- Email: [email protected]
GENEVE: a Montecarlo generator for neutrino interactions in the intermediate energy range
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PROCEEDINGS SUPPLEMENTS ELSEVIER
Nuclear Physics B (Proc. Suppl.) 112 (2002) 183-187
www.elscvicr.com/l~a~/nl~
GENEVE: a Montecarlo generator for Neutrino Interactions in the Intermediate Energy range F. Cavanna a *, O. Palamara b t aDip.to di Fisica e INFN, Univ. di L'Aquila, via Vetoio, 67010 L'Aquila, Italy bLaboratori Nazionali del Gran Sasso, INFN, s.s. 17bis km 18+910, Assergi (AQ), Italy GENEVE is a MonteCarlo code developed during the last few years inside the ICARUS Collaboration. It describes neutrino interactions on nuclear target in the "intermediate energy range" and therefore is well suited for simulation of atmospheric neutrino scattering. We provide here few indications about the models adopted for the simulation of quasi-eiastic interactions and of scattering processes proceeding via nucleon resonances excitation and decay. The code has been tested with comparisons with available data and an overall agreement turns out to be achieved. A gradual upgrade of the code is indeed necessary, according to many indications, reviewed during this Workshop, from more recent theoretical developments and experimental hints. More in general, the definitive assessment of a canonical MonteCarlo code for neutrino physics (in the intermediate energy range) has been identified as one of the most urgent task for a fully comprehensive understanding of the neutrino oscillation phenomenon. We believe that the only way to proceed relies on the forthcoming results of present and future generations of experiments, performed with best suited, available technologies, aiming to precise neutrino cross section measurements.
i. Introduction GENEVE (GEnerator of Neutrino EVEnts) is one of the MonteCarlo codes developed inside the ICARUS Collaboration. This code, in an early stage version, has been used at the time of the ICARUS proposal (1993) and later for Addendum to the Proposal (the T600 experiment, 1995) for the simulation of atmospheric neutrino interactions. GENEVE is conceived for simulation of neutrino interaction processes on nuclear target, lSAr4o in case of ICARUS, with neutrino energies ranging from O(100 MeV) up to few GeV (i.e. an "intermediate neutrino energy range"). The initial v energy is randomly extracted from one of the spectra available as " d a t a cards" (like atmospheric v-spectra or different types of "intermediate energy" beam spectra). The initial nucleon state is described according to a relativistic Fermi gas (RFG) model (see Sec.2).
*E-maih flavio.cavanna~aquila.infn.it ?E-maih ornella.palamara~lngs.infn.it
The simulation provides 4-momentum vectors for any particle emerging in final state after the Weak v scattering on the initial state nucleon (n or p) bound in the parent nucleus. In the GENEVE code, three issues are presently embedded at different levels of interconnection (and at different level of accuracy/development): . Simulation of quasi-elastic (QE) interactions (highest level of accuracy) . Simulation of interactions with Resonance production/decay (RES) (intermediate level) • Simulation of deep-inelastic (DIS) interactions (lower level). We will concentrate here on some details about the QE channel and RES channel 2. S i m u l a t i o n o f Q E v - i n t e r a c t i o n s The QE part of the GENEVE code has been progressively upgraded. It provides simulation
0920-5632/02/$ - see front matter© 2002 Publishedby ElsevierScienceB.V. PII S0920-5632(02)01767-X
184
E Cavanna, O. Palamara/Nuclear Physics B (Proc. Suppl.) 112 (2002) 183-187
for both CC and NC neutrino interactions on p and n target, with all u-, P-fiavours (re, v,, u~). Proton and neutron can be treated as free target or bound target in nuclei (1SAra0 nucleus is norre_ally used, but other nuclei may be chosen). Dynamics of the interaction is described by current-current Lagrangian (valid in the limit of Q2 << M~v)according to the "standard" notation from [1]. In this framework, the hadronic current is defined through the Vector, Axial and PseudoScalar Weak Form Factors of the nucleon. Under "standard hypotheses", (iso-triplet hypothesis, CVC-Conserved Vector Current, PCAC-Partially Conserved Axial Current, ..) only the Vector Form Factors F V, F ~ and the Axial Form Factor F A axe relevant (F Ps can be expressed in terms of FA). As in the case of the electro-magnetic Form Factors, F ~ , F ~ are described in terms of Sachs Form Factors, depending on the Vector Mass (set equal to M v = 0.84 GeV/c2), F A is assumed to be a dipole form (as for the Vector Form Factors), with FA(o) = --1.23 and MA = 1.03 GeV/c 2 (the somehow "controversial" world average value). From the current-current Lagrangian it is rather straightforward to obtain the v + N - , l(v') + N r CC (NC) cross-sections for free nucleon targets. In particular, the da/dQ 2 differential crosssection is parameterised 1 in the M C code, in terms of the Vector and Axial Weak Form Factors. For bound nucleon target, nuclear effects play a relevant role. Some of these, targe~ motion, binding energy and Pauli blocking are included in the simulation. Final state nucleon re-interactions inside the parent nucleus are taken into account only in a simplified approximation (see Sec. 3). Production of nuclear bound states is not considered at all since this is relevant at low energy (outside the range of energy considered for the MC purpose). According to [2], nuclear effects are calculated in the incoherent impulse approximation, with offshell kinematics for the nucleon target in its initial state, to guarantee 4-momentum conservation in 1Other relevant parameters in use are/~p - ~
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bution for the target nucleon embedded in nucleus A =is Ar4o, [Right] Off-sheU squared mass of the
target proton, as a function of[ ~ v I momentum. the scattering process. The remaining part (A-l) of the nucleus acts as "spectator", i.e. it is free and is on the mass-sheU. Even though an off-shell kinematics is assumed for the initial nucleon state, the weak process dynamics is assumed to be on-sheU, i.e. we identify the Form Factors for nucleon embedded in the nuclear matter with those for free nucleon. This assumption [4] is made reasonable because Fermi motion does not affect the 4-momentum transfer (Q2) to the target nucleon. The Fermi momentum I ~ l v I distribution for the target nucleon, normally fiat up to kF, is here modified to include a high-momentum component (tail, up to 4 GeV/c [2]), arising from nucleon-nucleon correlations inside the nucleus ("quasi-deuteron" formation). Values of kF for different nuclei are taken from [3], in case of At: kF(Ar) = 0.246 GeV/c. In Fig. 1 [Left] the distribution of Fermi momentum I ~ N I, in use in the MC code, for the target nucleon bound in A = Ar
E Cavanna, O. PalamaralNuclear Physics B (Proc. Suppl.) 112 (2002) 183-187
is reported. The off-shell mass of the target nucleon (proton) is reported in Fig. 1 [Right] as a function of its momentum I ~i~N [. In the GFNEVE MonteCarlo, the result of the
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185
pared to standard analytical approaches with averaged response functions (e.g. [5]). Moreover, as a peculiar feature of the GENEVE code, the crosssection, a(E~), for bound-nucleon target can be determined from the ratio (bin per bin) of the number of "good events" with the total number of generated events. The absolute cross-section (in 10-3Scm2 units) is obtained by normalisation to the free-nucleon case [1]. We report in Fig. 2 the v, QE-CC cross-sections a(E~), as obtained fromthe GENEVE MonteCarlo generation. Crosssections are reported separately for free nucleon and nucleon target bound in Ar nuclei. As benchmark information, assuming fixed E~ = 500 MeV, we report (a) the kinetic energy distributions, Fig. 3, for the final state particles (proton and muon) from v~ QE-CC interaction and (b) the angular distribution - relative to the:incident v~ direction - for proton and muon, Fig. 4. In both figures, solid curves refer to bound target nucleons (neutron) in At.
10
++..~m,(c,+v)
Figure 2. QE-CC ~,~ cross-sections a(E~)IE~, from the GENEVE MonteCarlo output, for neutron target .free [dashed] and bound in Ar nuclei [solid]. Comparison with some experimental data is also reported constraints from nuclear effects are investigated on statistical basis. In other words, after the initial state (v + N system) kinematics is randomly generated (Ev extracted from a given beam spectrum and I ~ N I from the distribution shown in Fig. 1) and the Q2 value is also randomly extracted and weighted according to the da/dQ 2 differential cross-section (calculated at the extracted Ev value), only those cases leading to final states with both particles (l + N') on the mass shell are tagged as "good events". In this scheme nucleon Fermi motion and binding energy 2 are automatically taken into account. This procedure allows, in particular, a more precise treatment of the v~,(~'e) CC event kinematics around the # (e) production threshold, com2The binding energy corresponds to the mass difference EB = ( M A - 1 + MN) -- M A. In case of Argon, EB = 11 MeV.
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3. QE-CC v, interaction (fixed E ~ = 500MeV MeV): kinetic energy distribution (GENEVE MonteCarlo) for final state proton [Top] and muon [Bottom]. Neutron target bound in Ar nuclei.
E Cavanna, O. Palamara/Nuclear Physics B (Proc. Suppl.) 112 (2002) 183-187
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Figure 4. QE-CC u~ interaction (fixed E~ = 500 MeV): angular distribution (GENEVE Mon-
teCarlo) for final state proton [Top] and muon [Bottom]. Neutron target bound in Ar nuclei. 3. S i m u l a t i o n of R E S u-interactions
Treatment of resonance excitation induced by neutrino interaction is very complicated from a theoretical point of view and consequently also at MonteCarlo simulation level. Nucleon has a complex radial and angular bound state structure. Usually the FKR model [6] is used, with the nucleon described as the ground state of three quarks bound by harmonic potential. Excitations of this state corresponds to the observed baryonic resonances A, N*. From de-excitation of the resonant state, pion production foUows. Each decay channel results from superposition and interference between all (kinematicaUy allowed) resonance amplitudes. A detailed cross sections calculation has been performed by Rein and Seghal [7]. In the GENEVE MonteCarlo this model has been adopted. Particular attention should be paid to the problem of connecting resonances (invariant mass W _< 2 GeV/c ~) and DIS regimes. In our MonteCarlo this problem has been approached in a still unsatisfactory way, namely the two contributions (for
each specific final state) have been weighted by hand to reproduce the total cross-section value from available experimental data. Due to the limited statistics of the data, this procedure may evidently introduce large errors. Finally, the probability of pion (and nucleon) re-interaction (absorption or re-scattering) inside the parent nucleus should also be carefully accounted for. The MonteCarlo code includes a charge-exchange matrix, defined by the ANP model [8], whose elements provides chargeexchange and change in direction probabilities. These values depend on the size of the parent nucleus (i.e. Ar nucleus, in our case) and on the energy of the pions. Moreover, at each scattering of the pion, on its way out of the nucleu§, there is an additional chance that it is absorbed. The absorption cross section has been coded according to [9]. 