Application Of Amplitude Analyses To Typical Hadron Processes

The main research objects of this thesis include the light mesons in the low-energy region of QCD,as well as the recently discovered exotic hadrons Pc(candidate for pentaquark)and X(6900)(candidate for tetraquark)by experiments.Firstly,we briefly introduce QCD and its characteristics of quark confinement and asymptotic freedom.The next section introduces the popular theories of low-energy effective QCD:chiral perturbation theory and resonance chiral theory,which are the theoretical basis for studying light mesons and exotic states in this thesis.After introducing the basic theoretical knowledge,we then describe in detail the theoretical aspects of amplitude analysis in our work.To study general hadronic processes,we start by analyzing the symmetry of the system.When dealing with spin-particle,the calculation of the amplitude also involves the treatment of polarization vectors.Also,it is necessary to decomposite the scattering amplitude into partial waves.The amplitude calculated by perturbation theory breaks the unitarity of the original amplitude,and the unitarization method(K-matrix method and Pade approximation)is used to restore its unitarity.After obtaining the unitarized amplitude,it is usual to extract pole information.Therefore,the last section of this chapter gives the T-matrix and S-matrix elements after analytical continuation by double and triple channel analysis.After discussing the relevant theoretical aspects of amplitude analysis,the theory tools are then applied to specified processes.In this chapter,we studied the properties of a0(980)and the width of di-photon in the coupled channel scatterings of triple channels(π0η,KK,and π0η’)and couple channels(π0η,KK),respectively.Firstly,the formula and determination of the strong interaction amplitude,T-matrix are given.Then,a joint fit of γγ→π0η,γγ→KK and γγ→π0η’ processes is carried out,including total cross sections,differential cross sections,and invariant mass spectra,etc.Then,based on the fixed scattering amplitudes,pole information is extracted and the di-photon width is extracted.Furthermore,the obtained radiative decay width is compared with that from different models,and relevant analysis is discussed.Finally,the corresponding conclusions of this work are given.According to the pole counting rule,the resonance state a0(980)is a Breit-Wigner type particle,and its di-photon width is 0.376± 0.050 keV.In the final part of the thesis,the phenomenological research of the exotic hadron is discussed.This section covers two works.The first work is based on the coupled channel scattering of J/ψp-D∑c-D∑c,constructed from the K-matrix which contains the Chew-Mandelstam function.With these amplitudes,we study the J/ψp spectrum in the Ab→ J/ψpK-decay process,according to the Au-Morgan-Pennington method.By fitting to the experimental data,and the decay width of Ab→J/ψpK-,the parameters are fixed.Based on the amplitudes,pole positions and corresponding widths can be extracted.Analyzing of the input and poles shows that Pc(4312)should be a molecular state composed of D∑c,Pc(4440)may be an S-wave compact pentaquark state,and the structure around Pc(4457)is most likely to be caused by cusp effect.Future experimental measurements of Λb→ D∑cK-and Λb→ D∑cK-decays will help to further study and determine the properties of these resonances.The second work is based on the experimental data of LHCb,ATLAS,and CMS,including the invariant mass spectrum of J/ψψ(2S)published by ATLAS.By constructing the interaction Lagrangians of four heavy vector mesons in the leading order within heavy quark spin symmetry,the scattering amplitudes of the leading and next-to-leading orders of the corresponding processes are calculated.Then,the scattering amplitudes after partial wave decomposition need to be unitarized and it is performed by Pade approximation.Next,the Au-Morgan-Pennington method containing final state interaction is used to construct the amplitude.Through fitting the experimental data,the unknown coupling coefficients in the effective Lagrangians are determined,and the pole information of the resonance state X(6900)is studied.The extracted pole information,combined with the pole counting rule,is used to study the properties of X(6900),which is helpful to distinguish the molecular and Breit-Wigner type particles.Finally,the above conclusion is further verified by extracting the phase shift of the scattering amplitude.In summary,this thesis investigates the use of amplitude analysis in typical hadronic processes and offers theoretical guidance for future experiments,demonstrating its scientific significance.Firstly,the corresponding partial wave amplitudes for the di-photon scattering into final states of two pseudoscalar mesons,specifically π0η,KK,and π0η’,are derived.Subsequently,the pole position and di-photon width of the a0(980)resonance are deduced,and its internal structure is analyzed.Furthermore,the cross-section of γγ →π0η’is predicted.Secondly,through the adoption of the K-matrix method,the three-channel scattering amplitudes of J/ψp—D∑c—D*∑c are constructed,where the decay amplitude of the Ab→J/ψpK-process by means of the final-state theorem is included.Experimental data is then fitted to analyze the pole positions of Pc(4312),Pc(4440),and Pc(4457),and to predict the branching ratios of their three-body decays.Analysis of the pole counting rules and trajectories establishes that Pc(4312)is a molecular state,Pc(4440)is a compact pentaquark state,and Pc(4457)arises from threshold effects.Lastly,partial wave analysis and unitarization are performed on the effective Lagrangian for heavy vector mesons J/ψJ/ψ—J/ψψ(2S)一J/ψψ(3770)to obtain scattering amplitudes.The pole positions and branching ratios are then determined through a fitting process and phase shift analysis.It is thereby determined that the X(6900)has quantum number 0++,confirming its interpretation as a compact tetraquark state.