TESTING GLUON DISTRIBUTION FUNCTION OF HADRONS IN LARGE PT PROCESS WITH DIRECT PHOTON EMISSION

In this paper we disscuse disscuse the physicsical aspect of cross-section differences Δ_AB^cγ=dσ(AB→cγX)-dσ(AB→cγX) and give the simple rules to select the elementary subprocesses which contribute to cross-section differences.
We bind a way to test the gluon distribution functions of hadrons through the measurement of cross-section difference or combination of cross-section differences in the large P_T process with direct photon emission. Moreover we obtain simple relations between each combination of cross-sections and the corresponding gluon distribution functions of proton, neutron, pion and daon:
G_p⁸(x)/(Δ_pp^hγ－Δ_pp^hγ)=G_n⁸(x)/(Δ_pp^hγ)=G_π⁸(x)/(Δ_π+p^hγ+Δ_π－p^hγ=G_K⁸(x)/(Δ_K+p^hγ+Δ_K－p^hγ)which are expected to be test in experiment.     

SPIN GAINT RESONANCE AND CORE POLARIZATION EFFECTS

The effects of the coupling term between field（Y₀σ₁）_1v and r²（Y₂σ₁）_1v coming fromtensor operator are discussed for the spin gaint dipole resonance.The effects of inclu-ding the field r^λ+1(Y_λ+1σ₁)_λv on the spin gaint multipole resonance and core polariza-tion are considered.     

THE EFFECTS OF THE CHARM STATE IN e-p DEEP INELASTIC SCATTERING

Using the fact that the proton contains the Charm State │uudcc〉 and combining its effects with the result of the usual calculations of A.J. Buras et.al., a better agreement of the theoretical value of the ratio R=σ_L/σ_T in e-p deep inelastic scattering with the experimental data is obtained.     

The Spin Effect of Antiproton-Nucleus Inelastic Collison

If the antiproton optical potential is inclusive of the spin orbit interaction term,the A(p,p)A* inelastic scattering not only can excited the normal parity states,but also can excited the abnormal parity states.There are also induced the polarization P_f(θ) at the inelastic scattering.In the framework of DWIA,we derived the inelastic scattering cross section (dσ/dΩ)_f,i,and polarization P_f(θ),and calculated the (dσ/dΩ)_f,i, and P_f(θ) for ¹²C(p,p)¹²C* with 2⁺,3^－ and 1⁺ states at antiproton energies of 46.8 and 179.7MeV.They fited experiment data quite well.Due to the abnormal partity states in the inelastic process have been measured,the spin orbit term can not be neglect.     

THE DIFFICULTY OF THE DECAY τ→πντ AND SPIN 3/2 HEAVY LEPTON

We discuss the suppression of the decay of heavy lepton τ into πv_τ,by assuming that τ and/or v_τ carry spin 3/2. For the case of spin 3/2 T and spin 1/2 v_τ, using the weak current ψ_μ^(τ)(a+b_^γ5)Ψ^(v_τ)we find that the πv_τ decay channel relative to the v_τv_ll^-channel is suppressed 12/5 times, while other decay channels are not changed appreciably. △R=σ（e⁺e^-→τ⁺τ^-）/σ（e⁺e^-→μ⁺μ^-） is also discussed.     

DECAY PROCESSES IN MASSIVE STRATON MODEL OF MESONS

Using the B-S wave functions of mesons in the massive straton model^[1], we discuss their weak decay, electromagnetic decay, and particularly hadronic decay processes. Not only f_π≈f_K, 1^－→l⁺l^－ rate are successfully explained, the predicted widths for various hadronic decays are also in good agreement with experimental data.     

ON THE PHASE AND THE REPRESENTATION TRANSFORMATIONS OF SUn BARYON AND MESON WAVE FUNCTIONS

The baryon and meson wave functions of SU_n symmetry under the Baird-Bie-denharn phase convention are given explicitly.The phase confusion is clarified andthe matrices of transformations between I-spin,U-spin and V-spin representationsare given for the IR（8）,（27）,（35） of SU₃.     

A DISCUSSION OF THE STRENGTH AND THE RANGE OF THE PHENOMENOLOGICAL NUCLEAR FORCE USING EXPERIMENTAL DATA IN HIGH ENERGY SCATTERING

Under the framework of the Bakamjian-Thomas theory,we discuss the qualitativeproperties of the phenomenological nuclear force V=V_R-iV₁ at high energy arediscussed by a comparision with the small angle scattering data.Because these data inhigh energy are insensitive to the spin,we suppose that the nuclear force at highenergies is spin-independent.The followings are obtained:i)for the Gaussian potential,X₃≌200 MeV and β₃≌0.95 fm,which are thestrength and the range of V₁ respectively;ii)in V_R,there is no hard repulsive core.Under a rough estimation,supposingthe range β₁>0.45 fm,we find the strength of the repulsive force,X₁<480 MeV;iii)all parameters are vary very slowly with energy.     

AN ANALYSIS OF FOUR-ELEMENT MODELS OF LEPTONS AND NON-DIAGONAL NEUTRAL CURRENTS

Due to the possible production of neutral and charge heavy leptons by v_μ, models consisting of four elements per "line", e.g. v_e, e^-, E⁰, E^- v_μ, μ^-, M^0, M^- v_τ, τ^-, T⁰, T^- ……are analysed. Non-diagonal neutral currents cannot be avoided. Nevertheless, a model is proposed within SU_（2）×U_（1） in which the process μ→eγ can still be suppressed by the Bjorken-Lane-Weinberg mechanism; various production cross-sections for heavy leptons are reasonable when compared with experiments. Models corresponding to SU_（3）×U（1） and still higher symmetries are discussed.     

SPACE-TIME PROPERTY OF FERMION NUMBER

Enlarging the dimensionality of Minkowski space from 4 to 5,and relating the restmass of particle with x₅ as m=—i（&#8706;/（&#8706;x_5）））we discuss the 5-dimensional non-linear con-formal group C（M₅）under which dx₁²+dx₂²+dx₃²-dx₀²+dx₅²=0 is invariant.The C（M₅）group is isomorphic to the linear group SO（5,2）from which we study thespace-time property of Fermion number,and the relations between half-integral（in-tegral）spin and odd（even）Fermion number are obtained.     

π-NUCLEAR DOUBLE CHARGE EXCHANGE REACTION AND NUCLEAR STRUCTURE

Using Glauber's multiple scattering theory, and using coherent fluctuation nuclearmodel, the double charge exchange (DEC) reaction cross sections for πon ¹⁶O and ¹⁸Ohave been calculated. The calculated values of the ratio of σ(¹⁸O(π⁺,π^-)¹⁸Ne)_g.s. toσ(¹⁶O(π⁺,π^-)¹⁶Ne)_g.s. fit the experimental data quite well. Just as predicted by ourcalculation, the angular distribution of ¹⁸O(π⁺,π^-)¹⁸Ne_g.s. in a recent experiment,exhibits an evident dip around 23°.     

THE SU2×SU2 BASIS AND THE PHYSICAL BASES FOR THE STATE VECTORS OF d-BOSON SYSTEMS AND THE TRACELESS BOSON OPERATORS (Ⅰ)

The group chain U₅O₅SU₂×SU₂ used by K. T. Hecht (1965) and by the othersprovides an important representation for expressing the physical basis of d-boson sys-tems. However the methods which have been introduced for this SU₂×SU₂ representa-tion to construct a physical basis is poorer in comparison with those for the otherrepresentations. In view of this we try to find appropriate methods to obtain the SU₂×SU₂ representation wave functions of the existing physical bases constructed byChacon et al. and by Szpikowski et al., In the present paper we analyse the SU₂×SU₂ tensor properties of the,bosonoperators and Vilenkin's traceless boson operators and express succinctly the elementaryvectors of the SU₂×SU₂ basis, the |PP SU₂×SU₂ > vectors, in terms of the tracelessoperators. With the help of this form of the| PP SU₂ SU₂> vectors we derive a simpleformula for obtaining the SU₂×SU₂ -representation wave functions of a physical basisfrom its (n_μ)-representation wave functions. Thus the problem mentioned above is partlysolved. The other parts of the solution of the problem will be found in a coming paper.     

THE STUDY OF SOME NON-SOLATED RESONANCES FOR THE 23Na （p,α）20Ne REACTION

The excitation functions of the ²³Na（p,α₀）²⁰Ne_g·s.and the ²³Na（p,α₁）²⁰Ne_lst reae-tion have been measured from E_p=1 to 2.5 MeV at θ_L=30°,150° and 30°,respectively.Around the resonance at 2.171 MeV,the excitation functions of the（p,α₀）reactionhave been measured at 12 angles,then,some angular distributions have been obtained from these excitation functions.In addition,the angular distribution of the（p,α₀）reaction for the resonance at 2.171 MeV has also been measured directly at energy ofthe resonance peak of the excitation function at 150°.For the resonance at 2.117MeV,the angular distribution have been measured at two energies,one at the energyof the resonance peak of the excitation function at 150°,another at the energy of thehalf maximum point of the resonance peak on the higher energy side.Around the re-sonance at 2.075 MeV,the excitation functions have been measured at 16 angles,andthe angular distribution has been obtained from three excitation functions.The an-gular distributions of the three resonances are not symmetric about 90°,and the posi-tions of the resonance peaks of these resonances varies with the angle of measurement.By means of the compound nucleus theory,discussions have been made for these non-solated resonances.     

