ЯДЕРНАЯ ФИЗИКА, 2007, том 70, № 4, с. 764-770
ЭЛЕМЕНТАРНЫЕ ЧАСТИЦЫ И ПОЛЯ
NUCLEAR EFFECTS IN LEPTOPRODUCTION OF SECONDARIES
© 2007 Ya. A. Berdnikov1), M. M. Ryzhinskiy1)*, Yu. M. Shabelski2)**
Received March 10, 2006
We estimate the energy losses in the case of deep-inelastic scattering on nuclear targets in terms of the effective change of the virtual photon energy. Our phenomenological results are in reasonable agreement with theoretical calculations. The difference in secondary production processes in hard and soft interactions is discussed.
PACS:25.30.-c, 25.75.Dw, 13.87.Fh
1. INTRODUCTION
The inclusive spectra of secondaries (pions, kaons, p, and p) measured in lepton—nucleus (lA) deep-inelastic scattering (DIS) [1—3] become more and more soft with the increase of atomic weight of the target. In this paper we consider the A dependences of these spectra using the same method as in our previous paper [4].
In the case of DIS only some part of the projectile lepton energy (v = El — E[) is transfered to the target. Thus, one can consider the virtual photon as the projectile to draw an analogy between the DIS and hadroproduction processes. It is convenient to analyze DIS data in terms of energy fractions of the virtual photon carried by the produced hadron. Therefore in this paper we will use the variable:
Eh
Zh = —,
V
(1)
where Eh is the energy of the produced hadron in the lab. frame.
At high energies in the case of nucleon target the maximum value of zh is close to unity (zhmax ^ ^ 1). In the case of nuclear target the situation is more complicated because there are many different contributions [5, 6] from the final-state interactions with nuclear matter which decrease the spectra at large zh. On the other hand, the processes which lead to the so-called cumulative effect [7—9] increase the boundaries of the available zh region3). The modification of parton structure function [10] should be accounted for.
!)St. Petersburg State Polytechnic University, Russia.
2)Petersburg Nuclear Physics Institute, RAS, Gatchina. E-mail: mryzhinskiy@phmf.spbstu.ru
E-mail: shabelsk@thd.pnpi.spb.ru
3)The last processes have rather small cross section.
In all processes on nuclear targets (except of the coherent ones) some fraction of energy is used for nuclear disintegration. The nuclear target is destroyed and several nucleons, as well as light nuclear fragments (say, a particles), appear in the final state. It can be considered as a phase-space limitation for the produced secondaries. The corresponding fraction of initial energy used on this effect numerically is not so small (it is many times larger than the nuclear binding energy).
The energy used for nuclear disintegration is taken from the beam or secondary-particle energy, primarely via some QCD process, discussed in [5, 6]. After several stages this energy transforms (in part, as a minimum) into kinetic energy of the target fragments. So the portion of the last kinetic energy allows us to estimate the primary energy losses all together. On the other hand, the phase-space limitation can be considered as an effective decrease of the incident beam energy.
In what follows we will consider the A dependences of secondary hadron leptoproduction in terms of zhA:
ZhA
Eh
v - Ea
(2)
and we assume that it is possible to find the shift EA for the case of interaction with nuclear target from the condition that the ratios of secondary multiplicities on nuclear and nucleon (Ea=i = 0) targets in terms of
zhA
RlA/lp(ZhA) = const(ZhA) ^ 1, (3)
whereas the same ratios in terms of zh
RlA/lp(Zh) = f (Zh). (4)
Evidently, such rescale is reasonable only for not very small zh values.
R
Kr/D
1.1 1.0 0.9 0.8 0.7 0.6
HERMES:
e+ + A ^ n0 + X at 27.5 GeV
(1/A)da/dz h
100
10
0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0
z h zh
Fig. 1. (a) Multiplicity ratio for identified neutral pions from a Kr target as a function of zh (for v > 7 GeV). (b) Neutral-pion multiplicities for hydrogen [2] and Kr (extracted from ratios in Fig. a).
(1/A)do/dz h
10°
10-
op
• Kr (shifted)
0.2 0.4 0.6 0.8 zh
Fig. 2. The same as in Fig. 1b, but the spectrum for Kr target was shifted according to Eq. (7) with EA = 1-0 GeV.
We will determine shifts Ea from the experimental data and we will compare them with several independent estimations. Such approach allows us, in particular, to investigate the energy (v) dependence of all nuclear effects. In conclusion we will compare our results with theoretical calculations [5, 6].
2. A DEPENDENCE OF SECONDARY LEPTOPRODUCTION AT LARGE zhA
The experimental results for semi-inclusive DIS on nuclei are usually presented in terms of the hadron multiplicity ratio RA/D, which represents the ratio of the number of hadrons of type h produced per DIS
a
RKr/D
} 1 i f 11 I p
i T : } 1 > } 1 1 1 1 1 } f 1 1 1 1 1
_I_I_I_I_I_I_I_I_I
0.2 0.4 0.6 0.8 1.0
z h
Fig. 3. Multiplicity ratio for identified neutral pions from a Kr target: (•) original ratio measured by HERMES [1], shifted ratios at (■) Ea = 1-2 GeV and (□) Ea = = 1-6 GeV.
event on a nuclear target of mass A to that from a deuterium target (D). The multiplicity ratio is defined as:
(5)
where is the yield of semi-inclusive
hadrons h from the nucleus A in a given zh bin.
