Sum Rules Research Articles

Variance sum rule: proofs and solvable models

Abstract We derive, in more general conditions, a recently introduced variance sum rule (VSR) [I. 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 2Dt, 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.

Generalized Optical Sum Rules for Light-Dressed Matter.

Light-driven matter can exhibit qualitatively distinct electronic and optical properties from those observed at equilibrium. We introduce generalized sum rules for the optical properties of light-driven molecules. Both classical and quantum light are considered. For classical light, the Floquet sum rules show that the sum of all Fourier components, indexed by n = -∞ to ∞, of the time-dependent dipole matrix elements between Floquet modes weighted by the corresponding quasienergy difference in the first Floquet Brillouin zone plus n driving frequency is a constant. Surprisingly, it is impossible to alter the energy exchange rate between matter and a perturbative external probe laser by a strong driving, even though the spectra can differ significantly from the bare ones. These developments provide guidance for the control of effective optical properties of matter by light fields.

Magnetic moments and axial charges of the octet hidden-charm molecular pentaquark family

In this work, we calculate the magnetic moment and axial charge of the octet hidden-charm molecular pentaquark family in quark model. The Coleman-Glashow sum rule for the magnetic moments of pentaquark family is always fulfilled independently of SU(3) symmetry breaking. In the 82f flavor representation, the magnetic moments of hidden-charm molecular pentaquark states with spin configuration JP=12−(12+⊗0−) are all equal to μc=0.38μN. The axial charges of octet hidden-charm molecular pentaquark states are quite small compared to the axial charge of nucleon. The axial charges of the pentaquark states with the spin configuration JP=12−(12+⊗0−) in 82f flavor representation are all zero. Published by the American Physical Society 2024

Doubly charmed pentaquark states in QCD sum rules

We have studied the mass spectra of doubly charmed pentaquark states in the Λc(*)D(*) and Σc(*)D(*) channels with JP=1/2±, 3/2±, and 5/2± within the framework of quantum chromodynamics sum rules. We use the parity projected sum rules to separate the contributions of negative and positive parities from the two-point correlations induced by the pentaquark interpolating currents. Our results show that the bound states of Pcc pentaquarks may exist in the ΛcD(12−), ΣcD(12−), ΣcD*(32−), Λc*D(32−), Λc*D*(52−) channels with negative-parity and ΣcD(12+), ΣcD*(32+), Σc*D(32+) channels with positive-parity, since their masses are predicted to be lower than the corresponding meson-baryon thresholds. However, they are still allowed to decay into the Ξcc(*)π final states via strong interaction. The triply charged Pcc+++(ccuud¯) and neutral Pcc0(ccddu¯) in the isospin quartet would definitely be pentaquark states due to their exotic charges. We suggest searching for these characteristic doubly charmed pentaquark signals in the Pcc+++→Ξcc(*)++π+/ρ+, Σc(*)++D(*)+ and Pcc0→Ξcc(*)+π−/ρ−, Σc(*)0D(*)0 decays in the near future. Published by the American Physical Society 2024

Trace anomaly form factors from lattice QCD

The hadron mass can be obtained through the calculation of the trace of the energy-momentum tensor in the hadron which includes the trace anomaly and sigma terms. The anomaly due to conformal symmetry breaking is believed to be an important ingredient for hadron mass generation and confinement. In this work, we will present the calculation of the glue part of the trace anomaly form factors of the pion up to Q2∼4.3 GeV2 and the nucleon up to Q2∼1 GeV2. The calculations are performed on a domain wall fermion ensemble with overlap valence quarks at seven valence pion masses varying from ∼250 to ∼540 MeV, including the unitary point ∼340 MeV. We calculate the radius of the glue trace anomaly for the pion and the nucleon from the z expansion. By performing a two-dimensional Fourier transform on the glue trace anomaly form factors in the infinite momentum frame with no energy transfer, we also obtain their spatial distributions for several valence quark masses. The results are qualitatively extrapolated to the physical valence pion mass with systematic errors from the unphysical sea quark mass, discretization effects in the renormalization sum rule, and finite-volume effects to be addressed in the future. We find the pion’s form factor changes sign, as does its spatial distribution, for light quark masses. This explains how the trace anomaly contribution to the pion mass approaches zero toward the chiral limit. Published by the American Physical Society 2024

