Study of the decay matrix for n'→nπ+π-π- using CLAS detector at Jlab

Abstract

In the present thesis work, we report the results of Dalitz plot analysis of the hadronic decay ⌘0 ! ⌘ ⇡+ ⇡− using CLAS detector through the photoproduction reaction $ p ! ⌘0 p. The dynamical information about the three-body decay of any meson can be obtained by studying the decay matrix and Dalitz plot is a tool to perform the study. The Dalitz plot is a scatter plot to study decay dynamics of a meson decaying into three bodies. As the three-body decay has two degrees of freedom, one can define two linearly independent variables X and Y to represent the decay in the phase space as: X = p3(T⇡+ − T⇡−)Y = (m⌘ + 2m⇡) m⇡ · T⌘ Q − 1. (2) Where T⌘, T⇡+ and T⇡− are the kinetic energies of the particles ⌘, ⇡+ and ⇡− respectively in the rest frame of the ⌘0 meson and Q = T⇡++T⇡−+T⌘. The m⌘ and m⇡ are the masses of ⌘ and ⇡ mesons respectively. The obtained Dalitz plot phase-space is parameterized with a general parametrization function given in equation (3), which gives the amplitude of the ⌘0 ! ⌘ ⇡+ ⇡− decay. The square of decay amplitude is given by,f(X, Y ) = M2 = A(1 + aY + bY 2 + cX + dX2). (3) Where a, b, c and d are the Dalitz plot parameters of the decay and A is the normalization constant. The parameters give information of the resonances, intermediating particles and interactions among the decay of final state particles.Physical observables e.g. decay width, phase shifts, quark mass ratio and parameters quantifying interactions can also be calculated from the Dalitz plot parameters. Also, a precise measurement of these parameters is needed for the correct input to the theoretical distribution of the e↵ective chiral Lagrangian.The Continuous Electron Beam Accelerator Facility (CEBAF) at Je↵erson Lab (JLab), Newport News, Virginia, USA has performed the “g12” experiment and collected the data during March - June 2008. The data is recorded using the CEBAF Large Acceptance Spectrometer(CLAS) detector and further used to perform the analysis.The complete reaction under study is “ $ p ! ⌘0(! ⌘ ⇡+ ⇡−) p” and events with one proton, one ⇡+, one ⇡− and any number of neutral particles are selected as skim condition out of all events available in “g12” dataset. In this analysis ⌘ and ⌘0 mesons are reconstructed as a missing particle. The ⌘0 meson is reconstructed with the information of incident photon, target proton and final state proton and it is represented as Mx(p). Similarly, ⌘ reconstruction uses incident photon, target proton and final state particles such as the proton, ⇡+ and ⇡− and it is denoted as Mx(p⇡+⇡-). The threshold energy for the production of ⌘0 meson is 1.45 GeVand the production cross-section of the ⌘0 meson drops significantly after 3.6 GeV. Hence the analysis is performed with all events with an incoming photon energy from the threshold of 1.45 up to 3.6 GeV. The Pluto [v5.42] event generator developed by the HADES collaboration is used in this analysis for the simulation. The 5 x 108 $ p ! ⌘0 p ! ⌘ ⇡+ ⇡− p events are generated using Pluto along with a model which is close to the real scenario. The incident photon beam is given a bremsstrahlung nature to reproduce the bremsstrahlung photon beam distribution of the incident photons. To make the simulation more realistic the measured di↵erential cross-section of the ⌘0 meson is used as input during event generation. The output of the Pluto with the above-mentioned model is first extracted in the standard CLAS “gamp” files and then processed with CLAS simulation suit in the following order:The gamp files are first converted into the format of the PART bank containing the event. • GSIM (Geant3-based simulation): GSIM in CLAS simulates the decay tracks of particles and finally the digitized information is sorted in other “raw” banks from the PART bank. • GPP (GSIM post-processor): The events are passed through GPP, which smears detector signal more accurately to reflect the actual resolution of g12 data and simulate the experimental conditions. • a1c: Finally the events are passed through a1c, which is a reconstruction program for the simulated data. The same program is used during data reconstruction.The next step is to improve the identification of the particles and signal to background ratio using conditions and corrections. All these conditions and corrections which are implemented in this analysis for data and simulation are listed in Table 1. This work used a Dalitz plot which has 30 bins in X and 30 bins of Y, which gives a total of 900 bins in Dalitz plot. Out of these 900 bins, those bins which fall Table 1: The list of conditions and corrections implemented to the g12 data and simulation. “g12” Experiment data Simulation Photon Multiplicity NA Beam Energy Correction NA Momentum Correction NA Removal of bad TOF paddle Applicable Geometric Fiducial Cut Applicable Kinematic Fit (1% probability cut) Applicable Vertex Length Cut (-70  vz  -110 cm) Applicable Vertex cross-sectional radius ( p v2x + v2 y  2 cm) Applicable Timing Cuts on proton, ⇡+ and ⇡− (tvert(TOF) and tvert(Tagger) ± 1.0 ns) Applicable | cos ✓center−of−mass of ⌘0 |  0.85 Applicable | Mx(p ⇡+ ⇡−) - 0.547 |  0.015 GeV Applicableoutside the phase space of decay or bins with very low acceptance (< 0.5%) are rejected. Finally, out of 337 bins are subtracted for background and a background subtracted Dalitz plot is obtained for further analysis and calculation of Dalitz plot parameters. Once all the conditions