Two classes of nonlocal Evolution Equations related by a shared Traveling Wave Problem

We consider reaction-diffusion equations and Korteweg-de Vries-Burgers (KdVB) equations, i.e. scalar conservation laws with diffusive-dispersive regularization. We review the existence of traveling wave solutions for these two classes of evolution equations. For classical equations the traveling wave problem (TWP) for a local KdVB equation can be identified with the TWP for a reaction-diffusion equation. In this article we study this relationship for these two classes of evolution equations with nonlocal diffusion/dispersion. This connection is especially useful, if the TW equation is not studied directly, but the existence of a TWS is proven using one of the evolution equations instead. Finally, we present three models from fluid dynamics and discuss the TWP via its link to associated reaction-diffusion equations

The flavor puzzle in multi-Higgs models

We reconsider the flavor problem in the models with two Higgs doublets. By studying two generation toy models, we look for flavor basis independent constraints on Yukawa couplings that will give us the mass hierarchy while keeping all Yukawa couplings of the same order. We then generalize our findings to the full three generation Standard Model. We find that we need two constraints on the Yukawa couplings to generate the observed mass hierarchy, and a slight tuning of Yukawa couplings of order 10%, much less than the Standard Model. We briefly study how these constraints can be realized, and show how flavor changing currents are under control for $K-\bar{K}$ mixing in the near-decoupling limit.Comment: 26 pages, typos are corrected, references are added, the final versio

Minimal Flavour Violation for Leptoquarks

Scalar leptoquarks, with baryon and lepton number conserving interactions, could have TeV scale masses, and be produced at colliders or contribute to a wide variety of rare decays. In pursuit of some insight as to the most sensitive search channels, We assume that the leptoquark-lepton-quark coupling can be constructed from the known mass matrices. We estimate the rates for selected rare processes in three cases: leptoquarks carrying lepton and quark flavour, leptoquarks with quark flavour only, and unflavoured leptoquarks. We find that leptoquark decay to top quarks is an interesting search channel.Comment: 17 pages, 2 figures, minor changes and references adde

Flavor of quiver-like realizations of effective supersymmetry

We present a class of supersymmetric models which address the flavor puzzle and have an inverted hierarchy of sfermions. Their construction involves quiver-like models with link fields in generic representations. The magnitude of Standard-Model parameters is obtained naturally and a relatively heavy Higgs boson is allowed without fine tuning. Collider signatures of such models are possibly within the reach of LHC in the near future.Comment: LaTeX, 17 pages, 3 figures. V2: reference adde

LHC Predictions from a Tevatron Anomaly in the Top Quark Forward-Backward Asymmetry

We examine the implications of the recent CDF measurement of the top-quark forward-backward asymmetry, focusing on a scenario with a new color octet vector boson at 1-3 TeV. We study several models, as well as a general effective field theory, and determine the parameter space which provides the best simultaneous fit to the CDF asymmetry, the Tevatron top pair production cross section, and the exclusion regions from LHC dijet resonance and contact interaction searches. Flavor constraints on these models are more subtle and less severe than the literature indicates. We find a large region of allowed parameter space at high axigluon mass and a smaller region at low mass; we match the latter to an SU(3)xSU(3)/SU(3) coset model with a heavy vector-like fermion. Our scenario produces discoverable effects at the LHC with only 1-2 inverse femtobarns of luminosity at 7-8 TeV. Lastly, we point out that a Tevatron measurement of the b-quark forward-backward asymmetry would be very helpful in characterizing the physics underlying the top-quark asymmetry.Comment: 35 pages, 10 figures, 4 table

