QCD Sum Rules Research Articles

Mixing angle of K1(1270/1400) and the KK¯1(1400) molecular interpretation of η1(1855)

Owing to the SU(3) symmetry breaking effect, the axial-vector kaons K1(1270) and K1(1400) are established to be mixtures of two P-wave K1A(P31) and K1B(P11) states. In QCD sum rules, we propose a new construction of the K1 current operators and calculate the two-point correlation functions by including the next-to-leading order four-quark condensates. The mixing angle is determined as θ=(46.95−0.23+0.25)° by reproducing the masses of K1(1270) and K1(1400). We further compose the KK¯1(1270) and KK¯1(1400) interpolating currents with exotic quantum numbers JPC=1−+ to investigate the possible molecular interpretation of the recently observed η1(1855) state. We calculate the correlation functions and perform the QCD sum rule analyses for these two molecular systems. However, the spectral functions are found to be negative in physical regions so that they are not able to provide reliable investigations of the KK¯1 molecular states. Published by the American Physical Society 2025

Form factors of Λb0→Λc(2595)+ within light-cone QCD sum rules

In this work, we calculated the form factors of the weak decay process Λb0→Λc(2595)+, where the final charm baryon represents an excited state with spin-parity 12-. Utilizing the light-cone QCD sum rules approach, we incorporated the contributions of the lowest two charm baryon states: the ground state Λc with JP=12+ and the excited state Λc(2595)+ with JP=12- in the hadronic representation of the Λb→Λc(2595)+ transition correlation function. This approach allows us to extract the form factors of the Λb0→Λc(2595)+ from Λb0→Λc+ transition. During the light-cone QCD sum rules procedure, we employed the light-cone distribution amplitudes (LCDAs) of the Λb baryon. Furthermore, by combining these form factors with the helicity amplitudes of the bottom baryon transition matrix elements, we calculated the differential decay widths for the processes Λb0→Λc(2595)+ℓ-ν¯ℓ and provided the optimal choice of the interpolating current for Λc in this process. Additionally, within the lifetime of Λb0, we obtained the absolute branching fractions for the semileptonic decays Λb0→Λc(2595)+ℓ-ν¯ℓ. With the branching fractions of Λb0→Λc(2595)+ℓ-ν¯ℓ calculated in this work, we also determined the parameter R(Λc(2595)+) which tests the lepton flavor universality. This parameter is defined as the ratio of branching fractions Br(Λb0→Λc(2595)+τ-ν¯τ) and Br(Λb0→Λc(2595)+μ-ν¯μ). Our results provide a valuable theoretical test for these decay channels and offer insights into the LCDAs of bottom baryons, paving the way for further in-depth investigations.

Investigation of the semileptonic decay Ξcc++→Ξc+ℓ¯νℓ within QCD sum rules

We study the semileptonic decay of the doubly heavy baryon Ξcc++ into the singly heavy baryon Ξc+ within the three-point QCD sum rule approach in two possible lepton channels. Our analysis includes perturbative as well as nonperturbative condensation contributions up to dimension 5. We evaluate the form factors of this semileptonic decay entering the amplitude described by the vector and axial vector transition currents. The fit functions of the form factors with respect to the transferred momentum squared are utilized to predict the decay widths and branching ratios of the Ξcc++→Ξc+ℓ¯νℓ channels. We compare our findings with other predictions in the literature. Our outcomes can be useful for experimental groups in their search for the weak decays of doubly heavy baryons and may be checked via future experiments such as LHCb. Published by the American Physical Society 2024

Constraining λBs by Bs→γ* and Bs→ϕ form factors

We calculate the form factors FV(q2,q′2) and FTV(q2,q′2) describing the Bs→γ* transition induced by the vector and tensor weak currents in a broad range of values of q2 and q′2 far below the quark thresholds in both q2 and q′2 channels. These form factors are calculated via the distribution amplitudes of the Bs-meson. We then interpolate the obtained results by a formula that contains pole at q′2=Mϕ2 and extract the residue which gives the Bs→ϕ transition form factors V(q2) and T1(q2). In this way we obtain theoretical predictions for these form factors without invoking quark-hadron duality and QCD sum rules. Furthermore, we calculate the relationship between V(0) and T1(0) and the parameter λBs(μ), the inverse moment of the Bs-meson distribution amplitude. Using the available predictions for V(0) and T1(0) coming from approaches not referring to the Bs-meson distribution amplitudes, we obtain the estimate λBs(μ≃mb)=(0.62±0.10) GeV. Published by the American Physical Society 2024

