arXiv subjects

Clifford Cheung

Publications and source records attributed to Clifford Cheung.

101 records · Page 6Linked to original sources

arXiv2009

A Duality For The S Matrix

We propose a dual formulation for the S Matrix of N = 4 SYM. The dual provides a basis for the "leading singularities" of scattering amplitudes to all orders in perturbation theory, which are sharply defined, IR safe data that uniquely determine the full amplitudes at tree level and 1-loop, and are conjectured to do so at all loop orders. The scattering amplitude for n particles in the sector with k negative helicity gluons is associated with a simple integral over the space of k planes in n dimensions, with the action of parity and cyclic symmetries manifest. The residues of the integrand compute a basis for the leading singularities. A given leading singularity is associated with a particular choice of integration contour, which we explicitly identify at tree level and 1-loop for all NMHV amplitudes as well as the 8 particle NNMHV amplitude. We also identify a number of 2-loop leading singularities for up to 8 particles. There are a large number of relations among residues which follow from the multi-variable generalization of Cauchy's theorem known as the "global residue theorem". These relations imply highly non-trivial identities guaranteeing the equivalence of many different representations of the same amplitude. They also enforce the cancellation of non-local poles as well as consistent infrared structure at loop level. Our conjecture connects the physics of scattering amplitudes to a particular subvariety in a Grassmannian; space-time locality is reflected in the topological properties of this space.

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arXiv2009

Amplitudes and Spinor-Helicity in Six Dimensions

The spinor-helicity formalism has become an invaluable tool for understanding the S-matrix of massless particles in four dimensions. In this paper we construct a spinor-helicity formalism in six dimensions, and apply it to derive compact expressions for the three, four and five point tree amplitudes of Yang-Mills theory. Using the KLT relations, it is a straightforward process to obtain amplitudes in linearized gravity from these Yang-Mills amplitudes; we demonstrate this by writing down the gravitational three and four point amplitudes. Because there is no conserved helicity in six dimensions, these amplitudes describe the scattering of all possible polarization states (as well as Kaluza-Klein excitations) in four dimensions upon dimensional reduction. We also briefly discuss a convenient formulation of the BCFW recursion relations in higher dimensions.

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arXiv2009

Non-Abelian Dark Sectors and Their Collider Signatures

Motivated by the recent proliferation of observed astrophysical anomalies, Arkani-Hamed et al. have proposed a model in which dark matter is charged under a non-abelian "dark" gauge symmetry that is broken at ~ 1 GeV. In this paper, we present a survey of concrete models realizing such a scenario, followed by a largely model-independent study of collider phenomenology relevant to the Tevatron and the LHC. We address some model building issues that are easily surmounted to accommodate the astrophysics. While SUSY is not necessary, we argue that it is theoretically well-motivated because the GeV scale is automatically generated. Specifically, we propose a novel mechanism by which mixed D-terms in the dark sector induce either SUSY breaking or a super-Higgs mechanism precisely at a GeV. Furthermore, we elaborate on the original proposal of Arkani-Hamed et al. in which the dark matter acts as a messenger of gauge mediation to the dark sector. In our collider analysis we present cross-sections for dominant production channels and lifetime estimates for primary decay modes. We find that dark gauge bosons can be produced at the Tevatron and the LHC, either through a process analogous to prompt photon production or through a rare Z decay channel. Dark gauge bosons will decay back to the SM via "lepton jets" which typically contain >2 and as many as 8 leptons, significantly improving their discovery potential. Since SUSY decays from the MSSM will eventually cascade down to these lepton jets, the discovery potential for direct electroweak-ino production may also be improved. Exploiting the unique kinematics, we find that it is possible to reconstruct the mass of the MSSM LSP. We also present decay channels with displaced vertices and multiple leptons with partially correlated impact parameters.

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arXiv2009

The S-Matrix in Twistor Space

The simplicity and hidden symmetries of (Super) Yang-Mills and (Super)Gravity scattering amplitudes suggest the existence of a "weak-weak" dual formulation in which these structures are made manifest at the expense of manifest locality. We suggest that this dual description lives in (2,2) signature and is naturally formulated in twistor space. We recast the BCFW recursion relations in an on-shell form that begs to be transformed into twistor space. Our twistor transformation is inspired by Witten's, but differs in treating twistor and dual twistor variables more equally. In these variables the three and four-point amplitudes are amazingly simple; the BCFW relations are represented by diagrammatic rules that precisely define the "twistor diagrams" of Andrew Hodges. The "Hodges diagrams" for Yang-Mills theory are disks and not trees; they reveal striking connections between amplitudes and suggest a new form for them in momentum space. We also obtain a twistorial formulation of gravity. All tree amplitudes can be combined into an "S-Matrix" functional which is the natural holographic observable in asymptotically flat space; the BCFW formula turns into a quadratic equation for this "S-Matrix", providing a holographic description of N=4 SYM and N=8 Supergravity at tree level. We explore loop amplitudes in (2,2) signature and twistor space, beginning with a discussion of IR behavior. We find that the natural pole prescription renders the amplitudes well-defined and free of IR divergences. Loop amplitudes vanish for generic momenta, and in twistor space are even simpler than their tree-level counterparts! This further supports the idea that there exists a sharply defined object corresponding to the S-Matrix in (2,2) signature, computed by a dual theory naturally living in twistor space.

