Lattice QCD calculation of hadronic light-by-light scattering

G. Venanzoni (Muon g-2), (2014), arXiv:1411.2555 [physics.ins-det]

Original

2014

Cited alongside, same era.

V. Pauk and M. Vanderhaeghen, Phys.Rev. D90

Original

2014

Cited alongside, same era.

We use the notation and conventions of [ 26 ] unless otherwise stated. The metric is mostly minus. The fine-structure constant reads α ≡ e 2 / ( 4 ​ π ) ≃ 1 / 137 \alpha\equiv{e^{2}}/({4\pi})\simeq 1/137 . The optical theorem for the scattering of scalar particles reads Im ℳ ( p 1 , p 2 → p 1 , p 2 ) = 2 E cm p cm σ tot ( p 1 , p 2 → anything ) {\rm Im}{\cal M}(p_{1},p_{2}\to p_{1},p_{2})=2E_{\rm cm}p_{\rm cm}\sigma_{\rm tot}(p_{1},p_{2}\to{\rm anything}) , with E cm E_{\rm cm} the total center-of-mass energy and p cm p_{\rm cm} the norm of the three-momentum of one of the particles in the center-of-mass frame

Cited in the paper.

We use capital letters to denote ‘Euclidean’ vectors, i.e. the metric in the scalar product of two such vectors is understood to be Euclidean

Cited in the paper.

In the notation of [ 8 ] , ℳ TT = 1 2 ( M + + , + + + M + − , + − ) {\cal M}_{\rm TT}=\frac{1}{2}({M}_{++,++}+{M}_{+-,+-}) in terms of the helicity amplitudes. By virtue of the optical theorem, the imaginary part of ℳ TT {\cal M}_{\rm TT} is proportional to the total unpolarized γ ∗ ​ γ ∗ → hadrons \gamma^{*}\gamma^{*}\to{\rm hadrons} cross-section. For the explicit expression of R μ ​ ν R^{\mu\nu} , see [ 11 ]

Cited in the paper.

One might be able to extend the reach to | ν | = ν π |\nu|=\nu_{\pi} with methods in the spirit of [ 27 ]

Cited in the paper.

M. Lüscher, S. Schaefer, et al. , “openQCD,” http://luscher.web.cern.ch/luscher/openQCD/

Cited in the paper.

G. Eichmann, C. S. Fischer, and W. Heupel, (2015), arXiv:1505.06336 [hep-ph]

Original

2015

Closest in time.