Search

The problem of nucleon-nucleon correlations and meson exchange currents has been vividly debated in connection with the neutrino-nucleus cross sections. In this work we focus on nucleon-nucleon correlations by discussing a formal correspondence between the approaches based on independent particles and the ab initio approaches involving correlated wave functions. We use a general technique based on unitary transformation mapping the Fermion operators relative to bare nucleons into quasi-particle operators relative to dressed nucleons. We derive formulas for spectral functions, response functions, momentum distribution, separation energy, general enough to be applied with any kind of effective nucleon-nucleon interaction. We establish the relation between the non-energy-weighted sum rule and the Fermi sea depopulation. With our tools we evaluate whether approaches based on effective interactions are compatible with the expected amount of correlations coming from ab initio calculations. For this purpose we use as a test the Fermi sea depopulation and the value of the kinetic energy per nucleon., To appear in EPJ ST - special issue "Neutrino Interactions in the Intermediate and High Energy Region"

We have achieved the isovector and isoscalar tensor form factors of the N ( 1535 ) state in the framework of the light-cone QCD sum rule approach. In numerical computations, we have considered the most general forms of the interpolating current for the nucleon and the tensor current together with the distribution amplitudes of the N ( 1535 ) resonance. We have shown that the squared momentum transfer, Q 2 , dependence of N ( 1535 ) tensor form factors is characterized by a multipole fit function. Our results provide a perspective of the momentum dependence of the tensor form factors and can help to improve our understanding of the internal structure of nucleon states.

We revisit light-cone sum rules with pion distribution amplitudes to determine the full set of local $$ \overline{B} $$ B ¯ → π form factors. To this end, we determine all duality threshold parameters from a Bayesian fit for the first time. Our results, obtained at small momentum transfer q2, are extrapolated to large q2 where they agree with precise lattice QCD results. We find that a modification to the commonly used BCL parametrization is crucial to interpolate the scalar form factor between the two q2 regions. We provide numerical results for the form factor parameters — including their covariance — based on simultaneous fit of all three form factors to both the sum rule and lattice QCD results. Our predictions for the form factors agree well with measurements of the q2 spectrum of the semileptonic decay $$ {\overline{B}}^0\to {\pi}^{+}{\mathrm{\ell}}^{-}{\overline{\nu}}_{\mathrm{\ell}} $$ B ¯ 0 → π + ℓ − ν ¯ ℓ . From the world average of the latter we obtain |Vub| = (3.77 ± 0.15) · 10−3, which is in agreement with the most recent inclusive determination at the 1 σ level.

We evaluate the masses and decay constants of the $0^+$ and $1^-$ open-charm $(\bar{c}\bar{d})(us)$ tetraquarks and molecular states from QCD spectral sum rules (QSSR) by using QCD Laplace sum rule (LSR). This method takes into account the stability criteria where the factorized perturbative NLO corrections and the contributions of quark and gluon condensates up to dimension-6 in the OPE are included. We confront our results with the $D^- K^+$ invariant mass recently reported by LHCb from $B^+ \to D^+(D^- K^+)$ decays. We expect that the resonance near the $D^- K^+$ threshold can be originated from the $0^{+}(D^-K^+)$ molecule and/or $D^- K^+$ scattering. The $X_0(2900)$ scalar state and the resonance $X_J(3150)$ (if $J = 0$) can emerge from a minimal mixing model, with a tiny mixing angle $\theta_0 \simeq (5.2 \pm 1.9)^0$, between a scalar Tetramole $({\cal T}_{\!\!{\cal M}0})$ (superposition of nearly degenerated hypothetical molecules and compact tetraquarks states with the same quantum numbers), having a mass $M_{{\cal T}_{\!\!{\cal M}0}} = 2743(18)$ MeV, and the first radial excitation of the $D^- K^+$ molecule with mass $M_{(DK)_1} = 3678(310)$ MeV. In an analogous way, the $X_1(2900)$ and the $X_J(3350)$ (if $J = 1$) could be a mixture between the vector Tetramole $({\cal T}_{\!\!{\cal M}1})$, with a mass $M_{{\cal T}_{\!\!{\cal M}1}} = 2656(20)$ MeV, and its first radial excitation having a mass $M_{{\cal T}_{\!\!{\cal M}1}} = 4592(141)$ MeV with an angle $\theta_0 \simeq (9.1 \pm 0.6)^0$. A (non)-confirmation of these statements requires experimental findings of the quantum numbers of the resonances at $3150$ and $3350$ MeV., Comment: Talk given at 23rd High-Energy Physics International Conference in Quantum Chromodynamics (QCD 20, 35th anniversary), 27-30 October 2020, Montpellier-France (v2: typos corrected, results unchanged)

This work deals with investigation of the helicity dependence of the γ → d → → π N N reaction channels near threshold and its implication to the helicity E-asymmetry and the Gerasimov-Drell-Hearn sum rule. Our formalism based on the one loop corrections to the impulse approximation due to nucleon and pion rescattering, uses the realistic Paris NN potential model for the deuteron wave function and the unitary isobar MAID-2007 model for the elementary γN → πN amplitude. We present results for the doubly polarized differential and total cross sections for parallel and antiparallel helicity states, the deuteron spin asymmetry, the helicity E-asymmetry, and the deuteron GDH integral in the near-threshold region. The influence of NN and πN final-state rescattering on the estimated results has been discussed. It is shown that the inclusion of NN rescattering is important, and its inclusion strongly affected the estimated results in both π ± - and π0-production channels. The inclusion of πN rescattering is found to be insignificant in π ± -production, but it has a non- negligible contribution in the case of π0-production. A comparison with predictions of other theoretical models is given.

