Study of multipion production in np-interaction at intermediate energies

Study of multipion production in np-interaction

at intermediate energies

AlexanderJerusalimov1,∗,SusannaArakelian1,AlexanderBelyaev1,VladimirLadygin1, and AlexanderTroyan1

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

Abstract.The reactions of the multipion production in np-interactions were

studied at the momenta of incident neutrons from 1.73 to 5.20 GeV/c. The

pions multiplicity of the studied reactions was from 2 to 6. It was shown that the characteristics of the reactions were satisfactory described within the framework of OPER-model (One Pion Reggeizied Exchange). Additionally the diagrams of one baryon exchange (OBE) were used for a better description of the data at

the momenta of incident neutrons below 3 GeV/c.

1 Introduction

Multi pion production in NN collisions is one way to obtain information about the NN,πN andππstates, including:

- dibaryons (including I=2 in ppπ),

- dipions (narrowσ-meson,ππstates with I=2), - pentaquarks (I=5/2, S=+1),

- missing resonances etc.

An important task is to test the models of pion production in NN-interactions such as Valencia model [4], Xu Cao model [5], (OPER+OBE) model [6–8].

Various modifications of the one pion exchange models (OPE) are used to describe the experimental data of the inelastic NN-, N ¯N- andπN-interactions. Parameters of these models are different for various processes and even for concrete reactions at various energies.

The most developed and detailed model of Reggeiziedπ-meson exchange is the model elaborated at ITEP [6]. The advantages of this model are:

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

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

2 Experiment

The neutron-proton interactions were studied by using the neutron beam and liquid hydrogen bubble (target) at the JINR Synchrophasotron [1]. Unique complete and precise data were obtained. It allowed one to carry out a detailed study of inelastic np interactions in a wide

range of energies using the quasimonochromatic neutrons with P0<2.5% under condition of

4πgeometry.

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

reaction channels was carried out by the standardχ2procedure using the corresponding con-straint equations [3].

A detailed description of the data processing and reaction channels separation was pre-sented in [2].

3

2

π

production

The reactionsnp→npπ+π−,np→ppπ−π0_andnp→dπ+_π−_{were studied at the momenta of}

incident neutrons P0=1.73, 2.23, 3.83 and 5.20 GeV/c. The cross sections of the considered

reactions were presented in [2].

3.1 Reactionnp→ npπ+π−

This reaction is characterized by the plentiful production of∆1232-resonance and a number of

N∗and∆∗resonances in Nππsystem.

The main diagrams describing the reaction are the following:

n

p

N

N

π

π π

n

p

N

N

π

π π

n

p N

N

π

π

π

n

p

N N

π

π π

π

OPER22 OPERh OPER13

Figure 1.Main OPER diagrams for the reactionnp→npπ+π−

At the momentum of incident neutrons P0 <3.0 GeV/c it is also necessary to take into

account the diagrams of one-baryon exchange (OBE):

n

p

n

p -π

+ π

) 0

∆

n (

n

p N

N

-π

+

π

) +

∆

p (

∆ n

p

n

p

-π

+ π

) +

∆

p (

n

p

N N

-π

+ π ) 0 ∆ n (

∆

OBE22 OBE13

The contributions of these diagrams into the reaction are presented in Fig.3.

[GeV/c]

0

P

2 4 6 8 10 12

[mb] σ -2 10 -1 10 1 10 -π + π np → np OPER22 OPER13 OPERh OBE22 OBE13

Figure 3.The contribution of the diagrams in

Figs.1and 2into the reactionnp→npπ+π−. Open

crosses present our data

The results of the study of the reactionnp → npπ+π− at P0=5.20 GeV/c are presented

in Fig. 4. One can see a good agreement between the experimental data and theoretical calculations. The signal ofρ-meson production is not observed inππ-combinations..

