Ππ System Research Articles

Exploring Light Meson Resonances in Two-Pion Photoproduction: A Regge Formalism Analysis

In the domain of hadron spectroscopy, the investigation of meson resonances plays a pivotal role. This study focuses on the significance of twopion photoproduction as a prominent avenue for studying meson resonances in the ππ system. By employing the Regge formalism, our model incorporates the background contribution from the well-known “Deck Mechanism” and emphasizes the significant ρ(770) resonance, representing the P-wave contribution arising from pomeron and f2 exchanges. The model is extended by accounting for scalar mesons, namely σ, f0(980) and f0(1370), contributing to the S-wave behavior, as well as the tensor meson f2(1270) corresponding to the D-wave contributions, while also considering non-resonant P- and S-wave components. The model contains a number of free parameters, which are constrained from a global fit of the available experimental data for angular moments up to L = 2 for M = 0, …, 2. The fitted angular moments are compared with experimental data obtained from CLAS. The key physical insights gained from the model are summarized. Furthermore, we extract the t-dependence of the Regge amplitude residue function for the subdominant exchanges, shedding light on their contribution to the overall dynamics.

Efficient operators for studying higher partial waves

An extended multi-hadron operator is developed to extract the spectra of irreducible representations in the finite volume. The irreducible representations of the cubic group are projected using a coordinate-space operator. The correlation function of this operator is computationally effcient to extract lattice spectra. In particular, this new formulation only requires propagator inversions from two distinct locations, at fixed physical separation. We perform a proof-of-principle study on a 243 × 48 lattice volume with mπ ≈ 900 MeV by isolating the spectra of A+1, E+ and T+2 of the ππ system with isospin-2 in the rest frame.

Study of the ππ system in a finite volume

We evaluate energy levels of the ππ system in the ρ channel in a finite volume using chiral unitary theory. We investigate ππ phase shifts and ρ meson properties using Lattice QCD data with high precision. We also shortly discuss the πK system in the K* channel in a finite volume.

THE ρ MESON IN FINITE VOLUME

We evaluate energy levels of the ππ system in the ρ channel in finite volume using chiral unitary theory. We investigate ππ phase shifts and ρ meson properties using Lattice QCD data with high precision. We also investigate the dependence on the π mass.

THE pp → dπ+π0 REACTION — A CASE OF ΔΔ EXCITATION WITHOUT ABC-EFFECT

The ABC effect, a low-mass enhancement in the invariant ππ mass, is observed in double-pionic fusion reactions leading to a bound nuclear system in the final state. From previous measurements there have been indications that this phenomenon is resctricted to the σ channel of the ππ system. With exclusive measurements of the pp → dπ+π0 reaction at Tp = 1.1 GeV we demonstrate that, indeed, the ABC effect does not occur in the vector-isovector ππ channel (ρ channel) despite the fact that the ΔΔ excitation is oberved to be the dominant reaction process. We also show that this reaction is well described by a t -channel ΔΔ excitation with the subsequent decay into the vector-isovector ππ channel given by the ρ channel operator.

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.

The [formula omitted] process in nuclei and the restoration of chiral symmetry

The results of an extensive campaign of measurements of the π → π π process in the nucleon and nuclei at intermediate energies are presented. The measurements were motivated by the study of strong ππ correlations in nuclei. The analysis relies on the composite ratio C π π A , which accounts for the clear effect of the nuclear medium on the ππ system. The comparison of the C π π A distributions for the ( π π ) I = J = 0 and ( π π ) I = 0 , J = 2 systems to the model predictions indicates that the C π π A behavior in proximity of the 2 m π threshold is explainable through the partial restoration of chiral symmetry in nuclei.

TWO-PION PRODUCTION IN pp COLLISIONS FROM THRESHOLD UP TO THE ΔΔ REGION AND THE ASPECT OF BOSE-EINSTEIN CORRELATIONS

The pp→ppπ+π- and pp→ppπ0π0 reactions have been measured at CELSIUS in the energy range Tp=775-1360 MeV using the WASA 4π detector. For Tp<1 GeV the data are in accordance with Roper excitation and σ correlations in the ππ system, respectively. For Tp>1 GeV they agree with ΔΔ excitation in the special configuration (ΔΔ)0+. For the π0π0 channel an enhancement at low Mπ0π0 masses is observed, which possibly points to Bose-Einstein correlations.

CP violation in the decays [formula omitted] in the presence of [formula omitted] mixing

We have recently shown that the large direct CP violation observed in the decay B0→π+π−, and the enhanced branching ratio for B0→π0π0, can be understood by invoking a small mixing of the ππ system with the dominant DD¯ channel. We examine here the analogous effect of DD¯↔KK¯ mixing on the rare decays B0→K0K¯0, B−→K−K0 and B0→K+K−. We find (a) significant values for the asymmetry parameters C and S in B0/B¯0→K0K¯0, (b) a possible enhancement of the suppressed mode B0→K+K−, (c) a correlation between the three decay channels following from a triangle relation between amplitudes AK0K¯0−AK+K−=AK−K0. The pattern of asymmetries and branching ratios is compared with that derived from the short-distance QCD penguin interaction.

S wave of pion-pion scattering from data on the reaction π − p → π 0 π 0 n

The results of recent experiments performed at KEK, Brookhaven National Laboratory, the Institute for High-Energy Physics (Protvino), and CERN to study the reaction π−p → π0π0n are analyzed in detail. For S-wave pion-pion scattering in the channel of isospin I=0, new data are obtained for the phase shift δ00 and the inelasticity parameter η00. Difficulties that arise in using, for the amplitudes of the S and D waves of the final π0π0 system, physical solutions selected on the basis of partial-wave analyses are discussed. It is noteworthy that other solutions are preferable in principle in the region of the invariant mass m of the π0π0 system above 1 GeV. With the aim of clarifying the situation and further studying the properties of the f0(980) resonance, it is proposed to perform, in the reaction π−p → π0π0n, an especially careful examination of the m region in the vicinity of the \(K\bar K\) threshold.

