Measurement ofαs(Q2)from the Gross–Llewellyn Smith Sum Rule

Abstract

We extract a set of values for the Gross -Llewellyn Smith sum rule at different values of 4momentum transfer squared (Q 2 ), by combining revised CCFR neutrino data with data from other neutrino deep-inelastic scattering experiments for 1 , Q 2 , 15 GeV 2 ͞c 2 . A comparison with the order a 3 s theoretical predictions yields a determination of a s at the scale of the Z-boson mass of 0.1146 0.009 0.012 . This measurement provides a new and useful test of perturbative QCD at low Q 2 , because of the low uncertainties in the higher order calculations. [S0031-9007 (98)07266-4] PACS numbers: 12.38.Qk, 11.55.Hx, 13.15. + g, 25.30.Pt The Gross-Llewellyn Smith (GLS) sum rule [1] predicts the integral R 1 0where xF 3 ͑x, Q 2 ͒ is the nonsinglet structure function measured in neutrino-nucleon (nN) scattering. In the naive quark parton model, the value of this integral should be three, the number of valence quarks in the nucleon. In perturbative quantum chromodynamics (PQCD), this integral is a function of a s ͑Q 2 ͒, the strong coupling constant.The GLS integral is one of the few physical quantities which has been calculated to next-to-next-to-leadingorder (NNLO) of perturbative QCD [2], and there are estimates of the next order term [3] [i.e., O͑a 4 s ͒]. In addition, there is a nonperturbative higher-twist contribution, proportional to 1͞Q 2 . This yields the GLS integral as a function of a s , of the form GLS 3

Extraction ofαsfrom the Gross–Llewellyn Smith sum rule using Borel resummation

“…We then confronted the resummed expressions with the Fermilab CCFR Collaboration data [13] for the GLS (at Q 2 = 2, 3.16 GeV 2 ) which already include the target mass corrections. Our central value prediction for the QCD coupling parameter, corresponding to the central GLS values of the CCFR, is α s (M Z ) ≈ 0.117 [see Eqs.…”

“…The values of the GLS sum rule M 3 (Q 2 ), for various specific Q 2 , have been obtained from the experimentally extracted values of the structure function F 3 (x; Q 2 ), by the Fermilab CCFR Collaboration [13]. They have large systematic experimental uncertainties, primarily because of the uncertainties in the normalization of xF 3 and in the integration in the regions x ≪ 1 and x > 0.5.…”

“…The CCFR group [13,14] carried out a numerical analysis similar to that of the authors of Ref. [46], but with the newer, lower, experimental data (34)-(35) for ∆(Q 2 ), and using in the TPS-part MS RSch (and RScl µ 2 = Q 2 ).…”

“…(27), the predicted value of α s (M 2 Z ) would decrease by about 0.002. Furthermore, the CCFR group mentioned that their central value increases to α s (3 GeV 2 ) ≈ 0.305 [14] and α s (M 2 Z ) = 0.118 [13,14] 14 when they set the twist-four (d = 2) contribution approximately equal to zero. Such higher-twist values for the GLS sum rule are suggested by the calculation by the authors of Ref.…”

“…In this work we apply them to the GLS sum rule. The CCFR analysis [13,14] of the GLS sum rule was based on evaluation of the truncated perturbation series (TPS) in MS scheme. Aside from the inherent ambiguity of the higher-twist contributions, this method gives predictions which are not stable under the inclusion of an additional term (∼ α 4 s ) in the TPS.…”