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We derive, in more general conditions, a recently introduced variance sum rule (VSR) (Di Terlizzi et al 2024 Science 383 971) involving variances of displacement and force impulse for overdamped Langevin systems in a nonequilibrium steady state (NESS). This formula allows visualising the effect of nonequilibrium as a deviation of the sum of variances from normal diffusion 2 Dt , with D the diffusion constant and t the time. From the VSR, we also derive formulas for the entropy production rate σ that, differently from previous results, involve second-order time derivatives of position correlation functions. This novel feature gives a criterion for discriminating strong nonequilibrium regimes without measuring forces. We then apply and discuss our results to three analytically solved models: a stochastic switching trap, a Brownian vortex, and a Brownian gyrator. Finally, we compare the advantages and limitations of known and novel formulas for σ in an overdamped NESS.

In this study, we constructed color singlet-singlet-type five-quark currents with isospins ( I , I 3 ) = ( 1 2 , 1 2 ) and ( 3 2 , 1 2 ) unambiguously to explore the D ¯ ∑ c , D ¯ ∑ c ∗ , D ¯ ∗ ∑ c , and D ¯ ∗ ∑ c ∗ pentaquark states via the quantum chromodynamics sum rules for the first time, where D ¯ , ∑ c , ⋯ , represent the color singlet clusters with the same quantum numbers as the corresponding physical mesons or baryons. The numerical results support assigning P c (4312), P c (4380), P c (4440), and P c (4457) as the D ¯ ∑ c , D ¯ ∑ c ∗ , D ¯ ∗ ∑ c , and D ¯ ∗ ∑ c ∗ pentaquark states, respectively, with the isospin I = 1 2 . The corresponding D ¯ ∑ c , D ¯ ∑ c ∗ , D ¯ ∗ ∑ c , and D ¯ ∗ ∑ c ∗ pentaquark states with the isospin I = 3 2 have slightly larger masses. The observations of the high pentaquark candidates in the J/ψ ∆ invariant mass spectrum would shed light on the nature of the P c states and contribute in distinguishing the scenarios of the color antitriplet-antitriplet-antitriplet-type and color singlet-singlet-type pentaquark states.

In this paper we revisit D s → f 0 ( 980 ) form factors from the light-cone sum rules based on the q ¯ q picture of f 0 ( 980 ) . The main motivation of this study is the decay width of D s + → π π S I = 0 e + ν e measured recently by BESIII collaboration and the D s → f 0 ( 980 ) form factor extracted under the resonant model, here the subscript S and superscript I = 0 indicate the S -wave isoscalar dipion system. Our result of the differential width of D s + → f 0 ( 980 ) ( → π π S I = 0 ) e + ν e decay obtained under the narrow width approximation is lower than the data, the result obtained under the resonant Flatté model is consistent with the data, indicating a sizable mixing ∼ 20 ∘ between s ¯ s and u ¯ u + d ¯ d of f 0 . In order to get a model independent prediction, we suggest to calculate D s → π π I = 0 form factors with the isoscalar dipion light-cone distribution amplitudes. Our calculation of D s → π π I = 0 form factors is carried out at leading twist level due to the finite knowledge of dipion system, the differential width shows a moderate evolution in contrast to that obtained from the narrow width approximation and the Flatté model. Since the D s → f 0 ( 980 ) form factors is dominated by the twist three contribution, further measurements on four-body semileptonic charm decays would help us to study the dimeson light-cone distribution amplitudes, especially for the subleading twist one.

In the literature, there are many algorithms for the computation of Feynman diagrams (Hahn, Nucl. Phys. B Proc. Suppl. 89 , 231–236 2000 ; Smirnov and Zeng, Comput. Phys. Commun. 302 , 109261 2024 ; Patel, Comput. Phys. Commun. 197 , 276–290 2015 ). QCD Sum Rules, however, differ from standard loop computations in several key aspects. One of the fundamental distinctions of the QCD Sum Rules technique is the inclusion of the Borel transformation (Shifman et al. Nucl. Phys. B 147 , 448–518 1979 ). To address this critical component, the borelT package is developed in Mathematica (Wolfram Research, Inc., 2023 ) , ensuring the integration of the Borel transformation into the algorithms.

