The static PQCD potential with modified boundary conditions

We calculate the potential between two static quarks in QCD using modified boundary conditions for the perturbative expansion. Through a change of the Feynman iepsilon prescription we effectively add a "sea" of gluons to the asymptotic states with energies below a given scale Lambda. We find that the standard result for the static potential gets corrections of order Lambda^2/Q^2 both at small and large momentum transfers Q^2. After resummation of the infrared sensitive corrections we find that the running coupling alpha_s(Q^2) freezes in the infrared and that the exchanged gluon gets an effective tachyonic mass. We verify that identical results are obtained in the Coulomb and Feynman gauges.Comment: 13 pages, 3 figures, updated version accepted for publication in JHEP, additions to introduction and discussion, references added, results unchange

Conformal Expansions: A Template for QCD Predictions

The use of conformal expansions for predictions in quantum chromodynamics is discussed as a way to avoid renormalization scheme and scale ambiguities, as well as factorial growth of perturbative coefficients due to renormalons. Special emphasis is given to the properties of an assumed skeleton expansion and its relation to the Banks-Zaks expansion. The relation of BLM scale-setting to the skeleton expansion is also discussed and new criteria for the applicability of BLM scale-setting are presented.Comment: 16 pages, Invited talk given at RADCOR-2000, Carmel CA, USA, 11-15 September, 200

Resummation and power corrections by Dressed Gluon Exponentiation

Event-shape distributions in $e^+e^-$ annihilation offer a unique lab oratory for understanding perturbative and non-perturbative aspects of QCD. Dressed Gluon Exponentiation is a resummation method designed to evaluate differ ential cross sections close to a kinematic threshold and provide the basis for parametrization of power corrections. The method and its application in the case of the thrust and the heavy jet mass distributions in the two-jet region are briefly presented.Comment: 5 pages, 3 figures in ps, talk given at XXXI International Symposium on Multiparticle Dynamics, Sept 1-7, 2001, Datong China. URL http://ismd31.ccnu.edu.cn

Closing the Window on Light Charged Higgs Bosons in the NMSSM

In the Next-to-Minimal SuperSymmetric Model (NMSSM) the lightest CP-odd Higgs bosons (a1) can be very light. As a consequence, in addition to the standard charged Higgs boson (h+) decays considered in the MSSM for a light charged Higgs (m_h+ < m_t), the branching fraction for h+ to a1 W can be dominant. We investigate how this signal can be searched for in t tbar production at the Large Hadron Collider (LHC) in the case that m_a1 \gtrsim 2m_B with the a1 giving rise to a single b bbar-jet and discuss to what extent the LHC experiments are able to discover such a scenario with an integrated luminosity \sim 20 fb-1. We also discuss the implications of the possible Higgs-signal observed at the LHC.Comment: 20 pages, 11 figures, some minor updates and clarifications, version accepted for publication in Advances in High Energy Physics special issue on The Next-to-Minimal Supersymmetric Standard Mode

Z2Z_2 breaking effects in 2-loop RG evolution of 2HDM

We investigate the effects of a $Z_2$ symmetry in the CP-conserving Two-Higgs-Doublet-Model (2HDM); which is often imposed to prevent Flavor-Changing-Neutral-Currents (FCNCs) at tree-level. Specifically, we analyze how a breaking of the $Z_2$ symmetry spreads during renormalization group evolution; employing general 2-loop renormalization group equations that we have derived. Evolving the model from the electroweak to the Planck scale, we find that while the case of an exact $Z_2$ symmetric 2HDM is very constrained, a soft breaking of the $Z_2$ symmetry extends the valid parameter space regions. The effects of a hard $Z_2$ breaking in the scalar sector as well as the stability of the flavor alignment ansatz are also investigated. We find that while a hard breaking of the $Z_2$ symmetry in the potential is problematic, since it speeds up the growth of quartic couplings, the generated FCNCs are heavily suppressed. Conversely, we also find that hard $Z_2$ breaking in the Yukawa sector at most gives moderate $Z_2$ breaking in the potential; whereas the FCNCs can become quite sizable far away from the $Z_2$ symmetric regions.Comment: 33 pages, journal versio

