4,637 research outputs found
On the second largest eigenvalue of the signless Laplacian
Let be a graph of order and let be
the eigenvalues of the -matrix of , also known as the signless Laplacian
of In this paper we give a necessary and sufficient condition for the
equality where In particular, this result solves
an open problem raised by Wang, Belardo, Huang and Borovicanin.
We also show that [ q_{2}(G) \geq\delta(G)] and determine that equality holds
if and only if is one of the following graphs: a star, a complete regular
multipartite graph, the graph or a complete multipartite graph of
the type .Comment: This version fills a gap in one proof, noticed by Rundan Xin
New Strongly Coupled Sector at the Tevatron and the LHC
We examine the possibility that a new strong interaction is accessible to the
Tevatron and the LHC. In an effective theory approach, we consider a scenario
with a new color-octet interaction with strong couplings to the top quark, as
well as the presence of a strongly coupled fourth-generation which could be
responsible for electroweak symmetry breaking. We apply several constraints,
including the ones from flavor physics. We study the phenomenology of the
resulting parameter space at the Tevatron, focusing on the the forward-backward
asymmetry in top pair production, as well as in the production of the
fourth-generation quarks. We show that if the excess in the top production
asymmetry is indeed the result of this new interaction, the Tevatron could see
the first hints of the strongly coupled fourth-generation quarks. Finally, we
show that the LHC with TeV and integrated
luminosity should observe the production of fourth-generation quarks at a level
at least one order of magnitude above the QCD prediction for the production of
these states.Comment: 8 pages, 12 figure
N-Relaxion: Large Field Excursions from a Few Site Relaxion Model
Relaxion models are an interesting new avenue to explain the radiative
stability of the Standard Model scalar sector. They require very large field
excursions, which are difficult to generate in a consistent UV completion and
to reconcile with the compact field space of the relaxion. We propose an N-site
model which naturally generates the large decay constant needed to address
these issues. Our model offers distinct advantages with respect to previous
proposals: the construction involves non-abelian fields, allowing for
controlled high energy behaviour and more model building possibilities, both in
particle physics and inflationary models, and also admits a continuum limit
when the number of sites is large, which may be interpreted as a warped extra
dimension.Comment: 7 pages, 2 figures; v2: version to appear in PR
Minimally extended SILH
Higgs boson compositeness is a phenomenologically viable scenario addressing
the hierarchy problem. In minimal models, the Higgs boson is the only degree of
freedom of the strong sector below the strong interaction scale. We present
here the simplest extension of such a framework with an additional composite
spin-zero singlet. To this end, we adopt an effective field theory approach and
develop a set of rules to estimate the size of the various operator
coefficients, relating them to the parameters of the strong sector and its
structural features. As a result, we obtain the patterns of new interactions
affecting both the new singlet and the Higgs boson's physics. We identify the
characteristics of the singlet field which cause its effects on Higgs physics
to dominate over the ones inherited from the composite nature of the Higgs
boson. Our effective field theory construction is supported by comparisons with
explicit UV models.Comment: Matches JHEP versio
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