17 resonance states (with 1232 <_ W < 1950 MeV/c 2) have been considered [10]. Following [7], the GEN EVE MonteCarlo provides a complete treatment of y- P-induced single-pion production 3 in (3+3) CC channels and (4+4) NC channels for both re, v~ flavours (28 reactions in total). As an example, the three CC single-pion cross sections for u and P reactions are reported in Fig. 5. As a distinctive feature of this MonteCarlo code, we should mention the treatment of the angular distribution of the final state particles (N', r) after resonance decay. An isotropic distribution, in the resonance rest frame, is usually assumed [7], however deviations from this behaviour have been reported from experimental data [11]. In our code we adopted a sophisticated model due to Novakowski [12], based on the expansion of the cross section in terms of spherical harmonics. The expansion coefficients are defined from selection rules on the angular momentum of the resonance states contributing to each individual decay channel. This formalism allows one to evaluate the polar angle between the direction of the emitted pion and the direction of the transferred 3-momentum. A tiny anisotropy in cos(0) distribution (the polar angle of emission in the resoaSingle-pion production via Coherent scattering is also included, according to [7]. Single ~ production and single kaon production are not included at the present stage
E Cavanna, O. Palamara/Nuclear Physics B (Proc. Suppl.) 112 (2002) 183-187
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Figure 5. R e s o n a n t C C single-pion cross sections f o r v [solid line] and P [dashed line] reactions: [top] v~ + p --* i t - + p + iv + and Pt~ + n --~ it+ + n + lr-, [centre] % + n ~ i t - + p + Tr° and P~+p #+ + n + Ir°, ]bottom] v~ + n --~ # - + n + Ir+ and p~ + p ~ it+ + p + I t - . nance rest frame) for the final pion is obtained. Further rotations drive to the determination of all kinematical variables in the lab frame. Direct comparison with experimental data is difficult due to distortions introduced by nuclear effects (pion re-scattering). Reconstruction of angular distributions, of final state particles from RES interactions, definitively represents an important, quite unexplored issue for new generation experiments. 4. Conclusions GENEVE is a MonteCarlo code developed during the last few years inside the ICARUS Collaboration. It describes neutrino interactions on nuclear target in the "intermediate energy range" and therefore it is well suited for simulation of atmospheric neutrino scattering. Amongst various distinctive features of this code we mention the precise treatment of the vt, (re) CC quasielastic event kinematics around the # (e) production threshold, where most of the atmospheric
187
neutrino events are concentrated. GENEVE is based on interaction models developed during the '70s and, whenever needed, on experimental parameters determined also from old neutrino experiments. Nevertheless, an overall agreement with available data is achieved. A gradual upgrade of the code is indeed necessary, according to many indications from more recent theoretical developments and some experimental hints. Many of these have been reviewed during this most interesting Nulnt01 Workshop. Nonetheless, we believe that the only way for a definitive assessment of a canonical MonteCarlo code for neutrino physics (in the intermediate energy range) will be provided by the results of present and future generations of experiment, performed with best suited, available technologies, aiming to precise neutrino cross section measurements. The GENEVE MonteCarlo is the result of efforts from many colleagues who have brought important contributions. The authors would like to acknowledge, in particular, the work of some former PhD students, C. Rossi, V. Molino and G. Ruscitti from l'Aquila University, and to thank P. Lipari and D. Casper for enlightening discussions. REFERENCES 1. C. Llwellyn-Smith, Phys. Rep. 3 (1972), 261. 2. A. Bodek and J. Ritchie, Phys. Rev. D23 (1981), 1070. 3. E. Monitz et al., Phys. Rev. Lett 26 (1971), 445• 4. A. Bodek, Phys. Rev. D8 (1974), 2331. A. Bodek et al., Phys. Rev. D20 (1979), 1471. 5. T.K. Gaisser and J.S. O'Connel, Phys. Rev. D34 (1986), 822. 6. R. Feynman, M. Kislinger and F. Ravndal, Phys. Rev. D3 (1971), 2706. 7. D. Rein and L.M. Sehgal, Ann. Phys. 133 (1981), 79. 8. L. Adler, S. Nussinov and E.A. Paschos, Phys. Rev. D9 (1974), 2125. 9. T.K. Gaisser, M. Nowakowskiand E.A. Paschos, Phys. l ~ v . D33 (1986), 1233• 10. Particle Data Group, Eur. Phys. Jou. C3 (1998), 49. 11. S.J. Barish et al., Phys. Lett. B91 (1980),161. P. Allen et al., Nucl. Phys. B264 (1986), 221. 12. M.Novakowski, Z. Phys. C35 (1987), 129.
