_{F}– symmetrical tip. Left: use

*F*– rescaling. Right: with

_{π}*you*to adjust the scale. The blue and green dots correspond to the two different sets of improvement coefficients (see section III). For clarity, the extrapolated results have been shifted to the left. Credit:

_{0}*High Energy Physics – Network*(2022). DOI: 10.48550/arXiv.2206.06582

The anomalous magnetic moment of the muon is a crucial parameter in particle physics because it allows precision testing of the established Standard Model. A new measurement of this quantity last year caused a stir because it reaffirmed a significant deviation from the theoretical prediction – in other words, the anomalous magnetic moment is larger than expected.

Physicists calculate the theoretical prediction based on the currently valid Standard Model of particle physics. In 2020, the Muon g-2 Theory Initiative – a group of 130 physicists with strong representation from Mainz – produced a consensus estimate which has since been accepted as a benchmark. Since then, several teams, including that of Prof. Hartmut Wittig from the PRISMA+ Pole of Excellence at the Johannes Gutenberg University Mainz (JGU), published new results on the contribution of the strong interaction using numerical lattice QCD simulations, which suggest that the la theoretical prediction tends towards experimental value.

“Even if it turns out that the discrepancy between theoretical and experimental results is actually smaller than we thought, it would still represent a major discrepancy,” explains Hartmut Wittig. “But it is still imperative for us to first understand why using different theoretical methods leads to such dissimilar results.”

**A new mystery that needs a solution**

The anomalous magnetic moment receives contributions from all fundamental interactions except gravity. The strong interaction or strong nuclear force which acts between elementary particles of matter called quarks and which is mediated by the exchange of gluons, is of particular importance when it comes to testing the Standard Model.

Recent calculations have focused on the so-called hadronic vacuum polarization (HVP) contribution to the muon magnetic moment, in which quark-antiquark pairs are continuously generated from a vacuum for a fraction of a second before vanishing at new.

“This is an extremely complex process to manage, and the level of uncertainty in the theoretical prediction is therefore largely determined by the effects of the strong interaction,” adds Wittig. As standard computational techniques cannot be used in this context or have not been sufficiently accurate to date, in the current consensus document the contribution of HVP has been determined using experimental data on various particle accelerators .

Ideally, the contribution of HVP could be calculated without relying on experimental data, using only quantum chromodynamics (QCD). QCD is the fundamental theory of the strong interaction between quarks mediated by gluons. However, QCD is an extremely difficult theory to handle in practice. The Mainz team uses a technique known as lattice field theory for this purpose.

Here, quarks and gluons are spread out over a discrete grid of dots that represent space-time, much like atoms in a crystal. The contribution of HVP to the anomalous magnetic moment of the muon can then be determined using supercomputers.

“A few years ago, the enormous technical challenges of such a calculation made it impossible to determine the HVP contribution with the necessary accuracy using lattice QCD. In the meantime, we have refined the method so that the accuracy of our result could correspond to that of the traditional approach which resorts to the use of experimental data,” emphasizes Wittig.

In the paper now available on the arXiv preprint server, Wittig and his team present the results of calculating a fraction of HVP particularly suitable for testing the consistency of the results of various network calculations and comparing them to estimates based on the traditional method. “As our result is equally accurate, it can be said that the lattice-based QCD calculation has passed its baptism of fire, which in itself is a huge success. Moreover, it is becoming increasingly clear that our QCD-based calculations really correspond to the newly presented calculations the results of the other teams.”

Wittig now turns his attention to the magnetic moment of the muon: “Our new lattice calculations make it more evident that the theoretical prediction value is likely to approach the measured result. This has generated quite a bit of excitement among my colleagues. We now focus on the problem of why the different methods used to assess the contribution of HVP should produce discordant results.And those of our colleagues who might be disappointed that the gap with the standard model is narrowing can be reassured by the fact that our new calculus has not made the gap between theory and experiment completely disappear.However you look at it, there is no doubt that there is a gap that requires an explanation. We still have a lot to understand.

Evidence of new physics from the magnetic moment of the muon? Maybe not, according to a new theoretical calculation

**More information:**

M. Cè et al, Observable window for the contribution of hadronic vacuum polarization to the g−2 muon of the QCD lattice, arXiv:2206.06582v1 [hep-lat]. doi.org/10.48550/arXiv.2206.06582

Provided by Universitaet Mainz

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