A progress in the inverse matrix method in QCD sum rules

In traditional QCD sum rules, the simple hadron spectral density model of the “delta-function-type ground state + theta-function-type continuous spectrum” determines that there is no perfect parameter selection. In recent years, inverse problem methods, particularly the inverse matrix method, have shown better handling of QCD sum rules. This work continues to develop the inverse matrix method. Considering that the narrow-width approximation may still be a good approximation, we separate the ground state from the spectral density. We then follow the general steps of the inverse matrix method to extract physical quantities such as decay constants that we may be more interested in.

Towards heavy double-gluon hybrid mesons with exotic quantum numbers in QCD sum rules

The double-gluon hybrid meson configuration was recently proposed and investigated within QCD sum rules. In this talk, we discuss the color structures of the double-gluon hybrid meson and construct current operators with exotic quantum numbers JPC=1−+ and 2+− for two of the structures. In the framework of QCD sum rules, we consider the condensates up to dimension-8 at the leading order of αs for both charmonium and the bottomonium systems. The results indicate that the masses of the 1−+ and 2+− charmonium double-gluon hybrid mesons are approximately 6.1−7.2 GeV and 6.3−6.4 GeV, respectively. As for the bottomonium systems, their masses fall within the range of 13.7−14.3 GeV and 12.6−13.3 GeV for the 1−+ and 2+− channels, respectively. Additionally, the charmonium hybrids could be produced in the radiative decays of bottomonium mesons in BelleII experiment.

Investigation on the Ω(2012) from QCD sum rules

We investigate the recently observed Ω(2012) baryon using QCD sum rules. By constructing P-wave Ω baryon currents and performing spin projection and parity projection, we obtain the masses of the JP=1/2− and 3/2− states as M1/2−=2.07−0.07+0.07GeV and M3/2−=2.05−0.10+0.09GeV, in good agreement with experiment. This suggests that Ω(2012) is likely to be a negative parity P-wave excited state, though its spin remains undetermined and requires further study of its decay properties.

BorelT.m: Borel Transformations in QCD Sum Rules with Mathematica

borelT.m: Borel Transformations in QCD Sum Rules with Mathematica

Mass spectra of strange double charm pentaquarks with strangeness S=−1

The observation of the Tcs¯(2900) indicates the potential existence of strange double charm pentaquarks based on the heavy antidiquark symmetry. We systematically study the mass spectra of strange double charm pentaquarks with strangeness S=−1 in both molecular and compact structures for quantum numbers JP=1/2−, 3/2−, 5/2−. By constructing the interpolating currents, the mass spectra can be extracted from the two-point correlation functions in the framework of QCD sum rule method. In the molecular picture, we find that the Ξc′+D*+, Ξc*+D*+, Ξcc*++K¯*0, and Ωcc*+ρ+ may form molecular strange double charm pentaquarks. In both pictures, the masses of the JP=1/2−,3/2− pentaquarks locate within the 4.2–4.6 GeV and 4.2–4.5 GeV regions, respectively. As all of them are above the thresholds of their strong decay channels, they behave as a broad state, making them challenging to be detected experimentally. On the other hand, the strange double charm pentaquark with JP=5/2− lies below its strong decay channel, which may be a very narrow state and easy to identify experimentally. The best observed channel is its semileptonic decay to double charm baryon. As the result, we strongly suggest experiments to search for JP=5/2− strange double charm pentaquarks first. Published by the American Physical Society 2024

Improved light-cone harmonic oscillator model for the ϕ -meson longitudinal leading-twist light-cone distribution amplitude and its effects to Ds+→ϕℓ+νℓ