We revisit the calculation of the strong couplings D∗Dπ and B∗Bπ from the QCD light-cone sum rules using the pion light-cone distribution amplitudes. The accuracy of the correlation function, calculated from the operator product expansion near the light-cone, is upgraded by taking into account the gluon radiative corrections to the twist-3 terms. The double spectral density of the correlation function, including the twist-2, 3 terms at $$ \mathcal{O}\left({\alpha}_s\right) $$ O α s and the twist-4 LO terms, is presented in an analytical form for the first time. This form allows us to use various versions of the quark-hadron duality regions in the double dispersion relation underlying the sum rules. We predict $$ {g}_{D^{\ast } D\pi}={14.1}_{-1.2}^{+1.3} $$ g D ∗ Dπ = 14.1 − 1.2 + 1.3 and $$ {g}_{B^{\ast } B\pi}={30.0}_{-2.4}^{+2.6} $$ g B ∗ Bπ = 30.0 − 2.4 + 2.6 when the decay constants of heavy mesons entering the light-cone sum rule are taken from lattice QCD results. We compare our results with the experimental value for the charmed meson coupling and with the lattice QCD calculations.

Employing light-cone QCD sum rule, we have acquired the magnetic moment of the Zc(3900) resonance by considering it as the molecular form of D(D^* ) ̅ and D^* D ̅ resonance with quantum numbers JPC = 1+−. The magnetic moment contains crucial knowledge about the internal organization of particles and their geometric configuration. Measurement of the magnetic moment of the Zc(3900) resonance in future experiments can be quite useful comprehension the inner organization of exotic resonances. A comparison of our numerical values on the magnetic moment with those estimated by the other theoretical models existing in literature is carried out., Zc(3900) parçacığının D(D^* ) ̅ ve D^* D ̅ molekül yapısında ve JPC = 1+− kuantum sayılarına sahip olduğu varsayılarak manyetik momenti Işık konisi KRD toplam kuralları kullanılarak elde edilmiştir. Manyetik moment parçacıkların geometrik konfigürasyonu ve içyapısı hakkında önemli bilgiler içermektedir. Gelecekteki deneylerde Zc(3900) rezonansının manyetik momentinin ölçülmesi, egzotik rezonansların iç organizasyonunu anlamak için oldukça yararlı olabilir. Bu çalışmada elde edilen sonuçlar ile literatürde var olan farklı modeller kullanılarak elde edilen sonuçların karşılaştırılması yapılmıştır.

The Thomas–Reiche–Kuhn (TRK) sum rule is a fundamental consequence of the position–momentum commutation relation for an atomic electron, and it provides an important constraint on the transition matrix elements for an atom. Here, we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light–matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light–matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light–matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics.

Studies of exotic nuclei are currently one of the most prolific in nuclear physics. Weak rates in germanium isotopes have a fundamental role in the dynamics of supernovae. Electron capture and beta-decay of germanium isotopes, specified by Gamow–Teller transitions, importantly modify the lepton fraction of the stellar matter. In this study, Gamow–Teller Transitions (GT) for $$^{62{-}72}$$ Ge are calculated using QRPA methods. The GT strength distributions are calculated using eight different QRPA models. QRPA models, namely single quasi-particle (sqp), Pyatov method (PM) and the schematic model (SM), are further divided into four subcategories. Using these models, Gamow–Teller distribution, total GT strengths along electron capture direction ( $$\sum $$ B(GT) $$_+$$ ) and Ikeda sum rule are calculated. The results of sqp, PM, and SM are also compared with previous theoretical calculations and measured strength distributions wherever available. It is expected that this study of GT properties would gain favor and may help to a better understanding of the presupernova evolution of massive stars.

In this paper, we design the Ξb(6227) as the pentaquark molecular states with quantum numbers $J^{P}=\frac {1}{2}^{\pm }$ to study its inner structure. We employ the QCD sum rule approach to calculate the masses and pole residues of pentaquark molecular states by taking the vacuum condensates up to dimension 13 in the operator product expansion. In comparison with the experiment data, it is found that our calculation results support assigning the Ξb(6227) to be the pentaquark molecular state with quantum number $J^{P}=\frac {1}{2}^{-}$ .

In this paper, an extensive study of exclusive baryonic decay Ξb → Ξl+l− (l = μ, τ) in non-universal Z' model is carried out. We use the form factors calculated by light cone QCD sum rule and analyse the effect of neutral gauge boson Z' on this decay. We study different physical observables like differential branching ratio, FB asymmetry, single and double lepton polarization asymmetries in the SM as well as in Z' model for this decay and represent graphically. We also estimate the numerical values of these kinematic observables in Z' model and compare with the SM. Our results indicate that these observables are very sensitive for both μ and τ channels which would provide signal for NP beyond the SM.

This work presents a system based on an ensemble of Convolutional Neural Networks (CNNs) and descriptors for bioimage classification that has been validated on different datasets of color images. The proposed system represents a very simple yet effective way of boosting the performance of trained CNNs by composing multiple CNNs into an ensemble and combining scores by sum rule. Several types of ensembles are considered, with different CNN topologies along with different learning parameter sets. The proposed system not only exhibits strong discriminative power but also generalizes well over multiple datasets thanks to the combination of multiple descriptors based on different feature types, both learned and handcrafted. Separate classifiers are trained for each descriptor, and the entire set of classifiers is combined by sum rule. Results show that the proposed system obtains state-of-the-art performance across four different bioimage and medical datasets. The MATLAB code of the descriptors will be available at https://github.com/LorisNanni.

Construction of multivariate tight framelets is known to be a challenging problem because it is linked to the difficult problem on sum of squares of multivariate polynomials in real algebraic geometry. Multivariate dual framelets with vanishing moments generalize tight framelets and are not easy to be constructed either, since their construction is related to syzygy modules and factorization of multivariate polynomials. On the other hand, compactly supported multivariate framelets with directionality or high vanishing moments are of interest and importance in both theory and applications. In this paper we introduce the notion of a quasi-tight framelet, which is a dual framelet, but behaves almost like a tight framelet. Let ϕ ∈ L 2 ( R d ) be an arbitrary compactly supported real-valued M -refinable function with a general dilation matrix M and ϕ ˆ ( 0 ) = 1 such that its underlying real-valued low-pass filter satisfies the basic sum rule. We first constructively prove by a step-by-step algorithm that we can always easily derive from the arbitrary M -refinable function ϕ a directional compactly supported real-valued quasi-tight M -framelet in L 2 ( R d ) associated with a directional quasi-tight M -framelet filter bank, each of whose high-pass filters has one vanishing moment and only two nonzero coefficients. If in addition all the coefficients of its low-pass filter are nonnegative, then such a quasi-tight M -framelet becomes a directional tight M -framelet in L 2 ( R d ) . Furthermore, we show by a constructive algorithm that we can always derive from the arbitrary M -refinable function ϕ a compactly supported quasi-tight M -framelet in L 2 ( R d ) with the highest possible order of vanishing moments. We shall also present a result on quasi-tight framelets whose associated high-pass filters are purely differencing filters with the highest order of vanishing moments. Several examples will be provided to illustrate our main theoretical results and algorithms in this paper.

Centroid energies, $$E_{\textrm{CEN}}$$ , of the isoscalar ( $$T=0$$ ) and isovector ( $$T=1$$ ) giant resonances of multipolarities $$L_{m}=0$$ –3 in $${}^{\mathrm{40,48}}$$ Ca, $${}^{\mathrm{68}}$$ Ni, $${}^{\mathrm{90}}$$ Zr, $${}^{\mathrm{116}}$$ Sn, $${}^{\mathrm{144}}$$ Sm, and $${}^{\mathrm{208}}$$ Pb, were calculated within the fully self-consistent spherical Hartree–Fock (HF)-based random-phase approximation (RPA) theory, using 33 different energy density functionals associated with Skyrme-type effective nucleon–nucleon interactions of the standard form commonly employed in the literature. We also calculate the Pearson linear correlation coefficients between each $$E_{\mathrm{CEN}}$$ and each bulk property of nuclear matter (NM), associated with the Skyrme interactions used in the calculations, and determine the sensitivity of $$E_{\mathrm{CEN}}$$ to bulk properties of NM. By comparing the calculated values of $$E_{\textrm{CEN}}$$ to the experimental data, we constrain the values of the bulk NM properties. We find that interactions associated with the values of the NM effective mass, $$m^{\ast}/m=0.70$$ –0.90, incompressibility coefficient, $$K_{\textrm{NM}}=210$$ –240 MeV, and the enhancement coefficient of the energy-weighted sum rule of the isovector giant dipole resonance, $$\kappa=0.25$$ –0.70, best reproduce the experimental data.

In a recent work (2016), the first author proved the fuzzy sum rule for the V-proximal subdifferential under some natural assumptions on an equivalent norm of the Banach spaces. In the present paper, we are going to prove that the class of Banach spaces satisfying the fuzzy sum rule is very large and contains all Lp spaces 1

The spectrum of spinless modes in a model with the $$SU{{(2)}_{L}} \times U{{(1)}_{R}}$$ symmetrical four-quark-interaction proposed by Miransky, Tanabashi, and Yamawaki is studied. For the sake of simplicity, only four-fermion interactions of top and bottom quarks are considered. The spinless modes result from spontaneous electroweak interaction symmetry breaking and are coupled quark–antiquark states associated with two $$SU\left( 2 \right)$$ Higgs doublets. Their dynamics is described by the effective Lagrangian obtained by the Schwinger–DeWitt method. The spectrum is represented by excitations of five types, the mass of each being expressed by the parameters of the model. It is shown that the model yields phenomenologically acceptable values of both the mass of quarks $${{m}_{t}} = 173\,\,{\text{GeV}}$$ and $${{m}_{b}} = 4.18\,\,{\text{GeV}}$$ and the mass of the standard Higgs state $${{m}_{{{{\chi }_{1}}}}} = 125\,\,{\text{GeV}}$$. The masses of the particles that comprise the second Higgs doublet, $${{m}_{{{{h}^{ \pm }}}}} = 275\,\,{\text{GeV}}$$, $${{m}_{{{{\chi }_{2}}}}} = 346\,\,{\text{GeV}}$$, and $${{m}_{{{{\phi }_{0}}}}} = 125\,\,{\text{GeV}}$$, have been calculated. The Nambu sum rule and the conditions for satisfying it in the theories with the broken $$~U{{(1)}_{A}}$$ symmetry are discussed

The spin response of the $$\vec{\gamma}\vec{d}\to\pi^{0}d$$ reaction near threshold is investigated. Our formalism based on the impulse approximation, uses the realistic Bonn $$NN$$ potential (full model) for the deuteron wave function and the unitary isobar MAID-2007 model for the elementary $$\gamma N\to\pi N$$ amplitude. We present the first results for the double polarized differential and total cross sections for parallel and antiparallel helicity states, the deuteron spin asymmetry, the helicity $$E$$ -asymmetry, the deuteron GDH integral, and the double spin asymmetries of the total cross section in the near-threshold region. Sensitivity of the estimated results to the $$D$$ -wave effect of the deuteron wave function for a realistic $$NN$$ potential is studied. We find an insignificant sensitivity of most of the estimated observables to the $$D$$ -wave component. A noticeable role is obtained only in the double polarized differential cross section with antiparallel spins of photon and deuteron $$d\sigma^{A}/d\Omega_{\pi}$$ close to the threshold energy at forward and backward pion angles as well as in the double spin asymmetry of the total cross section $$\sigma\tilde{T}_{20}$$ at relatively large photon energies. Thus, we compare results for these two observables using various $$NN$$ potential models with different $$D$$ -state probabilities, and a noticeable influence is found.