Entries 5612 _[GeV/c2_]

π N M 1.5 2 ] 2 b/0.04 GeV/c µ /dM [ σ d 0 500 1000 1500 2000

Entries 5612

+ π p, M + π p -π n

Entries 5612 ]

2 [GeV/c π N M 1.5 2 ] 2 b/0.04 GeV/c µ /dM [ σ d 0 200 400 600 800

Entries 5612

-π p, M -π p + π n

Entries 5612 [GeV/c2]

π π

N M

1.5 2 2.5

] 2 b/0.04 GeV/c µ /dM [ σ d ₀ 200 400 600

Entries 5612 -π , + π p, M -π + π p -π + π n Mean 0.6291

RMS 0.23

] 2 [GeV/c π π M 0.5 1 ] 2 b/0.04 GeV/c µ /dM [ σ d 0 100 200 300 400 500

Mean 0.6291 RMS 0.23

-π + π

Entries 2806

* N Θ

cos -1 -0.5 0 0.5 1

b/0.1] µ [ Θ /cos σ d ₀ 1000 2000

Entries 2806

neutrons

)

n *

Θ

cos( Mean -0.3469

* N Θ

cos -1 -0.5 0 0.5 1

b/0.1] µ [ Θ /dcos σ d 0 1000 2000

Mean -0.3469 ) p * Θ cos( protons

Mean 0.1658

* π

Θ

cos -1 -0.5 0 0.5 1

b/0.1] µ [ Θ /dcos σ d 0 200 400 600 800 1000

Mean 0.1658 -mesons

-π

Mean -0.1782

* π

Θ

cos -1 -0.5 0 0.5 1

b/0.1] µ [ Θ /dcos σ d ₀ 200 400 600 800 1000

Mean -0.1782

-mesons + π ) + π * Θ cos(

Figure 4.The distributions from the reactionnp→npπ+π−

at P0=5.20 GeV/c. Solid line – calculations

using OPER-model

The diagrams in Fig.1, however, were insufficient to get a full description of the reaction np→ npπ+π−_{at lower energies. The study of effective mass spectra of np-combinations at}

P0=2.23 and 1.73 GeV/c (Fig.5) has shown a clear peak near the threshold. Therefore the

model of Redgge poles with baryon exchange (OBE, see Fig2.) was used to describe these features.

Mean 1.989

1.9 2 2.1 2.2

] 2 b/0.010 GeV/c µ /dM [ σ d 0 50 100 150 200

Mean 1.989

a)

Mean 1.916

1.9 2 2.1

] 2 b/0.010 GeV/c µ /dM [ σ d 0 50

100 Mean 1.916

b)

Figure 5.The effective mass spectra

from the reactionnp→npπ+π−

at

a) P0=2.23 and b) 1.73 GeV/c.

The combined (OPER+OBE)-model allows one to get a good description of the charac-teristics of the reactionnp→npπ+π−_{at the momenta of incident neutrons in a region from}

P0=1.73 to P0=5.2 GeV/c.

More detailed results of the study of this reaction were presented in [9,10].

3.2 Reactionnp→ ppπ−_π0

We have also got a good description of the characteristics of the reactionnp→ ppπ−π0using the diagrams similar to the diagrams for the reactionnp→npπ+π−_{. The details of this study}

were presented in [9].

3.3 Reactionnp→ d pi+π−

The reaction np → dπ+π− _{is characterized by a fusion of neutron and proton into the}

deuteron. Thus it seems to be reasonable to take into account OBE diagrams shown in Fig.6 to describe the experimental data of this reaction:

n

p

d

-π

+ π

n p

n

p d

-π

+ π

n p

n

p

d -π

+ π

n p

Figure 6. Diagrams corresponding to the reactionnp → dπ+π−

in the framework of the one baryon exchange (OBE) model

In Fig. 7 one can see clear peaks in the masses ofπ+π−-combinations close to∼350 and∼400 MeV/c2 (so called ABC and DEF anomaly). These effects, momenta and mass distributions are good reproduced within framework of OBE model. But the theoretical curve for angular distributions of deuteron and pions are too sharp. It is necessary to develop further the OBE model to improve the description of the experimental data.

