Beketov, G V

Konovalov, B S

Kruchinin, S P

Selektor, Ya M

Shulyachenko, V N

Zombkovsky, S M

CERN Document Server

CERN LIBRARIES, GENEVA CM-P00100632 INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS, MOSCOW Report ITEF 816 INVESTIGATION OF THE A2 AND A3 MESON PRODUCTION IN π INTERACTIONS AT A MOMENTUM OF 4.45 GeV/c G.V. Beketov, S.M. Zombkovskij, B.S. Konovalov, S.P. Kruchinin, Ya.M. Selektor and V.N. Shulyachenko Moscow 1970 Translated from the German (DESY 13-Üb-132) at CERN by G. Grayer (Original : Russian) Not revised by the Translation Service (CERN Trans. Int. 71-8) Geneva June 1971 1. INTRODUCTION During the last year, the problem of the measurement of the quantum numbers of the A2 mesons was given great importance. This problem is complicated by the demonstration of the splitting of the A2 meson peaks1). The largest part of this work, in which an attempt was made to determine the quantum numbers of the A2 meson, is based on the analysis of A2 → ρπ decays. It can be fairly certainly established that this decay represents the principle A2 decay. The difficulty occurs in the establishment of the spin and parity of the A2 meson on top of the large background (~50-60%), of which the properties have still hardly been explored. In one work2) the task was undertaken of calculating the angular characteristics of the background, in so far as it influences the density of points in the Dalitz plot. This allows one to say that up to now the spin of the A2 meson is J = 2 and the parity is still not yet established. In the present work, the total effective cross-section for A2 and A3 meson production in the reactions π-p → A2-p, A2 → ρ0π- (1) and π-p → A3-p (2) at a momentum of 4.45 GeV/c is determined. We find values for the slope of the effective differential cross-section (d/dt') for the production of a 3π system in various mass intervals. An analysis of the density distribution of the points in the Dalitz diagram and the angular distri­bution perpendicular to the decay plane of the A2 meson was used. In this way the angular characteristics of the background and the influence of the Deck effect on the angular distribution was calculated. 2. THE EFFECTIVE MASS SPECTRUM In order to analyse the reactions (1) and (2), about 300,000 photo­graphs were examined; they were taken in a liquid hydrogen bubble chamber of 50 cm diameter with a π- meson beam of 4.47 GeV/c from the ITEF proton - 2 -syncbroton. Events of the reaction π-p → pπ+π-π- (3) were selected, for which Ρ(χ2) ≥ 0.5%, and the visible ionization of all tracks agreed with that expected for this reaction. A total of 2472 events of reaction (3) were obtained. The effective mass spectrum of the 3π sys­tem is given in Fig. 1. The interval of the A1 meson (950 < M ≤ 1150 MeV) has been investigated by us3). In the total 3π system mass spectrum a maximum is clearly distinguished due to the A2 meson; also a peak due to the A3 meson [πA(1640) meson] stands out weakly. In Fig. 1 the 3π system mass spectrum for the decay via reaction (3) is displayed (as a hatched histogram) following the cuts: (a) events were selected for which the effective mass of at least one of the π+π- systems lay in the ρ-mescm region (665 ≤ Mπ+π- < 865 MeV); and (b) events with peripheral Δ++(1236) isobar production were excluded [events with 1120 ≤ Μpπ+ ≤ 1340 MeV and |t∆++| < 0.3 (GeV/c)2 ]. As we have demonstrated elsewhere4), the exclusion of events forming a Δ++(1236) isobar with |t∆++| < 0.3 (GeV/c) is practically the same as excluding the whole peripheral background reaction π-p → Δ++(1236)π-π-. The ratio of the useful effect to no effect in the region of the A2 meson amounts to ~1:1. The maximum of the A2 meson corresponds to the mass MA2 ~ 1325 MeV, the half-width to 120-150 MeV. In Fig. 2 is displayed a mass spectrum of the 3π spectrum with the following cuts: (a) events with the smallest effective mass of the π+π- system lying in the ρ meson band and the square of the four-momentum transfer of this system is such