Abstract
Properly separating and subtracting renormalons in the framework of the op- erator product expansion (OPE) is a way to realize high precision computation of QCD effects in high energy physics. We propose a new method (FTRS method), which enables to subtract multiple renormalons simultaneously from a general observable. It utilizes a property of Fourier transform, and the leading Wilson coefficient is written in a one-parameter integral form whose integrand has suppressed (or vanishing) renormalons. The renormalon subtraction scheme coincides with the usual principal-value prescription at large orders. We perform test analyses and subtract the mathcal{O}left({Lambda}_{mathrm{QCD}}^4right) renormalon from the Adler function, the mathcal{O}left({Lambda}_{mathrm{QCD}}^2right) renormalon from the B → Xul overline{nu} decay width, and the mathcal{O} (ΛQCD) and mathcal{O}left({Lambda}_{mathrm{QCD}}^2right) renormalons from the B, D meson masses. The analyses show good consistency with theoretical expectations, such as improved convergence and scale dependence. In particular we obtain overline{Lambda} FTRS = 0.495 ± 0.053 GeV and ( {mu}_{pi}^2 )FTRS = −0.12 ± 0.23 GeV2 for the non-perturbative parameters of HQET. We explain the formulation and analyses in detail.
Highlights
After the discovery of the Higgs boson, particle physics entered the era of high precision physics through frontier experiments, such as the experiments at the LHC, the BELLE II experiment, etc
To evaluate [X(Q)]principal value (PV), we extend the formulation developed in ref. [18], which works for VQCD(r)
For large k, [X(Q)]FTRS converges to the renormalon-subtracted Wilson coefficient in the PV prescription, provided that the following assumptions which we made are satisfied: (i)Renormalons cancel between the Wilson coefficient and the corresponding operator matrix elements in the operator product expansion (OPE); (ii)The QCD beta function beyond five loops does not alter the analytic structure of the roots of the beta function which holds up to N4LL; (iii)There are no singularities except those which we suppress by the sine factor in the Borel plane
Summary
After the discovery of the Higgs boson, particle physics entered the era of high precision physics through frontier experiments, such as the experiments at the LHC, the BELLE II experiment, etc. In the OPE of an observable, ultraviolet (UV) and infrared (IR) contributions are factorized into the Wilson coefficients and non-perturbative matrix elements, respectively The former are calculated in perturbative QCD, while the latter are determined by non-perturbative methods. A similar cancellation was observed in the B meson partial widths in the semileptonic decay modes [6–8] These features were applied successfully in accurate determinations of fundamental physical constants such as the heavy quark masses [9–13], some of the Cabbibo-Kobayashi-Maskawa matrix elements [14, 15], and the strong coupling constant αs [16]. In appendix G, we investigate the case where unsuppressed renormalons (or singularities in the Borel plane) remain in the momentum space in the FTRS method and estimate the effects
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