Sum Rule Analysis Research Articles

Sum-rule inequalities and a toy model paradox

Fundamental inequalities for QCD sum-rules are applied to resolve a paradox recently encountered in a sum-rule calculation [A.A. Penin and A.A. Pivovarov, Phys. Lett. B 357 (1995) 427.]. This paradox was encountered in a toy model known to be free of resonances that yields an apparent resonance using a standard sum-rule stability analysis. Application of the inequalities does not support the existence of a well defined sum-rule calculation, and shows a strong distinction from typical behaviour in QCD.

QCD sum rule for S11(1535)

We propose a new interpolating field for S 11(1535) to determine its mass from QCD sum rules. In the nonrelativistic limit, this interpolating field dominantly reduces to two quarks in the s-wave state and one quark in the p-wave state. An optimization procedure, which makes use of a duality relation, yields the interpolating field which overlaps strongly with the negative-parity baryon and at the same time does not couple at all to the low-lying positive-parity baryon. Using this interpolating field and applying the conventional QCD sum rule analysis, we find that the mass of S 11 is reasonably close to the experimentally known value, even though the precise determination depends on the poorly known quark-gluon condensate. Hence our interpolating field can be used to investigate the spectral properties of S 11(1535).

ϱ - ω mixing via QCD sum rules with finite mesonic widths

Based on the analysis of both Borel and Finite-Energy QCD sum rules, the inclusion of finite mesonic widths leads to a dramatic effect on the predictions for the momentum dependence of the ϱ - ω mixing matrix element. It is shown that the ϱ - ω mixing matrix element traditionally discussed in the literature, has the same sign and similar magnitude in the space-like region as its on-shell value. This contrasts the zero-width result where the mixing matrix element is typically of opposite sign in the space-like region.

QCD sum rule analysis for the Λb → Λc semileptonic decay

The 1 m c and 1 m b corrections to the Λ b → Λ c semileptonic decay are analyzed by QCD sum rules. Within the framework of heavy quark effective theory, the subleading baryonic Isgur-Wise function of Λ b → Λ c has been calculated. It is shown that the corrections due to the 1 m Lagrangian insertion are negligibly small. The sizable 1 m Q effect to the decay lies only in the weak current. The decay spectrum and the branching ratio are given.

0f7/2 proton transfer on 55Mn.

Proton pickup data have been obtained through the {sup 55}Mn({ital d},{sup 3}He){sup 54}Cr ({ital E}{sub {ital d}} = 46 MeV) reaction in the 6{degree}{endash}30{degree} angular range using a magnetic spectrometer with a resolution of {approximately} 40 keV full width at half maximum. Spectroscopic factors associated with transitions to 24 {sup 54}Cr final states ({ital E}{sup {asterisk}}{le} 6.104 MeV) were determined from local, zero-range distorted-wave Born approximation analyses of the measured angular distributions allowing for l = 0, 1, 2, and 3 transfer. A spin-dependent sum-rule analysis of the 0{ital f}{sub 7/2} proton transfer data has been performed using complementary stripping data from a study of the {sup 55}Mn({alpha},{ital t}){sup 56}Fe reaction. The 0{ital f}{sub 7/2} proton transfer data have also been compared to results from a 0{ital f}1{ital p} shell-model calculation based on a new effective interaction for {ital A} = 41{endash}66 nuclei. {copyright} {ital 1996 The American Physical Society.}

Form-factors of semi-leptonic decays of heavy mesons

Semi-leptonic decays of quarkonia to quarkonia (e.g. B c → J /Ψ) offer a unique possibility to investigate the structure of confined systems. A QCD sum rule analysis yields a momentum transfer dependence which is much stronger than predicted by vector meson dominance. It is argued that this is a typical reflection of the bound state nature and its experimental investigation could give important insights into the nature of bound states in a confining theory.

QCD sum rule calculation of [formula omitted] transition form factor

We develop a QCD sum rule analysis of the form factor F γ ∗γ ∗π 0 (q 2, Q 2)in the region where virtuality of one of the spacelike photons is small q 2 ⪡ 1 GeV 2 while another is large: Q 2 ≳ 1 GeV 2. We construct the operator product expansion suitable for this kinematic situation and obtain a QCD sum rule for F γ ∗γ ∗π 0 (0, Q 2) ≡ F γγ ∗π 0 ( Q 2). Our results confirm expectation that the momentum transfer dependence of the leading-order contribution to F γ ∗π 0 ( Q 2) is close to interpolatio between its Q 2 = 0 value fixed by the axial anomaly and 1 Q 2 pQCD behaviour for large Q 2. Our approach, in contrast to pQCD, does not require explicit assumptions about the shape of the pion distribution amplitude ϕ π ( x). The absolute value of the 1 Q 2 term obtained in this paper favours ϕ π ( x) close to the asymptotic form ϕ π as( x) = 6 f π x(1 − x).