In this section we are going to analyze the ratio (5) in the following way. Suppose one has two zh spectra for DIS on nucleon and nuclear targets or on two different nuclei (light and heavy ones). Then one can shift the spectrum that corresponds to the heavy nucleus according to Eq. (2) by changing Ea parameter. Assuming that nuclear effects are small for very light nuclei, it is possible then to calculate the fraction of the virtual photon energy spent on nuclear effects. This may be done by calculating the ratio of the shifted spectrum to the spectrum that corresponds to the light nucleus. When this ratio is close to unity, then the corresponding shift will give the absolute value of energy loss caused by the mentioned nuclear effects.
For the purpose of our analysis we used the experimental data on DIS on nuclei measured by the HERMES Collaboraton [1, 2] as well as EMC data [3].
The HERMES results for deep-inelastic e+D and e+ Kr scattering at 27.5 GeV are available in terms of the ratio (5) for different set of secondaries (pions, kaons, p, and p) [1]. Neutral pion and averaged charged-pion multiplicities for DIS of positrons on
hydrogen at the same energy are published in [2]. Neglecting the difference between hydrogen and deuterium targets one can extract the multiplicity for pions produced on a heavy target (Kr) from the multiplicity ratio and absolute multiplicity spectrum for hydrogen. The measured ratio for neutral pions is presented in Fig. 1a. In Fig. 1b one can see extracted spectrum for Kr target (closed circles) as well as neutral-pion multiplicity for hydrogen (open circles) from [2]. One can see evident suppression of Kr spectrum in comparison with hydrogen one.
Having two multiplicity spectra for p and Kr targets one can analyze them in the way described above. Figure 2 represents the shifted Kr spectrum with Ea = 1 GeV (closed circles) as well as spectrum for hydrogen measured by HERMES (open circles).
Now to estimate how much energy of the virtual photon is spent on nuclear effects one should calculate the ratio (5) of the shifted Kr spectrum to the hydrogen spectrum. The calculated ratios are presented in Fig. 3 for different EA values (squares). The figure also represents original ratio without any shift (closed circles). One can see that corresponding values of energy losses lie between EA = 1.0 and 1.4 GeV.
Omitting intermediate calculations we present results of the analysis for charged pions (from the same experiment) at the same energies (see Fig. 4 for
and n-). From the last two figures (Figs. 3 and 4) one can see approximately the same suppression for all pions.
There are additional data on the market relevant for such an analysis, namely the data on deep-inelastic ¡iD and ¡Cu scattering at 100—280 GeV obtained by EMC [3]. They measured differential multiplicities of forward produced charged hadrons on both nuclei ((v) = 60 GeV), which can be used directly in our analysis as described above. The results of the analysis one can see in Fig. 5. Figure 5a represents multiplicities for D (closed circles) and Cu (open circles) targets measured by EMC, and Fig. 5b represents the ratios obtained with our analysis (squares) as well as the original EMC ratio (closed circles).
Results for energy losses obtained for Cu target Ea & 1.4 GeV are in reasonable agreement with those obtained for Kr target. However, HERMES measurements were done at (v) & 16 GeV, while EMC data were taken at (v) & 60 GeV. Therefore one can conclude that energy dependence of nuclear effects for all charged particles here is rather weak within the errors of the analysis.
Unfortunately, the inclusive spectra of identified secondaries are published only at one (HERMES)
R
Kr/D
Fig. 4. Multiplicity ratios for and n : (•) original ratio measured by HERMES [1], shifted ratios at (■) EA = 1.2 GeV and (□) Ea = 1.6 GeV
(1/A)da/dz h
EMC: a
+ A ^ h± + X at 100-280 GeV
R
Cu/D
10
100
10
1-1
<v> = 60 GeV
1.0
0.9
§
9
0.8
[]
[]
[] []
jj-
0 0.2 0.4 0.6 0.8 zh 0 0.2 0.4 0.6 0.8 1.0
z h
Fig. 5. (a) Differential hadron multiplicity as a function of zh for (o) Cu and (•) D. The statistical errors are of a similar size to the symbols, the systematic errors are not shown. (b) Multiplicity ratios for hadrons from Cu target: (•) original ratio measured by EMC [3], shifted ratios at (■) Ea = 1.2 GeV and (□) Ea = 1.6 GeV.
energy and we cannot discuss the energy dependence of our Ea parameter. However, there exist the experimental results [1] for Ra/d as a function of v. For pions these ratios increase with v and it
means that EA values have at least more weak v dependence than the linear one. The values of Ra/d
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