Nonrelativistic Renormalization Group Research Articles

Bottomonium hyperfine splitting on the lattice and in the continuum

We revise the analysis of the bottomonium hyperfine splitting within the lattice nonrelativistic QCD. The Wilson coefficients of the radiatively improved lattice action are evaluated by a semianalytic approach based on the asymptotic expansion about the continuum limit. The nonrelativistic renormalization group is used to estimate the high-order radiative corrections. Our result for the $1S$ hyperfine splitting is $M_{\Upsilon(1S)}-M_{\eta_b(1S)}=52.9\pm 5.5~{\rm MeV}$. It reconciles the predictions of the continuum and lattice QCD and is in very good agreement with the most accurate experimental measurement by Belle collaboration.

Erratum: Mass of theηbandαsfrom the Nonrelativistic Renormalization Group [Phys. Rev. Lett.92, 242001 (2004)

Received 1 December 2009DOI:https://doi.org/10.1103/PhysRevLett.104.199901©2010 American Physical Society

Spin dependence of heavy quarkonium production and annihilation rates: complete next-to-next-to-leading logarithmic result

The ratio of the photon mediated production or annihilation rates of spin triplet and spin singlet heavy quarkonium states is computed to the next-to-next-to-leading logarithmic accuracy within the nonrelativistic renormalization group approach. The result is presented in analytical form and applied to the phenomenology of t t ¯ , b b ¯ and c c ¯ systems. The use of the nonrelativistic renormalization group considerably improves the behaviour of the perturbative expansion and is crucial for accurate theoretical analysis. For bottomonium decays we predict Γ ( η b ( 1 S ) → γ γ ) = 0.659 ± 0.089 ( th. ) − 0.018 + 0.019 ( δ α s ) ± 0.015 ( exp. ) keV . Our results question the accuracy of the existing extractions of the strong coupling constant from the bottomonium annihilation. As a by-product we obtain a novel result for the ratio of the ortho- and parapositronium decay rates: the corrections of order α 4 ln 2 α and α 5 ln 3 α .

Mass of the eta b and alpha s from the nonrelativistic renormalization group.

We sum up the next-to-leading logarithmic corrections to the heavy-quarkonium hyperfine splitting, using the nonrelativistic renormalization group. On the basis of this result, we predict the mass of the eta(b) meson to be M(eta(b))=9421+/-11(th)+9-8(delta alpha(s)) MeV. The experimental measurement of M(eta(b)) with a few MeV error would be sufficient to determine alpha(s)(M(Z)) with an accuracy of +/-0.003. For the hyperfine splitting in charmonium, the use of the nonrelativistic renormalization group brings the perturbative prediction significantly closer to the experimental figure.

Formula omitted]–M(Bc) splitting from nonrelativistic renormalization group

We compute the hyperfine splitting in a heavy quarkonium composed of different flavors in next-to-leading logarithmic approximation using the nonrelativistic renormalization group. We predict the mass difference of the vector and pseudoscalar charm-bottom mesons to be M(B∗c)−M(Bc)=65±24 (th)+19−16(δαs) MeV.