References - Bogoliubov Laboratory of Theoretical Physics - JINR

√
δΔq8 x for Δq8 and γΔGx for ΔG. to provide the possibility of sign-changing scenarios
for Δs and ΔG, respectively.
We analyze the inclusive A1 and semi-inclusive Ah 1 asymmetries. We work in MS
factorization scheme. We use here the latest NLO parameterization on fragmentation
functions from Ref. [6]. Calculating F2 and F h 2 we use parameterization for R from [7]
and the recent NLO parameterization on unpolarized PDFs from Ref. [8].
For our analysis we collected all accessible in literature polarized DIS and SIDIS data.
We include the inclusive proton, deuteron and neutron data by SMC, E143, E155, E154,
COMPASS, HERMES, CLAS, The semi-inclusive data are collected by SMC, HERMES
and COMPASS. We include also the latest COMPASS data from Ref [3]. In total we have
232 points for the inclusive polarized DIS and 202 points for semi-inclusive polarized DIS.
For 16 fit parameters χ2 0|inclusive = 188.4 andχ2 0|semi−inclusive = 194.8 for DIS and SIDIS
data, while χ2 0 |total = 383.9 for the full set of data (434 points). Thus, one can conclude
that the fit quality is quite good: χ2 0/D.O.F. � 0.84.
The optimal values of our fit parameters are presented in Table 1. Certainly, the
Table 1: Optimal values of the global fit parameters at the initial scale Q 2 0 =1GeV 2 .
ΔΣ Δq3 Δq8
α 1.0227 -0.6342 -0.7916
β 3.3891 3.1418 = βΔq 3
γ 0.0 (fixed) 23.9180 36.8400
δ 0.0 (fixed) 0.0 (fixed) -13.7480
η 0.3846 1.2660 0.6170
ΔG Δū Δ ¯ d
α 0.9040 -0.3506 0.2802
β = βΔū 15.0 (fixed) = βΔū
γ -5.6703 0.0 (fixed) 0.0 (fixed)
δ 0.0000 (fixed) 0.0 (fixed) 0.0 (fixed)
η -0.1828 0.0672 -0.0792
construction of the best fit should be accompanied by the reliable method of uncertainties
estimation. We choose the modified Hessian method [9], [10] which well works (as well
as the Lagrange multipliers method – see [4] and references therein) even in the case of
deviation of χ 2 profile from the quadratic parabola, and was successfully applied in a lot of
physical tasks. Besides, very important question arises about choice of Δχ 2 determining
the uncertainty size. The standard choice is Δχ 2 = 1, just as we did before in Ref.
[5]. However, the such choice of Δχ 2 can lead to underestimation of uncertainties. The
alternative choice of Δχ 2 is based on the equation for the cumulative χ 2 distribution. In
our case (16 parameters) the Δχ 2 value is equal to 18.065. We calculate the uncertainties
for both Δχ 2 =1andΔχ 2 =18.065 options. The first moments of PDFs together with
their uncertainties are presented in Table 2.
Let us now discuss the obtained parameterization. First, one can see that the results
on the first moments Δ1Σ ≡ ηΔΣ and Δ1G ≡ ηΔG are very close to the respective
results (scenario with ΔG