Pis'ma v ZhETF, vol. 101, iss. 3, pp. 155-159 © 2015 February 10
Strong coupling constant from QCD analysis of the fixed-target DIS
data
A. V. KotikovV, V. G. Krivokhizhin+, B. G. Shaikhatdenov+
II Institut fur Theoretische Physik, Universität Hamburg, 22761 Hamburg, Germany Laboratory of Theoretical Physics Joint Institute for Nuclear Research, 141980 Dubna, Russia + Joint Institute for Nuclear Research, 141980 Dubna, Russia Submitted 10 December 2014
Deep inelastic scattering data on F2 structure function obtained in fixed-target experiments were analyzed in the valence quark approximation with a next-to-next-to-leading-order accuracy. The strong coupling constant is found to be aa (Ml) = 0.1157 ±0.0022 (total exp.error), which is seen to be well compatible with the average world value. This study is meant to at least partially explain differences in the predictions for observables at the LHC found recently, caused by usage of various sets of parton distribution functions obtained by different groups.
DOI: 10.7868/S0370274X15030017
1. Introduction. The cross-section values in LHC experiments, along with the extracted parameters, such as, for example, the mass of t quark and the strong coupling constant as(M|), depend strongly on the type of parton distribution funstions (PDFs) used in the analyses. Recently, large differences are found in both the cross-section values and extracted parameters, which were obtained by using Alekhin-Blumlein-Moch (ABM) [1] and Jimenez-Delgado-Reya (JR) PDF sets [2]. The latter were in turn derived mostly by fitting deep inelastic scattering (DIS) data. Other groups doing such an analysis, namely, CTEQ [3], NN21 Collaborations [4], and MSTW group [5], included in their fits additional experimental data (see the recent review [6] and references therein).
The differences are sometimes seen to be much larger than the individual PDF uncertainties [6, 7] and give rise to mostly different shapes of gluon densities and strong coupling constant as {Ml), which are in turn strongly correlated. The values of as(Af§) obtained using the ABM sets [1, 8] are considerably lower than those derived in other cases and can partially be explained [9] by the usage of the fixed flavor number scheme in the the ABM sets.
In the present brief report we will focus on the strong coupling constant value. Let us note another way of decreasing the value of as(M|) observed in [f, 8], which is associated with a so-called BCDMS effect. The effect comes about upon analyzing stiffly accurate BCDMS
-'-'e-mail: kotikov@mail.desy.de
data [10-12], which are very important in fitting the value of as(Af§), especially in the analyses based on mostly DIS data, which is the case for ABM sets. However, as it was shown in [13], those precise data were collected with large systematic errors within certain ranges, which can presumably be responsible for an effective decrease in the value of as(M|) (see [13-15]).
One of the most accurate processes to extract as(M|) values is the valence part of DIS structure function (SF) F2, which is free from any correlations with gluon density. Here we will only consider the valence part2'. The study closely follows those devoted to similar analyses [14, 15] performed at the next (NLO) and next-to-next-to-leading-order (NNLO) levels, respectively, which means that we consider systematic errors in BCDMS data in a different manner than it was done in [15] in order the study their influence on our results obtained in [14, 15], where as {Ml) value was shown to increase when we cut out BCDMS data with the largest systematic errors. Those results have recently been criticized in [8], where it was found that this effect is negligible. The authors of [8] supposed that the as{Ml) value increased due to systematic errors being neglected in BCDMS data in the analyses done in [14, 15].
Here, we will show that including the systematic errors in BCDMS data in a different way does not signif-
In the present paper we restrict analysis to the large x region. Consequently, the analysis is dubbed a "valence quark" one (simply signaling the absence of gluons) but actually the data on the total structure function F2(x,Q2) will be considered.
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A. V. Kotikov, V. G. Krivokhizhin, B. G. Shaikhatdenov
icantly alter our results derived in [14, 15]. Upon omitting BCDMS data with the largest systematic errors we obtain larger values of the coupling constant normalization as(M§) fitted to the experimental data. Moreover, the effect does not strongly depend on specific cut values, as it was observed earlier in [14, 15].
DIS structure function (SF) F2{x, Q2) is dealt with by analyzing SLAC, NMC, and BCDMS experimental data [10-12,16-18] at NNLO of massless pertur-bative QCD. As in our previous papers the function F2(x,Q2) is represented as a sum of the leading twist i1|QCD(x, Q2) and twist four terms
F2(X,Q2) = ffQCD(x,Q2
1 +
/14(3
~Q2
(i)
where F:f(^CD(x, Q2) denotes the twist-2 part together with target mass corrections. The part ~ h±(x) denotes the nonzero twist term corrections. For more details concerning an approach to analyzing the experimental data we adopt refer to [14, 19].
2. Results. As is known a valence quark analysis features no gluons taking part in the analysis; therefore, the cut imposed on the Bjorken variable (x > 0.25) effectively excludes the region where gluon density is believed to be non-negligible.
