Sum Rule Predictions Research Articles

CONSTRAINTS ON B→π, K TRANSITION FORM-FACTORS FROM EXCLUSIVE SEMILEPTONIC D-MESON DECAYS

According to the heavy-quark flavor symmetry, the B→π, K transition form-factors could be related to the corresponding ones of D-meson decays near the zero recoil point. With the recent precisely measured exclusive semileptonic decays D →πℓν and D→K ℓν, we perform a phenomenological study of B →π, K transition form-factors based on this symmetry. Using BK, BZ and Series Expansion parametrizations of the form-factor slope, we extrapolate B →π, K transition form-factors from [Formula: see text] to q2 = 0. It is found that, although being consistent with each other within error bars, the central values of our results for B →π, K form-factors at q2 = 0, [Formula: see text], are smaller than predictions of the QCD light-cone sum rules, but are in good agreements with the ones extracted from hadronic B-meson decays within the SCET framework. Moreover, smaller form-factors are also favored by the QCD factorization approach for hadronic B-meson decays.

Two-parton light-cone distribution amplitudes of tensor mesons

We present a detailed study of the two-parton light-cone distribution amplitudes for $1\,^3P_2$ nonet tensor mesons. The asymptotic two-parton distribution amplitudes of twist-2 and twist-3 are given. The decay constants $f_T$ and $f_T^\bot$ defined by the matrices of non-local operators on the lightcone are estimated using the QCD sum rule techniques. We also study the decay constants for $f_2(1270)$ and $f_2^\prime(1525)$ based on the hypothesis of tensor meson dominance together with the data of $\Gamma(f_2\to \pi\pi)$ and $\Gamma(f'_2\to K\bar K)$ and find that the results are in accordance with the sum rule predictions.

Spin12+, spin32+, and transition magnetic moments of low lying and charmed baryons

Magnetic moments of the low lying and charmed spin 1/2^+ and spin 3/2^+ baryons have been calculated in the SU(4) chiral constituent quark model (\chiCQM) by including the contribution from c \bar c fluctuations. Explicit calculations have been carried out for the contribution coming from the valence quarks, "quark sea" polarizations and their orbital angular momentum. The implications of such a model have also been studied for magnetic moments of the low lying spin 3/2^+ \to 1/2^+ and 1/2^+ \to 1/2^+ transitions as well as the transitions involving charmed baryons. We are able to achieve an excellent agreement with data for the case of low lying spin 1/2^+ baryons and spin 3/2^+ baryons. For the spin 1/2^+ and spin 3/2^+ charmed baryon magnetic moments, our results are consistent with the predictions of the QCD sum rules, Light Cone sum rules and Spectral sum rules. For the cases where "light" quarks dominate in the valence structure, the sea and orbital contributions are found to be fairly significant however, they cancel in the right direction to give the correct magnitude of the total magnetic moment. On the other hand, when there is an excess of "heavy" quarks, the contribution of the "quark sea" is almost negligible. The effects of configuration mixing and quark masses have also been investigated.

Quantifying the strength and asymmetry of giant resonances in the photorecombination ofSc3+and the photoionization ofSc2+

We report on strong interference effects for the dominant, highly correlated, broad, and asymmetric 3p53d2(2F5/2,7/2o) giant resonances in the photorecombination of Sc3+. Using a nonorthogonal perturbative multiconfiguration Breit-Pauli approach, we present theoretical photorecombination cross sections that are in line with the Test Storage Ring measurements of Schippers et al. In order to reproduce the observed asymmetric resonance profiles near threshold, it was necessary to include resonance-continuum interference. Also, we present Sc2+ photoionization cross sections that agree with the Advance Light Source measurements of Schippers et al. This perturbative method is based on analytical expressions for the cross sections in terms of computed energies and transition rates, thereby directly determining resonance strengths and Fano asymmetry parameters. Of particular note, our reported absolute cross sections are in excellent agreement with experimental results, in contrast to all previous theoretical calculations. Furthermore, the apparent violation of the sum rule prediction, determined both from our integrated photoionization cross sections and from experimental results, is found to be due to radiative damping of narrow resonances.

