Eduardo de Rafael

Muon (g − 2): Experiment and Theory

A review of the experimental and theoretical determinations of the anomalous magnetic moment of the muon is given. The anomaly is defined by a = (g − 2)/2, where the Land´ e g-factor is the proportionality constant that relates the spin to the magnetic moment. For the muon, as well as for the electron and tauon, the anomaly a differs slightly from zero (of the order 10 −3 ) because of radiative corrections. In the Standard Model, contributions to the anomaly come from virtual ‘loops’ containing photons and the known massive particles. The relative contribution from heavy particles scales as the square of the lepton mass over the heavy mass, leading to small differences in the anomaly for e, µ and τ . If there are heavy new particles outside the Standard Model which couple to photons and/or leptons, the relative effect on the muon anomaly will be ∼ (mµ/me) 2 ≈ 43 × 10 3 larger compared with the electron anomaly. Because both the theoretical and experimental values of the muon anomaly are determined to high precision, it is an excellent place to search for the effects of new physics or to constrain speculative extensions to the Standard Model. Details of the current theoretical evaluation and of the series of experiments that culminates with E821 at the Brookhaven National Laboratory, are given. At present the theoretical and the experimental values are known with a similar relative precision of 0.5 ppm. There is, however, a 3.4 standard-deviation difference between the two, strongly suggesting the need for continued experimental and theoretical study. (Some figures in this article are in colour only in the electronic version)

The Hadronic Light-by-Light Scattering Contribution to the Muon and Electron Anomalous Magnetic Moments

We review the current status of theoretical calculations of the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment. Different approaches and related issues such as OPE constraints and large breaking of chiral symmetry are discussed. Combining results of different models with educated guesses on the errors we come to the estimate

Nambu-Jona-Lasinio-like models and the low-energy effective action of QCD

a^{\rm HLbL}=(10.5\pm 2.6)\times 10^{-10}.

K → πℓ+ℓ− decays in the effective chiral lagrangian of the standard model

The text is prepared as a contribution to the {\it Glasgow White Paper on the present status of the Muon Anomalous Magnetic Moment}.

On QCD sum rules of the Laplace transform type and light quark masses

Abstract The Weinberg sum rules of the algebra of currents are reconsidered in the light of quantum chromodynamics (QCD). We derive new finite-energy sum rules which replace the old Weinberg sum rules. The new sum rules are convergent and the rate of convergence is explicitly calculated in perturbative QCD at the first non-trivial order. Phenomenological applications of these sum rules in the charged current sector are also discussed.

Four-quark operators and non-leptonic weak transitions

Abstract We present a derivation of the low-energy effective action of an extended Nambu-Jona-Lasinio (ENJL) model to O(p4) in the chiral counting. Two alternative scenarios are considered on how the ENJL model could originate as a low-energy approximation to QCD. The low-energy effective lagrangian we derive includes the usual pseudoscalar Goldstone modes, as well as the lower scalar, vector and axial-vector degrees of freedom. By taking appropriate limits, we recover most of the effective low-energy models discussed in the literature; in particular the gauged Yang-Mills vector lagrangian, the Georgi-Manohar constituent quark-meson model, and the QCD effective action approach model. Another property of the ensuing effective lagrangian is that it incorporates most of the short-distance relations which follow from QCD. (We derive these relations in the presence of all possible gluonic interactions to leading order in the 1 N c expansion.) Finally the numerical predictions are compared with the experimental values of the low-energy parameters.

K-K mixing in the standard model

It is shown, with the example of the experimentally known Adler function, that there is no matching in the intermediate region between the two asymptotic regimes described by perturbative QCD (for the very short-distances) and by chiral perturbation theory (for the very long-distances). We then propose to consider an approximation of large-Nc QCD which consists in restricting the hadronic spectrum in the channels with JP quantum numbers 0−, 1−, 0+ and 1+ to the lightest state and to treat the rest of the narrow states as a perturbative QCD continuum; the onset of this continuum being fixed by consistency constraints from the operator product expansion. We show how to construct the low-energy effective Lagrangian which describes this approximation. The number of free parameters in the resulting effective Lagrangian can be reduced, in the chiral limit where the light quark masses are set to zero, to just one mass scale and one dimensionless constant to all orders in chiral perturbation theory. A comparison of the corresponding predictions, to (p4) in the chiral expansion, with the phenomenologically known couplings is also made.

Electroweak hadronic contributions to the muon (g-2)

Abstract The decay amplitudes of K → π l + l − transitions (l = e or μ ) are calculated in chiral perturbation theory to lowest non-trivial order. This includes one-loop contributions as well as contributions from all possible tree level counterterms to the corresponding order in momenta and meson masses. After relating the local counterterms in the chiral realization to the lowest dimensional local transition operator at the quark level, only one combination of counterterm coupling constants appearing in the decay amplitudes remains unknown. Two possible solutions for this constant are found from a comparison with the experimentally known K + → π + e + e − decay rate. Predictions are then obtained for the rates of K + → π + μ + μ − , K s 0 → π 0 e + e − and K s 0 → π 0 μ + μ − decays as well as for the corresponding spectra in the invariant mass of the lepton pair. The CP -violating transition K L 0 → π 0 ‘γ’ → π 0 l + l − is also discussed.