Mean 0.3693 RMS 0.05266

] 2 [GeV/c

-π

+

π

M

0.3 0.4 0.5 0.6

]

2

events/(0.015 GeV/c

0 50 100 150

Mean 0.3693 RMS 0.05266

Mean 0.2297 RMS 0.06995

[GeV/c] d * P

0 0.1 0.2 0.3 0.4

events/(0.015 GeV/c)

0 50 100 150

Mean 0.2297 RMS 0.06995

Mean -0.01352 RMS 0.6075

d *

Θ

cos

-1 -0.5 0 0.5 1

events/0.2

0 100 200 300 400

Mean -0.01352 RMS 0.6075

Mdpi Entries 18 Mean 2.109 RMS 0.0376

] 2 [GeV/c

π d M

2 2.1 2.2 2.3

)

2

events/(0.015 GeV/c

0 100 200 300 400

Mdpi Entries 18 Mean 2.109 RMS 0.0376

Ppi Entries 13 Mean 0.1724 RMS 0.0458

[GeV/c]

π * P

0 0.1 0.2 0.3

events/(0.025 GeV/c)

0 200 400 600

Ppi Entries 13 Mean 0.1724 RMS 0.0458

Mean -0.01492 RMS 0.5986

π *

Θ

cos

-1 -0.5 0 0.5 1

events/0.2

0 200 400 600

Mean -0.01492 RMS 0.5986

Figure 7.The distributions for the reactionnp→dπ+π−

atP0=1.73 GeV/c. Solid line – calculations

As far as dipion masses concerned from the reactionnp→dπ+π−_atP

0=2.23 GeV/c, it

is difficult to say that ABC and DEF bumps are confidently observed. Obviously it is due to insufficient statistics.

The details of the study of this reaction were presented in [9].

4 3

π

and 4

π

production

The reactionsnp→ ppπ+π−_π−_{,np→ ppπ}+_π−_π−_π0_andnp→npπ+_π+_π−_π−_{were studied at}

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

considered reactions were presented in [2].

The following diagrams were taken into account to calculate the characteristics of the reactionsnp→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

Figure 8.Diagrams of OPER model for the reactions of 3πand 4πmeson production in np interactions

4.1 Reactionnp→ ppπ+π−π−

The results of the calculations using OPER model for the reactionnp→ppπ+π−π−are shown in Fig.9for the data atP0=5.2 GeV/c.

Entries 11582

] 2 [GeV/c

π

N M

1.2 1.4 1.6 1.8 2

)

2

Events/(0.02 GeV/c

0 500 1000

Entries 11582 M(p,pi+)

+ π

p

Entries 23164

] 2 [GeV/c

π

N M

1.2 1.4 1.6 1.8 2

)

2

Events/(0.02 GeV/c

0 500 1000

Entries 23164

M(p,pi-)

-π

p

Entries 23164

] 2 [GeV/c

π π

N M

1.5 2

)

2

Events/(0.02 GeV/c

0 200 400 600 800

Entries 23164

M(p,pi+,pi-)

-π + π

p

Entries 11582

] 2 [GeV/c

π π

M

0.4 0.6 0.8 1 1.2

)

2

Events/(0.02 GeV/c

0 200 400 600

Entries 11582

M(pi+,pi-)

-π + π

Entries 5791

] 2 [GeV/c

π π

M

0.4 0.6 0.8 1 1.2

)

2

Events/(0.02 GeV/c

0 100 200 300

Entries 5791

M(pi-,pi-)

-π

-π

Entries 5791

] 2 [GeV/c

π π π

M

0.5 1 1.5

)

2

Events/(0.02 GeV/c

0 50 100 150 200 250

Entries 5791

M(pi+,pi-,pi-)

-π -π + π

Entries 11582

*

Θ

cos

-1 -0.5 0 0.5 1

Events/0.1

0 500 1000 1500 2000

Entries 11582

cosT*(p)

protons

Entries 5791

*

Θ

cos

-1 -0.5 0 0.5 1

Events/0.1

0 100 200 300 400 500

Entries 5791

cosT*(pi+)

+ π

Entries 11582

*

Θ

cos

-1 -0.5 0 0.5 1

Events/0.1

0 200 400 600 800 1000

Entries 11582

cosT*(pi-)

-π

Figure 9. The distributions for the reactionnp→ ppπ+π−_π−

at P0=5.20 GeV/c. Solid line –

One can see a good agreement between the experimental data and theoretical calculations. Also a good description was obtained for this reaction at the incident momenta P0=3.83 and

4.42 GeV/c. The details of the study of this reaction were presented in [9].

4.2 Reactionnp→ ppπ+π−_π−_π0

The results of the calculations using OPER model for the reactionnp → ppπ+π−π−π0 _are

shown in Fig.10for the data atP0=5.20 GeV/c.