Semileptonic form factors D $ \rightarrow$ $ \pi$ , K and B $ \rightarrow$ $ \pi$ , K from a fine lattice

We extract the form factors relevant for semileptonic decays of D and B mesons from a relativistic computation on a fine lattice in the quenched approximation. The lattice spacing is a=0.04 fm (corresponding to a^{-1}=4.97 GeV), which allows us to run very close to the physical B meson mass, and to reduce the systematic errors associated with the extrapolation in terms of a heavy quark expansion. For decays of D and D_s mesons, our results for the physical form factors at q^2=0 are as follows: f_+^{D to pi}(0)= 0.74(6)(4), f_+^{D to K}(0)= 0.78(5)(4) and f_+^{D_s to K}(0)=0.68(4)(3). Similarly, for B and B_s we find: f_+^{B to pi}(0)=0.27(7)(5), f_+^{B to K}(0)=0.32(6)(6) and f_+^{B_s to K}(0)=0.23(5)(4). We compare our results with other quenched and unquenched lattice calculations, as well as with light-cone sum rule predictions, finding good agreement.

Formula omitted], [formula omitted] and [formula omitted] from (semi-)leptonic [formula omitted]-decays: Signals of New Physics?

We confront the recent improved measurements of the D(s) (semi-)leptonic decays with Lattice QCD (LQCD) with nf=3 flavours and QCD spectral sum rules (QSSR) predictions. D→μνμ leptonic width data compared with theoretical determinations of fD, leads to the value of the CKM mixing angle: |Vcd|=0.230(10)exp(9)th. Measured ratio of the D semi-leptonic widths combined with LQCD and QSSR predictions leads to the average |Vcd|/|Vcs|=0.2175(88), and then to |Vcs|=1.068(47). We consider the previous determinations as improvements of the existing estimates. Using the average data of the Ds→μνμ (respectively Ds→τντ) branching ratios, one obtains: |Vcs|fDsμ=(259±12) MeV (respectively |Vcs|fDsτ=(274±13) MeV), which can be compared with the average of the Standard Model (SM) values from LQCD and QSSR fDs=(240±7) MeV. If one uses the present determination of |Vcs|, there is an agreement with the SM prediction within 1σ. If instead, we impose the unitarity constraint |Vcs|⩽1, or assume (as frequently done) |Vcs|=|Vud|, we would obtain a deviation from the SM expectations ranging from 1.5 to 3σ, therefore, signaling some New Physics beyond the SM.

Can one control systematic errors of QCD sum rule predictions for bound states?

We study the possibility to control systematic errors of the ground-state parameters obtained by Shifman–Vainshtein–Zakharov (SVZ) sum rules, making use of the harmonic-oscillator potential model as an example. In this case, one knows the exact solution for the polarization operator, which allows one to obtain both the OPE to any order and the parameters (masses and decay constants) of the bound states. We determine the parameters of the ground state making use of the standard procedures of the method of QCD sum rules, and compare the obtained results with the known exact values. We show that in the situation when the continuum contribution to the polarization operator is not known and is modelled by an effective continuum, the method of sum rules does not allow to control the systematic errors of the extracted ground-state parameters.

