We extract the high-twist contribution to the neutrino-nucleon structure
function $xF_3^{(\nu+\bar{\nu})N}$ from the analysis of the data collected by
the IHEP-JINR Neutrino Detector in the runs with the focused neutrino beams at
the IHEP 70 GeV proton synchrotron. The analysis is performed within the
infrared renormalon (IRR) model of high twists in order to extract the
normalization parameter of the model. From the NLO QCD fit to our data we
obtained the value of the IRR model normalization parameter
$\Lambda^2_{3}=0.69\pm0.37~({\rm exp})\pm0.16~({\rm theor})~{\rm GeV}^2$. We
also obtained $\Lambda^2_{3}=0.36\pm0.22~({\rm exp})\pm0.12~({\rm theor})~{\rm
GeV}^2$ from a similar fit to the CCFR data. The average of both results is
$\Lambda^2_{3}=0.44\pm0.19~({\rm exp})~{\rm GeV}^2$.Comment: preprint IHEP-01-18, 7 pages, LATEX, 1 figure (EPS

A.A. Borisov

A.I. Kononov

A.I. Mukhin

A.S. Kozhin

A.S. Vovenko

A.V. Krasnoperov

Abbott

Adams

Alekhin

Ammosov

Anikeev

B.A. Popov

Baratov

Barnett

Beneke

Bethke

Bugorsky

Bunyatov

Dasgupta

Georgi

Kataev

M.M. Kirsanov

M.Y. Kazarinov

Mangano

Martin

N.I. Bozhko

O.L. Klimov

O.Y. Denisov

R.M. Fachrutdinov

S.A. Bunyatov

S.I. Alekhin

S.K. Chernichenko

S.N. Prakhov

S.V. Goryachev

Seligman

Sidorov

Stein

V.B. Anykeyev

V.I. Snyatkov

V.L. Tumakov

V.N. Goryachev

V.V. Lipajev

V.V. Tereshchenko

Varvell

Y.A. Batusov

Y.A. Nefedov

Y.I. Salomatin

Y.M. Sviridov

Physics Letters B

English

arXiv

Crossref

Determination of the high-twist contribution to the structure function xFνN3

We extract the high-twist contribution to the neutrino-nucleon structure function $xF_3^{(\nu+\bar{\nu})N}$ from the analysis of the data collected by the IHEP-JINR Neutrino Detector in the runs with the focused neutrino beams at the IHEP 70 GeV proton synchrotron. The analysis is performed within the infrared renormalon (IRR) model of high twists in order to extract the normalization parameter of the model. From the NLO QCD fit to our data we obtained the value of the IRR model normalization parameter $\Lambda^2_{3}=0.69\pm0.37~({\rm exp})\pm0.16~({\rm theor})~{\rm GeV}^2$. We also obtained $\Lambda^2_{3}=0.36\pm0.22~({\rm exp})\pm0.12~({\rm theor})~{\rm GeV}^2$ from a similar fit to the CCFR data. The average of both results is $\Lambda^2_{3}=0.44\pm0.19~({\rm exp})~{\rm GeV}^2$

Alekhin, S I

Anykeyev, V B

Batusov, Yu A

Borisov, A

Bozhko, N

Bunyatov, S A

Chernichenko, S K

Denisov, O Yu

Fachrutdinov, R M

Goryachev, V N

Kazarinov, Yu M

Kirsanov, M M

Klimov, O L

Kononov, A I

Kozhin, A S

Krasnoperov, A V

Lipaev, V V

Mukhin, A I

Nefedov, Yu A

Popov, B A

Prakhov, S N

Salomatin, Yu I

Snyatkov, V I

Sviridov, Yu M

Tereshchenko, V V

Tumakov, V L

Vovenko, A S

CERN Document Server

IHEP-01-18Determination of the high-twist contribution to thestructure function xF νN3S. I. Alekhin, V. B. Anykeyev, A. A. Borisov, N. I. Bozhko,S. K. Chernichenko, R. M. Fachrutdinov, V. N. Goryachev, S. V. Goryachev,M. M. Kirsanov, A. I. Kononov, A. S. Kozhin, V. V. Lipajev, A. I. Mukhin,Y. I. Salomatin, Y. M. Sviridov, V. L. Tumakov, A. S. VovenkoInstitute for High Energy Physics, 142284 Protvino, RussiaY. A. Batusov, S. A. Bunyatov, O. Y. Denisov, M. Y. Kazarinov, O. L. Klimov,A. V. Krasnoperov, Y. A. Nefedov, B. A. Popov, S. N. Prakhov,V. I. Snyatkov, V. V. TereshchenkoJoint Institute for Nuclear Research, Dubna, RussiaAbstractWe extract the high-twist contribution to the neutrino-nucleon structure functionxF(ν+ν)N3 from the analysis of the data collected by the IHEP-JINR Neutrino Detectorin the runs with the focused neutrino beams at the IHEP 70 GeV proton synchrotron.The analysis is performed within the infrared renormalon (IRR) model of high twistsin order to extract the normalization parameter of the model. From the NLO QCDfit to our data we obtained the value of the IRR model normalization parameter Λ23 =0.69  0.37 (exp)  0.16 (theor) GeV2. We also obtained Λ23 = 0.36  0.22 (exp) 0.12 (theor) GeV2 from a similar fit to the CCFR data. The average of both results isΛ23 = 0.44 0.19 (exp) GeV2.PACS numbers: 13.60.Hb,06.20.Jr,12.38.BxKeywords: high twists, deep inelastic scattering11. Attempts to extract the high twist (HT) contributions to the neutrino-nucleon deep-inelastic scattering (DIS) structure functions started many years ago [1], but have not leadto the ultimate answer up to now. The main diculty in this study is that due to thelinear rise of the total interaction cross-section with the incident neutrino energy Eν , thelargest data samples have been collected in experiments at relatively high neutrino energiesEν > 50 GeV. The region of the small momentum transfered Q, which is most relevantfor the study of the HT eects, is rather poorly populated by the data points coming fromthese experiments because of kinematical and/or methodical cuts. At lower neutrino energiesexperiments with very high luminosity are necessary to achieve the statistical precision inthe structure function measurements sucient for the quantitative estimation of the HTcontribution.The rst results on the twist-4 contribution to the neutrino-nucleon structure functionxF νN3 extracted from the analysis of data collected in a single experiment were reportedin Ref. [2]. The indication on a negative sign of this contribution given in this paper waslater conrmed with a better precision in Ref. [3]. Nevertheless, the experimental errorswere large in both cases which did not allow for a conclusive comparison with the availabletheoretical models of HT. Later the CCFR experiment at Fermilab collected large statisticaldata sample [4], which allowed for more precise determination of the twist-4 contribution toxF νN3 [5, 6], but the precision is still poor.The data of Ref. [7] from the IHEP-JINR Neutrino Detector can be used to improve ourknowledge of the HT contribution to the DIS structure functions. This experiment used aneutrino beam of relatively low energy (Eν < 30 GeV), but collected rather large statis-tics (5987 neutrino and 741 antineutrino charged-current (CC) interactions). The lowestQ2 is 0.55 GeV2 and the HT contribution would clearly manifest itself as a power-like cor-rection to the logarithmic-like leading twist (LT) dependence of the structure functions onQ. Meanwhile the Q range spanned by the data is limited (maximal Q2 is 20 GeV2) andfor this reason the simultaneous determination of the power-like and logarithmic-like termsis dicult. In the analysis of Ref. [7] we xed the HT contribution as it was dened fromother experiments and performed the next-to-leading-order (NLO) QCD analysis of our datain order to constraint the LT contribution. The value of the strong coupling constant αs,which mainly governs the Q dependence of the LT term, was determined from this analysisas α(MZ) = 0.123+0.010−0.013.At the same time the Q dependence of the LT contribution can be well constrained usingthe data from other experiments. The world average of αs(MZ) is known with the precisionof about 0.003 [8] and one can perform the analysis complimentary to the one of Ref. [7], i.e.,x the value of αs(MZ) at the world average and try to extract the HT contribution from thedata. An additional error estimated as variation of the results of the t under variation ofthe world average of αs(MZ) within its uncertainty should be ascribed thereafter. Meanwhilein most cases the total error in the HT contribution extracted using this approach would beless as compared with the results of the simultaneous t of the HT and the LT terms to thedata. The reduction of the error depends on the ratio of the error in αs(MZ) obtained insuch simultaneous t to the error in the world average. For our data this ratio is larger than3 and for this reason we extracted the HT contribution value from these data using the twith a xed value of αs.2. The analysis is based on the data collected with three independent exposures of theIHEP-JINR Neutrino Detector [9] to the wide-band neutrino and antineutrino beams [10]of Serpukhov U-70 accelerator. The exposure to the antineutrino beam (νµ-exposure) was2performed at the proton beam energy Ep = 70 GeV, whereas the two νµ-exposures werecarried out at Ep = 70 GeV and at Ep = 67 GeV. The energy of the selected νµ (νµ) CCevents was in the range of 6 < Eν(ν) < 28 GeV. The experimental set-up and the selectioncriteria of CC neutrino and antineutrino interactions are discussed in Ref. [11]. The F(ν+ν)N2and xF(ν+ν)N3 structure functions of nucleon have been measured as a function of x averagedover all Q2 permissible (the details of experimental procedures are described in Ref. [7]).These data were analyzed in the NLO QCD approximation in the modied minimal-subtraction (MS) renormalization-factorization scheme. The partons evolution code appliedin this analysis was used earlier for the global t of the parton distribution functions [12].The boundary parton distributions were chosen in the formxpNS(x, Q0) = ANSxaNS(1− x)bNS , xpS(x, Q0) = AS(1− x)bS ,xpG(x, Q0) = AG(1− x)bG (1)at Q20 = 0.5 GeV2, where indices NS, S, and G correspond to non-singlet, singlet, and gluondistributions, respectively. These distributions were substituted in the expressions for theLT contributions to F2,3xF(ν+ν)N,LT3 (x, Q) =∫ 1xdzzCq3(z, Q)pNS(x/z, Q),F(ν+ν)N,LT2 (x, Q) =∫ 1xdzzfCq2(z, Q) [pNS(x/z, Q) + pS(x/z, Q)] ++CG(z, Q)pG(x/z, Q)g (2)where C(z, Q) are the perturbative QCD coecient functions in the MS scheme. The pa-rameter ANS was calculated using the constraint∫ 10dxqNS = 3, and the parameter AG { fromthe momentum-conservation constraint, while other parameters of Eq. (1) were tted to thedata. The form of Eq. (1) was checked to be flexible enough, i.e., its complication did notlead to the improvement of the t.The target mass (TM) corrections of O(M2/Q2), as they are given in Ref. [13], wereapplied to the LT contribution. The HT contribution was parameterized in the additive formand within the infrared renormalon model (IRR) [14]. In this model the HT contribution isconnected with the LT one by the known coecient function and the only free parameterof the model is related to the total normalization. In particular, the HT contribution toxF(ν+ν)N3 reads [15, 16]H3(x, Q) = A02(FνN3 )∫ 1xdzzCIRR3 (z)pNS(x/z, Q), (3)where CIRR3 is the IRR model coecient function and A02(FνN3 ) denes the total normal-ization. The HT contribution to F(ν+ν)N2 contains the non-singlet term similar to Eq.(3)with the normalization parameter A02(FνN2 ) and the respective coecient function CIRR2 . Inaddition, the singlet and gluon terms calculated in Ref. [17] also come to the expression forthe HT contribution to F2 as it is given by the IRR model, but these terms are relevant forsmall x only and for this reason we used the non-singlet approximation for the calculationof the IRR contribution to F(ν+ν)N2 as well as for xF(ν+ν)N3 . Following Ref. [17], we describe3the general normalization of the HT contributions to F2,3 by the parameters 2,3, which areconnected with the parameters A02(FνN2,3 ) by the relationsA02(FνN2,3 ) = −2CFβ022,3, (4)where CF = 4/3 and β0 is the rst coecient of the QCD β-function. Both ways arecompletely equivalent if the number of active fermions in the expression for β0 does notdepend on Q. Meanwhile in order to provide self-consistency of the analysis, we changed nfin Eq. (4) from 3 to 4 at Q equal to the c-quark mass mc = 1.5 GeV. For this reason thevalue of A02 depends on Q in our case, although the numerical eect is inessential. The valueof αs(MZ) was xed at 0.118, which is close to the world average of Ref. [8]. As one can seein Fig.1 the analyzed data are insensitive to the parameter 2 and we xed it at the valueof 1 GeV2 inspired by the results of Ref. [16] on the analysis of charged leptons DIS data.The systematic errors on the data were accounted for in the covariance matrix approach,described in Ref. [18].Table 1: The results of the t of the IRR model to the data from dierent neutrino experi-ments. The value of χ2 over the number of data points (NDP) is given in the last column.Experiment 23[GeV2] 22[GeV2] χ2/NDPIHEP-JINR 0.69 0.37 1. 