Precise measurement of thee+e−→π+π−(γ

Abstract

A precise measurement of the cross section of the process e + e − → π + π − (γ) from threshold to an energy of 3 GeV is obtained with the initial-state radiation (ISR) method using 232 fb −1 of data collected with the BABAR detector at e + e − center-of-mass energies near 10.6 GeV. The ISR luminosity is determined from a study of the leptonic process e + e − → µ + µ − (γ)γISR, which is found to agree with the next-to-leading-order QED prediction to within 1.1%. The cross section for the process e + e − → π + π − (γ) is obtained with a systematic uncertainty of 0.5% in the dominant ρ resonance region. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the measured ππ cross section from threshold to 1.8 GeV is (514.1±2.2(stat)±3.1(syst))×10 −10 .

Search for sterile neutrinos decaying into pions at the LHC

“…which is related to F − ðsÞ by conservation of the vector SUð2Þ isospin current (CVC) as F 0 ðsÞ ¼ F − ðsÞ, can be obtained from current e þ e − → π þ π − data [43] up to ffiffi ffi s p < 3 GeV. In our case, we need to know the form factor up to m N ∼ 20 GeV, so we will need to do an extrapolation.…”

“…In our case, we need to know the form factor up to m N ∼ 20 GeV, so we will need to do an extrapolation. For this purpose we consider two theoretical models: one is the vector meson dominance model (VDM) used by the BABAR collaboration [43], and another is based on light front holographic QCD (LFH) [44]. The VDM parametrization for F 0 ðsÞ, which includes ρ-ω mixing, is given by [43] …”

“…where the Breit-Wigner functions BW i ðs; m i ; Γ i Þ and numerical values of all the coefficients fitted to the e þ e − → π þ π − data in the region ffiffi ffi s p < 3 GeV, can be found in [43] (see also [45]). Here no vector mesons heavier than 3 GeV contribute to F 0 ðsÞ, because no light unflavored vector mesons heavier than 3 GeV have been observed yet, qc and qb mesons [e.g.…”

Solving the wrong hierarchy problem

“…An analytical fit in terms masses of π and the vector mesons for e + e − → π + π − is given in ref. [61]. We use this result by rescaling the parameters of the fit to account for different meson masses in QCD .…”

“…We take the analytic model of the ππ contribution to R from ref. [61] and replace all dimensionful parameters by their QCD analogues and find Equation (A.6) must be used in the non-perturbative regime. We switch to the perturbative result for annihilation into the massless bifundamentals 8) when the perturbative and non-perturbative results become equal above s (m ρ ) 2 .…”