Studies of light Mesons at COMPASS

The COMPASS experiment has taken a large data set with a negative pion beam impinging on a liquid-hydrogen target to study the spectrum of light mesons in diﬀractive dissociation reactions. The properties of known resonances are studied, and new, possibly spin-exotic states are searched in three-pion ﬁnal states. A new state at about 1 . 4 GeV /c 2 with a 1 quantum numbers is observed in the decay to f 0 (980) π . The spin-exotic 1 − + wave is investigated in order to search for the controversial π 1 (1600).


Introduction
The Common Muon and Proton Apparatus for Structure and Spectroscopy (COMPASS) experiment is a fixed-target experiment located at CERN's Super Proton Synchrotron (SPS).One of its goals is to study the spectrum of light mesons.A 190 GeV/c negative hadron beam, consisting mostly of pions with a small admixture of kaons and anti-protons, impinges on a liquid hydrogen target, and diffractively produces the mesons under study.The decay products of these mesons are detected in a two-stage magnetic spectrometer (figure 1).Each of the two spectrometer stages is equipped with an electromagnetic calorimeter.This setup provides full coverage for charged and neutral particles, resulting in a homogenous acceptance over a wide kinematic range [1].
The reaction under study here is the diffractive production of mesons decaying into three pions, either into the π − π − π + or the π − π 0 π 0 final state.To this end, exclusive events with a squared four-momentum transfer to the target t between 0.1 GeV/c 2 and 1.0 GeV/c 2 have been selected in a three-pion mass range between 0.5 GeV/c 2 and 2.5 GeV/c 2 .This results in a huge dataset of 50 million π − π − π + and 3.5 million π − π 0 π 0 events.The invariant mass distributions of the two final states (figure 2) indicate a rich spectrum of contributing states.

Partial-wave analysis
To decompose the three-pion mass spectra into the individual spin-parity components, a partial-wave analysis employing the isobar model is used.Figure 3 sketches the process under study.The incoming beam π − diffractively scatters off a target proton producing an intermediate state X − , which subsequently decays into a two-pion isobar R ππ and a bachelor pion which have a relative orbital angular momentum L. The two-pion isobar then decays into two pions.By exploiting the kinematic distribution in the five phase-space variables of the decay products, information on the spin J, the parity P, and the spin-projection M ε of X − can be extracted [2].The mass spectra of the two-pion isobars of the π − π 0 π 0 final state are shown in figure 4. The isobars decaying to π − π 0 have isospin I = 1.The ρ (770) is clearly visible in figure 4(a).A smaller shoulder at higher masses suggests to also use the ρ 3 (1690).The π 0 π 0 isobars have isospin I = 0.Here the f 0 (980), the f 2 (1270), and the f 0 (1500) are identified by bumps and kinks on top of a broad (ππ) S component in figure 4(b).For the π − π − π + final state the two different isospin contributions cannot be separated.All isobars are π − π + isobars.The same isobars as for the π − π 0 π 0 final state are used.
Each partial wave corresponds to one state X − with its quantum numbers J PC M ε decaying via one particular decay chain R ππ π L. For the analyses presented in the following, states with spin J up to 6 are included.Also the angular momentum L between the isobar R ππ and the bachelor pion can go up to 6. Out of the possible combinations, 87 waves with non-negligible intensity are kept for the final model: 80 waves with a positive reflectivity ε = +1 and 7 with ε = −1.In addition one incoherent wave with an isotropic angular distribution is included [2].The same set of partial waves is used in the two analyses of the different final states.

