4,498 research outputs found
Upper Bounds on epsilon'/epsilon Parameters B_6^{(1/2)} and B_8^{(3/2)} from Large N QCD and other News
We demonstrate that in the large N approach developed by the authors in
collaboration with Bardeen, the parameters B_6^{(1/2)} and B_8^{(3/2)}
parametrizing the K\to\pi\pi matrix elements _0 and _2 of the
dominant QCD and electroweak operators receive both negative O(1/N) corrections
such that B_6^{(1/2)} < B_8^{(3/2)}<1 in agreement with the recent lattice
results of the RBC-UKQCD collaboration. We also point out that the pattern of
the size of the hadronic matrix elements of all QCD and electroweak penguin
operators Q_i contributing to the K\to \pi \pi amplitudes A_0 and A_2, obtained
by this lattice collaboration, provides further support to our large N
approach. In particular, a very precise lattice result for the matrix element
_0 implies for the corresponding parameter B_8^{(1/2)}=1.0\pm 0.2 to be
compared with large N value B_8^{(1/2)}=1.1\pm 0.1. We discuss briefly the
implications of these findings for the ratio epsilon'/epsilon. In fact, with
the precise value for B_8^{(3/2)} from RBC-UKQCD collaboration, our upper bound
on B_6^{(1/2)} implies epsilon'/epsilon in the SM roughly by a factor of two
below its experimental value (16.6\pm 2.3)\times 10^{-4}. We also briefly
comment on the parameter \hat B_K and the \Delta I=1/2$ rule.Comment: 19 pages, Additional section on results from other large N approaches
added. References added. Conclusions unchanged. Matches the version to appear
in JHE
Isospin-breaking in : Impact of at the Dawn of the 2020s
For direct CP-violation in decays, the usual isospin-breaking
effects at the percent level are amplified by the dynamics behind the rule and conventionally encoded in parameters. The
updated prediction of the
Chiral Perturbation Theory for the strong isospin-breaking due to
mixing confirms such a tendency but is quite sensitive to the
theoretical input value of the low-energy constant corresponding to the
flavour-singlet exchange contribution in this truncated octet scheme.
We rather exploit the phenomenological mixing as a probe for
the non-negligible flavour-singlet component of the physical pole to
find in a complete nonet scheme.
A large central value in the nonet scheme is thus substituted for a large
uncertainty in the octet one. Including the experimental mass
difference as the dominant electromagnetic isospin-breaking, we obtain for the
effective parameter entering the ratio an improved result
to be compared with
used in recent analyses of
. Accordingly, we get a reduction from
to
and thereby
an effective suppression of by isospin-breaking
corrections as large as relative to the recent RBC-UKQCD value.Comment: 18 pages, no figures, typos removed, additional clarifying comments
and one reference added, results unchanged. Version to appear in EPJ
The critical merger distance between two co-rotating quasi-geostrophic vortices
This paper examines the critical merger or strong interaction distance between two equal-potential-vorticity quasi-geostrophic vortices. The interaction between the two vortices depends on five parameters: their volume ratio, their height-to-width aspect ratios and their vertical and horizontal offsets. Due to the size of the parameter space, a direct investigation solving the full quasi-geostrophic equations is impossible. We instead determine the critical merger distance approximately using an asymptotic approach. We associate the merger distance with the margin of stability for a family of equilibrium states having prescribed aspect and volume ratios, and vertical offset. The equilibrium states are obtained using an asymptotic solution method which models vortices by ellipsoids. The margin itself is determined by a linear stability analysis. We focus on the interaction between oblate to moderately prolate vortices, the shapes most commonly found in turbulence. Here, a new unexpected instability is found and discussed for prolate vortices which is manifested by the tilting of vortices toward each other. It implies than tall vortices may merge starting from greater separation distances than previously thought.Publisher PDFPeer reviewe
The shape of vortices in quasi-geostrophic turbulence
Partially supported by the UK EPSRC (Grant GR/N11711)The present work discusses the most commonly occurring shape of the coherent vortical structures in rapidly rotating stably stratified turbulence, under the quasi-geostrophic approximation. In decaying turbulence, these vortices-coherent regions of the materially-invariant potential vorticity-dominate the flow evolution, and indeed the flow evolution is governed by their interactions. An analysis of several exceptionally high-resolution simulations of quasi-geostrophic turbulence is performed. The results indicate that the population of vortices exhibits a mean height-to-width aspect ratio less than unity, in fact close to 0.8. This finding is justified here by a simple model, in which vortices are taken to be ellipsoids of uniform potential vorticity. The model focuses on steady ellipsoids within a uniform background strain flow. This background flow approximates the effects of surrounding vortices in a turbulent flow on a given vortex. It is argued that the vortices which are able to withstand the highest levels of strain are those most likely to be found in the actual turbulent flow. Our calculations confirm that the optimal height-to-width aspect ratio is close to 0.8 for a wide range of background straining flows.Publisher PDFPeer reviewe
Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited
We prove a Cauchy identity for free quasi-symmetric functions and apply it to
the study of various bases. A free Weyl formula and a generalization of the
splitting formula are also discussed.Comment: 21 pages, Latex, 2 figure
The quasi-geostrophic ellipsoidal vortex model
We present a simple approximate model for studying general aspects of vortex interactions in a rotating stably-stratified fluid. The model idealizes vortices by ellipsoidal volumes of uniform potential vorticity, a materially conserved quantity in an inviscid, adiabatic fluid. Each vortex thus possesses 9 degrees of freedom, 3 for the centroid and 6 for the shape and orientation. Here, we develop equations for the time evolution of these quantities for a general system of interacting vortices. An isolated ellipsoidal vortex is well known to remain ellipsoidal in a fluid with constant background rotation and uniform stratification, as considered here. However, the interaction between any two ellipsoids in general induces weak non-ellipsoidal perturbations. We develop a unique projection method, which follows directly from the Hamiltonian structure of the system, that effectively retains just the part of the interaction which preserves ellipsoidal shapes. This method does not use a moment expansion, e.g. local expansions of the flow in a Taylor series. It is in fact more general, and consequently more accurate. Comparisons of the new model with the full equations of motion prove remarkably close.Publisher PDFPeer reviewe
Unwinding relaxation dynamics of polymers
The relaxation dynamics of a polymer wound around a fixed obstacle
constitutes a fundamental instance of polymer with twist and torque and it is
of relevance also for DNA denaturation dynamics. We investigate it by
simulations and Langevin equation analysis. The latter predicts a relaxation
time scaling as a power of the polymer length times a logarithmic correction
related to the equilibrium fluctuations of the winding angle. The numerical
data support this result and show that at short times the winding angle
decreases as a power-law. This is also in agreement with the Langevin equation
provided a winding-dependent friction is used, suggesting that such reduced
description of the system captures the basic features of the problem.Comment: 4 pages, 5 figures. Accepted for publication in Phys. Rev. Let
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