Session I 151

FRAGMENTATION FUNCTIONS IN NEUTRINO HYDROGEN INTERACTIONS

Aachen-Bonn-CERN-Mlinchen (MPI)-Oxford Collaboration

J. Blietschau, .J. Grassler, W. Krenz, D. Lanske, R. Schulte and H.H Seyfert III. Physikalisches Institut der Technischen Hochschule, Aachen, Germany.

K. Bockmann, C. Geich-Gimbel, H. Heilmann, T. Kokott, B. Nellen and R. Pech Physikalisches Institut der Universitat Bonn, Bonn, Germany.

L. Bacci~ P. Bosetti1 ), D.C. Cundy, A. Grant, P.O. Hulth, O.R.O. Morrison, R. Orava..::l, L. Pape, Ch. Peyrou, H. Saarikko3), W.G. Scott, E. Simopoulou4), A. Vayaki4) and H. Wachsmuth CERN, European Organisation for Nuclear Research, Geneva, Switzerland.

M. Aderholz, N. Schmitz, R. Settles, K.L. Wernhard and W. Wittek Max-Planck-Institut fur Physik und Astrophysik, Mlinchen, Germany.

R. Giles, P. Grossmann, R. McGow, G. Myatt, D.H. Perkins, D. Radojicic, P. Renton and B. Saitta Department of Nuclear Physics, Oxford, U.K.

presented by N. Schmitz

ABSTRACT The fragmentation of the u-quark is studied in the reac­ tion VµP~ µ-h± +anything. It is found that the single particle inclusive cross section does not factorize. Scaling deviations are observed in the fragmentation functions and are found to be in agreement with the leading order QCD prediction.

In this paper we report on a study of the distribution in fractional energy (z distributions) of secondary hadrons in charged current neutrino interactions in BEBC filled with hydrogen and exposed to a wideband horn­ focussed neutrino beam from the CERN SPS. The data sample consists of 5,600 charged current events with muons of p > 3 GeV/c identified in a two-plane µ External Muon Identifier. The average neutrino energy of the events is 40 GeV.

For each secondary hadron h± in the semi-inclusive reaction

( 1 ) we define the energy fraction z carried by the hadron as z = Eh/EH, where Eh is the laboratory energy of the hadron and EH that of all secondary hadrons including the correction for unobserved neutral particles. The z distribution + for positive or negative hadrons h- is given by the single particle inclusive cross section divided by the total inclusive cross section: ------1) CERN fellow from III. Physikalisches Institut der Technischen Hochschule, Aachen 2) Now at Fermilab 3) CERN visitor from University of Helsinki 4) Now at Demokritos, Athens 152 Session I

+ h- 2 2 (x,q I Z) da(x,q ) + 2 do-incl o-(z,q ) ( 2) 2 I 2 dx dq dz dx dq

The m-th moment of this distribution is defined as 1 + 2 o-(m,q ) J z m-1 0 ±( z,q 2) d z. ( 3) 0 + 2 2 Fig. 1 a shows o-(z,q ) for low and high q for those hadrons which travel forward in the overall hadronic center-of-mass system (xF > 0) . The latter selection (which is applied throughout this paper) is made in order to re­ duce contributions from target fragments so that according to the naive 2 quark-parton model for reaction (1) D±(z,q ) may be interpreted as the fragmentation function of the u-quark (contributions from sea quarks are neglected in this analysis). All values of W, the effective mass of the hadronic system, are included in Fig. 1a. For both positive and negative hadrons a significant q 2 dependence of D±(z,q2 ) is observed, the distribu­ tions becoming narrower with increasing q 2

In the naive quark-parton model the single particle inclusive cross 2 section factorizes, which means that D±(z,q ) as defined in (2) is inde­ pendent of x = q 2/(2Mv). To test this hypothesis we have plotted in Fig. 1b 2 D+(m = 3,q2 ) versus x as an example for three different intervals of q 2 One observes indeed that at high q the fragmentation moment is independent 2 + 2 of x; however at smaller q D (3,q ) increases significantly with x implying 2 non-factorization in this q region.

