scholarly journals Large order behavior in perturbation theory of the pole mass and the singlet static potential

2001 ◽  
Author(s):  
Antonio Pineda
Keyword(s):  
Perturbation Theory ◽  
Pole Mass ◽  
Static Potential ◽  
Large Order

scholarly journals Determination of α(Mz) from an hyperasymptotic approximation to the energy of a static quark-antiquark pair

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Cesar Ayala ◽  
Xabier Lobregat ◽  
Antonio Pineda
Keyword(s):  
Perturbation Theory ◽  
Energy Range ◽  
Short Distance ◽  
Weak Coupling ◽  
Strong Consistency ◽  
Lattice Data ◽  
Static Potential ◽  
Static Energy ◽  
Static Quark

Abstract We give the hyperasymptotic expansion of the energy of a static quark-antiquark pair with a precision that includes the effects of the subleading renormalon. The terminants associated to the first and second renormalon are incorporated in the analysis when necessary. In particular, we determine the normalization of the leading renormalon of the force and, consequently, of the subleading renormalon of the static potential. We obtain $$ {Z}_3^F $$ Z 3 F (nf = 3) = $$ 2{Z}_3^V $$ 2 Z 3 V (nf = 3) = 0.37(17). The precision we reach in strict perturbation theory is next-to-next-to-next-to-leading logarithmic resummed order both for the static potential and for the force. We find that the resummation of large logarithms and the inclusion of the leading terminants associated to the renormalons are compulsory to get accurate determinations of $$ {\Lambda}_{\overline{\mathrm{MS}}} $$ Λ MS ¯ when fitting to short-distance lattice data of the static energy. We obtain $$ {\Lambda}_{\overline{\mathrm{MS}}}^{\left({n}_f=3\right)} $$ Λ MS ¯ n f = 3 = 338(12) MeV and α(Mz) = 0.1181(9). We have also MS found strong consistency checks that the ultrasoft correction to the static energy can be computed at weak coupling in the energy range we have studied.

Three-quark static potential in perturbation theory

2010 ◽  
Vol 81 (5) ◽  
Author(s):  
Nora Brambilla ◽  
Jacopo Ghiglieri ◽  
Antonio Vairo
Keyword(s):  
Perturbation Theory ◽  
Static Potential

X. Large order estimates in perturbation theory

1979 ◽  
Vol 49 (2) ◽  
pp. 205-213 ◽  
Author(s):  
J. Zinn-Justin
Keyword(s):  
Perturbation Theory ◽  
Large Order

scholarly journals Sphalerons and large order behaviour of perturbation theory in lower dimension

1995 ◽  
Vol 434 (1-2) ◽  
pp. 245-263 ◽  
Author(s):  
V.A. Rubakov ◽  
O.Yu. Shvedov
Keyword(s):  
Perturbation Theory ◽  
Lower Dimension ◽  
Large Order
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