98 7 HADRONIZATION IN A NUCLEAR ENVIRONMENT J. J. VAN HUNEN (for the HERMES collaboration) Nationaal Instituut voor Kernfysica en Hoge-Energiefysica, NIKHEF Postbus 41882, 1009 DB Amsterdam, The Netherlands Hadrons produced in deep inelastic scattering on 2 H and 14 N have been observed to study the eect of the nuclear environment on hadronization. The attenuation of pions in nitrogen relative to deuterium has been determined at HERMES as function of the transfered energy () and the energy fraction transfered to the pion (z). A preliminary analysis shows a strong attenuation of pions in 14 N compared to 2 H, decreasing for larger values of. The dependence of the attenuation on z is found to be small. In this paper the preliminary results on the attenuation of pions will be presented. 1 Introduction The observation of hadrons in deep inelastic scattering on nuclear targets offers a way to investigate the fragmentation process which follows the hard scattering of a virtual photon from partons. The inuence of the nuclear environment on this process can be studied and used to extract information on the short time scales involved in hadron formation. Inclusive measurements of the structure function F 2 (x) for dierent targets have shown that the parton distributions in nucleons bound in nuclei dier from those in the free nucleon (EMC eect 1 ). The measurements presented in this paper, which were carried out at HERMES, go beyond these inclusive studies, as now the inuence of the nuclear medium on semi-inclusive processes is addressed. The deep inelastic scattering process on a nuclear target is visualized in gure 1. The formation time ( f ) is dened as the time between the initial hard interaction and the nal conguration of the hadron. The quantity studied in the experiment is the attenuation ratio (R A ), which is the number of observed hadrons per deep inelastic event for a target with atomic number A, divided by the same number for a deuterium target. R A (z; ) = 1 dn h Ne dzd 1 Ne dn h dzd A D ; (1) where is the energy transfered by the scattered positron, and z is the fraction of that is obtained by the formed hadron (h). N e is the number of (inclusive) deep inelastic events for each target.
k k 5 fm 0000000 1111111 111111111 00 11111111111 0000 0000 00000 1 11 11 0 111 0 111 11 11 0000 0000 00 11111111111 00 11111111111 111111111 0000000 1111111 τ f hadron Figure 1: Denition of the formation time. The indicated nuclear dimensions and estimates of f are typical for the conditions of the 14 N data taken at HERMES. Due to interactions between the formed (or developing) hadron and the nuclear environment the attenuation ratio can be smaller than 1. At larger the formation time is expected to increase due to time dilation (see section 2), resulting in a formation process which takes place largely outside the nucleus. The attenuation ratio is therefore expected to approach unity with increasing. For HERMES energies (4 < < 24) nuclear eects are expected to be large since the formation length is of the order of the size of the target. Measurements of the attenuation ratio for hadrons have been performed at SLAC 2 and CERN 3. The CERN (EMC) results for R A on Cu cover the energy domain up to 280 GeV and are close to unity. At SLAC the attenuation ratio was determined for 1 H, 2 H, Be, C, Cu, and Sn targets at a value of 10 GeV. The attenuation increases with the atomic number of the target, and shows only a weak dependence on z. However, the statistics of the SLAC data did not enable any binning in, which is required in order to extract information on f from such data. Moreover, no particle identication was available for the detected hadrons, thus causing ambiguities in the interpretation of the data. At HERMES the attenuation ratios can be measured with good statistics and good particle identication. Values of R A can thus be determined for pions and hadrons separately, as function of z,, and other variables such as the trans-
verse momentum (p t ), and the four-momentum of the virtual photon squared (-Q 2 ). In this report we present the rst preliminary results for measurements of R A on 14 N. To put the new results into perspective, a brief description of model calculations for R A is presented in section 2. In the next two sections the experiment and data analysis is given, while the results themselves are the subject of section 5. The conclusions are summarized in the last section. 