We revisit QCD calculations of radiative heavy meson decay form factors by including the subleading power corrections from the twist-two photon distribution amplitude at next-to-leading-order in $\alpha_s$ with the method of the light-cone sum rules (LCSR). The desired hard-collinear factorization formula for the vacuum-to-photon correlation function with the interpolating currents for two heavy mesons is constructed with the operator-product-expansion technique in the presence of evanescent operators. Applying the background field approach, the higher twist corrections from both the two-particle and three-particle photon distribution amplitudes are further computed in the LCSR framework at leading-order in QCD, up to the twist-four accuracy. Combining the leading power "point-like" photon contribution at tree level and the subleading power resolved photon corrections from the newly derived LCSR, we update theory predictions for the nonperturbative couplings describing the electromagnetic decay processes of the heavy mesons $H^{\ast \, \pm} \to H^{\pm} \, \gamma$, $H^{\ast \, 0} \to H^{0} \, \gamma$, $H_s^{\ast \, \pm} \to H_s^{\pm} \, \gamma$ (with $H=D, \, B$). Furthermore, we perform an exploratory comparisons of our sum rule computations of the heavy-meson magnetic couplings with the previous determinations based upon different QCD approaches and phenomenological models., Comment: 39 pages, 4 figures

We report results of our recent works [S. Narison, Int. J. Mod. Phys. A33 (2018) no. 10, 1850045; S. Narison. Addendum: Int. J. Mod. Phys. A33 (2018) no. 10, 1850045; S. Narison, Phys. Lett . B802 (2020) 135221.] where the correlations between the c,b -quark running masses m‾c,b , the gluon condensate 〈αsG2〉 and the QCD coupling αs in the MS‾ -scheme from an analysis of the charmonium and bottomium spectra and the Bc -meson mass. We use optimized ratios of relativistic Laplace sum rules (LSR) evaluated at the μ -subtraction stability point where higher orders PT and D≤6−8 -dimensions nonperturbative condensates corrections are included. We obtain [S. Narison, Int. J. Mod. Phys. A33 (2018) no. 10, 1850045; S. Narison. Addendum: Int. J. Mod. Phys. A33 (2018) no. 10, 1850045.] αs(2.85)=0.262(9) and αs(9.50)=0.180(8) from the (pseudo)scalar Mχ0c(0b)−Mηc(b) mass-splittings at μ=2.85(9.50) GeV. The most precise result from the charm channel leads to αs(Mτ)=0.318(15) and αs(MZ)=0.1183(19)(3) in excellent agreement with the world average: αs(MZ)=0.1181(11) [For a review, see e.g: S. Bethke, Nucl. Part. Phys. Proc . 282–284 (2017)149; C. Patrignani et al. (Particle Data Group), Chin. Phys . C40, 100001 (2016) and 2017 update.]. Updated results from a global fit of the (axial-)vector and (pseudo)scalar channels using Laplace and Moments sum rules @ N2LO [S. Narison, Int. J. Mod. Phys. A33 (2018) no. 10, 1850045; S. Narison. Addendum: Int. J. Mod. Phys. A33 (2018) no. 10, 1850045.] combined with the one from MBc [S. Narison, Phys. Lett . B802 (2020) 135221.] lead to the new tentative QCD spetral sum rules (QSSR) average: m‾c(m‾c)|average=1266(6) MeV and m‾b(m‾b)|average=4196(8) MeV. The values of the gluon condensate 〈αsG2〉 from the (axial)-vector charmonium channels combined with previous determinations in Table 1, leads to the new QSSR average: [S. Narison, Int. J. Mod. Phys. A33 (2018) no. 10, 1850045; S. Narison. Addendum: Int. J. Mod. Phys. A33 (2018) no. 10, 1850045.] 〈αsG2〉|average=(6.35±0.35)×10−2 Ge4 . Our results clarify the (apparent) discrepancies between different estimates of 〈αsG2〉 from J/ψ sum rule but also shows the sensitivity of the sum rules on the choice of the μ -subtraction scale. As a biproduct, we deduce the Bc -decay constants fBc=371(17) MeV and fBc(2S)≤139(6) MeV.

In this talk, I will discuss why previous experiments and theoretical considerations inevitably lead us to consider K* and K1 in nuclear matter [T. Song, T. Hatsuda and S.H. Lee, Phys. Lett. B 792, 160 (2019)]. I will also discuss the Weinberg type sum rule in the strangeness sector and derive a relation between chiral symmetry restoration and their mass difference. Using the kaon beam at JPARC, one could observe the mass shift of both of these particles in a nuclear target experiment, which will be the first step towards understanding the effects of chiral symmetry breaking in hadron masses.

Simplex gradients, essentially the gradient of a linear approximation, are a popular tool in derivative-free optimization (DFO). In 2015, a product rule, a quotient rule, and a sum rule for simplex...

The European physical journal / C 75(8), 375 (2015). doi:10.1140/epjc/s10052-015-3580-9, Published by Springer, Heidelberg

The expressions for the transition form factors (TFFs) of pseudoscalar mesons are derived in the context of the anomaly sum rule approach based on the dispersion representation of the axial anomaly and hypothesis of the global quark-hadron duality. The obtained solutions take into account the π$^{0}$-η-η′ mixing and the contribution of the gluon anomaly. It is shown that this method allows one to describe the TFFs for spacelike and timelike photon virtualities. The contribution of the gluon anomaly is estimated.

