The discrepancy between τ and e + e − spectral functions revisited and the consequences for the muon magnetic anomaly

Abstract

We revisit the procedure for comparing the ππ spectral function measured in τ decays to that obtained in e + e − annihilation. We re-examine the isospin-breaking corrections using new experimental and theoretical input, and find improved agreement between the τ − → π − π 0 ντ branching fraction measurement and its prediction using the isospin-breaking-corrected e + e − → π + π − spectral function, though not resolving all discrepancies. We recompute the lowest order hadronic contributions to the muon g − 2 using e + e − and τ data with the new corrections, and find a reduced difference between the two evaluations. The new tau-based estimate of the muon magnetic anomaly is found to be 1.9 standard deviations lower than the direct measurement.

Muon g − 2 vs LHC in supersymmetric models

“…The precise measurement of the muon anomalous magnetic moment (the muon g − 2) [3,4] has shown discrepancy from the SM prediction [5][6][7][8][9][10]. With dedicated efforts to determine hadronic contributions precisely, the latest result is ∆a µ ≡ a µ (exp) − a µ (SM) = (26.1 ± 8.0) × 10 −10 ,…”

Tests of hadronic vacuum polarization fits for the muon anomalous magnetic moment

“…First, a HLO µ is related directly to σ(e + e − → γ → hadrons) [14] and the associated electromagnetic (EM) current polarization function, which, unlike the model, has both an I = 1 and I = 0 component. Second, even for the I = 1 part there are subtleties involved in relating the spectral functions obtained from σ(e + e − → γ → hadrons) and non-strange τ decays [15,16]. Finally, since the τ data extends only up to s = m 2 τ , a model representation is required for the I = 1 spectral function beyond this point.…”

Review of Recent Calculations of the Hadronic Vacuum Polarisation Contribution

“…6 with those by [17]. The smaller correction of G EM in [15] is due to the exclusion of the contributions involving the ρωπ vertex.…”

“…(3), m τ is the τ mass, |V ud | the CKM matrix element, B X − and B e are the the branching fractions of τ − → X − (γ)ν τ (final state photon radiation is implied for τ branching fractions) and of τ − → e −ν e ν τ , (1/N x )dN x /ds is the normalised invariant mass spectrum of the hadronic final state, and R IB represents all the s-dependent isospinbreaking (IB) corrections and S EW corresponds to shortdistance electroweak radiative effects [15].…”

“…(4) is the ratio FSR(s)/G EM (s), where FSR(s) refers to the final state radiative corrections [16] in the π + π − channel, and G EM (s) denotes the long-distance radiative corrections of order α to the photon-inclusive τ − → π − π 0 ν τ spectrum [15]. The energy dependent corrections used in [15] are compared in Fig. 6 with those by [17].…”