A determination of sin2θ w and the lepton and quark electroweak couplings frome + e − data

Published data on lepton pair and quark pair final states ine ⁺ e ^? annihilation have been analysed in a self consistent way to yield values for the lepton and quark weak vector and axial vector couplings. Generation universality has been tested for the leptons and under the assumption of the standard model of the weak interaction, the parameter sin²θ _w has been determined separately for the lepton and quark sector. In the renormalisation scheme α,G _μ and sin²θ _w , the result for the lepton final states is sin²θ _w = 0.212±0.014 and for the hadron final states, sin²θ _w = 0.236±0.015. The combined result for this single parameter in the model is sin²θ _w = 0.223±0.011±0.007, corresponding tom _Z =93.0 _?1.8 ^+2.0 GeV.     

A measurement of the neutral current electroweak parameters using the fermilab narrow band neutrino beam

We report a measurement of the electroweak parameters sin₂θ ^w and ? based on the ratios of neutral current to charged current events measured in the Fermilab narrow-band neutrino beam at energies of 30–240 GeV. The data are fully corrected for radiative effects, heavy-quark production, and other effects. The best value for sin₂θ ^w obtained, sin₂θ ^w =0.239±0.011, is consistent with the most recent values fromW andZ production, as well as from other neutrino experiments.     

How to compare the SU(5) value of sin2θw with experiments?

We establish the relation between κsin²θ_w to be found from neutral-current experiments and sin²θ_w(Q) for Q=M_W predicted by grand unified theories. We then calculate sin²θ_W(M_W) in the minimal SU(5) model taking the M_W as well as M_x threshold effects into account. We find that these two threshold effects on sin²θ_W(M_W) cancel with each other and sin²θ_W(M_W)=0.211± 0.005.     

Weinberg angle in the neutrino-electron scattering

According to my recent analysis, in which the use ofM _z has been found to give a more precise sin² θ _w than the use ofG _F inv _μ e→v _μ e scattering, I make calculations of sin² θ w in this process withM _z input including the full one-loop and all the leading log corrections. The result from the present data of cross-section σ(v _μ e) = (1.55±0.20)x10^?42 E _v andZ boson massM _z =92.6±1.7 GeV is sin² θ _w =0.228±0.016, which is in good agreement with the value 0.227±0.014 derived through the usual method from the data of \(v_\mu ,\bar v_\mu e\) and \(v_e ,\bar v_e e\) scatterings, and quite consistent with the world-average sin² θ w=0.228±0.004.     

On the determination of sin2θw in semileptonic neutrino interactions

It is shown that if sin²θ_w is measured in semileptonic neutrino interactions then, contrary to a claim in the literature, the error due to unknown dynamical (higher-twist) corrections to the QCD parton model is small provided an isoscalar target is used. The largest contributions to σ_nc and σ_cc are related by isospin invariance alone. Neglecting heavy quarks and Kobayashi-Maskawa (KM) mixing, the parton model is only needed for very small terms and introduces an uncertainty in sin²θ_w which is probably less than 1%. There is a much larger theoretical error due to uncertainties in the element U_cs of the KM matrix and in the strange quark distribution. With the full range 0.80 ? | U_cs | 0.98 which is allowed phenomenologically, these uncetainties give δsin²θ_w = ± 0.008. There is also an error of ±0.004 due to uncertainties in |U_dc| and |U_du|.     

The effect of Higgses and “technions” on the calculation of sin2θw and Mx

The effect of the scalar sector on the calculation of sin²θ_w and M_x in grand unified theories is studied. We consider first elementary Higgs scalars and assume the “big desert” hypothesis. It is argued that Higgses other than the usual doublet can also be light (～ M_w). One can obtain bigger values for sin²θ_w by having light (～ M_w) scalar colour sextets which can give rise to interesting phenomenology. As an example, one can build an SU(5) model giving sin²θ_w ? 0.23 at the one-loop level. We also calculate the uncertainty in sin²θ_w and M_x due to the lack of knowledge of the specific masses of superheavy Higgses. We find that this uncertainty is small for reasonable SU(5) models but large in all the SO(10) versions except the minimal. Finally (and alternatively) we consider the effect of a technicolour interaction. The pseudo-Goldstone bosons (technions) increase the calculated sin²θ_w by as much as ～0.01 but M_x remains nearly unchanged. Second-order contributions due to the technifermions tend to cancel the increase on sin²θ_w and in turn increase M_x.     

