Renormalons and multi-loop estimates in scalar correlators, Higgs decay and quark-mass sum rules

Broadhurst, D.J.; Kataev, A.L.; Maxwell, C.J.

Abstract

The single renormalon-chain contribution to the correlator of scalar currents in QCD is calculated in the -scheme in the limit of a large number of fermions, Nf. At n-loop order we find that in the -scheme the factorial growth of the perturbative coefficients due to renormalons takes over almost immediately in the Euclidean region. The essential differences between the large-order growth of perturbative coefficients in the present scalar case, and in the previously-studied vector case are analysed. In the timelike region a stabilization of the corresponding perturbative series for the imaginary part, with n-loop behaviour Sn/[log(s/Λ2)]n−1, where Sn is essentially constant for n≤6, is observed. Only for n≥7 does one discern the factorial growth and alternations of sign. We use the new all-orders results to scrutinize the performance of multi-loop estimates, using a large-β0=(11Nc−2Nf)/12 approximation, the so-called “naive nonabelianization” procedure, and within the effective charges approach. The asymptotic behaviour of perturbative coefficients, in both large-Nf and large-Nc limits, is analysed both in the spacelike and timelike regions. A contour-improved resummation technique in the timelike region is developed. Some subtleties connected with scheme-dependence are analysed, and illustrated using results in the - and V-schemes. The all-orders series under investigation are summed up with the help of the Borel resummation method. The results obtained are relevant to the analysis of the theoretical uncertainties in the 4-loop extractions of the running and invariant s-quark masses from QCD sum rules, and in calculations of the Higgs boson decay width into a quark–antiquark pair.

Citation

Broadhurst, D., Kataev, A., & Maxwell, C. (2001). Renormalons and multi-loop estimates in scalar correlators, Higgs decay and quark-mass sum rules. Nuclear Physics B, 592(1-2), 247-293. https://doi.org/10.1016/s0550-3213%2800%2900575-7

• Journal Article Type: Article
• Publication Date: Jan 1, 2001
• Deposit Date: May 6, 2008
• Publicly Available Date: May 6, 2008
• Journal: Nuclear Physics B
• Print ISSN: 0550-3213
• Electronic ISSN: 1873-1562
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 592
• Issue: 1-2
• Pages: 247-293
• DOI: https://doi.org/10.1016/s0550-3213%2800%2900575-7
• Keywords: Renormalons, QCD perturbative series, Resummation of the effects of analytical continuation.
• Public URL: https://durham-repository.worktribe.com/output/1590810