Mesons

Our present views on the electronic structure of atoms are based on a variety of experimental results and theoretical models which are fully discussed in many elementary texts. In summary, an atom comprises a central, massive, positively charged nucleus surrounded by a more tenuous envelope of negative electrons. The nucleus is composed of neutrons ( n) and protons ([p, i.e. H ) of approximately equal mass tightly bound by the force field of mesons. The number of protons (2) is called the atomic number and this, together with the number of neutrons (A ), gives the atomic mass number of the nuclide (A = N + Z). An element consists of atoms all of which have the same number of protons (2) and this number determines the position of the element in the periodic table (H. G. J. Moseley, 191.3). Isotopes of an element all have the same value of 2 but differ in the number of neutrons in their nuclei. The charge on the electron (e ) is equal in size but opposite in sign to that of the proton and the ratio of their masses is 1/1836.1527. 

H. Yukawa (Kyoto) prediction of the existence of mesons on the basis of theoretical work on nuclear forces. 

C. F. Powell (Bristol) development of the photographic method of studying nuclear processes and discoveries regarding mesons made with this method. 

Princeton) discovery of violations of fundamental symmetry principles in the decay of neutral K-mesons. 

Eugen Merzbacher, Quantum Mechanics, Chapter 21, John Wiley and Sons, Inc., New York, 1961 Schweber, Bethe, and de Hoffmann, Mesons and Fields, Vol. 1, Section 8a, Harper and Row, New York, 1955. 

After the discovery of the combined charge and space symmetry violation, or CP violation, in the decay of neutral mesons [2], the search for the EDMs of elementary particles has become one of the fundamental problems in physics. A permanent EDM is induced by the super-weak interactions that violate both space inversion symmetry and time reversal invariance [11], Considerable experimental efforts have been invested in probing for atomic EDMs (da) induced by EDMs of the proton, neutron, and electron, and by the P,T-odd interactions between them. The best available limit for the electron EDM, de, was obtained from atomic T1 experiments [12], which established an upper limit of de < 1.6 x 10 27e-cm. The benchmark upper limit on a nuclear EDM is obtained from the atomic EDM experiment on Iyt,Hg [13] as d ig < 2.1 x 10 2 e-cm, from which the best restriction on the proton EDM, dp < 5.4 x 10 24e-cm, was also obtained by Dmitriev and Senkov [14]. The previous upper limit on the proton EDM was estimated from the molecular T1F experiments by Hinds and co-workers [15]. 

Meson Particles of mass that are intermediate between the masses of the electron and proton. 

Despite the successes, even with its generalizations, difficulties in thermal field theory remain to be overcome in order to deal with experimental and theoretical demands. In fact, numerous studies, in particular using quantum chromodynamics (A. Smilga, 2001), have been carried out in an attempt to understand, for instance, the quark-gluon plasma at finite temperature and in this common effort, some underlying aspects have been identified. For example, the coupling constants for 7r,a,w and p mesons decrease to zero at a certain critical temperature, which are, respectively, given by = 360 MeV, Tj = 95... 

As a further step, it is natural to make bosonization, using auxiliary meson fields 0 0, which provide ... 

Now the calculations of Gasser-Leutwyler couplings of their phenomenological chiral lagrangian (H.C. Kim et.al., 1984) and related with this problem the meson loops calculations are in progress. First results show exact reproducing of the famous chiral log terms in various correlators. 

Abstract. The —> um° decay is studied using the method of phenomenological chiral Lagrangians. Obtained in the framework of this method the expression of weak hadronic currents between vector and pseudoscalar mesons has been checked and it is shown that this decay channel proceeds only due to the — p - mixing diagram. 

Here, we consider the (ft —> unr° decay by the method of phenomenological chiral Lagrangians(PCL s)(Weinberg,1967). Studies of this decay channel is of interest in this model for the following reasons First, this decay channel is a unique laboratory for verification of weak hadron currents between pseudoscalar and vector meson states which was obtained earlier (Nasriddinov, 1998) within the formalism of phenomenological chiral Lagrangians... 

Second, this decay allows to study the nature of p,ui and (ft— meson mixing. Note,that in references (Nasriddinov, 1994 Nasriddinov, 2001) the problems of 7r° — rj - and io — (ft mixings have been studied on the basis of this model as well and obtained reasonable results for the r-lepton decay probabilities. In this calculation, we used ui — 0-mixing... 

According to the expression for weak hadronic currents between pseudoscalar and vector meson states (f), the Born amplitude of this decay is equal to zero, since the structure constants /i3j = fs3i = 0, (in other words, the current // responsible for the direct — um° decay (FIG.f) is zero). 

According to the method of phenomenological chiral Lagrangians (PCL s), this decay channel would originate via the intermediate D° — meson state (FIG. 2). In this case the weak interaction Lagrangian between (f) and D° mesons has the form given (Kalinovsky,1988) as... 

In the PCL the strong interaction Lagrangian of vector mesons with vector and pseudoscalar mesons has the form... 

The next diagram (FIG. 3) also does not contribute to the partial width for the 0 — W7r° decay. In this case the Lagrangian of the strong coupling of axial-vector mesons to vector and pseudoscalar mesons is derived in a similar way and has the form (Nasriddinov, 1994)... 

Finally the diagram with the intermediate oj meson (FIG. 5) does not contribute to the partial width of this decay channel also because of these structure constants. 

According to (2), the Lagrangians describing p -meson interaction with 10 and 7r° mesons (FIG. 6), and 0-meson interaction with p and 7T° mesons (FIG.7) have the forms, respectively... 

Figure 2. The diagram with the intermediate D° — meson, (S) anomalous strong-interection vertex.

Deser S., Goldberger M. L., Baumann K. and Thirring W. Energy Level Displacements in Pi-Mesonic Atoms, Phys. Rev. 96, 774-776 (1954) Anagnostopoulos D. F. et al., Precision measurements in pionic hydrogen, Nucl. Phys. A 721, 849-852 (2003). 

Accurate theoretical prediction of mass spectra and other properties of hadrons containing heavy quarks is important for mass spectra of hadrons for forthcoming experiments on the study of their properties. At present such facilities as Tevatron, LHC and JHF will have the opportunity to produce hadrons with one or more heavy quarks. The successful experiments at the Collider Detector at Fermilab Collaboration on the observation of the Bc meson (Abe et. ah, 1998) gives some hope to observe heavy quarkonia, also. 

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