A paragraph in"Handbook of QCD" by Mueller

[MathematicalPhysicist]

On page 210, it's written the following paragraph:

In particular the PQCD results for the pion form factor, the transition form factor $F_{\gamma \pi}(Q^2)$, and the $\gamma\gamma \to \pi \pi$ amplitudes are theorems of QCD and are as rigorous as the predictions for $R_{e^+e^-}(s)$, the evolution equations for structure functions, etc. Although the perturbative QCD analysis is complex, it's hard to imagine that any other viable description would be simpler. At this point there is no other theoretical approach which provides as comprehensive a description of exclusive phenomena.

What has changed since then? have we found a different theoretical approach to explain exclusive phenomena?

 

[ohwilleke]

The current state of the art in terms of calculating form factors and related quantities from first principles is the article whose abstract and citation I provide below, which is the first "from scratch" theoretical calculation of a PDF for protons and neutrons that is fully consistent with experimental results to within the relevant margins of error (which aren't small, as in all QCD calculations).

But this is done with Lattice QCD rather than PQCD. I am also not aware of comparable Lattice QCD work that is as successful as this nucleon paper being done for the pion form factor, although that surely must be coming very soon, if it hasn't already, as it is conceptually a very similar project and should actually be easier in some respects.

One of the great challenges of QCD is to determine the partonic structure of the nucleon from first principles. In this work, we provide such a determination of the unpolarized parton distribution function (PDF), utilizing the non-perturbative formulation of QCD on the lattice. We apply Radyushkin's pseudo-distribution approach to lattice results obtained using simulations with the light quark mass fixed to its physical value; this is the first ever attempt for this approach directly at the physical point. The extracted coordinate-space matrix elements are used to find the relevant physical Ioffe time distributions from a matching procedure. The full Bjorken-x dependence of PDFs is resolved using several reconstruction methods to tackle the ill-conditioned inverse problem encountered when using discrete lattice data. Another novelty of this calculation is the consideration of the combination with antiquarks qv+2q¯. The latter, together with the non-singlet valence quark PDF qv, provides information on the full distribution. Good agreement is found with PDFs from global fits already within statistical uncertainties and it is further improved by quantifying several systematic effects. The results presented here are the first ever ab initio determinations of PDFs fully consistent with global fits in the whole x-range. Thus, they pave the way to investigating a wider class of partonic distributions, such as e.g. singlet PDFs and generalized parton distributions. Therefore, essential and yet missing first-principle insights can be achieved, complementing the rich experimental programs dedicated to the structure of the nucleon.

Manjunath Bhat, Krzysztof Cichy, Martha Constantinou, Aurora Scapellato, "Parton distribution functions from lattice QCD at physical quark masses via the pseudo-distribution approach" Physics Review D (February 24, 2021) (open access version at arXiv:2005.02102) https://journals.aps.org/prd/abstract/10.1103/PhysRevD.103.034510.