ΛΛinteractions in finite-density QCD sum rules

The properties of \ensuremath{\Lambda} hyperons in pure \ensuremath{\Lambda} matter are studied with the finite-density quantum chromodynamics (QCD) sum rule approach. The first-order quark and gluon condensates in \ensuremath{\Lambda} nuclear matter are deduced from the chiral perturbation theory. The sum-rule predictions are sensitive to the four-quark condensates, $\ensuremath{\langle}\overline{q}q{\ensuremath{\rangle}}_{\ensuremath{\rho}}^{2}$ and $\ensuremath{\langle}\overline{q}q\ensuremath{\rangle}{}_{\ensuremath{\rho}}\ensuremath{\langle}\overline{s}s\ensuremath{\rangle}{}_{\ensuremath{\rho}}$, and the $\ensuremath{\pi}N$ sigma term. When $\ensuremath{\langle}\overline{q}q{\ensuremath{\rangle}}_{\ensuremath{\rho}}^{2}$ is nearly independent of density and $\ensuremath{\langle}\overline{q}q\ensuremath{\rangle}{}_{\ensuremath{\rho}}\ensuremath{\langle}\overline{s}s\ensuremath{\rangle}{}_{\ensuremath{\rho}}$ depends strongly on density, we can obtain weakly attractive $\ensuremath{\Lambda}\ensuremath{\Lambda}$ potentials (about several MeV) in the low \ensuremath{\Lambda} density region, which agrees with the information from the latest double \ensuremath{\Lambda} hypernucleus experiments. The nearly no-density dependence of $\ensuremath{\langle}\overline{q}q{\ensuremath{\rangle}}_{\ensuremath{\rho}}^{2}$ and strong density dependence of $\ensuremath{\langle}\overline{q}q\ensuremath{\rangle}{}_{\ensuremath{\rho}}\ensuremath{\langle}\overline{s}s\ensuremath{\rangle}{}_{\ensuremath{\rho}}$ can be explained naturally if the properties of $\ensuremath{\langle}\overline{q}q{\ensuremath{\rangle}}_{\ensuremath{\rho}}^{2}$ and $\ensuremath{\langle}\overline{q}q\ensuremath{\rangle}{}_{\ensuremath{\rho}}\ensuremath{\langle}\overline{s}s\ensuremath{\rangle}{}_{\ensuremath{\rho}}$ are assumed to be similar to those of $\ensuremath{\pi}\ensuremath{\pi}$ and $\overline{K}K$ in nuclear medium, respectively.

Form factors from light-cone sum rules withB-meson distribution amplitudes

New sum rules for B{yields}{pi},K and B{yields}{rho},K* form factors are derived from the correlation functions expanded near the light cone in terms of B-meson distribution amplitudes. The contributions of quark-antiquark and quark-antiquark-gluon components in the B meson are taken into account. Models for the B-meson three-particle distribution amplitudes are suggested, based on QCD sum rules in heavy-quark effective theory. Employing the new light-cone sum rules, we calculate the form factors at small momentum transfers, including SU(3)-violation effects. The results agree with the predictions of the conventional light-cone sum rules.

QCD tests of the puzzling scalar mesons

Motivated by several recent data, we test the QCD spectral sum rules (QSSR) predictions based on different proposals ($\overline{q}q$, $\overline{q}\overline{q}qq$, and gluonium) for the nature of scalar mesons. In the $I=1$ and $1/2$ channels, the unusual wrong splitting between the ${a}_{0}(980)$ and $\ensuremath{\kappa}(900)$ and the ${a}_{0}(980)$ width can be understood from QSSR within a $\overline{q}q$ assignment. However, none of the $\overline{q}q$ and $\overline{q}\overline{q}qq$ results can explain the large $\ensuremath{\kappa}$ width, which may suggest that it can result from a strong interference with nonresonant backgrounds. In the $I=0$ channel, QSSR and some low-energy theorems (LET) require the existence of a low mass gluonium ${\ensuremath{\sigma}}_{B}(1\text{ }\text{ }\mathrm{GeV})$ coupled strongly to Goldstone boson pairs which plays in the $U(1{)}_{V}$ channel, a similar role as the ${\ensuremath{\eta}}^{\ensuremath{'}}$ for the value of the $U(1{)}_{A}$ topological charge. The observed $\ensuremath{\sigma}(600)$ and ${f}_{0}(980)$ mesons result from a maximal mixing between the gluonium ${\ensuremath{\sigma}}_{B}$ and $\overline{q}q$ (1 GeV) mesons, a mixing scheme which passes several experimental tests. Okubo-Zweig-Izuki (OZI) violating $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, ${D}_{s}\ensuremath{\rightarrow}3\ensuremath{\pi}$ decays, and $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}S$ glueball filter processes may indicate that the ${f}_{0}(1500)$, ${f}_{0}(1710)$, and ${f}_{0}(1790)$ have significant gluonium components in their wave functions, while the ${f}_{0}(1370)$ is mostly $\overline{q}q$. Tests of these results can be provided by the measurements of the pure gluonium ${\ensuremath{\eta}}^{\ensuremath{'}}\ensuremath{\eta}$ and $4\ensuremath{\pi}$ specific $U(1{)}_{A}$ decay channels.

