search for the Θ 1530 pentaquark in antiproton he...

Nuclear Physics A 779 (2006) 116–141

Search for the Θ+(1530) pentaquarkin antiproton 4He annihilation at rest

A. Panzarasa ∗, G. Bendiscioli, A. Fontana, L. Lavezzi, P. Montagna,A. Rotondi, P. Salvini

Dipartimento di Fisica Nucleare e Teorica, Università di Pavia and INFN, Sezione di Pavia, Italy

E. Botta, T. Bressani, S. Costa, D. Calvo, A. Feliciello, A. Filippi,S. Marcello

Dipartimento di Fisica Sperimentale, Università di Torino and INFN, Sezione di Torino, Italy

M. Agnello, F. Iazzi, B. Minetti

Dipartimento di Fisica del Politecnico di Torino and INFN, Sezione di Torino, Italy

E. Lodi Rizzini, M. Corradini, L. Venturelli

Dipartimento di Chimica e Fisica per i Materiali, Università di Brescia and INFN, Sezione di Pavia, Italy

A. Zenoni, A. Donzella

Dipartimento di Meccanica, Università di Brescia and INFN, Sezione di Pavia, Italy

F. Balestra, M.P. Bussa, L. Busso, P. Cerello, O. Denisov, L. Ferrero,R. Garfagnini, A. Grasso, A. Maggiora, F. Tosello

Dipartimento di Fisica Generale “A. Avogadro”, Università di Torino and INFN, Sezione di Torino, Italy

D. Panzieri

Dipartimento di Scienze e Tecnologie Avanzate, Università del Piemonte Orientale and INFN, Sezione di Torino, Italy

0375-9474/$ – see front matter © 2006 Published by Elsevier B.V.doi:10.1016/j.nuclphysa.2006.08.006

A. Panzarasa et al. / Nuclear Physics A 779 (2006) 116–141 117

O.E. Gorchakov, S.N. Prakhov, A.M. Rozhdestvensky,G.M. Sapozhnikov, V.I. Tretyak

Joint Institute for Nuclear Research, Dubna, Russia

C. Cicalò, A. De Falco, A. Masoni, G. Puddu, S. Serci, G. Usai

Dipartimento di Scienze Fisiche, Università di Cagliari and INFN, Sezione di Cagliari, Italy

C. Curceanu (Petrascu), P. Gianotti, C. Guaraldo, A. Lanaro, V. Lucherini

Laboratori Nazionali di Frascati dell’INFN, Frascati, Italy

Received 23 December 2005; received in revised form 28 July 2006; accepted 2 August 2006

Available online 15 September 2006

Abstract

A research has been made to look for a signature of the positive-strangeness baryon resonance Θ+(1530),which is expected to decay into pK0. A peak is observed in the pπ+π− invariant mass distribution inantiproton– 4He annihilation reactions at rest with production of two π+π− pairs with invariant mass closeto the K0

Smass. The annihilation reactions on 4He can involve two to four nucleons producing an energy

blob characterized by high strangeness content. The peak is centred around 1560.0±3.7 MeV and its widthis very narrow. The statistical significance is 2.7; this value is considered of not sufficient significance toclaim support of the Θ+. The data were collected with the Obelix spectrometer at the LEAR machine ofCERN.© 2006 Published by Elsevier B.V.

Keywords: p̄– 4He annihilation; Pentaquark with strangeness S = 1

1. Introduction

The well-established hadrons are either combination of three valence quarks (baryons) or ofa quark and an antiquark (mesons), but the theory of the strong interactions allows for othertypes of hadrons, for instance baryons made of four quarks and one antiquark (pentaquarks).The existence of pentaquarks has been investigated for more than 30 years without convinc-ing experimental evidence, but recently a theoretical paper [1] has reawakened the interest onit and has led to a new round of experimental investigations. Ref. [1] predicts an exotic baryonwith quark content uudds̄, strangeness S = +1, mass about 1530 MeV, width less than 15 MeVand decay modes into nK+ and pK0. These predictions are based on the chiral soliton model,but alternative explanations have also been suggested in [2–4] invoking “molecules” of varioustightly-coupled quark configurations, and in [5–7]. Following these speculations, many experi-mental groups have looked for signals of the predicted baryon employing various beams, targets

* Corresponding author.E-mail address: [email protected] (A. Panzarasa).

118 A. Panzarasa et al. / Nuclear Physics A 779 (2006) 116–141

Table 1Summary of experiments which reported Θ+ observation. X = anything; (a) A = C, Si, Pb; (b) A = p,d , Ne. Forthe statistical significance the values are reported as given in the quoted papers, although most of them (c) are likelyoverestimated ([25,27,46]; see also Section 3.3). More realistic values evaluated in Ref. [27] are also shown. (d) Theseresults have not been confirmed by a recent analysis of high statistics data by the same group [45]

Experiment Reaction Mass (MeV) Width Γ (MeV) Statistical significance Ref.

