Search results for "Sum rule in quantum mechanics"
showing 10 items of 153 documents
Integrated photoabsorption strength and sum rules for a bound Dirac particle
1985
Relativistic effects in the integrated total photoabsorption cross section are discussed using a simple model of a Dirac particle bound in a central potential of scalar or vector type. The integrated strength is calculated explicitly and compared to a new relativistic extension of the TRK-sum rule using positive energy projection and to predictions from dispersion relations. M1 and E2 sum rules are also considered. In all cases the integrated strength exceeds the classical sum rule up to a few percent. The dispersion sum rule cannot be compared directly to the integrated strength since it contains a negative contribution from pair production in the potential field which is of the order of a…
Muonic-hydrogen Lamb shift: Dispersing the nucleon-excitation uncertainty with a finite-energy sum rule
2013
We assess the two-photon exchange contribution to the Lamb shift in muonic hydrogen with forward dispersion relations. The subtraction constant (T) over bar (0, Q(2)) that is necessary for a dispersive evaluation of the forward doubly virtual Compton amplitude, through a finite energy sum rule, is related to the fixed J = 0 pole generalized to the case of virtual photons. We evaluated this sum rule using excellent virtual photoabsorption data that are available. We find that the "proton polarizability correction" to the Lamb shift in muonic hydrogen is -(40 +/- 5) mu eV. We conclude that nucleon structure-dependent uncertainty by itself is unlikely to resolve the large (300 mu eV) discrepan…
Computing the dipole polarizability of 48Ca with increased precision
2018
We compute the electric dipole polarizability of 48Ca with an increased precision by including more correlations than in previous studies. Employing the coupled-cluster method we go beyond singles and doubles excitations and include leading-order three-particle-three-hole (3p-3h) excitations for the ground state, excited states, and the similarity transformed operator. We study electromagnetic sum rules, such as the bremsstrahlung sum rule m_0 and the polarizability sum rule alpha_D using interactions from chiral effective field theory. To gauge the quality of our coupled-cluster approximations we perform several benchmarks with the effective interaction hyperspherical harmonics approach in…
The Kadanoff–Baym approach to double excitations in finite systems
2011
We benchmark many-body perturbation theory by studying neutral, as well as non-neutral, excitations of finite lattice systems. The neutral excitation spectra are obtained by time-propagating the Kadanoff-Baym equations in the Hartree-Fock and second Born approximations. Our method is equivalent to solving the Bethe-Salpeter equation with a high-level kernel while respecting self-consistently, which guarantees the fulfillment of a frequency sum rule. As a result, we find that a time-local method, such as Hartree-Fock, can give incomplete spectra, while already the second Born, which is the simplest time-nonlocal approximation, reproduces well most of the additional excitations, which are cha…
The spin-dependent structure function g1(x) of the proton from polarized deep-inelastic muon scattering
1997
We present a new measurement of the virtual photon proton asymmetry $A_1^{\rm p}$ from deep inelastic scattering of polarized muons on polarized protons in the kinematic range $0.0008 1$ GeV$^{2}$. A perturbative QCD evolution in next-to-leading order is used to determine $g_1^{\rm p}(x)$ at a constant $Q^2$. At $Q^{2} = 10$ GeV$^{2}$ we find, in the measured range, $\int_{0.003}^{0.7} g_{1}^{\rm p}(x){\rm d}x = 0.139 \pm 0.006~({\rm stat})\pm 0.008~({\rm syst)} \pm 0.006~({\rm evol})$. The value of the first moment $\Gamma_{1}^{\rm p} = \int_{0}^{1} g_{1}^{\rm p}(x){\rm d}x$ of $g_{1}^{\rm p}$ depends on the approach used to describe the behaviour of $g_{1}^{\rm p}$ at low $x$. We find tha…
QCD condensates from tau-decay data: A functional approach
2004
We study a functional method to extract the V − A condensate of dimension 6 from a comparison of τ -decay data with the asymptotic space-like QCD prediction. Our result is in agreement within errors with that from conventional analyses based on finite energy sum rules.
Confronting QCD with the experimental hadronic spectral functions from tau-decay
2009
The (non-strange) vector and axial-vector spectral functions extracted from $\tau $-decay by the ALEPH collaboration are confronted with QCD in the framework of a Finite Energy QCD sum rule (FESR) involving a polynomial kernel tuned to suppress the region beyond the kinematical end point where there is no longer data. This effectively allows for a QCD FESR analysis to be performed beyond the region of the existing data. Results show excellent agreement between data and perturbative QCD in the remarkably wide energy range $s = 3 - 10 {GeV}^2$, leaving room for a dimension $d$ =4 vacuum condensate consistent with values in the literature. A hypothetical dimension $d$=2 term in the Operator Pr…
Chiral sum rules and duality in QCD
1998
The ALEPH data on the vector and axial-vector spectral functions, extracted from tau-lepton decays is used in order to test local and global duality, as well as a set of four QCD chiral sum rules. These are the Das-Mathur-Okubo sum rule, the first and second Weinberg sum rules, and a relation for the electromagnetic pion mass difference. We find these sum rules to be poorly saturated, even when the upper limit in the dispersion integrals is as high as $3 GeV^{2}$. Since perturbative QCD, plus condensates, is expected to be valid for $|q^{2}| \geq \cal{O}$$(1 GeV^{2})$ in the whole complex energy plane, except in the vicinity of the right hand cut, we propose a modified set of sum rules with…
Finite Energy Sum Rules with Legendre Polynomial Kernels
2016
Abstract In this note we report about a method to deal with finite energy sum rules. With a reasonable knowledge of the main resonances of the spectrum, the method guarantees that we can find a nice duality matching between the low energy hadronic data and asymptotic QCD at high energies.
The spin structure functiong1pof the proton and a test of the Bjorken sum rule
2016
New results for the double spin asymmetry A(1)(p) and the proton longitudinal spin structure function g(1)(p) are presented. They were obtained by the COMPASS Collaboration using polarised 200 GeV muons scattered off a longitudinally polarised NH3 target. The data were collected in 2011 and complement those recorded in 2007 at 160 GeV, in particular at lower values of x. They improve the statistical precision of g(1)(p)(x) by about a factor of two in the region x less than or similar to 0.02. A next-to-leading order QCD fit to the g(1) world data is performed. It leads to a new determination of the quark spin contribution to the nucleon spin, Delta Sigma, ranging from 0.26 to 0.36, and to a…