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SUMMARY:Sequence transformations and the asymptotic structure of perturbat
 ive QCD
DTSTART;VALUE=DATE-TIME:20260528T123000Z
DTEND;VALUE=DATE-TIME:20260528T133000Z
DTSTAMP;VALUE=DATE-TIME:20260423T043448Z
UID:indico-event-8576@indico.ific.uv.es
DESCRIPTION:We develop a unified framework based on nonlinear sequence tra
 nsformations to probe the asymptotic structure of perturbative QCD beyond 
 fixed-order expansions. Focusing on the hadronic $\\tau$-decay correction 
 $\\delta^{(0)}$\, we employ complementary approaches—Levin-type transfor
 mations and Shanks transformations implemented via Wynn’s $\\varepsilon$
 -algorithm and its generalizations\, to resum the divergent FOPT series an
 d extract higher-order information. These methods generate rational approx
 imants that encode the large-order behavior of the series\, yielding stabl
 e and consistent predictions for the coefficients $c_{n\,1}$ across indepe
 ndent transformation schemes.  We show that Levin-type transformations\, 
 through explicit remainder estimates\, and Shanks-type transformations\, v
 ia elimination of leading asymptotic errors\, provide complementary recons
 tructions of the same underlying structure. Together\, they capture renorm
 alon-driven factorial growth and provide a data-driven approximation to th
 e underlying Borel behavior without explicit multi-loop input. The resulti
 ng resummed predictions for $\\delta^{(0)}$ exhibit improved convergence a
 nd reduced truncation uncertainties. Our results establish sequence transf
 ormations as a systematic\, model-independent bridge between finite-order 
 perturbation theory and its asymptotic completion\, with direct implicatio
 ns for precision QCD phenomenology.\n\nhttps://indico.ific.uv.es/event/857
 6/
LOCATION:Universe 1001-Primera-1-1-1 - Paterna. Seminario
URL:https://indico.ific.uv.es/event/8576/
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