The Matrix Element Method: Past, Present, and Future
The increasing use of multivariate methods, and in particular the Matrix Element Method (MEM), represents a revolution in experimental particle physics. With continued exponential growth in computing capabilities, the use of sophisticated multivariate methods– already common– will soon become ubiquitous and ultimately almost compulsory. While the existence of sophisticated algorithms for disentangling signal and background might naively suggest a diminished role for theorists, the use of the MEM, with its inherent connection to the calculation of differential cross sections will benefit from collaboration between theorists and experimentalists. In this white paper, we will briefly describe the MEM and some of its recent uses, note some current issues and potential resolutions, and speculate about exciting future opportunities.

title: Interplay between Fermi gamma-ray lines and collider searches
abstract: A bstractWe explore the interplay between lines in the gamma-ray spectrum and LHC searches involving missing energy and photons. As an example, we consider a singlet Dirac fermion dark matter with the mediator for Fermi gamma-ray line at 130 GeV. A new chiral or local U(1) symmetry makes weak-scale dark matter natural and provides the axion or Z′ gauge boson as the mediator connecting between dark matter and electroweak gauge bosons. In these models, the mediator particle can be produced in association with a monophoton at colliders and it produces large missing energy through the decays into a DM pair or ZZ, Zγ with at least one Z decaying into a neutrino pair. We adopt the monophoton searches with large missing energy at the LHC and impose the bounds on the coupling and mass of the mediator field in the models. We show that the parameter space of the Z′ mediation model is already strongly constrained by the LHC 8TeV data, whereas a certain region of the parameter space away from the resonance in axion-like mediator models are bounded. We foresee the monophoton bounds on the Z′ and axion mediation models at the LHC 14 TeV.

title: The role of interference in unraveling the ZZ-couplings of the newly discovered boson at the LHC
abstract: We present a general procedure for measuring the tensor structure of the coupling of the scalar Higgs-like boson recently discovered at the LHC to two Z bosons, including the effects of interference among different operators. To motivate our concern with this interference, we explore the parameter space of the couplings in the effective theory describing these interactions and illustrate the effects of interference on the differential dilepton mass distributions. Kinematic discriminants for performing coupling measurements that utilize the effects of interference are developed and described. We present projections for the sensitivity of coupling measurements that use these discriminants in future LHC operation in a variety of physics scenarios.

title: From Lagrangians to Events: Computer Tutorial at the MC4BSM-2012 Workshop
abstract: This is a written account of the computer tutorial oered at the Sixth MC4BSM workshop at Cornell University, March 22-24, 2012. The tools covered during the tutorial include: FeynRules, LanHEP, MadGraph, CalcHEP, Pythia 8, Herwig++, and Sherpa. In the tutorial, we specify a simple extension of the Standard Model, at the level of a Lagrangian. The software tools are then used to automatically generate a set of Feynman rules, compute the invariant matrix element for a sample process, and generate both parton-level and fully hadronized/showered Monte Carlo event samples. The tutorial is designed to be self-paced, and detailed instructions for all steps are included in this write-up. Installation instructions for each tool on a variety of popular platforms are also provided.

title: Dark matter particle spectroscopy at the LHC: generalizing MT2 to asymmetric event topologies
abstract: We consider SUSY-like missing energy events at hadron colliders and critically examine the common assumption that the missing energy is the result of two identical missing particles. In order to experimentally test this hypothesis, we generalize the subsystem MT2 variable to the case of asymmetric event topologies, where the two SUSY decay chains terminate in different “children” particles. In this more general approach, the endpoint MT2(max) of the MT2 distribution now gives the mass $$ {\tilde M_p}\left( {\tilde M_c^{(a)},\tilde M_c^{(b)}} \right) $$ of the parent particles as a function of two input children masses $$ \tilde M_c^{(a)} $$ and $$ \tilde M_c^{(b)} $$. We propose two methods for an independent determination of the individual children masses M(a)c and M(b)c. First, in the presence of upstream transverse momentum PUTM the corresponding function $$ {\tilde M_p}\left( {\tilde M_c^{(a)},\tilde M_c^{(b)},{P_{\text{UTM}}}} \right) $$ is independent of PUTM at precisely the right values of the children masses. Second, the previously discussed MT2 “kink” is now generalized to a “ridge” on the 2-dimensional surface $$ {\tilde M_p}\left( {\tilde M_c^{(a)},\tilde M_c^{(b)}} \right) $$. As we show in several examples, quite often there is a special point along that ridge which marks the true values of the children masses. Our results allow collider experiments to probe a multi-component dark matter sector directly and without any theoretical prejudice.