Further prediction on the possible double-peak structure of the X17 particle

The [Formula: see text] particle, discovered by [A. J. Krasznahorkay et al., Phys. Rev. Lett. 116, 042501 (2016), doi:10.1103/PhysRevLett.116.042501] at ATOMKI, was recently confirmed in the [Formula: see text] invariant mass spectra by [K. U. Abraamyan, C. Austin, M. I. Baznat, K. K. Gudima, M. A. Kozhin, S. G. Reznikov and A. S. Sorin, arXiv:2311.18632] at JINR. We notice with surprise and interest that the [Formula: see text] seems to have a double-peak structure. This is in a possible coincidence with our QCD sum rule study of [H.-X. Chen, arXiv:2006.01018], where we interpreted the [Formula: see text] as a tetraquark state composed of four bare quarks ([Formula: see text]), and claimed that “A unique feature of this tetraquark assignment is that we predict two almost degenerate states with significantly different widths”. These two different tetraquark states are described by two different chiral tetraquark currents [Formula: see text] and [Formula: see text]. To verify whether the tetraquark assignment is correct or not, we replace the up and down quarks by the strange quarks, and apply the QCD sum rule method to study the other four chiral tetraquark currents [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. We calculate their correlation functions, and find that non-perturbative QCD effects do not contribute much to them. Our results suggest that there may exist four almost degenerate tetraquark states with masses about [Formula: see text] MeV. Each of these states is composed of four bare quarks, either [Formula: see text] or [Formula: see text].

Interpretation of X(3960) as the hidden charm-strange tetraquark states via QCD sum rules

Recently, a hadronic state, named X(3960), about 3.96 GeV with JPC=0++ was observed in LHCb experiment. From its the decay modes, it's reasonable to categorize this structure to novel hadronic state. In this paper, we examine the tetraquark interpretation for the structure of X(3960) in the configurations of [3c]cs⊗[3¯c]c¯s¯, and the QCD sum rules calculations of the mass spectrum are performing. Numerical results indicted that the observed X(3900) could be embedded into the [3c]cs⊗[3¯c]c¯s¯ configuration. Various X(3960) decay modes are evaluated, which are critical for pinning down its configuration and left for experimental verification. In the same way, we evaluate as well the c¯qc¯q, b¯sb¯s, and b¯qb¯q tetraquark state with 0++ quantum number in the configuration of [3c]cs⊗[3¯c]c¯s¯ and find that there might exist six such ground states.

Sum rule for the pseudo-Rényi entropy

By generalizing the density matrix to a transition matrix between two states, represented as |ϕ⟩ and |ψ⟩, one can define the pseudoentropy analogous to the entanglement entropy. In this paper, we establish an operator sum rule that pertains to the reduced transition matrix and reduced density matrices corresponding to the superposition states of |ϕ⟩ and |ψ⟩. It is demonstrated that the off-diagonal elements of operators can be correlated with the expectation value in the superposition state. Furthermore, we illustrate the connection between the pseudo-Rényi entropy and the Rényi entropy of the superposition states. We provide proof of the operator sum rule and verify its validity in both finite-dimensional systems and quantum field theory. We additionally demonstrate the significance of these sum rules in gaining insights into the physical implications of transition matrices, pseudoentropy, and their gravity dual. Published by the American Physical Society 2024

Sum rule comparison of narrowband and broadband sum frequency generation spectra and comparison with theory