In the present paper, we study the properties of ϕ-meson longitudinal leading-twist light-cone distribution amplitude ϕ2;ϕ∥(x,μ) by starting from a light-cone harmonic oscillator model for its wave function. To fix the input parameters, we derive the first ten order ξ moments of ϕ2;ϕ∥(x,μ) by using the QCD sum rules approach under the background field theory. The curves of ϕ2;ϕ∥(x,μ=2 GeV) tend to be a single-peak behavior, which is consistent with the latest lattice QCD result. To show how the twist-3 light-cone distribution amplitudes (LCDAs) affect the results, we consider two scenarios for the ϕ-meson chiral twist-3 LCDAs ϕ3;ϕ⊥(x) and ψ3;ϕ⊥(x), i.e., the ones using the Wandzura-Wilczek approximation with ϕ2;ϕ∥(x,μ) (S1) and the ones using self-consistent conformal expansion with second-order Gegenbauer moments a2;ϕ2 in this work (S2). As an application, we derive the Ds+→ϕ transition form factors (TFFs) by using the QCD light-cone sum rules. The TFFs at large recoil point for those two scenarios are given separately. As for the two TFF ratios γV and γ2, we obtain γV(S1)=1.755−0.005+0.008, γ2(S1)=0.852−0.133+0.135, γV(S2)=1.723−0.021+0.023, and γ2(S2)=0.785−0.104+0.100. After extrapolating those TFFs to the physically allowable region, we then obtain the transverse, longitudinal, and total decay widths for semileptonic decay Ds+→ϕℓ+νℓ. Then the branching fractions are B(S1)(Ds+→ϕe+νe)=(2.347−0.191+0.342)×10−3, B(S1)(Ds+→ϕμ+νμ)=(2.330−0.190+0.341)×10−3, B(S2)(Ds+→ϕe+νe)=(2.367−0.132+0.256)×10−3, and B(S2)(Ds+→ϕμ+νμ)=(2.349−0.132+0.255)×10−3, which show good agreement with the data issued by the BESIII, CLEO, and Collaborations. We finally calculate Ds+→ϕℓ+νℓ polarization and asymmetry parameters, which can be measured and tested in future experiments. Published by the American Physical Society 2024

Analysis of the hidden-charm-hidden-strange tetraquark mass spectrum via the QCD sum rules

In the present work, we construct the diquark-antidiquark type four-quark currents to investigate the mass spectrum of the ground state hidden-charm-hidden-strange tetraquark states with the quantum numbers JPC=0++, 1+−, 1++ and 2++ via the traditional QCD sum rules in a comprehensive way. We update old calculations, perform new calculations and analysis in a rigorous way, and take account of the net light-flavor SU(3) breaking effects in a consistent way. And we make more reasonable identifications for the X(3960), X(4140), X(4274), X(4500), X(4685) and X(4700) and supersede some old identifications. Furthermore, we consider our previous theoretical predictions, and make reasonable/suitable identifications of the new LHCb states hc(4000) and χc1(4010).

Light single-gluon hybrid states with various exotic quantum numbers

We apply the QCD sum rule method to study the light single-gluon hybrid states with various (exotic) quantum numbers. We construct 24 single-gluon hybrid currents and use 18 of them to calculate the masses of 44 single-gluon hybrid states with the quark-gluon contents q¯qg (q=u/d) and s¯sg. We concentrate on the hybrid states with the exotic quantum number JPC=1−+, whose masses and widths are calculated to be M|q¯qg;1−1−+⟩=1.67−0.17+0.15 GeV, Γ|q¯qg;1−1−+⟩=530−330+540 MeV, M|q¯qg;0+1−+⟩=1.67−0.17+0.15 GeV, Γ|q¯qg;0+1−+⟩=120−110+160 MeV, M|s¯sg;0+1−+⟩=1.84−0.15+0.14 GeV, and Γ|s¯sg;0+1−+⟩=100−80+110 MeV. Our results support the interpretations of the π1(1600) and η1(1855) as the hybrid states |q¯qg;1−1−+⟩ and |s¯sg;0+1−+⟩, respectively. Considering the uncertainties, our results suggest that the π1(1600) and η1(1855) may also be interpreted as the hybrid states |q¯qg;1−1−+⟩ and |q¯qg;0+1−+⟩, respectively. To differentiate these two assignments and to verify whether they are hybrid states or not, we propose to examine the a1(1260)π decay channel in future experiments. Published by the American Physical Society 2024

