On the next-to-next-to-leading order QCD corrections to heavy-quark production in deep-inelastic scattering

Abstract

The contribution of quarks with masses m Λ QCD is the only part of the structure functions in deepinelastic scattering (DIS) which is not yet known at the next-to-next-to-leading order (NNLO) of perturbative QCD. We present improved partial NNLO results for the most important structure function F 2 (x, Q 2 ) near the partonic threshold, in the high-energy (small-x) limit and at high scales Q 2 m 2 ; and employ these results to construct approximations for the gluon and quark coefficient functions which cover the full kinematic plane. The approximation uncertainties are carefully investigated, and found to be large only at very small values, x 10 −3 , of the Bjorken variable.

Charm production and QCD analysis at HERA and LHC

“…At next-to-next-to-leading order (NNLO) (O(α 3 s )) only approximate calculations are available. For F 2 , four out of the five massive Wilson coefficients are known at large scales Q 2 [64][65][66][67][68], and an estimate has been made for the remaining coefficient [69] based on the anticipated small-x behavior, a series of moments [70], and two-loop operator matrix elements [71,72]. e.g.…”

“…in Ref. [69] combined approximate expressions for three kinematic limits are given: in the limit of high partonic centre-of-mass energy squared,ŝ m 2 Q , in the threshold region,ŝ 4m 2 Q , and in the high-scale region Q 2 m 2 Q .…”

“…68 The correlations 67 Except that for dataset 5 in contrast to [60] all Q 2 bins were used including the lowest one Q 2 = 2.5 GeV 2 ; the applicability of pQCD for the charm data is ensured by the presence of a massive c quarkantiquark pair in the final state. 68 For the Λ + c measurement from [177], where no doubledifferential distribution is available, the single-differential cross sec- 69 The 3.5% luminosity uncertainty was treated as correlated between the charm and beauty measurements. In addition to the experimental uncertainties, the correlated fragmentation-fraction uncertainties were assigned to the data.…”

Phenomenology of QCD threshold resummation for gluino pair production at NNLL

“…They are formally treated as part of the hard scattering function on which the exponent has to be matched. Therefore, one introduces a second matching term g 0 C ij, I [23] as a power series in α s which is actually a function of N . If Coulomb corrections are not considered, g 0 C ij, I reduces to a factor one.…”

Three-Loop Contributions to the Gluonic Massive Operator Matrix Elements at General Values of N

“…The extension of the renormalization of the massive OMEs is given in [14]. The logarithmic contributions at general values of N for the contributions to F 2 (x, Q 2 ) are available [15][16][17]. 2 Furthermore, the NNLO heavy flavor Wilson coefficients in the asymptotic region were calculated for the structure function F L (x, Q 2 ) [3,20].…”