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arXiv2008

On-Shell Recursion Relations for Generic Theories

We show that on-shell recursion relations hold for tree amplitudes in generic two derivative theories of multiple particle species and diverse spins. For example, in a gauge theory coupled to scalars and fermions, any amplitude with at least one gluon obeys a recursion relation. In (super)gravity coupled to scalars and fermions, the same holds for any amplitude with at least one graviton. This result pertains to a broad class of theories, including QCD, N=4 SYM, and N=8 supergravity.

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arXiv2008

The Effective Field Theory of Inflation

We study the effective field theory of inflation, i.e. the most general theory describing the fluctuations around a quasi de Sitter background, in the case of single field models. The scalar mode can be eaten by the metric by going to unitary gauge. In this gauge, the most general theory is built with the lowest dimension operators invariant under spatial diffeomorphisms, like g^{00} and K_{mu nu}, the extrinsic curvature of constant time surfaces. This approach allows us to characterize all the possible high energy corrections to simple slow-roll inflation, whose sizes are constrained by experiments. Also, it describes in a common language all single field models, including those with a small speed of sound and Ghost Inflation, and it makes explicit the implications of having a quasi de Sitter background. The non-linear realization of time diffeomorphisms forces correlation among different observables, like a reduced speed of sound and an enhanced level of non-Gaussianity.

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arXiv2008

On the consistency relation of the 3-point function in single field inflation

The consistency relation for the 3-point function of the CMB is a very powerful observational signature which is believed to be true for every inflationary model in which there is only one dynamical degree of freedom. Its importance relies on the fact that deviations from it might be detected in next generation experiments, allowing us to rule out all single field inflationary models. After making more precise the already existing proof of the consistency relation, we use a recently developed effective field theory for inflationary perturbations to provide an alternative and very explicit proof valid at leading non trivial order in slow roll parameters.

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arXiv2007

(Extra)Ordinary Gauge Mediation

We study models of "(extra)ordinary gauge mediation," which consist of taking ordinary gauge mediation and extending the messenger superpotential to include all renormalizable couplings consistent with SM gauge invariance and an R-symmetry. We classify all such models and find that their phenomenology can differ significantly from that of ordinary gauge mediation. Some highlights include: arbitrary modifications of the squark/slepton mass relations, small mu and Higgsino NLSP's, and the possibility of having fewer than one effective messenger. We also show how these models lead naturally to extremely simple examples of direct gauge mediation, where SUSY and R-symmetry breaking occur not in a hidden sector, but due to the dynamics of the messenger sector itself.

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arXiv2007

Sequestering CP Violation and GIM-Violation with Warped Extra Dimensions

We propose a model of spontaneous CP violation to address the strong CP problem in warped extra dimensions that relies on sequestering flavor and CP violation. We assume that brane-localized Higgs Yukawa interactions respect a U(3) flavor symmetry that is broken only by bulk fermion mass and Yukawa terms. All CP violation arises from the vev of a CP-odd scalar field localized in the bulk. To suppress radiative corrections to theta-bar, the doublet quarks in this model are localized on the IR brane. We calculate constraints from flavor-changing neutral currents (FCNCs), precision electroweak measurements, CKM unitarity, and the electric dipole moments in this model and predict theta-bar to be at least about 10^-12.

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arXiv2007

The Plasma Puddle as a Perturbative Black Hole

We argue that the weak coupling regime of a large N gauge theory in the Higgs phase contains black hole-like objects. These so-called ``plasma puddles'' are meta-stable lumps of hot plasma lying in locally un-Higgsed regions of space. They decay via O(1/N) thermal radiation and, perhaps surprisingly, absorb all incident matter. We show that an incident particle of energy E striking the plasma puddle will shower into an enormous number of decay products whose multiplicity grows linearly with E, and whose average energy is independent of E. Once these ultra-soft particles reach the interior they are thermalized by the plasma within, and so the object appears ``black.'' We determine some gross properties like the size and temperature of the the plasma puddle in terms of fundamental parameters in the gauge theory. Interestingly, demanding that the plasma puddle emit thermal Hawking radiation implies that the object is black (i.e. absorbs all incident particles), which implies classical stability, which implies satisfaction of the Bekenstein entropy bound. Because of the AdS/CFT duality and the many similarities between plasma puddles and black holes, we conjecture that black objects are a robust feature of quantum gravity.

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arXiv2006

(Reverse) Engineering Vacuum Alignment

In the presence of spontaneous symmetry breaking, the alignment of the vacuum with respect to the gauge group is often controlled by quadratically divergent operators in the low energy non-linear sigma model. In principle the magnitudes and signs of these operators can be changed by making different assumptions about the ultraviolet physics, but in practice all known ways of regulating these theories preserve the naive vacuum alignment. We show that by "integrating in" different sets of heavy spin-one fields, it is possible to UV extend certain non-linear sigma models into two distinct UV insensitive theories. These UV extensions have identical low energy degrees of freedom but different radiative potentials, making it possible to engineer two different vacuum alignments for the original non-linear sigma model. Our construction employs "non-square" theory spaces which generically violate the common lore that the preferred vacuum alignment preserves the maximal gauge symmetry. By UV extending the SO(9)/(SO(4) X SO(5)) little Higgs model, we find a radiative potential that deviates from the naive expectation but does not stabilize the correct vacuum for proper electroweak symmetry breaking.

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