Determination ofπ±meson polarizabilities from theγγ→π+π−process

A fit of the experimental data to the total cross section of the process $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ in the energy region from threshold to 2500 MeV has been carried out using dispersion relations with subtractions for the invariant amplitudes, where the dipole and the quadrupole polarizabilities of the charged pion are free parameters. As a result, the sum and the difference of the electric and magnetic dipole and quadrupole polarizabilities of the charged pion have been found: $({\ensuremath{\alpha}}_{1}+{\ensuremath{\beta}}_{1}){}_{{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}}=(0.{18}_{\ensuremath{-}0.02}^{+0.11})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}{\mathrm{fm}}^{3},({\ensuremath{\alpha}}_{1}\ensuremath{-}{\ensuremath{\beta}}_{1}){}_{{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}}=(13.{0}_{\ensuremath{-}1.9}^{+2.6})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}{\mathrm{fm}}^{3},({\ensuremath{\alpha}}_{2}+{\ensuremath{\beta}}_{2}){}_{{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}}=(0.133\ifmmode\pm\else\textpm\fi{}0.015)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}{\mathrm{fm}}^{5},({\ensuremath{\alpha}}_{2}\ensuremath{-}{\ensuremath{\beta}}_{2}){}_{{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}}=(25.{0}_{\ensuremath{-}0.3}^{+0.8})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}{\mathrm{fm}}^{5}$. These values agree with the dispersion sum rule predictions. The value found for the difference of the dipole polarizabilities is consistent with the results obtained from scattering of high energy ${\ensuremath{\pi}}^{\ensuremath{-}}$ mesons off the Coulomb field of heavy nuclei [Yu. M. Antipov et al., Phys. Lett. B121, 445 (1983)] and from radiative ${\ensuremath{\pi}}^{+}$ photoproduction from the proton at MAMI [J. Ahrens et al., Eur. Phys. J. A 23, 113 (2005)], whereas it is at variance with the recent calculations in the framework of chiral perturbation theory.

Symmetry relations for heavy-to-light meson form factors at large recoil

The description of large-recoil heavy-to-light meson form factors is reviewed in the framework of soft-collinear effective theory. At leading power in the heavy-quark expansion, three classes of approximate symmetry relations arise. The relations are compared to experimental data for D → K* and Ds → φ form factors, and to light-cone QCD sum rule predictions for B → π and B → ρ form factors. Implications for the extraction of |Vub| from semileptonic B → ρ decays are discussed.

The gVσγ coupling constants in hadron electrodynamics

Recent measurements of the branching ratios for the decays ω→ π 0 π 0 γ and ρ 0→ π 0 π 0 γ lead to coupling constants of the Vσγ interaction ( V is a vector meson) one order of magnitude smaller than previously assumed to describe the threshold cross section of γ+ p→ p+ ρ 0 and the HERMES effect. The new g 2 Vσγ couplings are in contradiction with the predictions of the QCD sum rules, but are in agreement with vector meson dominance estimation of the σ→ γγ width.

Triple ionization of lithium by electron impact.

Ejection of the three electrons from lithium in a single electron collision has been observed for the first time. Triply charged lithium was observed in an ion time-of-flight spectrum following electron impact on a sample of ultracold, trapped lithium. The higher signal/background afforded by the trap environment made the observation of Li3+ possible. We measured the ratios of triple-to-double and double-to-single ionization at an impact energy of 1000 eV. The 3+/2+ ratio is approximately 0.001, a value 2 orders of magnitude lower than semiempirical predictions. We present a simple method that uses photoionization data combined with sum-rule analysis to predict the asymptotic charge-state ratios. The sum-rule predictions compare reasonably with experiment and shake calculations, but disagree sharply with the semiempirical estimates.

Random-phase approximation study of collective excitations in the Bose-Fermi mixed condensate of alkali-metal gases

We perform Random Phase Approximation (RPA) study of collective excitations in the bose-fermi mixed degenerate gas of Alkali-metal atoms at T=0. The calculation is done by diagonalization in a model space composed of particle-hole type excitations from the ground state, the latter being obtained from the coupled Gross-Pitaevskii and Thomas-Fermi equations. We investigate strength distributions for different combinations of bose and fermi multipole ($L$) operators with $L=0,1,2,3$. Transition densities and dynamical structure factors are calculated for collective excitations. Comparison with the sum rule prediction for the collective frequency is given. Time dependent behavior of the system after an external impulse is studied.

