Sum Rule Analysis Research Articles

Light-by-light scattering sum rules in light of new data

We evaluate the light-quark meson contributions to three exact light-by-light scattering sum rules in light of new data by the Belle Collaboration, which recently has extracted the transition form factors of the tensor meson $f_2(1270)$ as well as of the scalar meson $f_0(980)$. We confirm a previous finding that the $\eta, \eta^\prime$ and helicity-2 $f_2(1270)$ contributions saturate one of these sum rules up to photon virtualities around 1 GeV$^2$. At larger virtualities, our sum rule analysis shows an important contribution of the $f_2(1565)$ meson and provides a first empirical extraction of its helicity-2 transition form factor. Two further sum rules allow us to predict the helicity-0 and helicity-1 transition form factors of the $f_2(1270)$ meson. Furthermore, our analysis also provides an update for the scalar and tensor meson hadronic light-by-light contributions to the muon's anomalous magnetic moment.

Intrinsic and Extrinsic Ferromagnetism in Co-Doped Indium Tin Oxide Revealed Using X-Ray Magnetic Circular Dichroism

The effects of high-temperature annealing on ferromagnetic Co-doped Indium Tin Oxide (ITO) thin films have been investigated using X-ray diffraction (XRD), magnetometry, and X-Ray Magnetic Circular Dichroism (XMCD). Following annealing, the magnetometry results indicate the formation of Co clusters with a significant increase in the saturation magnetization of the thin films arising from defects introduced during cluster formation. However, sum rule analysis of the element-specific XMCD results shows that the magnetic moment at the Co sites is reduced after annealing. The effects of annealing demonstrate that the ferromagnetism observed in the as-deposited Co-doped ITO films arises from intrinsic defects and cannot be related to the segregation of metallic Co clusters.

Isospin breaking in the decay constants of heavy mesons from QCD sum rules

We present a study of the strong isospin-breaking (IB) effect, due in QCD to the difference between $u$- and $d$-quark masses, in the leptonic decay constants of charmed and beauty pseudoscalar and vector mesons using the method of QCD sum rules. We apply the sum-rule analysis to the decay constants of mesons containing one heavy quark and one light quark with the light mass in the range from the average $u/d$ quark mass to the strange-quark mass. We then analyse the dependence of the decay constants on the light quark mass and extract with good accuracy the IB ratios of decay constants at leading order in the mass difference $(m_d - m_u)$, obtaining: $(f_{D^+} - f_{D^0}) / f_{D} = 0.0047 (6)$, $(f_{D^{*+}} - f_{D^{*0}}) / f_{D^*} = 0.0068 (9)$, $(f_{B^0} - f_{B^+}) / f_{B} = 0.0047 (6)$, and $(f_{B^{*0}} - f_{B^{*+}}) / f_{B^*} = 0.0045 (5)$, which yield: $f_{D^+} - f_{D^0} = 0.97 \pm 0.13$ MeV, $f_{D^{*+}} - f_{D^{*0}} = 1.73 \pm 0.27$ MeV, $f_{B^0} - f_{B^+} = 0.90 \pm 0.13$ MeV, $f_{B^{*0}} - f_{B^{*+}} = 0.81 \pm 0.11$ MeV. In the case of the $D$-meson our finding is consistent with recent lattice QCD results, whereas it is much lower in the case of the $B$-meson showing a tension of $\approx 3$ standard deviations.

QCD sum rules for the neutron, Σ , and Λ in neutron matter

The nuclear density dependencies of the neutron and $\Sigma$ and $\Lambda$ hyperons are important inputs in the determination of the neutron star mass as the appearance of hyperons coming from strong attractions significantly changes the stiffness of the equation of state (EOS) at iso-spin asymmetric dense nuclear matter. In-medium spectral sum rules have been analyzed for the nucleon, $\Sigma$, and $\Lambda$ hyperon to investigate their properties up to slightly above the saturation nuclear matter density by using the linear density approximation for the condensates. The construction scheme of the interpolating fields without derivatives has been reviewed and used to construct a general interpolating field for each baryon with parameters specifying the strength of independent interpolating fields. Optimal choices for the interpolating fields were obtained by requiring the sum rules to be stable against variations of the parameters and the result to be consistent with known phenomenology. The optimized result shows that Ioffe's choice is not suitable for the $\Lambda$ hyperon sum rules. It is found that, for the $\Lambda$ hyperon interpolating field, the up and down quark combined into the scalar diquark structure $u^T C \gamma_5 d$ should be emphasized to ensure stable sum rules. The quasi-$\Sigma$ and -$\Lambda$ hyperon energies are always found to be higher than the quasineutron energy in the region $0.5 <\rho/\rho_0<1.5 $ where the linear density approximation in the sum-rule analysis is expected to be reliable.

