General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the sense of
a distribution, meaning that it holds for correlation functions smeared by smooth test functions. The conformal blocks for this OPE are conceptually extremely simple: they are products of 3-point functions. We construct the conformal blocks in 2-dimensional conformal field theory and show that the OPE in fact converges pointwise to an ordinary function in a specific kinematic region. Using microcausality, we also formulate a bootstrap equation directly in terms of momentum space Wightman functions.
Non-minimal Higgs sectors are strongly constrained by the agreement of the measured couplings of the 125 GeV Higgs with Standard Model predictions. This agreement can be explained by an approximate $mathbb{Z}_2$ symmetry under which the additional Hi
ggs bosons are odd. This allows the additional Higgs bosons to be approximately inert, meaning that they have suppressed VEVs and suppressed mixing with the Standard Model Higgs. In this case, single production of the new Higgs bosons is suppressed, but electroweak pair production is unsuppressed. We study the phenomenology of a minimal 2 Higgs doublet model that realizes this scenario. In a wide range of parameters, the phenomenology of the model is essentially fixed by the masses of the exotic Higgs bosons, and can therefore be explored systematically. We study a number of different plausible signals in this model, and show that several LHC searches can constrain or discover additional Higgs bosons in this parameter space. We find that the reach is significantly extended at the high luminosity LHC.
4D CFTs have a scale anomaly characterized by the coefficient $c$, which appears as the coefficient of logarithmic terms in momentum space correlation functions of the energy-momentum tensor. By studying the CFT contribution to 4-point graviton scatt
ering amplitudes in Minkowski space we derive a sum rule for $c$ in terms of $TTmathcal{O}$ OPE coefficients. The sum rule can be thought of as a version of the optical theorem, and its validity depends on the existence of the massless and forward limits of the $langle TTTT rangle$ correlation functions that contribute. The finiteness of these limits is checked explicitly for free scalar, fermion, and vector CFTs. The sum rule gives $c$ as a sum of positive terms, and therefore implies a lower bound on $c$ given any lower bound on $TTmathcal{O}$ OPE coefficients. We compute the coefficients to the sum rule for arbitrary operators of spin 0 and 2, including the energy-momentum tensor.
This 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 o
f 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.
The discovery of a 125 GeV Higgs boson at the Large Hadron Collider strongly motivates direct searches for additional Higgs bosons. In a type I two Higgs doublet model there is a large region of parameter space at $tanbeta > 5$ that is currently unco
nstrained experimentally. We show that the process $gg to H to A Z to ZZh$ can probe this region, and can be the discovery mode for an extended Higgs sector at the LHC. We analyze 9 promising decay modes for the $ZZh$ state, and we find that the most sensitive final states are $ellellellell bb$, $ellell jjbb$, $ellell u ugammagamma$ and $ellellellell +{}$missing energy.
In this paper we study a new class of supersymmetric models that can explain a 125 GeV Higgs without fine-tuning. These models contain additional `auxiliary Higgs fields with large tree-level quartic interaction terms but no Yukawa couplings. These h
ave electroweak-breaking vacuum expectation values, and contribute to the VEVs of the MSSM Higgs fields either through an induced quartic or through an induced tadpole. The quartic interactions for the auxiliary Higgs fields can arise from either D-terms or F-terms. The tadpole mechanism has been previously studied in strongly-coupled models with large D-terms, referred to as `superconformal technicolor. The perturbative models studied here preserve gauge coupling unification in the simplest possible way, namely that all new fields are in complete SU(5) multiplets. The models are consistent with the observed properties of the 125 GeV Higgs-like boson as well as precision electroweak constraints, and predict a rich phenomenology of new Higgs states at the weak scale. The tuning is less than 10% in almost all of the phenomenologically allowed parameter space. If electroweak symmetry is broken by an induced tadpole, the cubic and quartic Higgs self-couplings are significantly smaller than in the standard model.