2 Models for the attenuation Since it is not possible to describe hadronization in the framework of perturbative QCD, phenomenological models need to be used to obtain a value for R A which usually start from estimates of the formation time ( f ). One possibility is to use the hadron as a starting point and describe the formation time as a constant belonging to the hadron ( h ) times a Lorentz factor which is based on the hadron variables 4, f = h E h m h = h z m h : (2) Alternatively, it is possible to consider the quark which has been hit by the virtual photon as an unstable particle 5 with a lifetime q. In this case the Lorentz factor should be based on the quark variables, f = q E q m q = q m q : (3) Both expressions show an increase of f with, but only the rst expression shows a direct dependence on z and the mass of the hadron (m h ). It is noted that since the quark is o-shell, the mass of the quark (m q ) and thus q may be a function of Q 2. Hence, measurements of R A for dierent hadrons (m h ) and as function of z will enable a distinction between equation 2 and 3. The various expressions for f can be used to calculate R A. Since a hadron contains at least two constituents, which are not necessarely created at the same time, two time scales may be involved 6. The times c and f (gure 2) indicate the elapsed time between the initial quark-virtual photon interaction and the appearance of respectively, the rst and second constituent of the formed hadron. The two time scales c and f (or l c and l f in space coordinates) are not independent. It has been shown 6 that the energy of the formed hadron equals roughly the energy contained by the (LUND) string between l c and l f. Thus l f = zl + l c = z + l c (4)
string hadron 00 11 00 11 111111111 000000 111111 0000000 1111111 00 11 00 111111111 11 00 11 σ* σs σ h τc 00 11 000 111 τ f 00 11 00 11 00 11 t Figure 2: The relevant time scales are the formation time f and the constituent time c. with being the string constant ( 1 GeV/fm), and L the total string length. There are three cross sections involved in the interaction of the hadron with the nuclear environment: h is the (known) hadron-nucleon cross section, s is the cross section before the actual hadron is formed, which can be thought of as the interaction of the nuclear environment with the hadron constituents or, in the LUND picture, with the color string. The interpretation of the third cross section ( ) may be associated with interactions with the color eld while the constituents making up the hadron do not yet exist. The probability that neither the quark (q) nor the hadron (h) is interacting with a single nucleon in the nucleus is given by S A, Z lc Z lf S A (b; l) = 1? dl 0 A (b; l 0 )? s l lc dl 0 A (b; l 0 )? h Z 1 lf dl 0 A (b; l 0 ) : (5) At position (b,l) the hard scattering occurred, where the variable b is the impact parameter and l is the coordinate in the direction of the incident quark or hadron. A is the normalized nuclear density. The attenuation ratio can then be evaluated by integrating over the nuclear volume and accounting for possible interactions with (A-1) nucleons. Z 1 Z 1 R A = 2 bdb dl A (b; l)[s A (b; l)] A?1 (6) 0?1 In order to obtain a value for the formation time equation 6 should be tted to the data with l f,, and s as free parameters. 3 The HERMES spectrometer The HERMES experiment makes use of the HERA 27.5 GeV positron beam at DESY. The positrons scatter deep inelastically from an internal gas target. The
HERMES spectrometer 7 comprises a number of position sensitive detectors for track reconstruction. Scattered positrons and hadrons are detected under scattering angles between 40 and 220 mrad. For particle identication several detectors are available. The lead glass calorimeter, hodoscope scintillators, and transition radiation detector can be used for lepton-hadron separation, while the Cerenkov detector provides pion-hadron separation above 4 and below 14 GeV, and additional positron-hadron separation. The spectrometer magnet is a dipole magnet with a eld integral of 1.3 Tm. 4 Data analysis In 1997 data were taken using a high density 14 N target, resulting in about 2.6 million deep inelastic events. Part of the nitrogen data were taken with a maximum target density of about 7.10 15 Nucleons/cm 2, limited only by the lifetime of the positron beam which averaged about 4 hours during these (dedicated) run periods. It should be noted that these conditions were exceptional, as the contribution of the target to the lifetime of the HERA beam is usually limited to 45 hours. It is gratifying to observe that under these high rate conditions the trigger rate did not exceed 500 Hz, of which more than 92% were accepted, showing the low deadtime. In order to obtain a clean sample of deep inelastic events, constraints on Q 2, y (/beam energy), W 2 (squared four-momentum of the nal state), and x (momentum fraction of the quark participating in the hard scattering) are implied. These cuts are shown in table 1, together with the observed maximum values of the kinematic variables. Table 1: The applied constraints on the kinematic variables and the observed maximum values of these variables Variable: Q 2 y W 2 x Constraint: > 1 GeV 2 < 0.85 > 4 GeV 2 > 0.04 Maximum: < 19 GeV 2 - < 45 GeV 2 < 0.8 5 Results on the attenuation From the data that we have taken on 14 N and 2 H in 1997, the attenuation ratio of pions was determined as function of (gure 3). The statistical errors are small and, since the main sources for systematic errors (detector eciencies, acceptance eects, software tracking eciency) cancel in the ratio, also the systematic error is small.