Evidence of Charge Transfer and Orbital Magnetic Moment in Multiferroic CuFeO2

Soft X-ray absorption spectra (XAS) and magnetic circular dichroism (XMCD) of Fe and Cu L2,3 edges have been measured on the triangular lattice antiferromagnet CuFeO2. By applying sum rule analysis to the XMCD of Fe, the ratio of the orbital to spin magnetic moments is determined to be −0.071. Because the nominal valence of Fe in CuFeO2 was Fe3+ (3d5), the orbital magnetic moment was considered to be zero in the past. However, the present research demonstrates that the orbital magnetic moment of Fe takes a finite value and it is possibly due to Fe4+ (3d4), which is considered to be responsible for the strong magnetic anisotropy and the ferroelectricity. We compare the experimental results with the results of ab initio multiplet calculations based on the configuration interaction theory and discuss the anomalous electronic structures of Fe and Cu ions in CuFeO2.

Searching for hidden-charm baryonium signals in QCD sum rules

We give an explicit QCD sum rule investigation to hidden-charm baryonium states with the quark content $u\bar u d\bar d c\bar c$, spin $J=0/1/2/3$, and of both positive and negative parities. We systematically construct the relevant local hidden-charm baryonium interpolating currents, which can actually couple to various structures, including hidden-charm baryonium states, charmonium states plus two pions, and hidden-charm tetraquark states plus one pion, etc. We do not know which structure these currents couple to at the beginning, but after sum rule analyses we can obtain some information. We find some of them can couple to hidden-charm baryonium states, using which we evaluate the masses of the lowest-lying hidden-charm baryonium states with quantum numbers $J^P=2^-/3^-/0^+/1^+/2^+$ to be around 5.0 GeV. We suggest to search for hidden-charm baryonium states, especially the one of $J=3^-$, in the $D$-wave $J/\psi \pi \pi$ and $P$-wave $J/\psi \rho$ and $J/\psi \omega$ channels in this energy region.

A study of the valence shell absolute photoabsorption, photoionisation and photodissociation cross sections and the photoionisation quantum efficiency of carbonyl sulphide

The absolute photoabsorption, photoionisation and photodissociation cross sections and the photoionisation quantum efficiency of carbonyl sulphide have been measured using a double ion chamber and synchrotron radiation in the energy range from the ionisation threshold to 24eV. In addition to the absorption bands associated with well established Rydberg series, some previously unassigned features have been tentatively attributed to an f-type Rydberg series converging onto the B̃2Σ+ state ionisation threshold. Structure appearing in the photodissociation spectrum has been correlated with that observed in earlier fluorescence yields for emission, due mainly to the CS photofragment, occurring between 160 and 300nm. The photoionisation quantum efficiency reaches a plateau value close to unity for energies above ∼16eV. The predissociation of Rydberg states into neutral fragments does not appear to affect the photoionisation quantum efficiency of carbonyl sulphide to the extent that is commonly observed in other small molecules. A sum rule analysis has been carried out by combining the present absolute photoabsorption measurements with similar data covering the remaining energy regions.

QCD sum rule study of hidden-charm pentaquarks

We study the mass spectra of hidden-charm pentaquarks having spin $J = {1\over2}/{3\over2}/{5\over2}$ and quark contents $uud c \bar c$. We systematically construct all the relevant local hidden-charm pentaquark currents, and select some of them to perform QCD sum rule analyses. We find that the $P_c(4380)$ and $P_c(4450)$ can be identified as hidden-charm pentaquark states composed of an anti-charmed meson and a charmed baryon. Besides them, we also find a) the lowest-lying hidden-charm pentaquark state of $J^P = 1/2^-$ has the mass $4.33^{+0.17}_{-0.13}$ GeV, while the one of $J^P = 1/2^+$ is significantly higher, that is around $4.7-4.9$ GeV; b) the lowest-lying hidden-charm pentaquark state of $J^P = 3/2^-$ has the mass $4.37^{+0.18}_{-0.13}$ GeV, consistent with the $P_c(4380)$ of $J^P = 3/2^-$, while the one of $J^P = 3/2^+$ is also significantly higher, that is above $4.6$ GeV; c) the hidden-charm pentaquark state of $J^P = 5/2^-$ has a mass around $4.5-4.6$ GeV, slightly larger than the $P_c(4450)$ of $J^P = 5/2^+$.

Factorization and dispersion relations for radiative leptonic B decay

Applying the dispersion approach we compute perturbative QCD corrections to the power suppressed soft contribution of $B \to \gamma \ell \nu$ at leading twist. QCD factorization for the $B \to \gamma^{\ast}$ form factors is demonstrated explicitly for the hard-collinear transverse polarized photon at one loop, with the aid of the method of regions. While the one-loop hard function is identical to the matching coefficient of the QCD weak current $\bar u \, \gamma_{\mu \perp} \, (1- \gamma_5) \, b$ in soft-collinear effective theory, the jet function from integrating out the hard-collinear fluctuations differs from the corresponding one entering the factorization formula of $B \to \gamma \ell \nu$. Furthermore, we evaluate the sub-leading power contribution to the $B \to \gamma$ form factors from the three-particle $B$-meson distribution amplitudes (DAs) at tree level. The soft contribution to the $B \to \gamma$ form factors from the three-particle $B$-meson DAs is shown to be of the same power compared with the corresponding hard correction, in contrast to the two-particle counterparts. Numerically the next-to-leading-order QCD correction to the soft two-particle contribution in $B \to \gamma$ form factors will induce an approximately $\left (10 \sim 20 \right) \%$ shift to the tree-level contribution at $\lambda_B(\mu_0)=354 \, {\rm MeV}$. Albeit of power suppression parametrically, the soft two-particle correction can decrease the leading power predictions for the $B \to \gamma$ form factors by an amount of $\left (10 \sim 30 \right) \%$ with the same value of $\lambda_B(\mu_0)$. Employing the phenomenological model of the three-particle $B$-meson DAs inspired by a QCD sum rule analysis, the three-particle contribution to the $B \to \gamma$ form factors is predicted to be of ${\cal O} (1 \%)$, at leading order in $\alpha_s$, with the default theory inputs.

Enhancement of magnetic moment in ZnxFe3−xO4 thin films with dilute Zn substitution

Highly (111)-textured ZnxFe3−xO4 thin films were grown by pulsed laser deposition on silicon substrates. The spin and orbital magnetic moments of the ZnxFe3−xO4 thin films have been obtained by X-ray magnetic circular dichroism (XMCD) and sum rule analysis. The total magnetic moments thus extracted are in good agreement with the values obtained by vibrating sample magnetometer. Both the unquenched orbital moment and the ratio of orbital-to-spin moment first increase significantly with increasing Zn substitution at a low concentration range (0≤x≤0.1), and then decrease at a higher concentration (x = 0.3). The underlying site-specific doping mechanisms involved here have been elucidated by detailed analysis of the XMCD of ZnxFe3−xO4 films. Our work demonstrates a practical means to manipulate the spin-orbit coupling in the ZnxFe3−xO4 thin films via Zn impurity doping.

Mass of heavy-light mesons in a constituent quark picture with partially restored chiral symmetry

We probe effects of the partial chiral symmetry restoration to the mass of heavy-light mesons in a constituent quark model by changing the constituent quark mass of the light quark. Due to the competing effect between the quark mass and the linearly rising potential, whose contribution to the energy increases as the quark mass decreases, the heavy-light meson mass has a minimum value near the constituent quark mass typically used in the vacuum. Hence, the meson mass increases as one decreases the constituent quark mass consistent with recent QCD sum rule analyses, which show an increasing $D$ meson mass as the chiral order parameter decreases.