that |tπ+π-| ≤ 0.3 (GeV/c)2 were excluded; and (b) events with peripheral production of Δ++(1236) isobars were removed by the method described above. In Fig. 2b the effective mass spectrum of the 3π system from reaction (3) is seen, in which the effective mass of at least one of the π+π- sys­tems lies in the f0 meson band. - 3 -In the distributions of Figs. 2a and 2b the A3 meson peak is clearly recognized. The distribution of Figs. 2a and 2b were approximated by a Breit-Wigner curve for the A3 meson, with the curve for invariant phase space below. The phase space curve was calculated within limits by a Monte Carlo method, making use of the experimental histogram. The results of the fit using the least squares method are drawn as a continuous line in Figs. 2a and 2b. For the mass and width of the A3 meson, we find M = 1672 MeV, Γ = 128 MeV for the decay A3 → π+π-π-, and M = 1712 MeV, Γ = 128 MeV for the A3 → f0π- decay. The total production cross-section of the A2 and A3 mesons amounts to σA2 = (60 ± 7) µb; σ[A3- → (3π)-] = (90 ± 8) µb, and σ[A3- → f0π-] = (63 ± 7) µb (all errors are statistical). The value found for the effective cross-section for σ(A3- → f0π-) is very sensitive to the form of the curve of the background fit used; thus in our opinion the hypothesis that the decay of the A3 mesons takes place 100% through the A3- → f0π- channel is not excluded. In Figs. 3a and 3b the distributions of the number of events of reaction (3) against the magnitude of t' = |t - tmin| are represented graphically, where t is the square of the four-momentum transferred to the π- mesons from the 3π system, and tmin the smallest possible value for this magnitude at the given mass value of the 3π system. The dis­tribution of t' was found for the following mass intervals of the 3π system: (a) 975 ≤ M3π ≤ 1275 MeV; (b) 1275 < M3π ≤ 1375 MeV; (c) 1375 < M3π ≤ 1575 MeV; (d) 1575 ≤ M3π ≤ 1775 MeV; and (e) 1775 ≤ M3π ≤ 1975 MeV. The distribution was approximated by the exponential dN/dt' ~ exp (Bt') in the interval 0 < t ≤ 0.8 (GeV/c)2. By use of the maximum likelihood method we obtained the following values for the slope Β: Βa = 6.88 ± 0.39; Bb = 3.77 ± 0.56; Βc = 4.25 ± 0.39; Bd = 3.95 ± 0.39; and Βe = 3.38 ± 0.47 (GeV/c)-2. The large value for the slope for the A1 meson (975-1275 MeV) is consistent with the accepted assumption that the Deck effect supplies the main contribution to this mass region. At the large mass values a monotonic decrease of the slope with the mass of the 3π system is observed, suggesting the adoption of a contribution due to the peripheral diagram - 4 -at large mass values of the 3π system. The monotonic lapse of the fall-off of the slope Β with the 3π system mass is disturbed for the mass region of the A2 meson; in this mass region a substantial decrease in the slope is established. For the A2 meson production by exchange of poles belonging to the vacuum group, the effective differential cross-section dσ/dt' must go to zero at t' → 0. Due to the large background under the A2 meson peak, and also to the statistical limitations, a minimum at small t' is not es­tablished. 3. ANGULAR DISTRIBUTIONS AND THE DENSITY DISTRIBUTION OF THE POINTS IN THE DALITZ PLOT IN THE A2 MESON REGION The usual method of determining the quantum numbers of a 3π resonance consists of the analysis of the density of points in the Dalitz plot, and the analysis of the differential angular distributions of the decay prod­ucts of the resonance concerned. We carry out an analysis of the quantum number of the A2 mesons with the help of the projections of the Dalitz plot and by use of the angular distribution between the direction of the normal of the decay plane of the A2 mesons and the direction of the pri­mary π mesons (angle θ) in the S-system of the A2 mesons. The analysis was worked through for the quantum numbers JP = 2+ and 2-. The projection of the Dalitz plot for the A2 meson region on the M2π+π- axis is represented in Fig. 4a. The selection of the events corresponds to the