arXiv subjects

Donal O'Connell

Publications and source records attributed to Donal O'Connell.

At least 55 records · Page 3Linked to original sources

arXiv2012

Simple superamplitudes in higher dimensions

We provide simple superspaces based on a formulation of spinor helicity in general even dimensions. As a distinguishing feature these spaces admit a fermionic super-momentum conserving delta function solution to the on-shell supersymmetry Ward identities. Using these solutions, we present beautifully simple formulae for the complete three, four and five point superamplitudes in maximal super Yang-Mills theory in eight dimensions, and for the three and four point superamplitudes in ten dimensional type IIB supergravity. In addition, we discuss the exceptional kinematics of the three point amplitude, and the supersymmetric spinorial BCFW recursion, in general dimensions.

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arXiv2011

The Kinematic Algebra From the Self-Dual Sector

We identify a diffeomorphism Lie algebra in the self-dual sector of Yang-Mills theory, and show that it determines the kinematic numerators of tree-level MHV amplitudes in the full theory. These amplitudes can be computed off-shell from Feynman diagrams with only cubic vertices, which are dressed with the structure constants of both the Yang-Mills colour algebra and the diffeomorphism algebra. Therefore, the latter algebra is the dual of the colour algebra, in the sense suggested by the work of Bern, Carrasco and Johansson. We further study perturbative gravity, both in the self-dual and in the MHV sectors, finding that the kinematic numerators of the theory are the BCJ squares of the Yang-Mills numerators.

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arXiv2010

Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions

The spinor helicity formalism in four dimensions has become a very useful tool both for understanding the structure of amplitudes and also for practical numerical computation of amplitudes. Recently, there has been some discussion of an extension of this formalism to higher dimensions. We describe a particular implementation of the spinor-helicity method in ten dimensions. Using this tool, we study the tree-level S-matrix of ten dimensional super Yang-Mills theory, and prove that the theory enjoys a dual conformal symmetry. Implications for four-dimensional computations are discussed.

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arXiv2010

BCFW Recursion Relations and String Theory

We demonstrate that all tree-level string theory amplitudes can be computed using the BCFW recursion relations. Our proof utilizes the pomeron vertex operator introduced by Brower, Polchinski, Strassler, and Tan. Surprisingly, we find that in a particular large complex momentum limit, the asymptotic expansion of massless string amplitudes is identical in form to that of the corresponding field theory amplitudes. This observation makes manifest the fact that field-theoretic Yang-Mills and graviton amplitudes obey KLT-like relations. Moreover, we conjecture that in this large momentum limit certain string theory and field theory amplitudes are identical, and provide evidence for this conjecture. Additionally, we find a new recursion relation which relates tachyon amplitudes to lower-point tachyon amplitudes.

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arXiv2009

Mixed Action Effective Field Theory: an Addendum

We correct a mistake in the literature regarding the additive lattice spacing corrections to the mixed valence-sea meson mass and discuss the consequences for mixed action extrapolation formulae.

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arXiv2009

Universality of Mixed Action Extrapolation Formulae

Mixed action theories with chirally symmetric valence fermions exhibit very desirable features both at the level of the lattice calculations as well as in the construction and implementation of the low energy mixed action effective field theory. In this work we show that when such a mixed action effective field theory is projected onto the valence sector, both the Lagrangian and the extrapolation formulae become universal in form through next to leading order, for all variants of discretization methods used for the sea fermions. Our conclusion relies on the chiral nature of the valence quarks. The result implies that for all sea quark methods which are in the same universality class as QCD, the numerical values of the physical coefficients in the various mixed action chiral Lagrangians will be the same up to lattice spacing dependent corrections. This allows us to construct a prescription to determine the mixed action extrapolation formulae for a large class of hadronic correlation functions computed in partially quenched chiral perturbation theory at the one-loop level. For specific examples, we apply this prescription to the nucleon twist--2 matrix elements and the nucleon--nucleon system. In addition, we determine the mixed action extrapolation formula for the neutron EDM as this provides a nice example of a theta-dependent observable; these observables are exceptions to our prescription.

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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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arXiv2008

Signs of analyticity in fermion scattering

We show that the signs of the leading irrelevant interactions for Dirac fermions are constrained by the analytic structure of the S-matrix. If Regge behavior obtains, negative signs indicate the presence of higher-spin bound states that spoil the convergence of the dispersion integrals and drive the corresponding operators relevant. For nucleon-nucleon scattering, the negativity of some of the low-energy interactions signals the presence of a spin-1 bound state: the deuteron. We connect the divergence of the dispersion integral to the "Sommerfeld enhancement" of the cross-section for low-energy scattering. We also discuss how this illuminates potential pitfalls in using perturbative methods to understand the dependence of the low-energy nuclear interaction on the masses of the light quarks. Finally, we suggest the possibility of applying similar reasoning to the current-current operators in the electroweak effective lagrangian, where no bound states spoil convergence of the dispersion relations.

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arXiv2008

Causality as an emergent macroscopic phenomenon: The Lee-Wick O(N) model

In quantum mechanics the deterministic property of classical physics is an emergent phenomenon appropriate only on macroscopic scales. Lee and Wick introduced Lorentz invariant quantum theories where causality is an emergent phenomenon appropriate for macroscopic time scales. In this paper we analyze a Lee-Wick version of the O(N) model. We argue that in the large N limit this theory has a unitary and Lorentz invariant S matrix and is therefore free of paradoxes in scattering experiments. We discuss some of its acausal properties.

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arXiv2008

One-Loop Renormalization of Lee-Wick Gauge Theory

We examine the renormalization of Lee-Wick gauge theory to one loop order. We show that only knowledge of the wavefunction renormalization is necessary to determine the running couplings, anomalous dimensions, and vector boson masses. In particular, the logarithmic running of the Lee-Wick vector boson mass is exactly related to the running of the coupling. In the case of an asymptotically free theory, the vector boson mass runs to infinity in the ultraviolet. Thus, the UV fixed point of the pure gauge theory is an ordinary quantum field theory. We find that the coupling runs more quickly in Lee-Wick gauge theory than in ordinary gauge theory, so the Lee-Wick standard model does not naturally unify at any scale. Finally, we present results on the beta function of more general theories containing dimension six operators which differ from previous results in the literature.

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arXiv2007

Massive Vector Scattering in Lee-Wick Gauge Theory

We demonstrate that amplitudes describing scattering of longitudinally polarized massive vector bosons present in non-Abelian Lee-Wick gauge theory do not grow with energy and, hence, satisfy the constraints imposed by perturbative unitarity. This result contrasts with the widely-known violation of perturbative unitarity in the standard model with a very heavy Higgs. Our conclusions are valid to all orders of perturbation theory and depend on the existence of a formulation of the theory in which all operators are of dimension four or less. This can be thought of as a restriction on the kinds of higher dimension operator which can be included in the higher derivative formulation of the theory.

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arXiv2007

The Lee-Wick Standard Model

We construct a modification of the standard model which stabilizes the Higgs mass against quadratically divergent radiative corrections, using ideas originally discussed by Lee and Wick in the context of a finite theory of quantum electrodynamics. The Lagrangian includes new higher derivative operators. We show that the higher derivative terms can be eliminated by introducing a set of auxiliary fields; this allows for convenient computation and makes the physical interpretation more transparent. Although the theory is unitary, it does not satisfy the usual analyticity conditions.

