Ππ Invariant Mass Research Articles

Pion-pion scattering lengths from Ke4 and Cusp at NA48/2 experiment

In kaon decays the measurement of ππ scattering lengths ( a 0 and a 2 ) are accessible mainly through the study of kinematical properties in two decay modes. The classic way is based on the form factors analysis in K ± → π + π − e ± ν ( K e 4 ) decay. Thanks to the absence of other hadrons in the final state the ππ interaction can be analyzed in terms of phase shift variation with the ππ invariant mass. The preliminary results on a set of ∼ 1150000 K ± events collected in two years of data taking, will be discussed. The second way to evaluate the ππ scattering lengths is based on the accurate study of K ± → π ± π 0 π 0 Dalitz plot, in which the strong rescattering process π + π − → π 0 π 0 introduces a singularity in the shape of the distribution. The preliminary result based on more than ∼ 60 ⋅ 10 6 K ± → π ± π 0 π 0 decays is in good agreement with the measurement in K e 4 .

Measurement of ππ scattering lengths in Kaon decay by NA48/2

In kaon decays the measurement of ππ scattering lengths (a0 and a2) are accessible mainly through the study of kinematical properties in two decay modes. The classic one is based on the analysis of the form factors in the K± → π+π−e±v (Ke4). Thanks to the absence of other hadrons in the final state the ππ interaction can be analyzed in terms of variation of phase shift with the ππ invariant mass. The preliminary results on a partial set of ~ 670000 K± will be discussed. The second way to evaluate the ππ scattering lengths is based on the accurate study of K± → πππ0π0 Dalitz plot, in which the strong rescattering process π+π− → π0π0 introduces a singularity in the shape of the distribution. The preliminary result based on ~ 50 · 106 K± → π±π0π0 decays is in good agreement with the measurement in Ke44.

OBSERVATION OF THE ABC EFFECT IN THE FIRST EXCLUSIVE MEASUREMENTS OF pn → dπ0π0

The reaction pn → dπ0π0 constitutes the most fundamental system for the study of the ABC effect - a puzzling threshold enhancement in the ππ invariant mass spectrum of the ππ system in double-pionic fusion to nuclear bound states. The first exclusive measurements of this reaction have now been carried out at CELSIUS-WASA. They exhibit a striking low-mass enhancement in the ππ invariant mass spectrum, prove it to be a σ-channel phenomenon and falsify conventional theoretical models, which predict an associated high-mass enhancement not present in the new exclusive data. In the kinematically complete data sample we observe a ΔΔ excitation, where the interaction between the two Δ obviously plays a crucial role for the generation of the ππ low-mass enhancement.

LOW-MASS ππ ENHANCEMENT IN BARYONIC ππ PRODUCTION: ABC EFFECT REVISED BY EXCLUSIVE MEASUREMENTS

The ABC effect - a puzzling threshold enhancement in the ππ invariant mass spectrum of double-pionic fusion to nuclear bound states - has been investigated since 40 years by inclusive measurements without providing a conclusive interpretation. First exclusive measurements to this topic have now been carried out at CELSIUS-WASA. They confirm a huge ππ threshold enhancement, prove it to be of scalar-isoscalar nature, i.e., a σ-channel phenomenon and reveal the theoretically predicted high-mass enhancement in inclusive spectra to be of πππ rather than of ππ nature - falsifying thus corresponding model predictions for the ABC effect. From the kinematically complete data samples we infer that the interaction between the two Δ particles created in this process is of crucial importance.

ππ PRODUCTION IN PROTON-PROTON COLLISIONS

At CELSIUS-WASA the two-pion production in proton-proton collisisons has been measured exclusively from threshold up to the energy regime, where both of the collision partners are expected to be excited to the Δ state. The measurements constitute the first kinematically complete data samples of solid statistics in this energy range. Most of the data have been obtained for the π+π- and π0π0channels. Whereas at near-threshold energies the differential distributions can be succesfully explained by chiral dynamics and Roper excitation, respectively, the data for the π+π- channel in the ΔΔ region can be described only, if the special configuration (ΔΔ)0+ is assumed. The data for the π0π0 channel moreover exhibit a low-mass enhancement in the π0π0 invariant mass spectrum, which is reminiscent of the ABC-effect found in double-pionic fusion to light nuclei.

Observation of a cusp-like structure in the [formula omitted] invariant mass distribution from [formula omitted] decay and determination of the ππ scattering lengths

We report the results from a study of a partial sample of ∼2.3×107K±→π±π0π0 decays recorded by the NA48/2 experiment at the CERN SPS, showing an anomaly in the π0π0 invariant mass (M00) distribution in the region around M00=2m+, where m+ is the charged pion mass. This anomaly, never observed in previous experiments, can be interpreted as an effect due mainly to the final state charge exchange scattering process π+π−→π0π0 in K±→π±π+π− decay [N. Cabibbo, Phys. Rev. Lett. 93 (2004) 121801]. It provides a precise determination of a0−a2, the difference between the ππ scattering lengths in the isospin I=0 and I=2 states. A best fit to a rescattering model [N. Cabibbo, G. Isidori, JHEP 0503 (2005) 21] corrected for isospin symmetry breaking gives (a0−a2)m+=0.268±0.010(stat)±0.004(syst), with additional external uncertainties of ±0.013 from branching ratio and theoretical uncertainties. If the correlation between a0 and a2 predicted by chiral symmetry is taken into account, this result becomes (a0−a2)m+=0.264±0.006(stat)±0.004(syst)±0.013(ext).