NΘ+ /√

Nb(c)

NΘ+ /√

N + Nbmostlyestimated in [27]

a ZEUS ep → (pK0S)X 1522 ± 3 8 ± 4 (3.9−4.6) 4.7 [17]

b HERMES γ d → (pK0S)nsp 1526 ± 3 13 ± 9 3.4−4.3 2.7 [15]

1528 ± 2.6 ± 2.1 8 ± 2 3.7 [16]c SVD-2 pA → (pK0

S)X (a) 1526±3 ± 3 < 24 5.6c 2.4 [19a]

1523 ± 2 ± 3 < 14 8.0c 5.9 [19b]d NOMAD νA → (pK0

S)X 1528.7 ± 2.5 few MeV 4.3c 2.7 [21]

e JINR p(C3H8) → (pK0S)X 1540 ± 8 9.2 ± 1.8 5.5c 4.1 [20]f COSY-TOF pp → (pK0

S)Σ+ 1530 ± 5 18 ± 4 5.9c 3.7 [18]

3.7

g ITEP νμ(ν̄μ)A → (pK0S)K−Xb 1532.2 ± 1.3 < 12 7.1c 3.5 [13]h DIANA K+Xe → (pK0

S)X 1539 ± 2 < 9 4.4c 2.7 [10]

i SAPHIR γp → (nK+)K0S

1540 ± 6 < 25 4.8c 4.3 [12]l LEPS γ 12C → (nK+)K−X 1540 ± 10 < 25 4.6c 2.6 [8]

γ d → (nK+)K−X ≈1530 [9]m CLAS-d γ d → (nK+)K−p 1542 ± 5 < 21 (5.2 ± 0.6)c 3.5 [11]dn CLAS-p γp → (nK+)K−π+ 1555 ± 10 < 26 (7.8 ± 1.0)c 3.9 [14]o JINR np → (nK+)pK− 1541 ± 5 < 11 [22]

OBELIX p̄ 4He → (pK0S)K0

SX

→ (pK0S)K−X

→ (pK0S)ΛX

1560.0 ± 3.7 Verynarrow

– 2.7 (thispaper)

and detector configurations and a considerable number of them have observed a narrow res-onance (called Θ+) either in the nK+ or in the pK0S invariant mass distribution [8–22]. Themeasured values of the Θ+ mass and width are spread as shown in Table 1, where also the rele-vant statistical significance is quoted. In most of experiments this is evaluated through the ratioNΘ+/

√Nb , where NΘ+ is the number of the events in the Θ

+ peak and Nb the number of back-ground events under the peak. Most of the measured widths are consistent with the experimentalresolution, therefore they are upper limits for the true width, which might be much narrower(� 1−4 MeV) [23].

In spite of the above results, the existence of the Θ+ pentaquark is still under discussion fortheoretical and experimental reasons [23–30]. From the experimental point of view, the mainreason of perplexity is that there is also a considerable number of experiments that have notobserved it [31–44]. Moreover, two groups have confirmed their previous observations of Θ+ [9,19b], while another one has found no signal analyzing new data samples with high statistics [45].


In this paper we contribute to these topics with an investigation on the antiproton 4He annihi-lation by reanalyzing a set of data collected by the OBELIX Collaboration [47–49].

In Refs. [48,49] it has been put in evidence that the energy blob produced in the p̄ 4He an-nihilation at rest is an environment rich of strange quarks when several nucleons are involved,as demonstrated by the high production of π+π−π−K+ and π+π+π−K− (higher by a factorof 22 and 13, respectively, than the production in annihilation on hydrogen). Thus this environ-ment seems to be suited to search a strange baryon like Θ+. We shall look for it through thedecay Θ+ → pK0S → pπ+π−.

The following reaction channels with four and five prongs have been investigated:

p̄ 4He → (p2π+2π−)2nX(pπ+π−K−

)psnX,(

p2π+π−K−)2nX,(

ppπ+2π−)nX

where X stays for any undetected neutral mesons like π0 and K0L (shortly, neutrals), n is an un-detected neutron, p is a fast proton (with momentum pp > 300 MeV/c) and ps is a slow proton(i.e., with momentum < 300 MeV/c; it can be undetected or detected with unmeasured momen-tum). The measured pion and kaon momenta are higher than 80 and 150 MeV/c, respectively.Protons with momentum > 300 MeV/c are assumed to be involved in the annihilation process;hence, considering the unseen neutrons, the number of nucleons involved in the above reactionsmay be two to four. The final states in the above reactions can be reached directly or via inter-mediate states with strange and non-strange content as shown in Table 2. π∓, K± and p wereidentified through specific energy loss, momentum and velocity measurements; K0 (K̄0), Λ andΣ+ were detected via their π+π−, pπ− and pK0S decay modes, respectively; the N and Δbaryons were recognized via the p2π and pπ ones.

2. Data collection and event selection

The analysed events are just the same ones considered in Refs. [48,49]. Here we summarizethe main features of the raw data and of the criteria adopted to select the different event sets.

The raw data were collected with the magnetic spectrometer Obelix [50] using the 200 MeV/cantiproton beam extracted from LEAR at CERN. The spectrometer, with cylindrical symmetryaround the beam line coincident with the magnetic field axis, was made by a gas target, a spiralprojection chamber (to measure event vertex and prong multiplicity and to detect slow particleswithout measuring the momentum) and two scintillator barrels (for time-of-flight measurements)separated by six jet-drift chambers (for momentum, trajectory length and specific ionisationmeasurements). The beam was slowed down to stop in the target center. The 4He target wasat NTP.

