Publications
97 results found
, 2023, Encyclopedia of Cosmology, The, Set 2: Frontiers in Cosmology (in 3 Volumes), ISBN: 9789811289699
Together, these volumes will be a comprehensive review of the most important current topics in cosmology, discussing the important concepts and current status in each field, covering both theory and observation.These three volumes are ...
De Rham C, Kożuszek J, Tolley AJ, et al., 2023, Dynamical formulation of ghost-free massive gravity, Physical Review D, Vol: 108, ISSN: 2470-0010
We present a formulation of ghost-free massive gravity with flat reference metric that exhibits the full nonlinear constraint algebraically, in a way that can be directly implemented for numerical simulations. Motivated by the presence of higher order operators in the low-energy effective description of massive gravity, we show how the inclusion of higher-order gradient (dissipative) terms leads to a well-posed formulation of its dynamics. The formulation is presented for a generic combination of the minimal and quadratic mass terms (the phenomenologically interesting case) on any background. For concreteness, we then focus on the numerical evolution of the minimal model for spherically symmetric gravitational collapse of scalar field matter. This minimal model does not carry the relevant interactions to switch on an active Vainshtein mechanism, at least in spherical symmetry, thus we do not expect to recover usual general relativity behavior even for small graviton mass. Nonetheless we may ask what the outcome of matter collapse is for this gravitational theory. Starting with small initial data far away from the center, we follow the matter through a nonlinear regime as it falls towards the origin. For sufficiently weak data the matter disperses. However for larger data we generally find that the classical evolution breaks down resulting in the theory becoming infinitely strongly coupled without the presence of an apparent horizon shielding this behavior from an asymptotic observer.
Piazza F, Tolley AJ, 2023, Subadditive average distances and quantum promptness, CLASSICAL AND QUANTUM GRAVITY, Vol: 40, ISSN: 0264-9381
Auclair P, Bacon D, Baker T, et al., 2023, Cosmology with the Laser Interferometer Space Antenna, Living Reviews in Relativity, Vol: 26, ISSN: 1433-8351
The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational-wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational-wave observations by LISA to probe the universe.
De Rham C, Jaitly S, Tolley AJ, 2023, Constraints on Regge behavior from IR physics, Physical Review D, Vol: 108, ISSN: 2470-0010
We consider positivity constraints applicable to the effective field theory (EFT) of gravity in arbitrary dimensions. By considering scattering of indefinite initial and final states, we highlight the existence of a gravitational scattering amplitude for which full crossing symmetry is manifest and utilize the recently developed crossing symmetric dispersion relations to derive compact nonlinear bounds. We show that the null constraints built into these dispersion relations lead to a finite energy sum rule for gravity which may be extended to a one-parameter family of continuous moment sum rules. These sum rules enforce a UV-IR relation which imposes constraints on both the Regge trajectory and residue. We also highlight a situation where the Regge trajectory is uniquely determined in terms of the sub-Regge scale amplitude. Generically the Regge behavior may be split into an IR sensitive part calculable within a given EFT, which mainly depends on the lightest fields in nature, and an IR independent part, which is subject to universal positivity constraints following from unitarity and analyticity.
Arun KG, Belgacem E, Benkel R, et al., 2022, New horizons for fundamental physics with LISA, LIVING REVIEWS IN RELATIVITY, Vol: 25, ISSN: 2367-3613
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- Citations: 40
Gonzalez MC, de Rham C, Pozsgay V, et al., 2022, Causal effective field theories, Physical Review D: Particles, Fields, Gravitation and Cosmology, Vol: 106, Pages: 1-25, ISSN: 1550-2368
Physical principles such as unitarity, causality, and locality can constrain the space of consistent effective field theories (EFTs) by imposing two-sided bounds on the allowed values of Wilson coefficients. In this paper, we consider the bounds that arise from the requirement of low energy causality alone, without appealing to any assumptions about UV physics. We focus on shift-symmetric theories, and consider bounds that arise from the propagation around both a homogeneous and a spherically symmetric scalar field background. We find that low energy causality, namely the requirement that there are no resolvable time advances within the regime of validity of the EFT, produces two-sided bounds in agreement with compact positivity constraints previously obtained from 2→2 scattering amplitude dispersion relations using full crossing symmetry.