Earlier sum frequency generation (SFG) experiments involve one infrared and one visible laser, and a measurement of the intensity of the response, yielding data on the surface sensitive properties of the sample. Recently, both the real and imaginary components of the susceptibility were measured in two different sets of experiments. In one set, a broadband infrared laser was used, permitting observations at very short times, while in another set the infrared laser was narrowband, permitting higher spectral resolution. The differences in the spectrum obtained by the two will be most evident in studying narrow absorption bands, e.g., the band due to dangling OH bonds at a water interface. The direct comparisons in the integrated amplitude (sum rule) of the imaginary part of the dangling OH bond region differ by a factor of 3. Due to variations in experimental setup and data processing, corrections were made for the quartz reference, Fresnel factors, and the incident visible laser wavelength. After the corrections, the agreement differs now by the factors of 1.1 within broadband and narrowband groups and the two groups now differ by a factor of 1.5. The 1.5 factor may arise from the extra heating of the more powerful broadband laser system on the water surface. The convolution from the narrowband SFG spectrum to the broadband SFG spectrum is also investigated and it does not affect the sum rule. Theory and narrowband experiments are compared using the sum rule and agree to a factor of 1.3 with no adjustable parameters.

Mass spectra of heavy hybrid quarkonia and [formula omitted] mesons

Masses and current couplings of the charmonium and bottomonium hybrids c‾gc and b‾gb with spin-parities JPC=0++,0+−,0−+,0−− and 1++,1+−,1−+,1−− are calculated using QCD two-point sum rule method. Computations are performed by taking into account gluon condensates up to dimension 12 including terms ∼〈gs3G3〉2. The parameters of the bottom-charm hybrids b‾gc with quantum numbers JPC=0+,0−,1+, and 1− are calculated as well. In computations the dominance of the pole contribution to sum rule results is ensured. It is demonstrated that all charmonia hybrids decay strongly to two-meson final states. The bottomonium hybrids 0−+ and 1−+ as well as the bottom-charm hybrid mesons 0−(+) and 1−(+) may be stable against strong two-meson decay modes. Results of the present work are compared with ones obtained using the sum rule and alternative approaches. Our predictions for parameters of the heavy hybrid mesons may be useful to study their various decay channels which are important for interpretation of ongoing and future experiments.

The TDHF code Sky3D version 1.2

The Sky3D code has been widely used to describe nuclear ground states, collective vibrational excitations, and heavy-ion collisions. The approach is based on Skyrme forces or related energy density functionals. The static and dynamic equations are solved on a three-dimensional grid, and pairing is been implemented in the BCS approximation. This updated version of the code aims to facilitate the calculation of nuclear strength functions in the regime of linear response theory, while retaining all existing functionality and use cases. The strength functions are benchmarked against available RPA codes, and the user has the freedom of choice when selecting the nature of external excitation (from monopole to hexadecapole and more). Some utility programs are also provided that calculate the strength function from the time-dependent output of the dynamic calculations of the Sky3D code. New version program summaryProgram Title: Sky3DCPC Library link to program files:https://doi.org/10.17632/vzbrzvyrn4.2Developer's repository link:https://github.com/manybody/sky3dLicensing provisions: GPLv3Programming language: Fortran, with one post-processing utility in Python.Journal reference of previous version:: Schuetrumpf, B., Reinhard, P.G., Stevenson, P.D., Umar, A.S., and Maruhn, J.A. (2018). The TDHF code Sky3D version 1.1. Comput. Phys. Commun. 229 (2018) 211–213.Does the new version supersede the previous version?: Yes.Reasons for the new version: The capability of reproducing the nuclear strength function for a variety of newly-coded external boosts has been added.Nature of problem: Calculating nuclear multipole strength functions is a crucial probe that can help model the nuclear system and its structure properties. A variety of models exist for this task, such as QRPA (Quasiparticle Random Phase Approximation) and its variants, but such approaches are often limited due to symmetry constraints. Time-dependent Hartree Fock (TDHF) has been used to simulate nuclear vibrations and collisions between nuclei for low energies without assuming any symmetry in the system. This code extends the TDHF to calculate the multi-pole strength functions of atomic nuclei. We showcase its reliability by comparing it with the established RPA codes for the calculation of such strength functions.Solution method: We extended previous versions of the Sky3D code [1,2] to include an external boost of multipole type where the user can provide custom input that decides the nature of the multipole (monopole, quadrupole, octupole, and so on) boost. The principal aim is to calculate the multipole strength function, which is the Fourier transform of the time-dependent expectation value of the multipole operator, which has the same form as the external boost. The proper unit conversion is done so that one can extract the exact unit of the thus calculated strength function, which is comparable to the available literature in the field. The boundary conditions are chosen such that a Woods-Saxon-like function cuts off the external field, driving it to zero at the boundary.Summary of revisions: The ability to give a more general external field for excitation has been implemented, which can be of a chosen multipolarity and isospin nature. Then, as a function of time, moments for both isospins and for multipolarities up to L=5 are followed. A new analysis program is included to calculate strength functions and energy weighted sum rules. The ability to specify a mixing parameter in the pairing force is included. This allows a mixed surface-volume pairing to be selected in a way more compatable with QRPA codes for comparison. An updated Makefile is included which makes compilation on Apple silicon computers easier.