The value of sin2θw in atomic physics experiments

The one-loop electroweak radiative corrections to parity violation in atomic physics are calculated in the context of the standard SU(2) × U(1) model. We find that the corrections are small and that the effective value of sin²θ_w in such experiments is 0.219 ± 0.014 to be compared with 0.227 ± 0.010 deduced from high energy neutrino-nucleon scattering.     

Heavy particle effects in grand unified theories with fine-structure constant matching

We note the presence of very significant mismatchings in α(M_w) in some GUT predictions where superheavy particle effects have been included, and adopt a new method to correct them leading to new solutions for the GUT coupling, τ_p or sin²θ_w. An SO(10) model with a grand desert is also noted to yield τ_p ≅ 10³²−10³³ yr and sin²θ_w = 0.225−0.235.     

Further measurements of parity non-conservation in inelastic electron scattering

We have extended our earlier measurements of parity violating asymmetries in the inelastic scattering of longitudinally polarized electrons from deuterium to cover the range 0.15≤y≤0.36. The observed asymmetry shows only slight y dependence over this range. Our results are consistent with the expectations of the Weinberg-Salam model for a value of sin²θ_w= 0.224±0.020.     

Electroweak radiative corrections to neutrino and electron scattering and the value of sin2θw

We describe in detail the calculation of all first-order electroweak radiative corrections to total and differential neutrino cross sections and to the parity-violating asymmetry in ed scattering. We find that leading log approximations agree well with our exact result for the shape, but not necessarily the magnitude, of the corrections to $\text{d}\text{σ}{}^{\mathrm{<mtext>\nu ,</mtext><mtext>\nu </mtext>}}\text{/}\text{d}\text{γ}$ except for γ → 1. Corrections to total neutrino cross sections have also been calculated by Marciano and Sirlin; our results agree with theirs. The corrections to sin²θ_w are experiment dependent. If sin²θ_w is defined in the $\text{MS}$ scheme at a scale M_w, they reduce the average value found from the ratio of charged to neutral current neutrino scattering by 0.012 to 0.215 ± 0.015. They reduce the value obatained from the Paschos Wolfenstein relation by 0.008 to 0.221 ± 0.014. In ed scattering they reduce the value by 0.008 to 0.215 ± 0.015. Using a corrected value of 0.215 ± 0.015 and the first-order corrections to the mass formulae, the SU(2) × U(1) predictions for the vector boson masses are M_w = 83.1_?2.8^+3.1rmGeV and M_z = 93.8_?2.2^+2.5 GeV, about five GeV larger than obtained from the lowest order analysis.     

A determination of the leptonic neutral current couplings

An analysis is presented of the recent data which are sensitive to thee, μ and τ neutral current couplings. A fit combining all results (e ⁺ e ^?, μC,ve, eD, atoms) selects a unique solution in agreement with the standard-model expectation. Assuming lepton universality, the vector and axial-vector couplings are determined to bev=?0.013±0.048 anda=?0.520±0.014. Similarly we find (sin² θ=0.213±0.012,ρ=0.015±0.038) or (sin² θ=0.211α0.012, ρ≡1 which, combined with all other values, gives an average of sin² θ=0.216±0.006.     

An update analysis of deep-inelastic scattering data: A first indication of radiative correction effects?

The results of a new detailed analysis of all data of

-induced deep-inelastic scattering, inclusive of radiative correction effects, is reported. A remarkable improvement in determining the (squared) chiral coupling constants is obtained. Analyzed in terms of the SU(2)_L × U(1) parameters ? and sin²?_w they give ? = 1.001±0.012±0.008 and sin²?_w = 0.215±0.014±0.008. By a comparison with the results obtained without the inclusion of radiative corrections, a weak, but significant, indication about them can be argued.     

Leading logarithmic corrections to the weak leptonic and semi-leptonic low-energy hamiltonian

If one defines the parameters of the Weinberg-Salam theory at a momentum scale M = O(M_W, M_Z), the weak effective hamiltonian at a momentum scale μ ? M has logarithmically enhanced corrections, of order αln(M²/μ²). We present a computation of these corrections, for that part of the hamiltonian which leads to detectable weak-electromagnetic interference effects. The largest correction can be absorbed into a running sin²θ(μ). Other, smaller, corrections are estimated, taking into account the effect of strong interactions.An estimate of the non-logarithmically enhanced corrections is also given, by evaluating them in the limit sin²θ → 0. From the SLAC e - d asymmetry it was found sin²θ = 0.224 ± 0.020 at μ² ? 2 GeV². In correspondence, we find sin²θ(M) = 0.217 ± 0.020. This value, however, is subject to uncertainties deriving from the effect of the strange and of the antiquark parton sea.     

