SOME CONJECTURES ON THE MASS FORMULA OF CHARGED LEPTONS

In this note we propose that the electromagnetic self energy of lepton may beconnected with quantum number n by（ （δm）/m）=（1/（2π））n^-b ,in which b is a constant.Wefnrther propose that the cut-off value of momentum M is connected with gravitationalconstant κ and fine structure constant α by M=（1/√κ）αe^-1-b.So we obtainthe mass formula of charged leptons M=（1/√κ）α exp{-3/4-b-(1/3α)n^-b}.By using the masses of e^- and μ^- and the value of a as in put,we get the calculatedvalues of κ=（6.67231±0.00026）×10^-8cm³g^-1sec^-2and m_r=（1782.306±0.078）MeVwhich agree very well with experimental values κ=（6.6720±0.0041）×10^-8cm³g^-1sec^-2 and m_τ=(1782_-4⁺³)MeV respectively.The mass of the fourth charged leptonpredicted by the formula should be m=（11725.47±0.51）MeV,which can be checkedby experiments in the near future.We also discuss briefly the proposed formula andthe obtained results.     

THE U1 GAUGE FIELD IN A SUN GAUGE FIELD AND THE QUANTIZED VALUES OF DUAL CHARGES

Let F be a SU_N gauge field on the space-time manifold M₄, b_λ（x） （λ=0,1, 2, 3） the gauge potentials, the field strengths and Q（x） a Higgs field. All quantities b, f_λμ and Q（x） are SU_N'-valued, i.e. they are represented by N×N anti-hermitian traceless matrices.Let M₄' be the set of x such that Q（x）≠0 and define on M₄', where The following results are obtained:Theorem 1. The 1st set of Maxwell equations F_λμ,v+F_μv,λ+F_vλ,μ=0 are satisfied for arbitrary b_λ if and only if with Here s is an integer, 1≤s≤N-1.Suppose the conditions in theorem 1 are satisfied.Theorem 2. If s is a space-like two-dimensional surface, the value of dual charges contained in s defined by is equal to lq', where l is an integer and Theorem 3. The value of dual charges contained in S is equal to the integral which is independent of the gauge potentials.Theorem 4. The least positive value q' of dual charge can be attained by some Higgs fields.Remarks（a） When N=2, the results obtained are consistent with those of t Hooft, Arafune and Hou etc.（b） For N=3, we give an answer to the question of quantized values of dual charges which was discussed by Marciano and Pagels.（c） The Higgs field ø（x） is a mapping from M'₄ into the AⅢ type symmetric space SU_N/S(U_s X U_N-s) and the integral is an extension of Kronecker index for N=2.     

STRATO-GLUON MECHANISM FOR HADRONIC MULTIPLE PRODUCTION AND AVERAGE CHARGED MULTIPLICITY

By assuming that in a high energy hadronic collision process,N pairs of stratonsare produced together with gluons,the number of which is supposed to be propor-tional to the number of“bonds”between any two stratons,we are able to get a rela-tion between the Q-value and the number of pairs N:N=（α²+βQ）^1/2-α.The average charged multiplicity〈n_ch〉_theo is calculated,and is compared withthe experiments.The data of pp、π^±p、K^±p collisions all coincide with the theoreticalcurve in a wide range of energies.The deviation between the energy vs.chargedmultiplicity relations for meson-proton and proton-proton collision processes are ex-plained quantitatively.The average straton mass estimated from the theory is ingood agreement with that.given by other authors.     

THE VERTICAL DIFFERENTIAL MOMENTUM SPECTRUM OF THE MUON AT 3200M ABOVE SEA-LEVEL

The vertical differential momentum spectrum and the charge ratio of the cosmic ray muon, in the range(0.4—250GeV/c), has been measured by means of the magnetic spectrometer and the range-spectrometer in Yunnan station at 3200 m above the sea level. The present spectrum is in agreement with the differential spectrum of muons, measured by others at the same mountain altitude. In the 15—250GeV/c momentum range, the spectrum obtained from the present experiment is also in good agreement with the differential spectrum of the muon which has been determined by O.C. Allkofer et al. at the sea level. The charge ratio of the muon is almost constant in the range (5—100GeV/c). The average value is 1.30±0.06.     

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.     

ON NUCLEAR SINGLE-PARTICLE POTENTIALS（Ⅲ）SINGLEPARTICLE ENERGIES DETERMINED BY THE NONHERMITIAN POTENTIAL Uαβ=Mαβ（εβ）

In this paper the following results are proved:although the single-particle（sp）potential u_αβ=M_αβ（ε_β）defined in terms of the mass operator M_αβ（ω） is nonhermi-tian,the discrete energy eigenvalues determined by the Schrödinger equation h|γ>=（t+u）|γ>=ε_γ|γ> are real;moreover,they satisfy exactly the following relation:（ε_γ⁼±[E_nγ（N±1）—E₀（N）] where E₀（N）denotes the exact ground state energy of a closed-shell nucleus N,and E_nγ（N±1）are excat energy eigenvalues of its neighbouring N±1 nucleus.Further,in order to determine whether the bound state energies obtained by anyother sp potential may or not satisfy the above relation,a simple method is sugges-ted.It is shown that the amplitude renormalization of the sp Green function canalso be calculated easily by means of this method.     

Measurement of J/ψ→ηcγ at KEDR

We present a study of the inclusive photon spectra from 5.9 million J/ψ decays collected with the KEDR detector at the VEPP-4M e⁺e^－ collider. We measure the branching fraction of radiative decay J/ψ→η_cγ, η_c width and mass. Our preliminary results are: M(η_c)=2979.4±1.5±1.9 MeV/c², Γ(η_c) = 27.8±5.1±3.3 MeV, B(J/ψ→η_cγ)=(2.34±0.15±0.40)%.

