3,981 research outputs found
The Minimum Spectral Radius of Graphs with the Independence Number
In this paper, we investigate some properties of the Perron vector of
connected graphs. These results are used to characterize that all extremal
connected graphs with having the minimum (maximum) spectra radius among all
connected graphs of order with the independence number ,
respectively.Comment: 28 pages, 3 figure
The Wiener and Terminal Wiener indices of trees
Heydari \cite{heydari2013} presented very nice formulae for the Wiener and
terminal Wiener indices of generalized Bethe trees. It is pity that there are
some errors for the formulae. In this paper, we correct these errors and
characterize all trees with the minimum terminal Wiener index among all the
trees of order and with maximum degree .Comment: 13 page
decay in scalar and vector leptoquark scenarios
It has been shown that the anomalies observed in and decays can be
resolved by adding a single scalar or vector leptoquark to the Standard Model,
while constraints from other precision measurements in the flavour sector can
be satisfied without fine-tuning. To further explore these two interesting
scenarios, in this paper, we study their effects in the semi-leptonic
decay. Using the best-fit solutions for
the operator coefficients allowed by the current data of mesonic decays, we
find that (i) the two scenarios give similar amounts of enhancements to the
branching fraction and the
ratio , (ii) the
two best-fit solutions in each of these two scenarios are also
indistinguishable from each other, (iii) both scenarios give nearly the same
predictions as those of the Standard Model for the longitudinal polarizations
of and as well as the lepton-side forward-backward
asymmetry. With future measurements of these observables in
decay at the LHCb, the two leptoquark
scenarios could be further tested, and even differentiated from the other NP
explanations for the anomalies. We also discuss the
feasibility for the measurements of these observables at the LHC and the future
colliders.Comment: 29 pages, 4 tables and 2 figures; More references and the feasibility
for the measurements of the observables in these decays at the LHC and the
future colliders added, final version published in the journa
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