TY - JOUR

T1 - Full formula for heavy quarkonium energy levels at next-to-next-to-next-to-leading order

AU - Kiyo, Y.

AU - Sumino, Y.

N1 - Funding Information:
The authors are grateful to S. Recksiegel for pointing out a misprint in Appendix A . The works of Y.K. and Y.S., respectively, were supported in part by Grant-in-Aid for Scientific Research Nos. 26400255 and 26400238 from MEXT , Japan.
Publisher Copyright:
© 2014 The Authors.

PY - 2014/12/1

Y1 - 2014/12/1

N2 - We derive a full formula for the energy level of a heavy quarkonium state identified by the quantum numbers n, ℓ, s and j, up to O(αs5m) and O(αs5mlogαs) in perturbative QCD. The QCD Bethe logarithm is given in a one-parameter integral form. The rest of the formula is given as a combination of rational numbers, transcendental numbers (π, ζ(3), ζ(5)) and finite sums (besides the 3-loop constant -3 of the static potential whose full analytic form is still unknown). A derivation of the formula is given.

AB - We derive a full formula for the energy level of a heavy quarkonium state identified by the quantum numbers n, ℓ, s and j, up to O(αs5m) and O(αs5mlogαs) in perturbative QCD. The QCD Bethe logarithm is given in a one-parameter integral form. The rest of the formula is given as a combination of rational numbers, transcendental numbers (π, ζ(3), ζ(5)) and finite sums (besides the 3-loop constant -3 of the static potential whose full analytic form is still unknown). A derivation of the formula is given.

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U2 - 10.1016/j.nuclphysb.2014.10.010

DO - 10.1016/j.nuclphysb.2014.10.010

M3 - Article

AN - SCOPUS:84908315528

SN - 0550-3213

VL - 889

SP - 156

EP - 191

JO - Nuclear Physics B

JF - Nuclear Physics B

ER -