     

ON THE “DIRECT CHANNEL DIAGRAM” OF THE PRODUCTION OF THE （π+ π-）s S-STATE ATOMS

In this paper we work out the relativistic covariant B-S wave function for the（π⁺ π^-）_s atoms.Some properties of the“direct channel diagram”of the produc-tion the （π⁺ π^-）_s atoms are discussed by calculating the cross-section of the process π⁺ +n→p+（π⁺ π^-）_s with the help of the relativistic covariant wave function and assuming the lowest termin the perturbation expansion series of the quantized composite field theory——the“direct channel diagram”is dominant.Besides this calcuation perhaps presentsa rough estimate for the interesting process μ⁺ +n→（μ⁺ π^-）+p.     

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.     

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.     

Determination of J/ψ Leptonic Branching Fraction Via ψ(2S)→π+π－J/ψ

Two processes ψ(2S)→π⁺π^－J/ψ,J/ψ→1⁺1^－ and J/ψ→anything are carefully studied to get the J/ψ leptonic branching fractions with the ψ(2S)data at BES/BEPC.The results are B(J/ψ→e⁺e^－)=(5.90±0.07±0.16)% and B(J/ψ→μ⁺μ^－)=(5.96 ±0.08±0.16)%,and B_e/B_μ is estimated to be 0.990±0.018±0.024.Assuming B_e=B_μ,the leptonic branching fraction of the J/ψ is B(J/ψ→1⁺1^－)=(5.93±0.05 ± 0. 16 )%.This result is used to estimate the QCD scale factor ∧(nf/MS) and the strong coupling constant α_s.     

A METHOD FOR FINDING POTENTIALS CORRESPONDING TO POLYNOMIAL-FACTOR EIGENFUNCTIONS IN QUANTUM MECHANICS

A method for finding potentials corresponding to polynomial-factor eigenfunc-tions is given for the Schr（?）dinger equation as an example.It is shown that theeigen-solutions for harmonic and Columb's potentials in quantum mechanics are the twoexamples which can be given by this method and some other examples are discovered.This method and some results of this paper may be useful for hadron structure mo-del theory.One of the examples is the equation in Ref.（4）which is derived fromBethe-Salpeter equation for the case that the straton is tightly bounded in certain po-tential well.When this method is applied to that equation for three dimensionalcentral symmetric potential V（r）=V₀—2（N+（1/2））β^-1（√V₆r²）+（V₆r⁶）, some resultsare obtained as shown in Fig. 2 in which λ′ must be considered as a linear function of m².The so called“quasic Regge trajectory”behavior is manifested.     

SU（4）×S3α SCHEME OF STRATON MODEL AND THE NEWLY DISCOVERED HEAVY PARTICLE γ（9.5）

In this paper, the possibility that the newly discovered heavy particle γ （9.5） is a colour excited state of mesons in the SU（4）×S₃^α scheme of straton model is discussed. We point out that in the γ region, there are three colour excited states appearing as two peaks with mass difference about 0.5 GeV. The leptonic decays, hadronie decays, radiative decays, hadronic decays with electromagnetic interaction of the second order and the production behavior of γ are discussed. This model also predicts that many colour excited states of mesons accompanied with γ should exist with masses around 9.5 GeV and at least four weakly decaying particles should exist.     

EFFECT OF N PRODUCTION ON HIGH ENERGY PROTON SCATTERING BY NUCLEUS

The variable separation method of Glauber multiple scattering theory is developedto include the N^* production in the intermediate states and is used to calculate theinelastic scattering of proton by nucleus.Numerical results are compared with dataon p-¹²C^*（4⁺,14.08）at 1 GeV and it implies that the effects of N^* production tothe high-energy proton-nucleus scattering are noticeable.     

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.     

EXCITATION CURVES FOR SOME REACTIONS OF Al、Ti、V AND I

Excitation curves for the reaction ²⁷Al（n,α）²⁴Na,⁴6Ti（n,p）⁴⁶Sc,⁴⁸Ti（n,p）⁴⁸Sc,⁵¹V（n,α）⁴⁸Sc and ¹²⁷I（n,2n）¹²⁶I have been measured by the activation method in the4.5—18.3 MeV energy region.The cross section for the reactio ²⁷Al（n,α）²4Na was determined at 14.61±0.20 MeV.The measurement of neutron flux was performed using the associated particle method.The cross sections for other reactions were de-termined relative to the measured ²⁷Al（n,α）²⁴Na cross section.The resulting activities were measured employing a calibrated NaI（TI）scintillation counter.The values obtained were 117.5±3.0 mb,291.4±14.0mb,63.7±3.2 mb,16.8±0.9mb and 1656±68 mb respectively.A brief comparison with existing data was made.     

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.     

THE BEHAVIOURS OF F2ep(X,Q2)-F2en(X,Q2) AND THE SCALE-BREAKING PARAMETER

The scale-breaking parameter F₂^ep(x, Q²) of non-singlet component F₂^ep-F₂^en and some other quantities in the electro-production process are discussed by usinb the analytic expression for the distribution function of valence quarks in ha.drons up to leading log approximation given by a, previous paper^[1]. Comparisons with data are also given.

     

AN SU（4）×S3a SCHEME OF THE STRATON MODEL

In this paper, we propose an SU（4）×S₃^a scheme of the Straton Model and discuss the classification of mesons. We suggest the possible existence of several colour excited states with masses around 2 GeV in companion with charm mesons. We also discuss the properties and the experimental behavior of these colour excited states, especially, the possible contribution of these states in several new phenomena.     

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（∂/（∂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.