Fit in mass bins
As a first step, the partial-wave intensities are extracted in bins of the three-pion mass and the squared four-momentum transfer to the target t using a rank-1 fit. Figure 5 shows the incoherent sum of the intensities over the individual t bins for the 2 ++ 1 + ρ (770) πD wave, clearly showing the a 2 (1320), and the 4 ++ 1 + ρ (770) πG wave, clearly showing the a 4 (2040).The results from the π − π − π + channel (red markers) and the π − π 0 π 0 channel (blue markers) are in agreement.The two data sets are normalized using the intensity integrals in each individual plot so that the peak shapes can directly be compared.No dependence of the peak shapes on the squared four-momentum transfer t is observed for these two partial waves.Good agreement of the partial-wave intensities between the two final states is also found for other waves with large intensities, like the 1 ++ 0 + ρ (770) πS and 2 −+ 0 + f 2 (1270) πS waves [3].Also for waves with small intensities good agreement between the two final states is observed.One particularly interesting signal is observed in the 1 ++ 0 + f 0 (980) πP wave (figure 6) around 1.4 GeV/c 2 .This narrow structure, never observed before, could correspond to a possible new a 1 state.It is seen in the decay via the f 0 (980) isobar for both channels and for all t bins.Different parameterizations for the isobars have been tested to exclude a possible artifact from the employed model.
In addition to the intensities, also the phase difference between partial waves needs to be considered for a resonant interpretation of this signal.Figure 7 shows the phase difference between the 1 ++ 0 + f 0 (980) πP and the 4 ++ 1 + ρ (770) πG wave.A clear phase motion around 1.4 GeV/c 2 is visible at the position of the peak in the intensity spectrum.
In order to exclude possible artifacts caused by the particular choice for the parametrization of the isoscalar J PC = 0 ++ isobars, a partial-wave analysis was performed, in which the waves with (ππ) S , f 0 (980), and f 0 (1500) isobars are replaced by amplitudes piecewise constant in the two-pion mass [2].This new approach allows a rather model-independent extraction of the 0 ++ isobar amplitudes.The analysis shows a clear correlation between the new a 1 (1420) signal and the f 0 (980) as a decay product.

Fit to spin-density matrix
To further study this new signal, and to extract Breit-Wigner parameters, the mass dependence of a sub-set of the spin-density matrix was extracted for the π − π − π + channel [4].Apart from the intensities, also the interferences between the waves were taken into account.The three waves shown in figures 5 and 6 were used.The fit model included one Breit-Wigner resonance in each wave: the a 2 (1320) in the 2 ++ 1 + ρ (770) πD wave, the a 4 (2040) in the 4 ++ 1 + ρ (770) πG wave, and a new a 1 (1420) in the 1 ++ 0 + f 0 (980) πP wave.The Breit-Wigner parameters were extracted from a simultaneous fit to the spin-density submatrices of the three partial waves in all eleven t bins.Apart from the Breit-Wigner components used to describe the resonances, also a coherent t -dependent non-resonant contribution was allowed in each wave.The parameters of the Breit-Wigner functions and the coherent background were the same in all t bins, only the complex couplings were allowed to differ.
The partial-wave intensity of the 1 ++ 0 + f 0 (980) πP wave (blue markers in figure 6(b)) is described by a resonant contribution for the new a 1 (1420) (blue line) interfering with a non-resonant contribution (green line).The total intensity of the model is shown by the red line.The fit range is indicated by a full line, the dashed line shows the extrapolation beyond the range.

Conclusions
The COMPASS experiment has recorded a huge dataset to study resonances produced in diffractive dissociation into three pions.The large number of events allowed to increase the number of waves used in the partial-wave analysis, while still being able to also perform a t -dependent analysis.Breit-Wigner parameters have been extracted from a fit to the result of the spin-parity decomposition in mass bins.Apart from the well-known resonances, COMPASS found a new signal in the 1 ++ 0 + f 0 (980) πP wave around 1.4 GeV/c 2 .It is a rather narrow object featuring a well-defined mass and width, and appears only in the f 0 (980) decay mode.Its nature is still unclear, it could be the isospin partner of the f 1 (1420), but also other explanations have been put forward.The a 1 (1420) could be a genuine resonance as a two-quark-tetraquark mixed state [5].Also two explanations connecting the new a 1 (1420) to the known a 1 (1260) are proposed.The first explains the observed intensity spectra and phases in the 1 ++ 0 + f 0 (980) πP wave by a two-channel unitarized Deck amplitude interfering with the direct production of the a 1 (1260) [6].The second explains those by a singularity in a triangle diagram describing rescattering in the K − K * decay of the a 1 (1260) [7].

Figure 3 .
Figure 3. Sketch of the process under study.

Figure 4 .
Figure 4. Invariant mass spectra of the two possible two-pion subsystems of the π − π 0 π 0 final state.

Figure 5 .
Figure 5. Incoherent sum of partial-wave intensities over all t bins.

Figure 7 (
b) shows the interference between the 1 ++ 0 + f 0 (980) πP wave and the 4 ++ 1 + ρ (770) πG wave.The three different colors show three of the in total eleven t bins.Again the markers show the result from the partial-wave decomposition, while the lines show the behaviour of the resonance model.The parameters of the Breit-Wigner function describing the new a 1 (1420) are M = 1414 MeV/c 2 with a systematic error of +15 −13 MeV/c 2 for the mass, and Γ = 153 MeV/c 2 with a systematic error of +8 −23 MeV/c 2 for the width.The statistical errors are negligible.