| Since Victor Hess first discovered cosmic rays in 1912,the question of their origin is still waiting for a definite answer.Because the interstellar magnetic field will change the direction of cosmic rays,the origin of cosmic rays is mainly studied by observing the electrically neutral particles,such as gamma rays and neutrinos,produced when cosmic rays interact with the interstellar medium.The ultra-high energy gamma-ray spectrum is closely related to the acceleration and propagation mechanism of cosmic rays,so the origin and propagation of cosmic rays can be studied by observing ultra-high energy gamma-ray.The Lorentz invariance is a fundamental assumption of modern physics.Some frontier theories of physics,such as quantum gravity or string theory,suggest that the Lorentz invariance breaks at energies above a certain energy scale.As predicted by these theories,the energy spectra of ultra-high energy gamma-ray sources will have a sharp cut-off,and the cut-off energy is related to the Lorentz invariance violation energy scale.The Lorentz invariance violation energy scale can be studied by observing ultra-high energy gamma rays.To achieve sensitive detection of gamma rays above 100TeV,the scientists designed and constructed the LHAASO-KM2A air shower hybrid array in Daocheng,Sichuan Province.One of the fundamental science goals of KM2A is searching ultra-high energy gamma-ray sources and cosmic ray sources by observing ultra-high energy gamma rays over 100 TeV,studying and finding the origin of cosmic rays.KM2A has a coverage area of 1.36 km2,nearly 20 times the size of ASy.The array contains more than 5,000 ground-based electromagnetic particle detectors and 1,700 underground muon detectors,which gives KM2A the powerful ability to reject the cosmic-ray background.Above 100TeV,KM2A is the most sensitive ground-based gamma-ray observatory at present.One of the important work in this paper is exploring Lorentz invariance violation energy scales by analyzing whether there is a hard cut-off in the spectral energy distribution of gamma-ray emission from the LHAASO J2032+4102 and the Crab Nebula.Nevertheless,the results show no signs of the existence of sharp cut-offs observed for both sources.The data do not favor the existence of Lorentz invariant violation.By using the CLs method,the lower limit of the cut-off energy with a confidence of 95%is given,and the lower limit of the first and second-order Lorentz invariance violation energy scale is further obtained for each source,which improves constraints given by other experiments by more than one order of magnitude.These two limits provide the most strict constraints at present.The other key work is to measure the galactic diffuse gamma-ray emission based on the analysis of KM2A data.Most cosmic rays are rejected via gamma/hadron discrimination.The optimization of gamma/hadron discrimination is performed for diffuse gamma-ray emission analysis.It makes KM2A can reject 14000 cosmic rays with just one missed and at the same time keeps 60%gamma rays survived.In background estimation,the pseudo-large-scale structure anisotropy is eliminated by optimizing the time window of computational efficiency in background estimation,and the systematic error of background estimation is reduced.A relatively simplified and more efficient gamma-ray source scanning method has been established.The direction and the spectra energy distribution of Crab Nebula have been measured by this method.The results are consistent with the results from other experiments,proving that this scanning method,KM2A data,and background estimation are reliable.Next,gamma-ray sources in the region with |b|<10°and 15°<l<235° are scanned by this method,and their direction,extension,and energy spectra are measured.It provides a catalog of sources for defining the diffuse gamma-ray emission area and eliminating the contribution of gamma-ray sources when observing diffuse gamma-ray emission.Inner galaxy region |b|<5°,25°<l<100°,and outer galaxy region |b|<5°,130°<l<2000 are selected as investigated areas.Gamma-ray sources in these regions are masked by certain radii,as a result,most contributions from sources are excluded.After that,the residual contribution from gamma-ray sources to signals in diffuse gamma-ray emission areas is estimated via simulation and then excluded.The time sampling technique for the simulation of diffuse gamma-ray emission is developed,which solved the difficulties of calculating the expected number of signals of gamma-ray emission.The spectral energy distribution in a range of 1OTeV—630TeV is obtained via the forward-folding method and maximum likelihood method.For inner galaxy region,the power-law flux φ0 is found to be(1.10±0.05stat±0.10sys)×10-14TeV-1 cm-2s-1sr-1,the spectral index α=-2.92±0.04stat±0.10sys,For outer galaxy region,φ0=(0.41 ±0.04stat±0.04sys)×10-14 TeV-1cm-2s-1sr-1,α=-3.06±0.10stat±0.22sys Additionally,differential fluxes from 10TeV to 630TeV are given.This is the most accurate measurement with the largest energy interval and the most significant results over 10TeV,which is of great significance to the study of the origin and propagation of cosmic rays. |