PROCEEDINGS SUPPLEMENTS ELSEVIER
Nuclear Physics B (Proc. Suppl.) 112 (2002) 183-187
www.elscvicr.com/l~a~/nl~
GENEVE: a Montecarlo generator for Neutrino Interactions in the Intermediate Energy range F. Cavanna a *, O. Palamara b t aDip.to di Fisica e INFN, Univ. di L'Aquila, via Vetoio, 67010 L'Aquila, Italy bLaboratori Nazionali del Gran Sasso, INFN, s.s. 17bis km 18+910, Assergi (AQ), Italy GENEVE is a MonteCarlo code developed during the last few years inside the ICARUS Collaboration. It describes neutrino interactions on nuclear target in the "intermediate energy range" and therefore is well suited for simulation of atmospheric neutrino scattering. We provide here few indications about the models adopted for the simulation of quasi-eiastic interactions and of scattering processes proceeding via nucleon resonances excitation and decay. The code has been tested with comparisons with available data and an overall agreement turns out to be achieved. A gradual upgrade of the code is indeed necessary, according to many indications, reviewed during this Workshop, from more recent theoretical developments and experimental hints. More in general, the definitive assessment of a canonical MonteCarlo code for neutrino physics (in the intermediate energy range) has been identified as one of the most urgent task for a fully comprehensive understanding of the neutrino oscillation phenomenon. We believe that the only way to proceed relies on the forthcoming results of present and future generations of experiments, performed with best suited, available technologies, aiming to precise neutrino cross section measurements.
i. Introduction GENEVE (GEnerator of Neutrino EVEnts) is one of the MonteCarlo codes developed inside the ICARUS Collaboration. This code, in an early stage version, has been used at the time of the ICARUS proposal (1993) and later for Addendum to the Proposal (the T600 experiment, 1995) for the simulation of atmospheric neutrino interactions. GENEVE is conceived for simulation of neutrino interaction processes on nuclear target, lSAr4o in case of ICARUS, with neutrino energies ranging from O(100 MeV) up to few GeV (i.e. an "intermediate neutrino energy range"). The initial v energy is randomly extracted from one of the spectra available as " d a t a cards" (like atmospheric v-spectra or different types of "intermediate energy" beam spectra). The initial nucleon state is described according to a relativistic Fermi gas (RFG) model (see Sec.2).
*E-maih flavio.cavanna~aquila.infn.it ?E-maih ornella.palamara~lngs.infn.it
The simulation provides 4-momentum vectors for any particle emerging in final state after the Weak v scattering on the initial state nucleon (n or p) bound in the parent nucleus. In the GENEVE code, three issues are presently embedded at different levels of interconnection (and at different level of accuracy/development): . Simulation of quasi-elastic (QE) interactions (highest level of accuracy) . Simulation of interactions with Resonance production/decay (RES) (intermediate level) • Simulation of deep-inelastic (DIS) interactions (lower level). We will concentrate here on some details about the QE channel and RES channel 2. S i m u l a t i o n o f Q E v - i n t e r a c t i o n s The QE part of the GENEVE code has been progressively upgraded. It provides simulation
0920-5632/02/$ - see front matter© 2002 Publishedby ElsevierScienceB.V. PII S0920-5632(02)01767-X
184
E Cavanna, O. Palamara/Nuclear Physics B (Proc. Suppl.) 112 (2002) 183-187
for both CC and NC neutrino interactions on p and n target, with all u-, P-fiavours (re, v,, u~). Proton and neutron can be treated as free target or bound target in nuclei (1SAra0 nucleus is norre_ally used, but other nuclei may be chosen). Dynamics of the interaction is described by current-current Lagrangian (valid in the limit of Q2 << M~v)according to the "standard" notation from [1]. In this framework, the hadronic current is defined through the Vector, Axial and PseudoScalar Weak Form Factors of the nucleon. Under "standard hypotheses", (iso-triplet hypothesis, CVC-Conserved Vector Current, PCAC-Partially Conserved Axial Current, ..) only the Vector Form Factors F V, F ~ and the Axial Form Factor F A axe relevant (F Ps