Exploring light-cone sum rules for pion and kaon form factors

We analyze the higher-twist effects and the SU(3)-flavour symmetry breaking in the correlation functions used to calculate form factors of pseudoscalar mesons in the QCD light-cone sum rule approach. It is shown that the Ward identities for these correlation functions yield relations between twist-4 two- and three-particle distribution amplitudes. In addition to the relations already obtained from the QCD equations of motions, we have found a new one. With the help of these relations, the twist-4 contribution to the light-cone sum rule for the pion electromagnetic form factor is reduced to a very simple form. Simultaneously, we correct a sign error in the earlier calculation. The updated light-cone sum rule prediction for the pion form factor at intermediate momentum transfers is compared with the recent Jefferson Lab data. Furthermore, from the correlation functions with strange-quark currents the kaon electromagnetic form factor and the $K\to \pi$ weak transition form factors are predicted with $O(m_s)\sim O(m_K^2)$ accuracy.

Measurements of the Q2-dependence of the proton and neutron spin structure functions g1p and g1n

The structure functions g 1 p and g 1 n have been measured over the range 0.014< x<0.9 and 1< Q 2<40 GeV 2 using deep-inelastic scattering of 48 GeV longitudinally polarized electrons from polarized protons and deuterons. We find that the Q 2 dependence of g 1 p ( g 1 n ) at fixed x is very similar to that of the spin-averaged structure function F 1 p ( F 1 n ). From an NLO QCD fit to all available data we find Γ 1 p − Γ 1 n =0.176±0.003±0.007 at Q 2=5 GeV 2, in agreement with the Bjorken sum rule prediction of 0.182±0.005.

Comment on the heavy→light form factors

We propose a simple parameterization for the form factors in heavy to light decays, which satisfies the heavy quark scaling laws and avoids introducing the explicit “dipole” form. The illustration is provided with the set of lattice data for B→ π semileptonic decay. The resulting shape of the form factor also agrees with the QCD sum rule predictions.

Complete scissors mode strength in heavy deformed odd-mass nuclei: a case study of 165Ho and 169Tm

The low-energy dipole strength distributions in 165Ho and 169Tm have been studied in nuclear resonance fluorescence experiments at the S-DALINAC utilizing a Euroball Cluster detector. In the energy interval between 2.5 and 4.0 MeV, where the scissors mode is expected, 35 ground state transitions could be observed in 165Ho and 53 in 169Tm. Assuming M1 character for all these transitions corresponds to ΣB(M1) ↑= 1.54(23), μ N 2 and ΣB(M1) ↑= 2.15(63), μ N 2 for 165Ho and 169Tm, respectively. A statistical analysis is applied to the measured spectra which is capable of reconstructing the complete strength, including contributions of transitions below the observation limit, with the ratio between M1 and E1 excitations and their total strengths taken as an average over the even-mass neighbours. This results in summed M1 transition strengths of ΣB(M1) ↑= 3.54 −0.95 +0.75, μ N 2 ( 165Ho) and ΣB(M1) ↑= 3.36 −0.57 +1.00 μ N 2 ( 169Tm). The large variations of the summed dipole strength and the fragmentation in other deformed odd-mass nuclei can be reproduced by the same statistical ansatz. The total low-lying M1 strength in heavy deformed odd-mass nuclei is in agreement with the findings in the neighbouring even-mass nuclides as well as with sum-rule predictions.

Isospin Mixing in the Isobaric Analog State Derived from the (p,nIASp̃) Reaction on140Ce,172,174,176Yb, and208Pb

An exclusive coincidence experiment using the $({p,n}_{\mathrm{IAS}}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{p})$ reaction on ${}^{140}\mathrm{Ce}$, ${}^{172,174,176}\mathrm{Yb}$, and ${}^{208}\mathrm{Pb}$ was carried out for the first time by measuring decay protons from the isobaric analog states (IAS). Spreading widths of the IAS are deduced from the escape and total widths. The results show a strong isospin dependence which can be explained by the isospin mixing effect due to the coupling to the ${T}_{0}$ component among three multiplets ${T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}T}_{0}\ensuremath{-}1$, ${T}_{0}$, and ${T}_{0}+1$ of isovector monopole states in daughter nuclei. Empirical isospin mixing probabilities are found to be consistent with microscopic sum rule predictions.