Partitioning of the nonfixed excess energy and the reverse critical energy in CH2OH+→CHO++H2: A classical trajectory study

Dynamics of the four-centered elimination reaction CH2OH+→CHO++H2 has been investigated over the internal energy range 4.6–5.9 eV using the classical trajectory method. A realistic semiempirical potential reported previously [J. Chem. Phys. (in press, 1996)] has been used for the calculation. It has been found that the disposal of the nonfixed excess energy at the transition state and of the reverse critical energy can be considered independently as manifest in the sum rule analysis. The former is determined statistically while the latter dynamically. Based on the above idea, a method to determine the kinetic energy release distribution originating only from the reverse critical energy has been developed.

QCD sum rule analysis of the decays B-->Kl+l- and B-->K*l+l-

We use QCD sum rules to calculate the hadronic matrix elements governing the rare decays B\ensuremath{\rightarrow}K${\mathcal{l}}^{+}$${\mathcal{l}}^{\mathrm{\ensuremath{-}}}$ and B\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{*}}$${\mathcal{l}}^{+}$${\mathcal{l}}^{\mathrm{\ensuremath{-}}}$ induced by the flavor-changing neutral current b\ensuremath{\rightarrow}s transition. We also study relations among semileptonic and rare B\ensuremath{\rightarrow}${\mathit{K}}^{(\mathrm{*})}$ decay form factors. The analysis of the invariant mass distribution of the lepton pair in B\ensuremath{\rightarrow}${\mathit{K}}^{(\mathrm{*})}$${\mathcal{l}}^{+}$${\mathcal{l}}^{\mathrm{\ensuremath{-}}}$ and of the angular asymmetry in B\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{*}}$${\mathcal{l}}^{+}$${\mathcal{l}}^{\mathrm{\ensuremath{-}}}$ provides us with interesting tests of the standard model and its extensions. \textcopyright{} 1996 The American Physical Society.

QCD sum rule analysis of the mixed-isospin vector current correlator reexamined.

The mixed-isospin vector current correlator, $\langle 0\vert T(V^\rho_\mu V^\omega_\nu )\vert 0\rangle$ is evaluated using both QCD sum rules and Chiral Perturbation Theory (ChPT) to one-loop order. The sum rule treatment is a modification of previous analyses necessitated by the observation that those analyses produce forms of the correlator that fail to be dominated, near $q^2=0$, by the most nearby singularities. Inclusion of contributions associated with the $\phi$ meson rectify this problem. The resulting sum rule fit provides evidence for a significant direct $\omega\rightarrow\pi\pi$ coupling contribution in $e^+e^-\rightarrow\pi^+\pi^-$. It is also pointed out that results for the $q^2$-dependence of the correlator cannot be used to provide information about the (off-shell) $q^2$-dependence of the off-diagonal element of the vector meson propagator unless a very specific choice of interpolating fields for the vector mesons is made. The results for the value of the correlator near $q^2=0$ in ChPT are shown to be more than an order of magnitude smaller than those extracted from the sum rule analysis and the reasons why this suggests slow convergence of the chiral series for the correlator given.

In-plane and out-of-plane charge dynamics of high- tc cuprates

We propose a theoretical expression for the k- and ω-dependent dielectric function of a stack of two-dimensional layers coupled along the direction perpendicular to the layers, and discuss some of its properties. We argue that the plasma frequencies at k = 0 should correspond to those which are experimentally obtained from optical measurements on e.g. La 1 − x Sr x CuO 4 via the f- sum rule analysis, regardless of the fact that such systems are strongly correlated. We discuss some of the ramifications due to strong anisotropy of the charge transport in these systems, and the lack of coherence for the transport in the direction perpendicular to the layers.

A study of the absolute photoabsorption, photoionisation and photodissociation cross sections and the photoionisation quantum efficiency of sulphur dioxide from the ionisation threshold to 400 Å

The absolute photoabsorption, photoionisation and photodissociation cross sections and the photoionisation quantum efficiency of sulphur dioxide have been measured using a double ion chamber and monochromated synchrotron radiation. The absorption spectrum exhibits extensive vibrational structure extending from the ionisation threshold to approximately 750 Å. Many of the features can be arranged into vibrational progressions with spacings characteristic of the symmetrical stretching mode, in agreement with previous interpretations. The photoionisation quantum efficiency increases rapidly to reach a value of approximately unity around 880 Å, but at shorter wavelengths local minima are observed around 760, 820 and 870 Å. Some of the variations in the photoionisation quantum efficiency appear to be correlated with the absorption vibrational structure. A sum rule analysis has been carried out by combining the present absolute photoabsorption measurements with similar data covering the remaining wavelength regions.

