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.     

Experimental results on neutrino-electron scattering

A determination of sin² θ _w based on measurements of elastic scattering of muon-neutrinos and muon-anti-neutrinos on atomic electrons is described. These purely leptonic processes were studied using the CHARM calorimeter exposed to neutrino and antineutrino wide-band beams at the CERN super proton synchrotron. A total of 83±16 neutrino-electron and 112±21 antineutrino-electron events have been detected. From the measurement of the ratio of muon-neutrino and muon-antineutrino cross-sections a value of sin² θ _w =0.211±0.037 was obtained.     

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.     

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.     

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|.     

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.     

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.     

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.     

Electromagnetic corrections to neutrino processes in the leading logarithmic approximation,the value of sin θ and the W and Z masses

The parameters of the Weinberg-Salam model can be defined by amplitudes at a momentum scale M = O(M_W, M_Z). We derive the leading logarithmic e.m. correction to the relations giving the neutrino amplitudes at a momentum scale μ ? M in terms of sin²θ(M), α(M), M_W and M_Z. For leptonic processes, the Fermi constant is not corrected, but a running, universal, sin²θ(μ) > sin²θ(M) should be used. The Fermi constant for semileptonic processes is renormalized by a factor $\text{?(μ) > 1}$, for charged currents, and is not renormalized, for neutral current processes. The latter are described by the same sin²θ(μ) as the leptonic ones. We estimate that sin²θ(M) is about 0.013 smaller than the value of sin²θ obtained from semileptonic data with no correction, thereby improving the agreement with grand unified theories. The prediction for W (Z) masses and widths in terms of the low energy parameters are discussed. Using previous calculations at order α, we obtain predictions for the masses which are accurate up to and including terms of order (αlnM²)².     

Neutrino mixing and the mw/mz mass ratio

A comparison of neutral and charged current data according to the standard model provides bounds on neutrino mixing parameters, independently of the number of fermions. The mixing may also affect the determination of sin² θ and m_w/m_z.     

y and ν distributions for neutral current reactions of the Weinberg-type

The y and ν distributions for inclusive neutrino and antineutrino reactions arising from a neutral current of the Weinberg-type are investigated in the framework of two quark parton models. While the ν distributions appear of little use at present, we show that by making a cut in the y variable, one can determine sin²θ_W reasonably accurately, independent of the cross section determination, even with the present narrow-band dichromatic neutrino beam at NAL.     

Study of inclusive neutral current interactions of neutrinos and antineutrinos

We report on results from a study of hadron-energy distributions for ν and $\text{ν}$ inclusive neutral current interactions. There is no significant variation of the neutral to charged current total cross-section ratios R_ν and $\text{R}\text{ν}$ with neutrino energy. The space-time structure of neutral currents is dominated by V?A, with a significant admixture of V+A. The Weinberg-Salam model is in agreement with all data if sin²θ_w=0.24±0.02.     

Limits on neutrino oscillations derived from the ratio of neutral- to charged-current cross sections of neutrinos measured at the CERN SPS NBB

We present an analysis, in terms of neutrino oscillations, of the recent measurements of the ratio R of neutral-current to charged-current neutrino cross sections performed by the CDHS and CHARM Collaborations at the CERN Super Proton Synchroton narrow-band beam. The measurementswere aimed at the determination of sin² θ_w. Our analysis is based on the observation that muon-neutrino oscillations would decrease the number of interactions with a muon in the final state. The effect of oscillations on R can be studied, comparing the actual measurements with the value of R predicted by an independent measurement of sin² θ_w. Limits on ν_μ−ν_e, ν_μ−ν_τ, and ν_μ−ν_x oscillations are presented. They refer to a region of high mass squared difference of the two oscillating neutrinos (Δm² > 3 eV²). For high Δm² the limits on the mixing angle θ are very restrictive. In particular, for the transition ν_μ−ν_x (x≠e, τ) they represent the best available results for large intervals in Δm².     

