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Register a new userDiscovering leptonic forces using non-conserved currents
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Jeff A. Dror
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Differences in lepton number (i.e., $ L _e - L _mu $, $ L _e - L _tau $, $ L_mu - L _tau $, or combinations thereof) are not conserved charges in the Standard Model due to the observation of neutrino oscillations. We compute the divergence of the corresponding currents in the case of Majorana or Dirac-type neutrinos and show that, in the high energy limit, the vector interactions map onto those of a light scalar coupled to neutrinos with its coupling fixed by the observed neutrino masses and mixing. This leads to amplitudes with external light vectors that scale inversely with the vector mass. By studying these processes, we set new constraints on $ L _i - L _j $ through a combination of semi-leptonic meson decays, invisible neutrino decays, neutrinoless double beta decays, and observations of Big Bang Nucleosynthesis/supernova, which can be much stronger than previous limits for vector masses below an eV. These bounds have important implications on the experimental prospects of detecting $ L _i - L _j $ long-range forces.
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We discuss new bounds on vectors coupled to currents whose non-conservation is due to mass terms, such as $U(1)_{L_mu - L_tau}$. Due to the emission of many final state longitudinally polarized gauge bosons, inclusive rates grow exponentially fast in energy, leading to constraints that are only logarithmically dependent on the symmetry breaking mass term. This exponential growth is unique to Stueckelberg theories and reverts back to polynomial growth at energies above the mass of the radial mode. We present bounds coming from the high transverse mass tail of mono-lepton+missing transverse energy events at the LHC, which beat out cosmological bounds to place the strongest limit on Stueckelberg $U(1)_{L_mu - L_tau}$ models for most masses below a keV. We also discuss a stronger, but much more uncertain, bound coming from the validity of perturbation theory at the LHC.
The quantum effective action yields equations of motion and correlation functions including all quantum corrections. We discuss here how it encodes also Noether currents at the full quantum level. This holds both for covariantly conserved currents associated to real symmetries that leave the action invariant as well as for non-conserved Noether currents associated to extended symmetry transformations which change the action, but in a specific way. We discuss then in particular symmetries and extended symmetries associated to space-time geometry for relativistic quantum field theories. These encompass local dilatations or Weyl gauge transformation, local Lorentz transformations and local shear transformations. Together they constitute the symmetry group of the frame bundle GL$(d)$. The corresponding non-conserved Noether currents are the dilatation or Weyl current, the spin current and the shear current for which divergence-type equations of motion are obtained from the quantum effective action.
The recent experimental developments require a more precise theoretical study of weak decays of heavy baryon $Lambda_b^0$. In this work, we provide an updated and systematic analysis of both the semi-leptonic and nonleptonic decays of $Lambda^0_b$ into baryons $Lambda^+_c$, $Lambda$, $p$, and $n$. The diquark approximation is adopted so that the methods developed in the $B$ meson system can be extended into the baryon system. The baryon-to-baryon transition form factors are calculated in the framework of a covariant light-front quark model. The form factors $f_3, ~g_3$ can be extracted and are found to be non-negligible. The semi-leptonic processes of $Lambda^0_bto Lambda^+_c(p)l^-bar u_l$ are calculated and the results are consistent with the experiment. We study the non-leptonic processes within the QCD factorization approach. The decay amplitudes are calculated at the next-to-leading order in strong coupling constant $alpha_s$. We calculate the non-leptonic decays of $Lambda^0_b$ into a baryon and a s-wave meson (pseudoscalar or vector) including 44 processes in total. The branching ratios and direct CP asymmetries are predicted. The numerical results are compared to the experimental data and those in the other theoretical approaches. Our results show validity of the diquark approximation and application of QCD factorization approach into the heavy baryon system.
We provide a pedagogical introduction to extensions of the Standard Model in which the Higgs is composite. These extensions are known as models of dynamical electroweak symmetry breaking or, in brief, Technicolor. Material covered includes: motivations for Technicolor, the construction of underlying gauge theories leading to minimal models of Technicolor, the comparison with electroweak precision data, the low energy effective theory, the spectrum of the states common to most of the Technicolor models, the decays of the composite particles and the experimental signals at the Large Hadron Collider. The level of the presentation is aimed at readers familiar with the Standard Model but who have little or no prior exposure to Technicolor. Several extensions of the Standard Model featuring a composite Higgs can be reduced to the effective Lagrangian introduced in the text. We establish the relevant experimental benchmarks for Vanilla, Running, Walking, and Custodial Technicolor, and a natural fourth family of leptons, by laying out the framework to discover these models at the Large Hadron Collider.
We present a comprehensive study of the three-active plus $N$ sterile neutrino model as a framework for constraining leptonic unitarity violation induced at energy scales much lower than the electroweak scale. We formulate a perturbation theory with expansion in small unitarity violating matrix element $W$ while keeping (non-$W$ suppressed) matter effect to all orders. We show that under the same condition of sterile state masses $0.1, text{eV}^2 lesssim m^2_{J} lesssim (1-10), text{GeV}^2$ as in vacuum, assuming typical accelerator based long-baseline neutrino oscillation experiment, one can derive a very simple form of the oscillation probability which consists only of zeroth-order terms with the unique exception of probability leaking term $mathcal{C}_{alpha beta}$ of $mathcal{O} (W^4)$. We argue, based on our explicit computation to fourth-order in $W$, that all the other terms are negligibly small after taking into account the suppression due to the mass condition for sterile states, rendering the oscillation probability {em sterile-sector model independent}. Then, we identify a limited energy region in which this suppression is evaded and the effects of order $W^2$ corrections may be observable. Its detection would provide another way, in addition to detecting $mathcal{C}_{alpha beta}$, to distinguish between low-scale and high-scale unitarity violation. We also solve analytically the zeroth-order system in matter with uniform density to provide a basis for numerical evaluation of non-unitary neutrino evolution.
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