Searching for |Vcd| through the exclusive decay [formula omitted] within QCD sum rules

In this paper, we carry out an investigation into the semileptonic decays Ds+→K0ℓ+νℓ with ℓ=(e,μ) by employing the QCD light-cone sum rules approach. The vector transition form factor (TFF) f+Ds+K0(q2) for Ds+→K0 decay is calculated while considering its next-to-leading order contribution. Subsequently, we briefly introduce the twist-2, 3 kaon distribution amplitudes, which are calculated by using QCD sum rules within the framework of the background field theory. At the large recoil point, the TFF has f+Ds+K0(0)=0.692−0.026+0.027. Then, we extrapolate f+Ds+K0(q2) to the whole physical q2-region via the simplified z(q2,t)-series expansion, and the behavior of TFF f+Ds+K0(q2) is exhibited in the numerical results part, including the theoretical and experimental predictions for comparison. In addition, we compute the differential branching fraction B(Ds+→K0ℓ+νℓ) with the electron and muon channels, which are expected to be B(Ds+→K0e+νe)=3.379−0.275+0.301×10−3 and B(Ds+→K0μ+νμ)=3.351−0.273+0.299×10−3 as well as contained other results for comparison. Our results show good agreement with the BESIII measurements and theoretical predictions. Furthermore, we present our prediction with respect to the CKM matrix element |Vcd| by using the B(Ds+→K0e+νe) result from BESIII Collaboration, yielding |Vcd|=0.221−0.010+0.008. Finally, we provide the ratio between Ds+→K0e+νe and Ds+→ηe+νe channels, i.e.RK0/ηe=0.144−0.020+0.028.

Light tetraquark states with exotic quantum numbers JPC=2+−

We study the masses of light tetraquark states udu¯d¯, usu¯s¯, and sss¯s¯ with exotic quantum numbers JPC=2+− using the method of QCD sum rules. It is found that there is no tetraquark operator with two Lorentz indices coupling to the 2+− quantum numbers. To investigate such tetraquark states, we construct the interpolating tetraquark currents with three Lorentz indices and without a derivative operator. We calculate the correlation functions up to dimension-ten condensates and extract the 2+− invariant functions via the projector operator. Our results show that the masses of the udu¯d¯, usu¯s¯, and sss¯s¯ tetraquark states with JPC=2+− are about 3.3–3.5, 3.5–3.7, and 3.67 GeV, respectively. We further discuss the strong decays of these light tetraquarks into the two-meson and baryon-antibaryon final states and suggest to search for them in the ρπ, ωπ, ϕπ, b1π, h1π, KK¯*, KK¯1, ΔΔ¯, Σ*Σ¯*, Ξ*Ξ¯*, and ΩΩ¯ channels in the future. Published by the American Physical Society 2024

Lattice QCD determination of the normalization of the leading-twist photon distribution amplitude and susceptibility of the quark condensate

The normalization of the leading-twist photon distribution amplitude (DA), fγ⊥, is an important ingredient in the study of exclusive processes involving the photon emission by means of QCD sum-rules. In this paper we determine the up-, down- and strange-quark contribution to fγ⊥ by exploiting its relation to the zero-momentum two-point correlation function of the electromagnetic current Jemμ and the electric component of the tensor current Tμν. To that end we employ the gauge ensembles obtained by using Nf=2+1+1 Wilson-Clover twisted-mass quark flavors, generated by the Extended Twisted Mass (ETM) Collaboration, and after adding all sources of systematic uncertainties, we obtain a total error of 1.5% and 3.5%, respectively, for the light- (u and d) and strange-quark contribution to fγ⊥(2 GeV) in the MS¯ scheme, thus improving their accuracy by a factor of 2.3 and 2.8, respectively. For the strange-quark contribution fγ,s⊥(2 GeV), we observe a discrepancy with respect to previous lattice calculations. By combining our result with the world average lattice value of the chiral condensate, we obtain for the susceptibility of the quark condensate χdMS¯(2 GeV)≃χuMS¯(2 GeV)=2.17(12) GeV−2. Published by the American Physical Society 2024