can be expressed in terms of FA). As in the case of the electro-magnetic Form Factors, F ~ , F ~ are described in terms of Sachs Form Factors, depending on the Vector Mass (set equal to M v = 0.84 GeV/c2), F A is assumed to be a dipole form (as for the Vector Form Factors), with FA(o) = --1.23 and MA = 1.03 GeV/c 2 (the somehow "controversial" world average value). From the current-current Lagrangian it is rather straightforward to obtain the v + N - , l(v') + N r CC (NC) cross-sections for free nucleon targets. In particular, the da/dQ 2 differential crosssection is parameterised 1 in the M C code, in terms of the Vector and Axial Weak Form Factors. For bound nucleon target, nuclear effects play a relevant role. Some of these, targe~ motion, binding energy and Pauli blocking are included in the simulation. Final state nucleon re-interactions inside the parent nucleus are taken into account only in a simplified approximation (see Sec. 3). Production of nuclear bound states is not considered at all since this is relevant at low energy (outside the range of energy considered for the MC purpose). According to [2], nuclear effects are calculated in the incoherent impulse approximation, with offshell kinematics for the nucleon target in its initial state, to guarantee 4-momentum conservation in 1Other relevant parameters in use are/~p - ~
GFcosOc = 1.6632 x 0,9737 x 10 - 5 G e V - 1 .
=
3,71 and
~
7 3O
17,1i
kw- 0.24~ C,eV/¢
i:
~ u
12.1l
O.75
10
0.7
7J
t
S
0.8
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O.06
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0o
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0,2
0,4
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~
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I ....
I,,.
0,4
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(~I¢) Figure 1. [Lej~]Fermi momentum I ~ N f distri-
bution for the target nucleon embedded in nucleus A =is Ar4o, [Right] Off-sheU squared mass of the
target proton, as a function of[ ~ v I momentum. the scattering process. The remaining part (A-l) of the nucleus acts as "spectator", i.e. it is free and is on the mass-sheU. Even though an off-shell kinematics is assumed for the initial nucleon state, the weak process dynamics is assumed to be on-sheU, i.e. we identify the Form Factors for nucleon embedded in the nuclear matter with those for free nucleon. This assumption [4] is made reasonable because Fermi motion does not affect the 4-momentum transfer (Q2) to the target nucleon. The Fermi momentum I ~ l v I distribution for the target nucleon, normally fiat up to kF, is here modified to include a high-momentum component (tail, up to 4 GeV/c [2]), arising from nucleon-nucleon correlations inside the nucleus ("quasi-deuteron" formation). Values of kF for different nuclei are taken from [3], in case of At: kF(Ar) = 0.246 GeV/c. In Fig. 1 [Left] the distribution of Fermi momentum I ~ N I, in use in the MC code, for the target nucleon bound in A = Ar
E Cavanna, O. PalamaralNuclear Physics B (Proc. Suppl.) 112 (2002) 183-187
is reported. The off-shell mass of the target nucleon (proton) is reported in Fig. 1 [Right] as a function of its momentum I ~i~N [. In the GFNEVE MonteCarlo, the result of the
-I/f *\ :fl N 0t0-t
'I
185
pared to standard analytical approaches with averaged response functions (e.g. [5]). Moreover, as a peculiar feature of the GENEVE code, the crosssection, a(E~), for bound-nucleon target can be determined from the ratio (bin per bin) of the number of "good events" with the total number of generated events. The absolute cross-section (in 10-3Scm2 units) is obtained by normalisation to the free-nucleon case [1]. We report in Fig. 2 the v, QE-CC cross-sections a(E~), as obtained fromthe GENEVE MonteCarlo generation. Crosssections are reported separately for free nucleon and nucleon target bound in Ar nuclei. As benchmark information, assuming fixed E~ = 500 MeV, we report (a) the kinetic energy distributions, Fig. 3, for the final state particles (proton and muon) from v~ QE-CC interaction and (b) the angular distribution - relative to the:incident v~ direction - for proton and muon, Fig. 4. In both figures, solid curves refer to bound target nucleons (neutron) in At.
