Sum Rule Analysis Research Articles

QCD sum rules analysis of weak decays of doubly heavy baryons: the brightarrow c processes

A comprehensive study of brightarrow c weak decays of doubly heavy baryons is presented in this paper. The transition form factors as well as the pole residues of the initial and final states are respectively obtained by investigating the three-point and two-point correlation functions in QCD sum rules. Contributions from up to dimension-6 operators are respectively considered for the two-point and three-point correlation functions. The obtained form factors are then applied to a phenomenological analysis of semi-leptonic decays.

Soft X-ray absorption spectroscopy and magnetic circular dichroism under pulsed high magnetic field of Ni-Co-Mn-In metamagnetic shape memory alloy

In this study, X-ray absorption spectroscopy (XAS) experiments for Ni45Co5Mn36.7In13.3 metamagnetic shape memory alloy were performed under high magnetic fields up to 12 T using a pulsed magnet. Field–induced reverse transformation from martensite phase to austenite phase caused considerable changes in the magnetic circular dichroism (MCD) signals and the magnetic moments of the Mn, Ni, and Co with ferromagnetic coupling were determined. The spin magnetic moment, Mspin, and orbital magnetic moment, Morb, of Mn atom in the induced austenite ferromagnetic phase, estimated based on the sum-rule analysis, were 3.19 and 0.08 μB, respectively, resulting in an Morb / Mspin ratio of 0.03. In the element-specific magnetization curves obtained at 150 K, metamagnetic behavior associated with the field–induced reverse transformation was clearly observed and the transformation magnetic fields could be detected. There was almost no change in the magnetically averaged XAS spectrum for Mn-L2,3 edges between in the martensite and in the magnetic field-induced austenite phases, however, it was visible for Ni. This implies that Ni 3d-electrons mainly contribute to martensitic transformation.

Monte-Carlo based QCD sum rules analysis of X 0(2900) and X 1(2900)

Motivated by the very recent discovery of fully open-flavor exotic states X 0(2900) and X 1(2900) by the LHCb collaboration [], we study possible interpretations of these exotic states by QCD sum rules method. We have calculated mass and decay constant by traditional QCD sum rules analysis and Monte-Carlo based analysis. X 0(2900) and X 1(2900) are studied in molecular and diquark–antidiquark tetraquark pictures, respectively. Obtained mass results agree well with the masses observed in the experiment. We also made a Monte-Carlo based analysis within QCD sum rules for the mass and decay constant distributions to investigate the possible assignments for the structures of X 0(2900) and X 1(2900).

J/ψ near Tc

We calculate the mass shift and thermal decay width of the J/ψ near the QCD transition temperature Tc by imposing two independent constraints on these variables that can be obtained first by solving the Schrödinger equation and second from the QCD sum rule approach. While the real part of the potential is determined by comparing the QCD sum rule result for charmonium and the D meson to that from the potential model result, the imaginary potential is taken to be proportional to the perturbative form multiplied by a constant factor, which in turn can be determined by applying the two independent constraints. The result shows that the binding energy and the thermal width becomes similar in magnitude at around T=1.09Tc, above which the sum rule analysis also becomes unstable, strongly suggesting that the J/ψ will melt slightly above Tc.

New Λb(6072)0 state as a 2S bottom baryon

As a result of continuous developments, the recent experimental searches lead to the observations of new particles at different hadronic channels. Among these hadrons are the excited states of the heavy baryons containing single bottom or charmed quark in their valance quark content. The recently observed $\Lambda_b(6072)^0$ state is one of these baryons and possibly $2S$ radial excitation of the $\Lambda_b$ state. Considering this information from the experiment, we conduct a QCD sum rule analysis on this state and calculate its mass and current coupling constant considering it as a $2S$ radially excited $\Lambda_b$ resonance. For completeness, in the analyses, we also compute the mass and current coupling constant for the ground state $\Lambda_b^0$ and its first orbital excitation. We also consider the $\Lambda_c^+$ counterpart of each state and attain their mass, as well. The obtained results are consistent with the experimental data as well as existing theoretical predictions.

