A Comment on the Relationship Between Differential and Dimensional Renormalization

We show that there is a very simple relationship between differential and dimensional renormalization of low-order Feynman graphs in renormalizable massless quantum field theories. The beauty of the differential approach is that it achieves the same finite results as dimensional renormalization without the need to modify the space time dimension

The Hunting of the MR Model

We consider experimental signatures of the standard model's minimal supersymmetric extension with a continuous $U(1)_R$ symmetry (MR model). We focus on the ability of existing and planned electron-positron colliders to probe this model and to distinguish it from both the standard model and the standard model's minimal supersymmetric extension with a discrete $R$-parity.Comment: TeX (uses harvmac). 18 pages. Revision: added text and figure about effects of b-jet tagging at LEP II. 7 figures available on request. CTP \# 2190. HUTP-92/A05

Leptogenesis from oscillations and dark matter

An extension of the Standard Model with Majorana singlet fermions in the 1-100 GeV range can give rise to a baryon asymmetry at freeze-in via the CP-violating oscillations of these neutrinos: this is the well known ARS mechanism. In this paper we consider possible extensions of the minimal ARS scenario that can account not only for successful leptogenesis but also explain other open problems such as dark matter. We find that an extension in the form of a weakly coupled B-L gauge boson, an invisible QCD axion model, and the singlet majoron model can simultaneously account for dark matter and the baryon asymmetry.Comment: A relevant previously neglected process has been included, conclusions mostly unchanged. Matches published versio

The Dispirited Case of Gauged U(1)B−LU(1)_{B-L} Dark Matter

We explore the constraints and phenomenology of possibly the simplest scenario that could account at the same time for the active neutrino masses and the dark matter in the Universe within a gauged $U(1)_{B-L}$ symmetry, namely right-handed neutrino dark matter. We find that null searches from lepton and hadron colliders require dark matter with a mass below 900 GeV to annihilate through a resonance. Additionally, the very strong constraints from high-energy dilepton searches fully exclude the model for $150 \, \text{GeV} < m_{Z'} < 3 \, \text{TeV}$. We further explore the phenomenology in the high mass region (i.e. masses $\gtrsim \mathcal{O}(1) \, \text{TeV}$) and highlight theoretical arguments, related to the appearance of a Landau pole or an instability of the scalar potential, disfavoring large portions of this parameter space. Collectively, these considerations illustrate that a minimal extension of the Standard Model via a local $U(1)_{B-L}$ symmetry with a viable thermal dark matter candidate is difficult to achieve without fine-tuning. We conclude by discussing possible extensions of the model that relieve tension with collider constraints by reducing the gauge coupling required to produce the correct relic abundance.Comment: 21 pages, 8 figures. v2: References added. Matches the published versio

CP Violation in the SUSY Seesaw: Leptogenesis and Low Energy

We suppose that the baryon asymmetry is produced by thermal leptogenesis (with flavour effects), at temperatures $\sim 10^{9} - 10^{10}$ GeV, in the supersymmetric seesaw with universal and real soft terms. The parameter space is restricted by assuming that $l_\alpha \to l_\beta \gamma$ processes will be seen in upcoming experiments. We study the sensitivity of the baryon asymmetry to the phases of the lepton mixing matrix, and find that leptogenesis can work for any value of the phases. We also estimate the contribution to the electric dipole moment of the electron, arising from the seesaw, and find that it is (just) beyond the sensitivity of next generation experiments (\lsim 10^{-29} e cm). The fourteen dimensional parameter space is efficiently explored with a Monte Carlo Markov Chain, which concentrates on the regions of interest.Comment: 30 pages, 7 figure

Conformal Symmetry and Differential Regularization of the Three-Gluon Vertex

The conformal symmetry of the QCD Lagrangian for massless quarks is broken both by renormalization effects and the gauge fixing procedure. Renormalized primitive divergent amplitudes have the property that their form away from the overall coincident point singularity is fully determined by the bare Lagrangian, and scale dependence is restricted to $\delta$-functions at the singularity. If gauge fixing could be ignored, one would expect these amplitudes to be conformal invariant for non-coincident points. We find that the one-loop three-gluon vertex function $\Gamma_{\mu\nu\rho}(x,y,z)$ is conformal invariant in this sense, if calculated in the background field formalism using the Feynman gauge for internal gluons. It is not yet clear why the expected breaking due to gauge fixing is absent. The conformal property implies that the gluon, ghost and quark loop contributions to $\Gamma_{\mu\nu\rho}$ are each purely numerical combinations of two universal conformal tensors $D_{\mu\nu\rho}(x,y,z)$ and $C_{\mu\nu\rho}(x,y,z)$ whose explicit form is given in the text. Only $D_{\mu\nu\rho}$ has an ultraviolet divergence, although $C_{\mu\nu\rho}$ requires a careful definition to resolve the expected ambiguity of a formally linearly divergent quantity. Regularization is straightforward and leads to a renormalized vertex function which satisfies the required Ward identity, and from which the beta-function is easily obtained. Exact conformal invariance is broken in higher-loop orders, but we outline a speculative scenario in which the perturbative structure of the vertex function is determined from a conformal invariant primitive core by interplay of the renormalization group equation and Ward identities.Comment: 65 page