We considered events with two negative and two positive tracks and events with two negativeand three positive tracks connected to the annihilation vertex. Particle decays far from the primaryvertex were not detected. The particles were identified through the independent measurements ofvelocity (β), momentum (p) and specific energy loss (dE/dx). For a number of prongs all threequantities were measured, for others only p and dE/dx. The different particles were identifiedaccording to Fig. 1. A particular care was devoted to identify kaons, which are the minority of theprongs (about one per cent), in order to reduce as much as possible the contamination by pionsand protons while saving statistics. The residual contamination on the kaons was reduced by


Table 2Analyzed final states and possible intermediate states of the p̄4He annihilation involving Θ+ , kaons, N , Δ, Λ and Σbaryons. Additional neutrals (neutrons and, in some cases, mesons) are present. Intermediate states with undetected K0

L

are not included for the sake of simplicity (for instance, Θ+π+π−(K0L) → pK0

Sπ+π−(K0

L)). The considered N and

Δ baryons are the following: N(1440), N(1520), N(1535), Δ(1600) and Δ(1620); they decay mainly into p(n)2π andp(n)π

Final states Possible intermediate states n(K0S)

A pπ−π−π+π+ N(Δ) → (pπ+π−)π+π− 0N(Δ) → (pπ0π0)π+π−π+π−N(Δ) → (pπ0π−)π+π−π+N(Δ) → (pπ0)π+π−π+π−N(Δ) → (pπ−)π+π−π+pK0

SK0

S2

Σ+(1660)K0S

→ (pK0S)K0

S2

Θ+K0S

→ (pK0S)K0

S2

Λ(1520)K0Sπ+ → [Σ+π−]K0

Sπ+ → [(pπ0)π−](π+π−)π+ 1

Λ(1520)K0Sπ+ → [Σ0π0]K0

Sπ+ → [(Λγ )π0]K0

Sπ+ 1

Λ(1520)K0Sπ+ → [Λπ0π0]K0

Sπ+ 1

Λ(1115)K0Sπ+ 1

Σ0K0Sπ+ → (Λγ )K0s π+ 1

Σ+K0Sπ−π+ → (pπ0)(π−π+)π−π+ 1

B pπ−π+K− Θ+K− → (pK0S)K− 1

pK0SK− 1

Σ+(1660)K− → (pK0S)K− 1

C pπ−π+π+K− Θ+K−π+ → (pK0S)K−π+ 1

pK0Sπ+K− 1

pK0SK̄0∗ → pK0

SK−π+ 1

Σ+(1660)K−π+ → (pK0S)K−π+ 1

D ppπ+π−π− Different combinations of p, N , Δ and charged pions 0Θ+Λ(1115) → (pK0

S)Λ 1

Θ+Σ0 → (pK0S)Λγ 1

pΛ(1115)K0S

1

Σ+K0Spπ− → pπ0K0

Spπ− 1

a kinematical analysis of each event according to the criteria described in [47,48]. The analysisallowed to identify K0S (→ π+π−), K0∗ (→ π±K∓) and φ (→ K+K−) [49]. The numbers ofevents relevant to the reactions to be analyzed are given in Table 3.

3. Data analysis

3.1. pπ−π−π+π+ events

This event sample has the highest statistics and allows investigating subsamples with differentfeatures.


Fig. 1. Identification of positively charged particles (pions, kaons, protons and deuterons) through dE/dx vs. p (a) andβ vs. p (b). In each figure, the dotted lines include the kaon region [48].

Table 3Number of events for the different final states

pπ−π−π+π+ pπ−π+K− pπ−π+π+K− ppπ+π−π−

20 407 702 357 10 132


(1) The gross features of the p̄ 4He annihilation at rest are similar to those of the p̄p annihi-lation, but there are details which are specific of the annihilation on helium; these are due to thepossibility of the direct involvement in the annihilation process of more than one nucleon and tothe interaction between final mesons and nucleons [47–49]. In particular, Refs. [48,49] show thatin the four- and five-prong events there is a high increase of strangeness production compared tothe p̄p annihilation, when more than one nucleon is involved. This is put in evidence by the pro-duction of charged kaons. On the contrary, the neutral kaons do not display such an increase fora number of reasons. First of all, the kaons are produced in only few percent of the events [48].Then they are detected via the π+π− decay mode, which occurs only in 68.6% of the cases,and a large fraction of them [51] decay far from the annihilation fiducial volume (a sphere ofabout 0.5 cm); moreover the pions can lose energy interacting with the residual nucleons andlose memory of their origin [49]. The evidence of neutral kaons decreases while increasing thenumber of final particles (charged or neutral).As pointed out in Ref. [16], the π−π+ in variant mass distribution for annihilations on 4Hedisplays structures due to the presence of K0S and ρ(770), the relevance of which depends on theparticular event set. For the whole set of events considered here, there is no clear K0S peak, butonly a different behaviour of the π−π+ invariant mass distribution compared to the π+π+ plusπ−π− IM one (see Fig. 2(a)). A peak appears if we select event subsets according to Ref. [47]:for example, selecting events where the unseen particles are (almost) only neutrons (and no π0).This can be done considering a specific region in the scatter plot concerning the total measuredmomentum vs. the total measured energy. Fig. 2(b) shows the IM distribution for the events withthe total measured momentum in the interval 250−800 MeV/c and the total measured energygreater than about 2500 MeV. The presence of neutral kaons is indicated by a bump around495 MeV, which is absent in the π+π+ plus π−π− IM distribution. The two distributions aredifferent also for a contribution of the large ρ resonance. We stress that the evidence of the bumpis reduced by combinatorial effects, which increase the background with four entries for eachevent, while the number of K0S per event is one or two.As the presence of the Θ+ requires necessarily two K0S , we have looked for it within the eventsubset with 2 π+π− pairs with invariant mass (IM) close to the K0S mass. This choice maximizesthe visibility of the Θ+, if it exists. In the following we shall consider the number of eventswith two K0S , identified by the π

−π+ pairs with IM in the interval 495 ± 20 MeV. A roughestimation of the number of K0S per event in such interval is given by the difference betweenthe two histograms in Fig. 2(b) (about 335 over 3045 entries). As the events are 1/4 of theentries (761) and each event can contribute with one or two K0S , the number of events with twoK0S is at most 140 and its frequency 0.22. Applying the same calculation to the distribution forthe whole set of events in Fig. 2(a), the number of events with two K0S turns out to be 581 at most(over 1858) and its frequency 0.31.

