Sum Rules Research Articles

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.

Chiral properties of the nucleon interpolating current and θ -dependent observables

We revisit the chiral properties of nucleon interpolating currents, and show that of the two leading order currents j1 and j2, only two linear combinations j1±j2 transform covariantly under the anomalous U(1)A symmetry. As a result, calculations of quantities which vanish by symmetry in the chiral limit may produce unphysical results if carried out with different linear combinations of the currents. This includes observables such as electric dipole moments, induced by the quantum chromodynamics (QCD) parameter θ, and the θ-dependence of the nucleon mass. For completeness, we also exhibit the leading order results for nucleon electric dipole moments (dn,p) induced by θ, and the nucleon magnetic moments (μn,p), when calculated using QCD sum rules for both the covariant choices of the nucleon interpolating current. The results in each channel, conveniently expressed as the ratios, dn,p/μn,p, are numerically consistent, and reflect the required physical dependence on θ. Published by the American Physical Society 2024

Detecting the spread of valence-band Wannier functions by optical sum rules

Detecting the spread of valence-band Wannier functions by optical sum rules

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

Nonlinear corrections to the momentum sum rule

Nonlinear corrections to the momentum sum rule

Interaction of exotic states in a hadronic medium: the Z c (3900) case

We investigate the interactions of the charged exotic state Z c (3900) in a hadronic medium composed of light mesons. We study processes such as Zcπ→DD¯ , Zcπ→D*D¯* , Zcπ→DD¯* and the inverse ones. Using effective Lagrangians and form factors calculated with Quantum Chromodynamics (QCD) sum rules (treating the Z c (3900) as a tetraquark) we estimate the vacuum and thermally-averaged cross-sections of these reactions. We find that the Z c (3900) has relatively large interaction cross sections with the constituent particles of the hadronic medium. After that, we use the production and suppression cross sections in a rate equation to estimate the time evolution of the Z c multiplicity. We include the Z c decay and regeneration terms The coalescence model is employed to compute the initial Z c multiplicity for the compact tetraquark configuration. Our results indicate that the combined effects of hadronic interactions, hydrodynamical expansion, decay and regeneration affect the final yield, which is bigger than the initial value. Besides, the dependence of the Z c final yield with the centrality, center-of-mass energy and the charged hadron multiplicity measured at midrapidity [dNch/dη(η<0.5)] is also investigated.

A comparative study of transition oscillator strengths and static polarizabilities of the hydrogen atom confined in Gaussian potential

Abstract The multipole (dipole, quadrupole, and octopole) photon-absorption transition oscillator strengths for the ground state of hydrogen atom confined in Gaussian potential are investigated for a great variety of potential depths and confining radii. It is interestingly found that at fixed potential depth the gradual increase of confining radius shows first destructive and then constructive effect on the multipole oscillator strengths. Such an effect can be understood from the overlap between the initial and final states. Multipole polarizabilities of the system are obtained through the sum-over-states formalism where the contributions from both the bound and continuum spectra of the system are included. Although the separate bound and continuum contributions can not be determined accurately, due to the long-range nature of the Coulomb potential introduced by the nucleus, their summations can be obtained to reasonably good accuracy, leading to fast convergence of numerical calculations of multipole polarizabilities. The present results are compared with previous calculations available in the literature. Although good agreement is observed for the dipole polarizability, significant differences exist in the quadrupole polarizability and orders-of-magnitude differences appear in the octopole polarizability. The possible reason for such large differences is analyzed by comparing the sum rule of corresponding oscillator strengths.&amp;#xD;

Work Sum Rule for Open Quantum Systems.

A key question in the thermodynamics of open quantum systems is how to partition thermodynamic quantities such as entropy, work, and internal energy between the system and its environment. We show that the only partition under which entropy is nonsingular is based on a partition of Hilbert space, which assigns half the system-environment coupling to the system and half to the environment. However, quantum work partitions nontrivially under Hilbert-space partition, and we derive a work sum rule that accounts for quantum work at a distance. All state functions of the system are shown to be path independent once this nonlocal quantum work is properly accounted for. Our results are illustrated with application to a driven resonant level strongly coupled to a reservoir.