1.05 N pi /N dis (N) ----------- N pi /N dis (D) 1 0.95 0.9 0.85 PRELIMINARY 0.8 4 6 8 10 12 14 16 18 20 22 ν (GeV) Figure 3: The attenuation ratio of pions in nitrogen determined at HERMES as function of for dierent z cuts. The dominant systematic uncertainty is due to radiative eects. The radiative corrections for nitrogen and deuterium are dierent at low x, mainly due to the coherent contribution. At the EMC experiment the systematic uncertainty in the ratio due to the radiative corrections is less than 1%. For the HERMES results we expect a similar contribution. The lepton-hadron, as well as the pion-hadron, separation at HERMES is good and contributes not signicantly to the systematic uncertainty. Since the normalization is performed using the number of deep inelastic events there is no need to account for uncertainties in the integrated luminosity or target densities. Although the total systematic uncertainty has not yet been evaluated for these preliminary data, we expect a value of a few % only in view of the arguments presented above. The ratio shows a value of about 0.85 at 7 GeV and increases up to a value of about 0.95 at 20 GeV. Such an increase is expected 8 since at high the attenuation ratio is believed to approach unity for all nuclei. For above 15 GeV the HERMES data on 14 N are consistent with the EMC results for Cu,
while the SLAC measurement for hadrons in Cu at a value of 10 GeV (0.67 0.06) is lower than the HERMES measurement for pions in 14 N. We can use the parametrisation for the attenuation, determined at SLAC as function of the atomic number of the target nucleus, to estimate the attenuation of hadrons in 14 N. This leads to an attenuation ratio of 0.790.07 at a value of 10 GeV. The HERMES result is 0.9000.004, note however that the error is only statistical and hence is dominated by the aforementioned systematic uncertainty of a few %. In view of the fact that the SLAC result is for hadrons, while the HERMES result concerns pions the data are not inconsistent. Due to the relatively large error on the SLAC data, statements concerning the dierence between pions and hadrons can only be made after determination of the attenuation ratio for hadrons at HERMES. Dierent z cuts were used, namely z > 0.1 and z > 0.5. The HERMES data shows, in agreement with the experiment at SLAC, little dependence on z. In order discriminate between the dierent expressions of the formation time (equation 2 and 3) it is needed to explore the existing data set further, and determine the dependences on other variables such as m h (by selecting other identied hadrons, for example the meson) and Q 2. 6 Conclusions and outlook A preliminary analysis of the 14 N and 2 H data obtained at HERMES shows a strong attenuation of pions in 14 N. The attenuation ratio increases with, while the z dependence is found to be small. At a later stage a value of the formation time can be extracted from these data using a phenomenological model for the description of the attenuation. In order to study the hadron formation in more detail the attenuation of all hadrons (as opposed to pions only) in 14 N will be determined, as well as the dependence of the attenuation on other variables such as Q 2 and m h. References 1. J.J. Aubert et al., Phys. Lett. B 123, 275 (1983). 2. L.S. Osborne et al., Phys. Rev. Lett. 40, 25 (1624)1978. 3. J. Ashman et al., Z. Phys. C 52, 1 (1991). 4. K. Gottfried Phys. Rev. Lett. 32, 957 (1974). 5. A. Bialas and T. Chmaj Phys. Lett. B 133, 241 (1983). 6. A. Bialas, M. Gyulassy Nucl. Phys. B 291, 793 (1987). 7. The HERMES Spectrometer, submitted for publication in NIM. 8. G. van der Steenhoven, Nucl. Phys. A 662, 31c (1997).