Overview on neutrinos and the Daya Bay experiment

Neutrinos are elementary particles in the Standard Model. Neutrino oscillation is a quantum mechanical phenomenon beyond the Standard Model. Neutrino oscillation can be described by two independent mass-squared differences Δm ₂₁ ² , Δm ₃₁ ² (or Δm ₃₂ ² ) and a 3 × 3 unitary matrix, containing three mixing angles θ ₁₂, θ ₂₃, θ ₁₃, and one charge-parity (CP) phase. θ ₁₂ is about 34° and determined by solar neutrino experiments and the reactor neutrino experiment KamLAND. θ ₂₃ is about 45° and determined by atmospheric neutrino experiments and accelerator neutrino experiments. θ ₁₃ can be measured by either accelerator or reactor neutrino experiments. On Mar. 8, 2012, the Daya Bay Reactor Neutrino Experiment reported the first observation of non-zero θ ₁₃ with 5.2 standard deviations. In June, with 2.5× previous data, Daya Bay improved the measurement of sin²2θ ₁₃ = 0.089 ± 0.010(stat) ± 0.005(syst).     

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.     

Seasonal and energy dependence of solar neutrino vacuum oscillations

We make a global vacuum neutrino oscillation analysis of solar neutrino data, including the seasonal and energy dependence of the recent Super-Kamiokande 708-day results. The best fit parameters for ν_e oscillations to an active neutrino are δm²=4.42×10⁻¹⁰ eV², sin²2θ=0.93. The allowed mixing angle region is consistent with bi-maximal mixing of three neutrinos. Oscillations to a sterile neutrino are disfavored. Allowing an enhanced hep neutrino flux does not significantly alter the oscillation parameters.     

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.     

Employing low-power reactors in studying the mixing parameter sin<Superscript>2</Superscript>(2<Emphasis Type="Italic">θ</Emphasis><Subscript>13</Subscript>)

Measurement of the mixing parameter sin²(2θ₁₃) is one of the pressing problems in neutrino physics. Projects of reactor experiments characterized by a sensitivity of sin²(2θ₁₃)≈0.01 are being presently discussed. Almost all of them are based on the one reactor-two detectors scheme. Within this methodological approach, one employs an NPP reactor of power about a few GW for an antineutrino source and two detectors of identical configurations that are arranged at different distances from the reactor. In such experiments, the systematic error may be about 1%, which ensures a precision of about 0.01. In the present study, it is proposed to use, in a measurement of sin²(2θ₁₃), the existing SuperKamiokande (SK) detector combined with its own antineutrino source, a nuclear reactor of low thermal power, about 300 MW (low-power reactor, or LPR). Such an experiment can be performed within a rather short time. An analysis that studied various detection mechanisms revealed that the LPR-SK combination would make it possible to attain a sensitivity of sin²(2θ₁₃)≈0.002.     

The signature of E6 in precision measurements of sin2θw

Precision electroweak experiments can be used to extract three inequivalent values for sin²θ_w. Discrepancies between theses values which cannot be reconciled within the standard model could indicate new physics. In particular, clear signals of the effects of heavy exotic E₆ particles are possible. These effects are easily distinguished from those of a heavy to quark, supersymmetry, or a standard fourth generation.     

Updated limits on the electron neutrino mass and large angle oscillations from SN1987A

We supplement Maximum Likelihood methods with a Monte-Carlo simulation to re-investigate the SN1987A neutrino burst detection by the IMB and Kamiokande experiments. The detector simulations include background in the the latter and “dead-time” in the former. We consider simple neutrinosphere cooling models, explored previously in the literature, to explore the case for or against neutrino vacuum mixing and massive neutrinos. In the former case, involving kinematically irrelevant masses, we find that the full range of vacuum mixing angles, 0 ≤ sin² 2θv ≤ 1, is permitted, and the Maximum Likelihood mixing angle is sin² 2θv = 0.45. In the latter case we find that the inclusion of “dead-time” reduces previous m_νe upper bounds by 10%, and supplementing the Maximum Likelihood analysis with a Monte-Carlo goodness-of-fit test results in a further 15% reduction in the m_νe upper limit. Our 95% C.L. upper limit for m_νe is 19.6 eV, while the best fit value is ∼ 0 eV.