Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbative renormalization factors of three- and four-quark operators
  for domain-wall QCD   Renormalization factors for three- and four-quark operators, which appear in
the low energy effective Lagrangian of the proton decay and the weak
interactions, are perturbatively calculated in domain-wall QCD. We find that
the operators are multiplicatively renormalizable up to one-loop level without
mixing with any other operators that have different chiral structures. As an
application, we evaluate a renormalization factor for $B_K$ at the parameters
where previous simulations have been performed, and find one-loop corrections
to $B_K$ are 1-5% in these cases.

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The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
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The categories of this paper are: stat