A unified expression for topological invariants has been proposed recently to describe the topological order in Dirac models belonging to any dimension and symmetry class. We uncover a correspondence between the curvature function that integrates to this unified topological invariant and the quantum metric that measures the distance between properly defined many-body Bloch states in momentum space. Based on this metric-curvature correspondence, a time-resolved and angle-resolved photoemission spectroscopy experiment is proposed to measure the violation of spectral sum rule caused by a pulse electric field to detect the quantum metric, from which the topological properties of the system may be extracted., Comment: 8 pages, 2 figures

We report that spin polarization occurs over millimeters in polycrystalline bulk samples of chiral disilicide NbSi$_2$ and TaSi$_2$. As previously demonstrated in the experiments using single crystals of NbSi$_2$ and TaSi$_2$, electrical transport measurements allow detection of direct and inverse signals associated with the chirality-induced spin polarization even in the chiral polycrystals. The spin polarization signals also appear in nonlocal measurements, in which charge current flows only in the area millimeters away from the detection electrode. These data mean that the spin polarization phenomena occur regardless of the presence of crystalline grains in the polycrystals, indicating a robustness and resilience of the chirality-induced spin polarization. On the basis of the experimental data, we found that the sum rule holds for the spin transport signals. A distribution of handedness over the samples was determined on average in the polycrystals. While the mechanism of preserving the spin polarization over millimeters remains to be clarified, the present study may open up prospects of spin control and manipulation over macroscopic length scales using chiral materials., 6 pages, 5 figures

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 ($\pi^0$) 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 $p \to e^+ \pi^0 G$ 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., Comment: 24 pages, 4 figures; v2: version published in JHEP

We consider the renormalization-group evolution of the matrix element of $\langle 0| \bar{q}(z)_\beta [z,0]b(0)_\alpha| \bar{B}\rangle$, which can be used to define the distribution amplitudes for $B$ meson and widely applied in studies of $B$ meson decays. The contribution to the renormalization constant of the non-local operator $\bar{q}(z)_\beta [z,0]b(0)_\alpha$ is considered up to one-loop order in QCD. Since the quark fields in this operator are not directly coupled fields, momentum can not flow freely through this non-local operator. Momentum involved in this operator can be treated stringently in coordinate space. We find that the ultraviolet divergences regulated by dimensional parameter $\epsilon$ cancel with each other, and the evolution effect vanishes. The matrix element $\langle 0| \bar{q}(z)_\beta [z,0]b(0)_\alpha| \bar{B}\rangle$ escapes from the renormalization-group evolution. We then apply the matrix element in calculating $B\to\pi$ transition form factor, where the matrix element is obtained by using the $B$ meson wave function calculated in QCD-inspired potential model. By comparing with experimental data for the semileptonic decay of $B\to \pi \ell\nu$ and light-cone sum rule calculation, we analyse the perturbative and non-perturbative contributions to $B\to\pi$ transition form factor in the frame work of perturbative QCD approach. We find that the effectiveness of the suppression of Sudakov factor to soft contribution depends on the end-point behavior of $B$ meson wave function, and with the $B$-meson wave function used in this work, soft contribution can not be well suppressed. The hard contribution to the $B\to\pi$ transition form factor is about 59\%, and soft contribution can be as large as 41\% in the naive calculation. To make the perturbative calculation reliable, a soft momentum cutoff in the calculation and soft form factor have to be introduced., Comment: 11 pages, 2 figure, version to appear in Nucl. Phys. B

The branching fraction of the rare B s 0 → ϕ μ + μ - decay is measured using data collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to integrated luminosities of 1, 2, and 6 fb - 1 , respectively. The branching fraction is reported in intervals of q 2 , the square of the dimuon invariant mass. In the q 2 region between 1.1 and 6.0 GeV 2 / c 4 , the measurement is found to lie 3.6 standard deviations below a standard model prediction based on a combination of light cone sum rule and lattice QCD calculations. In addition, the first observation of the rare B s 0 → f 2 ′ ( 1525 ) μ + μ - decay is reported with a statistical significance of 9 standard deviations and its branching fraction is determined.

We briefly review the key aspect of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry and the trace anomaly. We use Ji$^\prime s$ invariant mass decomposition of the energy momentum tensor together with the trace anomaly, to discuss the mass budget of the nucleon and pion in the QCD instanton vacuum. A measure of the gluon condensate in the nucleon, is a measure of the compressibility of the QCD instanton vacuum as a dilute topological liquid., Comment: 17 pages, 2 figures

Nowadays High Energy Physics experiments can accumulate unprecedented statistics of heavy flavour decays that allows to apply new methods, based on the study of very rare phenomena, which used to be just desperate. In this paper we propose a new method to measure composition of $K^0$-$\overline{K}^0$, produced in a decay of heavy hadrons. This composition contains important information, in particular about weak and strong phases between amplitudes of the produced $K^0$ and $\overline{K}^0$. We consider possibility to measure these parameters with time-dependent $K^0 \to \pi^+ \pi^-$ analysis. Due to $CP$-violation in kaon mixing time-dependent decay rates of $K^0$ and $\overline{K}^0$ differ, and the initial amplitudes revealed in the $CP$-violating decay pattern. In particular we consider cases of charmed hadrons decays: $D^+ \to K^0 \pi^+$, $D_s^+ \to K^0 K^+$, $\Lambda_c \to p K^0$ and with some assumptions $D^0 \to K^0 \pi^0$. This can be used to test the sum rule for charmed mesons and to obtain input for the full constraint of the two body amplitudes of $D$-mesons., Comment: 12 pages, 4 figures

We propose sum rules of x-ray magnetic circularly polarized emission (XMCPE) at $L$ edges for $3d$ transition metals. By making use of combinations of incident and emitted photon helicities, $z$-component expectation values of spin, orbital, magnetic dipole, and quadrupole terms can be obtained separately. The fundamental difference in the sum rules between x-ray magnetic circular dichroism and XMCPE arises from the variety of electron transitions involving core states split by the spin-orbit interaction. The additional electron transition in XMCPE causes complicated angular dependence of the sum rule relation for the spin moment. Our findings promote future $L$-edge XMCPE measurements, which have not been observed at present.