It is suggestive to test whether the observed scaling violation is con­ 2 sistent with the prediction of leading order QCD. The prediction for the q evolution of non-singlet fragmentation moments is1 ) 2 -dNS • ln (-~L) m ( 4) A2 where c are unknown constants, dNS are the anomalous dimensions and A is m m the scale parameter of the theory. Experimentally a non-singlet combination 2 2 is obtained by taking the difference of D+(m,q ) and D-(m,q ). This follows from charge conjugation invariance and with the assumption that the z distributions in (2) are the fragmentation functions of a u-quark:

+ 2 + 2 + 2 - 2 Du(m,q ) ou(m,q ) Du(m,q ) Du(m,q ) ( 5)

+ + This formula is valid irrespective of the nature of the hadron (n-,K-,p/p). NS 2 Fig. 2 shows Du (m,q ) for m = 2 to 7 and for all W together with the result (solid lines) of a global fit (i.e. for all m simultaneously) of 2 2 equation (4) to the data in the region q > 1 GeV • The data are well re- produced by the QCD formula yielding a value for A of A = (0.54 ± 0.08) GeV. Session I 153

2 It should be pointed out, that the observed q dependence in Fig. 2 is 2 associated with the region of small W values; for W > 4 GeV no q depen­ dence is found.

According to (4) two non-singlet moments of order m and m when plotted 1 2 against each other on a log-log scale are expected to fall on a straight line with slope dN8 /dN8 . Fig. 3 shows plots of (D+-D-) and (for comparison) + - m2 m1 (D +D) for m 6, m 4 and m 7, m 3. In all cases the plots can 2 = 1 = 2 = 1 = be fitted by straight lines with experimental slopes as indicated. The slopes of the non-singlet moments (D+-D-) are in good agreement with the QCD prediction; the combinations (D + +D - ) on the other hand give substan- tially bigger slopes.

In conclusion, both Figs.2 and 3 show surprising agreement of the measured non-singlet momentswith the QCD prediction. This agreement may 2 however be coincidental since the q dependence is observed only if small values of w are included.

REFERENCES

1 ) J.F. Owens, Phys. Lett. 76B, 85 (1978); T. Uematsu, Phys. Lett. 79B, 97 (1978).

D+( 3,q 2 l

2 2 2 • + ve q 2 1- 2 GeV • q 1 - 2 GeV 2 2 0.8 2 2 "' + Ve q 5-40 GeV x q 2 - 5 GeV 2 2 2 0 - ve q 1 - 2 GeV o q 2 10-40 GeV 2 2 A - Ve 10 q 5-40 GeV 0.6 (bl 0.4 II ! l• ! ~ li ~ ~ 0.2 r~ ~ \"§ a a § ....z IN "O "O f 0 0.2 0.4 0.6 0.8 1.0 x

Fig. 1: a) z distributions of positive and negative hadrons for two different ranges of q 2 and for all W. b) m = 3 moment of positive hadrons, plotted as a function of x for 3 ranges in 2 q .

0.5 1.0 z 154 Session I

"'--, ____ I f 0.1 _,_f__,__ m•3

001 r

3 2 2 Fig. 2: Mom~nts of the non-singlet combination DN (m,q ) = D+(m,q ) - D (m,q2) plotted against q2 for all W. The curves show the results of a fit to the logarithmic dependence predicted by leading order QCD.

- 1.67!0.17 1.27!0.10 QCO: 1.76 - QCO: 1.29 0NS(6) t f / ~,,1/ q/ I ~1 '0"'141- 0.01,- / xlf+~,,- - 1 369 • 0 ~;,,, f / 0•17i.o-!711 f' It q/ /; 0·13i.o-13J- o.01~---'~-'---'~'-'---'--~',___-T,.~'-..__, .... 1 __1_~'--~ 0.02 0.1 0.1

Fig. 3: Logarithmic plots of m = 6 versus m = 4 and m = 7 versus m 3 mo$en~s for q2+> l Gev2 and for the hadron combinations (D -D) and (D +D ). The full lines show the fitted slopes while the broken lines show those predicted for DNS by leading order QCD.