Anomaly-free Model Building with Algebraic Geometry

We present a method to find anomaly-free gauged Froggatt-Nielsen type models using results from algebraic geometry. These methods should be of general interest for model building beyond the Standard Model (SM) when rational charges are required. We consider models with a gauged $U(1)$ flavor symmetry with one flavon and two Higgs doublets and three right-handed SM singlets to provide three model examples based on different physical assumptions. The models we study are: anomaly-free with no SM neutral heavy chiral fermions, anomaly-free with SM neutral heavy chiral fermions, and supersymmetric with SM neutral heavy chiral fermions where the anomalies cancel via the Green-Schwarz mechanism. With these different models we show how algebraic methods may be used in model building; both to reduce the charge constraints by calculation of Gr\"obner bases, and to find rational solutions to cubic equations using Mordell-Weil generators. Using these tools we find three phenomenologically viable models explaining the observed flavor structure.Comment: Changed to match published versio

Conformal Symmetry as a Template: Commensurate Scale Relations and Physics Renormalization Schemes

Commensurate scale relations are perturbative QCD predictions which relate observable to observable at fixed relative scale, such as the "generalized Crewther relation", which connects the Bjorken and Gross-Llewellyn Smith deep inelastic scattering sum rules to measurements of the e+ e- annihilation cross section. We show how conformal symmetry provides a template for such QCD predictions, providing relations between observables which are present even in theories which are not scale invariant. All non-conformal effects are absorbed by fixing the ratio of the respective momentum transfer and energy scales. In the case of fixed-point theories, commensurate scale relations relate both the ratio of couplings and the ratio of scales as the fixed point is approached. In the case of the $\alpha_V$ scheme defined from heavy quark interactions, virtual corrections due to fermion pairs are analytically incorporated into the Gell-Mann Low function, thus avoiding the problem of explicitly computing and resumming quark mass corrections related to the running of the coupling. Applications to the decay width of the Z boson, the BFKL pomeron, and virtual photon scattering are discussed.Comment: 27 pages, Talk presented at the Les Rencontres de Physique de la Vallee d'Aoste, La Thuile, Italy, February 28-March 6, 199

Higgs phenomenology in the Stealth Doublet Model

We analyze a model for the Higgs sector with two scalar doublets and a $Z_2$ symmetry that is manifest in the Yukawa sector but broken in the potential. Thus, one of the doublets breaks the electroweak symmetry and has tree-level Yukawa couplings to fermions, whereas the other doublet has no vacuum expectation value and no tree-level couplings to fermions. Since the $Z_2$ parity is broken the two doublets can mix, which leads to a distinct and novel phenomenology. This Stealth Doublet Model can be seen as a generalization of the Inert Doublet Model with a broken $Z_2$ symmetry. We outline the model and present constraints from theory, electroweak precision tests and collider searches, including the recent observation of a Higgs boson at the LHC. The charged scalar $H^\pm$ and the CP-odd scalar $A$ couple to fermions at one-loop level. We compute the decays of $H^\pm$ and $A$ and in particular the one-loop decays $A \to f \bar{f}$, $H^\pm \to f \bar{f}^\prime$, $H^\pm \to W^\pm Z$ and $H^\pm \to W^\pm \gamma$. We also describe how to calculate and renormalize such processes in our model. We find that if one of $H^\pm$ or $A$ is the lightest scalar, $H^\pm \to W^\pm \gamma$ or $A \to b \bar{b}$ are typically their respective dominating decay channels. Otherwise, the dominating decays of $H^\pm$ and $A$ are into a scalar and a vector. Due to the absence of tree-level fermion couplings for $H^\pm$ and $A$, we consider pair production and associated production with vector bosons and scalars at the LHC. If the parameter space of the model that favors $H^\pm \to W^\pm \gamma$ is realized in Nature, we estimate that there could be a considerable amount of such events in the present LHC data.Comment: 40 pages, 25 figures. Version 4. Minor updates, references added. Version to appear in PR