Analysis of the strong decays of SU(3) partners of the $\Omega(2012)$ baryon

Abstract We estimate the coupling constants and decay widths of the $SU(3)$ partners of the $\Omega(2012)$ hyperon, as discovered by the BELLE Collaboration, using the distribution amplitudes of the octet baryons within light cone sum rules method. Our study includes a comparison of the obtained results for the relevant decay widths with those derived within the framework of the flavor $SU(3)$ analysis. We observe a good agreement between the predictions of both approaches. Moreover, our results on the decay width of the $\Omega \to \Xi K$ is compatible with the existing experimental result within the uncertainties of the model predictions. These results can provide helpful insights for determining the nature of the $SU(3)$ partners of the $\Omega(2012)$ baryon. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

Investigation of Λ(1405)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda (1405)$$\\end{document} as a molecular pentaquark state

Λ(1405)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda (1405)$$\\end{document} is one of the interesting particles with its unclear structure and distinct properties. It has a light mass compared to its non-strange counterpart, despite the strange quark it carries. This situation puts the investigation of this resonance among the hot topics in hadron physics and collects attention to clarify its properties. In this study, we focus on the calculation of the mass and residue of the Λ(1405)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda (1405)$$\\end{document} resonance within the framework of QCD sum rules. We assign a structure in the form of a molecular pentaquark composed from admixture of K-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K^-$$\\end{document} meson-proton and K¯0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{K}^0$$\\end{document} meson-neutron. Using an interpolating current in this form, the masses and the current coupling constant are attained as m=1406±128MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=1406\\pm 128~\ ext {MeV}$$\\end{document} and λ=(3.35±0.35)×10-5GeV6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda =(3.35\\pm 0.35)\ imes 10^{-5}~\ ext {GeV}^6$$\\end{document} for and m=1402±141MeV\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m=1402\\pm 141~\ ext {MeV}$$\\end{document} and λ=(4.08±1.08)×10-5GeV6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda =(4.08\\pm 1.08)\ imes 10^{-5}~\ ext {GeV}^6$$\\end{document} for I Lorentz structures entering the calculations, respectively. The obtained mass values agree well with the experimental data supporting the plausibility of the considered structure.

Electronic structure, spectroscopy and photophysics of rubidium mono-sulphide

We investigated the nineteen first electronic states of the RbS diatomic using post Hartree-Fock configuration interaction methods at the internally contracted multi-reference configuration interaction (MRCI+(Q)) level. We thus mapped their respective potential energy curves with and without considering spin-orbit effects. After nuclear motion treatments, we derived their equilibrium distances, rotational and vibrational constants, and dissociation and electronic excitation energies. Moreover, an evaluation of the dipole moments of RbS was conducted, which in turn were used to evaluate the radiative lifetimes of the vibrational levels of RbS (X2П and A2Σ+) states. Computations show that spin-orbit interactions are important and cannot be omitted. Afterwards, and utilizing the sum rule approximation and the Franck–Condon factors, we computed both the bound-bound contributions and the bound-free terms. Our findings suggest that RbS exhibits intriguing characteristics suitable for laser cooling experiments. In sum, this work contributes to the understanding in-depth of the spectroscopy of RbS and predicts its use as a promising molecular system for laser cooling applications.