Entries 10668

] 2 [GeV/c π N M

1.2 1.4 1.6 1.8

)

2

Events/(0.02 GeV/c 0 500 1000

Entries 10668

M(p,pi+)

+

π

p

Entries 10668

] 2 [GeV/c π N M

1.2 1.4 1.6 1.8

)

2

Events/(0.02 GeV/c 0 200 400 600 800

Entries 10668

M(p,pi-)

-π

p

Entries 10668

] 2 [GeV/c π π N M

1.4 1.6 1.8 2 2.2

)

2

Events/(0.02 GeV/c 0 200 400 600

Entries 10668

M(p,pi+,pi-)

-π

π

p

Entries 10668

] 2 [GeV/c π π N M

1.4 1.6 1.8 2 2.2

)

2

Events/(0.02 GeV/c 0 200 400

Entries 10668

M(p,pi-,pi0) 0 π -π p

Entries 5334

] 2 [GeV/c π π M

0.4 0.6 0.8 1

)

2

Events/(0.02 GeV/c 0 100 200 300 400 500

Entries 5334

M(pi+,pi-)

-π

π

Entries 2667

] 2 [GeV/c π π M

0.4 0.6 0.8 1

)

2

Events/(0.02 GeV/c 0 50 100 150 200

Entries 2667

M(pi+,pi0)

0

π

π

Entries 5334

] 2 [GeV/c π 3 M

0.4 0.6 0.8 1 1.2 1.4

)

2

Events/(0.02 GeV/c 0 100 200 300 400

Entries 5334

M(pi+,pi-,pi0) 0 π -π + π ηω

Entries 546

] 2 [GeV/c η p M

1.6 1.8 2 2.2 2.4

)

2

Events/(0.02 GeV/c 0 10 20 30 40 50

Entries 546

M(p,eta)

η

p

Entries 5334

*

Θ

cos

-1 -0.5 0 0.5 1

Events/0.1

0 200 400 600

Entries 5334

cosT*(p)

protons

Entries 2667

*

Θ

cos

-1 -0.5 0 0.5 1

Events/0.1

0 50 100 150

Entries 2667

cosT*(pi+)

+

π

Entries 5334

*

Θ

cos

-1 -0.5 0 0.5 1

Events/0.1 0 100 200 300 400

Entries 5334

cosT*(pi-)

-π

Entries 2667

*

Θ

cos

-1 -0.5 0 0.5 1

Events/0.1 0 50 100 150 200 250

Entries 2667

cosT*(pi0)

0

π

Figure 10. The distributions for the reactionnp → ppπ+π−_π−_π0 _{at P}

0=5.20 GeV/c. Solid line –

calculations using OPER model

One can see a good agreement between the experimental data and theoretical calcula-tions. A clear signals ofη0_andω0_{mesons production are observed at the masses ofπ}+_π−_π0

combinations. To describe these peaks, the following diagrams were taken into account:

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 π ω 0 ρ -π d) n p p p ω + π -ρ -π c)

Figure 11.Diagrams of OPER model for the reactionsnp→ppπ−_η0_andnp→ppπ−_ω0

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

1535

resonance inπNinteraction with the consequent decayN∗

1535→Nη

0_{. The "hanged" diagrams}

c) and d) describeω0_{meson production due to π-ρ interaction.}

The results at P0=4.42 GeV/c and P0=3.83 GeV/c are not presented due to a poor

statis-tics. But OPER model also described satisfactorily the experimental distributions and the signals ofη0_andω0_{meson production at these energies.}

4.3 Reactionnp→ npπ+π+π−_π−

We have also got a good description of the characteristics of the reactionnp→npπ+π+π−_π−_.

The details of this study were presented in [9].

5 5

π

and 6

π

production

The reactionsnp→ ppπ+π+π−π−π−,np→ ppπ+π+π−π−π−π0andnp→npπ+π+π+π−π−π− were studied at the momenta of incident neutrons P0=5.20 GeV/c. The cross sections of these

reactions were presented in Tab.1.

