Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complete Set of Dimension-9 Operators in the Standard Model Effective
  Field Theory   We present a complete and independent list of the dimension 9 operator basis
in the Standard Model effective field theory by an automatic algorithm based on
the amplitude-operator correspondence. A complete basis (y-basis) is first
constructed by enumerating Young tableau of an auxiliary $SU(N)$ group and the
gauge groups, with the equation-of-motion and integration-by-part redundancies
all removed. In the presence of repeated fields, another basis (p-basis) with
explicit flavor symmetries among them is derived from the y-basis, which
further induces a basis of independent monomial operators through a systematic
process called de-symmetrization. Our form of operators have advantages over
the traditional way of presenting operators constrained by flavor relations, in
the simplicity of both eliminating flavor redundancies and identifying
independent flavor-specified operators. We list the 90456 (560) operators for
three (one) generations of fermions, all of which violate baryon number or
lepton number conservation; among them we find new violation patterns as
$\Delta B = 2$ and $\Delta L = 3$, which only appear at the dimensions $d \ge
9$.

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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat