Weak Interaction Hamiltonian Research Articles

Hybrid method to resolve the neutrino mass hierarchy bysupernova (anti)neutrino induced reactions

We introduce a hybrid method to determine the neutrino mass hierarchy by simultaneous measurements of responses of at least two detectors to antineutrino and neutrino fluxes from accretion and cooling phases of core-collapse supernovae. The (anti)neutrino-nucleus cross sections for 56Fe and 208Pb are calculated in the framework of the relativistic nuclear energy density functional and weak interaction Hamiltonian, while the cross sections for inelastic scattering on free protons p(ν̄e,e+)n are obtained using heavy-baryon chiral perturbation theory. The modelling of (anti)neutrino fluxes emitted from a protoneutron star in a core-collapse supernova include collective and Mikheyev-Smirnov-Wolfenstein effects inside the exploding star. The particle emission rates from the elementary decay modes of the daughter nuclei are calculated for normal and inverted neutrino mass hierarchy. It is shown that simultaneous use of (anti)neutrino detectors with different target material allows to determine the neutrino mass hierarchy from the ratios of νe- and ν̄e-induced particle emissions. This hybrid method favors neutrinos from the supernova cooling phase and the implementation of detectors with heavier target nuclei (208Pb) for the neutrino sector, while for antineutrinos the use of free protons in mineral oil or water is the appropriate choice.

Detailed description of exclusive muon capture rates using realistic two-body forces

Starting from state-by-state calculations of exclusive rates of the ordinary muon capture (OMC), we evaluated total muon-capture rates for a set of light- and medium-weight nuclear isotopes. We employed a version of the proton-neutron quasi-particle random phase approximation (pn-QRPA, for short) which uses as realistic nuclear forces the Bonn C-D one boson exchange potential. Special attention was paid on the percentage contribution to the total muon-capture rate of specific low-spin multipolarities resulting by summing over the corresponding multipole transitions. The nuclear method used offers the possibility of estimating separately the individual contributions to the total and partial rates of the polar-vector and axial-vector components of the weak interaction Hamiltonian for each accessible final state of the daughter nucleus. One of our main goals is to provide a reliable description of the charge changing transitions matrix elements entering the description of other similar semileptonic nuclear processes like the charged-current neutrino-nucleus reactions, the electron capture on nuclei, the single \b{eta}-decay mode, etc., which play important role in currently interesting laboratory and astrophysical applications like the neutrino-detection through lepton- nucleus interaction probes, and neutrino-nucleosynthesis. Such results can be also be useful in various ongoing muon-capture experiments at PSI, Fermilab, JPARC and RCNP.

Внески векторних резонансів у CP-асиметрію розпаду нейтрального B-мезона на мюон-антимюонну пару та нейтральний K*-мезон

Contributions of the processes ¯ B0d → ¯ K*0(→ K−п+) V with vector mesons V = p(770), w(782), ф(1020), J/w, w(2S), and others decaying into the м+м− pair to the CP-asymmetry in the decay ¯ B0d → ¯ K*0(→ K−п+)м+м− induced by the flavor-changing neutral currents are calculated. For the description of the transition b → sм+м−, the most general form of the effective weak-interaction Hamiltonian is applied. Predictions are made for the CP-asymmetry of the decay ¯ B0d → ¯ K*0(→ K−п+)м+м− in the framework of the standard model, as well for two scenarios of new physics. The obtained results are compared with experimental data of the LHCb Collaboration.

Considering collective degrees of freedom in the β decay of odd nuclei

The β decay of around 30 odd nuclei was calculated within the dynamic collective model using expressions for the reduced matrix elements of the weak-interaction Hamiltonian for U-type and V-type β decay obtained earlier by the authors. All of the many-phonon states of the yrast band of an even-even core contributing to the formation of the excited states of nuclei were taken into account. For β transitions with an intensity of >1%, the calculated logft values differ from the experimental values by no more than 0.2.

123I → 123Te β decay

The β decay of 123I has been calculated within the dynamic collective model developed by the authors earlier. The expression for the reduced matrix element of the weak-interaction Hamiltonian has been used for the partial β decay. The influence of the vacuum fluctuations and creation or annihilation of one or two phonons on the reduced β-decay probabilities is taken into account.

Charm mass dependence of the weak Hamiltonian in chiral perturbation theory

Suppose that the weak interaction Hamiltonian of four-flavour SU(4) chiral effective theory is known, for a small charm quark mass m_c. We study how the weak Hamiltonian changes as the charm quark mass increases, by integrating it out within chiral perturbation theory to obtain a three-flavour SU(3) chiral theory. We find that the ratio of the SU(3) low-energy constants which mediate Delta I=1/2 and Delta I=3/2 transitions, increases rather rapidly with m_c, as \sim m_c ln (1/m_c). The logarithmic effect originates from penguin-type charm loops, and could represent one of the reasons for the Delta I=1/2 rule.

Precision analysis of experiments studying the beta decay of the free neutron: Standard model and possibilities of its violation

The current status of experimental results on the beta decay of the free neutron is described. An analysis of these data shows that, within the present-day accuracy, the data are fully consistent with the Standard Model of electroweak interaction. At the same time, there exists the possibility of deviations from the Standard Model at a level of 1%. The possible violations due to the contributions of right-handed (WR) bosons, as well as of leptoquark mechanisms introducing anomalous scalar and tensor terms in the effective weak-interaction Hamiltonian, which include the right-handed neutrinos, are estimated. In the last case, the analysis is performed by an analytic method that makes it possible to take into account, for the first time, the possibility of CP violation.

Second-order corrections to correlations in muon capture

Muon capture by a nucleus with an arbitrary spin is considered. Second-order terms in 1/M in the effective weak-interaction Hamiltonian are taken into account. New terms in the Hamiltonian associated with the nucleon-nucleus potential are found. A general expression for the angular distribution of neutrinos (recoil nuclei) is derived for polarized muons and oriented target nuclei. Second-order contributions to the amplitudes M u (k) are obtained. This allows one to calculate second-order corrections to any integral and correlation characteristics in muon capture that are expressed in terms of M u (k).

Quasiparticle random phase approximation analysis of the double beta decay ofMo100to the ground state and excited states ofRu100

The beta decay rate of the ${1}^{+}$ ground state of $^{100}\mathrm{Tc}$ to the ground and excited states of $^{100}\mathrm{Mo}$ and $^{100}\mathrm{Ru}$ has been calculated using a combination of the charge-conserving and charge-nonconserving modes of the quasiparticle random phase approximation theory. These results, as well as the calculated E2 decay properties of $^{100}\mathrm{Mo}$ and $^{100}\mathrm{Ru}$, are compared with data. In addition, the two-neutrino double beta decay rates of $^{100}\mathrm{Mo}$ to the ground state and excited states of $^{100}\mathrm{Ru}$ are evaluated and analyzed using available experimental data. For completeness, the neutrinoless double beta decay rate of $^{100}\mathrm{Mo}$ is calculated and used to extract the value of the effective neutrino mass and the parameters of a general weak-interaction Hamiltonian.

Time reversal test in the nuclear muon capture

Possible effects of breaking CP-symmetry are looked for in the muon capture by a linearly polarized target nucleus. With this aim the recoil polarization in the partial transitions\(0\xrightarrow{{\mu ^ - }}I,1/2\xrightarrow{{\mu ^ - }}J\) and\(1\xrightarrow{{\mu ^ - }}I\) is investigated in a nuclear model independent way. It is shown that the hyperfine structure of the muonic atom significantly influences theT-odd correlations in the recoil polarization formula, and the expectation for theT- odd signal in case of the linearly polarized target is higher by one order of magnitude. We obtain the complete set of theT-odd observables which could enter the polarization formula. As an example, within the impulse approximation for the weak interaction hamiltonian, we analyse the nonstandard, CP-breaking extension of the Fermi theory using complex Fujii-Primakoff form factorGV eiφ.

A tool kit for staggered fermions

We analyze the symmetries of staggered fermions, both discrete and continuous. We present tools that allow a simple decomposition of representations of the continuum symmetries into representations of the discrete lattice symmetries, both at zero and non-zero spatial momenta. We use these tools to find the lattice transcriptions of the operators that appear in the weak interaction hamiltonian. We derive the lattice Ward identities that follow from the single partially conserved axial symmetry. Using these identities we find the lattice equivalents of the continuum PCAC relations. Combining all these tools, we obtain Ward identities for the matrix elements of the weak interaction hamiltonian, from which we derive the behavior of the matrix elements as the pion and kaon masses vanish. We find the same behavior as in the continuum.

Neutrino Mass, the Right-Handed Interaction and the Double Beta Decay. I: Formalism

In order to shed light on the important question whether neutrinos are Dirac of Majorana particles, the double β decay is investigated within a general form of weak interaction Hamiltonian. The systematic study is made on the 0^+ →J^+ nuclear transitions for the tow-neutrino and neutrinoless modes both in the two-nucleon- and N^*-mechanism. It is shown that for the neutrinoless mode, only the 0^+ →0^+ transition in the two-nucleon mechanism is allowed if there is no right-handed interaction. When the right-handed interaction gives a sizable contribution, the role of the 0^+ →2^+ transition becomes as important as the 0^+ →0^+ transition. The comparison of our results with the previous ones is also presented.

Effective Hamiltonian for C=1 Nonleptonic Interactions in the Kobayashi-Maskawa Model

The effective nonleptonic weak interaction Hamiltonian for the |ΔC|=1 processes is calculated by using the quantum chromodynamics with the color octet massless gluons and the renormalization group equations, in the Kobayashi-Maskawa model. The “penguin” diagram contributes to the effective Hamiltonian by the division of the range of virtual momenta integration. The U-spin operators are taken as the operator bases.

Effective Hamiltonian forΔS=1weak nonleptonic decays in the six-quark model

Strong-interaction corrections to the nonleptonic weak-interaction Hamiltonian are calculated in the leading-logarithmic approximation using quantum chromodynamics. Starting with a six-quark theory, the W boson, t quark, b quark, and c quark are successively considered as heavy and the effective Hamiltonian calculated. The resulting effective Hamiltonian for strangeness-changing nonleptonic decays involves u, d, and s quarks and has possible CP-violating pieces both in the usual (V-A)×(V-A) terms and in induced, penguin-type terms. Numerically, the CP-violating compared to CP-conserving parts of the latter terms are close to results calculated on the basis of the lowest-order penguin diagram.

Final-state interactions in muon capture by deuterons

Prompted in part by the disparate theoretical estimates in the literature, we present a systematic study of the influence of the $^{1}S_{0}n\ensuremath{-}n$ final-state interaction on rates for the reaction ${\ensuremath{\mu}}^{\ensuremath{-}}+d\ensuremath{\rightarrow}n+n+{\ensuremath{\nu}}_{\ensuremath{\mu}}$, treated in impulse approximation with the standard Primakoff effective weak-interaction Hamiltonian. Instead of beginning with a particular $n\ensuremath{-}n$ potential, we use as our basic input a set of four-parameter Bargmann models of the $^{1}S_{0}n\ensuremath{-}n$ phase shift. By solving a "restricted inverse problem" we generate the necessary radial functions from these phase shifts. This procedure enables us to examine in a consistent way the sensitivity of the total capture rates and neutron energy spectrum to uncertainties in the phase shifts. We find that changes in the phase shifts at either high or low energies do not affect the rates noticeably. Hence, we conclude that this reaction is not a good tool for determining the $n\ensuremath{-}n$ scattering length. In addition, we investigate the effects of varying the off-shell behavior of the $n\ensuremath{-}n$ interaction by means of the method of short-range unitary transforms of Coester et al. We then find that the rates change dramatically. The doublet capture rate, for example, can be shifted from the 375 ${\mathrm{sec}}^{\ensuremath{-}1}$ typical of the local potentials of the restricted inverse problem down to 236 ${\mathrm{sec}}^{\ensuremath{-}1}$. More accurate measurements of this rate could thus serve as constraints on the off-shell extrapolation of the $n\ensuremath{-}n$ interaction. Our results are in general agreement with those of Sotona and Truhl\'{\i}k.NUCLEAR REACTIONS ${\ensuremath{\mu}}^{\ensuremath{-}}+d\ensuremath{\rightarrow}n+n+{\ensuremath{\nu}}_{\ensuremath{\mu}}$; effect of $^{1}S_{0}n\ensuremath{-}n$ final-state interactions on rates, neutron spectra. Varied $n\ensuremath{-}n$ phase shifts and off-shell behavior.

The weak interaction Hamiltonian in L-matrix theory

Abstract : During the past three years the author and his collaborators have made a systematic study of matrices A and B which satisfy the Clifford conditions A sup 2 = B sup 2 = I AB = -BA. It was demonstrated that there is a 'shell structure' in the anticommuting matrices and a consequent telescoping of eigenvalues of an L-matrix which is a linear combination of anticommuting matrices. It is now observed that the form of the weak interaction Hamiltonian in elementary particle physics is an interesting manifestation of the shell structure. (Author)

Sakurai's Weak-Interaction Hamiltonian and theK10−K20Mass Difference

We show that Sakurai's effective weak Hamiltonian predicts a mass difference of the neutral kaons, which is both too large in magnitude and of the wrong sign when the weak ${{K}_{1}}^{0}$ self-mass is calculated with $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ scattering parameters favored by current algebra.

Possible Relation Between Lepton Nonconservation andCPNonconservation

A weak-interaction Hamiltonian is presented which can account in a unified way for the $\mathrm{CP}$ nonconservation observed in ${K}_{L}$ decay and for a possible lepton nonconservation associated with nuclear double-beta decay.

Seeming time-reversal violation in higher-order weak interactions

It is demonstrated within the framework of the intermediate vector boson theory that the interference between purely weak interaction graphs of different orders in g can lead to a seeming violation of time reversal T. This seeming violation is implied by the presence of triple scalar products in experimental cross sections, [Formula: see text], and may occur even if the primary weak interaction Hamiltonian is T invariant. The total scattering amplitude for a set of Feynman graphs is characterized by coefficients Gi. A necessary condition for the appearance of time-odd correlations is that the ratio Gi/Gj be complex.The theory is applied to the scattering of a neutron by an incident high-energy neutrino: νc + n → p + e−. Triple scalar products are shown to arise specifically from the interference between real and imaginary components of the total amplitude, constructed here from second- and sixth-order uncrossed ladder graphs. The essential imaginary components are divergence-free and emerge from poles in the integrand of the eightfold integral (sixth-order graph).Triple scalar products in dσ are proportional to m−6g8 (ln s)/s; there is no cancellation from crossed graphs of order six. Ladder graphs treated on an individual basis do not give rise to J ∙ p1 × p2 terms.

Theory ofCPNonconservation

A new current \ifmmode\times\else\texttimes\fi{} current weak interaction is constructed from the neutral vector and axial-vector currents which preserves the hypothesis of conserved vector current, universality, lepton conservation, and $\mathrm{CPT}$ invariance, but violates $\mathrm{CP}$ conservation. The complete weak interaction Hamiltonian is shown to be in agreement with present experiments.