Contribution of the ππ components of the sigma and rho mesons to pion-nucleon scattering

For elastic pion-nucleon scattering at a collision energy below the threshold for the production of two pions, dynamical effects are studied that are induced by the presence of a ππ component in the structure of the σ(400–1200) and ρ(770) resonances. These effects manifest themselves both in the Green’s functions for the sigma and rho mesons and in the form factors for the interaction of these mesons with nucleons. The scattering amplitude is calculated on the basis of the K-matrix formalism, the mechanism of dressing being taken into account in the πNN and πNΔ form factors and in the nucleon and delta-isobar Green’s functions. The method of dispersion relations is used to calculate the real parts of the form factors and functions that parametrize self-energy operators. It is shown that, if strong interaction is taken explicitly into account in the ππ system, elastic pion-nucleon scattering can be described satisfactorily without introducing a sigma meson as an elementary particle.

I = 2 pion scattering phase shift with Wilson fermions

We present results of phase shift for I = 2 S-wave ππ system with the Wilson fermions in the quenched approximation. The finite size method proposed by Lu¨scher is employed, and calculations are carried out atβ = 5.9 (a -1 = 1.934(16)GeV from m p ) on 24 3 × 60 , 32 3 × 0 , and 48 3 ×0 lattices.

Production of the f 0(980) resonance in the reaction π − p → π 0 π 0 n

Predictions of the model that relies on purely one-pion exchange and which describes well GAMS data on the rearrangement of the S-wave mass spectrum of the π0π0 system in the region of the f0(980) resonance with increasing −t in the reaction π−p → π0π0n are compared with detailed data that were recently obtained at the Brookhaven National Laboratory (BNL) for the m and t distributions of the number of events of the reaction π−p → π0π0n. An analysis revealed that these BNL data disagree with the predictions of this model. This suggests that a different mechanism must be responsible for the phenomenon discovered experimentally. Most likely, this is the a1-exchange mechanism.

Strong final state interactions in γγ→WW

We study the effects of a possible strong final state interaction among longitudinal W's in γγ→WW. The relevant partial wave amplitudes are modified by an Omnès function approximated by a Breit–Wigner form factor. We study the fractional cross section f00=σLL/σtot with both W's longitudinally polarised, in the presence of a J=2 resonance (M=2.5 TeV, Γ=500 GeV) or a J=0 resonance (M=1 TeV, Γ=1 TeV), whose parameters are scaled up from the f2 and σ resonances in the ππ system. We also examine the effects of final state interaction in the case of polarised photons (Jz=0 or Jz=2), and the impact on the Drell–Hearn–Gerasimov sum rule.

I = 2 pion scattering length and phase shift with Wilson fermions

We present preliminary results of scattering length and phase shift for I=2 S-wave ππ system with the Wilson fermions in the quenched approximation. The finite size method presented by Lüscher is employed, and calculations are carried out at β = 5.9 on a 24 3 × 60 and 32 3 × 60 lattice.

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

A partial wave analysis of the centrally produced π0π0 system in pp interactions at 450 GeV/c

A partial wave analysis of the π 0 π 0 system produced centrally in pp collisions at 450 GeV/c shows evidence for the f 0(980), f 0(1300) and f 0(1500) resonances. f 2(1270) is observed dominantly in the D 0 − wave. A broad enhancement is seen in the D-waves below 1 GeV.

A partial wave analysis of the centrally produced π0π0 system in pp interactions at 450 GeV/c

A partial wave analysis of the centrally produced π 0 π 0 channel has been performed in pp collisions using an incident beam momentum of 450 GeV/c. An unambiguous physical solution has been found. Evidence is found for the f 0(980), f 0(1300) and f 0(1500) in the the S-wave. and the f 2(1270) is observed dominantly in the D 0 −-wave. In addition, there is evidence for a broad enhancement in the D-wave below 1 GeV.

A study of the π0π0 system produced in charge exchange and central collisions

A study of the π 0 π 0 system produced in charge exchange π − p collisions at 38 and 100 GeV/c and in central pp interactions at 450 GeV/c has been carried out. The S wave has rather a complicated structure in both processes indicating the existence of several scalar resonances. The f 0(980) and f 0(1500) appear as dips at 1 and 1.5 GeV in the S wave for charge exchange reaction, and as shoulders at these masses in the S wave for central production. The production of the f 0(980), f 0(1300) and f 0(1500) in the reaction pp → pfπ 0 π 0 p s as a function of the dP T kinematical filter shows the behaviour differed from what has been observed for the undisputed q q − mesons. An extra f 0(2000) state is seen in the S wave for charge exchange reaction as a dip at 2 GeV. Resonances with higher spins, f 2(1270), f 4(205 C) and f 6(2510), have also been studied. All the three mesons are produced in the reaction π − p → π 0 π 0 n mainly via an one-pion exchange for small − t, whereas a natural-parity exchange dominates for large −t. The behaviour of the centrally produced f 2(1270) as a function of the dP T is consistent with what has been observed for other q q − states.

Study of the π0π0 system in pp central collisions at 450 GeV/c

The effective mass spectrum of π 0 pairs produced in pp central collisions ( pp → p f π 0 π 0 p s ) at 450 GeV/c, s = 29 GeV , below 1 GeV differs from that observed in peripheral charge exchange reactions. In particular, there is a large number of events between ππ-threshold and 1 GeV, that interfere with f 0(980) destructively. The possible existence of a broad S-wave state is suggested.