Sum Rule Approach Research Articles

The doubly charmed pseudoscalar tetraquarks [formula omitted] and [formula omitted

The mass and coupling of the doubly charmed JP=0− diquark–antidiquark states Tcc;s¯s¯++ and Tcc;d¯s¯++ that bear two units of the electric charge are calculated by means of QCD two-point sum rule method. Computations are carried out by taking into account vacuum condensates up to and including terms of tenth dimension. The dominant S-wave decays of these tetraquarks to a pair of conventional Ds+Ds0⁎+(2317) and D+Ds0⁎+(2317) mesons are explored using QCD three-point sum rule approach, and their widths are found. The obtained results mT=(4390±150)MeVandΓ=(302±113MeV) for the mass and width of the state Tcc;s¯s¯++, as well as spectroscopic parameters m˜T=(4265±140)MeV and Γ˜=(171±52)MeV of the tetraquark Tcc;d¯s¯++ may be useful in experimental studies of exotic resonances.

X(3872) and its heavy quark spin symmetry partners in QCD sum rules

X(3872) presents many surprises after its discovery more than ten years ago. Understanding its properties is crucial to understand the spectrum of possible exotic mesons. In this work, X(3872) meson and its heavy quark spin symmetry (HQSS) partners (including the mesons in the bottom sector) are studied within the QCD Sum Rules approach using a current motivated by the molecular picture of X(3872). We predict four heavy partners to X(3872) and bottomonium with the masses and J^{PC} quantum numbers. Obtained results are in good agreement with the previous studies and available experimental data within errors.

QCD sum rules for the Δ isobar in neutron matter

We study the properties of the $\Delta$ isobar in the symmetric and asymmetric nuclear matter using the QCD sum rules approach based on the energy dispersion relation. Allowing for different continuum thresholds for the polarization tensors with different dimensions, we find stable masses for the $\Delta$ in both the vacuum and the medium. Compared to the nucleon case, we find that the vector repulsion is smaller for the $\Delta$ while the scalar attraction is similar (75 MeV vector repulsion and 150 MeV scalar attraction in the symmetric matter). The smaller vector repulsion can be understood using the Pauli principle and a constituent quark model. Also the isospin dependence of the quasiparticle energy, which mainly comes from the vector self energy, is quite weak. We also allow for an explicit $\pi -N$ continuum contribution to the polarization function, but find its effect to be minimal. Phenomenological consequences of our results are discussed.

Spin Dynamics and Andreev-Bashkin Effect in Mixtures of One-Dimensional Bose Gases.

We investigate the propagation of spin waves in two-component mixtures of one-dimensional Bose gases interacting through repulsive contact potentials. By using quantum MonteCarlo methods we calculate static ground-state properties, such as the spin susceptibility and the spin structure factor, as a function of the coupling strengths and we determine the critical parameters for phase separation. In homogeneous mixtures, results of the velocity of spin waves and of its softening close to the critical point of phase separation are obtained by means of hydrodynamic theory and a sum-rule approach. We quantify the nondissipative drag effect, resulting from the Andreev-Bashkin current-current interaction between the two components of the gas, and we show that in the regime of strong coupling it causes a significant suppression of the spin-wave velocity.

Gamow-Teller transitions from high-spin isomers in N=Z nuclei

Gamow-Teller (GT) transitions from high-spin isomers are studied using the sum-rule approach and the shell model. The GT transition strengths from the high-spin isomeric states show a stronger collectivity than those from the ground states in two $N=Z$ nuclei, $^{52}$Fe and $^{94}$Ag. It is argued that the spin-up and spin-down Fermi spheres involved in the GT transitions from the high-spin isomeric states play important roles. These Fermi spheres are analogous to the isospin-up and isospin-down Fermi spheres for the GT transitions from the ground states in $N>Z$ nuclei and create a strong collectivity.

Breathing-mode frequency of a strongly interacting Fermi gas across the two- to three-dimensional crossover

We address the interplay between dimension and quantum anomaly on the breathing mode frequency of a strongly interacting Fermi gas harmonically trapped at zero temperature. Using a beyond-mean-field Gaussian pair fluctuation theory, we employ periodic boundary conditions to simulate the dimensionality of the system and impose a local-density approximation, with two different schemes, to model different trapping potentials in the tightly confined axial direction. By using a sum-rule approach, we compute the breathing mode frequency associated with a small variation of the trapping frequency along the weakly confined transverse direction and describe its behavior as a function of the dimensionality, from two to three dimensions, and of the interaction strength. We compare our predictions with previous calculations on the two-dimensional breathing mode anomaly and discuss their possible observation in ultracold Fermi gases of $^{6}\mathrm{Li}$ and $^{40}\mathrm{K}$ atoms.

The scalar and pseudoscalar hidden-charm tetraquark states with QCD sum rules

Based on the diquark configuration, we construct the diquark–antidiquark interpolating tetraquark currents with [Formula: see text] and [Formula: see text], which can couple to the scalar and pseudoscalar tetraquark states, respectively, since they are not conserved currents. Then, we investigate their two-point correlation functions including the contributions of the vacuum condensates up to dimension-10 and extract the masses and pole residues of the tetraquark states with [Formula: see text] and [Formula: see text] through the QCD sum rule approach. The predicted masses can be confronted with the experimental data in the future. Moreover, we briefly discuss the possible decay patterns of the tetraquark states.

Decay constants of pseudoscalar and vector mesons with improved holographic wavefunction**Supported by National Natural Science Foundation of China (11475055, 11675061, 11435003), Q. Chang is also supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China (201317), the Program for Science and Technology Innovation Talents in Universities of Henan Province (14HASTIT036), the Excellent Youth Foundation of HNNU.

We calculate the decay constants of light and heavy-light pseudoscalar and vector mesons with improved soft-wall holographic wavefuntions, which take into account the effects of both quark masses and dynamical spins. We find that the predicted decay constants, especially for the ratio fV/fP, based on light-front holographic QCD, can be significantly improved, once the dynamical spin effects are taken into account by introducing the helicity-dependent wavefunctions. We also perform detailed χ2 analyses for the holographic parameters (i.e. the mass-scale parameter κ and the quark masses), by confronting our predictions with the data for the charged-meson decay constants and the meson spectra. The fitted values for these parameters are generally in agreement with those obtained by fitting to the Regge trajectories. At the same time, most of our results for the decay constants and their ratios agree with the data as well as the predictions based on lattice QCD and QCD sum rule approaches, with only a few exceptions observed.

Subleading-power corrections to the radiative leptonic B \u2192 \u03b3\u2113\u03bd decay in QCD

Applying the method of light-cone sum rules with photon distribution amplitudes, we compute the subleading-power correction to the radiative leptonic B → γℓν decay from the twist-two hadronic photon contribution at next-to-leading order in QCD; and further evaluate the higher-twist “resolved photon” corrections at leading order in αs, up to twist-four accuracy. QCD factorization for the vacuum-to-photon correlation function with an interpolating current for the B-meson is established explicitly at leading power in Λ/mb employing the evanescent operator approach. Resummation of the parametrically large logarithms of mb2/Λ2 entering the hard function of the leading-twist factorization formula is achieved by solving the QCD evolution equation for the light-ray tensor operator at two loops. The leading-twist hadronic photon effect turns out to preserve the symmetry relation between the two B → γ form factors due to the helicity conservation, however, the higher-twist hadronic photon corrections can yield symmetry-breaking effect already at tree level in QCD. Using the conformal expansion of photon distribution amplitudes with the non-perturbative parameters estimated from QCD sum rules, the twist-two hadronic photon contribution can give rise to approximately 30% correction to the leading-power “direct photon” effect computed from the perturbative QCD factorization approach. In contrast, the subleading-power corrections from the higher-twist two-particle and three-particle photon distribution amplitudes are estimated to be of mathcal{O}left(3sim 5%right) with the light-cone sum rule approach. We further predict the partial branching fractions of B → γℓν with a photon-energy cut Eγ ≥ Ecut, which are of interest for determining the inverse moment of the leading-twist B-meson distribution amplitude thanks to the forthcoming high-luminosity Belle II experiment at KEK.