10
++..~m,(c,+v)
Figure 2. QE-CC ~,~ cross-sections a(E~)IE~, from the GENEVE MonteCarlo output, for neutron target .free [dashed] and bound in Ar nuclei [solid]. Comparison with some experimental data is also reported constraints from nuclear effects are investigated on statistical basis. In other words, after the initial state (v + N system) kinematics is randomly generated (Ev extracted from a given beam spectrum and I ~ N I from the distribution shown in Fig. 1) and the Q2 value is also randomly extracted and weighted according to the da/dQ 2 differential cross-section (calculated at the extracted Ev value), only those cases leading to final states with both particles (l + N') on the mass shell are tagged as "good events". In this scheme nucleon Fermi motion and binding energy 2 are automatically taken into account. This procedure allows, in particular, a more precise treatment of the v~,(~'e) CC event kinematics around the # (e) production threshold, com2The binding energy corresponds to the mass difference EB = ( M A - 1 + MN) -- M A. In case of Argon, EB = 11 MeV.
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3. QE-CC v, interaction (fixed E ~ = 500MeV MeV): kinetic energy distribution (GENEVE MonteCarlo) for final state proton [Top] and muon [Bottom]. Neutron target bound in Ar nuclei.
E Cavanna, O. Palamara/Nuclear Physics B (Proc. Suppl.) 112 (2002) 183-187
186
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Figure 4. QE-CC u~ interaction (fixed E~ = 500 MeV): angular distribution (GENEVE Mon-
teCarlo) for final state proton [Top] and muon [Bottom]. Neutron target bound in Ar nuclei. 3. S i m u l a t i o n of R E S u-interactions
Treatment of resonance excitation induced by neutrino interaction is very complicated from a theoretical point of view and consequently also at MonteCarlo simulation level. Nucleon has a complex radial and angular bound state structure. Usually the FKR model [6] is used, with the nucleon described as the ground state of three quarks bound by harmonic potential. Excitations of this state corresponds to the observed baryonic resonances A, N*. From de-excitation of the resonant state, pion production foUows. Each decay channel results from superposition and interference between all (kinematicaUy allowed) resonance amplitudes. A detailed cross sections calculation has been performed by Rein and Seghal [7]. In the GENEVE MonteCarlo this model has been adopted. Particular attention should be paid to the problem of connecting resonances (invariant mass W _< 2 GeV/c ~) and DIS regimes. In our MonteCarlo this problem has been approached in a still unsatisfactory way, namely the two contributions (for
each specific final state) have been weighted by hand to reproduce the total cross-section value from available experimental data. Due to the limited statistics of the data, this procedure may evidently introduce large errors. Finally, the probability of pion (and nucleon) re-interaction (absorption or re-scattering) inside the parent nucleus should also be carefully accounted for. The MonteCarlo code includes a charge-exchange matrix, defined by the ANP model [8], whose elements provides chargeexchange and change in direction probabilities. These values depend on the size of the parent nucleus (i.e. Ar nucleus, in our case) and on the energy of the pions. Moreover, at each scattering of the pion, on its way out of the nucleu§, there is an additional chance that it is absorbed. The absorption cross section has been coded according to [9]. 17 resonance states (with 1232 <_ W < 1950 MeV/c 2) have been considered [10]. Following [7], the GEN EVE MonteCarlo provides a complete treatment of y- P-induced single-pion production 3 in (3+3) CC channels and (4+4) NC channels for both re, v~ flavours (28 reactions in total). As an example, the three CC single-pion cross sections for u and P reactions are reported in Fig. 5. As a distinctive feature of this MonteCarlo code, we should mention the treatment of the angular distribution of the final state particles (N', r) after resonance decay. An isotropic distribution, in the resonance rest frame, is usually assumed [7], however deviations from this behaviour have been reported from experimental data [11]. In our code we adopted a sophisticated model due to Novakowski [12], based on the expansion of the cross section in terms of spherical harmonics. The expansion coefficients are defined from selection rules on the angular momentum of the resonance states contributing to each individual decay channel. This formalism allows one to evaluate the polar angle between the direction of the emitted pion and the direction of the transferred 3-momentum. A tiny anisotropy in cos(0) distribution (the polar angle of emission in the resoaSingle-pion production via Coherent scattering is also included, according to [7]. Single ~ production and single kaon production are not included at the present stage
E Cavanna, O. Palamara/Nuclear Physics B (Proc. Suppl.) 112 (2002) 183-187
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Figure 5. R e s o n a n t C C single-pion cross sections f o r v [solid line] and P [dashed line] reactions: [top] v~ + p --* i t - + p + iv + and Pt~ + n --~ it+ + n + lr-, [centre] % + n ~ i t - + p + Tr° and P~+p #+ + n + Ir°, ]bottom] v~ + n --~ # - + n + Ir+ and p~ + p ~ it+ + p + I t - . nance rest frame) for the final pion is obtained. Further rotations drive to the determination of all kinematical variables in the lab frame. Direct comparison with experimental data is difficult due to distortions introduced by nuclear effects (pion re-scattering). Reconstruction of angular distributions, of final state particles from RES interactions, definitively represents an important, quite unexplored issue for new generation experiments. 4. Conclusions GENEVE is a MonteCarlo code developed during the last few years inside the ICARUS Collaboration. It describes neutrino interactions on nuclear target in the "intermediate energy range" and therefore it is well suited for simulation of atmospheric neutrino scattering. Amongst various distinctive features of this code we mention the precise treatment of the vt, (re) CC quasielastic event kinematics around the # (e) production threshold, where most of the atmospheric
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neutrino events are concentrated. GENEVE is based on interaction models developed during the '70s and, whenever needed, on experimental parameters determined also from old neutrino experiments. Nevertheless, an overall agreement with available data is achieved. A gradual upgrade of the code is indeed necessary, according to many indications from more recent theoretical developments and some experimental hints. Many of these have been reviewed during this most interesting Nulnt01 Workshop. Nonetheless, we believe that the only way for a definitive assessment of a canonical MonteCarlo code for neutrino physics (in the intermediate energy range) will be provided by the results of present and future generations of experiment, performed with best suited, available technologies, aiming to precise neutrino cross section measurements. The GENEVE MonteCarlo is the result of efforts from many colleagues who have brought important contributions. The authors would like to acknowledge, in particular, the work of some former PhD students, C. Rossi, V. Molino and G. Ruscitti from l'Aquila University, and to thank P. Lipari and D. Casper for enlightening discussions. REFERENCES 1. C. Llwellyn-Smith, Phys. Rep. 3 (1972), 261. 2. A. Bodek and J. Ritchie, Phys. Rev. D23 (1981), 1070. 3. E. Monitz et al., Phys. Rev. Lett 26 (1971), 445• 4. A. Bodek, Phys. Rev. D8 (1974), 2331. A. Bodek et al., Phys. Rev. D20 (1979), 1471. 5. T.K. Gaisser and J.S. O'Connel, Phys. Rev. D34 (1986), 822. 6. R. Feynman, M. Kislinger and F. Ravndal, Phys. Rev. D3 (1971), 2706. 7. D. Rein and L.M. Sehgal, Ann. Phys. 133 (1981), 79. 8. L. Adler, S. Nussinov and E.A. Paschos, Phys. Rev. D9 (1974), 2125. 9. T.K. Gaisser, M. Nowakowskiand E.A. Paschos, Phys. l ~ v . D33 (1986), 1233• 10. Particle Data Group, Eur. Phys. Jou. C3 (1998), 49. 11. S.J. Barish et al., Phys. Lett. B91 (1980),161. P. Allen et al., Nucl. Phys. B264 (1986), 221. 12. M.Novakowski, Z. Phys. C35 (1987), 129.