A spin-polarized state is examined under charge current at room temperature without magnetic fields in chiral disilicide crystals NbSi_{2} and TaSi_{2}. We found that a long-range spin transport occurs over ten micrometers in these inorganic crystals. A distribution of crystalline grains of different handedness is obtained via location-sensitive electrical transport measurements. The sum rule holds in the conversion coefficient in the current-voltage characteristics. A diamagnetic nature of the crystals supports that the spin polarization is not due to localized electron spins but due to itinerant electron spins. A large difference in the strength of antisymmetric spin-orbit interaction associated with 4d electrons in Nb and 5d ones in Ta is oppositely correlated with that of the spin polarization. A robust protection of the spin polarization occurs over long distances in chiral crystals.

The on-shell matrix elements, or couplings $$ {g}_{H{H}^{\ast}\left({H}_1\right)\upgamma} $$ g H H ∗ H 1 γ , describing the $$ B{(D)}_q^{\ast } $$ B D q ∗ → B(D)qγ and B1q → Bqγ (q = u, d, s) radiative decays, are determined from light-cone sum rules at next-to-leading order for the first time. Two different interpolating operators are used for the vector meson, providing additional robustness to our results. For the D*-meson, where some rates are experimentally known, agreement is found. The couplings are of additional interest as they govern the lowest pole residue in the B(D) → γ form factors which in turn are connected to QED-corrections in leptonic decays B(D) → ℓ$$ \overline{\nu} $$ ν ¯ . Since the couplings and residues are related by the decay constants $$ {f}_{H^{\ast}\left({H}_1\right)} $$ f H ∗ H 1 and $$ {f}_{H^{\ast}\left({H}_1\right)}^T $$ f H ∗ H 1 T , we determine them at next-leading order as a by-product. The quantities $$ \left\{{f}_{H^{\ast}}^T,{f}_{H_1}^T\right\} $$ f H ∗ T f H 1 T have not previously been subjected to a QCD sum rule determination. All results are compared with the existing experimental and theoretical literature.

We revisit the experimental and theoretical status of $B \to \rho l \bar{\nu}$ and $B \to \omega l \bar{\nu}$ decays. We perform a combined fit of averaged spectra from Belle and Babar measurements with prior light cone sum rule calculations, in order to obtain more precise predictions over the full $q^2$ range. The extracted values of $|V_{ub}|$ from these combined fits exhibit smaller uncertainty compared to previous extractions from $B \to \rho l \bar{\nu}$ and $B \to \omega l \bar{\nu}$ decays and the central values are found to be smaller than values extracted from $B \to \pi l \nu$ or inclusive measurements. We use our fit results to obtain more precise predictions in and beyond the Standard Model for the lepton universality ratios $R(\rho)$ and $R(\omega)$, as well as several angular observables that are sensitive to the full $q^2$ distribution, such as the longitudinal polarization of the vector meson, the $\tau$ polarization, and its forward-backward asymmetry.

In this paper, we compare two different bandwidth bounds on array antennas with a ground plane. The first of these bounds is based on the fact that the antenna can be seen as a passive system, which implies that its response can be described in terms of a Herglotz function. This passivity-based bandwidth bound is closely related to a sum rule for lossless arrays over the ground plane. The second bound is a recently developed Q-factor based bound, valid for resonant structures. In this paper, it is shown that this latter bound strongly depends on the allowed shape and the electrical size of the element within the unit cell. It also depends on the size of the unit cell, corresponding to the interelement spacing. The Q-factor bound provides a sharper bound when the structure is resonant.

The static-response function of strongly interacting neutron matter contains crucial information on this interacting many-particle system, going beyond ground-state properties. In the present work, we tackle this problem with quantum Monte Carlo (QMC) approaches at several different densities, using both phenomenological forces and (for the first time) chiral effective field theory interactions. We handle finite-size effects via self-consistent energy-density functional (EDF) calculations for 8250 particles in a periodic volume. We combine these QMC and EDF computations in an attempt to produce a model-independent extraction of the static response function. Our results are consistent with the compressibility sum rule, which encapsulates the limiting behavior of the response function starting from the homogeneous equation of state, without using the sum rule as an input constraint. Our predictions on inhomogeneous neutron matter can function as benchmarks for other many-body approaches, thereby shedding light on the physics of neutron-star crusts and neutron-rich nuclei., Comment: 6 pages, 3 figures; v3 corresponds to published version

A sum rule for tidal Love number is derived from quantum field theory computations, which relates tidal susceptibility of a spinless body to transition rates of its single graviton emission processes. An analogous sum rule for electromagnetism is given as an example, which is substantiated by comparing to the solved problem of the hydrogen atom. Based on the semiclassical Hawking radiation spectrum, a finite nonvanishing value for quantum corrections to the Love number of Schwarzschild black holes in general relativity is computed using the sum rule, which is known to classically vanish., Comment: 5 pages, no figure; Published Version; any comments welcome

We present a consistent ab initio computation of the longitudinal response function ${R}_{L}$ in $^{40}\mathrm{Ca}$ using the coupled-cluster and Lorentz integral transform methods starting from chiral nucleon-nucleon and three-nucleon interactions. We validate our approach by comparing our results for ${R}_{L}$ in $^{4}\mathrm{He}$ and the Coulomb sum rule in $^{40}\mathrm{Ca}$ against experimental data and other calculations. For ${R}_{L}$ in $^{40}\mathrm{Ca}$ we obtain a very good agreement with experiment in the quasielastic peak up to intermediate momentum transfers, and we find that final state interactions are essential for an accurate description of the data. This work presents a milestone towards ab initio computations of neutrino-nucleus cross sections relevant for experimental long-baseline neutrino programs.