The structure, mixing angle, mass and couplings of the light scalar f0(500) and f0(980) mesons

The mixing angle, mass and couplings of the light scalar mesons f0(500) and f0(980) are calculated in the framework of QCD two-point sum rule approach by assuming that they are tetraquarks with diquark–antidiquark structures. The mesons are treated as mixtures of the heavy |H〉=([su][s¯u¯]+[sd][s¯d¯])/2 and light |L〉=[ud][u¯d¯] scalar diquark–antidiquark components. We extract from corresponding sum rules the mixing angles φH and φL of these states and evaluate the masses and couplings of the particles f0(500) and f0(980).

A resolution of the inclusive flavor-breaking τ |Vus| puzzle

We revisit the puzzle of |Vus| values obtained from the conventional implementation of hadronic-τ- decay-based flavor-breaking finite-energy sum rules lying >3σ below the expectations of three-family unitarity. Significant unphysical dependences of |Vus| on the choice of weight, w, and upper limit, s0, of the experimental spectral integrals entering the analysis are confirmed, and a breakdown of assumptions made in estimating higher dimension, D>4, OPE contributions identified as the main source of these problems. A combination of continuum and lattice results is shown to suggest a new implementation of the flavor-breaking sum rule approach in which not only |Vus|, but also D>4 effective condensates, are fit to data. Lattice results are also used to clarify how to reliably treat the slowly converging D=2 OPE series. The new sum rule implementation is shown to cure the problems of the unphysical w- and s0-dependence of |Vus| and to produce results ∼0.0020 higher than those of the conventional implementation employing the same data. With B-factory input, and using, in addition, dispersively constrained results for the Kπ branching fractions, we find |Vus|=0.2231(27)exp(4)th, in excellent agreement with the result from Kℓ3, and compatible within errors with the expectations of three-family unitarity, thus resolving the long-standing inclusive τ|Vus| puzzle.

New a1(1420) state: Structure, mass, and width

The structure, spectroscopic parameters and width of the resonance with quantum numbers ${J}^{PC}={1}^{++}$ discovered by the COMPASS Collaboration and classified as the ${a}_{1}(1420)$ meson are examined in the context of QCD sum rule method. In the calculations the axial-vector meson ${a}_{1}(1420)$ is treated as a four-quark state with the diquark-antidiquark structure. The mass and current coupling of ${a}_{1}(1420)$ are evaluated using QCD two-point sum rule approach. Its observed decay mode ${a}_{1}(1420)\ensuremath{\rightarrow}{f}_{0}(980)\ensuremath{\pi}$, and kinematically allowed ones, namely ${a}_{1}\ensuremath{\rightarrow}{K}^{*\ifmmode\pm\else\textpm\fi{}}{K}^{\ensuremath{\mp}}$, ${a}_{1}\ensuremath{\rightarrow}{K}^{*0}{\overline{K}}^{0}$ and ${a}_{1}\ensuremath{\rightarrow}{\overline{K}}^{*0}{K}^{0}$ channels are studied employing QCD sum rules on the light-cone. Our prediction for the mass of the ${a}_{1}(1420)$ state ${m}_{{a}_{1}}={1416}_{\ensuremath{-}79}^{+81}\text{ }\text{ }\mathrm{MeV}$ is in excellent agreement with the experimental result. Width of this state $\mathrm{\ensuremath{\Gamma}}=145.52\ifmmode\pm\else\textpm\fi{}20.79\text{ }\text{ }\mathrm{MeV}$ within theoretical and experimental errors is also in accord with the COMPASS data.