3/12CCFR 0.36 0.22 0.91 0.77 253/222The results of the t are given in Table 1 and in Fig. 1. The obtained contribution toxF(ν+ν)N3 is negative which supports the earlier observation of Refs. [2, 3] and is in agreementwith the results of Refs. [5, 6]. The HT contribution to F(ν+ν)N2 is negligible in the wholeregion of x spanned by the data. The value of 23 is determined from our data with the50% accuracy. For the comparison, in the NLO QCD t to the CCFR data on the structurefunction xF(ν+ν)N3 the value A02(FνN3 ) = −0.12  0.05 GeV2 was obtained in Ref. [5]. Thisestimate did not account for the systematic errors in the data, while the estimate accountingfor systematics is A02(FνN3 ) = −0.10  0.09 GeV2 [6], i.e., our result is the most preciseestimate of the IRR normalization parameter at the moment.The change of 23 under variation of αs(MZ) by 0.003 is 0.055 GeV2 and we considerthis shift as a theoretical error in 23. Another source of the theoretical error comes fromthe uncertainty due to the eect of the higher-order (HO) QCD corrections to the LT term.These eects may be especially important for our study since the data at rather low Q areinvolved in the analysis. The HO corrections generally make the Q dependence of the LTcontribution steeper, and correspondingly lead to the decrease of the HT contribution. Inorder to estimate the uncertainty due to neglected HO corrections, we repeated the t withthe QCD renormalization scale changed from the nominal value of Q to 2Q (see Ref. [19] for adetailed argumentation of this approach). The obtained shift in the value of 23 is 0.15 GeV2.Note that the signicant part of the error in the world average of αs(MZ) also come from theuncertainty due to neglected HO QCD corrections. For this reason the two considered sourcesof theoretical errors are correlated. Having no possibility to account for this correlation, wejust combine both errors in quadrature and estimate the total theoretical error in 23 as0.16 GeV2. One can see that the uncertainty in 3 is dominated by the experimental error,4Figure 1: The x dependence of the measured structure functions F(ν+ν)N2 (upper) andxF(ν+ν)N3 (lower). The average values of Q2 (GeV2) for the x bins are given in the up-per plot. The full curves give the result of the LT+HT t to the data, the dashed curvescorrespond to the 1σ bands of the HT contributions obtained from the t.5moreover accounting for the correlations of the separate sources of the theoretical error woulddecrease the latter.3. We also extracted the HT contribution to F νN2,3 from the CCFR data of Ref. [4] usingthe approach with αs xed. The value of the parameter 23 obtained from the NLO QCDanalysis of those data with x < 0.7 is given in Table 1. The CCFR data are sensitive tothe parameter 2 too, although the precision is poor and the tted value is comparable withzero within the errors1. The theoretical error in 23 estimated in the same way as for theanalysis of our data is 0.12 GeV2. Results for both experiments are comparable within theerrors and combining them we obtain the average23 = 0.44 0.19 (exp) GeV2. (5)In order to check universality of the IRR model scales with respect to the specic choiceof structure function in the DIS process, we compared this value with the results of Ref. [16]on the analysis of the charged-leptons DIS data. Since in Ref. [16] the results are given interms of parameter A02, we transformed our average (5) using Eq. (4). As a result, we obtainthat for nf = 3A02(FνN3 ) = −0.130 0.056 (exp) GeV2. (6)This value is smaller, than A02(FeN2 ) = −0.2 GeV2, given in Ref. [16], although withinthe errors both values are comparable. More precise conclusion about universality of theIRR model scales may be derived from the analysis of experimental data with improvedstatistics, which have been collected using the IHEP-JINR Neutrino Detector with a dierentconguration of the neutrino beam channel. The analysis of these data in order to extractthe structure functions is currently in progress. The data from the NuTeV collaboration[20], after their processing have been completed, may also be used to improve the precisionof the IRR scales determination. In far sight a potential neutrino factory would allow for adetailed cross-check of the IRR model predictions and, in particular, the determination ofthe IRR scales with an accuracy of several percent [21].In conclusion, we extract the high-twist contribution to the neutrino-nucleon structurefunction xF(ν+ν)N3 from the analysis of the data collected in the rst runs of the IHEP-JINRNeutrino Detector at the IHEP U-70 accelerator. We observe the negative HT contribution tothe structure function xF(ν+ν)N3 which supports the earlier observations. The normalizationscale of the IRR model extracted from the combined analysis of the IHEP-JINR and CCFRexperiments is about 1σ lower than the one extracted from the data on the structure functionF lN2 for the DIS of charged leptons.AcknowledgmentsWe are indebted to V.Braun, A.Kataev, A.Sidorov, E.Stein, and C.Weiss for stimulatingdiscussions. The work was supported by the RFBR grant 00-02-17432.References[1] L. F. Abbott and R. M. 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Mangano et al., in preparation.7