Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sphalerons in the Standard Model with a real Higgs singlet   Sphaleron energies within the standard model with a real Higgs singlet added
on are calculated. The coupled non-linear equations of motion are numerically
solved and the sphaleron energy evaluated for a set of parameters in the Higgs
potential. I find a small difference in the sphaleron energy compared to the
standard model. A slightly stronger constraint on the strength of the first
order phase transition thus results for this model.

30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol