Markus A. Luty

Asymmetric Dark Matter

We consider a simple class of models in which the relic density of dark matter is determined by the baryon asymmetry of the Universe. In these models a B-L asymmetry generated at high temperatures is transferred to the dark matter, which is charged under B-L. The interactions that transfer the asymmetry decouple at temperatures above the dark matter mass, freezing in a dark matter asymmetry of order the baryon asymmetry. This explains the observed relation between the baryon and dark matter densities for the dark matter mass in the range 5-15 GeV. The symmetric component of the dark matter can annihilate efficiently to light pseudoscalar Higgs particles a or via t-channel exchange of new scalar doublets. The first possibility allows for h{sup 0}{yields}aa decays, while the second predicts a light charged Higgs-like scalar decaying to {tau}{nu}. Direct detection can arise from Higgs exchange in the first model or a nonzero magnetic moment in the second. In supersymmetric models, the would-be lightest supersymmetric partner can decay into pairs of dark matter particles plus standard model particles, possibly with displaced vertices.

The a -theorem and the asymptotics of 4D quantum field theory

A bstractWe study the possible IR and UV asymptotics of 4D Lorentz invariant unitary quantum field theory. Our main tool is a generalization of the Komargodski-Schwimmer proof for the a-theorem. We use this to rule out a large class of renormalization group flows that do not asymptote to conformal field theories in the UV and IR. We show that the only possible UV and IR asymptotics described by perturbation theory have a vanishing trace of the stress-energy tensor, and are therefore conformal. Our arguments hold even for theories with gravitational anomalies. We also give a non-perturbative argument that excludes theories with scale but not conformal invariance. This argument holds for theories in which the stress-energy tensor is sufficiently nontrivial in a technical sense that we make precise.

Minimal conformal technicolor and precision electroweak tests

We study the minimal model of conformal technicolor, an SU(2) gauge theory near a strongly coupled conformal fixed point, with conformal symmetry softly broken by technifermion mass terms. Conformal symmetry breaking triggers chiral symmetry breaking in the pattern SU(4) → Sp(4), which gives rise to a pseudo-Nambu-Goldstone boson that can act as a composite Higgs boson. The top quark is elementary, and the top and electroweak gauge loop contributions to the Higgs mass are cut off entirely by Higgs compositeness. In particular, the model requires no top partners and no “little Higgs” mechanism. A nontrivial vacuum alignment results from the interplay of the top loop and technifermion mass terms. The composite Higgs mass is completely determined by the top loop, in the sense that mh/mt is independent of the vacuum alignment and is computable by a strong-coupling calculation. There is an additional composite pseudoscalar A with mass larger than mh and suppressed direct production at LHC. We discuss the electroweak fit in this model in detail. Corrections to

Scale Invariance, Conformality, and Generalized Free Fields

Z \to \bar{b}b

Strong conformal dynamics at the LHC and on the lattice

and the T parameter from the top sector are suppressed by the enhanced Sp(4) custodial symmetry. Even assuming that the strong contribution to the S parameter is positive and usuppressed, a good electroweak fit can be obtained for v/f ≲ 0.25, where v and f are the electroweak and chiral symmetry breaking scales respectively. This requires fine tuning at the 10% level.

Partially composite Higgs in supersymmetry

A bstractThis paper addresses the question of whether there are 4D Lorentz invariant unitary quantum field theories with scale invariance but not conformal invariance. An important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen is that trace of the energy-momentum tensor T could be a generalized free field. In this paper we rule out this possibility. The key ingredient is the observation that a unitary theory with scale but not conformal invariance necessarily has a non-vanishing anomaly for global scale transformations. We show that this anomaly cannot be reproduced if T is a generalized free field unless the theory also contains a dimension-2 scalar operator. In the special case where such an operator is present it can be used to redefine (“improve”) the energy-momentum tensor, and we show that there is at least one energy-momentum tensor that is not a generalized free field. In addition, we emphasize that, in general, large momentum limits of correlation functions cannot be understood from the leading terms of the coordinate space OPE. This invalidates a recent argument by Farnsworth-Luty-Prilepina (FLP). Despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in the present context.

Flavor in Minimal Conformal Technicolor

Conformal technicolor is a paradigm for new physics at the LHC that may solve the problems of strong electroweak symmetry breaking for quark masses and precision electroweak data. We give explicit examples of conformal technicolor theories based on a QCD-like sector. We suggest a practical method to test the conformal dynamics of these theories on the lattice.

Scale anomalies, states, and rates in conformal field theory

A bstractWe propose a framework for natural breaking of electroweak symmetry in supersymmetric models, where elementary Higgs fields are semi-perturbatively coupled to a strong superconformal sector. The Higgs VEVs break conformal symmetry in the strong sector at the TeV scale, and the strong sector in turn gives important contributions to the Higgs potential, giving rise to a kind of Higgs bootstrap. A Higgs with mass 125 GeV can be accommodated without any fine tuning. A Higgsino mass of order the Higgs mass is also dynamically generated in these models. The masses in the strong sector generically violate custodial symmetry, and a good precision electroweak fit requires tuning of order ~ 10%. The strong sector has an approximately supersymmetric spectrum of hadrons at the TeV scale that can be observed by looking for a peak in the WZ invariant mass distribution, as well as final states containing multiple W, Z, and Higgs bosons. The models also generically predict large corrections (either enhancement or suppression) to the h → γγ width.

Phenomenology of induced electroweak symmetry breaking

We construct a complete, realistic, and natural UV completion of minimal conformal technicolor that explains the origin of quark and lepton masses and mixing angles. As in “bosonic technicolor,” we embed conformal technicolor in a supersymmetric theory, with supersymmetry broken at a high scale. The exchange of heavy scalar doublets generates higher-dimension interactions between technifermions and quarks and leptons that give rise to quark and lepton masses at the TeV scale. Obtaining a sufficiently large top quark mass requires strong dynamics at the supersymmetry breaking scale in both the top and technicolor sectors. This is natural if the theory above the supersymmetry breaking also has strong conformal dynamics. We present two models in which the strong top dynamics is realized in different ways. In both models, constraints from flavor-changing effects can be easily satisfied. The effective theory below the supersymmetry breaking scale is minimal conformal technicolor with an additional light technicolor gaugino. We argue that this light gaugino is a general consequence of conformal technicolor embedded into a supersymmetric theory. If the gaugino has mass below the TeV scale it will give rise to an additional pseudo Nambu-Goldstone boson that is observable at the LHC.

Positive Energy Conditions in 4D Conformal Field Theory

A bstractThis paper presents two methods to compute scale anomaly coefficients in conformal field theories (CFTs), such as the c anomaly in four dimensions, in terms of the CFT data. We first use Euclidean position space to show that the anomaly coefficient of a four-point function can be computed in the form of an operator product expansion (OPE), namely a weighted sum of OPE coefficients squared. We compute the weights for scale anomalies associated with scalar operators and show that they are not positive. We then derive a different sum rule of the same form in Minkowski momentum space where the weights are positive. The positivity arises because the scale anomaly is the coefficient of a logarithm in the momentum space four-point function. This logarithm also determines the dispersive part, which is a positive sum over states by the optical theorem. The momentum space sum rule may be invalidated by UV and/or IR divergences, and we discuss the conditions under which these singularities are absent. We present a detailed discussion of the formalism required to compute the weights directly in Minkowski momentum space. A number of explicit checks are performed, including a complete example in an 8-dimensional free field theory.