Dmesons in a magnetic field

We investigate the mass spectra of open heavy flavor mesons in an external constant magnetic field within QCD sum rules. Spectral Ans\"atze on the phenomenological side are proposed in order to properly take into account mixing effects between the pseudoscalar and vector channels, and the Landau levels of charged mesons. The operator product expansion is implemented up to dimension-5 operators. As a result, we find for neutral $D$ mesons a significant positive mass shift that goes beyond simple mixing effects. In contrast, charged $D$ mesons are further subject to Landau level effects, which together with the mixing effects almost completely saturate the mass shifts obtained in our sum rule analysis.

Mass spectra ofZcandZbexotic states as hadron molecules

We construct charmonium-like and bottomonium-like molecular interpolating currents with quantum numbers J(PC)=1(+-) in a systematic way, including both color singlet-singlet and color octet-octet structures. Using these interpolating currents, we calculate two-point correlation functions and perform QCD sum rule analyses to obtain mass spectra of the charmonium-like and bottomonium-like molecular states. Masses of the charmonium-like q_bar c c_bar q molecular states for these various currents are extracted in the range 3.85-4.22 GeV, which are in good agreement with observed masses of the Zc resonances. Our numerical results suggest a possible landscape of hadronic molecule interpretations of the newly-observed Zc states. Mass spectra of the bottomonium-like q_bar b b_bar q molecular states are similarly obtained in the range 9.92-10.48 GeV, which support the interpretation of the Zb(10610) meson as a molecular state within theoretical uncertainties. Possible decay channels of these molecular states are also discussed.

In-situ XMCD evaluation of ferromagnetic state at FeRh thin film surface induced by 1 keV Ar ion beam irradiation and annealing

Surface ferromagnetic state of FeRh thin films irradiated with 1keV Ar ion-beam has been investigated by using soft X-ray Magnetic Circular Dichroism (XMCD). It was revealed that the Fe atoms of the samples were strongly spin-polarized after Ar ion-beam irradiation. Due to its small penetration depth, 1keV Ar ion-beam irradiation can modify the magnetic state at subsurface of the samples. In accordance with the XMCD sum rule analysis, the main component of the irradiation induced ferromagnetism at the FeRh film surface was to be effective spin magnetic moment, and not to be orbital moment. We also confirmed that the surface ferromagnetic state could be produced by thermal annealing of the excessively ion irradiated paramagnetic subsurface of the FeRh thin films. This novel magnetic modification technique by using ion irradiation and subsequent annealing can be a potential tool to control the surface magnetic state of FeRh thin films.

Perturbative QCD in acceptable schemes with holomorphic coupling

Perturbative QCD in mass independent schemes leads in general to running coupling a(Q2) which is nonanalytic (nonholomorphic) in the regime of low spacelike momenta |Q2|≲1 GeV 2. Such (Landau) singularities are inconvenient in the following sense: evaluations of spacelike physical quantities 𝒟(Q2) with such a running coupling a(κQ2)(κ~1) give us expressions with the same kind of singularities, while the general principles of local quantum field theory require that the mentioned physical quantities have no such singularities. In a previous work, certain classes of perturbative mass independent beta functions were found such that the resulting coupling was holomorphic. However, the resulting perturbation series showed explosive increase of coefficients already at N 4 LO order, as a consequence of the requirement that the theory reproduce the correct value of the τ lepton semihadronic strangeless decay ratio rτ. In this paper, we successfully extend the construction to specific classes of perturbative beta functions such that the perturbation series do not show explosive increase of coefficients, the perturbative coupling is holomorphic, and the correct value of rτ is reproduced. In addition, we extract, with Borel sum rule analysis of the V+A channel of the semihadronic strangeless decays of τ lepton, reasonable values of the corresponding D = 4 and D = 6 condensates.

QCD sum rule study of thed*(2380)

We systematically construct $I(J^P)=0(3^+)$ six-quark local interpolating currents without derivative operators. We discuss the best choice of operator, and select three $\Delta$-$\Delta$ like operators to perform QCD sum rule analyses to calculate the mass of the $d^*(2380)$. The mass extracted from this analysis is $M_{d^*} = 2.4\pm0.2$ GeV, consistent with the $d^*(2380)$ mass observed by the WASA detector at COSY. We also obtain a sum-rule lower mass bound $M_{d^*} > 2.25$ GeV. We also consider the effect of mixing of singlet dibaryon fields with the same quantum numbers, and perform the QCD sum rule analysis of the mixed interpolating current and extract the mass of the $d^*(2380)$ and its lower mass bound. With optimized mixing parameters, we find that the mixed current does not change the numerical result significantly.

