3π and 4π meson production in np interactions at intermediate energies

3

π

and 4

π

meson production in np interactions at intermediate

energies

A.P.Jerusalimov1_,A.V.Belyaev1_,V.P.Ladygin1_{,V.N.Pechenov}2_{, andYu.A.Troyan}1

1_{Joint Institute for Nuclear Research, 141980 Dubna, Russia}

2_{GSI Helmholtzzentrum fur Schwerionenforschung GmbH, 64291 Darmstadt, Germany}

Abstract.The study of 3πand 4πmeson production in np interactions was carried out at

the momenta of incident neutrons P0=3.83, 4.42 and 5.20 GeV/c. The characteristics of

the reactions were satisfactorily described by OPER model. For the better description of the reactionnp → ppπ+π−π−π0_{it was necessary to take into account the production of} η0_andω0_mesons.

1 Introduction

The study of multipion production in NN collisions is one way to obtain information about the NN, πN andππstates, including:

dibaryons (including I=2 in ppπ+),

dipions (narrowσ0_{meson,ππstate with I=2),}

pentaquarks (I=5/2, S=+1), missing resonances, etc.

Also the important task is the test of various models of pion production in NN interaction, such as, for example, Valencia model [1], Xu Cao model [2] and OPER model [3, 4].

2 Experiment

The neutron-proton interactions were studied using neutron beam and liquid hydrogen bubble (target) at the JINR Synchrophasotron [5]. The unique in fullness and precision data were obtained. It allowed to carry out the detailed study of inelastic np interactions in in a wide range of energies using the quasimonochromatic neutrons with P0<2.5% under condition of 4πgeometry.

The following reactions with 3 and 4πmesons in the final states were studied: np→ ppπ+_π−_π−_,

np→ ppπ+_π−_π−_π0_,

np→npπ+_π+_π−_π−

at the momenta of P0=3.83, 4.42 and 5.20 GeV/c (see figure 1).

The accuracy of the momentum and scattering angle reconstruction for the secondary charged particles wasσ_p/p ∼2% andσ_Θ ∼10 mrad, respectively. The separation of the reaction channels

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0

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4 4.5 5

a.u

0 0.05 0.1 0.15

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0

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δ

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3 3.5 4 4.5

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0 0.02 0.04 0.06 0.08

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0

P

4.5 5 5.5 6

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0 0.02 0.04 0.06

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=2.3% 0 P

δ

=5.20 GeV/c

0

P

Figure 1.The momentum distributions of the incident neutrons atP0=3.83, 4.42 and 5.20 GeV/c

were carried out by the standardχ2_{procedure using corresponding constraint equations [6]. Finally,}

the numbers of events that were selected for the further study:

P0=3.83 GeV/c P0=4.42 GeV/c P0=5.20 GeV/c

np→ ppπ+_π−_π− _{390 events 743 events 5790 events}

np→ ppπ+_π−_π−_π0 _{66 events 215 events 2666 events}

np→npπ+_π+_π−_π− _{83 events 344 events 4530 events}

The cross sections of the considered reactions were presented in [7].

3 Data analysis

This reaction is characterized by:

- plentiful production of theΔresonance, both from direct production and fromΔ∗andN∗ decays through the modeΔπ,

- large peripherality of the secondary nucleons.

The model of reggeizedπmeson exchange suggested in ITEP [3] was taken to describe the exper-imental distributions of the considered reactions. The advantages of this model are:

- small number of free parameters (3 in our case), - wide range of the described energies (2÷200 GeV),

- calculated values are automatically normalized to the reaction cross section.

The following diagrams were taken into account to calculate the characteristics of the reactions np→NN3πandnp→NN4π:

n

p

N

N

π

π π

a)

π

n

p

N

N

π

π π

c)

π

n

p N

N

π π π

b)

π

3.1 Reactionnp→ ppπ+π−π−

The results of the calculations using OPER model for the reactionnp → ppπ+π−π−are shown in figure 3 for the data atP0=5.2 GeV/c and in figure 4 for the data atP0=4.42 GeV/c andP0=3.83

GeV/c. One can see a good agreement between the experimental data and theoretical calculations.

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[GeV/c π

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Events/(0.02 GeV/c 0 500 1000

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M(p,pi-)

-π p

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[GeV/c π π

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M(p,pi+,pi-)

-π + π p

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M(pi+,pi-)

-π + π

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Events/(0.02 GeV/c 0 100 200 300

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M(pi-,pi-)

-π -π

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[GeV/c π π π M

0.5 1 1.5

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M(pi+,pi-,pi-)

-π -π + π

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Θ cos -1 -0.5 0 0.5 1

Events/0.1

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cosT*(p)

protons

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Θ cos -1 -0.5 0 0.5 1

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cosT*(pi+)

+ π

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Θ cos -1 -0.5 0 0.5 1

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0 200 400 600 800 1000

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cosT*(pi-)

-π

Figure 3.The distributions for the reactionnp→ ppπ+π−π−at P0=5.20 GeV/c. Solid line - calculations using

OPER model.

