Counting neutrinos and families in the standard electroweak model

Let n_ν be the number if neutrinos much lighter than their charged lepton partners. In the standard electroweak model, using low-energy particle physics data, we prove that n_ν<137. If moreover the up-type and down type quarks are also highly nondegenerate in mass n_ν<47. The limits are much tighter for nondegenerate leptonic mass spectra. If the ratio of the lepton masses in two consecutive families is about 10 then there are at most two neutrinos beyond the known ν_e, ν_μ and ν_τ. The same result is obtained for a mass spectrum à la Froggat and Nielsen.     

Limits of neutrino stability from the γ-ray flux measured in coincidence with neutrinos from SN 1987a

Limits for the neutrino decay ν_H→ν_L+γ, where ν_H and ν_L are assumed to be massive neutrinos withm_VH>m_VL, are presented using data from the Solar Maximum Mission satellite taken in coincidence with the detected neutrino burst from SN 1987A. These limits are essentially independent of supernova models and are and τ/m_νμ,τ>3.3×10¹⁴ s/eV for a thermal spectrum at a temperature .     

Limits on neutrino electromagnetic properties — an update

Limits on neutrino electromagnetic properties from laboratory experiments and astrophysical arguments are reviewed with an emphasis on the currently favored range of small neutrino masses. We derive a helioseismological limit on the charge and dipole moment for all flavors of e_ν6×10⁻¹⁴e and μ_ν4×10⁻¹⁰μ_B (Bohr magneton). The most restrictive limits remain those from the plasmon decay in globular-cluster stars of e_ν2×10⁻¹⁴e and μ_ν3×10⁻¹²μ_B.     

Mass and CKM matrices of quarks and leptons, the leptonic CP-phase in neutrino oscillations

A general approach for construction of quark and lepton mass matrices is formulated. The hierarchy of quarks and charged leptons (“electrons”) is large, it leads using the experimental values of mixing angles to the hierarchical mass matrix slightly deviating from the ones suggested earlier by Stech and including naturally the CP-phase.

The same method based on the rotation of generation numbers in the diagonal mass matrix is used in the electron–neutrino sector of theory, where neutrino mass matrix is determined by the Majorano see-saw approach. The hierarchy of neutrino masses, much smaller than for quarks, was used including all existing (even preliminary) experimental data on neutrino mixing.

The leptonic mass matrix found in this way includes the unknown value of the leptonic CP-phase. It leads to large ν_μν_τ oscillations and suppresses the ν_eν_τ and also ν_eν_μ oscillations. The explicit expressions for the probabilities of neutrino oscillation were obtained in order to specify the role of leptonic CP-phase. The value of time reversal effect (proportional to sin δ′) was found to be small 1%. However, a dependence of the values of ν_eν_μ,ν_eν_τ transition probabilities, averaged over oscillations, on the leptonic CP-phase has found to be not small – of order of ten percent.     

Reconciling cold dark matter with COBE/IRAS plus solar and atmospheric neutrino data

We present a model where an unstable MeV Majorana tau neutrino can naturally reconcile the cold dark matter model (CDM) with cosmological observations of large and small scale density fluctuations and, simultaneously, with data on solar and atmospheric neutrinos. The solar neutrino deficit is explained through long wavelength, so-called just-so oscillations involving conversions of ν_e into both ν_μ and a sterile species ν_s , while atmospheric neutrino data are explained through ν_μ to ν_e conversions. Future long baseline neutrino oscillation experiments, as well as some reactor experiments will test this hypothesis. The model is based on the spontaneous violation of a global lepton number symmetry at the weak scale. This symmetry plays a key role in generating the cosmologically required decay of the ν_τ with lifetime τ_ντ ≈ 10²-10⁴ seconds, as well as the masses and oscillations of the three light neutrinos ν_e, ν_μ and ν_s required in order to account for solar and atmospheric neutrino data. It also leads to the invisibly decaying Higgs signature that can be searched at LEP and future particle colliders.     