hatched his­togram of Fig. 1. The theoretical curves were calculated for the quantum numbers 2+ (continuous line) and 2- (broken line) in accordance with Frazer et al.5). The calculated curves were normalized to the total number of events m the histogram. The value of χ2 gives for the hypoth­eses of the quantum numbers 2+ and 2-: χ22+ = 28.53, and χ22- = 148.63, for 12 degrees of freedom. In Fig. 5 is shown the distribution of the number of events in the A2 meson region against cos θ (Fig. 5a) and from the control region (Fig. 5b). The control region was selected from both sides of the A2 meson band, corresponding to the mass intervals 1225 < Mπρ < 1275 MeV and 1375 < Mπρ < 1425 MeV. The distributions for the control regions were - 5 -summed, being compiled relative to cos θ = 0, in order to increase the statistical accuracy. The control distribution was approximated to the linear function a + b |cos θ|. For the parameters a and b, the values a = 32.9 and b = 17 were found. Under the assumptions that (i) the background in the A2 meson band possesses the same character as in the control band, and (ii) that the number of background events is equal to the total number of events in the control region, the lines in Fig. 5b were directly drawn for the quan­tum numbers 2+ and 2- (continuous line and broken line). The theoretical distribution in cos θ has been taken from Berman et al.6) and was indeed obtained by a simplified assumption about the A2 meson production mecha­nism. For all cases the assumption is that the A2 was produced by exchange of a pole belonging to the vacuum group, i.e. the P, P' or ρ poles. By this means one supposes that one can attribute the largest contribution to the density matrix element ρ11 if the spin and parity of the resonance lies in the natural series (1-, 2+, 3-, ...) or ρ00 when the spin and parity of the resonance is attributed to the series 1+, 2-, 3+, ... Taking into account the decay of the resonance, we adopt the quantum numbers 2-, in order that the A2 → ρ0π- decay takes place with the least angular momentum. From the above assumption the expression for the an­gular distribution (after taking into account the background) assumes the following form: W2+ (cos θ) = N1(1 - 3 cos2 θ + 4 cos4 θ) + (32.9 - 17|cos θ|), W2- (cos θ) = N2(1 - 2 cos2 θ + cos4 θ) + (32.9 - 17|cos θ|), where N1 and N2 are the normalization factors. The value for χ2 for the hypotheses of the quantum numbers 2+ and 2- are χ22+ = 12.7 and χ22- = 63.0 for 9 degrees of freedom. We find the centre of gravity of the A2 meson distribution at ~ 1325 MeV. This value for the A2 meson mass differs from the mean world value by about 20 MeV. The A2 meson maximum depends on the experimental cuts over the fairly wide mass interval of ~ 1290 to ~ 1340 MeV. The discrepancy can be easily explained either by a small (~ 1.5%) systematic - 6 -shift of the incoming momentum, or by a systematic displacement in the magnetic field values, or through both these effects together. If one claims that the exact discrepancy in this work is due to a systematic effect and not through the absence of a light A2 meson in our work and in some other experiments, then one can examine the angular distributions and the distribution of the points in the Dalitz plot for a light and heavy A2 meson. Although we have observed no "splitting" of the maximum of the A2 mesons, the mass distribution vas divided into two parts (at the position of the centre of gravity of the peak) and for each part the analysis of the quantum numbers was carried out. For the "light" (A2L) meson and for the "heavy" (A2H) meson we chose the mass range 1275-13/5 and 1325-1375 MeV. In Figs. 4b and 4c one sees the projection of the Dalitz plots for the mass intervals of the A2L and A2H mesons. The value for the χ2 for the hypotheses JP =2+ (continuous line) is equal to χ22+L = 11.9 for 10 degrees of freedom, and χ22+H = 24.4 for 11 degrees of freedom; for the hypotheses JP = 2-, χ22-L = 29.2 for 10 degrees of freedom, and