59 research outputs found
Charge-monopole versus Gravitational Scattering at Planckian Energies
The amplitude for the scattering of a point magnetic monopole and a point
charge, at centre-of-mass energies much larger than the masses of the
particles, and in the limit of low momentum transfer, is shown to be
proportional to the (integer-valued) monopole strength, assuming the Dirac
quantization condition for the monopole-charge system. It is demonstrated that,
for small momentum transfer, charge-monopole electromagnetic effects remain
comparable to those due to the gravitational interaction between the particles
even at Planckian centre-of-mass energies.Comment: 9 pages, revtex, IMSc/93-4
Astrophysical thermonuclear functions
As theoretical knowledge and experimental verification of nuclear cross
sections increases it becomes possible to refine analytic representations for
nuclear reaction rates. In this paper mathematical/statistical techniques for
deriving closed-form representations of thermonuclear functions are summarized
and numerical results for them are given.The purpose of the paper is also to
compare numerical results for approximate and closed-form representations of
thermonuclear functions.Comment: 17 pages in LaTeX, 8 figures available on request from
[email protected]
Novel CP-violating Effects in B decays from Charged-Higgs in a Two-Higgs Doublet Model for the Top Quark
We explore charged-Higgs cp-violating effects in a specific type III
two-Higgs doublet model which is theoretically attractive as it accommodates
the large mass of the top quark in a natural fashion. Two new CP-violating
phases arise from the right-handed up quark sector. We consider CP violation in
both neutral and charged B decays. Some of the important findings are as
follows. 1) Large direct-CP asymmetry is found to be possible for B+- to psi/J
K+-. 2) Sizable D-anti-D mixing effect at the percent level is found to be
admissible despite the stringent constraints from the data on K-anti-K mixing,
b to s gamma and B to tau nu decays. 3) A simple but distinctive CP asymmetry
pattern emerges in decays of B_d and B_s mesons, including B_d to psi/J K_S, D+
D-, and B_s to D_s+ D_s-, psi eta/eta^prime, psi/J K_S. 4) The effect of
D-anti-D mixing on the CP asymmetry in B+- to D/anti-D K+- and on the
extraction of the angle gamma of the unitarity triangle from such decays can be
significant.Comment: 32 pages, 5 figures, section V.A revised, version to appear in PR
The lifetime of B_c-meson and some relevant problems
The lifetime of the B_c-meson is estimated with consistent considerations on
all of the heavy mesons () and the double
heavy meson B_c. In the estimate, the framework, where the non-spectator
effects for nonleptonic decays are taken into account properly, is adopted, and
the parameters needed to be fixed are treated carefully and determined by
fitting the available data. The bound-state effects in it are also considered.
We find that in decays of the meson B_c, the QCD correction terms of the
penguin diagrams and the main component terms c_1O_1, c_2O_2 of the effective
interaction Lagrangian have direct interference that causes an enhancement
about 3 ~ 4% in the total width of the B_c meson.Comment: 27 pages, 0 figur
The check of QCD based on the tau-decay data analysis in the complex q^2-plane
The thorough analysis of the ALEPH data on hadronic tau-decay is performed in
the framework of QCD. The perturbative calculations are performed in 3 and
4-loop approximations. The terms of the operator product expansion (OPE) are
accounted up to dimension D=8. The value of the QCD coupling constant
alpha_s(m_tau^2)=0.355 pm 0.025 was found from hadronic branching ratio R_tau.
The V+A and V spectral function are analyzed using analytical properties of
polarization operators in the whole complex q^2-plane. Borel sum rules in the
complex q^2 plane along the rays, starting from the origin, are used. It was
demonstrated that QCD with OPE terms is in agreement with the data for the
coupling constant close to the lower error edge alpha_s(m_tau^2)=0.330. The
restriction on the value of the gluonic condensate was found
=0.006 pm 0.012 GeV^2. The analytical perturbative QCD was
compared with the data. It is demonstrated to be in strong contradiction with
experiment. The restrictions on the renormalon contribution were found. The
instanton contributions to the polarization operator are analyzed in various
sum rules. In Borel transformation they appear to be small, but not in spectral
moments sum rules.Comment: 24 pages; 1 latex + 13 figure files. V2: misprints are corrected,
uncertainty in alpha_s is explained in more transparent way, acknowledgement
is adde
Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals
High-order derivatives of analytic functions are expressible as Cauchy
integrals over circular contours, which can very effectively be approximated,
e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius
of convergence is equal, numerical stability strongly depends on r. We give a
comprehensive study of this effect; in particular we show that there is a
unique radius that minimizes the loss of accuracy caused by round-off errors.
For large classes of functions, though not for all, this radius actually gives
about full accuracy; a remarkable fact that we explain by the theory of Hardy
spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and
by the saddle-point method of asymptotic analysis. Many examples and
non-trivial applications are discussed in detail.Comment: Version 4 has some references and a discussion of other quadrature
rules added; 57 pages, 7 figures, 6 tables; to appear in Found. Comput. Mat
Chebyshev Solution of the Nearly-Singular One-Dimensional Helmholtz Equation and Related Singular Perturbation Equations: Multiple Scale Series and the Boundary Layer Rule-of-Thumb
The one-dimensional Helmholtz equation, Δ 2 u xx â u = f ( x ), arises in many applications, often as a component of three-dimensional fluids codes. Unfortunately, it is difficult to solve for ΔâȘ1 because the homogeneous solutions are expâ(± x /Δ), which have boundary layers of thickness O(1/Δ). By analyzing the asymptotic Chebyshev coefficients of exponentials, we rederive the OrszagâIsraeli rule [16] that Chebyshev polynomials are needed to obtain an accuracy of 1% or better for the homogeneous solutions. (Interestingly, this is identical with the boundary layer rule-of-thumb in [5], which was derived for singular functions like tanh([ x â1]/Δ).) Two strategies for small Δ are described. The first is the method of multiple scales, which is very general, and applies to variable coefficient differential equations, too. The second, when f ( x ) is a polynomial, is to compute an exact particular integral of the Helmholtz equation as a polynomial of the same degree in the form of a Chebyshev series by solving triangular pentadiagonal systems. This can be combined with the analytic homogeneous solutions to synthesize the general solution. However, the multiple scales method is more efficient than the Chebyshev algorithm when Δ is very, very tiny.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45436/1/11075_2004_Article_2865.pd
Basic Methods for Computing Special Functions
This paper gives an overview of methods for the numerical evaluation of special functions, that is, the functions that arise in many problems from mathematical physics, engineering, probability theory, and other applied sciences. We consider in detail a selection of basic methods which are
frequently used in the numerical evaluation of special functions: converging and asymptotic series, including Chebyshev expansions, linear recurrence relations, and numerical quadrature. Several other methods are available and some of these will be discussed in less detail. We give examples of recent software for special functions where these methods are used. We mention a list of new publications on computational aspects of special functions available on our website
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