Abstract: The process e(+)e(-) -> pi(+)pi(-)2 pi(0)gamma is investigated by means of the initial-state radiation technique, where a photon is emitted from the incoming electron or positron. Using 454.3 fb(-1) of data collected around a centerof- mass energy of root s = 10.58 GeV by the BABAR experiment at SLAC, approximately 150000 signal events are obtained. The corresponding nonradiative cross section is measured with a relative uncertainty of 3.6% in the energy region around 1.5 GeV, surpassing all existing measurements in precision. Using this new result, the channel's contribution to the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon is calculated as (g(mu)(pi+ pi-2 pi 0) – 2)/2 = (17.9 +/- 0.1(stat) +/- 0.6(syst)) x 10(-10) in the energy range 0.85 GeV < ECM < 1.8 GeV. In the same energy range, the impact on the running of the fine-structure constant at the Z(0)-pole is determined as Delta alpha(pi+ pi-2 pi 0) (M-Z(2)) = (4.44 +/- 0.02(stat) +/- 0.14(syst)) x 10(-4). Furthermore, intermediate resonances are studied and especially the cross section of the process e(+)e(-) -> omega pi(0) -> pi(+)pi(-)2 pi(0) is measured.

Abstract: The T2K experiment reports an updated analysis of neutrino and antineutrino oscillations in appearance and disappearance channels. A sample of electron neutrino candidates at Super-Kamiokande in which a pion decay has been tagged is added to the four single-ring samples used in previous T2K oscillation analyses. Through combined analyses of these five samples, simultaneous measurements of four oscillation parameters, vertical bar Delta m(32)(2)vertical bar, sin(2) theta(23), sin(2) theta(13), and delta(CP) and of the mass ordering are made. A set of studies of simulated data indicates that the sensitivity to the oscillation parameters is not limited by neutrino interaction model uncertainty. Multiple oscillation analyses are performed, and frequentist and Bayesian intervals are presented for combinations of the oscillation parameters with and without the inclusion of reactor constraints on sin(2) theta(13). When combined with reactor measurements, the hypothesis of CP conservation (delta(CP) = 0 or pi) is excluded at 90% confidence level. The 90% confidence region for delta(CP) is [-2.95, -0.44] ([-1.47, -1.27]) for normal (inverted) ordering. The central values and 68% confidence intervals for the other oscillation parameters for normal (inverted) ordering are Delta m(32)(2) = 2.54 +/- 0.08(2.51 +/- 0.08) x 10(-3) eV(2)/c(4) and sin(2) theta(23) = 0.55(-0.09)(+0.005) (0.55(-0.08)(+0.05)), compatible with maximal mixing. In the Bayesian analysis, the data weakly prefer normal ordering (Bayes factor 3.7) and the upper octant for sin(2) theta(23) (Bayes factor 2.4).

Abstract: An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However, if the transformation depends on field derivatives, the equivalence between the two systems is nontrivial due to the appearance of higher derivative terms in the equations of motion. To address this problem, we prove the following theorem on the relation between an invertible transformation and Euler-Lagrange equations: If the field transformation is invertible, then any solution of the original set of Euler-Lagrange equations is mapped to a solution of the new set of Euler-Lagrange equations, and vice versa. We also present applications of the theorem to scalar-tensor theories.