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arXiv2007

Neutrino Masses in the Lee-Wick Standard Model

Recently, an extension of the standard model based on ideas of Lee and Wick has been discussed. This theory is free of quadratic divergences and hence has a Higgs mass that is stable against radiative corrections. Here, we address the question of whether or not it is possible to couple very heavy particles, with masses much greater than the weak scale, to the Lee-Wick standard model degrees of freedom and still preserve the stability of the weak scale. We show that in the LW-standard model the familiar see-saw mechanism for generating neutrino masses preserves the solution to the hierarchy puzzle provided by the higher derivative terms. The very heavy right handed neutrinos do not destabilize the Higgs mass. We give an example of new heavy degrees of freedom that would destabilize the hierarchy, and discuss a general mechanism for coupling other heavy degrees of freedom to the Higgs doublet while preserving the hierarchy.

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arXiv2007

Two Meson Systems with Ginsparg-Wilson Valence Quarks

Unphysical effects associated with finite lattice spacing and partial quenching may lead to the presence of unphysical terms in chiral extrapolation formulae. These unphysical terms must then be removed during data analysis before physical predictions can be made. In this work, we show that through next-to-leading order, there are no unphysical counterterms in the extrapolation formulae, expressed in lattice-physical parameters, for meson scattering lengths in theories with Ginsparg-Wilson valence quarks. Our work applies to most sea quark discretization, provided that chiral perturbation theory is a valid approximation. We demonstrate our results with explicit computations and show that, in favorable circumstances, the extrapolation formulae do not depend on the unknown constant C_Mix appearing at lowest order in the mixed action chiral Lagrangian. We show that the I=1 KK scattering length does not depend on C_Mix in contrast to the I=3/2 K-pi scattering length. In addition, we show that these observables combined with f_K / f_pi and the I=2 pi-pi scattering length share only two linearly independent sets of counterterms, providing a means to test the mixed action theory at one lattice spacing. We therefore make a prediction for the I=1 KK scattering length.

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arXiv2006

Regulator Dependence of the Proposed UV Completion of the Ghost Condensate

Recently, it was shown that a renormalizable theory of heavy fermions coupled to a light complex boson could generate an effective action for the boson with the properties required to violate Lorentz invariance spontaneously through the mechanism of ghost condensation. However, there was some doubt about whether this result depended on the choice of regulator. In this work, we adopt a non-perturbative, unitary lattice regulator and show that with this regulator the theory does not have the properties necessary to form a ghost condensate. Consequently, the statement that the theory is a UV completion of the Higgs phase of gravity is regulator dependent.

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arXiv2006

Minimal Extension of the Standard Model Scalar Sector

The minimal extension of the scalar sector of the standard model contains an additional real scalar field with no gauge quantum numbers. Such a field does not couple to the quarks and leptons directly but rather through its mixing with the standard model Higgs field. We examine the phenomenology of this model focusing on the region of parameter space where the new scalar particle is significantly lighter than the usual Higgs scalar and has small mixing with it. In this region of parameter space most of the properties of the additional scalar particle are independent of the details of the scalar potential. Furthermore the properties of the scalar that is mostly the standard model Higgs can be drastically modified since its dominant branching ratio may be to a pair of the new lighter scalars.

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arXiv2006

GW Meson Scattering on a Staggered Sea

We discuss the structure of the NLO corrections to the chiral formulae for mesonic scattering processes in mixed action simulations using Ginsparg-Wilson valence quarks and staggered sea quarks. In particular, we show that the analytic contribution of the NLO chiral Lagrangian is the same as in QCD. We also comment on how this result restricts the dependence of the amplitudes on the unknown parameter C_Mix appearing in the chiral theory appropriate for these systems. We conclude with some comments on the explicit scattering lengths.

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arXiv2006

The Story of \cal O: Positivity constraints in effective field theories

We propose a simple method for identifying operators in effective field theories whose coefficients must be positive by causality. We also attempt to clarify the relationship between diverse positivity arguments that have appeared in the literature. We conjecture that the superluminal perturbations identified in non-positive effective theories are generally connected to instabilities that develop near the cutoff scale. We discuss implications for the ghost condensate, the chiral Lagrangian, and the Goldstone bosons of theories with spontaneous Lorentz violation.

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