38,587 research outputs found
Three-loop planar master integrals for heavy-to-light form factors
We calculate analytically the three-loop planar master integrals relevant for
heavy-to-light form factors using the method of differential equations. After
choosing a proper canonical basis, the boundary conditions are easy to be
determined, and the solution of differential equations is greatly simplified.
The results for seventy-one master integrals at general kinematics are all
expressed in terms of harmonic polylogarithms.Comment: 18 pages, 2 figure
Role of the effective payoff function in evolutionary game dynamics
In most studies regarding evolutionary game dynamics, the effective payoff, a
quantity that translates the payoff derived from game interactions into
reproductive success, is usually assumed to be a specific function of the
payoff. Meanwhile, the effect of different function forms of effective payoff
on evolutionary dynamics is always left in the basket. With introducing a
generalized mapping that the effective payoff of individuals is a non-negative
function of two variables on selection intensity and payoff, we study how
different effective payoff functions affect evolutionary dynamics in a
symmetrical mutation-selection process. For standard two-strategy two-player
games, we find that under weak selection the condition for one strategy to
dominate the other depends not only on the classical {\sigma}-rule, but also on
an extra constant that is determined by the form of the effective payoff
function. By changing the sign of the constant, we can alter the direction of
strategy selection. Taking the Moran process and pairwise comparison process as
specific models in well-mixed populations, we find that different fitness or
imitation mappings are equivalent under weak selection. Moreover, the sign of
the extra constant determines the direction of one-third law and risk-dominance
for sufficiently large populations. This work thus helps to elucidate how the
effective payoff function as another fundamental ingredient of evolution affect
evolutionary dynamics.Comment: This paper has been accepted to publish on EP
Influence of initial distributions on robust cooperation in evolutionary Prisoner's Dilemma
We study the evolutionary Prisoner's Dilemma game on scale-free networks for
different initial distributions. We consider three types of initial
distributions for cooperators and defectors: initially random distribution with
different frequencies of defectors; intentional organization with defectors
initially occupying the most connected nodes with different fractions of
defectors; intentional assignment for cooperators occupying the most connected
nodes with different proportions of defectors at the beginning. It is shown
that initial configurations for cooperators and defectors can influence the
stationary level of cooperation and the evolution speed of cooperation.
Organizations with the vertices with highest connectivity representing
individuals cooperators could exhibit the most robust cooperation and drive
evolutionary process to converge fastest to the high steady cooperation in the
three situations of initial distributions. Otherwise, we determine the critical
initial frequencies of defectors above which the extinction of cooperators
occurs for the respective initial distributions, and find that the presence of
network loops and clusters for cooperators can favor the emergence of
cooperation.Comment: Submitted to EP
Conical Defects, Black Holes and Higher Spin (Super-)Symmetry
We study the (super-)symmetries of classical solutions in the higher spin
(super-)gravity in AdS. We show that the symmetries of the solutions are
encoded in the holonomy around the spatial circle. When the spatial holonomies
of the solutions are trivial, they preserve maximal symmetries of the theory,
and are actually the smooth conical defects. We find all the smooth conical
defects in the , as well as in
and Chern-Simons gravity theories. In the bosonic higher spin
cases, there are one-to-one correspondences between the smooth conical defects
and the highest weight representations of Lie group. Furthermore we investigate
the higher spin black holes in and higher spin
(super-)gravity and find that they are only partially symmetric. In general,
the black holes break all the supersymmetries, but in some cases they preserve
part of the supersymmetries.Comment: 48 pages; more clarifications on conical defects in supersymmetric
cas
Quasi parton distribution functions at NNLO: flavor non-diagonal quark contributions
We present a next-to-next-to-leading order (NNLO) calculation of the quasi
parton distribution functions (Quasi-PDFs) in the large momentum effective
theory (LaMET). We focus on the flavor non-diagonal quark-quark channel and
demonstrate the LaMET factorization at the NNLO accuracy in the modified
minimal subtraction scheme. The matching coefficient between the quasi-PDF and
the light-cone PDF is derived. This provides a first step towards a complete
NNLO analysis of quasi-PDFs and to better understand the nucleon structures
from the first principle of QCD.Comment: 10 pages, 3 figures; v2: accepted for publication in Physical Review
D as a rapid communicatio
Black holes in Truncated Higher Spin AdS Gravity
We study the higher spin black holes in a truncated version of higher spin
gravity in . This theory contains only finite number of even spins
s=2,4,...,2N. We mainly focus on the simplest case, so-called (Type I and II)
spin gravity, which contains only spin 2 and spin 4 fields. This
spin gravity is as simple as spin 3 gravity, thus provides another
example to test various ideas on higher spin gravity. We find that the
asymptotical symmetry of this spin gravity is a classical
W(2,4)-symmetry. Moreover, we study the black hole solution with pure spin 4
hair and discuss its thermodynamics. One important feature of this black hole
is that its entropy could be written in compact forms. Furthermore, we
investigate a generated higher spin gravity. This higher spin gravity
only contains spin 2 and spin 6 fields which makes it different from other
kinds of higher spin gravity. We find the corresponding black hole with spin 6
hair, and discuss its thermodynamics analytically. It turns out that the black
holes with spin 4 or spin 6 hair constructed in this paper are the only black
holes with single higher spin hair, besides the spin 3 black hole found in
arXiv:1103.4304.Comment: 23 pages;minor revision, references added; published versio
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