Gerhardinger M, Giblin JTJJ, Tolley AJ, et al., 2022, Well-posed UV completion for simulating scalar Galileons, Physical Review D: Particles, Fields, Gravitation and Cosmology, Vol: 106, Pages: 1-10, ISSN: 1550-2368
The Galileon scalar field theory is a prototypical example of an effective field theory that exhibits the Vainshtein screening mechanism, which is incorporated into many extensions to Einstein gravity. The Galileon describes the helicity-zero mode of gravitational radiation, the presence of which has significant implications for predictions of gravitational waves from orbiting objects and for tests of gravity sensitive to additional polarizations. Because of the derivative nature of their interactions, Galileons are superficially not well posed as effective field theories. Although this property is properly understood merely as an artifact of the effective field theory truncation, and is not theoretically worrisome, at the practical level it nevertheless renders numerical simulation highly problematic. Notwithstanding, previous numerical approaches have successfully evolved the system for reasonable initial data by slowly turning on the interactions. We present here two alternative approaches to improving numerical stability in Galileon numerical simulations. One of these is a minor modification of previous approaches, which introduces a low-pass filter that amounts to imposing a UV cutoff together with a relaxation method of turning on interactions. The second approach amounts to constructing a (numerical) UV completion for which the dynamics of the high momentum modes is under control and for which it is unnecessary to slowly turn on nonlinear interactions. We show that numerical simulations of the UV theory successfully reproduce the correct Galileon dynamics at low energies, consistent with the low-pass filter method and with previous numerical simulations.
de Rham C, Tolley AJ, Zhang J, 2022, Causality constraints on gravitational effective field theories, Physical Review Letters, Vol: 128, Pages: 1-6, ISSN: 0031-9007
We consider the effective field theory of gravity around black holes, and show that the coefficients of the dimension-8 operators are tightly constrained by causality considerations. Those constraints are consistent with—but tighter than—previously derived causality and positivity bounds and imply that the effects of one of the dimension-8 operators by itself cannot be observable while remaining consistent with causality. We then establish in which regime one can expect the generic dimension-8 and lower order operators to be potentially observable while preserving causality, providing a theoretical prior for future observations. We highlight the importance of “infrared causality” and show that the requirement of “asymptotic causality” or net (sub)luminality would fail to properly diagnose violations of causality.
Chen CY-R, de Rham C, Margalit A, et al., 2022, A cautionary case of casual causality, The Journal of High Energy Physics, Vol: 25, Pages: 1-40, ISSN: 1029-8479
We distinguish between the notions of asymptotic causality and infrared causality for gravitational effective field theories, and show that the latter gives constraints consistent with gravitational positivity bounds. We re-explore the scattering of gravitational waves in a spherically symmetric background in the EFT of gravity in D ≥ 5, for which the leading-order correction to Einstein gravity is determined by the Gauss-Bonnet operator. We reproduce the known result that the truncated effective theory exhibits apparent time advances relative to the background geometry for specific polarisations, which naively signal a violation of causality. We show that by properly identifying the regime of validity of the effective theory, the apparent time advance can be shown to be unresolvable. To illustrate this, we identify specific higher-dimension operators in the EFT expansion which become large for potentially resolvable time advances, rendering the EFT expansion invalid. Our results demonstrate how staying within the confines of the EFT, neither infrared nor asymptotic causality are ever violated for Einstein-Gauss-Bonnet gravity, no matter how low the scale, and furthermore its causality can be understood without appealing to a precise UV completion such as string theory.
Alberte L, de Rham C, Jaitly S, et al., 2022, Reverse Bootstrapping: IR Lessons for UV Physics, PHYSICAL REVIEW LETTERS, Vol: 128, ISSN: 0031-9007
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- Citations: 22
Gonzalez MC, de Rham C, Tolley AJ, 2021, Scattering amplitudes for binary systems beyond GR, The Journal of High Energy Physics, Vol: 87, Pages: 1-36, ISSN: 1029-8479
Amplitude methods have proven to be a promising technique to perform Post-Minkowskian calculations used as inputs to construct gravitational waveforms. In this paper, we show how these methods can be extended beyond the standard calculations in General Relativity with a minimal coupling to matter. As proof of principle, we consider spinless particles conformally coupled to a gravitational helicity-0 mode. We clarify the subtleties in the matching procedure that lead to the potential for conformally coupled matter. We show that in the probe particle limit, we can reproduce well known results for the field profile. With the scattering amplitudes at hand, we compute the conservative potential and scattering angle for the binary system. We find that the result is a non trivial expansion that involves not only the coupling strengths, but also a non trivial dependence on the energy/momentum of the scattered particles.
Momeni A, Rumbutis J, Tolley AJ, 2021, Kaluza-Klein from colour-kinematics duality for massive fields, JOURNAL OF HIGH ENERGY PHYSICS, ISSN: 1029-8479
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- Citations: 13
Alberte L, de Rham C, Jaitly S, et al., 2021, QED positivity bounds, Physical Review D: Particles, Fields, Gravitation and Cosmology, Vol: 103, Pages: 1-26, ISSN: 1550-2368
We apply positivity bounds directly to a U(1) gauge theory with charged scalars and charged fermions, i.e., QED, minimally coupled to gravity. Assuming that the massless t-channel pole may be discarded, we show that the improved positivity bounds are violated unless new physics is introduced at the parametrically low scale Λnew∼(emMPl)1/2, consistent with similar results for scalar field theories, far lower than the scale implied by the weak gravity conjecture. This is sharply contrasted with previous treatments which focus on the application of positivity bounds to the low energy gravitational Euler-Heisenberg effective theory only. We emphasize that the low cutoff is a consequence of applying the positivity bounds under the assumption that the pole may be discarded. We conjecture an alternative resolution that a small amount of negativity, consistent with decoupling limits, is allowed and is not in conflict with standard UV completions, including weakly coupled ones.
Tolley AJ, Wang Z-Y, Zhou S-Y, 2021, New positivity bounds from full crossing symmetry, JOURNAL OF HIGH ENERGY PHYSICS, ISSN: 1029-8479
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- Citations: 72
Alberte L, de Rham C, Jaitly S, et al., 2020, Positivity bounds and the massless spin-2 pole, Physical Review D: Particles, Fields, Gravitation and Cosmology, Vol: 102, Pages: 1-34, ISSN: 1550-2368
The presence of a massless spin-2 field in an effective field theory results in a t-channel pole in the scattering amplitudes that precludes the application of standard positivity bounds. Despite this, recent arguments based on compactification to three dimensions have suggested that positivity bounds may be applied to the t-channel pole subtracted amplitude. If correct, this would have deep implications for UV physics and the weak gravity conjecture. Within the context of a simple renormalizable field theory coupled to gravity we find that applying these arguments would constrain the low-energy coupling constants in a way which is incompatible with their actual values. This contradiction persists on deforming the theory. Further enforcing the t-channel pole subtracted positivity bounds on such generic renormalizable effective theories coupled to gravity would imply new physics at a scale parametrically smaller than expected, with far-reaching implications. This suggests that generically the standard positivity bounds are inapplicable with gravity, and we highlight a number of issues that impinge on the formulation of a three-dimensional amplitude which simultaneously satisfies the required properties of analyticity, positivity, and crossing symmetry. We conjecture instead a modified bound that ought to be satisfied independently of the precise details of the high energy completion.
Momeni A, Rumbutis J, Tolley AJ, 2020, Massive gravity from double copy, The Journal of High Energy Physics, Vol: 30, Pages: 1-36, ISSN: 1029-8479
We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.
de Rham C, Tolley AJ, 2020, Causality in curved spacetimes: The speed of light and gravity, PHYSICAL REVIEW D, Vol: 102, Pages: 1-33, ISSN: 1550-7998
Within the low-energy effective field theories of quantum electrodynamics and gravity, the low-energy speed of light or that of gravitational waves can typically be mildly superluminal in curved spacetimes. Related to this, small scattering time advances relative to the curved background can emerge from known effective field theory coefficients for photons or gravitons. We clarify why these results are not in contradiction with causality, analyticity or Lorentz invariance, and highlight various subtleties that arise when dealing with superluminalities and time advances in the gravitational context. Consistent low-energy effective theories are shown to self-protect by ensuring that any time advance and superluminality calculated within the regime of validity of the effective theory is necessarily unresolvable, and cannot be argued to lead to a macroscopically larger light cone. Such considerations are particularly relevant for putting constraints on cosmological and gravitational effective field theories and we provide explicit criteria to be satisfied so as to ensure causality.