THE COLLECTIVE MOTION OF THE BAG AND THE NUCLEON STRUCTURE FUNCTIONS

Using the hypothesis of the bag-quarks' wave-function with the property of transla-tion invariance, and introducing a Lorentz-invariant effective Lagrangian, we have cal-culated the nucleon deep -inelastic structure functions In our calculation the4-momentum conservation is satisfied automatically, while the resultant structurefunctions are positive-definite and vanish when x>1. Furthermore, using the assumptionof the asymptotic freedom, we obtain explicitly the Bjorken scaling, the approximateexpession F₁ (x～1)∝(1--x)⁴, and by the way, a new counting rule Computercalculation gives the F₂(x) curve which seems to be consistent with the data in therange of 0.4<x<1.     

ON THE IRREDUCIBLE REPRESENTATIONS OF THE COMPACT SIMPLE LIE GROUPS OF RANK 2(I)

In this paper, we analyse the commutation relations of the infintesimal opera-tors of the group SU₃ and find that the eight infinitesimal operators of the groupSU₃ can be written as a scalar operator A, three angular momentum operators (L₁,L_o, L_-1,)and two sets of the irreducible tensor operators of rank 1/2, （T_±1/2,V±1/2）By means of the commutation relations of these operators, all irreducible represen-tations of the group SU₃ can be easily obtained. In this pape, the matrices corresponding to these operators in the irreduciblerepresentation（λμ）, are given; therefore the irreducible representation and its re-presentation space R^λμ are completely defined. Besides, a method for calculatingthe scalar factors of the reduction coefficients and the symmetric relations of thosefactors are also given. As examples, the scalar factors of the reduction coefficientsof （λμ）×（10）, （λμ）×（01）, （λμ）×（20） and （λμ）×（11） are calculated. In the last part of this paper, we define the irreducible tensor operators ofthe group SU₃ and prove the corresponding Wigner-Eckart theory. The method used in the discussion of the group SU₃ be extended to allof the compact simple Lie groups of rank 2 and we shall discuss them in two suc-ceeding papers.     

A STRUCTURE MODEL OF STRATONS AND LEPTONS

A subquark model is proposed. According to this model, stratons and leptons are consisted of rishons T and V, which are multiplets of group SU_H(3)×SU_C(3)×SU_G(2)×SU(2)×U(1). Three generations of both stratons and leptons are obtained naturally. In this model, proton decay modes are μ^－e⁺e⁺ or e^－μ⁺μ⁺.     

A RECURSIVE FORMULA FOR THE CLEBSCH-GORDAN COEFFICIENTS OF SUn GROUP

It is proved that under the Gelfand-Biedenharn phase convention any SU_n singletfactor （SF） belongs to the type of the derivable or underivable,designated as （SU_nSF）d and （SU_r SF） respectively,and （SU_n SF）d=（SU_r SF）,n=r+1,r+2,….Therefore the calculation of any SU_n Clebsch-Gordan coefficients is reduced to thecalculation of a few underivable singlet factor （SU_r SF）.     

TRACELESS OPERATORS AND SO6 WAVE FUNCTIONS OF sd BOSONS

Traceless operators of sd bosons are introduced and used to construct the SU₆SO₆SO₅SO₃ wave functions of sd bosons according to the method of T.S.Yang     

THE BEHAVIOR OF THE PHASE-SHIFT IN THE BAKAMJIAN-THOMAS THEORY

The behavior of the phase-shift of the Bakamjian-Thomas theory and its relationwith the phenomenological nuclear force V=V_RiV_I at high energy are explored.Two limits are obtained:It is found that the repulsive core with a sharp outer edge may induce a characteris-tic oscillation of Re δ₁,and Im δ₁ is sensitive to V₁.The conclusion is that the analy-sis of the phase-shift extending to higher energy is relevant in determining therepulsive core and the imaginary part of the nuclear force.     

THE REGGE TRAJECTORY OF MESONS AND THE SU(4) MASS RELATIONS

A relativistic equation of motion of a two particle system under the constraints p_i²-m_i²-U(x²)=0.(i=1,2), where U(x²) is an infinite spherical square well poten-tial, is applied to the SU(4) quark model of mesons. A set of linear mass relations areobtained. Instead of the linear relation between J and M², the Regge trajectory ob-tained is a relation between p_nl² and M², where ζ_nlπ are zeros of the spherical Besselfunctions. The new trajectory seems more satisfactory than the former one.