Pseudoscalar Density Research Articles

ℼ<sup>±</sup> -,ℼ<sup>0</sup>-meson electroweak decays within relativistic quark model based on point form of Poincaré-invariant quantum mechanics

In the course of work the integral representation of ℼ0-meson form-factor of ℼ0 → γγ process has been obtained within relativistic quark model based on point form of Poincaré-invariant quantum mechanics taking into account anomalous magnetic moments of κυ and κⅾ quarks. The parameters obtained using pseudoscalar density constant gℼ± , current masses of υ- and ⅾ-quarks as well as decay constant ℼ± → ℓ±νℓ were used for numerical modeling of Fℼ0γ(t) form-factor in time-like region. Similar calculations for ℼ0 → γγ decay characteristics with reference to quark structure in point form of Poincaré-invariant quantum mechanics have been carried out for the first time.

Nonperturbative running of the quark mass for Nf=3 QCD from the chirally rotated Schrödinger functional

We study the renormalization group (RG) running of the quark mass, for ${N}_{f}=3$ QCD with Wilson fermions in a mixed action setup, with standard Schr\"odinger functional (SF) boundary conditions for sea quarks and chirally rotated Schr\"odinger functional ($\ensuremath{\chi}\mathrm{SF}$) boundary conditions for valence quarks. This necessitates the tuning of the boundary factor ${z}_{\mathrm{f}}({g}_{0}^{2})$ of the $\ensuremath{\chi}\mathrm{SF}$ valence action, in order to ensure that QCD symmetries are fully recovered in the continuum. The properties of this novel setup are monitored through the ratios ${Z}_{S}/{Z}_{P}$ and ${\mathrm{\ensuremath{\Sigma}}}_{S}/{\mathrm{\ensuremath{\Sigma}}}_{P}$ of the renormalization parameters and step scaling functions of the scalar and pseudoscalar densities. Where comparison is possible, our ${Z}_{S}/{Z}_{P}$ results are found to agree with previous determinations, based on a mass ratio method [G. M. de Divitiis et al. (ALPHA Collaboration), Eur. Phys. J. C 79, 797 (2019)] and Ward identities [ J. Heitger et al. (ALPHA Collaboration), Eur. Phys. J. C 80, 765 (2020); J. Heitger et al., Eur. Phys. J. C 81, 606 (2021)], with Schr\"odinger functional boundary conditions. The behavior of ${\mathrm{\ensuremath{\Sigma}}}_{S}/{\mathrm{\ensuremath{\Sigma}}}_{P}$ confirms the theoretical expectations of $\ensuremath{\chi}\mathrm{SF}$ QCD, related to the restoration of the theory's symmetries in the continuum limit. From the step-scaling function of the pseudoscalar density we obtain the quark mass RG-running function from hadronic to perturbative energy scales. This is fully compatible with the earlier result obtained in a similar setup for Wilson quarks with Schr\"odinger functional boundary conditions [I. Campos et al., Eur. Phys. J. C 78, 387 (2018)], and provides a strong universality test for the two lattice setups.

Vortical Effects for Free Fermions on Anti-De Sitter Space-Time

Here, we study a quantum fermion field in rigid rotation at finite temperature on anti-de Sitter space. We assume that the rotation rate Ω is smaller than the inverse radius of curvature ℓ−1, so that there is no speed of light surface and the static (maximally-symmetric) and rotating vacua coincide. This assumption enables us to follow a geometric approach employing a closed-form expression for the vacuum two-point function, which can then be used to compute thermal expectation values (t.e.v.s). In the high temperature regime, we find a perfect analogy with known results on Minkowski space-time, uncovering curvature effects in the form of extra terms involving the Ricci scalar R. The axial vortical effect is validated and the axial flux through two-dimensional slices is found to escape to infinity for massless fermions, while for massive fermions, it is completely converted into the pseudoscalar density −iψ¯γ5ψ. Finally, we discuss volumetric properties such as the total scalar condensate and the total energy within the space-time and show that they diverge as [1−ℓ2Ω2]−1 in the limit Ω→ℓ−1.

Nonperturbative renormalization of the quark chromoelectric dipole moment with the gradient flow: Power divergences

The $CP$-violating quark chromoelectric dipole moment (qCEDM) operator, contributing to the electric dipole moment (EDM), mixes under renormalization and---particularly on the lattice---with the pseudoscalar density. The mixing coefficient is power-divergent with the inverse lattice spacing squared, $1/{a}^{2}$, regardless of the lattice action used. We use the gradient flow to define a multiplicatively renormalized qCEDM operator and study its behavior at small flow time. We determine nonperturbatively the linearly divergent coefficient with the flow time, $1/t$, up to subleading logarithmic corrections, and compare it with the 1-loop perturbative expansion in the bare and renormalized strong coupling. We also discuss the $\mathrm{O}(a)$ improvement of the qCEDM defined at positive flow time.

Short flow-time coefficients of CP -violating operators

Measurements of a permanent neutron electric dipole moment (EDM) potentially probe Beyond-the-Standard Model (BSM) sources of CP-violation. At low energy the CP-violating BSM interactions are parametrized by flavor-conserving CP-violating operators of dimension higher than four. QCD calculations of the nucleon matrix elements of these operators are required to fully reconstruct the sources and magnitudes of the different CP-violating contributions to the nucleon EDM. Herein we study the quark-chromo electric dipole moment (qCEDM) operator and the three-gluon Weinberg operator. The non-perturbative determination, using lattice QCD, of the nucleon matrix elements of these CP-violating operators is hampered by their short-distance behavior. Under renormalization these operators mix with lower dimensional operators, which induces power divergences in the lattice spacing, as the continuum limit is approached. We study the short-distance behavior of the qCEDM and the Weinberg operators using the gradient flow. We perform a short flow time expansion and determine, in perturbation theory, the expansion coefficients of the linearly-divergent terms stemming from the mixing with the pseudoscalar density and the topological charge, confirming the expectations of the operator product expansion. We introduce a new method to perform calculations at non-zero flow-time for arbitrary values of the external momenta. This method allows us to work in four dimensions for most of the calculations described in this paper, avoiding the complications associated with defining $\gamma_5$ in generic d dimensions. We show that leading contributions in the external momenta can be reproduced by defining $\gamma_5$ using the 't Hooft-Veltman-Breitenlohner-Maison scheme.

Ward identity determination of Z_{mathrm {S}}/Z_{mathrm {P}} for N_{mathrm {f}}=3 lattice QCD in a Schr\xf6dinger functional setup

We derive chiral Ward identities for lattice QCD with Wilson quarks and N_{mathrm{f}}ge 3 flavours, on small lattices with Schrödinger functional boundary conditions and vanishingly small quark masses. These identities relate the axial variation of the non-singlet pseudoscalar density to the scalar one, thus enabling the non-perturbative determination of the scale-independent ratio Z_{mathrm {S}}/Z_{mathrm {P}} of the renormalisation parameters of these operators. We obtain results for N_{mathrm{f}}=3 QCD with tree-level Symanzik-improved gluons and Wilson-Clover quarks, for bare gauge couplings which cover the typical range of large-volume N_{mathrm{f}}= 2+1 simulations with Wilson fermions at lattice spacings below 0.1,fm. The precision of our results varies from 0.3 to 1%, except for the coarsest lattice, where it is 2%. We discuss how the Z_{mathrm {S}}/Z_{mathrm {P}} ratio can be used in the non-perturbative calculations of {mathrm {O}}(a) improved renormalised quark masses.

Dalitz decays of vector mesons in relativistic quark model

In the course of work, basing on the previously developed method for calculating integral representations of decay constants for pseudoscalar and vector mesons in the frame of point form of Poincare-covariant quark model, the research of ω- and ϕ-mesons decays form-factors for Dalitz decays has been carried out. It is shown that the usage of the pseudoscalar density constant with integral representations of decay constants , and leads to parameters which can be used for the study of decay form-factors. As a result of the work, the behaviour of (t) Fωπγ* (t) and Fϕηγ* (t) form-factors compared with the experimental data in the interval q < 0.5 GeV is researched.

Decays of light mesons in the relativistic quark model

In the framework of the relativistic quark model based on the point form of the Poincaré-invariant quantum mechanics, the parameters were fixed using the integral representations of the lepton decay constants of pseudoscalar and vector mesons containing u-, d- and s-quarks. As a result of numerical calculations using the oscillator wave function, the basic parameters of the model are obtained using the pseudoscalar density constant and current quark masses. The analysis showed that the obtained calculation results in the framework of the model and the experimental data on the lepton decays of hadrons agree well with each other. As a result, the calculation method is generalized to the case of hadronic transitions with γ-quantum emission and a subsequent calculation of the integral representations of radiative decay constants of pseudoscalar and vector mesons. The obtained values of the anomalous magnetic moments are compared with the baryon data. As a test of the model, the authors studied the behavior of the form-factors of radiative decays of vector mesons with a subsequent comparison to the modern experimental data in the q &lt; 0.5 GeV range where the resonance effects are insignificant. As a result, self-consistent descriptions of lepton and radiative transitions were obtained within the framework of the model proposed by the authors.

Nπ -state contamination in lattice calculations of the nucleon pseudoscalar form factor

The nucleon-pion-state contribution in the QCD 3-point function of the pseudoscalar density is calculated to leading order in chiral perturbation theory. It predicts a nucleon-pion-state contamination in lattice estimates for the pseudoscalar form factor $G_{\rm P}(Q^2)$ determined with the plateau method. Depending on the momentum transfer $Q^2$ the contamination varies between -20% and +50% for a source-sink separation of 2 fm. The nucleon-pion-state contamination also causes violations in the generalized Goldberger-Treiman relation among the pseudoscalar and the axial nucleon form factors, the dominant source being the nucleon-pion-state contamination in the induced pseudoscalar form factor $\tilde{G}_{\rm P}(Q^2)$. Comparing the chiral perturbation theory predictions with lattice results of the PACS collaboration we find reasonable agreement even for source-sink separations as small as 1.3 fm.

Locality and multi-level sampling with fermions

Multi-level Monte Carlo sampling techniques exploit the locality of quantum field theory to provide a solution in purely-bosonic quantum field theories to the signal-to-noise ratio problem that affects the lattice determination of a large class of quantities. However, it is not straightforward to generalize multi-level sampling to lattice theories with fermionic content, such as QCD, due to the loss of manifest locality after the fermion path integral is performed. We discuss how the decrease of the fermion propagator with Euclidean distance induces a systematic approximation of the fermion propagator and the fermion determinant, in which the gauge field dependence of distant spacetime regions is completely factorized. This allows us to apply multi-level sampling to the lattice QCD computation of hadronic observables, such as mesonic and baryonic correlators. In particular, we show an application of this strategy to the disconnected contribution to the correlator of two flavour-singlet pseudoscalar densities, which results in a significant increase of the signal-to-noise ratio when a two-level sampling scheme is used.

Isovector axial form factors of the nucleon in two-flavor lattice QCD

We present a lattice calculation of the nucleon isovector axial and induced pseudoscalar form factors on the CLS ensembles using [Formula: see text] dynamical flavors of nonperturbatively [Formula: see text]-improved Wilson fermions and an [Formula: see text]-improved axial current together with the pseudoscalar density. Excited-state effects in the extraction of the form factors are treated using a variety of methods, with a detailed discussion of their respective merits. The chiral and continuum extrapolation of the results is performed both using formulae inspired by Heavy Baryon Chiral Perturbation Theory (HBChPT) and a global approach to the form factors based on a chiral effective field theory (EFT) including axial vector mesons. Our results indicate that careful treatment of excited-state effects is important in order to obtain reliable results for the axial form factors of the nucleon, and that the main remaining error stems from the systematic uncertainties of the chiral extrapolation. As final results, we quote [Formula: see text], [Formula: see text], and [Formula: see text] for the axial charge, axial charge radius and induced pseudoscalar charge, respectively, where the first error is statistical and the second is systematic.

Strange and charm quark spins from the anomalous Ward identity

We present a calculation of the strange and charm quark contributions to the nucleon spin from the anomalous Ward identity (AWI). It is performed with overlap valence quarks on 2+1-flavor domain-wall fermion gauge configurations on a $24^3 \times 64$ lattice with the light sea mass at $m_{\pi} = 330$ MeV. To satisfy the AWI, the overlap fermion for the pseudoscalar density and the overlap Dirac operator for the topological density, which do not have multiplicative renormalization, are used to normalize the form factor of the local axial-vector current at finite $q^2$. For the charm quark, we find that the negative pseudoscalar term almost cancels the positive topological term. For the strange quark, the pseudoscalar term is less negative than that of the charm. By imposing the AWI, the strange $g_A(q^2)$ at $q^2 =0$ is obtained by a global fit of the pseudoscalar and the topological form factors, together with $g_A(q^2)$ and the induced pseudoscalar form factor $h_A(q^2)$ at finite $q^2$. The chiral extrapolation to the physical pion mass gives $\Delta s + \Delta {\bar{s}} = -0.0403(44)(78)$.

Local factorization of the fermion determinant in lattice QCD

We introduce a factorization of the fermion determinant in lattice QCD with Wilson-type fermions that leads to a bosonic action which is local in the block fields. The interaction among gauge fields on distant blocks is mediated by multiboson fields located on the boundaries of the blocks. The resultant multiboson domain-decomposed hybrid Monte Carlo passes extensive numerical tests carried out by measuring standard gluonic observables. The combination of the determinant factorization and of the one of the propagator, that we put forward recently, paves the way for multilevel Monte Carlo integration in the presence of fermions. We test this possibility by computing the disconnected correlator of two flavor-diagonal pseudoscalar densities, and we observe a significant increase of the signal-to-noise ratio due to a two-level integration.

Influence of the pseudoscalar condensate gradient on the cooling regime of compact stars

We consider the processes in compact stars that arise during the potential formation of a pseudoscalar condensate in finite volumes. We do not propose specific hypotheses about the nature of this condensate. Considering that in the regions with a changing pseudoscalar density, photon propagation can be described in the framework of Maxwell–Chern–Simons electrodynamics, we find the reflection/transmission coefficients for regions with different densities. We study the fermion spectrum in the presence of an axial field considering the pseudoscalar condensate gradient. We also study the influence of the modified photon and fermion spectra on the cooling process of compact stars.

Small flow-time representation of fermion bilinear operators

Fermion bilinear operators of mass dimension 3, such as the axial-vector and vector currents, the pseudo-scalar and scalar densities, whose normalizations are fixed by Ward–Takahashi (WT) relations, are related to small flow-time behavior of composite operators of fermion fields evolved by Lüscher’s flow equation. The representations can be useful in lattice numerical simulations, as recently demonstrated by the WHOT QCD collaboration for the chiral condensation of the [Formula: see text] quantum chromodynamics (QCD) at finite temperature.

Domain decomposition, multilevel integration, and exponential noise reduction in lattice QCD

We explore the possibility of computing fermionic correlators on the lattice by combining a domain decomposition with a multi-level integration scheme. The quark propagator is expanded in series of terms with a well defined hierarchical structure. The higher the order of a term, the (exponentially) smaller its magnitude, the less local is its dependence on the gauge field. Once inserted in a Wick contraction, the gauge-field dependence of the terms in the resulting series can be factorized so that it is suitable for multi-level Monte Carlo integration. We test the strategy in quenched QCD by computing the disconnected correlator of two flavor-diagonal pseudoscalar densities, and a nucleon two-point function. In either cases we observe a significant exponential increase of the signal-to-noise ratio.

Stellar matter with pseudoscalar condensates

In this work we consider how the appearance of gradients of pseudoscalar condensates in dense systems may possibly influence the transport properties of photons in such a medium as well as other thermodynamic characteristics. We adopt the hypothesis that in regions where the pseudoscalar density gradient is large the properties of photons and fermions are governed by the usual lagrangian extended with a Chern-Simons interaction for photons and a constant axial field for fermions. We find that these new pieces in the lagrangian produce non-trivial reflection coefficients both for photons and fermions when entering or leaving a region where the pseudoscalar has a non-zero gradient. A varying pseudoscalar density may also lead to instability of some fermion and boson modes and modify some properties of the Fermi sea. We speculate that some of these modifications could influence the cooling rate of stellar matter (for instance in compact stars) and have other observable consequences. While quantitative results may depend on precise astrophysical details most of the consequences are quite universal and consideration should be given to this possibility.

Electric Dipole Moment of the Neutron from 2+1 Flavor Lattice QCD.

We compute the electric dipole moment d(n) of the neutron from a fully dynamical simulation of lattice QCD with 2+1 flavors of clover fermions and nonvanishing θ term. The latter is rotated into a pseudoscalar density in the fermionic action using the axial anomaly. To make the action real, the vacuum angle θ is taken to be purely imaginary. The physical value of dd(n) is obtained by analytic continuation. We find d(n)=-3.9(2)(9)×10(-16) θ e cm, which, when combined with the experimental limit on d(n), leads to the upper bound |θ|≲7.4×10(-11).

Fierz bilinear formulation of the Maxwell–Dirac equations and symmetry reductions

We study the Maxwell–Dirac equations in a manifestly gauge invariant presentation using only the spinor bilinear scalar and pseudoscalar densities, and the vector and pseudovector currents, together with their quadratic Fierz relations. The internally produced vector potential is expressed via algebraic manipulation of the Dirac equation, as a rational function of the Fierz bilinears and first derivatives (valid on the support of the scalar density), which allows a gauge invariant vector potential to be defined. This leads to a Fierz bilinear formulation of the Maxwell tensor and of the Maxwell–Dirac equations, without any reference to gauge dependent quantities. We show how demanding invariance of tensor fields under the action of a fixed (but arbitrary) Lie subgroup of the Poincaré group leads to symmetry reduced equations. The procedure is illustrated, and the reduced equations worked out explicitly for standard spherical and cylindrical cases, which are coupled third order nonlinear PDEs. Spherical symmetry necessitates the existence of magnetic monopoles, which do not affect the coupled Maxwell–Dirac system due to magnetic terms cancelling. In this paper we do not take up numerical computations. As a demonstration of the power of our approach, we also work out the symmetry reduced equations for two distinct classes of dimension 4 one-parameter families of Poincaré subgroups, one splitting and one non-splitting. The splitting class yields no solutions, whereas for the non-splitting class we find a family of formal exact solutions in closed form.

Fermion Interactions, Cosmological Constant and Space-Time Dimensionality in a Unified Approach Based on Affine Geometry

One of the main features of unified models, based on affine geometries, is that all possible interactions and fields naturally arise under the same standard. Here, we consider, from the effective Lagrangian of the theory, the torsion induced 4-fermion interaction. In particular, how this interaction affects the cosmological term, supposing that a condensation occurs for quark fields during the quark-gluon/hadron phase transition in the early universe. We explicitly show that there is no parity-violating pseudo-scalar density, dual to the curvature tensor (Holst term) and the spinor-bilinear scalar density has no mixed couplings of A-V form. On the other hand, the space-time dimensionality cannot be constrained from multidimensional phenomenological models admitting torsion.