Isoscalar Tensor Research Articles

Transversity PDFs of the proton from lattice QCD with physical quark masses

We present a lattice QCD calculation of the transversity isovector- and isoscalar-quark parton distribution functions (PDFs) of the proton utilizing a perturbative matching at next-to-leading-order (NLO) accuracy. Additionally, we determine the isovector and isoscalar tensor charges for the proton. In both calculations, the disconnected contributions to the isoscalar matrix elements have been ignored. The calculations are performed using a single ensemble of Nf=2+1 highly improved staggered quarks simulated with physical-mass quarks and a lattice spacing of a=0.076 fm. The Wilson-clover action, with physical quark masses and smeared gauge links obtained from one iteration of hypercubic smearing, is used in the valence sector. Using the NLO operator product expansion, we extract the lowest four to six Mellin moments and the PDFs via a neural network from the matrix elements in the pseudo-PDF approach. In addition, we calculate the PDFs in the quasi-PDF approach with hybrid-scheme renormalization and the recently developed leading-renormalon resummation technique, at NLO with the resummation of leading small-x logarithms. Published by the American Physical Society 2024

Evidence supporting the existence of Pc(4380)± from the recent measurements of Bs→J/ψpp¯

Very recently, the LHCb collaboration released the newest measurements of $B_s \to J/\psi p\bar{p}$, where an enhancement structure near 4.34 GeV was observed in the invariant mass spectrum of $J/\psi p$ with the statistical significance of $3.1-3.7$ $\sigma$. In this work, by performing a combined analysis for the three invariant mass spectra of $B_s \to J/\psi p\bar{p}$, we find that this $J/\psi p$ structure near 4.34 GeV can correspond to the contributions from the $P_c(4380)^+$ state with the assumption of $J^{P}=3/2^{-}$ together with the reflections of $B_s \to (f_2^{*} \to p\bar{p})J/\psi$. Here, $P_c(4380)$ was first observed in $\Lambda_b \to J/\psi p K$ but not confirmed in the updated LHCb data in 2019, and $f_2^{*}$ means the exciting light isoscalar tensor meson around 2.0 GeV. Thus, this provides a possible evidence to support the existence of the pentaquark $P_c(4380)$. Specifically, the assumed spin parity $J^{P}=3/2^{-}$ of $P_c(4380)$ is consistent with a prediction of the theoretical explanation of an $S$-wave $\bar{D}\Sigma_c^*$ molecular bound state.

Tensor form factors of [formula omitted] state via light-cone QCD

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, Q2, 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.

Tensor force effect on the neutron shell closure in super-heavy elements

A systematic study of the effect of tensor force on the evolution of shell structure in even-even super-heavy nuclei in the region of proton numbers Z=114, 120 and 126 and in the region of neutron numbers 178 $\le$ N $\le$ 188 is presented. We use, in this investigation, the Hartree-Fock framework by means of different types of Skyrme functionals in two cases with and without tensor force. The Bardeen-Cooper-Schriefer (BCS) approximation has been used to treat the pairing correlations. By investigating structural and decay properties of nuclei under consideration, it is found that N=184 shell gap is more enhanced by the tensor interaction which depends on the isoscalar tensor coupling constant $C_0^J$ of the used Skyrme interactions. In the case without tensor interaction, this gap is significant only for T22, T24, T42 and SLy5. So, it disappears with T46, T64 and T66, and is too weak for T26, T44 and T62. Without exception, the shell gap at N=184 becomes more pronounced when the tensor part is taken into account.

Isovector and isoscalar tensor form factors of N(1535)→N transition in light-cone QCD

We have applied isovector and isoscalar tensor current to evaluate the tensor form factors of the $ N(1535) \rightarrow N $ transition with the help of the light-cone QCD sum rule method. In numerical computations, have used the most general forms of the interpolating current for the nucleon and the tensor current together with two different sets of the input parameters in the DAs of the $N(1535)$ state. We have obtained that the values of $N(1535) \rightarrow N$ transition tensor form factors very sensitive to the input parameters of the distribution amplitudes of the $N(1535)$ state. We have acquired that the $Q^2$ dependence of $N(1535) \rightarrow$ transition tensor form factors is well defined by a p-pole fit function.

Isovector and isoscalar tensor charges of the nucleon from lattice QCD

We present results for the iso-vector and flavor diagonal tensor charges $g^{u-d}_T$, $g^{u}_T$, $g^{d}_T$, and $g^{s}_T$ needed to probe novel tensor interactions at the TeV scale in neutron and nuclear $\beta$-decays and the contribution of the quark electric dipole moment (EDM) to the neutron EDM. The lattice QCD calculations were done using nine ensembles of gauge configurations generated by the MILC collaboration using the HISQ action with 2+1+1 dynamical flavors. These ensembles span three lattice spacings $a \approx 0.06, 0.09$ and $0.12 $ fm and three quark masses corresponding to the pion masses $M_\pi \approx 130, 220$ and $310 $ MeV. Using estimates from these ensembles, we quantify all systematic uncertainties and perform a simultaneous extrapolation in the lattice spacing, volume and light quark masses for the connected contributions. The final estimates of the connected nucleon (proton) tensor charge for the iso-vector combination is $g_T^{u-d} = 1.020(76) $ in the $\bar{\text{MS}}$ scheme at $2$ GeV. The additional disconnected quark loop contributions needed for the flavor-diagonal matrix elements are calculated using a stochastic estimator employing the truncated solver method with the all-mode-averaging technique. We find that the size of the disconnected contribution is smaller than the statistical error in the connected contribution. This allows us to bound the disconnected contribution and include it as an additional uncertainty in the flavor-diagonal charges. After a continuum extrapolation, we find $g_T^{u} = 0.774(66) $, $g_T^{d} = -0.233(28) $ and $g_T^{u+d} = 0.541(67) $. The strangeness tensor charge, that can make a significant contribution to the neutron EDM due to the large ratio $m_s/m_{u,d}$, is $g_T^{s}=0.008(9)$ in the continuum limit.

Localization of the glueball and possible decuplets of tensor mesons

We continue the study of flavor aspects of strong interaction. The answer to the question of glueball existence is probably a necessary step in this investigation. The existence of the glueball implies the existence of the decuplets. The model we consider requires that the mass of meson decuplet dominated by the glueball is enclosed between the masses of the ideal nonet N and S states.This description is applied to the two sets of the tensor mesons. One of them comprises the well-known particles that are attributed to the widely known nonet 2++. We argue that they belong to a decuplet if there exists the isoscalar tensor meson having the mass obeying the condition on the gluebal-dominated meson; the meson f2(1430) could be a candidate. Another set includes a large number of mesons lying in the 2 GeV region. This set is used to test the ability of the model to select particles belonging to the decuplet.

Excited States and Strength Functions of 4He in Correlated Gaussians

Resonances and continuum states of 4He are studied using correlated Gaussians. Applicability of the square-integrable functions is tested with use of a complex scaling method. All the known levels of 4He up to the excitation energy of 26 MeV are well understood with a realistic nucleon-nucleon potential. The importance of the tensor force is stressed. Strength functions for isoscalar monopole and spin-dipole tensor operators are investigated.

Mass spectrum and strong decays of isoscalar tensor mesons

In this work, we present a systematic study of the observed isoscalar tensor $f_2$ states. With the detailed analysis of the mass spectrum and calculation of the $f_2$ two-body strong decays, we extract information of their underly structures, and try to categorize them into the conventional tensor meson family ($n^{3}P_{2}$ $(n=1,2,3,4)$ and $m^{3}F_{2}$ ($m=1,2$)). We also give predictions for other decay modes of these tensor mesons, which are useful for further experimental investigations.

Global nuclear structure effects of the tensor interaction

A direct fit of the isoscalar spin-orbit (SO) and both isoscalar and isovector tensor coupling constants to the f(5/2)-f(7/2) SO splittings in Ca-40, Ni-56, and Ca-48 nuclei requires a drastic redu ...

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: The case of the relativistic harmonic oscillator

We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and $\gamma^5$ chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry related problems have the same spectrum, but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.

Quasi-particle interaction in nuclear matter from chiral pion–nucleon dynamics

Based on a recent chiral approach to nuclear matter we calculate the in-medium interaction of nucleons at the Fermi surface | p → 1 , 2 | = k f . The isotropic part of this quasi-particle interaction is characterized by four density-dependent (dimensionful) Fermi-liquid parameters: f 0 ( k f ) , f 0 ′ ( k f ) , g 0 ( k f ) and g 0 ′ ( k f ) . In the approximation to 1 π-exchange and iterated 1 π-exchange (which as such leads already to a good nuclear matter equation of state) we find a spin–isospin interaction strength of g 0 ′ ( 2 m π ) = 1.14 fm 2 , compatible with existing empirical values. The consistency relations to the nuclear matter compressibility K and the spin/isospin asymmetry energies serve as a check on our perturbative calculation. In the next step we include systematically the contributions from 2 π-exchange with virtual Δ ( 1232 ) -isobar excitation which have been found important for good single-particle properties and spin-stability of nuclear matter. Without any additional short-distance terms (contributing proportional to k f 2 ) the spin-dependent Fermi-liquid parameters g 0 ( k f 0 ) and g 0 ′ ( k f 0 ) come out far too large. Estimates of these short-distance parameters from realistic NN-potentials go in the right direction, but sizeable enhancement factors are still needed to reproduce the empirical values of g 0 ( k f 0 ) and g 0 ′ ( k f 0 ) . This points towards the importance of higher order iterations subsumed in the induced interaction. We consider also the tensor part of the quasi-nucleon interaction at the Fermi surface. In comparison to the leading 1 π-exchange tensor interaction we find from the 2 π-exchange corrections almost a doubling of the isoscalar tensor strength h 0 ( k f ) , whereas the isovector tensor strength h 0 ′ ( k f ) is much less affected. These features are not changed by the inclusion of the chiral πNΔ-dynamics. The l = 1 tensor Fermi-liquid parameters h 1 ( k f ) and h 1 ′ ( k f ) follow a similar pattern.

Tensor coupling and pseudospin symmetry in nuclei

In this work we study the contribution of the isoscalar tensor coupling to the realization of pseudospin symmetry in nuclei. Using realistic values for the tensor coupling strength, we show that this coupling reduces noticeably the pseudospin splittings, especially for single-particle levels near the Fermi surface. By using an energy decomposition of the pseudospin energy splittings, we show that the changes in these splittings come by mainly through the changes induced in the lower radial wave function for the low-lying pseudospin partners, and by changes in the expectation value of the pseudospin-orbit coupling term for surface partners. This allows us to confirm the conclusion already reached in previous studies, namely that the pseudospin symmetry in nuclei is of a dynamical nature.

Systematization of tensor mesons and the determination of the 2++ glueball

It is shown that new data on the (JPC=2++) resonances in the mass range M∼1700–2400 MeV support the linearity of the (n, M2) trajectories, where n is the radial quantum number of the quark-antiquark state. In this way, all the vacancies for the isoscalar tensor qq mesons in the range up to 2450 MeV are filled in. This allows one to fix the broad f2 state with M=2000±30 MeV and Г=530±40 MeV as the lowest-tensor glueball.

Proton-Antiproton annihilation at 900 MeV/c into $\pi^0\pi^0\pi^0, \pi^0\pi^0\eta$ and $\pi^0\eta\eta$

The three reactions $\overline{p}p \rightarrow \pi^0\pi^0\pi^0$ , $\pi^0\pi^0\eta$ and $\pi^0\eta\eta$ in proton-antiproton annihilation in flight at 900 MeV/c are used to search for isoscalar $0^{++}$ and $2^{++}$ mesons in the mass range 1000–2000 MeV, in particular the $f_0(1710)$ . The description of both $\pi^0\pi^0\pi^0$ and $\pi^0\eta\eta$ data sets requires an isoscalar tensor resonance decaying into $\pi^0\pi^0$ and $\eta\eta$ with a mass of $(1867\pm46)$ MeV and a width of $(385\pm58)$ MeV. The ratio of partial widths $\Gamma(\eta\eta)/\Gamma(\pi\pi)$ is $0.27 \pm 0.10$ . The analyses of both $\pi^0\pi^0\pi^0$ and $\pi^0\eta\eta$ show no signal for the $f_0(1710)$ . The $\pi^0\eta\eta$ data set shows a strong signal of the $f_2^{\prime}(1525)$ suggesting a large OZI rule violation for tensor meson production in $\overline{p}p$ annihilation. The $\pi^0\pi^0\pi^0$ data set also requires the $f_2(1565)$ . The signal for the $f_2(1810)$ reported by earlier experiments is confirmed neither in $\pi^0\pi^0\pi^0$ nor in $\pi^0\eta\eta$ . The analysis of $\pi^0\pi^0\eta$ leads to an isovector tensor state decaying into $\pi^0\eta$ with a mass of $(1698\pm44)$ MeV and a width of $(265\pm55)$ MeV.

Chiral 3π-exchangeNNpotentials: Results for diagrams proportional togA4andgA6

We calculate in (two-loop) chiral perturbation theory the local NN-potentials generated by the three-pion exchange diagrams proportional to g_A^4 and g_A^6. Surprisingly, we find that the total isoscalar central $3\pi$-exchange potential vanishes identically. The individually largest $3\pi$-exchange potentials are of isoscalar spin-spin, isovector central and isoscalar tensor type. For these potentials simple analytical expressions can be given. The strength of these dominant $3\pi$-exchange potentials at r=1.0 fm is 4.6 MeV, 2.9 MeV and 1.4 MeV, respectively. Furthermore, we observe that the spin-spin and tensor potentials due to the diagrams proportional to g_A^6 do not exist in the infinite nucleon mass limit.

Filtering overpopulated isoscalar tensor states with mass relations

Schwinger-type mass formulas are used to analyze glueball-meson mixing for isoscalar tensor mesons. In one solution, the f{sub J}(2220) is the physical glueball, and in the other the glueball is distributed over various states, with f{sub 2}(1810) having the largest glueball component. Neither the f{sub 2}(1565) nor the f{sub J}(1710) are among the physical states without assuming significant coupling to decay channels. The decay f{sub 2}(1525){yields}{pi}{pi} is consistent with experiment, and f{sub J}(2220) is neither narrow nor decays flavor democratically. (c) 2000 The American Physical Society.

Tensor glueball–meson mixing phenomenology

The overpopulated isoscalar tensor states are sifted using Schwinger-type mass relations. Two solutions are found: one where the glueball is the fJ(2220), and one where the glueball is more distributed, with f2(1820) having the largest component. The f2(1565) and fJ(1710) cannot be accommodated as glueball-(hybrid) meson mixtures in the absense of significant coupling to decay channels. f2'(1525) -> pi pi is in agreement with experiment. The fJ(2220) decays neither flavour democratically nor is narrow.

Phase-shift analysis of NN scattering below 160 MeV: Indication for a strong tensor force.

A new phase-shift analysis of NN scattering in the energy range 15--160 MeV is presented. The analysis is based on the carefully reviewed world pp+np data, including recent results for higher-order spin observables in n-p scattering. The latter are essential to determine the mixing parameter ${\mathrm{\ensuremath{\varepsilon}}}_{1}$ which is directly related to the isoscalar tensor force. ${\mathrm{\ensuremath{\varepsilon}}}_{1}$ displays a high trend, in agreement with recent analyses above 140 MeV, and is only reproduced by potential models with a strong tensor force. The prediction of the full Bonn potential is too low by 20% for energies above 40 MeV. All other I=0 phase shifts show agreement with potential models; in particular, the notorious problem with $^{1}$${\mathit{P}}_{1}$ around 50 MeV has disappeared. Around 25 MeV a ten parameter fit based purely on np data agrees with the corresponding fit to the pp data and reveals no indication of anomalous charge independence breaking.

Evidence for a multiquark state in [formula omitted] annihilation at rest

We have observed an isoscalar tensor meson at a mass of 1565 ± 10 MeV/ c 2 and a width of 170 ± 20 MeV/ c 2. The resonance is seen in pp annihilation at rest into π + π − π 0 from P states of antiprotonic hydrogen atoms.