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We introduce on-shell variables for Heavy Particle Effective Theories (HPETs) with the goal of extending Heavy Black Hole Effective Theory to higher spins and of facilitating its application to higher post-Minkowskian orders. These variables inherit the separation of spinless and spin-inclusive effects from the HPET fields, resulting in an explicit spin-multipole expansion of the three-point amplitude for any spin. By matching amplitudes expressed using the on-shell HPET variables to those derived from the one-particle effective action, we find that the spin-multipole expansion of a heavy spin-$s$ particle corresponds exactly to the multipole expansion (up to order $2s$) of a Kerr black hole, that is, without needing to take the infinite spin limit. Finally, we show that tree-level radiative processes with same-helicity bosons emitted from a heavy spin-$s$ particle exhibit a spin-multipole universality.

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A bstract
In this work we derive for the first time the complete gravitational cubic-in-spin effective action at the next-to-leading order in the post-Newtonian (PN) expansion for the interaction of generic compact binaries via the effective field theory for gravitating spinning objects, which we extend in this work. This sector, which enters at the fourth and a half PN (4.5PN) order for rapidly-rotating compact objects, completes finite-size effects up to this PN order, and is the first sector completed beyond the current state of the art for generic compact binary dynamics at the 4PN order. At this order in spins with gravitational nonlinearities we have to take into account additional terms, which arise from a new type of worldline couplings, due to the fact that at this order the Tulczyjew gauge for the rotational degrees of freedom, which involves the linear momentum, can no longer be approximated only in terms of the four-velocity. One of the main motivations for us to tackle this sector is also to see what happens when we go to a sector, which corresponds to the gravitational Compton scattering with quantum spins larger than one, and maybe possibly also get an insight on the inability to uniquely fix its amplitude from factorization when spins larger than two are involved. A general observation that we can clearly make already is that even-parity sectors in the order of the spin are easier to handle than odd ones. In the quantum context this corresponds to the greater ease of dealing with bosons compared to fermions.

Abstract We introduce a — somewhat holographic — dictionary between gravitational observables for scattering processes (measured at the boundary) and adiabatic invariants for bound orbits (in the bulk), to all orders in the Post-Minkowskian (PM) expansion. Our map relies on remarkable connections between the relative momentum of the twobody problem, the classical limit of the scattering amplitude and the deflection angle in hyperbolic motion. These relationships allow us to compute observables for generic orbits (such as the periastron advance ∆Φ) through analytic continuation, via a radial action depending only on boundary data. A simplified (more geometrical) map can be obtained for circular orbits, enabling us to extract the orbital frequency as a function of the (conserved) binding energy, Ω(E), directly from scattering information. As an example, using the results in Bernet al. [36, 37], we readily derive Ω(E) and ∆Φ(J, E) to two-loop orders. We also provide closed-form expressions for the orbital frequency and periastron advance at tree-level and one-loop order, respectively, which capture a series of exact terms in the Post-Newtonian expansion. We then perform a partial PM resummation, using a no-recoil approximation for the amplitude. This limit is behind the map between the scattering angle for a test-particle and the two-body dynamics to 2PM. We show that it also captures a subset of higher order terms beyond the test-particle limit. While a (rather lengthy) Hamiltonian may be derived as an intermediate step, our map applies directly between gauge invariant quantities. Our findings provide a starting point for an alternative approach to the binary problem. We conclude with future directions and some speculations on the classical double copy.

We apply on-shell methods to the bottom-up construction of electroweak amplitudes, allowing for both renormalizable and non-renormalizable interactions. We use the little-group covariant massive-spinor formalism, and flesh out some of its details along the way. Thanks to the compact form of the resulting amplitudes, many of their properties, and in particular the constraints of perturbative unitarity, are easily seen in this formalism. Our approach is purely bottom-up, assuming just the standard-model electroweak spectrum as well as the conservation of electric charge and fermion number. The most general massive three-point amplitudes consistent with these symmetries are derived and studied in detail, as the primary building blocks for the construction of scattering amplitudes. We employ a simple argument, based on tree-level unitarity of four-point amplitudes, to identify the three-point amplitudes that are non-renormalizable at tree level. This bottom-up analysis remarkably reproduces many low-energy relations implied by electroweak symmetry through the standard-model Higgs mechanism and beyond it. We then discuss four-point amplitudes. The gluing of three-point amplitudes into four-point amplitudes in the massive spinor helicity formalism is clarified. As an example, we work out the ψcψ Zh amplitude, including also the non-factorizable part. The latter is an all-order expression in the effective-field-theory expansion. Further constraints on the couplings are obtained by requiring perturbative unitarity. In the ψcψ Zh example, one for instance obtains the renormalizable-level relations between vector and fermion masses and gauge and Yukawa couplings. We supplement our bottom-up derivations with a matching of three- and fourpoint amplitude coefficients onto the standard-model effective field theory (SMEFT) in the broken electroweak phase. This establishes the correspondence with the usual Lagrangian approach and paves the way for SMEFT computations in the on-shell formalism.