Study of D→a0(980)e+νe decay in the light-cone sum rules approach

Within the QCD light-cone sum rule (LCSR) approach, we investigate the transition form factors of $D\rightarrow a_0(980)$ up to the twist-3 light-cone distribution amplitudes (LCDAs) of the scalar meson $a_0(980)$ in the two-quark picture. Using these form factors, we calculate the differential decay widths and branching ratios of the $D\rightarrow a_0(980) e^+ \nu_e$ semileptonic decays. We obtain ${\mathcal B}(D^0\rightarrow a_0^- (980) e^+ \nu_e)=(4.08^{+1.37}_{-1.22})\times 10^{-4}$ and ${\mathcal B}(D^+\rightarrow a_0^0 (980) e^+ \nu_e)=(5.40^{+1.78}_{-1.59})\times 10^{-4}$. The results are sensitive to the $a_0(980)$ inner structure. These decays can be searched for at BESIII experiment, and any experimental observations will be useful to identify internal quark contents of the $a_0(980)$ meson, which will shed light on understanding theoretical models.

Reconsideration of the B→K* transition form factors within the QCD light-cone sum rules

In this paper, we study the $B\ensuremath{\rightarrow}{K}^{*}$ transition form factors (TFFs) within the QCD light-cone sum rules (LCSR) approach. Two correlators, i.e., the usual one and the right-handed one, are adopted in the LCSR calculation. The resultant LCSRs for the $B\ensuremath{\rightarrow}{K}^{*}$ TFFs are arranged according to the twist structure of the ${K}^{*}$-meson light-cone distribution amplitudes (LCDAs), whose twist-2, twist-3, and twist-4 terms behave quite differently by using different correlators. We observe that the twist-4 LCDAs, though generally small, shall have sizable contributions to the TFFs ${A}_{1/2}$, $V$, and ${T}_{1}$; thus, the twist-4 terms should be kept for a sound prediction. We also observe that, even though different choices of the correlator lead to different LCSRs with different twist contributions, the large correlation coefficients for most of the TFFs indicate that the LCSRs for different correlators are close to each order, not only for their values at the large recoil point ${q}^{2}=0$ but also for their ascending trends in the whole ${q}^{2}$ region. Such a high degree of correlation is confirmed by their application to the branching fraction of the semileptonic decay $B\ensuremath{\rightarrow}{K}^{*}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. Thus, a proper choice of correlator may inversely provide a chance for probing uncertain LCDAs; i.e., the contributions from those LCDAs can be amplified to a certain degree via a proper choice of correlator, thus amplifying the sensitivity of the TFFs and, hence, their related observables, to those LCDAs.

In-medium pseudoscalar D/B mesons and charmonium decay width

Using QCD sum rules and chiral SU(3) model, we investigate the effect of temperature, density, strangeness fraction and isospin asymmetric parameter on the shift in masses and decay constants of the pseudoscalar $D$ and $B$ meson in hadronic medium, which consist of nucleons and hyperons. The in-medium properties of $D$ and $B$ mesons within QCD sum rule approach depend upon the quark and gluon condensates. In chiral SU(3) model, quark and gluon condensates are introduced through the explicit symmetry breaking term and the trace anomaly property of the QCD, respectively and are written in terms of scalar fields $\sigma$, $\zeta$, $\delta$ and $\chi$. Hence, through medium modification of $\sigma$, $\zeta$, $\delta$ and $\chi$ fields, we obtain the medium modified masses and decay constants of $D$ and $B$ mesons. As an application, using $^3 P_0$ model, we calculate the in-medium decay width of the higher charmonium states $ \psi(3686)$, $\psi(3770)$ and $\chi(3556)$ to the $D \bar{D}$ pairs, considering the in-medium mass of $D$ mesons. These results may be important to understand the possible outcomes of high energy physics experiments, e.g., CBM and PANDA at GSI, Germany.