(2) As shown in Table 2, the Θ+ pentaquark may be present only in a fraction of the eventswith the intermediate state containing two K0S . The pπ

+π− invariant mass (IM) distribution forthose with two π+π− pairs with IM in the interval 495 ± 20 MeV is shown in Fig. 3(a). Onecan see two peaks, one close to 1500 MeV and the other close to 1550 MeV. We assume thatthe latter one is associated to the Θ+ pentaquark. The interval ±20 MeV around the K0S mass isabout twice our resolution. This has been evaluated by means of a best fit calculation on the K0Speak in the annihilation reaction p̄p → 2π+2π−X measured with our apparatus [49]; it leads


Fig. 2. (a) π−π+ invariant mass distribution for all the events (full histogram), the relevant π+π+ plus π−π− distribu-tion (dotted histogram) and their difference. The dotted histogram is normalized in order to erase the difference on the leftside region. The full vertical lines indicate the K0

Sand the ρ masses and the dashed ones the ±20 MeV interval around

the K0S

mass. The total number of entries concerns the full histogram. (b) Signature of K0S

in the π+π− invariant massdistribution for the final statepπ−π−π+π+ with an unseen fast neutron and no π0. π−π+ invariant mass distribution(full); π+π+ plus π−π− invariant mass distribution (dotted) and their difference. The total number of entries concernsthe full histogram.

to m(K0S) = (494.08 ± 0.14) MeV and σgaussian = (9.3 ± 0.7) MeV (see Fig. 4); consideringthe extremely narrow K0S width, σ measures our experimental resolution. While enlarging theinterval, the peak at 1550 MeV disappears progressively.Note also that, due to the four π+π− combinations, each pπ+π−π+π− event may contribute tothe pπ+π− IM distribution with two or with four entries with both π+π− pairs with IM close to


Fig. 3. (a) pπ+π− invariant mass distribution for events with two π+π− pairs with invariant mass in the interval495 ± 20 MeV. (b) Scatter plot for pπ− IM vs. pπ+π− IM. The horizontal line identifies the Λ(1115) invariant mass.

the K0S mass. However, as a matter of fact, only few events over 375 contribute with four entries;therefore, the entries are twice the events. Of course, entries relevant to uncorrelated particles aredistributed at random according to the phase-space in the histograms, while those arising fromresonance decay are concentrated around the proper mass.The scatter plot IM(pπ−) vs. IM(pπ+π−) in Fig. 3(b) shows that there is no reflexion of the Λ,N and Δ decays into pπ− on the Θ+ peak.We notice that the analysis of the pπ−π−π+π+ events is affected negligibly by the possibleambiguity in the mass identification of protons and charged pions and kaons, as protons cannotbe confused with pions (see Fig. 1) and the events with strangeness are only few percent.


Fig. 4. K0S

peak in the annihilation reaction p̄p → 3π±K∓ .

(3) As pointed out in Table 2, contributions to the pπ+π− IM distribution come from thepπ+π−π+π− phase-space, from pK0SK̄0S , Σ+(1660)K0S and N and Δ resonances. The N andΔ have full widths ranging between 100 and 450 MeV and two of them have their mass closeto that expected for the Θ+ : N+(1520), which has a probability of 45% to decay into p(n)2π ,a mass in the interval 1515–1530 MeV and a full width of 100–135 MeV, and N(1535), whichhas a much lower probability to decay into p(n)2π(1–10%), a mass in the interval 1520–1555MeV and a full width of 100–250 MeV [52]. Considering our resolution and statistics, onlyN(1520) is observable and is just the peak close to 1500 MeV in Fig. 3(a).As N and Δ resonances do not require that the π+π− IM is equal to the K0S mass, we expectthat they contribute to the pπ+π− IM distribution also for events with π+π− IM outside the K0Sregion, for instance inside the regions 545 ± 20 MeV and 445 ± 20 MeV. The relevant pπ+π−IM distribution is shown in Fig. 5, where there is a peak around 1525 MeV, but no peak close to1550 MeV.

(4) We note that the widths of the N(1520) peaks in Figs. 3(a) and 5 appear to be narrowerthan the intrinsic full width (about 120 MeV) and the peak position in Fig. 5 is somewhat shiftedwith respect to that in Fig. 3(a). By means of Monte Carlo calculations, we have looked for theorigin of these facts and verified that it is manifold: a mismatch between the proton and pionmomentum distributions intrinsic to the N(1520) decay and the experimental ones, the cuts onthe π+π− IM distribution and statistical fluctuations. As an example of our calculations, Fig. 6compares the Monte Carlo momentum distributions for the particles emitted in the decay ofN(1520) produced in the process p̄2p → N(1520)π+π−π0 → (pπ+π−)π+π−π0 with theexperimental distributions relevant to the reaction p̄ 4He → p2π+2π−X used to build up Fig. 3.The experimental distributions are affected by the involvement of unseen particles (neutral pionsand/or fast neutrons) and by meson–nucleon and nucleon–nucleon rescattering. Moreover, it iswell known that the mass and the width of a resonance produced in the nuclear matter may besomewhat different from those of the same resonance produced in the free space. Finally, Fig. 6shows that the momenta of protons and pions produced by the N(1520) decay are distributedabove 550 and 280 MeV/c, respectively; hence, the limited acceptance of our apparatus at lowmomenta has no influence on them.