Measurement of the neutral to charged current cross section ratio in neutrino and antineutrino interactions

We report on the analysis of inclusive neutral current events produced in neutrino and antineutrino narrow band beams. We find for incident neutrino energies in the range 12–200 GeV and for hadron energies above 12 GeV a neutral to charged current cross-section ratio of R_v = 0.293 ± 0.010 for incident neutrinos, and $\text{R}{}_{\mathrm{<mtext>v</mtext>}}\text{= 0.35 ± 0.03}$ for antineutrinos. These ratios are consistent with the Weinberg-Salam model, with sin²θ_w = 0.24 ± 0.02.     

Fit of the mixing angles in the six quark model and predictions on theB meson lifetime

Experimental data are used to constrain the parameters of the six quark mixing model and of a composite quark model. A combined fit of the mixing angles in the Kobayashi-Maskawa scheme gives sinθ ₁=0.228±0.011 and error contours around the best values sinθ ₂=0.12 and sinθ ₃≈0. From this, a limit of τ _B >0.35×10^?13 s for the mean lifetime of bottom-flavoured hadrons is obtained. For the composite quark model of Katsumata and Tomozawa, a value of τ _B =(0.22?0.23)10_?13 s is derived.     

A new measurement of the ratio of the cross sections of muon-neutrino and muon-antineutrino scattering on electrons

A new experimental determination of the electro-weak mixing angle θ_W is reported based on a second exposure of the CHARM calorimeter to the CERN-SPS wide-band beam. The ratio R of muon-neutrino- and muon-antineutrino-electron scattering cross section has been determined from a sample of 37 ± 10 and 35 ± 10 events. The experimental result is R = 1.26_?0.45^+0.72, corresponding to a value of sin²θ_W = 0.216 ± 0.055. The total sample of events collected in the CHARM calorimeter during the two exposures is $\text{(83 ± 16)ν}{}_{\mathrm{\mu }}\text{e}\text{events and}\text{(112 ± 21)}\text{ν}{}_{\mathrm{\mu }}\text{e}$ events, leadint to the final result sin²θ_W = 0.215 ± 0.032. The systematic error is estimated to be ± 0.012.     

Weak-electromagnetic unification and broken S4 symmetry

A left-right symmetrical model on weak-electromagnetic unification with four neutral gauge particles obeying S₄ symmetry in their mass generation mechanism is proposed. The Weinberg-Salam results are obtained with sin²θ_w fixed naturally to be 0.25, and further results about superweak interactions are also given.     

A precise determination of the electroweak mixing angle from semileptonic neutrino scattering

The cross-section ratio of neutral-current and charged-current semileptonic interactions of muon-neutrinos on isoscalar nuclei has been measured with the result:R ^v =0.3093±0.0031 for hadronic energy larger than 4 GeV. From this ratio we determined the electroweak mixing angle sin² θ _W , wherem _c is the charm-quark mass in GeV/c². Comparison with direct measurements ofm _w andm _z determines the radiative shift of the intermediate boson mass Δr=0.077±0.025(exp.)±0.038(syst.), in agreement with the prediction. Assuming the validity of the electroweak standard theory we determined ?=0.990?0.013(m _c ?1.5)±0.009(exp.)±0.003(theor.).     

New relations between ℓN-scattering cross sections and neutral current parameters

New relations which connect cross sections with neutral current parameters have been obtained in deep inelastic and (quasi-)elastic _v ^(?) N-,e ^±(μ^±)N-scattering; the relations are independent of the structure functions and formfactors of the nucleon. A known example is the Paschos-Wolfenstein relation in _v ^(?) N-scattering. The relations have been obtained with allowance for the contribution of the extraZ′-boson which makes it possible to use them both for extractions of the Standard Model parameters (ρ, sin²θ _w ) and for the search for some manifestations of new physics.     

Early unification and the Weinberg angle in the SU(4)4 grand unified model

In the framework of the grand unified gauge group SU(4)⁴ we discuss possibilities to reconcile the low unification scale (10⁵?10⁷ GeV) with the acceptable value of sin²θ_w. We consider various specific models which differ by the values of the intermediate mass scale, the choice of the fermion multiplets and by the embedding of the electroweak group SU(2) into SU(4)⁴. The class of theories with early unification and correct sin²θ_w is constructed. They all predict new non-sequential fermions which are SU(2)_L,R singlets and have unconventional electric charges. Cosmological implications of such theories are discussed and it is argued that new particles may well account for the positive results of searches for fractional charge in terrestrial matter.