A bstract
We develop a general formalism for computing classical observables for relativistic scattering of spinning particles, directly from on-shell amplitudes. We then apply this formalism to minimally coupled Einstein-gravity amplitudes for the scattering of massive spin 1/2 and spin 1 particles with a massive scalar, constructed using the double copy. In doing so we reproduce recent results at first post-Minkowskian order for the scattering of spinning black holes, through quadrupolar order in the spin-multipole expansion.

A bstract
We present a map between the tree-level Standard Model Effective Theory (SMEFT) in the Warsaw basis and massive on-shell amplitudes. As a first step, we focus on the electroweak sector without fermions. We describe the Feynman rules for a particular choice of input scheme and compare them with the 3-point massive amplitudes in the broken phase. Thereby we fix an on-shell basis which allows us to study scattering amplitudes with recursion relations. We hope to open up new avenues of exploration to a complete formulation of massive EFTs in the on-shell language.

A bstract
We formulate an effective field theory describing large mass scalars and fermions minimally coupled to gravity. The operators of this effective field theory are organized in powers of the transfer momentum divided by the mass of the matter field, an expansion which lends itself to the efficient extraction of classical contributions from loop amplitudes in both the post-Newtonian and post-Minkowskian regimes. We use this effective field theory to calculate the classical and leading quantum gravitational scattering amplitude of two heavy spin-1/2 particles at the second post-Minkowskian order.

The aim of this note is to describe the computation of post-Minkowskian Hamiltonians in modified theories of gravity. Exploiting a recent relation between scattering amplitudes of massive scalars and potentials for relativistic point-particles we derive a contribution to post-Minkowskian Hamiltonians at second order in the Newton's constant coming from R3 modifications in General Relativity. Using this result we calculate the associated contribution to the scattering angle for binary black holes at second post-Minkowskian order, showing agreement in the non-relativistic limit with previous results for the bending angle of a massless particle around a static massive source in R3 theories. Keywords: Post-Minkowskian Hamiltonians, Scattering angle, Cubic gravity

We study the link between classical scattering of spinning black holes and quantum amplitudes for massive spin-s particles. Generic spin orientations of the black holes are considered, allowing their spins to be deflected on par with their momenta. We rederive the spin-exponentiated structure of the relevant tree-level amplitude from minimal coupling to Einstein’s gravity, which in the s→∞ limit generates the black holes’ complete series of spin-induced multipoles. The resulting scattering function is seen to encode in a simple way the known net changes in the black-hole momenta and spins at first post-Minkowskian order. We connect our findings to a rigorous framework developed elsewhere for computing such observables from amplitudes.

We describe the computation of post-Minkowskian Hamiltonians in general relativity from scattering amplitudes. Using a relativistic Lippmann-Schwinger equation, we relate perturbative amplitudes of massive scalars coupled to gravity to the post-Minkowskian Hamiltonians of classical general relativity to any order in Newton’s constant. We illustrate this by deriving a Hamiltonian for binary black holes without spin up to second order in the post-Minkowskian expansion and explicitly demonstrate the equivalence with the recently proposed method based on an effective field theory matching.

A bstract
We provide evidence that the classical scattering of two spinning black holes is controlled by the soft expansion of exchanged gravitons. We show how an exponentiation of Cachazo-Strominger soft factors, acting on massive higher-spin amplitudes, can be used to find spin contributions to the aligned-spin scattering angle, conjecturally extending previously known results to higher orders in spin at one-loop order. The extraction of the classical limit is accomplished via the on-shell leading-singularity method and using massive spinor-helicity variables. The three-point amplitude for arbitrary-spin massive particles minimally coupled to gravity is expressed in an exponential form, and in the infinite-spin limit it matches the effective stress-energy tensor of the linearized Kerr solution. A four-point gravitational Compton amplitude is obtained from an extrapolated soft theorem, equivalent to gluing two exponential three-point amplitudes, and becomes itself an exponential operator. The construction uses these amplitudes to: 1) recover the known tree-level scattering angle at all orders in spin, 2) recover the known one-loop linear-in-spin interaction, 3) match a previous conjectural expression for the one-loop scattering angle at quadratic order in spin, 4) propose new one-loop results through quartic order in spin. These connections link the computation of higher-multipole interactions to the study of deeper orders in the soft expansion.

A bstract
In this paper, we explore the physics of electromagnetically and gravitationally coupled massive higher spin states from the on-shell point of view. Starting with the three-point amplitude, we focus on the simplest amplitude characterized by matching to minimal coupling in the UV. In the IR, for charged states this leads to g = 2 for arbitrary spin, and the leading deformation corresponds to the anomalous magnetic dipole moment. We proceed to construct the (gravitational) Compton amplitude for generic spins via consistent factorization. We find that in gravitation couplings, the leading deformation leads to inconsistent factorization. This implies that for systems with Gauge ² = Gravity relations, such as perturbative string theory, all charged states must have g = 2. It is then natural to ask for generic spin, what is the theory that yields such minimal coupling. By matching to the one body effective action, we verify that for large spins the answer is Kerr black holes. This identification is then an on-shell avatar of the no- hair theorem. Finally using this identification as well as the newly constructed Compton amplitudes, we proceed to compute the spin-dependent pieces for the classical potential at 2PM order up to degree four in spin operator of either black holes.

We present the amplitude for classical scattering of gravitationally interacting massive scalars at third post-Minkowskian order. Our approach harnesses powerful tools from the modern amplitudes program such as generalized unitarity and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. Adapting methods for integration and matching from effective field theory, we extract the conservative Hamiltonian for compact spinless binaries at third post-Minkowskian order. The resulting Hamiltonian is in complete agreement with corresponding terms in state-of-the-art expressions at fourth post-Newtonian order as well as the probe limit at all orders in velocity. We also derive the scattering angle at third post-Minkowskian order.

Weoutline the program to apply modern quantum field theory methods to calculate observables in classical general relativity through a truncation to classical terms of the multigraviton, two-body, on-shell scattering amplitudes between massive fields. Since only long-distance interactions corresponding to nonanalytic pieces need to be included, unitarity cuts provide substantial simplifications for both post-Newtonian and post-Minkowskian expansions. We illustrate this quantum field theoretic approach to classical general relativity by computing the interaction potentials to second order in the post-Newtonian expansion, as well as the scattering functions for two massive objects to second order in the post-Minkowskian expansion. We also derive an all-order exact result for gravitational light-by-light scattering.

We combine tools from effective field theory and generalized unitarity to construct a map between on-shell scattering amplitudes and the classical potential for interacting spinless particles. For general relativity, we obtain analytic expressions for the classical potential of a binary black hole system at second order in the gravitational constant and all orders in velocity. Our results exactly match all known results up to fourth post-Newtonian order, and offer a simple check of future higher order calculations. By design, these methods should extend to higher orders in perturbation theory.

We demonstrate equivalences, under simple mappings, between the dynamics of three distinct systems---(i) an arbitrary-mass-ratio two-spinning-black-hole system, (ii) a spinning test black hole in a background Kerr spacetime, and (iii) geodesic motion in Kerr---when each is considered in the first post-Minkowskian (1PM) approximation to general relativity, i.e. to linear order $G$ but to all orders in $1/c$, and to all orders in the black holes' spins, with all orders in the multipole expansions of their linearized gravitational fields. This is accomplished via computations of the net results of weak gravitational scattering encounters between two spinning black holes, namely the net $O(G)$ changes in the holes' momenta and spins as functions of the incoming state. The results are given in remarkably simple closed forms, found by solving effective Mathisson-Papapetrou-Dixon-type equations of motion for a spinning black hole in conjunction with the linearized Einstein equation, with appropriate matching to the Kerr solution. The scattering results fully encode the gauge-invariant content of a canonical Hamiltonian governing binary-black-hole dynamics at 1PM order, for generic (unbound and bound) orbits and spin orientations. We deduce one such Hamiltonian, which reproduces and resums the 1PM parts of all such previous post-Newtonian results, and which directly manifests the equivalences with the test-body limits via simple effective-one-body mappings.