X-ray magnetic circular dichroism spectroscopy of transition metal thin films

A review is given of the principles underlying X-ray magnetic circular dichroism (XMCD) spectroscopy. The main strengths of the technique are highlighted. They are the quantitative determination of spin and orbital magnetic moments and their anisotropies through sum rule analysis of experimental spectra. A discussion is given why and how the spin and orbital magnetic moments in transition metal thin films are modified relative to the bulk. Selected XMCD results for thin films are discussed. “Non-magnetic” spacer layers sandwiched between magnetic layers are shown to become magnetic. The orbital moment is shown to become anisotropic in thin films, revealing that it is the microscopic origin of the magnetocrystalline anisotropy.

A study of the absolute photoabsorption, photoionisation and photodissociation cross sections and the photoionisation quantum efficiency of carbon dioxide from the ionisation threshold to 345 Å

Abstract The absolute photoabsorption, photoionisation and photodissociation cross sections and the photoionisation quantum efficiency of sulphur dioxide have been measured using a double ion chamber and monochromated synchrotron radiation. The absorption spectrum exhibits extensive vibrational structure extending from the ionisation threshold to approximately 750 A. Many of the features can be arranged into vibrational progressions with spacings characteristic of the symmetrical stretching mode, in agreement with previous interpretations. The photoionisation quantum efficiency increases rapidly to reach a value of approximately unity around 880 A, but at shorter wavelengths local minima are observed around 760, 820 and 870 A. Some of the variations in the photoionisation quantum efficiency appear to be correlated with the absorption vibrational structure. A sum rule analysis has been carried out by combining the present absolute photoabsorption measurements with similar data covering the remaining wavelength regions.

Comment on "Equation of state and phase diagrams for dense multi-ionic mixture plasmas"

An equation of state for dense fluid binary-ionic mixture (BIM) plasmas was derived recently by Ogata, Iyetomi, Ichimaru, and Van Horn [Phys. Rev. E 48, 1344 (1993)] from extensive Monte Carlo simulations data. They emphasized in particular the significance of finding negative deviation from the linear-mixing approximation. In this Comment, I show that the important features of their results are the outcome of their particular choice for the equation of state of the one-component plasma, which has relatively large error bars that have not been properly taken into account and are not necessarily borne out by their data for the binary mixtures. I repeated their analysis of their same data for the bindary mixtures, but used another, comparable, one-component plasma fluid equation of state to find always positive deviations from linear mixing, in contradiction also with the sum-rule analysis of their free energy with respect to the zero separation of the screening potentials.

Comparison of branching ratio and sum-rule analyses of magnetic circular dichroism in x-ray-absorption spectroscopy.

Two localized picture methods of analyzing the magnetic circular dichroism in x-ray absorption will be applied to experimental results: the branching ratio (BR) and sum rule (SR) approaches. A derivation of the BR formulas and detailed comparison to the SR expressions will be made, including error estimations. The BR approach will be seen to be a limiting case form of the SR spin-moment expression and provide a simple picture of the underlying physics in magnetic x-ray circular dichroism absorption in 3{ital d} magnetic materials.

Δ(1232) in nuclei and QCD sum rules

We show how pion-nucleus scattering data can be used to constrain four-quark in-medium matrix elements, whose uncertainty is currently the most important problem inhibiting the use of QCD sum rules to study hadrons in nuclear matter, a problem related to early-universe phase transitions. We take an important step towards determining the matrix elements by extracting a value for a particular linear combination using the Isobar-Doorway model propagator of the in-medium \ensuremath{\Delta}(1232) and a QCD sum rule analysis of both the free and in-medium \ensuremath{\Delta}.

Testing QCD sum rule techniques on the lattice.

Results for the first test of the ``crude'' QCD continuum model, commonly used in QCD Sum Rule analyses, are presented for baryon correlation functions. The QCD continuum model is found to effectively account for excited state contributions to the short-time regime of two-point correlation functions and allows the isolation of ground state properties. Confusion in the literature surrounding the physics represented in point-to-point correlation functions is also addressed. These results justify the use of the ``crude'' QCD continuum model and lend credence to the results of rigorous QCD Sum Rule analyses.

Nucleon properties from unconventional interpolating fields.

Interpolating fields, used to excite hadrons from the QCD vacuum in nonperturbative field-theoretic investigations of hadron properties, are explored with an emphasis on unconventional nucleon interpolators. The QCD continuum model for excited state contributions to QCD correlation functions is a central element in extracting the physics contained in these alternate correlation functions. The analysis confirms the independence of nucleon properties obtained from different interpolating fields. However, this independence comes about in a trivial manner. These results provide a resolution to the long standing debate over the optimal nucleon interpolating field to be used in QCD Sum Rule analyses.

QCD sum rules and chiral logarithms

Standard QCD sum-rule analyses of the nucleon mass give results that are inconistent with chiral perturbation theory due to an overly simple continuum ansatz on the phenomenological side of the sum rule. We show that a careful treatment of the continuum, including π- N states and other states with virtual pions, resolves the inconsistency associated with chiral logs.