Alberto Sirlin

Radiative corrections to νμ + N → μ− + X and their effect on the determination of ϱ2 and sin2θW

Abstract We study the O(α) corrections to σ T ( ν μ + N → μ − + X). The coefficient of the leading O( α ln m Z ) contribution is given by a general theorem as in the case of β decay, while the energy scale accompanying m Z in the argument of the logarithm as well as mass singularities and non-logarithmic terms are obtained by a detailed quark-parton model calculation. The effect of muon mass singularities, when there is an experimental vut in the low range of the y distribution, is also investigated. Combining these new results with our previous analysis of σ T ( ν μ + N → ν μ + X), we calculate theSU(2) L × U(1) parameter ϱ ( ν μ ;h) 2 and evaluate the effect of the O(α) corrections on the determination of sin 2 θ W exp from deep inelastic ν μ scattering. Applying these corrections to existing data, we obtain the weigthed average sin 2 θ W exp = 0.216 ± 0.010 ± 0.004. This value when used in conjuction with our previous analysis of the W ± and Z 0 masses provides the predictions m W = 83.0 −2.8 +3.0 GeV and m Z = 93.8 −2.4 +2.5 GeV. For the weak interaction angle defined by modified minimal subtraction we find sin 2 θ W ( m W ) = 0.215 ± 0.010 ± 0.004, which is in very good agreement with the SU(5) prediction we have recently given.

Large mW, mZ behaviour of the O(α) corrections to semileptonic processes mediated by W

Abstract Using the current algebra formulation of radiative corrections and working in the framework of the SU(2) L × U(1) × SU(3) c theory, we derive a theorem that governs the large m W , m Z behaviour of the O(α) corrections to general semileptonic processes mediated by W. The leading asymptotic dependence is logarithmic with a universal coefficient not affected by the strong interactions. As a byproduct, we obtain the leading asymptotic effect induced perturbatively by the strong interactions, which is of O(ln ln ( m W / Λ )).

Improved Calculation of Electroweak Radiative Corrections and the Value of V~u~d

A new method for computing hadronic effects on electroweak radiative corrections to low-energy weak interaction semileptonic processes is described. It employs high order perturbative QCD results originally derived for the Bjorken sum rule along with a large QCD-motivated interpolating function that matches long- and short-distance loop contributions. Applying this approach to the extraction of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element Vud from superallowed nuclear beta decays reduces the theoretical loop uncertainty by about a factor of 2 and gives Vud=0.97377(11)(15)(19). Implications for CKM unitarity are briefly discussed.

RELATIONS BETWEEN THE ON-SHELL AND MS FRAMEWORKS AND THE MW-MZ INTERDEPENDENCE

It is shown that the recently introduced radiative corrections Δr and Δrw automatically incorporate the leading higher-order contributions arising from resummation of one-loop femionic contributions. With slight modifications, they can be made to include all such contributions (not just the leading ones). Simple relations between Δr, Δrw, Δr sin2θw and sin2gqw(mz) are derived. These expressions bridge the MS and on-shell renormalization schemes and are very useful to compute γr and sin2θw in thecase of large mw. The mw-mz interdependence is expressed in two equivalent ways: in terms of Δr and in terms of the parameter p = mw2mz2cos2gqw(mz). Applications of the expressions derived in the paper are illustrated numerically.

Dependence of the Higgs coupling hMS(M) on mH and the possible onset of new physics

The simple renormalization framework previously discussed by one of us is extended to treat the Higgs potential of the standard model. As an application, we obtain in a straightforward manner the one-loop correction δ(M) in the natural relation h(M) = √12 GμmH2[1 + δ(M)], where mH is the physical mass of the Higgs boson, Gμ the accurately known μ decay coupling constant and h(M) the MS quartic Higgs coupling at mass scale M. The correction δ(M) contains contributions proportional to ξ ≡ mH2/mZ2 and ξ−1 and become large for ξ⪢1 or ξ⪡1. The dependence of h(M) on M and mH is analyzed by combining our one-loop results (which provide initial conditions) and approximate analytic solutions of relevant renormalization group equations. A parameter Mc, which roughly describes the mass scale at which perturbation theory breaks down and the possible onset of new physics, is discussed as a function of mH.