QCD bounds on leading-order hadronic vacuum polarization contributions to the muon anomalous magnetic moment

QCD bounds on the leading-order (LO) hadronic vacuum polarization (HVP) contribution to the anomalous magnetic moment of the muon [aμHVP,LO, aμ=(g−2)μ/2] are determined by imposing Hölder inequalities and related inequality constraints on systems of finite-energy QCD sum rules. This novel methodology is complementary to lattice QCD and data-driven approaches to determining aμHVP,LO. For the light-quark (u, d, s) contributions up to five-loop order in perturbation theory in the chiral limit, LO in light-quark mass corrections, next-to-leading order in dimension-four QCD condensates, and to LO in dimension-six QCD condensates, we find that (657.0±34.8)×10−10≤aμHVP,LO≤(788.4±41.8)×10−10, bridging the range between lattice QCD and data-driven values. Published by the American Physical Society 2024

Parameters of the tensor tetraquark [formula omitted]

The mass and width of the tensor tetraquark T=bbc‾c‾ with spin-parity JP=2+ are calculated in the context of the QCD sum rule method. The tetraquark T is modeled as a diquark-antidiquark state built of components bTCγμb and c‾γνCc‾T with C being the charge conjugation matrix. The mass m=(12.795±0.095)GeV of the exotic tensor meson T is found by means of the two-point sum rule approach. Its full width Γ is evaluated by considering processes T→Bc−Bc−, Bc−Bc⁎−, and Bc⁎−Bc⁎−. Partial widths of these decays are computed by means of the three-point sum rule approach which is used to determine the strong couplings at relevant tetraquark-meson-meson vertices. Predictions obtained for the width ΓT=55.5−9.9+10.6MeV, as well as the mass of the tetraquark T can be useful in investigations of fully heavy four-quark mesons.

Doubly-charm and doubly-bottom pentaquark molecular states via the QCD sum rules

In this work, the doubly-charm and doubly-bottom pentaquark molecular states [Formula: see text] and [Formula: see text] are studied via the QCD sum rules. Sixteen color singlet-singlet type currents with the definite isospin-spin-parity [Formula: see text] are constructed to interpolate the corresponding hadronic states with the same quantum numbers. The masses and pole residues of those doubly-heavy pentaquark molecular states are calculated, the results show that their masses are all below the corresponding meson-baryon thresholds, which means that they are possible bound states, not resonant states, moreover, the possible decay channels for the doubly-charm molecular states are given.

Strong decays of Pcs(4338) and its high isospin cousin via QCD sum rules

In the present work, the strong decays of the newly observed Pcs(4338) as well as its high isospin cousin Pcs(4460) are studied via the QCD sum rules. According to conservation of isospin, spin, and parity, the hadronic coupling constants in four decay channels are obtained; then, the partial decay widths are obtained. The total width of the Pcs(4338) coincides with the experimental data nicely, while the predictions for the Pcs(4460) can be testified in the future experiment and shed light on the nature of the Pcs(4338). Published by the American Physical Society 2024

Semileptonic Ωb→Ωcℓν¯ℓ transition in full QCD

We investigate the semileptonic decay of Ωb→Ωcℓν¯ℓ in three lepton channels. To this end, we use the QCD sum rule method in three point framework to calculate the form factors defining the matrix elements of these transitions. Having calculated the form factors as building blocks, we calculate the decay widths and branching fractions of the exclusive decays in all lepton channels and compare the results with other theoretical predictions. The obtained results for branching ratios and ratio of branching fractions at different leptonic channels may help experimental groups in their search for these weak decays. Comparison of the obtained results with possible future experimental data can be useful to check the order of consistency between the standard model theory predictions and data on the heavy baryon decays. Published by the American Physical Society 2024