Heavy quark expansion for heavy-light light-cone operators

Abstract

We generalize the celebrated heavy quark expansion to nonlocal QCD operators. By taking nonlocal heavy-light current on the light-cone as an example, we confirm that the collinear singularities are common between QCD operator and the corresponding operator in heavy quark effective theory (HQET), at the leading power of 1/M expansion. Based on a perturbative calculation in operator form at one-loop level, a factorization formula linking QCD and HQET operators is investigated and the matching coefficient is determined. The matching between QCD and HQET light-cone distribution amplitudes (LCDAs) as well as other momentum distributions of hadron can be derived as a consequence.

B -meson light-cone distribution amplitude from Euclidean quantities

“…[57]. From the perspectives of the continuum QCD, the newly introduced distribution amplitude ψ þ B ðx; μÞ can be further matched onto the Euclidean HQET quantity φ þ B ðξ; μÞ by integrating out the short-distance fluctuations at the heavy-quark mass scale, in analogy to the hard-collinear factorization formula obtained in [58,59]. Furthermore, determining hadronic distribution functions on the light shell can be also achieved by constructing the spatial correlation functions of suitable local partonic currents and by establishing the desired QCD factorization formulas in coordinate space directly [60][61][62][63][64].…”

Inverse moment of the $B$-meson quasi distribution amplitude

“…µ Q and µ L are the scales that define the IMs of quasi and light-cone DAs, respectively. We note that, a very similar multiplication-type matching relation was introduced in [45], which connects the IMs of LCDAs defined in HQET and full QCD; it can also be reproduced from the convolution-type matching between the LCDAs defined in QCD and HQET [46,47]. Another example is the matching of IMs of quasi-PDF and the normal PDF.…”

B -meson Ioffe-time distribution amplitude at short distances

“…By including the anomalous dimension of the decay constant, one will find that the above equation reproduces the RGE for heavy-light light-cone operator (see, e.g., Ref. [37,38]).…”

“…Similar to the PDF case, one can use the nonlocal light-cone OPE. To determine the hard function, we also need the oneloop correction to the light-cone ITDA, which can be extracted from the one-loop correction to the light-cone operator [37]. The result reads…”