Vector Matrix Elements Research Articles

Measurements and computational analysis of the natural decay of Lu176

Background: Mainly because of its long half-life and despite its scientific relevance, spectroscopic measurements of $^{176}\mathrm{Lu}$ forbidden $\ensuremath{\beta}$ decays are very limited and lack formulation of shape factors. A direct precise measurement of its Q value is also presently unreported. In addition, the description of forbidden decays provides interesting challenges for nuclear theory. The comparison of precise experimental results with theoretical calculations for these decays can help to test underlying models and can aid the interpretation of data from other experiments.Purpose: Perform the first precision measurements of $^{176}\mathrm{Lu}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay spectra and attempt the observation of its electron capture decays, as well as perform the first precision direct measurement of the $^{176}\mathrm{Lu}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay Q value. Compare the shape of the precisely determined experimental $\ensuremath{\beta}$ spectra to theoretical calculations, and compare the end point energy to that obtained from an independent Q value measurement.Method: The $^{176}\mathrm{Lu}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay spectra measurements and the search for electron capture decays were performed with an experimental setup that employed lutetium-containing scintillator crystals and a NaI(Tl) spectrometer for coincidence counting. The $\ensuremath{\beta}$ decay Q value was determined via high-precision Penning trap mass spectrometry (PTMS) with the LEBIT facility at the National Superconducting Cyclotron Laboratory. The $\ensuremath{\beta}$-spectrum calculations were performed within the Fermi theory formalism with nuclear structure effects calculated using a shell model approach.Results: Both $\ensuremath{\beta}$ transitions of $^{176}\mathrm{Lu}$ were experimentally observed and corresponding shape factors formulated in their entire energy ranges. The search for electron capture decay branches led to an experimental upper limit of $6.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ relative to its $\ensuremath{\beta}$ decays. The $^{176}\mathrm{Lu}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay and electron capture Q values were measured using PTMS to be 1193.0(6) and 108.9(8) keV, respectively. This enabled precise $\ensuremath{\beta}$ end point energies of 596.2(6) and 195.3(6) keV to be determined for the primary and secondary $\ensuremath{\beta}$ decays, respectively. The conserved vector current hypothesis was applied to calculate the relativistic vector matrix elements. The $\ensuremath{\beta}$-spectrum shape was shown to significantly depend on the Coulomb displacement energy and on the value of the axial vector coupling constant ${g}_{A}$, which was extracted according to different assumptions.Conclusion: The implemented self-scintillation method has provided unmatched observations of $^{176}\mathrm{Lu}$, independently validated by the first direct measurements of its $\ensuremath{\beta}$-decay Q value by Penning trap mass spectrometry. Theoretical study of the main $\ensuremath{\beta}$ transition led to the extraction of very different effective ${g}_{A}$ and ${log}_{10}\phantom{\rule{0.16em}{0ex}}f$ values, showing that a high-precision description of this transition would require a realistic nuclear structure with nucleus deformation.

Partial muon capture rates in A=3 and A=6 nuclei with chiral effective field theory

Searches for neutrinoless double-$\ensuremath{\beta}$ decay rates are crucial in addressing questions within fundamental symmetries and neutrino physics. The rates of these decays depend not only on unknown parameters associated with neutrinos, but also on nuclear properties. In order to reliably extract information about the neutrino, one needs an accurate treatment of the complex many-body dynamics of the nucleus. Neutrinoless double-$\ensuremath{\beta}$ decays take place at momentum transfers on the order of $100\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}/c$ and require both nuclear electroweak vector and axial current matrix elements. Muon capture, a process in the same momentum transfer regime, has readily available experimental data to validate these currents. In this Letter, we present results of ab initio calculations of partial muon capture rates for $^{3}\mathrm{He}$ and $^{6}\mathrm{Li}$ nuclei using variational and Green's function Monte Carlo computational methods. We estimate the impact of the three-nucleon interactions, the cutoffs used to regularize two-nucleon $(2N)$ interactions, and the energy range of $2N$ scattering data used to fit these interactions.

Second-forbidden nonunique $$\beta ^-$$ decays of $$^{59,60}$$Fe:possible candidates for $$g_{\mathrm{A}}$$ sensitive electron spectral-shape measurements

In this work, we present a theoretical study of the electron spectral shapes for the second-forbidden nonunique $\beta^-$-decay transitions $^{59}\textrm{Fe}(3/2^-)\to\,^{59}\textrm{Co}(7/2^-)$ and $^{60}\textrm{Fe}(0^+)\to\,^{60}\textrm{Co}(2^+)$ in the framework of the nuclear shell model. We have computed the involved wave functions by carrying out a complete $0\hbar\omega$ calculation in the full $fp$ model space using the KB3G and GXPF1A effective interactions. When compared with the available data, these interactions predict the low-energy spectra and electromagnetic properties of the involved nuclei quite successfully. This success paves the way for the computations of the $\beta$-decay properties, and comparison with the available data. We have computed the electron spectral shapes of the mentioned decay transitions as functions of the value of the weak axial coupling $g_{\rm A}$. By comparing these computed shapes with the measured spectral shapes allows then to extract the effective value of $g_{\rm A}$ for these decay transitions. This procedure, coined the spectrum-shape method (SSM) in several earlier studies, complements the method of determining the value of $g_{\rm A}$ by reproducing the (partial) half-lives of decay transitions. Here we have enhanced the original SSM by constraining the value of the relativistic vector matrix element, $^V\mathcal{M}^{(0)}_{KK-11}$, using the conserved vector-current hypothesis (CVC) as a starting point. We hope that this finding would be a strong incentive to measure the spectral shapes in the future.

Toward accurate form factors for B -to-light meson decay from lattice QCD

We present the results of a lattice QCD calculation of the scalar and vector form factors for the unphysical $B_s\to\eta_s$ decay, over the full physical range of $q^2$. This is a useful testing ground both for lattice QCD and for our wider understanding of the behaviour of form factors. Calculations were performed using the highly improved staggered quark (HISQ) action on $N_f = 2 + 1 + 1$ gluon ensembles generated by the MILC Collaboration with an improved gluon action and HISQ sea quarks. We use three lattice spacings and a range of heavy quark masses from that of charm to bottom, all in the HISQ formalism. This permits an extrapolation in the heavy quark mass and lattice spacing to the physical point and nonperturbative renormalisation of the vector matrix element on the lattice. We find results in good agreement with previous work using nonrelativistic QCD $b$ quarks and with reduced errors at low $q^2$, supporting the effectiveness of our heavy HISQ technique as a method for calculating form factors involving heavy quarks. A comparison with results for other decays related by SU(3) flavour symmetry shows that the impact of changing the light daughter quark is substantial but changing the spectator quark has very little effect. We also map out form factor shape parameters as a function of heavy quark mass and compare to heavy quark effective theory expectations for mass scaling at low and high recoil. This work represents an important step in the progression from previous work on heavy-to-heavy decays ($b\to c$) to the numerically more challenging heavy-to-light decays.

Lattice QCD calculation of the B(s)→D(s)*ℓν form factors at zero recoil and implications for |Vcb|

We present results of a lattice QCD calculation of $B\to D^*$ and $B_s\to D_s^*$ axial vector matrix elements with both states at rest. These zero recoil matrix elements provide the normalization necessary to infer a value for the CKM matrix element $|V_{cb}|$ from experimental measurements of $\bar{B}^0\to D^{*+}\ell^-\bar{\nu}$ and $\bar{B}^0_s\to D_s^{*+}\ell^-\bar{\nu}$ decay. Results are derived from correlation functions computed with highly improved staggered quarks (HISQ) for light, strange, and charm quark propagators, and nonrelativistic QCD for the bottom quark propagator. The calculation of correlation functions employs MILC Collaboration ensembles over a range of three lattice spacings. These gauge field configurations include sea quark effects of charm, strange, and equal-mass up and down quarks. We use ensembles with physically light up and down quarks, as well as heavier values. Our main results are $\mathcal{F}^{B\to D^*}(1)= 0.895\pm 0.010_{\mathrm{stat}}\pm{{0.024}_{\mathrm{sys}}}$ and $\mathcal{F}^{B_s\to D_s^*}(1)= 0.883\pm 0.010_{\mathrm{stat}}\pm{0.028_{\mathrm{sys}}}$. We discuss the consequences for $|V_{cb}|$ in light of recent investigations into the extrapolation of experimental data to zero recoil.

TYPICAL MITRAL VALVE CHORDAE TENDINEAE AND ABNORMALLY LOCATED CHORDAE TENDINEAE OF THE HUMAN HEART LEFT VENTRICLE IN THE INVESTIGATION BY METHOD OF LASER POLARIMETRY

The paper presents the results of studying the sections of the human left ventricle chordae tendineae by laser polarimetry method, which allowed to conduct a systematic analysis of the topography of the anisotropic properties of collagen fibers, elastic fibers and cardiomyocytes obtained through the intensity distribution at different polarization orientations of images of Stokes parameter vector, polarization maps and Mueller matrix elements and their corresponding statistical moments of the 1-st – 4-th order.

Strange mass corrections to hyperonic semi-leptonic decays in statistical model

The spin distributions, weak decay matrix elements for strange baryon octets with SU(3) breaking effects is studied. We systematically apply operator formalism along with statistical method to study JP= strange baryon octets for their low energy properties. Baryon is taken as an ensemble of quark-gluon Fock states in sea with three valence quarks to have spin-1/2, color-1 and flavor-8 quantum numbers. Detailed balance principle is applied to calculate the probabilities of each Fock states, with the inclusion of mass correction of strange quark in order to check the SU(3) breaking in weak decays constants and spin distributions. A dominant contribution from the vector sea is verified as compared to scalar and tensor sea, also the symmetry breaking correction leads to the deviations in the value of axial vector matrix elements ratio from experimental values by 17%. Present framework suggests a stronger base to choose statistical model with detailed balance principle to verify the experimental and theoretical values available and hence provide a deeper understanding to the strange baryon structure. Symmetry breaking effects lead to reduction in the values of axial matrix elements. Its contribution has a significant role in determining the validity of present approach.

Search for 14.4 keV solar axions from M1 transition of 57Fe with CUORE crystals

We report the results of a search for axions from the 14.4 keV M1 transition from 57Fe in the core of the sun using the axio-electric effect in TeO2 bolometers. The detectors are 5 × 5 × 5 cm3 crystals operated at about 10 mK in a facility used to test bolometers for the CUORE experiment at the Laboratori Nazionali del Gran Sasso in Italy. An analysis of 43.65 kg⋅d of data was made using a newly developed low energy trigger which was optimized to reduce the energy threshold of the detector. An upper limit of 0.58 c⋅kg−1⋅d−1 is established at 95% C.L., which translates into lower bounds fA ⩾ 3.12 × 105 GeV 95% C.L. (DFSZ model) and fA ⩾ 2.41 × 104 GeV 95% C.L. (KSVZ model) on the Peccei-Quinn symmetry-breaking scale, for a value of S = 0.5 of the flavor-singlet axial vector matrix element. These bounds can be expressed in terms of axion masses as mA ⩽ 19.2 eV and mA ⩽ 250 eV at 95% C.L. in the DFSZ and KSVZ models respectively. Bounds are given also for the interval 0.35 ⩽ S ⩽ 0.55.

The axial form factor of the nucleon

The parity violation programs at MIT-Bates, Jefferson Lab and Mainz are presently focused on developing a better understanding of the sea-quark contributions to the vector matrix elements of nucleon structure. The success of these programs will allow precise semi-leptonic tests of the Standard Model such as that planned by the QWeak collaboration. In order to determine the vector matrix elements, a good understanding of the nucleon's axial vector form factor as seen by an electron, G^e_A, is also required. While the vector electroweak form factors provide information about the nucleon's charge and magnetism, the axial form factor is related to the nucleon's spin. Its Q2=0 value at leading order, g_A, is well known from nucleon and nuclear beta decay, and its precise determination is of interest for tests of CKM unitarity. Most information about its Q2 dependence comes from quasielastic neutrino scattering and from pion electroproduction, and a recent reanalysis of the neutrino data have brought these two types of measurements into excellent agreement. However, these experiments are not sensitive to additional higher order corrections, such as nucleon anapole contributions, that are present in parity-violating electron scattering. In this talk I will attempt to review what is presently known about the axial form factor and its various pieces including the higher order contributions, discuss the the various experimental sectors, and give an update on its determination through PV electron scattering.

Observation of the rare decay [formula omitted

A search for the decay KS→π0μ+μ− has been made by the NA48/1 Collaboration at the CERN SPS accelerator. The data were collected during 2002 with a high-intensity KS beam. Six events were found with a background expectation of 0.22−0.11+0.18 events. Using a vector matrix element and unit form factor, the measured branching ratio is B(KS→π0μ+μ−)=[2.9−1.2+1.5(stat)±0.2(syst)]×10−9.

Observation of the rare decay KS→π0e+e−

A search for the decay KS→π0e+e− has been made by the NA48/1 experiment at the CERN SPS accelerator. Using data collected during 89 days in 2002 with a high-intensity KS beam, 7 events were found with a background of 0.15 events. The branching fraction BR(KS→π0e+e−,mee>0.165 GeV/c2)=(3.0+1.5−1.2(stat)±0.2(syst))×10−9 has been measured. Using a vector matrix element and a form factor equal to one, the measurement gives BR(KS→π0e+e−)=(5.8+2.9−2.4)×10−9.

Quenching of weak interactions in nucleon matter

We have calculated the one-body Fermi and Gamow-Teller charge-current, and vector and axial-vector neutral-current nuclear matrix elements in nucleon matter at densities of 0.08, 0.16 and 0.24 fm$^{-3}$ and proton fractions ranging from 0.2 to 0.5. The correlated states for nucleon matter are obtained by operating on Fermi-gas states by a symmetrized product of pair correlation operators determined from variational calculations with the Argonne v18 and Urbana IX two- and three-nucleon interactions. The squares of the charge current matrix elements are found to be quenched by 20 to 25 % by the short-range correlations in nucleon matter. Most of the quenching is due to spin-isospin correlations induced by the pion exchange interactions which change the isospins and spins of the nucleons. A large part of it can be related to the probability for a spin up proton quasi-particle to be a bare spin up/down proton/neutron. We also calculate the matrix elements of the nuclear Hamiltonian in the same correlated basis. These provide relatively mild effective interactions which give the variational energies in the Hartree-Fock approximation. The calculated two-nucleon effective interaction describes the spin-isospin susceptibilities of nuclear and neutron matter fairly accurately. However $\geq$ 3-body terms are necessary to reproduce the compressibility. All presented results use the simple 2-body cluster approximation to calculate the correlated basis matrix elements.

Anomalous chiral behavior in quenched lattice QCD

A study of the chiral behavior of pseudoscalar masses and decay constants is carried out in quenched lattice QCD with Wilson fermions. Using the modified quenched approximation to cure the exceptional configuration problem, accurate results are obtained for pion masses as low as $\ensuremath{\approx}200 \mathrm{MeV}.$ The anomalous chiral log effect associated with quenched ${\ensuremath{\eta}}^{\ensuremath{'}}$ loops is studied in both the relation between ${m}_{\ensuremath{\pi}}^{2}$ vs ${m}_{q}$ and in the light-mass behavior of the pseudoscalar and axial vector matrix elements. The size of these effects agrees quantitatively with a direct measurement of the ${\ensuremath{\eta}}^{\ensuremath{'}}$ hairpin graph, as well as with a measurement of the topological susceptibility, thus providing several independent and quantitatively consistent determinations of the quenched chiral log parameter $\ensuremath{\delta}.$ For $\ensuremath{\beta}=5.7$ with clover-improved fermions ${(C}_{\mathrm{sw}}=1.57)$ all results are consistent with $\ensuremath{\delta}=0.065\ifmmode\pm\else\textpm\fi{}0.013.$

Lattice study of the decay [formula omitted] model-independent determination of | Vub |

We present results of a lattice computation of the vector and axial-vector current matrix elements relevant for the semileptonic decay B 0 → ϱ + − v l . The computations are performed in the quenched approximation of lattice QCD on a 24 3 x 48 lattice at β = 6.2, using an O( a) improved fermionic action. Our principal result is for the differential decay rate, dΓ/ dq 2, for the decay B 0 → ϱ +l − v l in a region beyond the charm endpoint, allowing a model-independent extraction of | V ub | from experimental measurements. Heavy quark symmetry relations between radiative and semileptonic decays of B mesons into light vector mesons are also discussed.

Lattice QCD Calculation of Flavor Singlet Matrix Elements andN-NScattering Lengths

We report on our recent study of flavor singlet matrix elements calculated with the wall source method without gauge fixing. Results are presented for the mass difference between $\eta^{\prime}$ and pseudoscalar octet mesons, the $\pi$-N $\sigma$ term and the proton axial vector matrix elements. An exploratory calculation of the N-N scattering lengths is also discussed including a phenomenological study with one-boson exchange potentials.

Scalar and axial vector matrix elements of proton in quenched QCD: Calculation of both connected and disconnected contributions

$\pi$-$N$ $\sigma$ term and proton axial vector matrix elements are calculated including disconnected contributions with a variant wall source method using the Wilson quark action at $\beta=5.7$ in quenched QCD. For the $\sigma$ term, we find $\sigma_{disc}/\sigma_{conn}=2.35(46)$ and $\sigma=44(6)$MeV--60(9)MeV. The fraction of proton spin carried by quarks is $\Delta\Sigma=\Delta{u}+\Delta{d}+\Delta{s}=+0.638(54)-0.347(46)-0.109(30)= +0.18(10)$.

Origin of difference between u-bar and d-bar partons in the nucleon.

Using the Euclidean path-integral formulation for the hadronic tensor, we show that the violation of the Gottfried sum rule does not come from the disconnected quark-loop insertion. Rather, it comes from the connected (quark line) insertion involving quarks propagating in the backward time direction. We demonstrate this by studying sum rules in terms of the scalar and axial- vector matrix elements in lattice gauge calculations. The effects of eliminating backward time propagation are presented.

Strangeness matrix elements in the nucleon

We investigate the strangeness “content” of the proton in three nucleonic models: a simple relativistic meson-loop picture, a naive nonrelativistic quark model with mesons, and an extended cloudy bag model. In each case, pseudoscalar mesons are included. Nucleon matrix elements involving strange quarks are generated through the formation of a kaon cloud. We concentrate on the last two models, with the one free parameter chosen to reproduce the electromagnetic nucleon observables. We give theoretical predictions for F 2 s(0), the strange quark contribution to the weak magnetic form factor, 〈 r 2〉 s, the strangeness radius of the nucleon, and g A s, the strangeness axial vector matrix element. We observe a strong dependence of the strange quark matrix elements on the choice of the momentum cutoff or bag size.

Method of loops applied to lattice gauge theory

The eigenvalue problem for the Hamiltonian of SU(2) lattice gauge theory is formulated in the loop representation, which is based on the fact that the physical Hilbert space can be spanned by states which are labeled by loops. Since the inner product between loop states can be calculated analytically, the eigenvalue problem is expressed in terms of vector components and matrix elements with respect to the loop basis. A small-scale numerical computation in 2+1 dimensions yields results which agree with results obtained from other methods.

Nuclear spin-dependent parity violation in light atoms

We discuss several assumptions on the heavy quark axial vector matrix elements of the proton. We emphasize the role of the axial vector isoscalar neutral current induced by the axial-vector-current anomaly. Then we re-evaluate the standard model predictions for nuclear spin-dependent parity violating effects in light atoms taking into account the EMC results and the theoretical prediction of the quark spin content of the proton.