37 research outputs found
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.Comment: 11 pages, no figure
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.Comment: 7 pages, 1 figur
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.Comment: 4 pages, 2 figure
A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory
We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour
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.Comment: 17 pages, 7 figure
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.Comment: 21 pages, 2 figures, 2 tables. Version to be published in PRD.
Improved discussion in Sec. III B. Added reference
Ginsparg-Wilson Pions Scattering in a Sea of Staggered Quarks
We calculate isospin 2 pion-pion scattering in chiral perturbation theory for
a partially quenched, mixed action theory with Ginsparg-Wilson valence quarks
and staggered sea quarks. We point out that for some scattering channels, the
power-law volume dependence of two pion states in nonunitary theories such as
partially quenched or mixed action QCD is identical to that of QCD. Thus one
can extract infinite volume scattering parameters from mixed action
simulations. We then determine the scattering length for both 2 and 2+1 sea
quarks in the isospin limit. The scattering length, when expressed in terms of
the pion mass and the decay constant measured on the lattice, has no
contributions from mixed valence-sea mesons, thus it does not depend upon the
parameter, C_Mix, that appears in the chiral Lagrangian of the mixed theory. In
addition, the contributions which nominally arise from operators appearing in
the mixed action O(a^2 m_q) Lagrangian exactly cancel when the scattering
length is written in this form. This is in contrast to the scattering length
expressed in terms of the bare parameters of the chiral Lagrangian, which
explicitly exhibits all the sicknesses and lattice spacing dependence allowed
by a partially quenched mixed action theory. These results hold for both 2 and
2+1 flavors of sea quarks.Comment: 27 pages, 3 figures. Mistakes corrected in Eqs. (37), (42). Improved
discussion in section 4 and related results in Eqs. (33), (37), (40) and
(42). Added references. Version to be published in PR
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.Comment: 24 pages, 1 figure
Type D spacetimes and the Weyl double copy
We study the double-copy relation between classical solutions in gauge theory and gravity, focusing on four-dimensional vacuum metrics of algebraic type D, a class that includes several important solutions. We present a double copy of curvatures that applies to all spacetimes of this type—the Weyl double copy—relating the curvature of the spacetime to an electromagnetic field strength. We show that the Weyl double copy is consistent with the previously known Kerr–Schild double copy, and in fact resolves certain ambiguities of the latter. The most interesting new example of the classical double copy presented here is that of the C-metric. This well-known solution, which represents a pair of uniformly accelerated black holes, is mapped to the Liénard–Wiechert potential for a pair of uniformly accelerated charges. We also present a new double-copy interpretation of the Eguchi–Hanson instanton