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High Precision QCD Calculation by Renormalon Subtraction and Applications to Heavy Quark Systems

Hayashi, Yuuki 東北大学

2023.03.24

概要

To overcome renormalon problem in QCD
Frontier experiments at the LHC and Belle II have validated the Standard Model (SM) of
particle physics to a high degree of accuracy, which has required theorists to accurately calculate observables. Perturbation theory is a powerful method to systematically calculate
physical quantities in general quantum field theory. In particular in quantum chromodynamics (QCD), recent improvements in computational techniques and algorithms have
made it possible to achieve higher-order calculations for various quantities. For example,
the 5-loop (next-to-next-to-next-to-next-to leading order (N4 LO) level) correction to the
QCD beta function [1], the 3-loop (N3 LO level) correction to the static QCD potential
[2, 3, 4], and the 4-loop (N3 LO level) correction to the heavy quark mass relation (poleMS mass relation) [5, 6, 7] were calculated. As a property of QCD, the QCD effects give
important contributions to observables on a wide range of scales. Due to the asymptotic
freedom of QCD, the higher-order perturbative calculations make the theoretical predictions more precise for the high-scale observables. On the other hand, for systems with a
scale of about O(1 − 10) GeV, specifically those involving bottom or charm quarks, the
theoretical uncertainties caused by ‘renormalons’ have limited the accuracy of perturbative calculations.
Renormalon [8, 9, 10, 11] is a concept that originates from an IR gluon in a particular
loop diagram, which is known to cause the perturbative coefficients to factorially diverge.
This is one of the reasons why perturbative expansion is asymptotic series, indicating that
it is impossible to calculate the true value of observables by perturbative calculations
alone in principle. Considering renormalons, the best prediction accuracy achievable
using perturbative calculations is estimated as (ΛQCD /Q)2u with (half-)integer u for an
observable with typical scale Q ≫ ΛQCD . Here, ΛQCD ∼ 300 MeV is the non-perturbative
scale of QCD, indicating that the uncertainty caused by renormalon, which is the limit
of perturbative calculations, is associated with a non-perturbative (low-energy) physics.
For a system of the electroweak scale physics, ΛQCD /Q ∼ 0.1% would be negligible at
present, while for a system of the bottom or charm quarks, ΛQCD /Q ∼ 10% jeopardizes the
precision of the prediction significantly. Today, in the era of high-precision experiments on
flavor physics, it is required to remove the uncertainty due to renormalons from theoretical
predictions. ...

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