Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operators up to Dimension Seven in Standard Model Effective Field Theory
  Extended with Sterile Neutrinos   We revisit the effective field theory of the standard model that is extended
with sterile neutrinos, $N$. We examine the basis of complete and independent
effective operators involving $N$ up to mass dimension seven (dim-7). By
employing equations of motion, integration by parts, and Fierz and group
identities, we construct relations among operators that were considered
independent in the previous literature, and find seven redundant operators at
dim-6, sixteen redundant operators and two new operators at dim-7. The correct
numbers of operators involving $N$ are, without counting Hermitian conjugates,
$16~(L\cap B)+1~(\slashed{L}\cap B)+2~(\slashed{L}\cap\slashed{B})$ at dim-6,
and $47~(\slashed{L}\cap B)+5~(\slashed{L}\cap\slashed{B})$ at dim-7. Here
$L/B~(\slashed L/\slashed B)$ stands for lepton/baryon number conservation
(violation). We verify our counting by the Hilbert series approach for $n_f$
generations of the standard model fermions and sterile neutrinos. When
operators involving different flavors of fermions are counted separately and
their Hermitian conjugates are included, we find there are $29~(1614)$ and
$80~(4206)$ operators involving sterile neutrinos at dim-6 and dim-7
respectively for $n_f=1~(3)$.

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The categories of this paper are: astro-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat