We propose a mechanism for stabilizing the size of the extra dimension in the Randall-Sundrum scenario. The potential for the modulus field that sets the size of the fifth dimension is generated by a bulk scalar with quartic interactions localized on the two 3-branes. The minimum of this potential yields a compactification scale that solves the hierarchy problem without fine tuning of parameters.Comment: 8 pages, LaTeX; minor typo correcte

Using Effective Field Theory (EFT) methods we present a Lagrangian formalism which describes the dynamics of non-relativistic extended objects coupled to gravity. The formalism is relevant to understanding the gravitational radiation power spectra emitted by binary star systems, an important class of candidate signals for gravitational wave observatories such as LIGO or VIRGO. The EFT allows for a clean separation of the three relevant scales: rs, the size of the compact objects, r the orbital radius and r/v, the wavelength of the physical radiation (where the velocity v is the expansion parameter). In the EFT radiation is systematically included in the v expansion without need to separate integrals into near zones and radiation zones. Using the EFT, we show that the renormalization of ultraviolet divergences which arise at v 6 in post-Newtonian (PN) calculations requires the presence of two non-minimal worldline gravitational couplings linear in the Ricci curvature. However, these operators can be removed by a redefinition of the metric tensor, so that the divergences at arising at v 6 have no physically observable effect. Because in the EFT finite size features are encoded in the coefficients of non-minimal couplings, this implies a simple proof of the decoupling of internal structure for spinless objects to at least order v 6 . Neglecting absorptive effects, we find that the power counting rules of the EFT indicate that the next set of short distance operators, which are quadratic in the curvature and are associated with tidal deformations, do not play a role until order v 10 . These operators, which encapsulate finite size properties of the sources, have coefficients that can be fixed by a matching calculation. By including the most general set of such operators, the EFT allows one to work within a point particle theory to arbitrary orders in v.

We explore the phenomenology of a stabilized modulus field in the RandallSundrum scenario. It is found that if the large separation between branes arises from a small bulk scalar mass then the modulus (i.e. radion) is likely to be lighter than the lowest Kaluza-Klein excitations of bulk fields, and consequently may be the first direct signature of the model. Four-dimensional general covariance completely determines the couplings of the modulus to Standard Model fields. The strength of these couplings is determined by a single parameter which is set by the TeV rather than the Planck scale. *

It is likely that the LHC will observe a color- and charge-neutral scalar whose decays are consistent with those of the standard model (SM) Higgs boson. The Higgs interpretation of such a discovery is not the only possibility. For example, electroweak symmetry breaking could be triggered by a spontaneously broken, nearly conformal sector. The spectrum of states at the electroweak scale would then contain a narrow scalar resonance, the pseudo-Goldstone boson of conformal symmetry breaking, with Higgs-boson-like properties. If the conformal sector is strongly coupled, this pseudodilaton may be the only new state accessible at high energy colliders. We discuss the prospects for distinguishing this mode from a minimal Higgs boson at the LHC and ILC. The main discriminants between the two scenarios are (i) cubic self-interactions and (ii) a potential enhancement of couplings to massless SM gauge bosons.

We construct perturbative classical solutions of the Yang-Mills equations coupled to dynamical point particles carrying color charge. By applying a set of color to kinematics replacement rules first introduced by Bern, Carrasco and Johansson (BCJ), these are shown to generate solutions of d-dimensional dilaton gravity, which we also explicitly construct. Agreement between the gravity result and the gauge theory double copy implies a correspondence between non-Abelian particles and gravitating sources with dilaton charge. When the color sources are highly relativistic, dilaton exchange decouples, and the solutions we obtain match those of pure gravity. We comment on possible implications of our findings to the calculation of gravitational waveforms in astrophysical black hole collisions, directly from computationally simpler gluon radiation in Yang-Mills theory.

