Search results for " Perturbation theory"
showing 10 items of 358 documents
Chiral dynamics in the low-temperature phase of QCD
2014
We investigate the low-temperature phase of QCD and the crossover region with two light flavors of quarks. The chiral expansion around the point $(T,m=0)$ in the temperature vs. quark-mass plane indicates that a sharp real-time excitation exists with the quantum numbers of the pion. An exact sum rule is derived for the thermal modification of the spectral function associated with the axial charge density; the (dominant) pion pole contribution obeys the sum rule. We determine the two parameters of the pion dispersion relation using lattice QCD simulations and test the applicability of the chiral expansion. The time-dependent correlators are also analyzed using the Maximum Entropy Method, yie…
Inverse amplitude method in pi pi scattering in chiral perturbation theory to two loops
2002
The inverse amplitude method is used to unitarize the two loop $\pi\pi$ scattering amplitudes of SU(2) Chiral Perturbation Theory in the $I=0,J=0$, $I=1,J=1$ and $I=2,J=0$ channels. An error analysis in terms of the low energy one-loop parameters $\bar l_{1,2,3,4,}$ and existing experimental data is undertaken. A comparison to standard resonance saturation values for the two loop coefficients $\bar b_{1,2,3,4,5,6} $ is also carried out. Crossing violations are quantified and the convergence of the expansion is discussed.
Double pi(0) photoproduction off the proton at threshold
2003
The reaction $\gamma p \to \pi^0 \pi^0 p$ has been measured using the TAPS BaF$_2$ calorimeter at the tagged photon facility of the Mainz Microtron accelerator. Chiral perturbation theory (ChPT) predicts that close to threshold this channel is significantly enhanced compared to double pion final states with charged pions. In contrast to other reaction channels, the lower order tree terms are strongly suppressed in 2$\pi^0$ photoproduction. The consequence is the dominance of pion loops in the 2$\pi^0$ channel close to threshold - a result that opens new prospects for the test of ChPT and in particular its inherent loop terms. The present measurement is the first which is sensitive enough fo…
Chiral Perturbation Theory
1995
47 páginas, 4 figuras, 4 tablas.-- arXiv:hep-ph/9502366v1
Spinorial formulation of the GW-BSE equations and spin properties of excitons in two-dimensional transition metal dichalcogenides
2021
In many paradigmatic materials, such as transition metal dichalcogenides, the role played by the spin degrees of freedom is as important as the one played by the electron-electron interaction. Thus an accurate treatment of the two effects and of their interaction is necessary for an accurate and predictive study of the optical and electronic properties of these materials. Despite the fact that the GW-BSE approach correctly accounts for electronic correlations, the spin-orbit coupling effect is often neglected or treated perturbatively. Recently, spinorial formulations of GW-BSE have become available in different flavors in material-science codes. However, an accurate validation and comparis…
Time-Independent Canonical Perturbation Theory
2001
First we consider the perturbation calculation only to first order, limiting ourselves to only one degree of freedom. Furthermore, the system is to be conservative, ∂ H∕∂ t = 0, and periodic in both the unperturbed and perturbed case. In addition to periodicity, we shall require the Hamilton–Jacobi equation to be separable for the unperturbed situation. The unperturbed problem H0(J0) which is described by the action-angle variables J0 and w0 will be assumed to be solved. Thus we have, for the unperturbed frequency: $$\displaystyle{ \nu _{0} = \frac{\partial H_{0}} {\partial J_{0}} }$$ (10.1) and $$\displaystyle{ w_{0} =\nu _{0}t +\beta _{0}\;. }$$ (10.2) Then the new Hamiltonian reads, up t…
Chiral corrections to the SU(2) x SU(2) Gell-Mann-Oakes-Renner relation
2010
The next to leading order chiral corrections to the SU(2) x SU(2) Gell-Mann-Oakes- Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order P…
Computation of conical intersections by using perturbation techniques
2005
Multiconfigurational second-order perturbation theory, both in its single-state multiconfigurational second-order perturbation theory (CASPT2) and multistate (MS-CASPT2) formulations, is used to search for minima on the crossing seams between different potential energy hypersurfaces of electronic states in several molecular systems. The performance of the procedures is tested and discussed, focusing on the problem of the nonorthogonality of the single-state perturbative solutions. In different cases the obtained structures and energy differences are compared with available complete active space self-consistent field and multireference configuration interaction solutions. Calculations on dif…
Multiconfigurational second-order perturbation study of the decomposition of the radical anion of nitromethane
2004
The doublet potential energy surfaces involved in the decomposition of the nitromethane radical anion (CH(3)NO(2) (-)) have been studied by using the multistate extension of the multiconfigurational second-order perturbation method (MS-CASPT2) in conjunction with large atomic natural orbital-type basis sets. A very low energy barrier is found for the decomposition reaction: CH(3)NO(2) (-)--[CH(3)NO(2)](-)--CH(3)+NO(2) (-). No evidence has been obtained on the existence of an isomerization channel leading to the initial formation of the methylnitrite anion (CH(3)ONO(-)) which, in a subsequent reaction, would yield nitric oxide (NO). In contrast, it is suggested that NO is formed through the …
Antiproton over proton and K$^-$ over K$^+$ multiplicity ratios at high $z$ in DIS
2020
The $\bar{\rm p} $ over p multiplicity ratio is measured in deep-inelastic scattering for the first time using (anti-) protons carrying a large fraction of the virtual-photon energy, $z>0.5$. The data were obtained by the COMPASS Collaboration using a 160 GeV muon beam impinging on an isoscalar $^6$LiD target. The regime of deep-inelastic scattering is ensured by requiring $Q^2$ > 1 (GeV/$c$)$^2$ for the photon virtuality and $W > 5$ GeV/$c^2$ for the invariant mass of the produced hadronic system. The range in Bjorken-$x$ is restricted to $0.01 < x < 0.40$. Protons and antiprotons are identified in the momentum range $20 ��60$ GeV/$c$. In the whole studied $z$-region, the $\…