title: Superpartner mass measurement technique using 1D orthogonal decompositions of the Cambridge transverse mass variable M(T2).
abstract: We propose a new model-independent technique for mass measurements in missing energy events at hadron colliders. We illustrate our method with the most challenging case of a single-step decay chain. We consider inclusive same-sign chargino pair production in supersymmetry, followed by leptonic decays to sneutrinos χ+ χ+ → ℓ+ ℓ'+ ν(ℓ)ν(ℓ') and invisible decays ν(ℓ) → ν(ℓ) χ(1)(0). We introduce two one-dimensional decompositions of the Cambridge MT2 variable: M(T2∥) and M(T2⊥), on the direction of the upstream transverse momentum P→T and the direction orthogonal to it, respectively. We show that the sneutrino mass Mc can be measured directly by minimizing the number of events N(Mc) in which MT2 exceeds a certain threshold, conveniently measured from the end point M(T2⊥)(max) (Mc).

title: Multi-lepton signals of the Higgs boson
abstract: A bstractThe possibility of searching for the Higgs boson in channels with multiple non-resonant leptons is evaluated in light of recent advances in multi-lepton search techniques at the LHC. The total multi-lepton Higgs signal exceeds the four lepton gold-plated resonant mode, but is spread over many channels with same-sign di-lepton, tri-lepton, and four lepton final states. While any individual channel alone is not significant, the exclusive combination across multiple channels is shown to provide a sensitivity nearly comparable to other discovery level searches for the Higgs boson. We estimate that with 5 fb−1 of data, existing non-optimized multi-lepton searches at the LHC could exclude the Higgs boson to 95 % CL at a few times the predicted Standard Model cross section in the mass range 120 − 150 GeV. Refinements focused specifically on the Higgs boson signal are suggested that would further increase sensitivity. We illustrate the possibility of discerning patterns in production and decay modes using correlations across multiple channels by comparing sensitivities to Standard Model, Fermi-phobic, and b-phobic Higgs bosons.

title: Vacua and instantons of ghost-free massive gravity
abstract: Recently discovered models of ghost-free massive gravity and bigravity are characterized by a nontrivial potential that gives rise to a rich vacuum structure. We review maximally symmetric vacua of the de Rham-Gabadadze-Tolley (dRGT) massive gravity and of the Hassan-Rosen (HR) bigravity and discuss their perturbative stability. In particular, we discuss perturbations about self-accelerating vacua in HR bigravity and argue that, analogously to what was found in the case of dRGT gravity, some of them contain strongly coupled modes. We then show that it is impossible to construct regular instantons connecting different classically stable vacua of dRGT gravity without violating energy conservation or the null energy condition.

title: Unified approach to cosmic acceleration
abstract: We present a unified framework for the study of late time cosmic acceleration. Using methods of effective field theory, we show that existing proposals for late time acceleration can be subsumed in a single framework, rather than many compartmentalized theories. We construct the most general action consistent with symmetry principles, derive the background and perturbation evolution equations, and demonstrate that for special choices of our parameters we can reproduce results already existing in the literature. Lastly, we lay the foundation for future work placing phenomenological constraints on the parameters of the effective theory. Although in this paper we focus on late time acceleration, our construction also generalizes the effective field theory of inflation to the scalar-tensor and multifield case for perturbatively constructed backgrounds.

title: Searching for $t \to c h$ with Multi-Leptons
abstract: The results of a multi-lepton search conducted by the CMS collaboration with 5 fb$^{-1}$ of data collected from 7 TeV $pp$ collisions are used to place the first bound on the rare flavor-changing decay of the top quark to a Higgs boson and charm quark. Combining results from a number of exclusive three- and four-lepton search channels yields an estimated upper limit of ${\rm Br}(t \to ch) < 2.7%$ for a Higgs boson mass of 125 GeV. The sensitivity of future dedicated searches for $t \to c h$ could be improved by adding exclusive same sign di-lepton channels, as well as by sub-dividing channels based on $b$-quark tagging and partial kinematic top quark and Higgs boson tagging. This bound may be interpreted more widely within a range of new physics processes that yield final states with a $W$-boson in association with a Higgs boson. For such processes with kinematics that are similar to top--anti-top production and decay, the estimated limit on cross section times branching ratio corresponds to roughly $\sigma \cdot {\rm Br}(pp \to WhX) < 9$ pb.

title: Quantum aspects of massive gravity II: non-Pauli-Fierz theory
abstract: We investigate the non-Pauli-Fierz (nPF) theory, a linearized massive gravity with a generic graviton mass term, which has been ignored due to a ghost in its spectrum and the resultant loss of unitarity. We first show that it is possible to use the Lee-Wick mechanism, a unitarization through the decay of a ghost, in order to handle the sixth mode ghost of nPF, and then check for the quantum consistency. Once proven to be consistent, nPF could become a viable candidate for a large distance modification of gravity, because it naturally solves the intrinsic problems that most darkenergy/modified gravity models suffer from: It smoothly converges to general relativity at short distances, and the small graviton mass necessary to modify gravity at large scales can be stable under the radiative corrections from the minimal gravity-to-matter coupling.