Investigation on the Ω(2012) from QCD sum rules

We study the recently observed Ω(2012) baryon in quantum chromodynamics (QCD) sum rules. We construct the P-wave Ω baryon currents with a covariant derivative, and perform spin projection to obtain the currents with total spin 1/2 and 3/2. We then apply the parity-projected QCD sum rules to separate the contributions of the positive and negative parity states. We extract the masses of JP=1/2− and 3/2− states to be M1/2−=2.07−0.07+0.07 GeV and M3/2−=2.05−0.10+0.09 GeV. Both results are in good agreement with the experimental result. Therefore, it is likely that the Ω(2012) is a negative parity state, which is interpreted as a P-wave excited state in the quark model. However, its spin is not determined in the present analysis, which can be done by detailed study on its decay properties. Published by the American Physical Society 2024

Integrated photonuclear cross sections in the giant dipole resonance of odd-mass actinide nuclei

This study explores the integrated total photonuclear cross section (σ0) within the context of the giant dipole resonance (GDR) in odd-mass actinide nuclei. Using artificial neural networks (ANNs) and adaptive neuro-fuzzy ınference system (ANFIS) machine learning algorithms, we analyze the GDR behaviors associated with the σ0 values in these nuclei. The modeling results obtained from ANFIS and ANN are compared among themselves and with the Translational Galilean Invariant Quasiparticle Phonon Nuclear Model (TGI-QPNM) and experimental data. Machine learning analysis and TGI-QPNM results provide valuable insights into the GDR characteristics of odd-mass actinides, shedding light on their photonuclear properties. The ANFIS model has achieved an R2 value of 0.98 and an RMSE of 0.19, while the ANN model (LM) has yielded an R2 value of 0.95 and an RMSE of 0.24. These findings deepen our understanding of nuclear physics, underscoring the role of artificial intelligence techniques in deciphering complex phenomena within nuclear structures. In conclusion, our study suggests that the ANFIS model, in agreement with TGI-QPNM results, generally outperforms the ANN (LM) method and could be a more effective tool for estimating the energy-weighted sum rule for GDR.

Light-ray sum rules and the c-anomaly

In a four-dimensional quantum field theory that flows between two fixed points under the renormalization group, the change in the conformal anomaly ∆a has been related to the average null energy. We extend this result to derive a sum rule for the other anomaly coefficient, ∆c, in terms of the stress tensor three-point function. While the sum rule for ∆a is an expectation value of the averaged null energy operator, and therefore positive, the result for ∆c involves the off-diagonal matrix elements, so it does not have a fixed sign.

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Stability criteria and calculus rules via conic contingent coderivatives in Banach spaces

This paper addresses the study of novel constructions of variational analysis and generalized differentiation that are appropriate for characterizing robust stability properties of constrained set-valued mappings/multifunctions between Banach spaces important in optimization theory and its applications. Our tools of generalized differentiation revolve around the newly introduced concept of ε-regular normal cone to sets and associated coderivative notions for set-valued mappings. Based on these constructions, we establish several characterizations of the central stability notion known as the relative Lipschitz-like property of set-valued mappings in infinite dimensions. Applying a new version of the constrained extremal principle of variational analysis, we develop comprehensive sum and chain rules for our major constructions of conic contingent coderivatives for multifunctions between appropriate classes of Banach spaces.

Analysis of the Ξc∗K¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi _c^* {\\bar{K}}$$\\end{document} molecular pentaquark state by its electromagnetic properties

We are systematically studying the electromagnetic characteristics of multiquark systems to shed light on their internal structure, whose nature and quantum numbers are controversial. In this study, we investigate the magnetic dipole, electric quadrupole, and magnetic octupole moments of the Ξc∗K¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi _c^*{\\bar{K}}$$\\end{document} state within the context of the QCD light-cone sum rule. During this analysis, we posit that the Ξc∗K¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi _c^*{\\bar{K}}$$\\end{document} state assumes a molecular structure with quantum numbers JP=32-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^P = \\frac{3}{2}^-$$\\end{document}. The extracted outcomes are given as μΞc∗K¯=0.15-0.03+0.04μN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _{\\Xi _c^*{\\bar{K}}} = 0.15^{+0.04}_{-0.03}\\,\\mu _N$$\\end{document}, QΞc∗K¯=(-0.93-0.17+0.22)×10-3fm2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {Q}}_{\\Xi _c^*{\\bar{K}}} = (-0.93^{+0.22}_{-0.17})\ imes 10^{-3}\\,\ extrm{fm}^{\ extrm{2}}$$\\end{document}, and OΞc∗K¯=(-0.45-0.09+0.10)×10-4fm3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}_{\\Xi _c^*{\\bar{K}}} = (-0.45^{+0.10}_{-0.09})\ imes 10^{-4}\\,{\ extrm{fm}}^{\ extrm{3}}$$\\end{document}. The findings of this study, when considered alongside other pertinent characteristics, may assist in elucidating the nature of this controversial phenomenon.