Fig. 5. pπ+π− invariant mass distribution for events with two π+π− pairs with IM outside the interval 495 ± 20 (seetext).

We have also verified that the apparatus acceptance and the event selection criteria adoptedto produce the histogram in Fig. 3 have a negligible effect on the features of a peak likethe expected Θ+. For example, Fig. 7 compares the momentum distributions obtained witha Monte Carlo calculation for the particles emitted in the process p̄2p → Θ+(1530)Kπ0 →(pK̄)Kπ0(Γ (Θ+) = 25 MeV) with the experimental ones for the protons and the K0S enteringthe histogram in Fig. 3. The Monte Carlo and experimental distributions are fairly superimposed.

(5) According to Table 2, Θ+ is not present in the intermediate state containing a K0S andΛ(1115) pair. Fig. 8 shows the pπ+π− IM distribution for events with the π+π− IM within495 ± 20 MeV and the pπ− IM within 1115 ± 20 MeV: really, the Θ+ peak is not visible.

(6) Moreover, neither the N(1520) peak nor the Θ+ one are visible in the inclusive pπ+π−distribution concerning the whole pπ+π−π+π− sample (Fig. 9(a)), which is very similar to thepπ+π− plus pπ+π− one, and the Θ+ peak is not visible in the pπ+π− distribution concerningall events where at least one IM falls in the 495 ± 20 MeV interval (Fig. 9(b)). The distributionsof Fig. 9(a) are similar to phase-pace distributions obtained by Monte Carlo calculations: for in-stance, Figs. 9(c) show the distributions for the reaction p̄2p → pπ+π−π+π−2π0, where 2π0accounts approximately for the energy and momentum carried by the unseen particles in thereactions on helium. Fig. 9(d) shows the Monte Carlo phase-space distribution for the reactionp̄2p → pK0K̄02π0 which is quite different from the previous one; this stresses that the K0 arethe minority in the data, as expected (strange particles are produced in few percent of the events).Note that the limited apparatus acceptance at low momenta affects negligibly the distributions.

In conclusion, the pπ+π− IM distribution for the subset of the pπ−π−π+π+ events, wherethe Θ+ may be expected, shows a peak close to 1550 MeV with a width of the order of 30 MeV.

3.2. ppπ+π−π−, pπ−π+K− and pπ−π+π+K− events

These event samples separately contribute little to the pπ+π− statistics; all together con-tribute with a statistics about 1/2 that of pπ+π+π−π−.


Fig. 6. Comparison between Monte Carlo (grey) and experimental (white) momentum distributions. The dis-tributions are normalized to the same area. Proton (a), (c) and pion (b), (d) momentum distributions. TheMonte Carlo calculations concern an annihilation process where the resonance N(1520) is produced, namelyp̄2p → N(1520)π+π−π0 → (pπ+π−)π+π−π0; in this case proton and pion momenta are constrained by theN(1520) mass. The experimental data concern the reaction p̄4He → p2π+2π−X. (a) and (b): momentum distributionsbefore the cut on the π+π− invariant mass (two π+π− pairs with invariant mass within the interval m(K0

S)± 20 MeV);

(c) and (d): momentum distributions after the cut on the π+π− invariant mass.

(1) In ppπ+π−π−, Θ+ is expected only in the presence of a K0S and Λ pair; here this con-straint acts in a way opposite to that for the reaction pπ+π−π+π− (see Section 3.1, point (5)).Fig. 10(a) shows the pπ+π− IM distribution for the π+π− IM within 495 ± 20 MeV and the


Fig. 7. Comparison between Monte Carlo (grey) and experimental (white) momentum distributions. (a) Protons and(b) kaons emitted in the process p̄2p → Θ+(1530)Kπ0 → (pK̄)Kπ0 and in the reaction p̄4He → pK0

SK0

SX.

Fig. 8. π+π− invariant mass distribution for events with one π+π− pair with IM within 495 ± 20 and one pπ− pairwithin IM within 1115±20 MeV.

pπ− IM within 1115±20 MeV. The background is increased by a factor of two by combinatorialeffects.

(2) In pπ−π+K− and pπ−π+π+K−, Θ+ requires the presence of only one K0S . Fig. 10(b)shows the pπ+π− IM distribution for the π+π− IM within 495 ± 20 MeV. The background isincreased by a factor of two for pπ−π+π+K− (87 entries) and is not increased for pπ−π+K−(68 events).


Fig. 9. (a) Experimental pπ+π− invariant mass distribution for all p4π events (full histogram); it is very close tothe relevant pπ+π+ plus pπ−π− invariant mass distribution. (b) Experimental pπ+π− invariant mass distributionconcerning only the π+π− pair combinations where at least one π+π− pair has invariant mass close to the K0

Smass;

note the difference with Fig. 3(a), which concerns events with two π+π− pairs with invariant mass close to the K0S

mass; (c) Monte Carlo calculation for the p̄2p → pπ+π−π+π−2π0 reaction with (dotted histogram) and without(full histogram) apparatus acceptance; (d) Monte Carlo calculation for the reaction p̄2p → pK0K̄02π0 with (dottedhistogram) and without (full histogram) apparatus acceptance.