Electronic structures and magnetization reversal in Li0.5FeCr1.5O4

By employing temperature (T)-dependent soft x-ray magnetic circular dichroism (XMCD) in the Fe and Cr 2p absorption edges, the electronic structures of Li0.5FeCr1.5O4 spinel ferrite, which exhibits magnetization compensation, have been investigated. This work provides evidence that (i) both Fe and Cr ions are trivalent, (ii) most of Fe3+ ions occupy the A (Td) sites, while Cr3+ ions occupy the B (Oh) sites, (iii) the magnetic moments of Fe and Cr ions are coupled antiferromagnetically, and (iv) they are reversed at ∼255 K. The sum-rule analysis of Fe and Cr 2p XMCD spectra reveals that the orbital magnetic moments of Fe and Cr ions in Li0.5FeCr1.5O4 are much larger than those of metallic Fe and Cr, implying the large spin–orbit coupling and the non-fully occupied t2g orbitals of Fe3+ and Cr3+ ions. Based on these findings, we have provided a comprehensive model for the electronic and spin configurations of Fe and Cr ions in (Fe)A[Li0.5Cr1.5]BO4.

The Drightarrow rho semileptonic and radiative decays within the light-cone sum rules

The measured branching ratio of the D meson semileptonic decay D rightarrow rho e^+ nu _e, which is based on the 0.82~{mathrm{fb}^{-1}} CLEO data taken at the peak of psi (3770) resonance, disagrees with the traditional SVZ sum rules analysis by about three times. In the paper, we show that this discrepancy can be eliminated by applying the QCD light-cone sum rules (LCSR) approach to calculate the Drightarrow rho transition form factors A_{1,2}(q^2) and V(q^2). After extrapolating the LCSR predictions of these TFFs to whole q^2-region, we obtain 1/|V_{mathrm{cd}}|^2 times Gamma (D rightarrow rho e nu _e) =(55.45^{+13.34}_{-9.41})times 10^{-15}~mathrm{GeV}. Using the CKM matrix element and the D^0(D^+) lifetime from the Particle Data Group, we obtain mathcal{B} (D^0rightarrow rho ^- e^+ nu _e) = (1.749^{+0.421}_{-0.297}pm 0.006)times 10^{-3} and mathcal{B} (D^+ rightarrow rho ^0 e^+ nu _e) = (2.217^{+0.534}_{-0.376}pm 0.015)times 10^{-3}, which agree with the CLEO measurements within errors. We also calculate the branching ratios of the two D meson radiative processes and obtain mathcal{B}(D^0rightarrow rho ^0 gamma )= (1.744^{+0.598}_{-0.704})times 10^{-5} and mathcal{B}(D^+ rightarrow rho ^+ gamma ) = (5.034^{+0.939}_{-0.958})times 10^{-5}, which also agree with the Belle measurements within errors. Thus we think the LCSR approach is applicable for dealing with the D meson decays.

Hidden-bottom and -charm hexaquark states in QCD sum rules

In this paper, we investigate the spectra of the prospective hidden-bottom and -charm hexaquark states with quantum numbers J^{PC }= 0^{++}, 0^{-+}, 1^{++} and 1^{--} in the framework of QCD sum rules. By constructing appropriate interpreting currents, the QCD sum rules analyses are performed up to dimension 12 of the condensates. Results indicate that there exist two possible baryonium states in b-quark sector with masses 11.84 pm 0.22 GeV and 11.72 pm 0.26 GeV for 0^{++} and 1^{--}, respectively. The corresponding hidden-charm partners are found lying respectively at 5.19 pm 0.24 GeV and 4.78 pm 0.23 GeV. Note that these baryonium states are all above the dibaryon thresholds, which enables their dominant decay modes could be measured at BESIII, BELLEII, and LHCb detectors.

Axial vector cc and bb diquark masses from QCD Laplace sum rules

Constituent mass predictions for axial vector (i.e., $J^P=1^+$) $cc$ and $bb$ colour antitriplet diquarks are generated using QCD Laplace sum-rules. We calculate the diquark correlator within the operator product expansion to NLO, including terms proportional to the four- and six-dimensional gluon and six-dimensional quark condensates. The sum-rules analyses stabilize, and we find that the mass of the $cc$ diquark is 3.51~GeV and the mass of the $bb$ diquark is 8.67~GeV. Using these diquark masses as inputs, we calculate several tetraquark masses within the Type-II diquark-antidiquark tetraquark model.