In the present paper, we first give a detailed study on the pQCD corrections to the leading-twist part of BSR. Previous pQCD corrections to the leading-twist part derived under conventional scale-setting approach up to ${\cal O}(\alpha_s^4)$-level still show strong renormalization scale dependence. The principle of maximum conformality (PMC) provides a systematic way to eliminate conventional renormalization scale-setting ambiguity by determining the accurate $\alpha_s$-running behavior of the process with the help of renormalization group equation. Our calculation confirms the PMC prediction satisfies the standard renormalization group invariance, e.g. its fixed-order prediction does scheme-and-scale independent. In low $Q^2$-region, the effective momentum of the process is small and to have a reliable prediction, we adopt four low-energy $\alpha_s$ models to do the analysis. Our predictions show that even though the high-twist terms are generally power suppressed in high $Q^2$-region, they shall have sizable contributions in low and intermediate $Q^2$ domain. By using the more accurate scheme-and-scale independent pQCD prediction, we present a novel fit of the non-perturbative high-twist contributions by comparing with the JLab data., Comment: 14 pages,14 figures

In the paper, the double-Debye and double-overdamped-oscillator models are considered for parametrization of the terahertz (THz) dielectric response of human brain tissues. Experimental data can be accurately reproduced for the intact tissues and gliomas using both models. While the double-Debye dielectric model is widely used in THz biophotonics, the double-overdamped-oscillator model appears to be more physically rigorous, since it satisfies the sum rule. In our opinion, the described double-overdamped-oscillator model is important for further research and development in THz biophotonics and neurodiagnosis of tumors.

We have studied the masse spectra for the $cc\overline{b}\overline{b}$ and $bb\overline{c}\overline{c}$ tetraquark states with quantum numbers ${J}^{P}={0}^{\ifmmode\pm\else\textpm\fi{}},{1}^{\ifmmode\pm\else\textpm\fi{}}$, and ${2}^{+}$. We systematically construct the interpolating currents with various spin-parity quantum numbers and calculate their two-point correlation functions in the framework of QCD moment sum rule method. Our calculations show that the masses are about 12.3--12.4 GeV for the positive parity $cc\overline{b}\overline{b}$ tetraquark ground states with ${J}^{P}={0}^{+},{1}^{+},{2}^{+}$, while 12.8--13.1 GeV for the negative parity channels with ${J}^{P}={0}^{\ensuremath{-}},{1}^{\ensuremath{-}}$. The mass predictions for the positive parity $cc\overline{b}\overline{b}$ ground states are lower than the ${B}_{c}{B}_{c}$ threshold, implying that these tetraquarks can only decay via weak interaction and thus are expected to be stable and narrow.

To extract the Cabibbo-Kobayashi-Maskawa (CKM) matrix element |Vub|, we have re-analyzed all the available inputs (data and theory) on the B → πℓν decays including the newly available inputs on the form-factors from light cone sum rule (LCSR) approach. We have reproduced and compared the results with the procedure taken up by the Heavy Flavor Averaging Group (HFLAV), while commenting on the effect of outliers on the fits. After removing the outliers and creating a comparable group of data-sets, we mention a few scenarios in the extraction of |Vub|. In all those scenarios, the extracted values of |Vub| are higher than that obtained by HFLAV. Our best results for |Vub|exc. are (3.94 ± 0.14) × 10−3 and $$ \left({3.93}_{-0.15}^{+0.14}\right) $$ 3.93 − 0.15 + 0.14 × 10−3 in frequentist and Bayesian approaches, respectively, which are consistent with that extracted from inclusive decays |Vub|inc. within 1 σ confidence interval.

The spectroscopic properties of single heavy spin-1/2 $\Lambda_{Q}$, $\Sigma_{Q}$, $\Xi^{(\prime)}_{Q}$ and $ \Omega_{Q}$ baryons are investigated at finite temperature in the framework of thermal QCD sum rule. We discuss the behavior of the mass and residue of these baryons with respect to temperature taking into account contributions of non-perturbative operators up to dimension eight. We include additional operators coming from the Wilson expansion due to breaking the Lorentz invariance at non-zero temperature. The obtained results show that the mass of these baryons remain stable up to roughly $T=108$ MeV while their residue are unchanged up to $T=93$ MeV. After these points, the mass and residue start to diminish by increasing the temperature. The shifts in the mass and residue for both the bottom and charm channels are considerably large and we observe the melting of these baryons near to the pseudo-critical temperature determined by recent lattice QCD calculations. We present our results for the mass of these baryons with both the positive and negative parity at $ T\rightarrow 0 $ limit, which are consistent with the existing theoretical predictions as well as experimental data., Comment: 15 Pages, 3 Figures and 11 Tables

We propose a novel pentaquark picture for singly heavy baryons based on chiral symmetry and heavy quark spin symmetry, and investigate a mass spectrum of the positive-parity and negative-parity heavy baryons. Our analysis shows that the Roper-like singly heavy baryons $$\varLambda _c(2765)$$ and $$\varXi _c(2967)$$ are dominated by pentaquark states. Also, symmetry relations such as a sum rule for the baryon masses and an extended Goldberger-Treiman relations are derived. Furthermore, we show that the suppression of a direct decay of the Roper-like singly heavy baryons is naturally explained. Those findings provide useful information on possibility of the pentaquark state of the singly heavy baryons for future experiments and lattice simulations.

Among the most widely traded fish in the world, Tuna is an important fish due to their nutritional value. In the export industry, these fish are manually sorted into various species. In this paper, an automated system is suggested to speed up these industries in order to satisfy the growing need for tuna and its products. Three species of tuna are used here. The contrast of each image is enhanced by using a preprocessing step. Head, abdomen and tail region images are then split from the images. Different parameters then augment these images to get a class balanced dataset. The resulting augmented images are applied to four pre-trained models. The sum rule combines the predictions from the four networks for a region. The combined scores of three region-based predictions are used in the majority voting ensemble to get the final image-wise prediction. Different performance measures are used to evaluate the system, and results show that the proposed system classifies tuna fishes with an accuracy of 95.65%.