and corrections are implemented, a background subtraction is performed to extract the ⌘0 ! ⌘ ⇡+ ⇡− events and eliminate all other channels which lead to the same final state of one proton, one ⇡+ and one ⇡−. To cross-check the analysis and increase the confidence of the results, the Dalitz plot parameters are calculated with the following two di↵erent methods:Acceptance correction method: The ⌘0 ! ⌘ ⇡+ ⇡− decay contribution for each Dalitz plot bin is corrected for acceptance, without considering the migration of events from one bin to other. • Smearing matrix method: In this method, the fits are performed directly to the Dalitz plot from data along with a function. This function takes care of the acceptance in the same bin and also acceptance due to the migration from neighboring bins using a smearing matrix.The number of bins selected along the Dalitz variables X and Y are higher than the resolution of these variables, so these two independent methods yield similar Dalitz plot parameters within the statistical errors, which also serves as a cross-check to the analysis. The calculated Dalitz plot parameters a, b, c and d from both the methods are given in Table 2.In this thesis, the dominant decay mode of ⌘0 which is ⌘0 ! ⌘ ⇡+ ⇡− is studied. The decay also produces ⌘0 ! 3⇡ decay which is an isospin violating mode and it is through a mixing of ⌘0 - ⇡0 meson. This e↵ect arises from the light quark mass di↵erences. Hence this study is an indirect probe to understand the decay dynamics of mesons. This decay information is studied with the help of a Dalitz plot distribution. The results from this Dalitz plot distribution is then compared to reported experiments.To gain more confidence over extraction of events from the experiment, a measurement of the cross-section of ⌘0 is also done and compared to the previous g11 measurement. The generated events used in the analysis were also modeled very carefully to appear as close to nature. A very sensitive background subtraction is performed to both the smooth and in-peak backgrounds. The goodness of fit is reflected in the '2/ndf of each bins which is above 0.5 and below 2 even for the bins with low statistics. Also, the fit to the whole Dalitz plot yields a reasonable '2/ndf of 1.16, which shows the quality of the fit. The Dalitz plot parameters are calculated with two independent methods and matches within the statistical errors from both the methods because of the choice of wide binning, which is 3 times more than the resolution of Dalitz variables X and Y. The choice of the binning is a result of the optimization of the total number of events and the resolution of the Dalitz variables. The “Smearing matrix method” being a more realistic approach has been used to present the final Dalitz plot parameters and to perform systematic studies in the analysis.A comparison of the g12 Dalitz plot parameters with the other experimental results is shown in the Table 3. The parameters a and b from the CLAS g12 measurement are consistent within 1 ( to the results reported by the VES and shows disagreements with the BESIII parameters. The parameter c which indicates Cparity violation in the strong interaction when it deviates from zero. In the present analysis, the c parameter is consistent to zero within 1.5 (. The parameters c and d from g12 measurement is consistent with both the experiments. The Dalitz plot parameters are also compared to neutral decay mode of the ⌘0 meson, the ⌘0 ! ⌘ ⇡0 ⇡0 decay for the measurements from the GAMS, A2 Collaboration at MAMI and the BESIII Collaboration. Our parameters for ⌘0 ! ⌘ ⇡+ ⇡− decay show deviation by 4 standard deviations from all the measurement of neutral decay mode of ⌘0 meson for the Dalitz parameters a and b. Our measurement seems to agree within statistical limits for the parameter d to both the recent measurements from A2 Collaboration at MAMI and the BESIII Collaboration.A comparison of the g12 Dalitz plot parameters with the U(3) Chiral e↵ective theory is shown in the Table 4. The value of b and d from g12 measurement as well as from the previous measurements largely deviate from zero. However, the framework U(3) chiral unitary approach and U(3) chiral e↵ective field theory in combination with a relativistic coupled-channels approach predict b and d to be zero which recommends the theory to include the final state interaction corrections in the chiral model for pseudoscalar mesons. The theory⇤ in the Table 4 is resulting from theoretical fits which include the VES data.The ⌘0 ! ⌘ ⇡+ ⇡− decay is also used to study a scalar intermediate particle. The ⌘0 and ⌘ meson are pseudoscalars and both has an isospin (I) of 0. The isospin I, for both the ⇡+ and ⇡− is 1. Due to the conservation of 3rd component of the isospin (I3), the ⌘0 meson can decay into ⇡+ and ⇡− through an intermediate scalar meson. Hence, we looked at the invariant mass of ⇡+ ⇡− distribution and compared it to the theoretical distribution which considers intermediate states of decays. A good sensitivity to the parameters of the ( meson decay to the ⇡+ ⇡− in the ⌘0 ! ⌘ ⇡+ ⇡− decay is found and compared to the Nonlinear Sigma Model Lagrangian (NLSM) and Generalized Linear Sigma Model (GLSM). The right-centered distribution of the acceptance corrected invariant mass of ⇡+ ⇡− mesons, M(⇡+ ⇡−) distribution from CLAS g12 data is due to the ( contribution. However, in the absence of ( meson from the NLSM, the centeredness of M(⇡+ ⇡−) shifts from right towards the left.