A bstract
We provide universal expressions for the classical piece of the amplitude given by the graviton/photon exchange between massive particles of arbitrary spin, at both tree and one loop level. In the gravitational case this leads to higher order terms in the post-Newtonian expansion, which have been previously used in the binary inspiral problem. The expressions are obtained in terms of a contour integral that computes the Leading Singularity, which was recently shown to encode the relevant information up to one loop. The classical limit is performed along a holomorphic trajectory in the space of kinematics, such that the leading order is enough to extract arbitrarily high multipole corrections. These multipole interactions are given in terms of a recently proposed representation for massive particles of any spin by Arkani-Hamed et al. This explicitly shows universality of the multipole interactions in the effective potential with respect to the spin of the scattered particles. We perform the explicit match to standard EFT operators for S = $$ \frac{1}{2} $$ 1 2 and S = 1. As a natural byproduct we obtain the classical pieces up to one loop for the bending of light.

A bstract
In this work we propose to use leading singularities to obtain the classical pieces of amplitudes of two massive particles whose only interaction is gravitational. Leading singularities are generalizations of unitarity cuts. At one-loop we find that leading singularities obtained by multiple discontinuities in the t-channel contain all the classical information. As the main example, we show how to obtain a compact formula for the fully relativistic classical one-loop contribution to the scattering of two particles with different masses. The non-relativistic limit of the leading singularity agrees with known results in the post-Newtonian expansion. We also compute a variety of higher loop leading singularities including some all-loop families and study some of their properties.

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0 × 10[superscript -21]. It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410[+160 over -180] Mpc corresponding to a redshift z = 0.09[+0.03 over -0.04]. In the source frame, the initial black hole masses are 36[+5 over -4]M[subscript ⊙] and 29[+4 over -4]M[subscript ⊙], and the final black hole mass is 62[+4 over -4]M[subscript ⊙], with 3.0[+0.5 over -0.5]M[subscript ⊙]c[superscript 2] radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

We compute the leading post-Newtonian and quantum corrections to the Coulomb
and Newtonian potentials using the full modern arsenal of on-shell techniques;
we employ spinor-helicity variables everywhere, use the Kawai-Lewellen-Tye
(KLT) relations to derive gravity amplitudes from gauge theory and use
unitarity methods to extract the terms needed at one-loop order. We stress that
our results are universal and thus will hold in any quantum theory of gravity
with the same low-energy degrees of freedom as we are considering. Previous
results for the corrections to the same potentials, derived historically using
Feynman graphs, are verified explicitly, but our approach presents a huge
simplification, since starting points for the computations are compact and
tedious index contractions and various complicated integral reductions are
eliminated from the onset, streamlining the derivations. We also analyze the
spin dependence of the results using the KLT factorization, and show how the
spinless correction in the framework are easily seen to be independent of the
interacting matter considered.

Employing induced representations of the Lorentz group (Wigner's little group
construction), formalism for constructing heavy particle effective Lagrangians
is developed, and Lagrangian constraints enforcing Lorentz invariance of the S
matrix are derived. The relationship between Lorentz invariance and
reparameterization invariance is established and it is shown why a standard
ansatz for implementing reparameterization invariance in heavy fermion
effective Lagrangians breaks down at order 1/M^4. Formalism for fields of
arbitrary spin and for self-conjugate fields is presented, and the extension to
effective theories of massless fields is discussed.

The classical effects that arise from the loop diagrams and the relationship between the classical terms and the long range effects of massless particles were investigated. The loop expansion associates factor of h̄ with each loop, which suggests the tree diagrams to associate with classical physics. It was observed that the presence of classical corrections were associated with a specific nonanalytic term in momentum space. The results show that the in the presence of at least two massless propagators, classical physics can arise from loop contributions.

Using the novel diagrammatic rules recently proposed by Cachazo, Svrcek, and Witten, I give a compact, manifestly Lorentz-invariant form for tree-level gauge-theory amplitudes with three opposite helicities. Comment: 12 pages, 1 figure

We treat general relativity as an effective field theory, obtaining the full nonanalytic component of the scattering matrix potential to one-loop order. The lowest order vertex rules for the resulting effective field theory are presented and the one-loop diagrams which yield the leading nonrelativistic post-Newtonian and quantum corrections to the gravitational scattering amplitude to second order in G are calculated in detail. The Fourier transformed amplitudes yield a nonrelativistic potential and our result is discussed in relation to previous calculations. The definition of a potential is discussed as well and we show how the ambiguity of the potential under coordinate changes is resolved. Comment: 27 pages, 17 figures

A technique for translating the classical scattering function of two gravitationally interacting bodies into a corresponding (effective one-body) Hamiltonian description has been recently introduced [Phys.\ Rev.\ D {\bf 94}, 104015 (2016)]. Using this technique, we derive, for the first time, to second-order in Newton's constant (i.e. one classical loop) the Hamiltonian of two point masses having an arbitrary (possibly relativistic) relative velocity. The resulting (second post-Minkowskian) Hamiltonian is found to have a tame high-energy structure which we relate both to gravitational self-force studies of large mass-ratio binary systems, and to the ultra high-energy quantum scattering results of Amati, Ciafaloni and Veneziano. We derive several consequences of our second post-Minkowskian Hamiltonian: (i) the need to use special phase-space gauges to get a tame high-energy limit; and (ii) predictions about a (rest-mass independent) linear Regge trajectory behavior of high-angular-momenta, high-energy circular orbits. Ways of testing these predictions by dedicated numerical simulations are indicated. We finally indicate a way to connect our classical results to the quantum gravitational scattering amplitude of two particles, and we urge amplitude experts to use their novel techniques to compute the 2-loop scattering amplitude of scalar masses, from which one could deduce the third post-Minkowskian effective one-body Hamiltonian.

A novel approach to the Effective One-Body description of gravitationally interacting two-body systems is introduced. This approach is based on the post-Minkowskian approximation scheme (perturbation theory in G, without assuming small velocities), and employs a new dictionary focussing on the functional dependence of the scattering angle on the total energy and the total angular momentum of the system. Using this approach, we prove to all orders in v/c two results that were previously known to hold only to a limited post-Newtonian accuracy: (i) the relativistic gravitational dynamics of a two-body system is equivalent, at first post-Minkowskian order, to the relativistic dynamics of an effective test particle moving in a Schwarzschild metric; and (ii) this equivalence requires the existence of an exactly quadratic map between the real (relativistic) two-body energy and the (relativistic) energy of the effective particle. The same energy map is also shown to apply to the effective one-body description of two masses interacting via tensor-scalar gravity.

We give an introduction to the heavy-quark effective theory and the $1/m_Q$ expansion, which provide the modern framework for a systematic, model-independent description of the properties and decays of hadrons containing a heavy quark. We discuss the applications of these concepts to spectroscopy and to the weak decays of $B$ mesons.

The reparameterization invariance in Heavy Quark Effective Theory is reconsidered. Starting from an effective Lagrangian derived from QCD full theory, a consistent transformation law for the heavy quark effective field under the variation of the parameter upsilon is obtained and the reparameterization invariance in the effective Lagrangian is shown.

The next-to-next-to-leading order spin-squared interaction potential for
generic compact binaries is derived for the first time via the effective field
theory for gravitating spinning objects in the post-Newtonian scheme. The
spin-squared sector constitutes an intricate sector, as it requires the
consideration of the point particle action beyond minimal coupling, and mainly
involves the spin-squared worldline couplings, which are quite complex,
compared to the worldline couplings from the minimal coupling part of the
action. This sector also involves the linear in spin couplings, as we go up in
the loop order, i.e.~in the nonlinearity of the interaction. Hence, we
encounter here a proliferation of the relevant Feynman diagrams, and a
significant increase of the computational complexity. We present the evaluation
of the interaction potential in detail, going over all contributing diagrams.
The computation employs the nonrelativistic gravitational fields, which are
also advantageous for spin dependent sectors. This spin-squared correction,
which enters at the fourth post-Newtonian order for rapidly rotating compact
objects, completes the conservative sector up to the fourth post-Newtonian
accuracy. The robustness of the effective field theory for gravitating spinning
objects is shown here once again, as demonstrated in a recent series of papers
by the authors, which obtained all spin dependent sectors, required up to the
fourth post-Newtonian accuracy. The effective field theory of spinning objects
allows to directly obtain the equations of motion, and to obtain corresponding
Hamiltonians in a straightforward manner, and these will be derived for the
potential obtained here in a forthcoming paper.

