Sum Rule Technique Research Articles

Semi-leptonic three-body proton decay modes from light-cone sum rules

Using light-cone sum rule techniques, we estimate the form factors which parametrise the hadronic matrix elements that are relevant for semi-leptonic three-body proton decays. The obtained form factors allow us to determine the differential rate for the decay of a proton (p) into a positron (e+), a neutral pion (π0) and a graviton (G), which is the leading proton decay channel in the effective theory of gravitons and Standard Model particles (GRSMEFT). The sensitivity of existing and next-generation neutrino experiments in detecting the p → e+π0G signature is studied and the phenomenological implications of our computations for constraints on the effective mass scale that suppresses the relevant baryon-number violating GRSMEFT operator are discussed.

About the exotic structure of Zcs

Very recently a new hadronic structure around 3.98 GeV was observed in BESIII experiment. From its decay modes, it is reasonable for people to assign it to the category of exotic state, say Zcs+, the stranged-parter of Zc(3900). This finding indicates for the first time the tetraquark with strange quark in hidden-charm sector, and hence has a peculiar importance. By virtue of the QCD Sum Rule technique, we analyze the Zcs+ about its possible configuration and physical properties, and find it could be configured as a mixture of two types of structures, [1c]c¯u⊗[1c]s¯c and [1c]c¯c⊗[1c]s¯u, or [3c]c¯u⊗[3¯c]s¯c and [3c]c¯c⊗[3¯c]s¯u, with JP=1+. Physically, it then appears to be the emergence of a compound of four possible currents in each configuration, which tells that the single current evaluation of hadron spectroscopy and their decay properties are sometimes not enough. We find that in both cases the energy spectra may fit well with the experimental observation within the uncertainties, i.e. 3.98 GeV, while be noted that the molecular state is not favored by vector-meson-exchange model. Various Zcs+(3980) decay modes are evaluated, which are critical for pinning down its configuration and left for experimental verification. We also predict the mass of Zcs0, the neutral partner of Zcs+(3980), and analyze its dominant decay probabilities.

Gluonic tetracharm configuration of X(6900)

Recently, a new hadronic structure at around 6.9 GeV was observed in an LHCb experiment. From its limited yet known decay mode, one could still determine that it contains at least four charm quarks and hence belongs to the category of exotic state. This finding indicates for the first time the tetracharm exotic states and is therefore quite importance. In this letter, we propose a nature hybrid interpretation for the structure of X(6900), i.e. in [3¯c]cc⊗[8c]G⊗[3c]c¯c¯ configuration with JPC=0++, and by using the QCD Sum Rule technique we performed mass spectrum calculation. The results showed that the observed X(6900) could be a gluonic tetracharm state, and some other structures may exist, e.g., one around 7.2 GeV in the tetracharm hybrid configuration and with JPC=0−+. We also predict the tetrabottom hybrid states, leaving for future experiment.

Sum rules for CP-violating operators of Weinberg type

We estimate the size of the hadronic matrix elements of CP-violating three-gluon and four-gluon Weinberg operators using sum-rule techniques. In the three-gluon case, we are able to reproduce the expressions given in earlier works, while the four-gluon results obtained in this article are new. Our paper therefore represents the first systematic study of contributions to the electric dipole moment of the neutron due to CP-violating dimension-six and dimension-eight operators. We provide many details on both the derivation of the sum rules as well as the analysis of the uncertainties that plague our final predictions.

Quark correlations in the ground and excited nucleon states via the photo-absorption sum rules

The account of the dynamical correlations of quarks composing the nucleons is necessary for relevant description of nucleon and nuclear interactions. The present work is devoted to the use of the technique of known integral sum rules for the cross-sections and amplitude of the photo-hadron processes. In particular, a kind of the visual representation and quantification of the valence quark correlation characteristics referring to the photo-excitation of the nucleon resonances can be presented.

In the Pursuit of $X(5568)$ and its Charmed Partner

The recent observation by the D$\O$ collaboration of the first tetraquark candidate with four different quark flavors $(u, d, s$ and $ b)$ in the $B^0_s\pi^{\pm}$ channel having a narrow structure, has still not been confirmed by other collaborations. Further independent experiments are required either to confirm the $X(5568)$ state or to set limits on its production. Though quantum numbers are not exactly clear, the results existing in the literature indicate that it is probably an axial-vector or scalar state candidate. In this study, mass and pole residue of the $X(5568)$ resonance assuming as a tightly bound diquark, with spin-parity both $J^{P}=1^{+}$ or $J^{PC}=0^{++}$ are calculated using two-point Thermal SVZ sum rules technique by including condensates up to dimension six. Moreover, its partner in the charm sector is also discussed. Investigations defining the thermal properties of $X(5568)$ and its charmed partner may provide valuable hints and information for the upcoming experiments such as CMS, LHCb and PANDA.

