Constraints on the hadronic light-by-light in the Melnikov-Vainshtein regime

Abstract

The muon anomalous magnetic moment continues to attract attention due to the possible tension between the experimentally measured value and the theoretical Standard Model prediction. With the aim to reduce the uncertainty on the hadronic light-by-light contribution to the magnetic moment, we derive short-distance constraints in the Melnikov-Vainshtein regime which are useful for data-driven determinations. In this kinematical region, two of the four electromagnetic currents are close in the four-point function defining the hadronic light-by-light tensor. To obtain the constraints, we develop a systematic operator product expansion of the tensor in question to next-to-leading order in the expansion in operators. We evaluate the leading in αs contributions and derive constraints for the next-to-leading operators that are also valid nonperturbatively.

Theory of g-2

“…The SDCs on HLbL have recently seen further improvement as well: perturbative and nonperturbative corrections to the OPEs in the different asymptotic limits were studied in Refs. [62][63][64] and were used for improved matching based on a model of excited pseudoscalars in Ref. [54]; see also Refs.…”

Hadronic Light-by-Light Corrections to the Muon Anomalous Magnetic Moment

“…However, further study regarding the matching procedure is still needed. Recently, two works [118,119] were published regarding the extension of the background OPE framework to the mixed-virtuality regimes of the HLbL tensor. To illustrate the broader range of use of the background field framework that we used in this work, we briefly review their results.…”

Puzzles in the hadronic contributions to the muon anomalous magnetic moment

“…The uncertainty on HLbL is now dominated on the one hand by the contributions of hadronic resonances in the (1-2) GeV range, which were estimated using hadronic models, on the other hand by the matching to short-distance constraints (SDCs) that follow from the operator-product expansion (OPE). Therefore, since the publication of the WP, efforts were directed towards an improved evaluation of these sub-dominant contributions, addressing scalar resonances beyond the 𝑓 0 (500) [10], axial-vector resonances [11][12][13][14], tensor resonances and 𝐷-waves [15,16], which require a modification of the dispersive framework itself [17], as well as the SDCs on HLbL [12,[18][19][20]. Work is in progress to combine all these developments, together with improvements of the 𝜂, 𝜂 ′ pole contributions [21][22][23][24], into a full data-driven evaluation of 𝑎 HLbL 𝜇 .…”