An optimized basis for hadronic light-by-light scattering

We present a new basis for the hadronic light-by-light (HLbL) tensor that is optimized for the evaluation of narrow-resonance contributions to HLbL scattering in the anomalous magnetic moment of the muon. As main advantage, kinematic singularities are manifestly absent for pseudoscalar, scalar, and axial-vector states, while the remaining singularities for tensor resonances are minimized, even avoided for special cases, and simple crossing relations among the scalar functions maintained. We scrutinize the properties of this new basis for the scalar-QED pion box, demonstrating that the partial-wave convergence even slightly improves compared to our previous work, and discuss the physical sum rules that ensure basis independence of the HLbL contribution. Finally, we provide explicit expressions for narrow (pseudo-)scalar, axial-vector, and tensor intermediate states in terms of their respective transition form factors.

Noether invariance theory for the equilibrium force structure of soft matter

We give details and derivations for the Noether invariance theory that characterizes the spatial equilibrium structure of inhomogeneous classical many-body systems, as recently proposed and investigated for bulk systems (Sammüller et al 2023 Phys. Rev. Lett. 130 268203). Thereby an intrinsic thermal symmetry against a local shifting transformation on phase space is exploited on the basis of the Noether theorem for invariant variations. We consider the consequences of the shifting that emerge at second order in the displacement field that parameterizes the transformation. In a natural way the standard two-body density distribution is generated. Its second spatial derivative is thereby balanced by two further and different two-body correlation functions, which respectively introduce thermally averaged force correlations and force gradients in a systematic and microscopically sharp way into the framework. Separate exact self and distinct sum rules express this balance. We exemplify the validity of the theory on the basis of computer simulations for the Lennard–Jones gas, liquid, and crystal, the Weeks–Chandler–Andersen fluid, monatomic Molinero–Moore water at ambient conditions, a three-body-interacting colloidal gel former, the Yukawa and soft-sphere dipolar fluids, and for isotropic and nematic phases of Gay–Berne particles. We describe explicitly the derivation of the sum rules based on Noether’s theorem and also give more elementary proofs based on partial phase space integration following Yvon’s theorem.

QCD parameters and SM-high precision from e+e−→ Hadrons: Updated

1. I report an update of my previous comparison of the theoretical value of the muon anomaly aμ≡12(g−2)μ with the new measurement. One finds: Δaμ≡aμexp−aμth=(143±42th±22exp)×10−11 indicating about 3σ discrepancy between the SM predictions and experiment.2. I improve the estimate of QCD power corrections up to dimension D=12 and provide a new estimate of the ones up to D=20 within the Shifman-Vainshtein-Zahkarov (SVZ) expansion by combining the ratio of the SVZ Borel/Laplace sum rules (LSR) with the Braaten-Pich and the author (BNP) τ-like decay moments for the I=1 vector current. The results summarized in Table 1 confirm a violation of the factorization of the four-quark condensates and the value of the gluon one 〈αsG2〉 from some other sources. Up to D=20, I do not observe any factorial nor exponential growth of the size of these power corrections.3. I use these new values of power corrections to extract αs from the BNP lowest moment. To order αs4, I find within the SVZ expansion: αs(Mτ)=0.3081(50)fit(71)αs5 [resp. 0.3260(47)fit(62)αs5] implying αs(MZ)=0.1170(6)(3)evol [resp. 0.1192(6)(3)evol] for Fixed Order (FO) [resp. Contour Improved (CI)] PT series. They lead to the mean: αs(Mτ)|SVZ=0.3180(58)fit(99)syst and αs(MZ)|SVZ=0.1182(14)(3)evol where the systematic error(syst) takes into account the discrepancy between the FO and CI results. Using the lowest BNP moment, we also obtain from the V+A component of τ-decay data: αs(Mτ)|τ,V+A=0.3040(76)fit(68)syst giving: αs(MZ)|τ,V+A=0.1166(8)(3)evol. The average of the two determinations from e+e− and τ-decay is: 〈αs(Mτ)〉=0.3111(71) which implies 〈αs(MZ)〉=0.1174(10)(3)evol.4. Some (eventual) contributions beyond the SVZ expansion (1/Q2, instantons and duality violation) are discussed in Sections 10 and 11.