The histograms in Fig. 10 are summed up in Fig. 11, the structure of which resembles to Fig. 3in spite of the lower statistics. While increasing the ±20 MeV intervals, the “evidence” of thepeaks disappears.

3.3. Summary

Fig. 12 shows the pπ+π− IM distribution for all our events together with a phase-space-likeIM distribution obtained considering the pπ+π+ and pπ−π− proton–pion combinations insteadof pπ+π−. The two distributions are very similar, and this indicates that the phase space is dom-inant in the inclusive pπ+π− IM distribution, as expected according to Section 3.1, point (6).

Fig. 13 reports the pπ+π− IM distribution sum of the histograms in Figs. 3 and 11 togetherwith the similar distribution relevant to pπ+π+ and pπ−π−. The latter one has been fitted witha smooth function (χ2r = 0.87, P = 0.64), which turns out to have a behaviour very close tothat of the pπ+π− IM distributions relevant to the reactions p̄2p → pπ+π−π+π−2π0 andp̄2p → pK0K̄02π0 shown in Fig. 14. The apparatus acceptance has been considered in theMonte Carlo calculations.


Fig. 10. pπ+π− invariant mass distribution (see text). (a) 2p3π events; (b) pπ−π+K− plus the pπ−π+π+K− events.

We have fitted the histogram of Fig. 13(a) in different steps. First, we have verified that thebackground function alone is not suitable to fit the histogram (χ2r = 2.1, P = 1.410−6). Second,the addition of two Gaussians to account for the two peaks improves the fit, but it remains un-satisfactory (χ2r = 1.6, P = 4.210−3, Fig. 15(a)); in particular, it turns out that the backgroundfunction does not fit well the data in the region of higher IM. Presumably, this reflects the factthat in the data there is some contribution from N and Δ resonances which is absent in the phase-space. Finally, we have restricted the best fit calculation to the interval 1.43–1.7 GeV, combiningin different ways the background and the Gaussian functions. We have obtained results whichare equivalent statistically, but differ for the number of events in the Θ+ peak. Typical resultsare shown in Figs. 15(b) (χ2r = 0.68, P = 0.83, NΘ+ = 46) and (c) (χ2r = 0.65, P = 0.84,NΘ+ = 59).


Fig. 11. Sum of the histograms of Figs. 10(a) and 10(b).

The fit on the Θ+ peak leads to

m(Θ+

) = (1560.0 ± 3.7) MeV,σgaussian = (10.76 ± 4.51) MeV.

The σ value is equal within the errors to our resolution (9.3 MeV, see the fit on the K0S peakin Fig. 4); hence also the Θ+ width is likely very narrow, as that of K0S . The number of eventsin the Θ+ peak represents a lower limit for the events with two K0S among the events with twoπ+π− pairs with invariant mass close to that of K0S (±20 MeV); considering that the events areone half the entries, the relevant frequency is 46/352 = 0.13. Number of events and frequencyare compatible with the upper limits estimated at the point (6) of Section 3.1.

We note that the Θ+ peak cannot be the effect of rescattering between mesons and residualnucleons as this works against the visibility of the peak: K− and K̄0 can be absorbed (K̄N →Λ(Σ)π ) and the particle momentum changes due to the elastic scattering losing memory of thepion origin.

Concerning the N(1520) peak, we have

M(1520) = (1504.6 ± 3.6) MeVa value different from the expected one (1515–1530 MeV) due to the facts discussed at point (3)in Section 3.1.

3.4. Statistical analysis

Once verified that the observed peak is not the effect of the apparatus acceptance or an indirectsignature of known physical signals, we have verified that it is not the trivial effect of a statisticalfluctuation. To be prudent, in the following statistical analysis we assume that number of Θ+ isequal to the lowest number found in the previous study (NΘ+ = 46). As the total number of theentries in the four bins containing the peak is N = 206, the number of background entries underthe peak is Nb = 160.


Fig. 12. (a) pπ+π− invariant mass distribution for all events. (b) pπ+π+ and pπ−π− invariant mass distribution forall events.

We follow two ways: the study of the statistical fluctuations on the background and the boot-strap method proposed time ago by Efron [53].

3.4.1. Statistical fluctuations on the backgroundFig. 16 shows the distribution of the statistical deviations from the smooth background func-

tion of the number of events in the four bins covered by the Θ+ peak in Fig. 13. The distributionis the result of 1143 random drawings on the smooth function repeated 1000 times; 1143 is thenumber of entries in Fig. 13. The standard deviation is σ = 11.8; hence the number of the ex-perimental events in the peak (46) is 3.7σ over the background and is the result of a statistical


Fig. 13. (a) Full statistics for the pπ+π− invariant mass distribution relevant to events where Θ+ may be expected.(b) Phase-space like distribution (see text).

fluctuation with the probability of 0.01%. The same result is obtained if a Gaussian accountingfor the N(1520) peak is added to the smooth function.