Structure of the Ξb(6227)− resonance

We explore the recently observed $\Xi_b(6227)^{-}$ resonance to fix its quantum numbers. To this end, we consider various possible scenarios: It can be considered as either 1P/2S excitations of the $\Xi_b^-$ and $\Xi_b'(5935)^{-}$ ground state baryons with spin-$\frac{1}{2}$ or 1P/2S excitations of the ground state $\Xi_b(5955)^{-}$ with spin-$\frac{3}{2}$. We calculate the masses of the possible angular-orbital $1P$ and $2S$ excited states corresponding to each channel employing the QCD sum rule technique. It is seen that all the obtained masses are in agreement with the experimentally observed value, implying that the mass calculations are not enough to distinguish the quantum numbers of the state under question. Therefore, we extend the analysis to investigate the possible decays of the same excited states into $\Lambda_b^0 K^-$ and $\Xi_b^-\pi$. Using the light cone QCD sum rule method, we calculate the corresponding strong coupling constants, which are used to extract the decay widths of the modes under consideration. Our results on decay widths indicate that the $\Xi_b(6227)^{-}$ is $1P$ angular-orbital excited state of the $\Xi_b(5955)^{-}$ baryon with quantum numbers $J^P=\frac{3}{2}^{-}$.

On properties of low-lying spin-1 hadron resonances

Properties of low-lying spin-1 hadron resonances are described in the review. It is shown how the Nambu–Jona-Lasinio model can be extended in the chiral invariant way by new tensor interactions. New mass formulas are obtained, which are not based on unitary symmetry groups but involve particles from different multiplets even with opposite parity. They all are in good agreement with experimental data. Dynamic properties of spin-1 mesons confirmed by the calculations performed using the QCD sum rule technique and the lattice calculations are understood and explained.

Transition Form Factors ofχb2(1P)→Bcl¯νin QCD

The form factors of the semileptonicχb2(1P)→Bcl¯νdecay are calculated by using the QCD sum rule technique. The results obtained are then used to estimate the decay widths of this transition in all lepton channels. The orders of decay rates indicate that this transition is accessible at LHC for all lepton channels.

Complex-energy approach to sum rules within nuclear density functional theory

The linear response of the nucleus to an external field contains unique information about the effective interaction, correlations, and properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or EDF. But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. To establish an efficient framework to compute sum rules of the response that is adaptable to the optimization of the nuclear EDF and large-scale surveys of collective strength, we have developed a new technique within the complex-energy FAM based on the QRPA. To compute sum rules, we carry out contour integration of the response function in the complex-energy plane. We benchmark our results against the conventional matrix formulation of the QRPA theory, the Thouless theorem for the energy-weighted sum rule, and the dielectric theorem for the inverse energy-weighted sum rule. We demonstrate that calculated sum-rule values agree with those obtained from the matrix formulation of the QRPA. We also discuss the applicability of both the Thouless theorem about the energy-weighted sum rule and the dielectric theorem for the inverse energy-weighted sum rule to nuclear density functional theory in cases when the EDF is not based on a Hamiltonian. The proposed sum-rule technique based on the complex-energy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method is very efficient and well-adaptable to parallel computing. The FAM formulation is especially useful when standard theorems based on commutation relations involving the nuclear Hamiltonian and external field cannot be used.

Energy production in varyingαtheories

Aims. On the basis the theoretical model proposed by Bekenstein for {\alpha}'s variation, we analyze the equations that describe the energy exchange between matter and both the electromagnetic and the scalar fields. Methods. We determine how the energy flow of the material is modified by the presence of a scalar field. We estimate the total magnetic energy of matter from the "sum rules techniques". We compare the results with data obtained from the thermal evolution of the Earth and other planets. Results. We obtain stringent upper limits to the variations in {\alpha} that are comparable with those obtained from atomic clock frequency variations. Conclusions. Our constraints imply that the fundamental length scale of Bekenstein's theory "lB" cannot be larger than Planck's length "lP".

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.

