Search results for "sum rule"
showing 10 items of 186 documents
Sum rules across the unpolarized Compton processes involving generalized polarizabilities and moments of nucleon structure functions
2018
We derive two new sum rules for the unpolarized doubly virtual Compton scattering process on a nucleon, which establish novel low-$Q^2$ relations involving the nucleon's generalized polarizabilities and moments of the nucleon's unpolarized structure functions $F_1(x,Q^2)$ and $F_2(x,Q^2)$. These relations facilitate the determination of some structure constants which can only be accessed in off-forward doubly virtual Compton scattering, not experimentally accessible at present. We perform an empirical determination for the proton and compare our results with a next-to-leading-order chiral perturbation theory prediction. We also show how these relations may be useful for a model-independent …
The SVZ plasmon
1985
The sum rule technique of Shifman, Vainshtein and Zakharov is applied to a non-relativistic many-body system, the homogeneous, degenerate electron gas. The operator product expansion for the nonrelativistic correlation function is derived and shown to be equivalent in lowest order to a moment expansion. The nonperturbative terms in this expansion characterize the interacting ground state (“vacuum”) of the system. For the electron gas they can be related to the correlation energy which is very well known. Following as close as possible the SVZ procedure the mass of the plasmon (i.e. the dispersion coefficient of the collective plasma excitation) is calculated and compared with results from c…
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…
Study of the D*ρ system using QCD sum rules
2013
In this talk I present a study of the $D^* \rho$ system made by using the method of QCD sum rules. Considering isospin and spin projectors, we investigate the different configurations and obtain three $D^*$ mesons with isospin $I=1/2$, spin $S=0$, $1$, $2$ and with masses $2500\pm 67$ MeV, $2523\pm60$ MeV, and $2439\pm119$ MeV, respectively. The last state can be related to $D^*_2(2460)$ (spin 2) listed by the Particle Data Group, while one of the first two might be associated with $D^*(2640)$, whose spin-parity is unknown. In the case of $I=3/2$ we also find evidences of three states with spin 0, 1 and 2, respectively, with masses $2467\pm82$ MeV, $2420\pm128$ MeV, and $2550\pm56$ MeV.
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…