Radiative corrections to GV/Gμ in simple extensions of the SU(2) × U(1) gauge model

Abstract The radiative corrections of order α to the ratio GV/Gμ are estimated in the framework of two simple hadronic extensions of the SU(2) × U(1) gauge model. One involves four quarks with integral charges; the other, three colored quartets. The results are remarkably simple: we recover the corresponding results of the local V-A theory with the mass mZ of the Z vector meson substituted for the cutoff Λ. A phenomenological analysis shows that for a large range of values of mZ, these estimates are of the correct sign and order of magnitude to verify, on the basis of the present data, the universality of the weak interactions in the sense of Cabibbo. The SU(2) × U(1) model has an interesting consequence: by implying a big lower bound for mZ, it gives rise in a natural manner to large corrections of order α. The role of the strong interactions in the treatment of the short distance behavior in these calculations is qualitatively discussed.

Dimensional regularization of infrared divergences

Abstract An analysis of the application of dimensional regularization to infrared divergences in lowest order radiative corrections is presented. The main emphasis of the paper is to show explicitly how dimensional regularization can lead in some cases of considerable interest to very simple and elegant evaluations of infrared divergent contributions and their associated finite parts, and to pinpoint the mathematical reason for the equivalence with the traditional method of regularization.

The Muon g-2 and the bounds on the Higgs boson mass

After a brief review of the muon g-2 status, we analyze the possibility that the present discrepancy between experiment and the standard model (SM) prediction may be due to hypothetical errors in the determination of the hadronic leading-order contribution to the latter. In particular, we show how an increase of the hadroproduction cross section in low-energy e{sup +}e{sup -} collisions could bridge the muon g-2 discrepancy, leading however to a decrease on the electroweak upper bound on M{sub H}, the SM Higgs boson mass. That bound is currently M{sub H} 114.4 GeV (95% C.L.). By means of a detailed analysis we conclude that this solution of the muon g-2 discrepancy is unlikely in view of current experimental error estimates. However, if this turns out to be the solution, the 95% C.L. upper bound on M{sub H} is reduced to about 130 GeV which, in conjunction with the experimental lower bound, leaves a narrow window for the mass of this fundamental particle.

Solar neutrinos: Radiative corrections in neutrino-electron scattering experiments.

Radiative corrections to the electron recoil-energy spectra and to total cross sections are computed for neutrino-electron scattering by solid neutrinos. Radiative corrections change monotonically the electron recoil spectrum for incident 8B neutrinos, with the relative probability of observing recoil electrons being reduced by about 4% at the highest electron energies. For p-p and 7Be neutrinos, the recoil spectra are not affected significantly. Total cross sections for solar neutrino-electron scattering are reduced by about 2% compared to previously computed values. We also calculate the recoil spectra from 13N and 15O neutrinos including radiative corrections.

Precise calculation of MW, sin^2 theta_MSbar, and sin^2 theta_eff

Abstract The two-loop O( g 4 M t 2 M W 2 ) corrections are incorporated in the theoretical calculation of MW, sin 2 θ W (M Z ) , and sin2 θefflept, as functions of MH. The analysis is carried out in a previously proposed MS formulation and two novel on-shell resummation schemes. It is found that the inclusion of the new effects sharply decreases the scheme and residual scale dependence of the calculations. QCD corrections are incorporated in two different approaches. Comparison with the world average of sin2 θefflept leads to MH = 127−71+143GeV and MW = 80.367 ± 0.048 GeV, with small variations among the six calculations.The two-loop O(g^4 mt^2/mw^2) corrections are incorporated in the theoretical calculation of MW, sin^2 theta_MSbar(MZ), and sin^2 theta_eff, as functions of MH. The analysis is carried out in a previously proposed MSbar formulation and two novel on-shell resummation schemes. It is found that the inclusion of the new effects sharply decreases the scheme and residual scale dependence of the calculations. QCD corrections are incorporated in two different approaches. Comparison with the world average of sin^2 theta_eff leads to MH= 127 +143 -71 GeV and MW= 80.367 +/- 0.048 GeV, with small variations among the six calculations.