Formula omitted] pentaquarks in QCD sum rules

We study pentaquark states with strangeness S = + 1 and I J π = 0 1 2 ± , 1 1 2 ± , 0 3 2 ± , 1 3 2 ± within the QCD sum rule technique. In order to obtain reliable results with this method, it is indispensable to establish a valid Borel window, where the operator product expansion (OPE) converges and the presumed ground state pole dominates the sum rules. By constructing the sum rules from the difference of two carefully chosen independent correlators and calculating the OPE up to dimension 14, such a Borel window can be established. This then leads to our main conclusion that the state with qantum numbers 0 3 2 + appears to be the most probable candidate for the experimentally observed Θ + ( 1540 ) . Furthermore, states with 0 1 2 − , 1 1 2 − , 1 3 2 + are also obtained at slightly higher mass regions.

Effective Lagrangian for two-photon and two-gluon decays ofP-wave heavy quarkoniumχc0,2andχb0,2states

In the traditional non-relativistic bound state calculation, the two-photon decay amplitudes of the $P$-wave $\chi_{c0,2}$ and $\chi_{b0,2}$ states depend on the derivative of the wave function at the origin which can only be obtained from potential models. However by neglecting the relative quark momenta, the decay amplitude can be written as the matrix element of a local heavy quark field operator which could be obtained from other processes or computed with QCD sum rules technique or lattice simulation. Following the same line as in recent work for the two-photon decays of the $S$-wave $\eta_{c}$ and $\eta_{b}$ quarkonia, we show that the effective Lagrangian for the two-photon decays of the $P$-wave $\chi_{c0,2}$ and $\chi_{b0,2}$ is given by the heavy quark energy-momentum tensor local operator or its trace, the $\bar{Q}Q$ scalar density and that the expression for $\chi_{c0}$ two-photon and two-gluon decay rate is given by the $f_{\chi_{c0}}$ decay constant and is similar to that of $\eta_{c}$ which is given by $f_{\eta_{c}}$. From the existing QCD sum rules value for $f_{\chi_{c0}}$, we get $5\rm keV$ for the $\chi_{c0}$ two-photon width, somewhat larger than measurement, but possibly with large uncertainties.

Heavy-baryon properties with NLO accuracy in perturbative QCD

We present an analysis of the static properties of heavy baryons at next-to-leading order in the perturbative expansion of QCD. We obtain analytical next-to-leading order three-loop results for the two-point correlators of baryonic currents with one finite-mass quark field for a variety of quantum numbers of the baryonic currents. We consider both the massless limit and the HQET limit of the correlator as special cases of the general finite-mass formula and find agreement with previous results. We present closed-form expressions for the moments of the spectral density. We determine the residues of physical baryon states using sum-rule techniques.

Coupling constants of D*DsK and Ds*DK processes

We calculate the coupling constants of $D^*D_sK$ and $D_s^*DK$ vertices using the QCD sum rules technique. We compare results obtained in the limit of SU(4) symmetry and found that the symmetry is broken on the order of 40%.

D∗DsK and Ds∗DK vertices in a QCD sum rule approach

Abstract We calculate the strong form factors and coupling constants of D ∗ D s K and D s ∗ D K vertices using the QCD sum rules technique. In each case we have considered two different cases for the off-shell particle in the vertex: the lightest meson and one of the heavy mesons. The method gives the same coupling constant for each vertex. When the results for different vertices are compared, they show that the SU(4) symmetry is broken by around 40%.

MODELLING THE NON-PERTURBATIVE VACUUM OF QCD

The properties of the non-perturbative vacuum of QCD are modelled within the framework of a bosonized QCD Hamiltonian. The Hamiltonian includes fermion (valence quarks and quark-antiquark pairs) and bosons (pairs of gluons) interacting via effective interactions. The couplings between these degrees of freedom are fixed from the phenomenology and the Hamiltonian is transformed into a boson basis to map quark-antiquark pairs and pairs of gluons. With these elements we calculate the parameters which define gluon and fermion condensates and compare their values with the ones obtained by applying sum rule techniques. The agreement between the results is rather good, in spite of the simplicity of the model.

Diffused vorticity approach to the oscillations of a rotating Bose-Einstein condensate confined in a harmonic plus quartic trap

The collective modes of a rotating Bose-Einstein condensate confined in an attractive quadratic plus quartic trap are investigated. Assuming the presence of a large number of vortices we apply the diffused vorticity approach to the system. We then use the sum rule technique for the calculation of collective frequencies, comparing the results with the numerical solution of the linearized hydrodynamic equations. Numerical solutions also show the existence of low-frequency multipole modes which are interpreted as vortex oscillations.

Light-cone distribution amplitudes for the light 11P1mesons

We present a study of light-cone distribution amplitudes of the light $1^1P_1$ mesons. The first few Gegenbauer moments of leading twist light-cone distribution amplitudes are calculated by using the QCD sum rule technique.