Matrix Elements Of Tensor Research Articles

Nonrelativistic nuclear reduction for tensor couplings in dark matter direct detection and μ→e conversion

The nonrelativistic effective field theory (NRET) is widely used in dark matter direct detection and charged-lepton flavor violation studies through μ→e conversion. However, existing literature has not fully considered tensor couplings. This study fills this gap by utilizing an innovative tensor decomposition method, extending NRET to incorporate previously overlooked tensor interactions. This development is expected to have a significant impact on ongoing experiments seeking physics beyond the Standard Model and on our understanding of the new-physics interactions. Notably, we identify additional operators in μ→e conversion that are absent in scalar and vector couplings. To support further research and experimental analyses, comprehensive tables featuring tensor matrix elements and their corresponding operators are provided. Published by the American Physical Society 2024

Gravitational form factors of charmonia

We investigate the gravitational form factors of charmonium. Our method is based on a Hamiltonian formalism on the light front known as basis light-front quantization. The charmonium mass spectrum and light-front wave functions were obtained from diagonalizing an effective Hamiltonian that incorporates confinement from holographic QCD and one-gluon exchange interaction from light-front QCD. We proposed a quantum many-body approach to construct the hadronic matrix elements of the energy momentum tensor T++ and T+−, which are used to extract the gravitational form factors A(Q2) and D(Q2). The obtained form factors satisfy the known constraints, e.g., the von Laue condition. From these quantities, we also extract the energy, pressure and light-front energy distributions of the system. We find that hadrons are multilayer systems. Published by the American Physical Society 2024

Quantum Chaos and Level Dynamics

We review the application of level dynamics to spectra of quantally chaotic systems. We show that the statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss in detail different statistical measures involving level dynamics, such as level avoided-crossing distributions, level slope distributions, or level curvature distributions. We show both the aspects of universality in these distributions and their limitations. We concentrate in some detail on measures imported from the quantum information approach such as the fidelity susceptibility, and more generally, geometric tensor matrix elements. The possible open problems are suggested.

Gluon gravitational structure of hadrons of different spin

The gravitational form factors (GFFs) of hadrons encode the matrix elements of the energy momentum tensor of QCD. These quantities describe how energy, spin, and various mechanical properties of hadrons are carried by their quark and gluon constituents. We present the gluon GFFs of the pion, nucleon, $\rho$ meson, and $\Delta$ baryon as functions of the squared momentum transfer $t$ in the region $0 \leq -t < 2 \; \text{GeV}^2$, as determined in a lattice QCD study with pion mass $m_{\pi} = 450(5) \; \text{MeV}$. By fitting the extracted GFFs using multipole and z-parameter expansion functional forms, we extract various gluon contributions to the energy, pressure, and shear force distributions of the hadrons in the 3D and 2D Breit frames as well as in the infinite momentum frame. We also obtain estimates for the corresponding gluon mechanical and mass radii, as well as the forward-limit gluon contributions to the momentum fraction and angular momentum of the hadrons.

Few-nucleon matrix elements in pionless effective field theory in a finite volume

Pionless effective field theory in a finite volume (FVEFT$_{\pi\!/}$) is investigated as a framework for the analysis of multi-nucleon spectra and matrix elements calculated in lattice QCD (LQCD). By combining FVEFT$_{\pi\!/}$ with the stochastic variational method, the spectra of nuclei with atomic number $A\in\{2,3\}$ are matched to existing finite-volume LQCD calculations at heavier-than-physical quark masses corresponding to a pion mass $m_\pi=806$ MeV, thereby enabling infinite-volume binding energies to be determined using infinite-volume variational calculations. Based on the variational wavefunctions that are constructed in this approach, the finite-volume matrix elements of various local operators are computed in FVEFT$_{\pi\!/}$ and matched to LQCD calculations of the corresponding QCD operators in the same volume, thereby determining the relevant one and two-body EFT counterterms and enabling an extrapolation of the LQCD matrix elements to infinite volume. As examples, the scalar, tensor, and axial matrix elements are considered, as well as the magnetic moments and the isovector longitudinal momentum fraction.

Sensitivity of nuclear matrix elements of 0νββ of Ca48 to different components of the two-nucleon interaction

In the present work, we examine the sensitivity of nuclear matrix elements (NMEs) for light neutrino-exchange mechanism of neutrinoless double beta decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) of $^{48}\mathrm{Ca}$ to the central, spin-orbit, and tensor components of two-nucleon interaction. The NMEs are calculated in the nuclear shell-model framework in $fp$-model space using frequently used GXPF1A interaction and a new effective interaction named GX1R of $pf$ shell. The decomposition of the shell-model two-nucleon interactions into their individual components is performed using spin-tensor decomposition. The NMEs are calculated in closure approximation by using optimal value of the closure energy. The results shows that the total NMEs calculated with the central component of the interactions are of positive sign. By adding spin-orbit part to central part of the interactions, sign of the total NMEs gets change, and in absolute value, NMEs decreases by about $15\text{--}18%$. Sign change in total NMEs are again seen by adding tensor part to the $\text{central}+\text{spin}\ensuremath{-}\text{orbit}$ part of the interactions. Similar trends of sign change are also observed for Fermi, Gamow-Teller, and tensor matrix elements. Thus we infer that SO and T part mostly cancel the effects of each other in NMEs calculations. For both the interactions, the total NMEs calculated with the C part is found to be $20%$ enhanced as compared to the NMEs calculated with the total interactions. With new GX1R interaction, there is about $1\text{--}3%$ increments in the total NMEs as compared to NMEs with GXPF1A interaction. This increments comes from the modifications of isospin $T=1$ tensor force two-nucleon matrix elements to bring the characteristic properties of tensor force into the GX1R interaction.

Poincaré constraints on the gravitational form factors for massive states with arbitrary spin

In this work we analyse the constraints imposed by Poincar\'e symmetry on the gravitational form factors appearing in the Lorentz decomposition of the energy-momentum tensor matrix elements for massive states with arbitrary spin. By adopting a distributional approach, we prove for the first time non-perturbatively that the zero momentum transfer limit of the leading two form factors in the decomposition are completely independent of the spin of the states. It turns out that these constraints arise due to the general Poincar\'e transformation and on-shell properties of the states, as opposed to the specific characteristics of the individual Poincar\'e generators themselves. By expressing these leading form factors in terms of generalised parton distributions, we subsequently derive the linear and angular momentum sum rules for states with arbitrary spin.

Anatomy of varepsilon '/varepsilon beyond the standard model

We present for the first time a model-independent anatomy of the ratio varepsilon '/varepsilon in the context of the Delta S = 1 effective theory with operators invariant under QCD and QED and in the context of the standard model effective field theory (SMEFT) with the operators invariant under the full SM gauge group. Our goal is to identify the new physics scenarios that are probed by this ratio and which could help to explain a possible deviation from the SM that is hinted by the data. To this end we derive a master formula for varepsilon '/varepsilon , which can be applied to any theory beyond the standard model (BSM) in which the Wilson coefficients of all contributing operators have been calculated at the electroweak scale. The relevant hadronic matrix elements of BSM operators are from the Dual QCD approach and the SM ones from lattice QCD. Within SMEFT, the constraints from K^0 and D^0 mixing as well as electric dipole moments limit significantly potential new physics contributions to varepsilon '/varepsilon . Correlations of varepsilon '/varepsilon with Krightarrow pi nu {bar{nu }} decays are briefly discussed. Building on our EFT analysis and the model-independent constraints, we discuss implications of a possible deviation from the SM in varepsilon '/varepsilon for model building, highlighting the role of the new scalar and tensor matrix elements in models with scalar mediators.

High-energy neutrino-nucleus interactions

High-energy neutrino-nucleus interactions are discussed by considering neutrino-oscillation experiments and ultra-high-energy cosmic neutrino interactions. The largest systematic error for the current neutrino oscillation measurements comes from the neutrino-nucleus interaction part, and its accurate understanding is essential for high-precision neutrino physics, namely for studying CP violation in the lepton sector. Depending on neutrino beam energies, quasi-elastic, resonance, Regge, or/and deep inelastic scattering (DIS) processes contribute to the neutrino cross section. It is desirable to have a code to calculate the neutrino-nucleus cross section in any kinematical range by combining various theoretical descriptions. On the other hand, the IceCube collaboration started obtaining cross section data up to the 1015 eV range, so that it became necessary to understand ultra-high-energy neutrino interactions beyond the artificial lepton-accelerator energy range. For future precise neutrino physics including the CP measurement, it is also necessary to understand accurate nuclear corrections. The current status is explained for nuclear corrections in DIS structure functions. The possibility is also discussed to find gravitational sources within nucleons and nuclei, namely matrix elements of quark-gluon energy-momentum tensor. They could be probed by neutrino interactions without replying on direct ultra-weak “gravitational interactions” with high-intensity neutrino beams, possibly at a future neutrino factory, by using techniques of hadron tomography.

Nucleon charges with dynamical overlap fermions

We calculate the scalar and tensor charges of the nucleon in 2+1-flavor lattice QCD, for which the systematics of the renormalization of the disconnected diagram is well controlled. Numerical simulations are performed at a single lattice spacing a = 0.11 fm. We simulate four pion masses, which cover a range of $m_\pi \sim$ 290 - 540 MeV, and a single strange quark mass close to its physical value. The statistical accuracy is improved by employing the so-called low-mode averaging technique and the truncated solver method. We study up, down, and strange quark contributions to the nucleon charges by calculating disconnected diagrams using the all-to-all quark propagator. Chiral symmetry is exactly preserved by using the overlap quark action to avoid operator mixing among different flavors, which complicates the renormalization of scalar and tensor matrix elements and leads to possibly large contamination to the small strange quark contributions. We also study the nucleon axial charge with contribution from the disconnected diagram. Our results are in reasonable agreement with experiments and previous lattice studies.

Some QCD/gravity intersections

Gravitational form factors are the matrix elements of the Belinfante energy momentum tensor (EMT) which naturally incorporate the hadron structure and the equivalence principle. The relocalization property allowing to transform EMT to the Belinfante form provides the “kinematical” counterpart of the famous [Formula: see text] problem. The equivalence principle may be approximately valid for quarks and gluons separately in non-perturbative (NP)QCD, and this conjecture is supported by the experimental and lattice data. The extra-dimensional gravity leading to holographic AdS/QCD is supporting the relation of quark transverse momentum to the Regge slope, discovered by V.N. Gribov.

Neutrinoless double beta nuclear matrix elements around mass 80 in the nuclear shell-model

The observation of the neutrinoless double-beta decay can determine whether the neutrino is a Majorana particle or not. For theoretical nuclear physics it is particularly important to estimate three types of matrix elements, namely Fermi ( F ), Gamow-Teller ( GT ), and tensor ( T ) matrix elements. In this paper, we carry out shell-model calculations and also pair-truncated shell-model calculations to check the model dependence in the case of mass A =82 nuclei.

Tensor force and delta excitation for the structure of light nuclei

We treat explicitly Δ(1232) isobar degrees of freedom using a bare nucleon-nucleon interaction for few-body systems, where Δ excitations can be the origin of the three-body force via the pion exchange. We adopt the Argonne two-body potential including Δ, named as AV28 potential, and study the role of Δ explicitly in two-body and three-body systems. It was found that the additional Δ states generate strong tensor correlations caused by the transitions between N and Δ states, and change tensor matrix elements largely from the results with only nucleons. We studied the effects of three-body force in the triton and obtained 0.8 MeV attraction due to the intermediate Δ excitation. Due to the lack of the total binding energy for the triton in the delta model, we further studied carefully the effects of the delta excitation in various two body channels and compared with the nucleon only model in the AV14 potential. We modified slightly the AV28 potential in the singlet S channel so that we could reproduce the triton binding energy due to the appropriate amount of the three-body force effects.

Reduction of Volume Integrals to Nonsingular Surface Integrals for Matrix Elements of Tensor and Vector Green Functions of Maxwell Equations

A procedure for the evaluation of matrix elements of tensor and vector Green functions with linear basis functions appearing in volumetric integral equations in electromagnetics is presented. The procedure reduces six-dimensional volumetric integrals with singular integrands to four-dimensional surface integrals with nonsingular integrands-hence, it offers simplicity and accuracy achieved at low computational cost.

Effect of the Tensor Force on the Charge Exchange Spin-Dipole Excitations ofPb208

The charge exchange spin-dipole (SD) excitations of 208Pb are studied by using a fully self-consistent Skyrme Hartree-Fock plus random phase approximation formalism which includes the tensor interaction. It is found, for the first time, that the tensor correlations have a unique, multipole-dependent effect on the SD excitations; that is, they produce a softening of 1{-} states, but a hardening of 0{-} and 2{-} states. This paves the way to a clear assessment of the strength of the tensor terms. We compare our results with a recent measurement, showing that our choice of tensor terms improves the agreement with experiment. The robustness of our results is supported by the analytic form of the tensor matrix elements.

Maple procedures for the coupling of angular momenta. An up-date of the Racah module

An up-date of the Racah module is presented, adopted to Maple 11 and 12, which supports both, algebraic manipulations of expressions from Racah's algebra as well as numerical computations of many functions and symbols from the theory of angular momentum. The functions that are known to the program include the Wigner rotation matrices and n-j symbols, Clebsch–Gordan and Gaunt coefficients, spherical harmonics of various kinds as well as several others.

Neutrinoless double-βdecay in the microscopic interacting boson model

We present a formalism for calculating nuclear matrix elements of double-$\ensuremath{\beta}$ decay within the framework of the microscopic interacting boson model. We calculate Fermi, Gamow-Teller, and tensor matrix elements in the decay of Ge-Se-Mo-Te-Xe-Nd-Sm and compare our results with those of the shell-model (SM) and of the quasiparticle random-phase approximation (QRPA). Our results are in agreement with QRPA. We discuss simple features of the matrix elements and give a formula that allows one to estimate matrix elements in terms of the number of valence proton and neutron pairs.

Unique second-forbidden β transitions: Decay of 137Cs

The intensity of the 283.4-keV γ line in the decay of 137Cs has been measured. The value obtained is used to determine the probability of the unique second-forbidden β transition of the 7/2+ → 1/2+ type: (8.7 ± 2.0) × 10−4% of the number of decays; this value corresponds to log f2unt = 16.45 ± 0.12. The intensity of the possible E5 transition at 378.3 keV is estimated to be < 0.9 × 10−4%. The technique for determining the values of log f2unt in calculations of the tensor matrix elements in the Cartesian and spherical coordinate systems is discussed. The possible intensity of the unique second-forbidden β transition between the ground states of 129I and 129Xe is estimated to be Iβ ≈ 0.1% of the number of decays of 129I.

Fullerene Quantum Gyroscope

We report the observation of quantized rotational states of a diatomic C2 unit in solid endohedral fullerene C(2)Sc(2)@C(84). The rotational transitions induce a periodic line pattern in the low energy Raman spectrum. The rotational constant B and the C-C distance were found to be 1.73 cm(-1) and 0.127 nm, respectively. Density functional calculations revealed an intrinsic rotational barrier of the order of only a few meV for the C2 unit. The Schrödinger equation involving the potential barrier was solved and the Raman tensor matrix elements were calculated, yielding good quantitative agreement with the experiment. To our best knowledge this is the first intrinsic rotational spectrum of a diatomic plane molecular rotor.

True and effective polarizability tensors for asymmetric-top molecules: The rotational Raman spectra of H 2S and D 2S

Higher order contributions to the rotational matrix elements of the equilibrium polarizability tensor are here derived from the components of the effective polarizability, obtained by contact transformation of the true polarizability tensor. These are used to simulate the rotational Raman spectrum of H 2S. The J-dependent intensity contribution from the (first-order) centrifugal distortion term is needed to give a good comparison with the observed spectrum. The best calculated spectrum is that having an integrated intensity which is consistent with the polarizability anisotropy obtained from the earlier depolarization ratio measurement. The calculation serves to determine the relative signs of both the equilibrium polarizability components and the derivatives with respect to normal coordinates—only one sign combination yields a calculated spectrum which agrees with the observed one. The cubic anharmonicity term also makes a significant isotopedependent contribution to the J-independent terms. These values were then used to derive the effective polarizability components for D 2S from the true ones, and they give a calculated spectrum and integrated intensity which agree well with observed results.