Probing the Quark Orbital Angular Momentum at Electron-Ion Colliders Using Exclusive π^{0} Production.

We propose to detect signals from quark orbital angular momentum (OAM) through exclusive π^{0} production in electron- (longitudinally polarized) proton collisions. Our analysis demonstrates that the sin2ϕ azimuthal angular correlation between the transverse momentum of the scattered electron and the recoil proton serves as a sensitive probe of quark OAM. Additionally, we present a numerical estimate of the asymmetry associated with this correlation for the kinematics accessible at the Electron-Ion Colliders in the U.S. and China. This study aims to pave the way for the first experimental study of quark OAM in relation to the Jaffe-Manohar spin sum rule.

Construction of symbols satisfying sum rules of order p using standard pairs

In this paper, using standard pairs, we present a method to construct symbols satisfying the sum rules of order [Formula: see text] for any given [Formula: see text]. It is shown that using matrix polynomial theory symbols, symmetric or non-symmetric, satisfying the sum rules of order [Formula: see text] can be constructed efficiently. The construction is illustrated using various examples.

Diffusion model approach to simulating electron-proton scattering events

Generative artificial intelligence is a fast-growing area of research offering various avenues for exploration in high-energy nuclear physics. In this work, we explore the use of generative models for simulating electron-proton collisions relevant to experiments like the Continuous Electron Beam Accelerator Facility and the future Electron-Ion Collider (EIC). These experiments play a critical role in advancing our understanding of nucleons and nuclei in terms of quark and gluon degrees of freedom. The use of generative models for simulating collider events faces several challenges such as the sparsity of the data, the presence of global or eventwide constraints, and steeply falling particle distributions. In this work, we focus on the implementation of diffusion models for the simulation of electron-proton scattering events at EIC energies. Our results demonstrate that diffusion models can reproduce relevant observables such as momentum distributions and correlations of particles, momentum sum rules, and the leading electron kinematics, all of which are of particular interest in electron-proton collisions. Although the sampling process is relatively slow compared to other machine-learning architectures, we find diffusion models can generate high-quality samples. We foresee various applications of our work including inference for nuclear structure, interpretable generative machine learning, and searches of physics beyond the Standard Model. Published by the American Physical Society 2024

Axion‐Like Interactions and CFT in Topological Matter, Anomaly Sum Rules and the Faraday Effect

AbstractFundamental aspects of chiral anomaly‐driven interactions in conformal field theory (CFT) in four spacetime dimensions are discussed. These interactions find application in very general contexts, from early universe plasma to topological condensed matter. The key shared characteristics of these interactions are outlined, specifically addressing the case of chiral anomalies, both for vector currents and gravitons. In the case of topological materials, the gravitational chiral anomaly is generated by thermal gradients via the (Tolman–Ehrenfest) Luttinger relation. In the CFT framework, a nonlocal effective action, derived through perturbation theory, indicates that the interaction is mediated by excitation in the form of an anomaly pole, which appears in the conformal limit of the vertex. To illustrate this, it is demonstrated how conformal Ward identities (CWIs) in momentum space allow to reconstruct the entire chiral anomaly interaction in its longitudinal and transverse sectors just by inclusion of a pole in the longitudinal sector. Both sectors are coupled in amplitudes with an intermediate chiral fermion or a bilinear Chern–Simons current with intermediate photons. In the presence of fermion mass corrections, the pole transforms into a cut, but the absorption amplitude in the axial‐vector channel satisfies mass‐independent sum rules related to the anomaly in any chiral interaction. The detection of an axion‐like/quasiparticle in these materials may rely on a combined investigation of these sum rules, along with the measurement of the angle of rotation of the plane of polarization of incident light when subjected to a chiral perturbation. This phenomenon serves as an analog of a similar one in ordinary axion physics, in the presence of an axion‐like condensate, which is rederived using axion electrodynamics.

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