Since a twist expansion starts to be applicable only above Q2 ~ 1 GeV2 the cut Q2 > 1 GeV2 on data is imposed throughout.
A starting point of the evolution is Q2 = 90 GeV2 for BCDMS and all datasets, and Q20 = 20 GeV2 - for combined SLAC and NMC datasets. These Q2 values are close to the average values of Q2 spanning the respective data. The heavy quark thresholds are taken at Q2 =m2.
2.1. BCDMS data. Analysis starts with the most precise experimental data [10-12] obtained by the BCDMS muon scattering experiment for large Q2 values. A complete set of data includes 607 points when the cut x > 0.25 is imposed.
As in [14, 15] the data with largest systematic errors are cut out by imposing certain limits on the kinematic variable Y = (E0 - E)/E0 (where E0 and E are lep-ton's initial and final energies, respectively [13]). The following Y cuts depending on the limits put on x are imposed:
Y > 0.14 for 0.3 < X < 0.4,
Y > 0.16 for 0.4 < X < 0.5,
Y > Ycut3 for 0.5 < X < 0.6,
Y > Ycut4 for 0.6 < X < 0.7,
Y > Ycut5 for 0.7 < X < 0.8.
An impact of experimental systematic errors on the results of QCD analysis is studied for a few sets of Ycut3, Ycut4, and Ycut5 cuts given in Table 1.
Table 1
A set of Ycut3, 1'™M, and values used
in the analysis
Wycut 1 2 3 4 5
*cut3 0.16 0.16 0.18 0.22 0.23
Vcut4 0.18 0.20 0.20 0.23 0.24
^cut5 0.20 0.22 0.22 0.24 0.25
Following the analyses performed in [14, 15], we arrive at similar results: as values for both original and modified (by cuts) datasets are shown in Table 2, where a total systematic error is estimated in quadrature by using the method somewhat different from that utilized in our earlier analyses (Afycut = 0 corresponds to the case without Y cuts). Namely, instead of accounting for those errors by the multiplication procedure (an old approach outlined in [15]), here they are taken altogether in quadrature from the very beginning.
Upon the cuts imposed (in what follows we work with a set Afycut = 5), only 452 points left available for analysis. Fitting them according to the procedure outlined above the following results are obtained:
as(M|) = 0.1155 ± 0.0016 (stat) ± ± 0.0030 (syst) ± 0.0007 (norm),
(2)
where an abbreviation "norm" denotes the experimental data normalization error stemming from the difference of the fits with free and fixed normalizations of BCDMS data subsets [10-12] having different values of the beam energy.
Performing the fits of SLAC and NMC experimental data [16-18] we obtain results, which are very similar to those derived in [15] while fitting SLAC, NMC, and BFP data altogether. Therefore, we do not present here results of the analyses with only SLAC and NMC data included, although note that the results are compatible within errors with those given above in (2) based on the analysis of BCDMS data alone. Thus, we can put all the data together and fit them simultaneously.
2.2. SLAC, BCDMS, and NMC datasets. As in the case of BCDMS data analysis the cuts imposed are x > 0.25 and iVycut = 5 (see Table 1). Then, an overall set of data consists of 756 points.
In order to determine the region where perturba-tive QCD is applicable we start by analyzing the data without a contribution of twist-four terms (that is
Table 2
NNLO values for various sets of Y cuts
x2 as (Ml) ± as(M§)±
Number quad. syst. err. ± stat. error ± stat. error Total
of points (mult. syst, err.) quad. syst. err. mult. syst. err. syst, error
0 607 446 (642) 0.1064 ± 0.0012 0.1056 ± 0.0012 0.0054
1 502 361 (481) 0.1132 ± 0.0015 0.1127 ± 0.0015 0.0039
2 495 357 (477) 0.1135 ± 0.0015 0.1130 ± 0.0015 0.0038
3 489 352 (463) 0.1140 ± 0.0015 0.1136 ± 0.0015 0.0036
4 458 350 (427) 0.1150 ± 0.0016 0.1144 ± 0.0016 0.0031
5 452 325 (421) 0.1155 ± 0.0016 0.1149 ± 0.0016 0.0030
F2 = f1^00) and perform several fits with the cut Q2 > gradually increased. Table 3 demonstrates that the quality of fits appears to be acceptable already at Q2 = 2GeV2.
Now, the twist-four corrections are added and the data with a global cut Q2 > 1 GeV2 is fitted. As in the previous studies [14, 15] it is clearly seen that higher twists improve the fit quality, with an insignificant discrepancy in the values of the coupling constant to be quoted below.
Finally,4' using the valence quark evolution analyses of SLAC, NMC, and BCDMS experimental data for SF F2 with no account for twist-four corrections and the cut Q2 > 2GeV2, we obtain (with x2/DOF = 1.03)
as(M2) = 0.1161 ±0.0003 (stat) ± ± 0.0018 (syst) ± 0.
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