Evidence against naive truncations of the OPE from e+e−→hadrons below charm

The operator product expansion (OPE), truncated in dimension, is employed in many contexts. An example is the extraction of the strong coupling, $\alpha_s$, from hadronic $\tau$-decay data, using a variety of analysis methods based on finite-energy sum rules. Here, we reconsider a long-used method, which parametrizes non-perturbative contributions to the $I=1$ vector and axial vacuum polarizations with the OPE, setting several higher-dimension coefficients to zero in order to implement the method in practice. The assumption that doing this has a negligible effect on the value of $\alpha_s$ is tantamount to the assumption that the low-dimension part of the OPE converges rapidly with increasing dimension near the $\tau$ mass. Were this assumption valid, it would certainly have to be valid at energies above the $\tau$ mass as well. It follows that the method can be tested using data obtained from $e^+e^-\to\mbox{hadrons}$, as they are not limited by the kinematic constraints of $\tau$ decays. We carry out such an investigation using a recent high-precision compilation for the $R$-ratio, arguing that it provides insights into the validity of the strategy, even if it probes a different, though related channel. We find that $e^+e^-$-based tests call into question the implied assumption of rapid convergence of the low-dimension part of the OPE around the $\tau$ mass, and thus underscore the need to restrict finite-energy sum-rule analyses to observables which receive only contributions from lower-order terms in the OPE.

Evidence for Rigid Triaxial Deformation in Ge76 from a Model-Independent Analysis

An extensive, model-independent analysis of the nature of triaxial deformation in ^{76}Ge, a candidate for neutrinoless double-beta (0νββ) decay, was carried out following multistep Coulomb excitation. Shape parameters deduced on the basis of a rotational-invariant sum-rule analysis provided considerable insight into the underlying collectivity of the ground-state and γ bands. Both sequences were determined to be characterized by the same β and γ deformation parameter values. In addition, compelling evidence for low-spin, rigid triaxial deformation in ^{76}Ge was obtained for the first time from the analysis of the statistical fluctuations of the quadrupole asymmetry deduced from the measured E2 matrix elements. These newly determined shape parameters are important input and constraints for calculations aimed at providing, with suitable accuracy, the nuclear matrix elements relevant to 0νββ.

Testing the tetraquark mixing framework from QCD sum rules for a0(980)

According to a recent proposal of the tetraquark mixing framework, the two light-meson nonets in the $J^{P}=0^{+}$ channel, namely the light nonet composed of $a_0 (980)$, $K_0^* (800)$, $f_0 (500)$, $f_0(980)$, and the heavy nonet of $a_0 (1450)$, $K_0^* (1430)$, $f_0 (1370)$, $f_0 (1500)$, can be expressed by linear combinations of the two tetraquark types, one type containing the spin-0 diquark and the other with the spin-1 diquark. Among various consequences of this mixing model, one surprising result is that the second tetraquark with the spin-1 diquark configuration is more important for the light nonet. In this work, we report that this result can be supported by the QCD sum rule calculation. In particular, we construct a QCD sum rule for the isovector resonance $a_0(980)$ using an interpolating field composed of both tetraquark types and then perform the operator product expansion up to dimension 10 operators. Our sum rule analysis shows that the spin-1 diquark configuration is crucial in generating the $a_0(980)$ mass. Also, the mixed correlation function constructed from the two tetraquark types is found to have large strength which seems consistent with what the tetraquark mixing framework is advocating. On the other hand, the correlation function from the interpolating field with the spin-0 diquark configuration alone fails to predict the $a_0(980)$ mass mostly by the huge negative contribution from dimension 8 operators.