The QCD axion sum rule

We demonstrate that the true QCD axion that solves the strong CP problem can be found in all generality outside the customary standard QCD band, with QCD being the sole source of Peccei-Quinn breaking. The essential reason is that the basis of axion-gluon interactions does not need to coincide with the mass basis. Specifically, we consider the case in which the QCD axion field is not the only singlet scalar in Nature but it mixes with other singlet scalars (besides the η′). We determine the exact mathematical condition for an arbitrary N-scalar potential to be Peccei-Quinn invariant. Such potentials provide extra sources of mass for the customary axion without enlarging the Standard Model gauge symmetry. The contribution to the axion mass stemming from the QCD topological susceptibility is shown to be shared then among the N axion eigenstates through a precise sum rule. Their location can only be displaced to the right of the standard QCD band. We demonstrate that the axion closest to this band can be displaced from it by a factor of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{N} $$\\end{document} at most, and this corresponds to the case in which all axion signals are maximally deviated. Conversely, if one axion is found on the standard QCD band, the other eigenstates will be out of experimental reach. Our results imply that any ALP experiment which finds a signal to the right of the standard QCD axion band can be solving the strong CP problem within QCD, with the associated N − 1 excitations to be found in an area of parameter space that we determine. We illustrate the results and phenomenology in some particular cases.

Medical image fusion with deep neural networks

Medical image fusion aims to fuse multiple images from a single or multiple imaging modes to enhance their corresponding clinical applications in diagnosing and evaluating medical problems, a trend that has attracted increasing attention. However, most recent medical image fusion methods require prior knowledge, making it difficult to select image features. In this paper, we propose a novel deep medical image fusion method based on a deep convolutional neural network (DCNN) for directly learning image features from original images. Specifically, source images are first decomposed by low rank representation to obtain the principal and salient components, respectively. Following that, the deep features are extracted from the decomposed principal components via DCNN and fused by a weighted-average rule. Then, considering the complementary between the salient components obtained by the low rank representation, a simple yet effective sum rule is designed to fuse the salient components. Finally, the fused result is obtained by reconstructing the principal and salient components. The experimental results demonstrate that the proposed method outperforms several state-of-the-art medical image fusion approaches in terms of both objective indices and visual quality.

The photon content of the neutron

In this work, we complete our CT18qed study with the neutron’s photon parton distribution function (PDF), which is essential for the nucleus scattering phenomenology. Two methods, CT18lux and CT18qed, based on the LUXqed formalism and the DGLAP evolution, respectively, to determine the neutron’s photon PDF have been presented. Various low-Q2 non-perturbative variations have been carefully examined, which are treated as additional uncertainties on top of those induced by quark and gluon PDFs. The impacts of the momentum sum rule as well as isospin symmetry violation have been explored and turned out to be negligible. A detailed comparison with other neutron’s photon PDF sets has been performed, which shows a great improvement in the precision and a reasonable uncertainty estimation. Finally, two phenomenological implications are demonstrated with photon-initiated processes: neutrino-nucleus W-boson production, which is important for the near-future TeV–PeV neutrino observations, and the axion-like particle production at a high-energy muon beam-dump experiment.