This document proposes a collection of simplified models relevant to the design of new-physics searches at the Large Hadron Collider (LHC) and the characterization of their results. Both ATLAS and CMS have already presented some results in terms of simplified models, and we encourage them to continue and expand this effort, which supplements both signature-based results and benchmark model interpretations. A simplified model is defined by an effective Lagrangian describing the interactions of a small number of new particles. Simplified models can equally well be described by a small number of masses and cross-sections. These parameters are directly related to collider physics observables, making simplified models a particularly effective framework for evaluating searches and a useful starting point for characterizing positive signals of new physics. This document serves as an official summary of the results from the 'Topologies for Early LHC Searches' workshop, held at SLAC in September

If electroweak symmetry breaking arises via strong dynamics, electroweak precision tests and flavour physics experiments suggest that the minimal model should closely resemble the Standard Model at the LHC. I describe two directions going beyond the minimal model that result in radically different physics at the LHC. One direction extends the Higgs sector and the other involves composite leptoquark states. IntroductionStrong coupling provides a solution of the electroweak hierarchy problem that is natural in the literal sense of the word. That is to say, we already have an example in Nature where a hierarchy, namely the one between the proton mass and, say, the Planck scale, is generated by a stronglycoupled theory, QCD. As such, and given the problems suffered by the only weakly-coupled candidate that can stabilize the hierarchy, namely supersymmetry, strongly-coupled dynamics remains an attractive mechanism for electroweak symmetry breaking.But strongly-coupled dynamics has severe problems of its own, in the form of clashes with electroweak precision tests and flavour-changing neutral currents. The former can be solved, to some extent, by clever use of symmetries. To see how this may occur, let me first remark that we do not yet know what the 'symmetry' of electroweak symmetry is. Certainly, we do know that it contains the SU (3) × SU (2) L × U (1) Y of the Standard Model (SM) as a gauged subgroup, but it is quite possible that the true global symmetry of the strongly-coupled sector is somewhat larger. If we enlarge the SU (2) L × U (1) Y to SU (2) L × SU (2) R ≃ SO(4) (which is an accidental symmetry of the renormalizable SM Higgs potential), then we find that the W and Z bosons automatically obtain their measured mass ratio. 1 Furthermore, by adding the discrete parity that interchanges L ↔ R (or equivalently enlarging SO(4) to O(4)), we can suppress unwanted corrections to the coupling Zbb. 2 The remaining nuisance is the S-parameter, which, alas, no symmetry can forbid without simultaneously forbidding electroweak symmetry breaking. Nevertheless, one can still use symmetry to argue that S, although it cannot vanish, could be small.The argument goes as follows. If SU (2) L were a symmetry of the vacuum, then S would indeed vanish. 3 This implies that S must be proportional to some positive power of the electroweak vev, v; in fact, since S transforms as an SU (2) L triplet, whilst v transforms as a doublet, we have that S ∝ v 2 . Now, S is dimensionless, so we must have that S ≃ v 2 /f 2 , where the scale f is set by the strong dynamics; if we could arrange for v/f to be somewhat less than unity, by some dynamical accident, then we might end up with an acceptably-small value for S. One way to do this is to further enlarge the global symmetry of the strong sector to SO(5) and then to decree that strong dynamics breaks it to SO(4). 4 The theory then contains four

We attempt to explain recent anomalies in semileptonic B decays at LHCb via a composite Higgs model, in which both the Higgs and an SU(2) L -triplet leptoquark arise as pseudo-Goldstone bosons of the strong dynamics. Fermion masses are assumed to be generated via the mechanism of partial compositeness, which largely determines the leptoquark couplings and implies non-universal lepton interactions. The latter are needed to accommodate tensions in the b → sµµ dataset and to be consistent with a discrepancy measured at LHCb in the ratio of B + → K + µ + µ − to B + → K + e + e − branching ratios. The data imply that the leptoquark should have a mass of around a TeV. We find that the model is not in conflict with current flavour or direct production bounds, but we identify a few observables for which the new physics contributions are close to current limits and where the leptoquark is likely to show up in future measurements. The leptoquark will be pair-produced at the LHC and decay predominantly to third-generation quarks and leptons, and LHC13 searches will provide further strong bounds.

We address electroweak baryogenesis in the context of composite Higgs models, pointing out that modifications to the Higgs and top quark sectors can play an important rôle in generating the baryon asymmetry. Our main observation is that composite Higgs models that include a light, gauge singlet scalar in the spectrum [as in the model based on the symmetry breaking pattern SO(6) → SO(5)], provide all necessary ingredients for viable baryogenesis. In particular, the singlet leads to a strongly first-order electroweak phase transition and introduces new sources of CP violation in dimensionfive operators involving the top quark. We discuss the amount of baryon asymmetry produced and the experimental constraints on the model.

Abstract:We consider the application of endpoint techniques to the problem of mass determination for new particles produced at a hadron collider, where these particles decay to an invisible particle of unknown mass and one or more visible particles of known mass. We also consider decays of these types for pair-produced particles and in each case consider situations both with and without initial state radiation. We prove that, in most (but not all) cases, the endpoint of an appropriate transverse mass observable, considered as a function of the unknown mass of the invisible particle, has a kink at the true value of the invisible particle mass. The co-ordinates of the kink yield the masses of the decaying particle and the invisible particle. We discuss the prospects for implementing this method at the LHC.

We re-examine the kinematic variable mT 2 and its relatives in the light of recent work by Cheng and Han. Their proof that mT 2 admits an equivalent, but implicit, definition as the 'boundary of the region of parent and daughter masses that is kinematically consistent with the event hypothesis' is far-reaching in its consequences. We generalize their result both to simpler cases (mT , the transverse mass) and to more complex cases (mT Gen). We further note that it is possible to re-cast many existing and unpleasant proofs (e.g. those relating to the existence or properties of "kink" and "crease" structures in mT 2) into almost trivial forms by using the alternative definition. Not only does this allow us to gain better understanding of those existing results, but it also allows us to write down new (and more or less explicit) definitions of (a) the variable that naturally generalizes mT 2 to the case in which the parent or daughter particles are not identical, and (b) the inverses of mT and mT 2 -which may be useful if daughter masses are known and bounds on parent masses are required. We note the implications that these results may have for future matrix-element likelihood techniques.

We construct effective field theories in which gravity is modified via spontaneous breaking of local Lorentz invariance. This is a gravitational analogue of the Higgs mechanism. These theories possess additional graviton modes and modified dispersion relations. They are manifestly well-behaved in the UV and free of discontinuities of the van Dam-Veltman-Zakharov type, ensuring compatibility with standard tests of gravity. They may have important phenomenological effects on large distance scales, offering an alternative to dark energy. For the case in which the symmetry is broken by a vector field with the wrong sign mass term, we identify four massless graviton modes (all with positive-definite norm for a suitable choice of a parameter) and show the absence of the discontinuity.

I consider the two-body decay of a particle at a hadron collider into a visible and an invisible particle, generalizing W → eν, where the masses of the decaying particle and the invisible decay particle are, a priori, unknown. I prove that the transverse mass, when maximized over possible kinematic configurations, can be used to determine both of the unknown masses. I argue that the proof can be generalized to cover cases such as decays of pair-produced superpartners to the lightest, stable superpartner at the Large Hadron Collider.