Table 1.Cross-sections of 5πand 6πmeson production

reaction cross-section (µb)

np→ ppπ+π+π−π−π− 18.7±4.1 np→ ppπ+π+π−π−π−π0 3.6±1.0 np→npπ+π+π+π−_π−_π− _3.7±1.0

The only reaction np → ppπ+π+π−π−π− was studied in details. Other reactions (6π production) have had too poor statistics.

The following diagrams were taken into account to calculate the characteristics of the reaction of 5π-meson production:

n

p

p

p

π

π π

-π

π

π

π

n

p

p p

π

π

π

π

π

π

π

+

Figure 12.Diagrams of OPER model for the reactionnp→ppπ+π+π−_π−_π−

Fig.13shows a good agreement between the experimental data and theoretical calcula-tions by means of OPER-model.

6 Conclusion

Multiπ-meson production in np-interactions is provided by the excitation and decay of∆∗ -and N∗-resonances (taken from PWA and GIM).

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

consid-DelPP

π P M

1.2 1.4 1.6 1.8

]

2

Events/[0.02 MeV/c

0 20 40 60 80 100

DelPP +

π

p

Del0

π P M

1.2 1.4 1.6 1.8

]

2

Events/[0.02 GeV/c

0 50 100

Del0

-π

p

Ppipi1

π π P M

1.4 1.6 1.8 2

]

2

Events/[0.02 MeV/c

0 50 100 150

Ppipi1

-π

π

p

Ppipi2

π π P M

1.4 1.6 1.8 2

]

2

Events/[0.02 MeV/c

0 20 40 60

Ppipi2 +

π

π

p

Ppipi3

π π P M

1.4 1.6 1.8 2

]

2

Events/[0.02 MeV/c

0 20 40 60 80

Ppipi3

-π

-π

p

pipi1

π π M

0.4 0.6 0.8 1

]

2

Events/[0.02 MeV/c

0 50 100

pipi1

-π

π

pipi2

π π M

0.4 0.6 0.8 1

]

2

Events/[0.02 MeV/c

0 5 10 15 20 25

pipi2

+

π

π

pipi3

π π M

0.4 0.6 0.8 1

]

2

Events/[0.02 MeV/c

0 20 40 60

pipi3

-π

-π

CSTP

*

Θ

cos

-1 -0.5 0 0.5 1

Events/[0.1

0 10 20 30 40

CSTP protons

CSTpip

*

Θ

cos

-1 -0.5 0 0.5 1

Events/[0.1

0 10 20 30

CSTpip

+

π

CSTpim

*

Θ

cos

-1 -0.5 0 0.5 1

Events/[0.1

0 10 20 30 40

CSTpim

-π

Figure 13. The distributions for the reactionnp → ppπ+π+π−_π−_π−

at P0=5.20 GeV/c. Solid line –

calculations using OPER model

OPER-model allows one to get a good description of the characteristics from 2 up to 6 pion production in np interactions. At lower energies ( P0<3 GeV/c) it is necessary to take into account another mechanism of the reactions (such as OBE-model).

(OPER+OBE)-model can be used as an efficient tool to simulate various reactions of hadron interactions: NICA project, HADES set-up, intranuclear interactions (hA and AA).

References

[1] A.P.Gasparian et al. Prib.Tekh.Eksp.,77, 2, 37 (1977) [2] C.Besliu et al. Sov.J.Nucl.Phys.43, 565 (1986)

[3] J.P. Berge, F.T. Solmitz and H.D. Taft, Rev.Sci.Instrum.32, 338 (1961) [4] L. Alvarez-Ruso, E. Oset, E. Hernandez. NP A633, 519 (1998) [5] Xu Cao, Bing-Song Zou and Hu-Shan Xu. PR C81, 065201 (2010) [6] L.A. Ponomarev, Sov.J.Part.Nucl.7, 70 (1976)

[7] A.P. Jerusalimov, arXiv:1203.3330[nucl-th] (2012). A.P. Jerusalimov, arXiv:1208.3982[nucl-th] (2012)

[8] A.B. Kaidalov and A.F. Nilov, Sov.J.Nucl.Phys. 41, 490 (1985). Sov.J.Nucl.Phys.52, 1060 (1990)