Short-distance HLbL contributions to the muon anomalous magnetic moment beyond perturbation theory
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Springer
Received: September 1, Revised: September 22, Accepted: September 24, Published: October 30,
2020 2020 2020 2020
Johan Bijnens,a Nils Hermansson-Truedsson,b Laetitia Laubb and Antonio Rodr´ıguez-S´ ancheza a
Department of Astronomy and Theoretical Physics, Lund University, S¨ olvegatan 14A, SE 223-62 Lund, Sweden b Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Universit¨ at Bern, Sidlerstrasse 5, CH–3012 Bern, Switzerland
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: The hadronic light-by-light contribution to the muon anomalous magnetic moment depends on an integration over three off-shell momenta squared (Q2i ) of the correlator of four electromagnetic currents and the fourth leg at zero momentum. We derive the short-distance expansion of this correlator in the limit where all three Q2i are large and in the Euclidean domain in QCD. This is done via a systematic operator product expansion (OPE) in a background field which we construct. The leading order term in the expansion is the massless quark loop. We also compute the non-perturbative part of the next-to-leading contribution, which is suppressed by quark masses, and the chiral limit part of the next-to-next-to leading contributions to the OPE. We build a renormalisation program for the OPE. The numerical role of the higher-order contributions is estimated and found to be small. Keywords: Nonperturbative Effects, Perturbative QCD, Precision QED ArXiv ePrint: 2008.13487
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)203
JHEP10(2020)203
Short-distance HLbL contributions to the muon anomalous magnetic moment beyond perturbation theory
Contents 1 Introduction
1
2 The HLbL tensor
2 5 5 9 10 12 12 13 13 13 13 15 15
4 Calculation of the HLbL contributions 4.1 The quark loop 4.2 Contributions from diagrams with one cut quark line 4.3 Contributions from four-quark operators 4.4 The gluon matrix element
16 16 18 21 22
5 Numerical results
23
6 Conclusions and prospects
24
ˆi A A set of Lorentz projectors for the Π
27
B Four-quark reduction
30
ˆi C Explicit expressions for the Π C.1 The quark loop C.2 Some massless quark loop limits C.2.1 Q1 ∼ Q3 Q2 C.2.2 Q1 ∼ Q2 Q3 C.2.3 Q2 ∼ Q3 Q1 C.3 Contributions from diagrams with one-cut quark lines C.4 Gluon matrix element contributions
32 32 37 38 38 38 39 41
D Derivation of (4.15) up to n = 3
43
–i–
JHEP10(2020)203
3 The operator product expansion: a theoretical description 3.1 General framework 3.2 The operator mixing 3.2.1 Qµν 2 3.2.2 Qµν 3−6 3.2.3 Qµν 7 ˆ (µ) 3.2.4 Full matrix U MS 3.3 Values of the matrix elements µν 3.3.1 Qµν 5 and Q6 µν µν 3.3.2 Qµν 2 , Q3 and Q4 µν 3.3.3 Q7 µν 3.3.4 Qµν 8,1 and Q8,2
1
Introduction
showing a 3.7σ tension with the very precise experimental value [2, 3], −11 aexp . µ = 116 592 091(63) × 10
(1.2)
The experimental value is expected to be significantly improved [4, 5]. In case the discrepancy grows thi
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