17,047 research outputs found
NLO Productions of and with a Global Extraction of the Jet Transport Parameter in Heavy Ion collisions
In this work, we pave the way to calculate the productions of and
mesons at large in p+p and A+A collisions at the RHIC and
the LHC. The meson fragmentation functions (FFs) in vacuum at
next-to-leading order (NLO) are obtained by evolving NLO DGLAP evolution
equations with rescaled FFs at initial scale GeV from
a broken SU(3) model, and the FFs in vacuum are taken from AKK08
parametrization directly. Within the framework of the NLO pQCD improved parton
model, we make good descriptions of the experimental data on and
in p+p both at the RHIC and the LHC. With the higher-twist
approach to take into account the jet quenching effect by medium modified FFs,
the nuclear modification factors for meson and meson at
the RHIC and the LHC are presented with different sets of jet transport
coefficient . Then we make a global extraction of at the
RHIC and the LHC by confronting our model calculations with all available data
on 6 identified mesons: , , , , , and
. The minimum value of the total for productions of
these mesons gives the best value of for Au+Au
collisions with GeV at the RHIC, and for Pb+Pb collisions with TeV at the LHC
respectively, with the QGP spacetime evolution given by an event-by-event
viscous hydrodynamics model IEBE-VISHNU. With these global extracted values of
, the nuclear modification factors of , , ,
, , and in A+A collisions are presented, and
predictions of yield ratios such as and at
large in heavy-ion collisions at the RHIC and the LHC are provided.Comment: 9 pages, 13 figures, 1 tabl
Derivatives of tangent function and tangent numbers
In the paper, by induction, the Fa\`a di Bruno formula, and some techniques
in the theory of complex functions, the author finds explicit formulas for
higher order derivatives of the tangent and cotangent functions as well as
powers of the sine and cosine functions, obtains explicit formulas for two Bell
polynomials of the second kind for successive derivatives of sine and cosine
functions, presents curious identities for the sine function, discovers
explicit formulas and recurrence relations for the tangent numbers, the
Bernoulli numbers, the Genocchi numbers, special values of the Euler
polynomials at zero, and special values of the Riemann zeta function at even
numbers, and comments on five different forms of higher order derivatives for
the tangent function and on derivative polynomials of the tangent, cotangent,
secant, cosecant, hyperbolic tangent, and hyperbolic cotangent functions.Comment: 17 page
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