|
In physics, the Gell-Mann–Okubo mass formula provides a sum rule for the masses of hadrons within a specific multiplet, determined by their isospin (''I'') and strangeness (or alternatively, hypercharge) : where ''a''0, ''a''1, and ''a''2 are free parameters. The rule was first formulated by Murray Gell-Mann in 1961〔 〕 and independently proposed by Susumu Okubo in 1962.〔 〕〔 〕 Isospin and hypercharge are generated by SU(3), which can be represented by eight hermitian and traceless matrices corresponding to the "components" of isospin and hypercharge. Six of the matrices correspond to flavor change, and the final two correspond to the third-component of isospin projection, and hypercharge. ==Theory== The mass formula was obtained by considering the representations of the Lie algebra su(3). In particular, the meson octet corresponds to the root system of the adjoint representation. However, the simplest, lowest-dimensional representation of su(3) is the fundamental representation, which is three-dimensional, and is now understood to describe the approximate flavor symmetry of the three quarks ''u'', ''d'', and ''s''. Thus, the discovery of not only an su(3) symmetry, but also of this workable formula for the mass spectrum was one of the earliest indicators for the existence of quarks. This formula is ''phenomenological'', describing an approximate relation between meson and baryon masses, and may be superseded as theoretical work in quantum chromodynamics advances. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Gell-Mann–Okubo mass formula」の詳細全文を読む スポンサード リンク
|