Modifying the Magnetic Anisotropy of an Iron Porphyrin Molecule by an on-Surface Ring-Closure Reaction

The magnetic properties of adsorbed metalloporphyrin molecules can be altered or tuned by the substrate, additional axial ligands, or changes to the molecules’ macrocycle. These modifications influence the electronic configuration of the fourfold-coordinated central metal ion that is responsible for the metalloporphyrins’ magnetic properties. We report a substantial increase in the effective spin moment obtained from sum-rule analysis of X-ray magnetic circular dichroism for an iron metalloporphyrin molecule on Au(111) through its conversion from iron(II)-octaethylporphyrin to iron(II)-tetrabenzoporphyrin in a surface-assisted ring-closure ligand reaction. Density functional theory calculations with additional strong Coulomb correlation (DFT+U) show that the on-surface reaction alters the conformation of the molecule, increasing its planarity and the ion–surface distance. A spin-Hamiltonian fit of the magnetization as a function of field reveals a substantial increase in the intra-atomic magnetic dipole term (Tz) and a decrease in the magnitude of the easy-plane anisotropy upon ring closure. This consequence of the ring closure demonstrates how new magnetic properties can be obtained from on-surface reactions, resulting here in significant modifications to the magnetic anisotropy of the Fe ion, and sheds light onto the molecule–substrate interaction in these systems.

QCD sum rule studies of s s {bar{s}} {bar{s}} tetraquark states with J^{PC} = 1^{+-}

We apply the method of QCD sum rules to study the structure X newly observed by the BESIII Collaboration in the phi eta ^prime mass spectrum in 2.0–2.1 GeV region in the J/psi rightarrow phi eta eta ^prime decay. We construct all the s s {bar{s}} {bar{s}} tetraquark currents with J^{PC} = 1^{+-}, and use them to perform QCD sum rule analyses. One current leads to reliable QCD sum rule results and the mass is extracted to be 2.00^{+0.10}_{-0.09} GeV, suggesting that the structure X can be interpreted as an s s {bar{s}} {bar{s}} tetraquark state with J^{PC} = 1^{+-}. The Y(2175) can be interpreted as its s s {bar{s}} {bar{s}} partner having J^{PC} = 1^{--}, and we propose to search for the other two partners, the s s {bar{s}} {bar{s}} tetraquark states with J^{PC} = 1^{++} and 1^{-+}, in the eta ^prime f_0(980), eta ^prime K {bar{K}}, and eta ^prime K {bar{K}}^* mass spectra.

Exploratory study of χc1(4140) and like states in QCD sum rules

In this work, we chose three molecular and three diquark–antidiquark currents with the quark content cc¯ss¯ and JPC=0++,1++,2++, and estimated the masses and the meson coupling constants of the ground states coupling to these currents in the framework of QCD sum rules. In operator product expansion, we considered the terms including dimension eight, and we performed pole contribution tests carefully. According to our results, all of these currents couple to the ground states with degenerate masses which are in 10 MeV vicinity of χc1(4140). Therefore, with a QCD sum rules analysis, it is not possible to conclude that χc1(4140) has a dominant molecular or diquark–antidiquark content. However, there may be three states degenerate in mass, with positive charge conjugation and different isospins.

Revisiting [formula omitted] as a 0+ tetraquark state from QCD sum rules

Stimulated by the renewed observation of Ds0⁎(2317) signal and its updated mass value 2318.3±1.2±1.2MeV/c2 in the process e+e−→Ds⁎+Ds0⁎(2317)−+c.c. by BESIII Collaboration, we devote to reinvestigate Ds0⁎(2317) as a 0+ tetraquark state from QCD sum rules. Technically, four different possible currents are adopted and high condensates up to dimension 12 are included in the operator product expansion (OPE) to ensure the quality of QCD sum rule analysis. In the end, we obtain the mass value 2.37−0.36+0.50GeV with the factorization parameter ρ=1 (or 2.23−0.24+0.78GeV with ρ=3) for the scalar–scalar current, which agrees well with the experimental data of Ds0⁎(2317) and could support its explanation as a 0+ scalar–scalar tetraquark state. The final result for the axial–axial configuration is calculated to be 2.51−0.43+0.61GeV with ρ=1 (or 2.52+0.76−0.52GeV with ρ=3), which is still consistent with the mass of Ds0⁎(2317) considering the uncertainty, and then the possibility of Ds0⁎(2317) as a axial–axial tetraquark state can not be excluded. For the pseudoscalar–pseudoscalar and the vector–vector cases, their unsatisfactory OPE convergence makes that it is of difficulty to find rational work windows to further acquire hadronic masses.

