Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-loop unitarity constraints on the Higgs boson coupling   We use the results of Maher {\em et al.\/} (preceding paper) to construct the
matrix of $j=0$ partial-wave two-body and $2\rightarrow3$ scattering amplitudes
for the scattering of longitudinally polarized gauge bosons $W_L^\pm$, $Z_L$
and Higgs bosons $H$ correct to two loops in the high-energy, heavy-Higgs limit
$\sqrt{s}\gg M_H\gg M_W$. We show explicitly that the energy dependence of the
$2\rightarrow2$ amplitudes can be completely absorbed into a running quartic
Higgs coupling $\lambda_s= \lambda_s(s,M_H^2)$ and factors which involve small
anomalous dimensions and remain near unity. After diagonalizing the matrix of
partial-wave amplitudes, we use an Argand-diagram analysis to show that the
elastic scattering amplitudes are approximately unitary and weakly interacting
for $\lambda_s\alt2.3$, but that three-loop corrections are necessary to
restore unitarity for larger values of $\lambda_s$. That is, the interactions
in the Higgs sector of the standard model are effectively strong with respect
to the perturbative expansion for $\lambda_s\agt2.3$. The bound
$\lambda_s\alt2.3$ for a weakly interacting theory translates to a physical
Higgs mass $M_H\alt380$ GeV if the bound is to hold for energies up to a few
TeV, or $M_H\leq155$ GeV in perturbatively unified theories with mass scales of
order $10^{16}$ GeV.

15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
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The categories of this paper are: math-ph