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Register a new userMatrix elements of four-quark operators and Delta L=2 hyperon decays
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The study of neutrinoless double beta decays of nuclei and hyperons require the calculation of hadronic matrix elements of local four-quark operators that change the total charge by two units Delta Q=2 . Using a low energy effective Lagrangian that induces these transitions, we compute these hadronic matrix elements in the framework of the MIT bag model. As an illustrative example we evaluate the amplitude and transition rate of Sigma- -> p e- e-, a decay process that violates lepton number by two units (Delta L=2). The relevant matrix element is evaluated without assuming the usual factorization approximation of the four-quark operators and the results obtained in both approaches are compared.
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We compute the rates of semileptonic B_A to B_Bl^-l^- (l=e or mu) hyperon transitions in a model where intermediate states involve loops of baryons and a Majorana neutrino. These rates turn out to be well below present experimental bounds and other theoretical estimates. From the experimental upper limit on the Xi^- to pmu^-mu^- decay, we derive the bound <m_{mu mu}> < 22 TeV for the effective Majorana mass of the muon neutrino. Also, an estimate of background contributions for these decays due to the allowed B_A to B_Bl^-l^-bar{ u}bar{ u} decays are provided.
Hadronic matrix elements of local four-quark operators play a central role in non-leptonic kaon decays, while vacuum matrix elements involving the same kind of operators appear in inclusive dispersion relations, such as those relevant in $tau$-decay analyses. Using an $SU(3)_Lotimes SU(3)_R$ decomposition of the operators, we derive generic relations between these matrix elements, extending well-known results that link observables in the two different sectors. Two relevant phenomenological applications are presented. First, we determine the electroweak-penguin contribution to the kaon CP-violating ratio $varepsilon/varepsilon$, using the measured hadronic spectral functions in $tau$ decay. Second, we fit our $SU(3)$ dynamical parameters to the most recent lattice data on $Ktopipi$ matrix elements. The comparison of this numerical fit with results from previous analytical approaches provides an interesting anatomy of the $Delta I = frac{1}{2}$ enhancement, confirming old suggestions about its underlying dynamical origin.
A sensitive search for the rare decays Omega^- to Lambda pi^- and Xi^0 to p pi^- has been performed using data from the 1997 run of the HyperCP (Fermilab E871) experiment. Limits on other such processes do not exclude the possibility of observable rates for |Delta S| = 2 nonleptonic hyperon decays, provided the decays occur through parity-odd operators. We obtain the branching-fraction limits B(Omega^- to Lambda pi^-)< 2.9 x 10^{-6} and B(Xi^0 to p pi^-)< 8.2 x 10^{-6}, both at 90% confidence level.
By the analysis of the world data base of elastic electron scattering on the proton and the neutron (for the latter, in fact, on $^2H$ and $^3He$) important experimental insights have recently been gained into the flavor compositions of nucleon electromagnetic form factors. We report on testing the Graz Goldstone-boson-exchange relativistic constituent-quark model in comparison to the flavor contents in low-energy nucleons, as revealed from electron-scattering phenomenology. It is found that a satisfactory agreement is achieved between theory and experiment for momentum transfers up to $Q^2sim$ 4 GeV$^2$, relying on three-quark configurations only. Analogous studies have been extended to the $Delta$ and the hyperon electromagnetic form factors. For them we here show only some sample results in comparison to data from lattice quantum chromodynamics.
The complete renormalization of the weak Lagrangian to chiral order q^2 in heavy baryon chiral perturbation theory is performed using heat kernel techniques. The results are compared with divergences appearing in the calculation of Feynman graphs for the nonleptonic hyperon decay Lambda -> p pi^- and an estimate for the size of the counterterm contributions to the s-wave amplitudes in nonleptonic hyperon decays is given.
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