Flavor Violating Higgs Decays

We study a class of nonstandard interactions of the newly discovered 125 GeV Higgs-like resonance that are especially interesting probes of new physics: flavor violating Higgs couplings to leptons and quarks. These interaction can arise in many frameworks of new physics at the electroweak scale such as two Higgs doublet models, extra dimensions, or models of compositeness. We rederive constraints on flavor violating Higgs couplings using data on rare decays, electric and magnetic dipole moments, and meson oscillations. We confirm that flavor violating Higgs boson decays to leptons can be sizeable with, e.g., h -> tau mu and h -> tau e branching ratios of order 10% perfectly allowed by low energy constraints. We estimate the current LHC limits on h -> tau mu and h -> tau e decays by recasting existing searches for the SM Higgs in the tau-tau channel and find that these bounds are already stronger than those from rare tau decays. We also show that these limits can be improved significantly with dedicated searches and we outline a possible search strategy. Flavor violating Higgs decays therefore present an opportunity for discovery of new physics which in some cases may be easier to access experimentally than flavor conserving deviations from the Standard Model Higgs framework.Comment: 39 pages, 12 figures, 3 tables; v2: Improved referencing, updated mu -> 3e bounds to include large loop contributions, corrected single top constraints; conclusions unchanged; matches version to be published in JHEP; v3: included 2-loop contributions in mu -> e conversion, improved discussion of tau -> 3 mu and of EDM constraints on FV top-Higgs couplings; conclusions unchange

Charged-Higgs phenomenology in the Aligned two-Higgs-doublet model

The alignment in flavour space of the Yukawa matrices of a general two-Higgs-doublet model results in the absence of tree-level flavour-changing neutral currents. In addition to the usual fermion masses and mixings, the aligned Yukawa structure only contains three complex parameters, which are potential new sources of CP violation. For particular values of these three parameters all known specific implementations of the model based on discrete Z_2 symmetries are recovered. One of the most distinctive features of the two-Higgs-doublet model is the presence of a charged scalar. In this work, we discuss its main phenomenological consequences in flavour-changing processes at low energies and derive the corresponding constraints on the parameters of the aligned two-Higgs-doublet model.Comment: 46 pages, 19 figures. Version accepted for publication in JHEP. References added. Discussion slightly extended. Conclusions unchange

(De)Constructing a Natural and Flavorful Supersymmetric Standard Model

Using the framework of deconstruction, we construct simple, weakly-coupled supersymmetric models that explain the Standard Model flavor hierarchy and produce a flavorful soft spectrum compatible with precision limits. Electroweak symmetry breaking is fully natural; the mu-term is dynamically generated with no B mu-problem and the Higgs mass is easily raised above LEP limits without reliance on large radiative corrections. These models possess the distinctive spectrum of superpartners characteristic of "effective supersymmetry": the third generation superpartners tend to be light, while the rest of the scalars are heavy.Comment: 36 pages, 4 figures ; v2: references added, expanded discussion of FCNC

Three little pieces for computer and relativity

Numerical relativity has made big strides over the last decade. A number of problems that have plagued the field for years have now been mostly solved. This progress has transformed numerical relativity into a powerful tool to explore fundamental problems in physics and astrophysics, and I present here three representative examples. These "three little pieces" reflect a personal choice and describe work that I am particularly familiar with. However, many more examples could be made.Comment: 42 pages, 11 figures. Plenary talk at "Relativity and Gravitation: 100 Years after Einstein in Prague", June 25 - 29, 2012, Prague, Czech Republic. To appear in the Proceedings (Edition Open Access). Collects results appeared in journal articles [72,73, 122-124

MFV Reductions of MSSM Parameter Space

The 100+ free parameters of the minimal supersymmetric standard model (MSSM) make it computationally difficult to compare systematically with data, motivating the study of specific parameter reductions such as the cMSSM and pMSSM. Here we instead study the reductions of parameter space implied by using minimal flavour violation (MFV) to organise the R-parity conserving MSSM, with a view towards systematically building in constraints on flavour-violating physics. Within this framework the space of parameters is reduced by expanding soft supersymmetry-breaking terms in powers of the Cabibbo angle, leading to a 24-, 30- or 42-parameter framework (which we call MSSM-24, MSSM-30, and MSSM-42 respectively), depending on the order kept in the expansion. We provide a Bayesian global fit to data of the MSSM-30 parameter set to show that this is manageable with current tools. We compare the MFV reductions to the 19-parameter pMSSM choice and show that the pMSSM is not contained as a subset. The MSSM-30 analysis favours a relatively lighter TeV-scale pseudoscalar Higgs boson and $\tan \beta \sim 10$ with multi-TeV sparticles.Comment: 2nd version, minor comments and references added, accepted for publication in JHE