3.2 Reactionnp→ ppπ+π−π−π0

The results of the calculations using OPER model for the reactionnp→ ppπ+π−π−π0_{are shown in}

figure 5 for the data atP0=5.20 GeV/c.

One can see a good agreement between the experimental data and theoretical calculations except the region ofη0 andω0 mesons at the masses ofπ+π−π0 combinations. As far as it concerned the description ofη0andω0mesons it is necessary to take into account the diagrams of the type that are showed in figure 6.

The diagrams 6a and 6b describeη0_{-meson production through the production ofN}∗

1535resonance

inπNinteraction with the consequent decayN₁₅₃₅∗ →Nη0_{. The "hanged" diagrams 6c and 6d describe}

η0_{meson production due to a-π or σ-η interaction.}

The results at P0=4.42 GeV/c and P0=3.83 GeV/c are not presented due to a small statistics. But

OPER model also described satisfactorily the experimental distribution and the signal ofη0 _andω0

mesons production was also observed at these energies.

3.3 Reactionnp→npπ+π+π−π−

The results of the calculations using OPER model for the reactionnp→ npπ+π+π−π−are shown in figure 7 for the data atP0=5.2 GeV/c and in figure 8 for the data atP0=4.42 GeV/c andP0=3.83

GeV/c.

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M(p,pi+)

+ π

p

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M(p,pi+,pi-) -π + π p

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50 100

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M(p,pi+,pi-) -π + π p

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M(pi+,pi-)

-π + π

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M(pi+,pi-,pi-) -π -π + π

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-π + π

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M(pi+,pi-,pi-) -π -π + π

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Events/0.1 0 50 100 150 200 250

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cosT*(p)

protons

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Events/0.1 0 20 40 60 80 100

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protons

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Θ cos -1 -0.5 0 0.5 1

Events/0.1 0 10 20 30 40

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cosT*(pi+)

+

π

=4.42 GeV/c

0

P P₀=3.83 GeV/c

Figure 4.The distributions for the reactionnp→ppπ+π−π−at P0=4.42 GeV/c and P0=3.83 GeV/c. Solid line

-calculations using OPER model.

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M(p,pi-,pi0) 0 π -π p

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-π + π

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M(pi+,pi0)

0 π + π

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M(pi+,pi-,pi0) 0 π -π + π ηω

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M(p,eta) η p 1535 * N

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protons

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+

π Entries 5334

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Events/0.1 0 100 200 300 400

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-π

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*

Θ cos

-1 -0.5 0 0.5 1

Events/0.1 0 50 100 150 200 250

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cosT*(pi0)

0 π

Figure 5.The distributions for the reactionnp→ppπ+π−π−π0_{at P}

0=5.20 GeV/c. Solid line - calculations using

OPER model.

4 Conclusion

Multiπmesons production in np interaction is provided by the excitation andNπandNππdecays ofΔ∗andN∗resonances (taken from PWA and GIM).

The large peripherality of the secondary hadrons leads to the idea to use some exchange models (π, P etc. exchange).

n

p

p

p

-π η

0 π

b)

1535 *+

N

n

p

p

p

-π

η 0

π

a)

1535 *+

N

n

p

p

p

0 a

0 π

d)

-π

0 σ

η

η

n

p

p p

η

+ π

-a

c)

-π

Figure 6.Diagrams of OPER model for the reactionnp→ppπ−η0_.

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p -π + π

n

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p + π + π

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protons neutrons

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cos -1 -0.5 0 0.5 1

Events/0.1

0 500 1000

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cosT*(pi+)

+ π -π

Figure 7.The distributions for the reactionnp→npπ+π+π−π−at P0=5.20 GeV/c. Solid line - calculations using

OPER model.

OPER model allows to obtain a good description of the characteristics of 3 and 4 pions production in np interactions.

To get a better description of the reactionnp→ ppπ+π−π−π0_{it is necessary take into accountη}0

andω0production.

References

[1] L. Alvarez-Ruso, E. Oset, E. Hernandez, NP A633, 519 (1998) [2] Xu Cao, Bing-Song Zou and Hu-Shan Xu, PR C81, 065201 (2010) [3] L. Ponomarev, Part. and Nucl.7, 186 (1976) (in Russian)

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-π + π n

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+ π-_π

=4.42 GeV/c

0

P P₀=3.83 GeV/c

Figure 8.The distributions for the reactionnp→npπ+π+π−π−at P0=4.42 GeV/c and P0=3.83 GeV/c. Solid line