Ground-state wave function of plutonium in PuSb as determined via x-ray magnetic circular dichroism

Measurements of x-ray magnetic circular dichroism (XMCD) and x-ray absorption near-edge structure (XANES) spectroscopy at the Pu ${M}_{4,5}$ edges of the ferromagnet PuSb are reported. Using bulk magnetization measurements and a sum rule analysis of the XMCD spectra, we determine the individual orbital [${\ensuremath{\mu}}_{\mathrm{L}}=2.8(1){\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{Pu}$] and spin moments [${\ensuremath{\mu}}_{\mathrm{S}}=\ensuremath{-}2.0(1){\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{Pu}$] of the Pu $5f$ electrons. Atomic multiplet calculations of the XMCD and XANES spectra reproduce well the experimental data and are consistent with the experimental value of the spin moment. These measurements of $\ensuremath{\langle}{L}_{z}\ensuremath{\rangle}$ and $\ensuremath{\langle}{S}_{z}\ensuremath{\rangle}$ are in excellent agreement with the values that have been extracted from neutron magnetic form factor measurements, and confirm the local character of the $5f$ electrons in PuSb. Finally, we demonstrate that a split ${M}_{5}$ as well as a narrow ${M}_{4}$ XMCD signal may serve as a signature of $5f$ electron localization in actinide compounds.

Direct observation of ferromagnetism in grain boundary phase of Nd-Fe-B sintered magnet using soft x-ray magnetic circular dichroism

We have investigated the magnetism of the grain boundary (GB) phase in a Nd14.0Fe79.7Cu0.1B6.2 sintered magnet using soft x-ray magnetic circular dichroism (XMCD) at the Fe L2,3-edges. Soft XMCD spectra were measured from the fractured surface that was confirmed to be covered with a thin GB phase by Auger electron spectroscopy. The magnetic moment of Fe in the GB phase was estimated to be mGB=1.4 μB at 30 °C using the sum rule analysis for XMCD spectra, which is 60% of that of Fe in the Nd2Fe14B compound. The temperature dependence of mGB evaluated with reference to Fe in the Nd2Fe14B phase indicated that the Curie temperature of the GB phase is more than 50 °C lower compared to that of Nd2Fe14B.

What binds quarks together at different momentum scales? A conceptual scenario

The binding effects of quarks within hadrons are discussed in terms of the pion distribution amplitude over longitudinal momentum fractions. To understand the behavior of this quantity at different momentum scales, the concept of synchronization in complex systems has been employed. It is argued that at low momentum scales, the quarks get correlated by nonlocal quark/gluon condensates that cause an endpoint-suppressed, mainly bimodal structure of the pion distribution amplitude inferred from a sum-rule analysis. The mass generation mechanism, within the framework of Dyson–Schwinger equations, and evolution effects pull these two peaks back to the center to form at Q2→∞ the asymptotic distribution amplitude which represents the most synchronized q¯q state.

The influence of Nd dopants on spin and orbital moments in Nd-doped permalloy thin films

Magnetic properties of NdX-Ni80Fe20(1−X) thin films have been investigated using x-ray absorption spectroscopy and x-ray magnetic circular dichroism (XMCD) at room temperature. With the Nd concentration increasing, the ratio of orbital-to-spin moment of Ni and Fe increases significantly, indicating that the spin-orbit coupling in permalloy thin films is enhanced due to the Nd impurities. The spin and orbital moments have been obtained by the sum rules analysis, which shows that the Nd impurities lead to a strong dispersion of spin moments of Fe and Ni while have no effect on orbital moments in Nd-doped permalloy thin films. Element-specific XMCD hysteresis loops suggest an antiferromagnetic coupling between the magnetic moments of Nd and permalloy at room temperature. The static magnetic properties have been studied by vibrating sample magnetometer for comparison, which shows a nice agreement with the XMCD results.