3.4.2. Statistical significance and bootstrap statistical methodThe statistical significance of the Θ+ peak is given by the ratio

S = NΘ+σΘ+

, (1)

where σΘ+ includes all uncertainties on NΘ+ (due to statistics, entry selection, background esti-mation and best fit procedures). Eq. (1) measures how much the peak differs from zero in units


Fig. 14. pπ+π− invariant mass distributions for events with two π+π− pairs with IM close to that of K0S

: Monte Carlo

calculations relevant to the reactions p̄2p → pπ+π−π+π−2π0 (a) and p̄2p → pK0K̄02π0 (b). Full histograms:apparatus acceptance neglected; dotted histograms: acceptance considered; lines: best fit function from (b) normalized tothe maximum of the dotted histogram.

of its own standard deviation. Some approximate expressions are usually considered for it, wherethe approximations concern specifically the evaluation of σΘ+ .

When NΘ+ comes from the difference NΘ+ = N − Nb between the observed events in thepeak region and the background events under the peak, the uncertainty is given by the relation

σΘ+ =√

σ 2b + σ 2N. (2)In the case of Poisson statistics Eq. (2) becomes

σΘ+ =√

Nb + N (3)


Fig. 15. Best fit to the histogram of Fig. 14(a) with the smooth function of Fig. 11(b) and two Gaussians. Best fit on theinterval 1.43–1.7 MeV; the Gaussians are fitted on the background function. Best fit on the interval 1.43–1.7 MeV; thebackground function and the Gaussians are fitted together.

and the significance is

S1 = NΘ+√Nb + N . (4)

In order to apply to our data Eq. (4), we have verified that they follow the standard Poissonstatistics, in spite that we have summed up four different reaction channels with different number


Fig. 16. Statistical fluctuations around the background function in the Θ+ peak region.

of entries and the background evaluation is complicated. For this check, we have applied to thedata two methods: a Monte Carlo toy model and a non-parametric bootstrap model.

In the toy model we have generated a background and a pentaquark resonance in each of theobserved channels and have studied the statistical fluctuations on the total number of entries inthe peak region, in the background and in the peak by applying the same selection criteria usedfor the analysis of the real data. The obtained result is that all the fluctuations on the entriesfollow closely the Poisson statistics.

Since this procedure neglects the peak-background interference and the detector acceptance,we have used also the non-parametric bootstrap method [52]. According to this method, whichprocesses the real data instead of simulated data, we have considered the samples of experimentalfour-momenta of Table 3 and have generated, by an at random selection with replacement, newsamples of the same size as the original ones. Owing to the replacement mechanism, some ofthe original entries will appear several times in the sample, some others will not appear at all.By iterating this procedure we have obtained a big number (≈ 10 000) of bootstraps samples.We have produced for each sample the pπ+π− invariant mass distribution following the sameprocedure adopted to obtain Fig. 13 and have calculated the numbers of total, background andpeak entries in the peak region. We recall that the entries in the final histogram of Fig. 13(a) aretwice the events from which they are generated; to distinguish event and entry distributions, weindicate the numbers of total, background and peak entries in the peak region with Ne, Nbe andNΘ+e , respectively. The fluctuations on these quantities deduced from this artificial ensemblehave the property to reproduce, under rather broad conditions, the true experimental errors ratherclosely. The more important of these conditions is the symmetry around the mean value of thebootstrap distributions [52] which, in our case, is well verified, as shown in Fig. 17. The resultsof the bootstrap analysis are in agreement with those of the Monte Carlo toy model and showthat the numbers of entries in our invariant mass distributions follow the Poisson statistics.

On the basis of this analysis, we use the Poisson errors and report the significance S1 inTable 4. It includes all the correlated uncertainties, including those on the background.

The S1 value is an underestimation as the calculation ignores that the number of the entries aretwice that of the events (see Sections 3.1 and 3.2) and the entries coming from the backgroundevents are distributed differently from those coming from the peak events. As we have verifiedthrough Monte Carlo calculations, the background events, which are distributed at random ac-cording to phase-space, contribute to each bin in the histogram of Fig. 15(a) with a number of


Fig. 17. NΘ+ = N − Nb distribution obtained by the bootstrap method. The left-right symmetry around the mean valueassures that it follows the Poisson statistics.

Table 4Θ+ signal and background events in the peak region and values of the significance according to Eqs. (4)Ne Nbe NΘ+e S1206 ± 14.3 160 ± 12.6 46 ± 19.1 46/19.1 = 2.4N Nb NΘ+

126 ± 15.7 80 ± 6.3 46 ±√

15.72 + 6.32 = 46 ± 16.9 46/16.9 = 2.7

entries twice the events on the average (see Fig. 18(a)). Instead, in the case of events in a narrowpeak, only one half of the entries are distributed at random (those with incorrect combination of pand π+π−), while one half is concentrated in the peak region (see Fig. 18(b)). The behaviourof the distribution coming from the N(1520) decays is middle between the previous ones (seeFig. 18(c)). As the background under the peak at 2200 MeV is contributed mainly by phase-spaceevents and the number of peak events is NΘ+ = NΘ+e = 46, the number of background events is

Nb � Nbe/2 = 1602

±√

160

2= 80 ± 6.3

and the total number of events is

N � (Ne − Nbe/2) ±√

Ne + Nbe4

= 126 ± 15.7.

According to Eq. (2), the error on NΘ+ is σΘ+ = ±√

σ 2e + σ 2b = ±√

286.2 = ±16.9. Therelevant S1 value is given in Table 4.

