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Fine gradings of complex simple Lie algebras and Finite Root Systems
A -grading on a complex semisimple Lie algebra , where is a finite
abelian group, is called quasi-good if each homogeneous component is
1-dimensional and 0 is not in the support of the grading.
Analogous to classical root systems, we define a finite root system to be
some subset of a finite symplectic abelian group satisfying certain axioms.
There always corresponds to a semisimple Lie algebra together with a
quasi-good grading on it. Thus one can construct nice basis of by means
of finite root systems.
We classify finite maximal abelian subgroups in \Aut(L) for complex
simple Lie algebras such that the grading induced by the action of on
is quasi-good, and show that the set of roots of in is always a
finite root system. There are five series of such finite maximal abelian
subgroups, which occur only if is a classical simple Lie algebra
violation induced by the double resonance for pure annihilation decay process in Perturbative QCD
In Perturbative QCD (PQCD) approach we study the direct violation in the
pure annihilation decay process of
induced by the and
double resonance effect. Generally, the violation is small in the
pure annihilation type decay process. However, we find that the violation
can be enhanced by double interference when the invariant masses
of the pairs are in the vicinity of the resonance. For
the decay process of , the
maximum violation can reach 28.64{\%}
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