical semileptonic and nonleptonic processes our universality is shown to be valid satisfactorily.

Muon capture in nuclei

Theoretical calculations of the total capture rate for muons in certain light nuclei (40Ca,16O,12C,4He) have been carried out with cognizance taken of the important role played by giant dipole resonances in the capture process. The calculation involves the following steps: 1) Relating the dipole contribution of the vector interaction to its unretarded value by the use of the ground-state elastic form factor. 2) Relating the unretarded dipole part of the vector interaction to an integral over the photo-disintegration cross-section (by the use of isotopic-spin invariance) and using empirical photo-disintegration data to evaluate this contribution. 3) Using the Wigner supermultiplet theory to relate the matrix elements of the axial vector and induced pseudoscalar interaction to those of the vector interaction. 4) Using the shell model (with and without the closure approximation) to evaluate other multipolar contributions and recoil correction terms. The assumptions implicit in the above steps have been examined in as much detail as present knowledge permits. In particular, arguments are given on the basis of several models to justify step 1). The basic assumption involved in the supermultiplet theory used in step 3) is that of weak spin-dependence of the forces. This theory predicts that the giant electric dipole resonance is one of a family (vector supermultiplet) of giant resonances involving spins and isospins. Evidence for the existence of at least one other such resonance is shown to exist in inelastic electron scattering data on16O. The effect of spin-dependence of the forces in splitting this giant resonance supermultiplet is investigated by examining the 0−, 1−, and 2− particle-hole states calculated by Lewis for16O: its effect in our calculations is relatively small. Agreement between theory and experiment is within the uncertainties of both (but with the possibility of a real discrepancy in1He) thus exhibiting general consistency of muon capture with the universality of weak interactions. Inelastic electron scattering data can be a rich source of information to serve as the basis for better calculations and for exploring the giant resonance supermultiplet.

Current-generated algebras

We assume that a component of the F-spin current is utilized as part or all of the vector weak current for strongly interacting particles. Likewise we assume that the same component of an axial vector current octet is part or all of the axial vector weak current. The space integrals of the time components of these two octets then generate, by repeated equal time commutation relations, some algebra. We describe the classification of these possible algebras and give some examples. The algebra SU(3) × SU(3) proposed earlier is not only the smallest of these possible candidates. It is also uniquely selected if the two octets exhaust the whole weak current of strongly interacting particles and if that current has the same algebraic properties as the weak current of the known leptons, in accord with the principle of universality of weak interactions.

On the universality of weak interactions

In classical physics the electromagnetic interactions can be introduced, on account of their universality, by the well-known formal procedure: pμ→pμ−(e/c)Aμ. The universal gravitational interaction is also introduced formally as a change in metric: δμν→gμν=δμν+χμν. In analogy with these classical examples of universal interactions we shall propose here to introduce the universal leptonic interactions by a similar formal procedure of replacing baryonic currents Jμ, Yμ (strangeness-conserving and violating currents) and boson-field operators ∂μπ and ∂μK appearing in the non-leptonic interaction Lagrangian: ℒ=l[Jμ+∂μK+Yμ+∂μπ+h. c.] by Jμ→Jμ+αLμ, Yμ→Yμ+βLμ, and ∂μπ→∂μπ+αr0Lμ, ∂μK→∂μK+βr0Lμ, where \(L_\mu = [(\bar e + \bar \mu )\gamma _\mu (1 + \gamma _5 )v]\) is the usual leptonic current, r0=1.4·10−13 cm; α and β are constants which can be determined as α=1/4 and β=1. Then almost all leptonic interactions are introduced by this formal procedure and the predictions from the new Lagrangian are compared with experiments. The agreements are satisfactory, e.g., the well-known small probabilities of the leptonic decays of hyperons are reproduced by our new Lagrangian.

On the Universality of the Weak Interactions

The universality of weak decay interactions is applied to the introduction of weak interactions using a formal substitution similar to that in the electromagnetic caee. The Latgrangian equation for the no-weak-interaction case is corrected by addition of multipole interaction terms for baryons and bosons and by substitution of universal lepton interaction terms. Thus, the lepton decays of hyperons and beta decays can be described, and almost all the known weak interactions can be derived qualitatively but not quantitatively. (D.L.C.)