Hadronic light-by-light contribution to $a_μ$: extended Nambu-Jona-Lasinio, chiral quark models and chiral Lagrangians

Abstract

This talk discusses our old work on the hadronic light-by-light contribution to the muon anomalous magnetic moment and some more recent contributions. I discuss the various contributions starting with pseudo-scalar meson exchange, the quark-and pion-loop, as well as scalar and a 1exchange. For the π 0 -exchange I point out a possible large enhancement when only connected contributions are included. For the quark-loop I include some comments about the more recent estimates of this contribution. The pion-loop is discussed in more detail, in particular I discuss our unpublished work on including effects from a 1 and the polarizability.

Lattice calculation of the pion transition form factor π0→γ*γ*

“…In the double virtual case, no experimental data exist yet but some results from the BESIII experiment are expected in the coming years in the range [17,23]. Therefore, the dependence of the double-virtual form factor in the kinematical range of interest [0 − 1] GeV 2 for the computation of the hadronic light-by-light contribution to the muon g − 2 is still unknown and the available estimates all rely on phenomenological models [1,10]. The model parameters are either fixed using theoretical and experimental constraints from various sources or by fitting the experimental data of the single-virtual form factor and then extrapolating to the double-virtual case, i.e.…”

“…Also, in recent years, more and more precise lattice QCD calculations of the HVP have become available but are not yet competitive with the dispersive approach [6][7][8][9]. However, the HLbL contribution to the muon g − 2 cannot fully be related to direct experimental information and current determinations usually rely on model assumptions where systematic errors are difficult to estimate [1,10,11]. However, recently a dispersive approach was proposed [12] which relates the, presumably, numerically dominant pseudoscalar-pole contribution, as depicted in Fig.…”

Leading-order hadronic contribution to the electron and muon g-2

“…Evaluation of non-perturbative effects is possible by using experimental data in conjunction with Dispersion Relations (DR), by low energy effective modeling via a Resonance Lagrangian Approach (RLA) ( Vector Meson Dominance (VMD) implemented in accord with chiral structure of QCD) [1][2][3], like the Hidden Local Symmetry (HLS) or the Extended Nambu Jona-Lasinio (ENJL) models, or by lattice QCD. Specifically: (a) HVP via a dispersion integral over e + e − → hadrons data (1 independent amplitude to be determined by one specific data channel) (see e.g.…”

“…In the conserved vector current (CVC) limit τ spectra should be identical to the isovector part I = 1 of the e + e − spectra, as illustrated in figure 5. Including the I = 1 τ → ππν τ data available from [41][42][43][44][45] in the range [0.63-0.96] GeV one obtains [35]: which improves the LO HVP as given in (3). We briefly summarize recent progress in data collection as follows.…”

On the Hadronic light-by-light contribution to the muon $g-2$

“…This talk is mainly an update of my talk from two years ago [1] and has thus a very large overlap with it. In addition, this writeup should be read together with a number of other contributions to this and the previous workshop [2].…”