Search

We investigate the contributions of the hadronic structure of the neutron to radiative $O(\alpha E_e/m_N)$ corrections (or the inner $O(\alpha E_e/m_N)$ RC) to the neutron beta decay, where $\alpha$, $E_e$ and $m_N$ are the fine-structure constant, the electron energy and the nucleon mass, respectively. We perform the calculation within the effective quantum field theory of strong low-energy pion-nucleon interactions described by the linear $\sigma$-model with chiral $SU(2) \times SU(2)$ symmetry and electroweak hadron-hadron, hadron-lepton and lepton-lepton interactions for the electron-lepton family with $SU(2)_L \times U(1)_Y$ symmetry of the Standard Electroweak Theory (Ivanov et al., Phys. Rev. D99, 093006 (2019)). We show that after renormalization, carried out in accordance with Sirlin's prescription (Sirlin, Phys. Rev. 164, 1767 (1967)), the inner $O(\alpha E_e/m_N)$ RC are of the order of a few parts of $10^{-5} - 10^{-4}$. This agrees well with the results obtained in (Ivanov et al., Phys. Rev. D99, 093006 (2019))., Comment: accepted by Phys.Rev.D

In the framework of the Standard Model (SM) a theoretical description of the neutron beta decay is given at the level of 10^{-5}. The neutron lifetime and correlation coefficients of the neutron beta decay for a polarized neutron, a polarized electron and an unpolarized proton are calculated at the account for i) the radiative corrections of order O(\alpha E_e/m_N) ~ 10^{-5} to Sirlin's outer and inner radiative corrections of order O(\alpha/\pi), ii) the corrections of order O(E^2_e/m^2_N) ~ 10^{-5}, caused by weak magnetism and proton recoil, and iii) Wilkinson's corrections of order 10^{-5} (Wilkinson, Nucl. Phys. A377, 474 (1982)). These corrections define the SM background of the theoretical description of the neutron beta decay at the level of 10^{-5}, which is required by experimental searches of interactions beyond the SM with experimental uncertainties of a few parts of 10^{-5}., Comment: 35 pages, 1 figure, The manuscript is revised in accordance with the version accepted for publication in Physical Review D

In the standard effective V - A theory of low-energy weak interactions (i.e. in the Standard Model (SM)) we analyze the structure of the correlation coefficients S(E_e) and U(E_e), where E_e is the electron energy. These correlation coefficients were introduced to the electron-energy and angular distribution of the neutron beta decay by Ebel and Feldman ( Nucl. Phys. 4, 213 (1957)) in addition to the set of correlation coefficients proposed by Jackson et al. (Phys. Rev. 106, 517 (1957)). The correlation coefficients $S(E_e)$ and $U(E_e)$ are induced by simultaneous correlations of the neutron and electron spins and electron and antineutrino 3-momenta. These correlation structures do no violate discrete P, C and T symmetries. We analyze the contributions of the radiative corrections of order O(alpha/pi), taken to leading order in the large nucleon mass m_N expansion, and corrections of order O(E_e/m_N), caused by weak magnetism and proton recoil. In addition to the obtained SM corrections we calculate the contributions of interactions beyond the SM (BSM contributions) in terms of the phenomenological coupling constants of BSM interactions by Jackson et al. (Phys. Rev. 106, 517 (1957)) and the second class currents by Weinberg (Phys. Rev. 112, 1375 (1958))., Comment: 13 pages, the manuscript is revised. arXiv admin note: text overlap with arXiv:2101.01014

We analyze the correlation coefficient T(E_e), which was introduced by Ebel and Feldman (Nucl. Phys. 4, 213 (1957)). The correlation coefficient T(E_e) is induced by the correlations of the neutron spin with the antineutrino 3-momentum and the electron spin with the electron 3-momentum. Such a correlation structure is invariant under discrete P, C and T symmetries. The correlation coefficient T(E_e), calculated to leading order in the large nucleon mass m_N expansion, is equal to T(E_e) = - 2 g_A(1 + g_A)/(1 + 3 g^2_A) = - B_0, i.e. of order |T(E_e)| ~ 1, where $g_A$ is the axial coupling constant. Within the Standard Model (SM) we describe the correlation coefficient $T(E_e)$ at the level of 10^{-3} by taking into the radiative corrections of order O(\alpha/\pi) or the outer model-independent radiative corrections, where \alpha is the fine-structure constant, and the corrections of order O(E_e/m_N), caused by weak magnetism and proton recoil. We calculate also the contributions of interactions beyond the SM, including the contributions of the second class currents., Comment: 15 pages, some typos are corrected

We calculate the contributions of weak magnetism and proton recoil of order O(E^2_e/m^2_N)~10^{-5}, i.e. to next-to-next-to-leading order in the large nucleon mass expansion, to the neutron lifetime and correlation coefficients of the neutron beta decay, where E_e and m_N are the electron energy and the nucleon mass, respectively. We analyze the electron-energy and angular distribution for the neutron beta decay with a polarized neutron, a polarized electron and an unpolarized proton. Together with Wilkinson's corrections (Nucl. Phys. A 377, 474 (1982) and radiative corrections of order O(alpha E_e/m_N) ~ 10^{-5} (Phys. Rev. D 99, 093006 (2019)), calculated as next--to--leading order corrections in the large nucleon mass $m_N$ expansion to Sirlin's corrections of order O(alpha/pi) (Phys. Rev. 164, 1767 (1967)), the corrections of order O(E^2_e/m^2_N) ~ 10^{-5} provide an improved level of precision of the theoretical background of the neutron beta decay, calculated in the Standard Model, for experimental searches of contributions of interactions beyond the Standard Model., Comment: 22 pages, no figures, we have corrected Ref.[30] and Eq.(22)

We analyze the contributions of the one-pion-pole (OPP) exchange, caused by strong low-energy interactions, and the pseudoscalar interaction beyond the Standard Model (BSM) to the correlation coefficients of the neutron beta-decays for polarized neutrons, polarized electrons and unpolarized protons. The strength of contributions of pseudoscalar interactions is defined by the effective coupling constant C_ps = C^(OPP)_ps + C^(BSM)_ps. We show that the contribution of the OPP exchange is of order C^(OPP)_ps ~ - 10^(-5). The effective coupling constant C^(BSM)_ps of the pseudoscalar interaction BSM can be in principle complex. Using the results, obtained by Gonzalez-Alonso et al.( Prog. Part. Nucl. Phys. 104, 165 (2019)) we find that the values of the real and imaginary parts of the effective coupling constant C^(BSM)_ps are constrained by - 3.5x10^{-5} < ReC^(BSM)_ps < 0 and ImC^(BSM)_ps < - 2.3x10^(-5), respectively. The obtained results can be used as a theoretical background for experimental searches of contributions of interactions BSM in asymmetries of the neutron beta-decays with a polarized neutron, a polarized electron and an unpolarized proton at the level of accuracy of a few parts of $10^{-5}$ or even better (Abele, Hyperfine Interact.237, 155 (2016))., Comment: 12 pages, the paper is fully revised and accepted for publication in Nuclear Physics B

We calculate the radiative corrections of order O(alpha E_e/m_N) as next-to-leading order corrections in the large nucleon mass expansion to Sirlin's radiative corrections of order O(alpha/pi) to the neutron lifetime. The calculation is carried out within a quantum field theoretic model of strong low-energy pion--nucleon interactions described by the linear sigma-model (LsM) with chiral SU(2)xSU(2) symmetry and electroweak hadron-hadron, hadron-lepton and lepton-lepton interactions for the electron-lepton family with SU(2)_L x U(1)_Y symmetry of the Standard Electroweak Model (SEM). Such a quantum field theoretic model is some kind a hadronized version of the Standard Model (SM). From a gauge invariant set of the Feynman diagrams with one-photon exchanges we reproduce Sirlin's radiative corrections of order O(alpha/pi), calculated to leading order in the large nucleon mass expansion, and calculate next-to-leading corrections of order O(alpha E_e/m_N). This confirms Sirlin's confidence level of the radiative corrections O(alpha E_e/m_N). The contributions of the LsM are taken in the limit of the infinite mass of the scalar isoscalar sigma-meson. In such a limit the LsM reproduces the results of the current algebra (Weinberg, Phys. Rev. Lett. {\bf 18}, 188 (1967)) in the form of effective chiral Lagrangians of pion-nucleon interactions with non--linear realization of chiral SU(2)xSU(2) symmetry. In such a limit the L$\sigma$M is also equivalent to Gasser-Leutwyler's chiral quantum field theory or chiral perturbation theory (ChPT) with chiral SU(2)xSU(2)symmetry and the exponential parametrization of a pion-field (Ecker, Prog. Part. Nucl. Phys. {\bf 35}, 1 (1995))., Comment: 50 pages, 7 figures. a few typos are corrected. arXiv admin note: text overlap with arXiv:1805.09702

We calculate the correlation coefficients of the electron-energy and electron-antineutrino angular distribution of the neutron beta decay with polarized electron and unpolarised neutron and proton. The calculation is carried out within the Standard Model (SM) with the contributions, caused by the weak magnetism, proton recoil and radiative corrections of order of 10^{-3}, Wilkinson's corrections of order 10^{-5}$(Wilkinson, Nucl. Phys. A377, 474 (1982) and Ivanov et al., Phys. Rev. C95, 055502 (2017)) and the contributions of interactions beyond the SM. The obtained results can be used for the analysis of experimental data on searches of interactions beyond the SM at the level of 10^{-4} (Abele, Hyperfine Interact. 237, 155 (2016)). The contributions of G-odd correlations are calculated and found at the level of 10^{-5} in agreement with the results obtained by Gardner and Plaster (Phys. Rev. C87, 065504 (2013)) and Ivanov et al. (Phys. Rev. C98, 035503 (2018))., Comment: 20 pages, 4 figures.The functions in Eq.(A.8) are corrected. arXiv admin note: text overlap with arXiv:1805.03880

As we have pointed out in (arXiv:1806.10107 [hep-ph]), the existence of neutron dark matter decay modes "n -> chi + anything", where "chi" is a dark matter fermion, for the solution of the neutron lifetime problem changes priorities and demands to describe the neutron lifetime "tau_n = 888.0(2.0)s", measured in beam experiments and defined by the decay modes "n -> p + anything", in the Standard Model (SM). The latter requires the axial coupling constant "lambda" to be equal to "lambda = - 1.2690" (arXiv:1806.10107 [hep-ph]). Since such an axial coupling constant is excluded by experimental data reported by the PERKEO II and UCNA Collaborations, the neutron lifetime "tau_n = 888.0(2.0)s" can be explained only by virtue of interactions beyond the SM, namely, by the Fierz interference term of order "b ~ - 10^{-2}" dependent on scalar and tensor coupling constants. We give a complete analysis of all correlation coefficients of the neutron beta decays with polarized neutron, taking into account the contributions of scalar and tensor interactions beyond the SM with the Fierz interference term "b ~ - 10^{-2}". We show that the obtained results agree well with the contemporary experimental data that does not prevent the neutron with the rate of the decay modes "n -> p + anything", measured in beam experiments, to have dark matter decay modes "n -> chi + anything"., Comment: 12 pages, 1 figure. arXiv admin note: text overlap with arXiv:1805.03880, arXiv:1806.10107, arXiv:1807.04604, it is accepted for publication in Nuclear Physics B

We discuss an investigation of the dark matter decay modes of the neutron, proposed by Fornal and Grinstein (Phys. Rev. Lett. 120 191801 (2018)) and Ivanov et al. ( arXiv:1806.10107 [hep-ph]) for solution of the neutron lifetime anomaly problem, through the analysis of the electrodisintegration of the deuteron d into dark matter fermions chi and protons p close to threshold. We calculate the triple-differential cross section for the reaction e^- + d ->\chi + p + e^- and propose to search for such a dark matter channel in coincidence experiments on the electrodisintegration of the deuteron e^- + d -> n + p + e^- into neutrons n and protons close to threshold with outgoing electrons, protons and neutrons in coincidence. A missing of neutron signals should testify a detection of dark matter fermions., Comment: 19 pages, 5 figures, the manuscript is revised

We analyse the discrepancy between the neutron lifetimes measured in the bottle and beam experiments. Following Fornal and Grinstein (Phys. Rev. Lett. 120, 191801 (2018)) we propose an explanation of such a puzzle by the dark matter channels of the neutron decay. However, unlike Fornal and Grinstein in addition to the dark matter decay channel n -> \chi + e^- + e^+, where \chi is a dark matter Dirac fermion and (e^-e^+) is an electron--positron pair, we assume the existence of the dark matter channel n -> chi + \nu_e + \bar{\nu}_e, where \nu_e \bar{\nu}_e is the electron neutrino-antineutrino pair. This allows to describe the discrepancy between the measurements of the neutron lifetime even in case of an unobservability of the dark matter decay channel n -> \chi + e^- + e^+, which may be below the reaction threshold. The existence of the coupling n -> \chi + e^- + e^+ can be observed experimentally by measuring electron-neutron scattering e^- + n -> \chi + e^- at very low electron energies, induced with the strength as of the decay n -> \chi + \nu_e + \bar{\nu}_e$. We propose a gauge invariant quantum field theory model with SU_L(2)\times U_R(1) \times U_R'(1)\times U''_L(1) symmetry for the UV completion of the effective (n\chi \ell \bar{\ell}) interaction, where \ell(\bar{\ell}) is electron (positron) or neutrino(antineutrino)., Comment: 26 pages, 11 figures, a quark level formulation of our model is added

Within the standard V - A theory of weak interactions, Quantum Electrodynamics (QED) and the linear sigma-model (LsM) of strong low-energy hadronic interactions we analyse gauge and infrared properties of hadronic structure of the neutron and proton in the neutron beta decay to leading order in the large nucleon mass expansion. We show that the complete set of Feynman diagrams describing radiative corrections of order O(\alpha/\pi), induced by hadronic structure of the nucleon, to the rate of the neutron beta decay is gauge non-invariant and unrenormalisable. We show that a gauge non-invariant contribution does not depend on the electron energy in agreement with Sirlin's analysis of contributions of strong low-energy interactions (Phys. Rev. 164, 1767 (1967)). We show that infrared divergent and dependent on the electron energy contributions from the neutron radiative beta decay and neutron beta decay, caused by hadronic structure of the nucleon, are cancelled in the neutron lifetime. Nevertheless, we find that divergent contributions of virtual photon exchanges to the neutron lifetime, induced by hadronic structure of the nucleon, are unrenormalisable even formally. Such an unrenormalizability can be explained by the fact that the effective V - A vertex of hadron-lepton current-current interactions is not a vertex of the combined quantum field theory including QED and LsM, which are renormalizable theories., Comment: 9 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1806.04630 and arXiv:1805.09702

Within the standard V - A theory of weak interactions, Quantum Electrodynamics (QED) and the linear sigma-model (LsM) of strong low-energy hadronic interactions we analyse infrared properties of hadronic structure of the neutron and proton in the neutron beta decays to leading order in the large nucleon mass expansion. We confirm validity and high confidence level of contributions of hadronic structure of the nucleon to the radiative corrections, calculated by Sirlin (Phys. Rev. 164, 1767 (1967)) to leading order in the large nucleon mass expansion. At the level of order 10^{-5} relative to Sirlin's infrared divergent contribution to the neutron radiative beta decay (inner bremsstrahlung) we find an infrared divergent contribution, induced by hadronic structure of the nucleon through the one-pion-pole exchange, to the rate of the neutron lifetime from the neutron radiative beta decay, which should be cancelled by contributions of virtual photon exchanges to the neutron beta decay. Following Ivanov et al. 1805.09702 [hep-ph] we argue that a consistent analysis of such a cancellation may be carried out well in the combined quantum field theory including the Standard Electroweak Model (SEM) and the LsM of strong low-energy interactions, where the effective V - A hadron-lepton current-current vertex is caused by the W^- - electroweak-boson exchange., Comment: 6 pages, 2 figures. we have modified Eq.(11) and corrected a misprint in Eq.(12). arXiv admin note: text overlap with arXiv:1806.08699, arXiv:1805.09702

Within the standard V - A theory of weak interactions, Quantum Electrodynamics (QED) and the linear sigma-model (LsM) of strong low-energy hadronic interactions we analyse gauge properties of hadronic structure of the neutron and proton in the neutron radiative beta-decay. We show that the Feynman diagrams, describing contributions of hadronic structure to the amplitude of the neutron radiative beta-decay in the tree-approximation for strong low-energy interactions in the LsM, are gauge invariant. In turn, the complete set of Feynman diagrams, describing the contributions of hadron-photon interactions in the one-hadron-loop approximation, is not gauge invariant. In the infinite limit of the scalar sigma-meson, reproducing the current algebra results (Weinberg, Phys. Rev. Lett. 18, 188 (1967)), and to leading order in the large nucleon mass expansion the Feynman diagrams, violating gauge invariance, do not contribute to the amplitude of the neutron radiative beta-decay in agreement with Sirlin's analysis of strong low-energy interactions in neutron beta decays. We assert that the problem of appearance of gauge non-invariant Feynman diagrams of hadronic structure of the neutron and proton is related to the following. The vertex of the effective V-A weak interactions does not belong to the combined quantum field theory including the LsM and QED. We argue that gauge invariant set of Feynman diagrams of hadrons, coupled to real and virtual photons in neutron beta decays, can be obtained within the combined quantum field theory including the Standard Electroweak Model (SEM) and the LsM, where the effective V-A vertex of weak interactions is a result of the W^- - electroweak boson exchange., Comment: 31 pages, 9 figures

We analyse the electron--energy and angular distribution of the neutron beta decay with polarized neutron and electron and unpolarized proton, calculated in Phys. Rev. C 95, 055502 (2017) within the Standard Model (SM), by taking into account the contributions of interactions beyond the SM. After the absorption of vector and axial vector contributions by the axial coupling constant and Cabibbo-Kobayashi-Maskawa (CKM) matrix element (Bhattacharya et al., Phys. Rev. D 85, 054512 (2012) and so on) these are the contributions of scalar and tensor interactions only. The neutron lifetime, correlation coefficients and their averaged values, and asymmetries of the neutron beta decay with polarized neutron and electron are adapted to the analysis of experimental data on searches of contributions of interactions beyond the SM. Using the obtained results we propose some estimates of the values of the scalar and tensor coupling constants of interactions beyond the SM. We use the estimate of the Fierz interference term "b_F = - 0.0028 +/- 0.0026" by Hardy and Towner (Phys. Rev. C 91, 025501 (2015)), the neutron lifetime "tau_n = 880.2(1.0)s"(Particle Data Group, Chin. Phys. C 40, 100001 (2016)) and the experimental data "N_{\exp} = 0.067 +/- 0.011_{\rm stat.} +/- 0.004_{\rm syst.}" for the averaged value of the correlation coefficient of the neutron-electron spin-spin correlations, measured by Kozela et al. (Phys. Ref. C 85, 045501 (2012)). The contributions of G-odd correlations are calculated and found at the level of 10^{-5} in agreement with the results obtained by Gardner and Plaster (Phys. Rev. C 87, 065504 (2013))., Comment: 15 pages, 1 figure

In the Standard Model (SM) we calculate the decay rate of the neutron radiative beta decay to order "O(\alpha^2/\pi^2 ~ 10^{-5})", where "\alpha$"is the fine--structure constant, and radiative corrections to order "O(\alpha/\pi ~ 10^{-3})". The obtained results together with the recent analysis of the neutron radiative beta decay to next-to-leading order in the large proton-mass expansion, performed by Ivanov et al. Phys. Rev. D95, 033007 (2017), describe recent experimental data by the RDK II Collaboration (Bales et al., Phys. Rev. Lett. 116, 242501 (2016)) within 1.5 standard deviations. We argue a substantial influence of strong low-energy interactions of hadrons coupled to photons on the properties of the amplitude of the neutron radiative beta decay under gauge transformations of real and virtual photons., Comment: 46 pages, 6 figures

We give a precision analysis of the correlation coefficients of the electron-energy spectrum and angular distribution of the beta decay and radiative beta decay of the neutron with polarized neutron and electron to order 10^(-3). The calculation of correlation coefficients is carried out within the Standard model with contributions of order 10^(-3), caused by the weak magnetism and proton recoil, taken to next-to-leading order in the large proton mass expansion, and with radiative corrections of order "alpha/pi ~ 10^(-3", calculated to leading order in the large proton mass expansion. The obtained results can be used for the planning of experiments on the search for contributions of order 10^(-4) of interactions beyond the Standard model., Comment: 12 pages, 2 figures, The functions in Eq.(A.9) are corrected

In the Standard Model of electroweak interactions and in the tree--approximation we calculate the rate and branching ratio of the neutron radiative beta decay with one-real photon emission by taking into account the contributions of the weak magnetism and proton recoil to order 1/m_p of the large proton mass m_p expansion. We find that the obtained contributions of the weak magnetism and proton recoil increase the rate and branching ratio of the neutron radiative beta decay by about 0.70%. This is large compared with the contribution of the weak magnetism and proton recoil of about 0.16% to the rate of the neutron beta decay, calculated in Phys. Rev. D88, 073002 (2013)., Comment: 15 pages, 1 figure

We calculate the chameleon field profile, confined between two parallel plates, filled with air at pressure $P = 10^{-4}\,{\rm mbar}$ and room temperature and separated by the distance $L$, in the chameleon field theory with Ratra--Peebles self--interaction potential with index $n = 1$. We give the exact analytical solution in terms of Jacobian elliptic functions, depending on the mass density of the ambient matter. The obtained analytical solution can be used in qBounce experiments, measuring transition frequencies between quantum gravitational states of ultracold neutrons and also for the calculation of the chameleon field induced Casimir force for the CANNEX experiment. We show that the chameleon--matter interactions with coupling constants $\beta \le 10^4$ can be probed by qBounce experiments with sensitivities $\Delta E \le 10^{-18}\,{\rm eV}$. At $L = 30.1\,{\rm \mu m}$ we reproduce the result $\beta < 5.8\times 10^8$, obtained by Jenke {\it et al.} Phys. Rev. Lett. {\bf 112}, 151105 (2014)) at sensitivity $\Delta E \sim 10^{-14}\,{\rm eV}$. In the vicinity of one of the plates our solution coincides with the solution, obtained by Brax and Pignol (Phys. Rev. Lett. {\bf 107}, 111301 (2011)) (see also Ivanov {\it et al.} Phys. Rev. D {\bf 87}, 105013 (2013)) above a plate at zero density of the ambient matter., Comment: 1 figure, 8 pages, the incorrect value rho = 1.188x10^(-8)g/cm^3 is replaced by the correct one rho =1.188x10^(-10)g/cm^3

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly-coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments., Comment: 246 pp, around 128 figures; v2 adds material, references, and corrections suggested by readers of v1 -- to be submitted to EPJC

We calculate the chameleon field potential for ultracold neutrons, bouncing on top of one or between two neutron mirrors in the gravitational field of the Earth. For the resulting non--linear equations of motion we give approximate analytical solutions and compare them with exact numerical ones for which we propose the analytical fit. The obtained solutions may be used for the quantitative analysis of contributions of a chameleon field to the transition frequencies of quantum states of ultra-cold neutrons bound in the gravitational field of the Earth., Comment: 11 pages, 4 figures

We analyze topological charge contributions from classical SU(2) center vortices with shapes of planes and spheres using different topological charge definitions, namely the center vortex picture of topological charge, a discrete version of F\~{F} in the plaquette and hypercube definitions and the lattice index theorem. For the latter the zeromodes of the Dirac operator in the fundamental and adjoint representations using both the overlap and asqtad staggered fermion formulations are investigated. We find several problems for the individual definitions and discuss the discrepancies between the different topological charge definitions. Our results show that the interpretation of topological charge in the background of center vortices is rather subtle., Comment: 8 pages, 8 figures

We calculate the neutrino masses, using the experimental data on the periods of the time modulation of the K-shell electron capture (EC) decay rates of the H-like heavy ions, measured at GSI. The corrections to neutrino masses, caused by interaction of massive neutrinos with the strong Coulomb field of the daughter ions, are taken into account., Comment: 3 pages, 1 figure

We study the influence of center vortices on the low-lying eigenmodes of the Dirac operator, in both the overlap and asqtad formulations. For center-projected configurations, one finds that the low-lying near-zero modes are present in the staggered (asqtad) formulation, but not in the overlap and "chirally-improved" formulations. We argue that this is due to the absence of a field-independent chiral symmetry in the latter formulations, when the Dirac operator is evaluated on the very rough configurations generated by center projection. We also confirm and extend the results of Kovalenko et al. [Phys. Lett. B 648, 383 (2007)], finding strong correlations between center vortex locations, and the scalar density of low-lying Dirac eigenmodes on unprojected lattices, in both asqtad and overlap formulations. It is found that the low-lying eigenmodes have their largest concentrations in point-like regions, rather than on submanifolds of higher dimensionality., Comment: Presented at Lattice 2008