The new S1 value is a bit higher than that calculated previously. The significance of 2.7 meansthat the peak is a statistical fluctuation with the probability of 0.35%. This result is in agreement,although more restrictive, with that deduced in Section 3.4.1. We notice that if repeat the abovecalculations considering the higher value for NΘ+ obtained in Section 3.3 (NΘ+ = 59), we obtainfor S1 the values 3.14 ( 0.17%) and 4.4 (0.002%), respectively.

Compared with the significance of the other experiments (see Table 1), our S1 value is closeto the lower values.


Fig. 18. Monte Carlo calculations of the pπ+π− invariant mass distributions for events selected with two π+π− pairswith invariant mass close to the K0

Smass (±20 MeV). The limited acceptance of the apparatus in the low momentum

region has been taken into account. (a) Phase-space for the reaction p̄2p → pπ+π−π+π−2π0: IM distribution for the“original events” (grey histogram) and for the entries due to the combinatorial effect (two entries per event; white his-togram). The two distributions have the same shape. (b) Reaction p̄2p → Θ+(1560)π+π−2π0 → pπ+π−π+π−2π0:invariant mass distribution for the “original events” (grey histogram) and for the entries due to the combinatorial ef-fect (two entries per event, white histogram). A number of entries (half of the entries) equal to that of the eventsare distributed as in the grey histogram. For the resonance a width of 5 MeV has been assumed. (c) Reactionp̄2p → N(1520)π+π−2π0 → pπ+π−π+π−2π0. The width has been assumed to be 120 MeV. Invariant mass forthe original events (grey histogram) and for the relevant entries (white histogram with double statistics).


4. Discussion

In the light of our analysis, we discuss some features of the other experiments.The experimental concerns about Θ+ include the statistical significance of the observed

peaks, the discrepancy between the mass measured in the nK+ and pK0S → pπ+π− decaymodes, the physical meaning of the cuts used to enrich and even to see the signal, the back-ground not completely understood (kinematical reflections included), nuclear target effects and,overall, the fact that several experiments did not see it. Detailed discussions of all this can befound in [25–27,29,30].

Now we discuss the features of the identification of Θ+ through the pK0S decay mode and, forthe sake of simplicity, assume that two strange particles at most are produced. The probability todetect the Θ+, if it exists, increases if it is possible to reject the events where the presence of Θ+can be excluded a priori. With reference to Table 2, we recall that pπ+π− may appear in thefinal state of a lot of intermediate states, strange and not strange, with S = +1 and S = −1. Thefinal states compatible with the presence of Θ+ are only those including two π+π− pairs bothwith IM ≈ 495 MeV (through the decays Θ+K̄0 → (pK0)K̄0 → pK0SK0S) and one π+π− pairwith IM ≈ 495 MeV in company with one K−.

On the contrary, a π+π− pair in a final state with a K+ is the signature of K̄0 (hence pπ+π−cannot be the memory of Θ+) and, in company with K+K−, cannot be originated from a strangeparticle. Therefore, the detection of only one π+π− pair accumulates a lot of background, whichmay sink the Θ+ peak. If the final state contains more than one proton or more than two chargedpions, the background increases more and more due to combinatorial effects. In conclusion it islikely that the Θ+ peak, if it exists, may not be observed in inclusive reactions, as it is demon-strated by our Figs. 9 and 12.

This is just the case of most of the experiments which did not observe the Θ+. Most of themdetected only pπ+π− in high multiplicity final states and, in some cases, unclean incomingbeams were used (unknown mixtures of proton, pions and kaons) [25,26].

As far as it concerns the Θ+ detection via the nK+ decay mode (see reactions i–o in Table 1),the Θ+ strangeness is +1 without ambiguity.

Θ+ was observed via the nK+ or the pK0S → pπ+π− decay modes in the experimentssummarized in Table 1. In the reactions f–h the strangeness carried by K0S is defined throughthe incoming K+ and the outgoing K− and Σ+, respectively. Such a check is lacking in thereactions a–e.

5. Conclusion

We contribute to the researches on the Θ+ pentaquark analysing, for the first time, antiprotonannihilation data. We have looked for a signal of the existence of the Θ+ via its pK0S → pπ+π−decay mode analysing the pπ+π− invariant mass distribution in the annihilation reactions at rest

p̄ 4He → (p2π+2π−)2nX(pπ+π−K−

)psnX,(

p2π+π−K−)2nX,(

ppπ+2π−)nX.

The research has been motivated by the fact that these reactions, where two to four nucleonsare involved in the annihilation, assure favourable conditions for the creation of strange particles.


The favourable features of our analysis can be summarized as follows.

(i) The reactions are (partially) exclusive;(ii) the Θ+ signal is found in subsets of reactions where it is expected and is absent where it

is not expected;(iii) reflections of other resonances are likely absent;(iv) the background is fairly understood.

We have found a peak around the invariant mass value 1560.0 ± 3.7 MeV with a very narrowwidth. The mass value agrees with the values obtained in experiments which studied the Θ+ →nK+ decay mode.

The weak point of our analysis is the poor statistics. For this reason we have studied care-fully the statistical features of the invariant mass distributions in order to evaluate correctly thestatistical significance, which turns out to be at least 2.7 and means that the peak is not a trivialstatistical fluctuation with the probability of 99.65%. This value is considered of not sufficientsignificance to claim support of the Θ+. Anyway, similar results have been obtained also in otherexperiments (see Table 1) and the meaning of their statistical significance is discussed deeply inRef. [54].

Acknowledgements

Thanks are due to the Dr. Stefania Vecchi of the INFN Section of Bologna for her carefulreading of the paper and suggestions.

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