The direct bandgap of gray α-tin investigated by infrared ellipsometry

Using Fourier-transform infrared ellipsometry, the authors provide spectroscopic evidence about the valence band (VB) structure of diamond-like α-tin. The mid-infrared dielectric function of α-tin grown pseudomorphically on InSb or CdTe by molecular beam epitaxy shows a strong E¯0 peak near 0.41 eV. This peak is assigned to allowed intravalence band transitions from the Γ7− (electron-like) VB to the Γ8+v heavy hole VB and/or interband transitions from Γ7− to the Γ8+c light “hole” conduction band. The strength of this peak requires a hole density in the mid-1018 cm−3 range at room temperature, which might be caused by unintentional doping, by thermal electron-hole pair generation, or by the possibility that the L6+ conduction band might have an energy slightly lower than the Γ8+ VB maximum. Alternatively, this E¯0 peak might be enhanced by the M-shape of the Γ7− VB caused by interactions with the Γ7+ split-off hole VB. A sum-rule analysis of the dielectric function between 0.16 and 6.5 eV is consistent with a high-frequency dielectric constant of 24, which has at most a weak temperature dependence between 100 and 300 K.

Mass calculations of light quarkonium, exotic JPC=0+− hybrid mesons from Gaussian sum rules

We extend previous calculations of leading-order correlation functions of spin-0 and spin-1 light quarkonium hybrids to include QCD condensates of dimensions five and six, with a view to improving the stability of QCD sum-rules analyses in previously unstable channels. Based on these calculations, prior analyses in the literature, and its phenomenological importance, we identify the exotic $J^{PC}=0^{+-}$ channel as the most promising for detailed study. Using Gaussian sum-rules constrained by the H\"older inequality, we calculate masses of light (nonstrange and strange) quarkonium hybrid mesons with $J^{PC}=0^{+-}$. We consider single narrow, single wide, and double narrow resonance models, and find that the double narrow resonance model yields the best agreement between QCD and phenomenology. In both non-strange and strange cases, we find hybrid masses of $2.60$ GeV and $3.57$ GeV.

B0−B¯0 mixing: Matching to HQET at NNLO

We compute perturbative matching coefficients to the heavy quark effective theory (HQET) representation for the QCD effective local $\mathrm{\ensuremath{\Delta}}B=2$ Hamiltonian that determines the mass difference in the ${B}^{0}\text{\ensuremath{-}}{\overline{B}}^{0}$ system of states. We report on the results at next-to-next-to-leading order in the strong coupling constant for matching coefficients of two physical operators in HQET. Our results provide firm confirmation that the recent next-to-leading order sum rules analysis of the bag parameter ${B}_{q}$ is stable with regard of inclusion of higher order radiative corrections. As a byproduct of our calculation we give a fully analytical solution for the one-loop QCD-to-HQET matching problem: we present the explicit formulas for the renormalization of four-quark operators of the full bases in both QCD and HQET and the expressions for matching coefficients in a closed form.

Element-specific magnetic properties of mixed 3d−4f metallacrowns

Single molecule magnets comprising rare earth metals are of high interest due to the unquenched orbital moments of the rare earth ions that result in a large energy barrier for magnetization reversal. We investigate the magnetic properties of polynuclear $3d\text{\ensuremath{-}}4f15$-MC-5 metallacrowns using x-ray magnetic circular dichroism of powder samples at a temperature of 7 K in a magnetic field of 7 T. The sum rule analysis reveals element-specific spin and orbital moments. The magnetic moments of the $3d$ transition metal Ni(II) ions are coupled antiferromagnetically to each other and contribute only little to the total molecular moment. The spin and orbital moments of the rare earth ions are unexpectedly smaller than the ionic values resulting from Hund's rules. We explain the reduction of the orbital magnetic moment by a finite magnetic anisotropy. Considering an energy functional including magnetic anisotropy and Zeeman energy the powder average reveals a magnetic anisotropy of 28 meV (340 K) in the case of Dy(III) and 7 meV (85 K) in the case of Tb(III). The spin moments agree with the ionic value, too, when the expectation values of the dipole operator are considered.