Properties of the proposed τ charged lepton

The anomalous eμ and 2-prong μx events produced in e⁺e⁻ annihilation are used to determine the properties of the proposed τ charged lepton. We find the τ mass is 1.90 ± 0.10 GeV/c²; the mass of the associated neutrino, ν_τ, is less than 0.6 GeV/c² with 95% confidence; V - A coupling is favored over V + A coupling for the τ − ν_τ current; and the leptonic branching ratios are 0.186 ± 0.010 ± 0.028 from the eμ events and 0.175 ± 0.027 ± 0.030 from the μx events where the first error is statistical and the second is systematic.     

Level-level correlation and absorption in nuclear reactions

Level-level correlation in nuclear reactions is discussed in general and it is shown that in the presence of level-level correlations, N_μ = Σ_a|g_μa|²/Γ_μ > 7 , where T is the average absorption in the eigen channels.     

Electron-muon permutation symmetry and multiplicatively conserved lepton number in gauge theories

The similarity between the weak interactions of electron and muon is extended to the principle that all e and μ interactions in gauge models are invariant under e ↔ μ exchange. This necessitates the existence of two Higgs doublets φ_e and φ_μ, and an extended e ↔ μ permutation invariance. After symmetry-breaking, a multiplicatively conserved “permutation parity” π = ± 1 for all particles naturally emerges, with π_μ = −π_e = 1. The model forbids μ → eγ but predicts e⁻e⁻ → μ⁻μ⁻ mediated by π = −1 Higgs bosons at 10⁻¹¹ times the rate of typical weak cross sections.     

Light Dirac neutrinos in left-right symmetric and horizontal gauge models

We describe a scheme to generate light Dirac neutrinos. It uses a heavy symmetry-breaking scale to avoid introducing very small couplings or vacuum expectation values. We show how the scheme can be applied to left-right symmetric and to horizontal gauge models with four generations of fermions. In these models neutrino oscillations occur only between pairs of generations (e.g. ν_e−ν_τ oscillations can occur with no ν_μ−ν_e or ν_μ−ν_τ oscillations).     

Tri-bimaximal mixing and the neutrino oscillation data

Following recent results from the SNO solar neutrino experiment and the K2K long-baseline neutrino experiment, the combined existing data on neutrino oscillations now point strongly to a specific form for the lepton mixing matrix, with effective bimaximal mixing of ν_μ and ν_τ at the atmospheric scale and effective trimaximal mixing for ν_e with ν_μ and ν_τ at the solar scale (hence ‘tri-bimaximal’ mixing). We give simple mass-matrices leading to tri-bimaximal mixing, and discuss its relation to the Fritzsch–Xing democratic ansatz.     

The pion form factor at a timelike momentum transfer of approximately 1 fm from π electroproduction at threshold

From an extrapolation of threshold π⁺ electroproduction data combined with a kinematical constraint at an unphysical point, we derive the value of the pion form factor at a time-like value of the momentum transfer k²_π 1 fm⁻². The result is F_π(k²_π) = 1.19 ± 0.1. From this value, using a twice subtracted dispersion relation, we obtain r_π 0.98 ± 0.24 fm.     

Rigorous pion-pion scattering lengths from threshold πN → ππN data

A new evaluation of the universal ππ scattering length relation is used to extract the ππ s-wave scattering lengths from threshold pion production data. Previous work has shown that the chiral perturbation series relating threshold pion production to ππ scattering lengths appears to converge well only for the isospin-2 case, giving a₂ = −0.031 ± 0.007m_π⁻¹. A model-independent and data-insensitive universal curve then implies a₀ = 0.235 ± 0.03m_π⁻¹ for the isospin-0 scattering length.     

Tests of second-class currents

We argue that the presence of second-class neutral currents can be tested from the observations of and electron polarisation in η→π⁰e⁺e^-. Consequences of this model in η→π^±eν_e,τ^±→ηπ^±ν_τ and τ^±→ωπ^±ν_τ decays which would establish second-class charged currents are also discussed.     