An effective field theory for gravitating spinning objects in the
post-Newtonian approximation is formulated in the context of the binary
inspiral problem. We aim at an effective action, where all field modes below
the orbital scale are integrated out. We spell out the relevant degrees of
freedom, in particular the rotational ones, and the associated symmetries.
Building on these symmetries, we introduce the minimal coupling part of the
point particle action in terms of gauge rotational variables. We then proceed
to construct the spin-induced nonminimal couplings, where we obtain the leading
order couplings to all orders in spin for the first time. We specify to a gauge
for the rotational variables, where the unphysical degrees of freedom are
eliminated already from the Feynman rules, and all the orbital field modes are
conveniently integrated out. The equations of motion of spin are then directly
obtained via a proper variation of the action, and they take on a simple form.
We implement this effective field theory for spin to derive all spin dependent
potentials up to next-to-leading order to quadratic level in spin, namely up to
the third post-Newtonian order for rapidly rotating compact objects. For the
implementations we use the nonrelativistic gravitational field decomposition,
which is found here to eliminate higher-loop Feynman diagrams also in spin
dependent sectors, and facilitates derivations. Finally, the corresponding
Hamiltonians are also straightforwardly obtained from the potentials derived
via this formulation. Thus, the formulation is ideal for the treatment of
further higher order spin dependent sectors.

We utilize generalized unitarity and recursion relations combined with
effective field theory(EFT) techniques to compute spin dependent interaction
terms for inspiralling binary systems in the post newtonian(PN) approximation.
Using these methods offers great computational advantage over traditional
techniques involving feynman diagrams, especially at higher orders in the PN
expansion. As a specific example, we reproduce the spin-orbit interaction up to
2.5 PN order as also the leading order $S^2$(3PN) hamiltonian for an arbitrary
massive object. We also obtain the unknown $S^3$(3.5PN) spin hamiltonian for an
arbitrary massive object in terms of its low frequency linear response to
gravitational perturbations, which was till now known only for a black hole.
Furthermore, we derive the missing $S^4$ Hamiltonian at leading order(4PN) for
an arbitrary massive object and establish that a minimal coupling of a massive
elementary particle to gravity leads to a black hole structure. Finally, the
Kerr metric is obtained as a series in $G_N$ by comparing the action of a test
particle in the vicinity of a spinning black hole to the derived potential.

The ``natural'' magnetic moment of a particle of spin S is generally
assumed to be that given by the Belinfante conjecture and has the
gyromagnetic ratio g=1/S. Thus, for the spin 1/2 electron we find the
Dirac value ge=2. However, in the standard model the charged W-boson, a
spin-one particle, is found to have gW+=2. We discuss this
result and argue that the natural value for any particle of spin S
should be g=2, independent of spin.

We show that classical space–times can be derived directly from the S-matrix for a theory of massive particles coupled to a massless spin two particle. As an explicit example we derive the Schwarzchild space–time as a series in GNGN. At no point of the derivation is any use made of the Einstein–Hilbert action or the Einstein equations. The intermediate steps involve only on-shell S-matrix elements which are generated via BCFW recursion relations and unitarity sewing techniques. The notion of a space–time metric is only introduced at the end of the calculation where it is extracted by matching the potential determined by the S-matrix to the geodesic motion of a test particle. Other static space–times such as Kerr follow in a similar manner. Furthermore, given that the procedure is action independent and depends only upon the choice of the representation of the little group, solutions to Yang–Mills (YM) theory can be generated in the same fashion. Moreover, the squaring relation between the YM and gravity three point functions shows that the seeds that generate solutions in the two theories are algebraically related. From a technical standpoint our methodology can also be utilized to calculate quantities relevant for the binary inspiral problem more efficiently then the more traditional Feynman diagram approach.