χ22-H = 29.5 for 11 degrees of freedom. The angular distribution for the mass region of the A2L and the A2H mesons referred to cos θ = 0 were added, thus increasing the statistical accuracy. The distribution for the A2L meson mass region is displayed graphically in Fig. 5c, and that of the A2H in Fig. 5d. The value of χ2 for the hypotheses JP = 2+ and 2- gives χ22+L = 3.6; χ22+H = 7.7 and χ22-L = 17.7, χ22+H = 46.1 for 4 degrees of freedom. Excluding the Deck effect by the above method leads to the values χ22+L = 4.7; χ22+H = 9.2; χ22-L = 17.4; and χ22-L = 45.3 for 4 degrees of freedom. The corresponding distributions and the theoretical curves are displayed in Figs. 5g and 5h. The continuous represents the hypothesis JP = 2+, the broken line the hypothesis JP = 2-. Thus the analysis of spins and parity of the A2 meson gives the quantum numbers JP = 2+, for the A2L and A2H mesons as well as for the "single" A2 meson, in agreement with a series of other works7). To conclude we thank V.U. Vladimiroky, G.K. Kliger and A.B. Kaidalov for numerous useful comments. - 7 -REFERENCES 1) H. Bens, G.E. Chicovani et al., Phys. Letters 28 Β, 233 (1968). 2) J. Ballam, A.D. Brody, G.B. Chadwick et al., Phys. Rev. Letters 21, 934 (1968). Ν.M. Cason, Phys. Rev. 148, 1283 (1966). 3) G.V. Beketov, S.M. Zombovskij et al., Preprint ITEF-775 (1970). 4) G.V. Beketov, S.M. Zombovskij et al., Preprint ITEF-767 (1970). 5) W.R. Frazer, J.R. Fulco and F.R. Harpern, Phys. Rev. 136 B, 1207 (1964). 6) S.M. Berman and M. Jacob, Phys. Rev. 139 B, 1023 (1965). 7) R. Baud, H. Benz et al., Phys. Letters 31 B, 397 (1970). H. Aguilar-Benitez, J. Barlow, L.D. Jacobs et al., Phys. Letters 29 B, 62 (1969). - 8 -Figure captions Fig. 1 : Effective mass distribution of the 3π system from reaction (1). The hatched distributions are the events for which the lowest effective mass of the π+π- systems lies in the ρ meson band [events with the production of Δ++(1236) isobars with |t∆++| < 0.3 GeV/c were excluded]. Fig. 2 : The distribution of the effective mass of the 3π system from reaction (1). a) Events for which at least one π+π- system lies in the mass interval of the ρ meson and |tπ+π-| < 0.3 (GeV/c)2; thus events with production of Δ++(1236) isobars with |t∆++| < 0.3 (GeV/c)2 are excluded. b) Events for which the effective mass of at least one π+π- system lies in the f0 meson mass region. Fig. 3 : Distribution of the number of events of reaction (1) against t' = |t - tmin| for different mass intervals of the 3π system: a) 975 ≤ M3π ≤ 1275 MeV b) 1275 < M3π ≤ 1375 MeV c) 1375 < M3π ≤ 1575 MeV d) 1575 < M3π ≤ 1775 MeV e) 1775 < M3π ≤ 1975 MeV. Fig. 4 : Distribution of the number of events from the A2 meson band (1275 < M3π < 1375 MeV) against M2π+π-. The selection of events corresponds to the hatched histogram of Fig. 1. The theoretical curves refer to the hypothesis JP = 2+ (continuous line) and JP = 2- (broken line). - 9 -Fig. 5 : Distribution of the number of events against cos θ: a) for the control region (1225 < Mρπ < 1275 MeV and 1375 < Mρπ < 1425 MeV); b) for the A2 meson region (1275 < Mρπ < 1375 MeV); c) for the A2L meson region (1275 < Mρπ < 1325 MeV); d) for the A2H meson region (1325 < Mρπ < 1375 MeV); e, f) for the control region and the A2 meson region, excluding the events with |tρ| < 0.5 (GeV/c); g, h) for the A and A2H meson regions; events with |tρ| < 0.5 (GeV/c.)2 were excluded; the theoretical curves correspond to the hypotheses JP =2+ (continuous line) and JP = 2- (broken line). Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 

Investigation of the $A_{2}$ and $A_{3}$ meson production in $\pi^{-}p$ interactions at a momentum of 4.45 GeV/c

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Investigation of the A2A_{2}A2​ and A3A_{3}A3​ meson production in π−p\pi^{-}pπ−p interactions at a momentum of 4.45 GeV/c

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Investigation of the $A_{2}$ and $A_{3}$ meson production in $\pi^{-}p$ interactions at a momentum of 4.45 GeV/c