A global treatment of VMD physics up to the φ: II. τ decay and hadronic contributions to g−2

Abstract

Relying on the Hidden Local Symmetry (HLS) model equipped with a mechanism breaking the U(3)/SU(3)/ SU(2) symmetries and generating a dynamical vector meson mixing, it has been shown that a global fit successfully describes the cross sections for the e + e − → π + π − , e + e − → (π 0 /η)γ and e + e − → π 0 π + π − annihilation channels. One extends this global fit in order to include also the dipion spectra from the τ decay, taking into account all reported information on their statistical and systematic errors. A model accounting for lineshape distortions of the ρ ± spectrum relative to ρ 0 is also examined when analyzing the τ data behavior within the global fit framework. One shows that a successful account for e + e − annihilation data and τ spectra can be simultaneously reached. Then, issues related with nonperturbative hadronic contributions to the muon g −2 are examined in details. It is shown that all e + e − data considered together allow for improved and motivated estimates for the a μ (π + π − ), the π + π − loop contribution to the muon g − 2; for instance, integrated between 0.630 and 0.958 GeV, we find a μ (π + π − ) = 359.62 ± 1.62 (in units of 10 −10 ), a 40% improvement of the current uncertainty. The effects of the various τ samples in the context of a global fit procedure leads to conclude that different lineshape distortions are revealed by the ALEPH, BELLE and CLEO data samples. Relying on global fits to the data quoted above, one also provides motivated estimates of the π + π − , π 0 γ , ηγ and π 0 π + π − contributions to a μ up to 1 GeV with the smallest possible uncertainties. These estimates are based on various global fit configurations, each yielding a good probability.

An update of the HLS estimate of the muon g−2

“…As noted elsewhere [13,20], based on the available data, auxiliary HLS fits do not improve by letting δM ρ floating. This justified reducing the model freedom by fixing this additional parameter to 0.…”

“…The importance of decay information on ρ 0 → e + e − to determine IB effects has been emphasized in only a few previous works [7,13,20]. Within the BHLS model, the ratio f ργ (s)/f ρW exhibits non-negligible IB effects for this particular coupling (see Fig.…”

“…6 of [19], is outlined in the header of Sect. 5 below; for the τ spectra, the statistical & systematic error covariance matrices provided by the various Collaborations [21][22][23] are added in order to perform the fits [13,20].…”

“…It has been shown [13,19,20] that L HLS is insufficient in order to get a good simultaneous account of the e + e − → π + π − annihilation data and of the dipion spectrum measured in the τ ± → ν τ π ± π 0 decay. A consistent solution to this problem is provided by the vector field mixing mechanism first introduced in [18].…”

“…Therefore, the vector meson squared mass matrix M 2 0 , which is diagonal at tree level, undergoes corrections at one-loop. The perturbation matrix δM 2 (s) [18][19][20] depends on the square of the momentum flowing through the vector meson lines. The diagonal entries acquire selfmass corrections-noticeably the ρ 0 entry absorbs the pion loop-but non-diagonal entries are also generated which correspond to transitions among the ideal ρ 0 , ω and φ meson fields which originally enter the HLS Lagrangian: 8 (s).…”