Open charm-bottom axial-vector tetraquarks and their properties

The charged axial-vector J^{P}=1^{+} tetraquarks Z_{q}=[cq][bar{b} bar{q} ] and Z_{s}=[cs][bar{b} bar{s}] with the open charm-bottom contents are studied in the diquark–antidiquark model. The masses and meson–current couplings of these states are calculated by employing a QCD two-point sum rule approach, where the quark, gluon and mixed condensates up to eight dimensions are taken into account. These parameters of the tetraquark states Z_{q} and Z_{s} are used to analyze the vertices Z_q B_c rho and Z_s B_c phi to determine the strong g_{Z_qB_c rho } and g_{Z_sB_c phi } couplings. For these purposes, the QCD light-cone sum rule method and its soft-meson approximation are utilized. The couplings g_{Z_qB_c rho } and g_{Z_sB_c phi }, extracted from this analysis, are applied for evaluating the strong Z_q rightarrow B_c rho and Z_s rightarrow B_c phi decays’ widths, which are essential results of the present investigation. Our predictions for the masses of the Z_{q} and Z_{s} states are confronted with similar results available in the literature.

Radial excitations of the decuplet baryons

The ground and first excited states of the decuplet baryons are studied using the two-point QCD sum rule approach. The mass and residue of these states are computed and compared with the existing experimental data and other theoretical predictions. The results for the masses of the ground state particles as well as the excited Delta and Sigma ^{*} states are in good consistency with experimental data. Our results on the excited Xi ^{*} and Omega ^{-} states reveal that the experimentally poorly known Xi (1950) and Omega ^{-}(2250) can be assigned to the first excited states in Xi ^{*} and Omega ^{-} channels, respectively.

X-ray circular magnetic dichroism in the presence of strong spin fluctuations

The use of X-ray magnetic circular dichroism (XMCD) spectra for determininghe t magnitude of atomic magnetic moments in compounds of rare-earth and transition elements is discussed. The standard sum rule approach often yields a magnitude of moments that is often smaller than values obtained from magnetic measurements. We attribute this to strong spin fluctuations in the surface layers in which XMCD signals form. A way of determining the values of local magnetic moments in the presence of strong fluctuations is proposed and tested.

Open charm-bottom scalar tetraquarks and their strong decays

The mass and meson-current coupling of the diquark-antidiquark states with the quantum numbers $J^{P}=0^{+}$ and quark contents $Z_{q}=[cq][\bar {b} \bar q ]$ and $Z_{s}=[cs][\bar {b} \bar s]$ are calculated using two-point QCD sum rule approach. In calculations the quark, gluon and mixing condensates up to eight dimensions are taken into account. The parameters of the scalar tetraquarks extracted from this analysis are employed to explore the strong vertices $Z_q B_c \pi $, $Z_q B_c \eta $ and $Z_s B_c \eta $ and compute the couplings $g_{Z_qB_c \pi }$, $g_{Z_qB_c \eta }$ and $g_{Z_sB_c \eta }$. The strong couplings are obtained within the soft-meson approximation of QCD light-cone sum rule method: they form, alongside with other parameters, the basis for evaluating the widths of $Z_q \to B_c \pi$, $% Z_q \to B_c \eta$ and $Z_s \to B_c \eta$ decays. Obtained in this work results for the mass of the tetraquarks $Z_{q}$ and $Z_{s}$ are compared with available predictions presented in the literature.

Charm quark mass with calibrated uncertainty

We determine the charm quark mass hat{m}_c from QCD sum rules of the moments of the vector current correlator calculated in perturbative QCD at mathcal{O} (hat{alpha }_s^3). Only experimental data for the charm resonances below the continuum threshold are needed in our approach, while the continuum contribution is determined by requiring self-consistency between various sum rules, including the one for the zeroth moment. Existing data from the continuum region can then be used to bound the theoretic uncertainty. Our result is hat{m}_c(hat{m}_c) = 1272 pm 8 MeV for hat{alpha }_s(M_Z) = 0.1182, where the central value is in very good agreement with other recent determinations based on the relativistic sum rule approach. On the other hand, there is considerably less agreement regarding the theory dominated uncertainty and we pay special attention to the question how to quantify and justify it.