Search results for "PERTURBATION"
showing 10 items of 811 documents
Computational determination of the dominant triplet population mechanism in photoexcited benzophenone
2014
In benzophenone, intersystem crossing occurs efficiently between the S-1(n pi(star)) state and the T-1 state of dominant n pi(star) character, leading to excited triplet states after photoexcitation. The transition mechanism between S-1(n pi(star)) and T-1 is still a matter of debate, despite several experimental studies. Quantum mechanical calculations have been performed in order to assess the relative efficiencies of previously proposed mechanisms, in particular, the direct S-1 -> T-1 and indirect S-1 -> T-2(pi pi(star)) -> T-1 ones. Multiconfigurational wave function based methods are used to discuss the nature of the relevant states and also to determine minimum energy paths a…
Diagonalization of indefinite saddle point forms
2020
We obtain sufficient conditions that ensure block diagonalization (by a direct rotation) of sign-indefinite symmetric sesquilinear forms as well as the associated operators that are semi-bounded neither from below nor from above. In the semi-bounded case, we refine the obtained results and, as an example, revisit the block Stokes operator from fluid dynamics.
Dispersion relation bounds forππscattering
2008
Axiomatic principles such as analyticity, unitarity, and crossing symmetry constrain the second derivative of the $\ensuremath{\pi}\ensuremath{\pi}$ scattering amplitudes in some channels to be positive in a region of the Mandelstam plane. Since this region lies in the domain of validity of chiral perturbation theory, we can use these positivity conditions to bound linear combinations of ${\overline{l}}_{1}$ and ${\overline{l}}_{2}$. We compare our predictions with those derived previously in the literature using similar methods. We compute the one-loop $\ensuremath{\pi}\ensuremath{\pi}$ scattering amplitude in the linear sigma model (LSM) using the $\overline{\mathrm{MS}}$ scheme, a result…
S=−1meson-baryon unitarized coupled channel chiral perturbation theory and theS01resonances Λ(1405) and -Λ(1670)
2003
The $s-$wave meson-baryon scattering is analyzed for the strangeness $S=-1$ and isospin I=0 sector in a Bethe-Salpeter coupled channel formalism incorporating Chiral Symmetry. Four channels have been considered: $\pi \Sigma$, $\bar K N$, $\eta \Lambda$ and $K \Xi$. The required input to solve the Bethe-Salpeter equation is taken from lowest order Chiral Perturbation Theory in a relativistic formalism. There appear undetermined low energy constants, as a consequence of the renormalization of the amplitudes, which are obtained from fits to the $\pi\Sigma\to\pi\Sigma$ mass-spectrum, to the elastic $\bar K N \to \bar K N$ and $ \bar K N\to \pi \Sigma$ $t$--matrices and to the $ K^- p \to \eta \…
Threshold Neutral Pion Photoproduction on the Proton
2015
The neutral pion photoproduction on the proton near threshold has a very small scattering cross section when compared to the charged channels, which in ChPT is explained by strong cancellations between the lowest order pieces. Therefore it is very sensitive to higher-order corrections of chiral perturbation theory. We perform a fully covariant calculation up to chiral order p^3 and we investigate the effect of the inclusion of the Delta(1232) resonance as an explicit degree of freedom. We show that the convergence improves, leading to a much better agreement with data at a wide range of energies.
xloops - Automated Feynman diagram calculation
1998
The program package xloops, a general, model independent tool for the calculation of high energy processes up to the two-loop level, is introduced. xloops calculates massive one- and two-loop Feynman diagrams in the standard model and related theories both analytically and numerically. A user-friendly Xwindows frontend is part of the package. xloops relies on the application of parallel space techniques. The treatment of tensor structure and the separation of divergences in analytic expressions is described in this scheme. All analytic calculations are performed with Maple. We describe the mathematical methods and computer algebra techniques xloops uses and give a brief introduction how to …
Sharp estimates and saturation phenomena for a nonlocal eigenvalue problem
2011
Abstract We determine the shape which minimizes, among domains with given measure, the first eigenvalue of a nonlocal operator consisting of a perturbation of the standard Dirichlet Laplacian by an integral of the unknown function. We show that this problem displays a saturation behaviour in that the corresponding value of the minimal eigenvalue increases with the weight affecting the average up to a (finite) critical value of this weight, and then remains constant. This critical point corresponds to a transition between optimal shapes, from one ball as in the Faber–Krahn inequality to two equal balls.
Properties of hyperons in chiral perturbation theory
2009
The development of chiral perturbation theory in hyperon phenomenology has been troubled due to power-counting subtleties and to a possible slow convergence. Furthermore, the presence of baryon-resonances, e.g. the lowest-lying decuplet, complicates the approach, and the inclusion of their effects may become necessary. Recently, we have shown that a fairly good convergence is possible using a renormalization prescription of the loop-divergencies which recovers the power counting, is covariant and consistent with analyticity. Moreover, we have systematically incorporated the decuplet resonances taking care of both power-counting and $consistency$ problems. A model-independent understanding o…
Determination of the chiral couplingsL10andC87from semileptonicτdecays
2008
Using recent precise hadronic {tau}-decay data on the V-A spectral function, and general properties of QCD such as analyticity, the operator product expansion, and chiral perturbation theory, we get accurate values for the QCD chiral order parameters L{sub 10}{sup r}(M{sub {rho}}) and C{sub 87}{sup r}(M{sub {rho}}). These two low-energy constants appear at order p{sup 4} and p{sup 6}, respectively, in the chiral perturbation theory expansion of the V-A correlator. At order p{sup 4} we obtain L{sub 10}{sup r}(M{sub {rho}})=-(5.22{+-}0.06)x10{sup -3}. Including in the analysis the two-loop (order p{sup 6}) contributions, we get L{sub 10}{sup r}(M{sub {rho}})=-(4.06{+-}0.39)x10{sup -3} and C{s…
On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
1986
Consider a fami ly of vector fCelds x~ on the plane. This fami ly depends on a parameter ~ ~ /R A, for some A ~ /~, and is supposed to be 0 ~ in (m,~) 6 /i~ 2X /~A. Suppose that for ~ = O, the vector f i e l d X o has a separatrix loop. This means that X o has an hyperbol ic saddle point s o and that one of the stable separatr ix of 8 o coincides with one of the unstable one. The union of th is curve and s o is the loop ?. A return map is defined on one side of r .