Energy evolution of the moments of the hadron distribution in QCD jets including NNLL resummation and NLO running-coupling corrections

Abstract

The moments of the single inclusive momentum distribution of hadrons in QCD jets, are studied in the next-to-modified-leading-log approximation (NMLLA) including next-to-leading-order (NLO) corrections to the α s strong coupling. The evolution equations are solved using a distorted Gaussian parametrisation, which successfully reproduces the spectrum of charged hadrons of jets measured in e + e − collisions. The energy dependencies of the maximum peak, multiplicity, width, kurtosis and skewness of the jet hadron distribution are computed analytically. Comparisons of all the existing jet data measured in e + e − collisions in the range √ s ≈ 2-200 GeV to the NMLLA+NLO * predictions allow one to extract a value of the QCD parameter Λ QCD , and associated two-loop coupling constant at the Z resonance α s (m 2 Z ) = 0.1195 ± 0.0022, in excellent numerical agreement with the current world average obtained using other methods.

Off-shell Fragmentation

“…The z dependence in g 2 and D can be taken out with a simple trick used in the ModifiedLeading-Log Approximation (MLLA) [6]. Using ζ = ln(1/z) and Y = ln(M 2 /Λ 2 ) we can write …”

Determination ofαsat NLO*+NNLL from a global fit of the low-zparton-tohadron fragmentation functions ine+e−and DIS collisions

“…As explained in [9], a 1 and a 2 are hard constants depending on the number of active flavors N f and on the C F and N c Casimirs of the fundamental and adjoint representation of the SU(3) color group respectively; and λ = ln(Q 0 /Λ QCD ) is the hadronization parameter at which the shower stops. The terms ∝ a 1 and a 2 provide respectively NLL and NNLL corrections.…”

“…In order to incorporate O(α 3/2 s ) contributions, going beyond the O(α s ) terms obtained in older approaches, the matrix elements of the evolution Hamiltonian should be expanded up to terms ∝ Ω, followed by its diagonalisation, which results into two eigenvalues P ±± (Ω) in the new D ± (Ω, Q) basis. This procedure leads to the following equation for the eigenvector D + [9],…”

“…of the hadron multiplicity in jets) have yielded more precise α s results consistent with the world average [8]. Recently, we have presented a novel extraction of α s based on the fit of the energy evolution of the first four moments of the low-z parton-to-hadron FFs including resummations of next-to-next-to-leading logarithms (NNLL or NMLLA) complemented with NLO* running-coupling corrections 1 , where more terms have been consistently added to the perturbative expansion compared to previous works, and where a large set of experimental FF data has been systematically analysed for the first time [9][10][11]. Thus, by fitting the experimental single-inclusive hadron distribution for jets at various energies to the DG parametrization (1), one can determine α s from the corresponding energydependence of its fitted moments.…”

“…In a second stage, we do a combined study of e + e − and DIS jet FF data, including a few (older) datasets not incorporated in our previous analyses [9][10][11], and we carry out a single global fit of all DG moments, rather than independent ones for e + e − and DIS collisions, in order to extract a more precise value of α s .…”