Minimal renormalization without ε-expansion: Three-loop amplitude functions of the 0(n) symmetric Φ theory in three dimensions below Tc

We present an analytic three-loop calculation for thermodynamic quantities of the O(n) symmetric Φ⁴ theory below T_c within the minimal subtraction scheme at fixed dimension d = 3. Goldstone singularities arising at an intermediate stage in the calculation of O(n) symmetric quantities cancel among themselves leaving a finite result in the limit of zero external field. From the free energy we calculate the three-loop terms of the amplitude functions ƒ_Φ, F₊ and F₋ of the order parameter and the specific heat above and below Tc, respectively, without using the e = 4-d expansion. A Borel resummation for the case n = 2 yields resummed amplitude functions f_Φ and F₋ that are slightly larger than the one-loop results. Accurate knowledge of these functions is needed for testing the renormalization-group prediction of critical-point universality along the λ₋line of superfluid ⁴He. Combining the three-loop result for F₋ with a recent five-loop calculation of the additive renormalization constant of the specific heat yields excellent agreement between the calculated and measured universal amplitude ratio A⁺/A^- of the specific heat of ⁴He. In addition we use our result for f_Φ to calculate the universal combination Rc of the amplitudes of the order parameter, the susceptibility and the specific heat for n = 2 and n = 3. Our Borel-resummed three-loop result for R_c is significantly more accurate than the previous result obtained from the ε-expansion up to O(ε².     

Magnetic moment of the Δ (1232) resonance

The reaction γp → π^°γ′p has been measured with the TAPS BaF₂ calorimeter at the Mainz Microtron accelerator facility MAMI for energies between √2 = 1221–1331 MeV. Cross sections differential in angle and energy have been determined for the photon γ′ in three bins of the excitation energy. This reaction channel provides access to the magnetic dipole moment of the Δ⁺(1232) resonance and, for the first time, a value of μ_Δ+ = (2.7^+1.0_−1.3(stat) ± 1.5(syst) ± (theor)) π_N has been extracted.     

Globally conformal invariant gauge field theory with rational correlation functions

Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V_κ(x₁,x₂) of dimension (κ,κ). For a globally conformal invariant (GCI) theory we write down the OPE of V_κ into a series of twist (dimension minus rank) 2κ symmetric traceless tensor fields with coefficients computed from the (rational) 4-point function of the scalar field.

We argue that the theory of a GCI hermitian scalar field of dimension 4 in D=4 Minkowski space such that the 3-point functions of a pair of 's and a scalar field of dimension 2 or 4 vanish can be interpreted as the theory of local observables of a conformally invariant fixed point in a gauge theory with Lagrangian density .     

Low-energy expansion of meson form factors

We calculate the corrections to various low-energy theorems concerning the behaviour of the pseudoscalar meson form factors near t=0. In particular we discuss (i) the Ademollo-Gatto theorem, (ii) Sirlin's relation between the K_l3 form factor ƒ₊^Kπ(t) and the electromagnetic form factors, (iii) the Callan-Treiman relation, and (iv) the Dashen-Weinstein relation, which connects the slope λ₀ of ƒ₀^Kπ(t) with the ratio F_K/F_π. Furthermore, we point out a remarkable isospin breaking effect which is clearly visible in the experimental rates of the decays K⁺→π⁰e⁺ν, K⁰→π⁻e⁺ν.     

Positivity of energy in five dimensional classical unified field theories, II

Five dimensional classical unified field theories as well as Yang-Mills theory with gauge group U(1), are described in terms of a Lorentzian five dimensional space V₅ with metric tensor γβ which admits a space-like Killing vector ζ. It is assumed that: (1) V₅ has the topology of V₄ x S¹, S¹ is a circle and V₄ is a four dimensional Lorentzian space that is asymptotically flat and (2) the Einstein tensor Γ_β of V₅ satisfies Γ_β Uυ^{β 0} where U and υ are future oriented time-like vectors with γ_βυζ^β = 0. The spinor approach of Witten [4], Nester [3] and Moreschi and Sparling [5] is used to show that the conserved five dimensional energymomentum vector P = ifΓ_β = 0 then V₅ must admit a time-like Killing vector. Lichnerowicz's results [1] then imply that V₅ must be flat. A lower bound for P⁴ (the mass) similar to that found by Gibbons and Hull [6] is obtained.