Sum rules are a useful characterization of transition strength functions for atomic nuclei. Unlike the Ikeda sum rule for single Gamow–Teller transitions, as a result of SU(4) breaking, double Gamow–Teller transition sum rules depend upon the detailed many-body wavefunctions. In order to systematically investigate the double Gamow–Teller (DGT) transition sum rules, we approximate the shell-model ground state with nucleon-pair condensates, with angular-momentum projection after variation, and use expectation values to compute the 2β[sup.−] and 2β[sup.+] sum rules. For even–even nuclei in the 1s0d and 1p0f valence spaces, we quantitatively estimate the model-dependent fractions of the DGT sum rules, and analyze the importance of the double isospin analog state to the DGT strength function, relative to SU(4) predictions.

In this paper, we address double parton scattering (DPS) in pA collisions. Within the Light-Front approach, we formally derive the two contributions to the nuclear double parton distribution (DPD), namely: DPS1, involving two partons from the same nucleon, and DPS2, where the two partons belong to different parent nucleons. We then generalize the sum rule for hadron DPDs to the nuclear case and analytically show how all contributions combine to give the expected results. In addition partial sum rules for the DPDs related to DPS1 and DPS2 mechanisms are discussed for the first time. The deuteron system is considered for the first calculation of the nuclear DPD by using a realistic wave function obtained from the very refined nucleon-nucleon AV18 potential, embedded in a rigorous Poincaré covariant formalism. Results are used to test sum rules and properly verify that DPS1 contribution compares with the DPS2 one, although smaller. We also introduce EMC-like ratios involving nuclear and free DPDs to address the potential role of DPS in understanding in depth the EMC effect.

Ashby’s law of requisite variety allows a comparison of systems with their environments, providing a necessary (but not sufficient) condition for system efficacy: A system must possess at least as much complexity as any set of environmental behaviors that require distinct responses from the system. However, to account for the dependence of a system’s complexity on the level of detail—or scale—of its description, a multi-scale generalization of Ashby’s law is needed. We define a class of complexity profiles (complexity as a function of scale) that is the first, to our knowledge, to exhibit a multi-scale law of requisite variety. This formalism provides a characterization of multi-scale complexity and generalizes the law of requisite variety’s single constraint on system behaviors to a class of multi-scale constraints. We show that these complexity profiles satisfy a sum rule, which reflects a tradeoff between smaller- and larger-scale degrees of freedom, and we extend our results to subdivided systems and systems with a continuum of components.

The normalization of X‐ray absorption near‐edge structure (XANES) spectra is required for comparing spectral features and extracting quantitative information in analytical techniques such as linear combination analysis, principal component analysis and multivariate curve resolution. Most published data are normalized to the edge‐jump, but normalization to the spectral area has also been applied. The latter is particularly attractive if only a small energy range around the absorption can be recorded reliably. Here, the two normalization methods are compared at the L3‐edge of Pt, Pd and Rh, and at the Ni K‐edge using experimental and calculated spectra. Normalization to the spectral area is found to be a viable approach if the range for the area normalization is sufficiently large. Normalization of XANES data to the spectral area is shown to be a viable normalization method with an error of a few percent as evaluated by comparison with calculated spectra and spectra normalized to the edge‐jump.

In this work we study the meson vertex D s D K ∗ using the QCD sum rules. We compute the three-point correlation functions for the three cases of different off-shell mesons. The form factors for each case are fitted to the numerical calculation of the correlation functions, and the coupling constant of the vertex is obtained by comparing the form factors at their respective off-shell meson pole. The result obtained for the coupling constant is g D s D K ∗ = 2 . 29 - 0.41 + 0.65 .

Motivated by the recent observation of the JP=1+ resonance X(2085) in the pΛ¯ system by the BESIII collaboration, we study the molecular states of pΛ¯ and pΣ¯ with baryon-antibaryon structures within the framework of the QCD sum rules. Non-perturbative contributions up to dimension 13 in quark operator expansion (OPE) are considered. Our calculation results indicate the possible existence of six pΛ¯ and pΣ¯ molecular states with quantum numbers JP=0-,0+,1- , which do not support X(2085), or at least not its main component, being a pΛ¯ or pΣ¯ molecular state. Additionally, the previously observed state X(2075) also lies in the vicinity of pΛ¯ and pΣ¯ molecular states, and its inner structure might not be entirely transparent, rather possibly a mixture of tetraquark and hexaquark states. The possible decay modes of the concerned states are analyzed.