Heavy quarkonium [formula omitted] transitions and a possible [formula omitted] state

π + π − transitions of heavy quarkonia, especially the ϒ ( 3 S ) → ϒ ( 1 S ) π + π − decay process, are revisited. In the framework of the Chiral Unitary Theory (ChUT), the S wave ππ final state interaction (FSI) is included. It is found that when an additional intermediate state with J P = 1 + and I = 1 is introduced, not only the ππ invariant mass spectrum and the cos θ π ∗ distribution in the ϒ ( 3 S ) → ϒ ( 1 S ) π + π − process can simultaneously be well explained, but also a consistent description for other bottomonia π + π − transitions can be obtained. As a consequence, the mass and the width of the intermediate state are predicted. From the quark content analysis, this state should be a b b ¯ q q ¯ state.

LOW ENERGY DOUBLE-PION PHOTOPRODUCTION IN NUCLEI

We have investigated π0π0 and π±π0 photoproduction off complex nuclei. Simulations have been performed by means of a semi-classical BUU transport model including a full coupled-channel treatment of the final state interactions. We show that the target mass dependence of the π0π0 invariant mass spectrum as measured by the TAPS collaboration can be explained without introducing medium effects beyond absorption and quasi-elastic scattering of the final state particles. On the other hand, we find considerable discrepancies with the data in the π±π0 channel, which are not understood.

Low-energy ππ photoproduction off nuclei

In the present Letter we investigate π0π0 and π±π0 photoproduction off complex nuclei at incident beam energies of 400–460 MeV. Simulations of two pion photoproduction on protons and nuclei are performed by means of a semi-classical BUU transport model including a full coupled-channel treatment of the final state interactions. Elastic scattering of the final state pions with the nucleons in the surrounding nuclear medium is found to yield a downward shift of the ππ invariant mass distribution. We show that the target mass dependence of the π0π0 invariant mass spectrum as measured by the TAPS Collaboration can be explained without introducing medium effects beyond absorption and quasi-elastic scattering of the final state particles. On the other hand, we find considerable discrepancies with the data in the π±π0 channel, which are not understood.

Partial wave analysis of theπ0π0system produced inπ−pcharge exchange collisions

A partial wave analysis of the π0π0 system produced in the charge exchange reaction π−p→π0π0n at an incident momentum of 18.3 GeV/c is presented as a function of the π0π0 invariant mass mπ0π0 and momentum transfer squared |t| from the incident π− to the outgoing π0π0 system. For small values of |t|, the S-wave intensity shows a broad enhancement at low mπ0π0 with a sharp dip in the vicinity of the f0(980). A dip is also observed in the vicinity of the f0(1500). There is a rapid variation of the S to D0 relative phase difference in these mass regions. For large values of |t|, the f0(980) appears as a bump. The f2(1270), observed in D waves, is produced dominantly by π exchange at low values of |t| and a2 exchange at higher values of |t|.Received 12 January 2000DOI:https://doi.org/10.1103/PhysRevD.64.072003©2001 American Physical Society

The σ-meson production in excited ϒ decay processes: phenomenological analyses

We analyze the ππ production amplitudes in the excited ϒ decay processes, ϒ(2 S)→ ϒ(1 S) π + π −, ϒ(3 S)→ ϒ(1 S) π + π − and ϒ(3 S)→ ϒ(2 S) π + π −, and the ππ and K K ̄ production amplitudes in the charmonium decay processes, ψ(2 S)→ J/ ψπ + π − and J/ψ→φπ +π −, φK +K − , including the possible effect of light σ production. The amplitudes are parametrized by the sum of Breit–Wigner amplitudes for the σ and the other relevant particles and of the direct 2 π-production amplitude, following the VMW method. All the ππ (and K K ̄ ) invariant mass spectra are reproduced well with the σ Breit–Wigner amplitudes by using the common parameters, m σ =526 +48 −37 MeV and Γ σ =301 +145 −100 MeV, which is almost consistent with the values obtained in our previous phase shift analyses.

Assessment of the equivalent photon approximation for the process [formula omitted

The contribution of the virtual process γγ → π + π − is evaluated, first treating the quantum electrodynamics exactly and then using the equivalent photon approximation. The dependence on electron scattering angles, electron energies, ππ invariant mass and γπ momentum transfer is investigated. The approximation is very good if both electron scattering angles are less than 0.1 rad, but is 20%–40% too big (depending on the precise version used) if either angle is integrated over. It is explained that the approximation is not Lorentz invariant; numerical results are given only for beams with anti-parallel momenta.