Recently, Randall and Sundrum proposed a solution to the hierarchy problem where the background spacetime is five dimensional. There are two 3-branes, and the mass scale for fields that propagate on one of the 3-branes is exponentially suppressed relative to the fundamental scale of the theory, which is taken to be the Planck mass M Pl . In this Brief Report we show that bulk fields with a five dimensional mass term of order M Pl have, after integrating over the extra dimension, modes with four-dimensional masses that are exponentially suppressed as well. This opens the possibility that in this scenario the standard model matter fields may correspond to degrees of freedom that are not confined to a 3-brane. ͓S0556-2821͑99͒00822-X͔ PACS number͑s͒: 04.50.ϩh It has been recently proposed that the existence of additional compact spatial dimensions could account for the large hierarchy between the electroweak scale and the Planck scale ͓1͔. In these higher dimensional models, spacetime is usually taken to be the product of a four-dimensional spacetime and a compact n-manifold. While gravity can propagate freely through the extra dimensions, standard model fields are confined to four-dimensional spacetime. Observers in this threedimensional wall ͑a ''3-brane''͒ will then measure an effective Planck scale M Pl 2 ϭM nϩ2 V n , where V n is the volume of the compact space. If V n is large enough, the fundamental Planck scale M can be on the order of 1 TeV, removing the hierarchy between the weak and Planck scales. Unfortunately, the presence of large extra dimensions does not necessarily provide a completely satisfactory resolution of the hierarchy problem, which resurfaces in the form of the large ratio between M and the compactification scale c ϭV n Ϫ1/n . Randall and Sundrum ͓2͔ have proposed a higher dimensional scenario that is based on a non-factorizable geometry, and which accounts for the ratio between the Planck scale and weak scales without the need to introduce a large hierarchy between M and c . Their model consists of a spacetime with a single S 1 /Z 2 orbifold extra dimension. Threebranes with opposite tensions reside at the orbifold fixed points, and together with a finely tuned negative bulk cosmological constant serve as sources for five-dimensional gravity.1 The resulting spacetime metric contains a redshift factor which depends exponentially on the radius of the compactified dimension:where x are Lorentz coordinates on the four-dimensional surfaces of constant , and Ϫрр ͓with (x,) and (x,Ϫ) identified, and the 3-branes located at ϭ0,]. Here, r c sets the size of the extra dimension, and k is taken to be on the order of the Planck scale.It is shown in ͓2͔ that the four-dimensional Planck scale is given byso that M Pl is of order M. Also, a field confined to the 3-brane at ϭ with mass parameter m 0 will have a physical mass given by mϭm 0 e Ϫkr c . Thus, if kr c is around 12, the weak scale is dynamically generated while all fundamental mass scales are on the order of the Planck scale; i.e., there is no v...

In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian.The EFT also systematically captures "post-Minkowskian" corrections to the multipole expansion due to non-linear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the way, we encounter both logarithmic short distance (UV) and long wavelength (IR) divergences. We show that the UV divergences can be (1) absorbed into a renormalization of the multipole moments and (2) resummed via the renormalization group. The IR singularities are shown to cancel from properly defined physical observables. As a concrete example of the formalism, we use this EFT to reproduce a number of post-Newtonian corrections to the gravitational wave energy flux from non-relativistic binaries, including long distance effects up to 3PN (v 6 ) order. Our results verify that the factorization of scales proposed in the NRGR framework of Goldberger and Rothstein is consistent up to order 3PN.

We derive a long wavelength effective point particle description of four-dimensional Schwarzschild black holes. In this effective theory, absorptive effects are incorporated by introducing degrees of freedom localized on the worldline that mimic the interaction between the horizon and bulk fields.The correlation functions of composite operators in this worldline theory can be obtained by standard matching calculations. For example, we obtain the low frequency two-point function of multipole worldline operators by relating them to the long wavelength graviton black hole absorptive cross section. The effective theory is then used to predict the leading effects of absorption in several astrophysically motivated examples, including the dynamics of non-relativistic black hole binary inspirals and the motion of a small black hole in an arbitrary background geometry. Our results can be written compactly in terms of absorption cross sections, and can be easily applied to the dissipative dynamics of any compact object, e.g. neutron stars. The relation of our methodology to that developed in the context of the AdS/CFT correspondence is discussed.