1,280 research outputs found
ON THE 82-TH SMARANDACHE’S PROBLEM
The main purpose of this paper is using the elementary method to study the asymptotic properties of the integer part of the k-th root positive integer, and give two interesting asymptotic formulae
Masses of Scalar and Axial-Vector B Mesons Revisited
The SU(3) quark model encounters a great challenge in describing even-parity
mesons. Specifically, the quark model has difficulties in
understanding the light scalar mesons below 1 GeV, scalar and axial-vector
charmed mesons and charmonium-like state . A common wisdom for
the resolution of these difficulties lies on the coupled channel effects which
will distort the quark model calculations. In this work, we focus on the near
mass degeneracy of scalar charmed mesons, and , and its
implications. Within the framework of heavy meson chiral perturbation theory,
we show that near degeneracy can be qualitatively understood as a consequence
of self-energy effects due to strong coupled channels. Quantitatively, the
closeness of and masses can be implemented by adjusting
two relevant strong couplings and the renormalization scale appearing in the
loop diagram. Then this in turn implies the mass similarity of and
mesons. The interaction with the Goldstone boson is
crucial for understanding the phenomenon of near degeneracy. Based on heavy
quark symmetry in conjunction with corrections from QCD and effects, we
obtain the masses of and mesons, for example,
,
with being
corrections. We find that the predicted mass difference of 48 MeV
between and is larger than that of MeV
inferred from the relativistic quark models, whereas the difference of 15 MeV
between the central values of and is much smaller than
the quark model expectation of MeV.Comment: 21 pages, 1 figure, to appear in Eur. Phys. J. (2017). arXiv admin
note: text overlap with arXiv:1404.377
An open problem on Jeśmanowicz\u27 conjecture concerning primitive Pythagorean triples
Let (m>31) be an even integer with (gcd(m,31)=1). In this paper, using some elementary methods, we prove that the equation ((m^2-31^2)^x+(62m)^y=(m^2+31^2)^z) has only the positive integer solution ((x,y,z)=(2,2,2)). This result resolves an open problem raised by T. Miyazaki ({em Acta Arith.} 186 (2018), 1--36) about Je\u27smanowicz\u27 conjecture concerning primitive Pythagorean triples
General Split Variational Inclusion Problem in Hilbert Spaces
We consider a general split variational inclusion problem (GSFVIP) and propose an algorithm for finding the solutions of GSFVIP in Hilbert space. We establish the strong convergence of the proposed algorithm to a solution of GSFVIP. Our results extend and improve the related results in the literature
Top quark decays with flavor violation in the B-LSSM
The decays of top quark are extremely rare processes in the
standard model (SM). The predictions on the corresponding branching ratios in
the SM are too small to be detected in the future, hence any measurable signal
for the processes at the LHC is a smoking gun for new physics. In the extension
of minimal supersymmetric standard model with an additional local
gauge symmetry (B-LSSM), new gauge interaction and new flavor changing
interaction affect the theoretical evaluations on corresponding branching
ratios of those processes. In this work, we analyze those processes in the
B-LSSM, under a minimal flavor violating assumption for the soft breaking
terms. Considering the constraints from updated experimental data, the
numerical results imply ,
, and in our
chosen parameter space. Simultaneously, new gauge coupling constants
in the B-LSSM can also affect the numerical results of
.Comment: 20 pages, 4 figures, published in EPJC. arXiv admin note: substantial
text overlap with arXiv:1803.0990
from the semileptonic decay and the properties of the meson distribution amplitude
The improved QCD light-cone sum rule (LCSR) provides an effective way to deal
with the heavy-to-light transition form factors (TFFs). Firstly, we adopt the
improved LCSR approach to deal with the TFF up to twist-4
accuracy. Due to the elimination of the most uncertain twist-3 contribution and
the large suppression of the twist-4 contribution, the obtained LCSR shall
provide us a good platform for testing the -meson leading-twist DA. For the
purpose, we suggest a new model for the -meson leading-twist DA
(), whose longitudinal behavior is dominantly determined by a
parameter . Moreover, we find its second Gegenbauer moment .
Varying within certain region, one can conveniently mimic the -meson DA
behavior suggested in the literature. Inversely, by comparing the estimations
with the experimental data on the -meson involved processes, one can get a
possible range for the parameter and a determined behavior for the
-meson DA. Secondly, we discuss the TFF at the maximum recoil
region and present a detailed comparison of it with the pQCD estimation and the
experimental measurements. Thirdly, by applying the LCSR on , we
study the CKM matrix element \Vcb together with its uncertainties by adopting
two types of processes, i.e. the -type and the -type.
It is noted that a smaller shows a better agreement with the
experimental value on \Vcb. For example, for the case of , we obtain
and , whose first (second)
uncertainty comes from the squared average of the mentioned theoretical
(experimental) uncertainties.Comment: 13 pages, 10 figures. Reference updated and discussion improved. To
be published in Nucl.Phys.
The -meson longitudinal leading-twist distribution amplitude
In the present paper, we suggest a convenient model for the vector
-meson longitudinal leading-twist distribution amplitude
, whose distribution is controlled by a single parameter
. By choosing proper chiral current in the correlator, we obtain
new light-cone sum rules (LCSR) for the TFFs , and ,
in which the -order provides dominant
contributions. Then we make a detailed discussion on the
properties via those TFFs. A proper choice of can
make all the TFFs agree with the lattice QCD predictions. A prediction of
has also been presented by using the extrapolated TFFs, which
indicates that a larger leads to a larger . To
compare with the BABAR data on , the longitudinal leading-twist
DA prefers a doubly-humped behavior.Comment: 7 pages, 3 figures. Discussions improved and references updated. To
be published in Phys.Lett.
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