The explicit form for the spin projection operators introduced by Fronsdal is calculated for arbitrary spin and applied to first-order processes involving four fermions. The matrix element for the most general nonderivative interaction is found for the special case in which two of the particles have spin 1/2 . The method of relating matrix elements written in different orders is extended to this case. The theory is applied to the decay of the mu meson, extending the work of Caianiello. It is found that the experimental decay spectrum can be equally well fitted by an assignment of spin 1/2 or 32. The method is then applied to the Fermi decay of hyperons. Lifetimes are calculated for decays in which the initial particle has a spin of 1/2 or 32, and the final particles all have spin 1/2 . All the lifetimes are less than 2 orders of magnitude longer than the corresponding observed lifetimes for the normal mode of decay. The hypothesis of a universal Fermi interaction is extended to include fermions of arbitary spin. Under this hypothesis, the experimental muon spectrum is most closely reproduced with spin 32. The results also indicate that the muon has the same particle-antiparticle character as an electron of the same charge.

We present techniques which enable one to calculate quickly the amplitudes for many scattering processes in the high-energy limit. As an illustration of the method, these are applied to the diagrams for pp --> V + 0, 1 or 2 jets, where V = W+/- or Z0. The form of the results lends itself to immediate numerical evaluation.

In this paper we include spin and multipole moment effects in the formalism used to describe the motion of extended objects recently introduced in hep-th/0409156. A suitable description for spinning bodies is developed and spin-orbit, spin-spin, and quadrupole-spin Hamiltonians are found at leading order. The existence of tidal as well as self-induced finite size effects is shown, and the contribution to the Hamiltonian is calculated in the latter. It is shown that tidal deformations start formally at O(v6) and O(v10) for maximally rotating general and compact objects, respectively, whereas self-induced effects can show up at leading order. Agreement is found for the cases where the results are known.

The Rarita-Schwinger formalism for fermion fields is brought to a Lagrangian form in the case of arbitrary spin. The requirement that all differential equations of the field should follow from the variation of an action integral necessitates the introduction of additional fields in the theory. By demanding that these auxiliary variables vanish in the case of no interaction, an explicit form is obtained for the Lagrangian. The resulting theory is found to reproduce the usual formalism in the case of spin 3/2, and turns out to be in agreement with results obtained by Chang for spin values 5/2 and 7/2. The Galilean limit of the minimally coupled equations yields the minimal Galilean-invariant theory of Hagen and Hurley. The g factor turns out to be 1/s, in accordance with a long-standing conjecture.

An explicit form is obtained for the Lagrangian of an arbitrary-spin boson field. This is achieved by introducing auxiliary field variables which are required to vanish in the free-field limit. For s≤4 the results are found to be in agreement with those obtained by Chang. Canonical commutation rules are derived and the equations of motion are brought to first-order form, thereby facilitating the introduction of minimal electromagnetic coupling. It is found that, upon taking the Galilean limit, the (6s+1)-component Galilean-invariant theory of Hagen and Hurley results. The g factor is found to be 1/s, thereby confirming a long-standing conjecture.

The HQET and NRQCD Lagrangian is computed to order
αs/m3. The computation is performed using
dimensional regularization to regulate the ultraviolet and infrared
divergences. The results are consistent with reparametrization
invariance to order 1/m3. Some subtleties in the matching
conditions for NRQCD are discussed.

I construct a Lorentz invariant effective field theory description of QCD in the presence of heavy quarks at energies large compared to the QCD scale and small compared to the heavy quark mass, formalizing the ideas of Isgur and Wise and of Eichten and Hill. The theory is built by “integrating in” degrees of freedom to implement a superselection rule for the velocity of the heavy quark.

We present new recursion relations for tree amplitudes in gauge theory that give very compact formulas. Our relations give any tree amplitude as a sum over terms constructed from products of two amplitudes of fewer particles multiplied by a Feynman propagator. The two amplitudes in each term are physical, in the sense that all particles are on-shell and momentum conservation is preserved. This is striking, since it is just like adding certain factorization limits of the original amplitude to build up the full answer. As examples, we recompute all known tree-level amplitudes of up to seven gluons and show that our recursion relations naturally give their most compact forms. We give a new result for an eight-gluon amplitude, A(1+,2−,3+,4−,5+,6−,7+,8−). We show how to build any amplitude in terms of three-gluon amplitudes only.