We present an $\mathcal{O}(\ensuremath{\alpha})$ Standard Model calculation of the inner radiative corrections to Gamow-Teller $\ensuremath{\beta}$ decays. We find that a priori contributions arise from the photonic vertex correction and $\ensuremath{\gamma}W$ box diagram. Upon evaluation most elastic contributions vanish due to crossing symmetry or cancellation between isoscalar and isovector photonic contributions, leaving only the polarized parity-odd contribution, i.e., the Gamow-Teller equivalent of the well-known axial $\ensuremath{\gamma}W$ box contribution for Fermi decays. We show that weak magnetism contributes significantly to the Born amplitude, and consider additional hadronic contributions at low energy using a holomorphic continuation of the polarized Bjorken sum rule constrained by experimental data. We perform the same procedure for the Fermi inner radiative correction through a combination of the running of Bjorken and Gross-Llewellyn Smith sum rules. We discuss heavy flavor, higher-twist, and target mass corrections and find a significant increase at low momentum from the latter. We find ${\mathrm{\ensuremath{\Delta}}}_{R}^{A}=0.02532(22)$ and ${\mathrm{\ensuremath{\Delta}}}_{R}^{V}=0.02473(27)$ for axial and vector inner radiative corrections, respectively, resulting in ${\mathrm{\ensuremath{\Delta}}}_{R}^{A}\ensuremath{-}{\mathrm{\ensuremath{\Delta}}}_{R}^{V}=0.60(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, which allows us to extract ${g}_{A}^{0}$ for the first time to our knowledge. We discuss consequences for comparing experimental data to lattice calculations in beyond Standard Model fits. Further, we show how some traditional $\ensuremath{\beta}$ decay calculations contain part of this effect but fail to account for cancellations in the full $\mathcal{O}(\ensuremath{\alpha})$ result. Finally, we correct for a double-counting instance in the isospin $T=1/2$ mirror decay extraction of $|{V}_{ud}|$, the up-down matrix element of the Cabibbo-Kobayashi-Maskawa matrix element, resolving a long-standing tension and leading to increased precision.

Here, we use the Schwinger–DeWitt approach to address the four-fermion composite Higgs effective model proposed by Miransky, Tanabashi and Yamawaki (MTY). The surprising benefit of such an approach is that it is possible to ascribe to a SM-type Higgs a quark–antiquark structure of predominantly a b¯b nature with a small t¯t admixture, which in turn yields a Higgs mass compatible with the observed value of 125 GeV. We discuss this result in a detailed and pedagogical way, as it goes against the common belief that this model and akin composite descriptions should predict a Higgs mass-of-order of twice the top quark mass, contrary to empirical evidence. A further aspect of this approach is that it highlights the link of the SU(2)L×U(1)R symmetric four-fermion MTY model interactions of the heavy quark family to a specific two-Higgs-doublet model (2HDM), and the necessity to go beyond the one Higgs doublet to obtain the empirical Higgs mass within composite models. By appropriately fixing the symmetry-defining interaction parameters, we show that the resulting CP-preserving spectrum harbors the following collective states at the electroweak scale ΛEW=246 GeV: a light scalar to which the standard Higgs is associated, a heavier neutral state preconized as the Nambu partner of the standard Higgs within the Nambu sum rule, the expected triplet of Goldstone bosons associated with the longitudinal polarizations of the electroweak massive bosons, and a neutral pseudoscalar state that in the limit of a global U(1)A symmetry would be a Goldstone mode. The anomalous breaking of this axial symmetry is a subleading effect in a large Nc counting scheme, and we discuss how it modifies the leading-order Nambu sum rule result and its relevance for the qualitative description of the spectrum.

In $$ {B}_c^{-} $$ B c − → J/ψ(→ μ+μ−)τ−$$ {\overline{\nu}}_{\tau } $$ ν ¯ τ decay, the three-momentum $$ {\boldsymbol{p}}_{\tau^{-}} $$ p τ − cannot be determined accurately due to the decay products of τ− inevitably include an undetected ντ. As a consequence, the angular distribution of this decay cannot be measured. In this work, we construct a measurable angular distribution by considering the subsequent decay τ− → π−ντ. The full cascade decay is $$ {B}_c^{-} $$ B c − → J/ψ(→ μ+μ−)τ−(→ π−ντ)$$ {\overline{\nu}}_{\tau } $$ ν ¯ τ , in which the three-momenta $$ {\boldsymbol{p}}_{\mu^{+}},{\boldsymbol{p}}_{\mu^{-}} $$ p μ + , p μ − , and $$ {\boldsymbol{p}}_{\pi^{-}} $$ p π − can be measured. The five-fold differential angular distribution containing all Lorentz structures of the new physics (NP) effective operators can be written in terms of twelve angular observables ℐi(q2, Eπ). Integrating over the energy of pion Eπ, we construct twelve normalized angular observables $$ {\hat{\mathrm{\mathcal{I}}}}_i $$ ℐ ̂ i (q2) and two lepton-flavor-universality ratios $$ R\left({P}_{L,T}^{J/\psi}\right) $$ R P L , T J / ψ (q2). Based on the Bc → J/ψ form factors calculated by the latest lattice QCD and sum rule, we predict the q2 distribution of all $$ {\hat{\mathrm{\mathcal{I}}}}_i $$ ℐ ̂ i and $$ R\left({P}_{L,T}^{J/\psi}\right) $$ R P L , T J / ψ both within the Standard Model and in eight NP benchmark points. We find that the benchmark BP2 (corresponding to the hypothesis of tensor operator) has the greatest effect on all ℐi and $$ R\left({P}_{L,T}^{J/\psi}\right) $$ R P L , T J / ψ , except $$ {\hat{\mathrm{\mathcal{I}}}}_5 $$ ℐ ̂ 5 . The ratios $$ R\left({P}_{L,T}^{J/\psi}\right) $$ R P L , T J / ψ are more sensitive to the NP with pseudo-scalar operators than the ℐi. Finally, we discuss the symmetries in the angular observables and present a model-independent method to determine the existence of tensor operators.