Precise determination of αs from relativistic quarkonium sum rules

Abstract

We determine the strong coupling α s (m Z ) from dimensionless ratios of roots of moments of the charm-and bottom-quark vector and charm pseudo-scalar correlators, dubbed R X,n q ≡ (M X,n q ) 1 n /(M X,n+1 q ) 1 n+1 , with X = V, P , as well as from the 0-th moment of the charm pseudo-scalar correlator, M P,0 c . In the quantities we use, the mass dependence is very weak, entering only logarithmically, starting at O(α 2 s ). We carefully study all sources of uncertainties, paying special attention to truncation errors, and making sure that orderby-order convergence is maintained by our choice of renormalization scale variation. In the computation of the experimental uncertainty for the moment ratios, the correlations among individual moments are properly taken into account. Additionally, in the perturbative contributions to experimental vector-current moments, α s (m Z ) is kept as a free parameter such that our extraction of the strong coupling is unbiased and based only on experimental data. The most precise extraction of α s from vector correlators comes from the ratio of the charm-quark moments R V,2 c and reads α s (m Z ) = 0.1168 ± 0.0019, as we have recently discussed in a companion letter. From bottom moments, using the ratio R V,2 b , we find α s (m Z ) = 0.1186 ± 0.0048. Our results from the lattice pseudo-scalar charm correlator agree with the central values of previous determinations, but have larger uncertainties due to our more conservative study of the perturbative error. Averaging the results obtained from various lattice inputs for the n = 0 moment we find α s (m Z ) = 0.1177 ± 0.0020. Combining experimental and lattice information on charm correlators into a single fit we obtain α s (m Z ) = 0.1170 ± 0.0014, which is the main result of this article.

Small-momentum expansion of heavy-quark correlators in the large-β0 limit and αs extractions

“…Their use in the case of the vector current was introduced in refs. [10,11] where it was shown that they can be employed for precise extractions of α s thanks to their reduced mass dependence and to the fact that these ratios can be accurately determined from R qq (s) experimental data, benefiting from positive correlations between the moments M V q,n and M V q,n+1 . The general structure of the perturbative expansion of the moments R δ q,n is…”

“…At the scales we consider here, the ambiguity of the Borel integral is numerically quite small, as we will show in the next sections, which simply reflects the fact that the non-perturbative corrections in the OPE, dominated by the gluon condensate contribution, are rather small. This is particularly true for bottom quark moments, where the non-perturbative contributions can be neglected for all practical purposes [9,11].…”

“…In obtaining the above result we are tacitly assuming that the non-perturbative corrections in the OPE are smaller than the perturbative contribution such that they can be expanded out. The knowledge of the gluon-condensate contribution shows that this is an excellent approximation for the bottom and a very good one for the charm [10,11] Since the ratios R δ q,n are designed so as to cancel the explicit mass factor of eq. (2.7), their Borel transforms do not have the term proportional to γ (0) m /u which vanishes in eq.…”

“…These coefficients, in turn, can be calculated reliably in perturbative QCD (pQCD) for not too large values of n. This type of sum-rules has been, for a long time, the basis for precise determinations of the charm-and bottom-quark masses (m c and m b ) [3][4][5][6][7][8][9]. Recently, it has been shown that dimensionless ratios of roots of moments M V q,n are also an important source of reliable information about α s [10,11]. Given the present status of the experimental measurements, and the fact that α s extractions at low energies often result in accurate predictions for α (n f =5) s (m Z ), the ratios of charm-quark moments lead to a particularly precise determination of the strong coupling.…”

The Schwarzian sector of higher spin CFTs

“…There are indications that bulk theory has an infinite number of local fields [20]. Furthermore, since the theory lacks a gap in its spectrum and owing to bounds on the branching time, sub-AdS locality might be absent [21]. These two features bear resemblance to higher spin gravity theories in AdS.…”