Since fields in the heavy quark effective theory are described by both a velocity and a residual momentum, there is redundancy in the theory: small shifts in velocity may be absorbed into a redefinition of the residual momentum. We demonstrate that this trivial reparameterisation invariance has non-trivial consequences: it relates coefficients of terms of different orders in the expansion and requires linear combinations of these operators to be multiplicatively renormalised. For example, the operator in the effective lagrangian has zero anomalous dimension, coefficient one, and does not receive any non-perturbative contributions from matching conditions. We also demonstrate that this invariance severely restricts the forms of operators which may appear in chiral lagrangians for heavy particles.

Massive gravity has seen a resurgence of interest due to recent progress
which has overcome its traditional problems, yielding an avenue for addressing
important open questions such as the cosmological constant naturalness problem.
The possibility of a massive graviton has been studied on and off for the past
70 years. During this time, curiosities such as the vDVZ discontinuity and the
Boulware-Deser ghost were uncovered. We re-derive these results in a
pedagogical manner, and develop the St\"ukelberg formalism to discuss them from
the modern effective field theory viewpoint. We review recent progress of the
last decade, including the dissolution of the vDVZ discontinuity via the
Vainshtein screening mechanism, the existence of a consistent effective field
theory with a stable hierarchy between the graviton mass and the cutoff, and
the existence of particular interactions which raise the maximal effective
field theory cutoff and remove the ghosts. In addition, we review some
peculiarities of massive gravitons on curved space, novel theories in three
dimensions, and examples of the emergence of a massive graviton from
extra-dimensions and brane worlds.

Recent work involving virtual excitation of a spin (3/2) baryon resonance is seen to contain two distinct problems. The Feynman propagator for spin (3/2) from the Rarita-Schwinger formalism has often been mistaken for its on-mass-shell limit. In nonrelativistic work the direct channel exchange of a Delta resonance is normally included, but with the exclusion of a term for the intermediate anti-Delta. It is shown that both of these terms are of equal importance in the resonance region for the case of nucleon Compton scattering.

We implement at the Lagrangian level a natural'' electromagnetic coupling prescription, different from the minimal one, and proposed a long time ago by Weinberg. This prescription yields, for elementary particles of [ital arbitrary][minus][ital spin], a gyromagnetic ratio [ital g]=2 at the tree level. This value is already known to arise in renormalizable theories for spin 1/2 and spin 1, is suggested by the classical, relativistic equations of the spin polarization, and is also found for arbitrary-spin, charged excitations of the open string.

Recently, by using the known structure of one-loop scattering amplitudes for gluons in Yang-Mills theory, a recursion relation for tree-level scattering amplitudes has been deduced. Here, we give a short and direct proof of this recursion relation based on properties of tree-level amplitudes only.

We investigate all the four-body graviton interaction processes: $gX\rightarrow \gamma X$, $gX\rightarrow gX$, and $gg\rightarrow gg$ with $X$ as an elementary particle of spin less than two in the context of linearized gravity except the spin-3/2 case. We show explicitly that gravitational gauge invariance and Lorentz invariance cause every four-body graviton scattering amplitude to be factorized. We explore the implications of this factorization property by investigating polarization effects through the covariant density matrix formalism in each four-body graviton scattering process. Comment: 45 pages, figures are included (uses pictex), RevTex

We present an Effective Field Theory (EFT) 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: r_s, 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. 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.

A rigorous QCD analysis of the inclusive annihilation decay rates of heavy quarkonium states is presented. The effective-field-theory framework of nonrelativistic QCD is used to separate the short-distance scale of annihilation, which is set by the heavy quark mass $M$, from the longer-distance scales associated with quarkonium structure. The annihilation decay rates are expressed in terms of nonperturbative matrix elements of 4-fermion operators in nonrelativistic QCD, with coefficients that can be computed using perturbation theory in the coupling constant $\alpha_s(M)$. The matrix elements are organized into a hierarchy according to their scaling with $v$, the typical velocity of the heavy quark. An analogous factorization formalism is developed for the production cross sections of heavy quarkonium in processes involving momentum transfers of order $M$ or larger. The factorization formulas are applied to the annihilation decay rates and production cross sections of S-wave states, up to corrections of relative order $v^3$, and of P-wave states, up to corrections of relative order $v^2$. Comment: Revised to clarify the velocity-scaling rules for spin-flip transitions, to correct error estimates, and to emphasize probabilities of Fock states, rather than amplitudes, 117 pages in REVTEX plus 11 Postscript figures. Erratum to Phys. Rev. D article included as a separate file, 4 pages in REVTEX