Barausse E, Berti E, Hertog T, et al., 2020, Prospects for fundamental physics with LISA, General Relativity and Gravitation, Vol: 52, Pages: 1-33, ISSN: 0001-7701
In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the very broad range of topics that might be relevant to LISA,we present here a sample of what we view as particularly promising fundamental physics directions. We organize these directions through a “science-first” approach that allows us to classify how LISA data can inform theoretical physics in a variety of areas. For each of these theoretical physics classes, we identify the sources that are currently expected to provide the principal contribution to our knowledge, and the areas that need further development. The classification presented here should not be thought of as cast in stone, but rather as a fluid framework that is amenable to change with the flow of new insights in theoretical physics.
Tolley AJ, 2020, TT(T)over-bar deformations, massive gravity and non-critical strings, JOURNAL OF HIGH ENERGY PHYSICS, ISSN: 1029-8479
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- Citations: 40
Alberte L, de Rham C, Momeni A, et al., 2020, EFT of interacting spin-2 fields, The Journal of High Energy Physics, Vol: 2020, Pages: 1-57, ISSN: 1029-8479
We consider the effective field theory of multiple interacting massive spin-2 fields. We focus on the case where the interactions are chosen so that the cutoff is the highest possible, and highlight two distinct classes of theories. In the first class, the mass eigenstates only interact through potential operators that carry no derivatives in unitary gauge at leading order. In the second class, a specific kinetic mixing between the mass eigenstates is included non-linearly. Performing a decoupling and ADM analysis, we point out the existence of a ghost present at a low scale for the first class of interactions. For the second class of interactions where kinetic mixing is included, we derive the full Λ3-decoupling limit and confirm the absence of any ghosts. Nevertheless both formulations can be used to consistently describe an EFT of interacting massive spin-2 fields which, for a suitable technically natural tuning of the EFT, have the same strong coupling scale Λ3. We identify the generic form of EFT corrections in each case. By using Galileon Duality transformations for the specific case of two massive spin-2 fields with suitable couplings, the decoupling limit theory is shown to be a bi-Galileon.
Alberte L, Rham CD, Momeni A, et al., 2019, Positivity constraints on interacting pseudo-linear spin-2 fields
We explore the effective field theory for single and multiple interactingpseudo-linear spin-2 fields. By applying forward limit positivity bounds, weshow that among the parameters contributing to elastic tree level scatteringamplitude, there is no region of compatibility of the leading interactions witha standard local UV completion. Our result generalizes to any number ofinteracting pseudo-linear spin-2 fields. This results have significantimplications for the organization of the effective field theory expansion forpseudo-linear fields.
de Rham C, Heisenberg L, Tolley AJ, 2019, Spin-2 fields and the weak gravity conjecture, Physical Review D: Particles, Fields, Gravitation and Cosmology, Vol: 100, Pages: 1-20, ISSN: 1550-2368
Recently, it has been argued that application of the weak gravity conjecture (WGC) to spin-2 fields implies a universal upper bound on the cutoff of the effective theory for a single spin-2 field. We point out here that these arguments are largely spurious, because of the absence of states carrying spin-2 Stückelberg U(1) charge, and because of incorrect scaling assumptions. Known examples such as Kaluza-Klein theory that respect the usual WGC do so because of the existence of a genuine U(1) field under which states are charged, as in the case of the Stückelberg formulation of spin-1 theories, for which there is an unambiguously defined U(1) charge. Theories of bigravity naturally satisfy a naive formulation of the WGC, MW<MPl, since the force of the massless graviton is always weaker than the massive spin-2 modes. It also follows that theories of massive gravity trivially satisfies this form of the WGC. We also point out that the identification of a massive spin-2 state in a truncated higher derivative theory, such as Einstein-Weyl-squared or its supergravity extension, bears no relationship with massive spin-2 states in the UV completion, contrary to previous statements in the literature. We also discuss the conjecture from a swampland perspective and show how the emergence of a universal upper bound on the cutoff relies on strong assumptions on the scale of the couplings between the spin-2 and other fields, an assumption which is known to be violated in explicit examples.
Alberte L, Rham CD, Momeni A, et al., 2019, Positivity constraints on interacting spin-2 fields
The consistency of the EFT of two interacting spin-2 fields is checked byapplying forward limit positivity bounds on the scattering amplitudes toexclude the region of parameter space devoid of a standard UV completion. Wefocus on two classes of theories that have the highest possible EFT cutoff,namely those theories modelled on ghost-free interacting theories of a singlemassive spin-2 field. We find that the very existence of interactions betweenthe spin-2 fields implies more stringent bounds on all the parameters of theEFT, even on the spin-2 self-interactions. This arises for two reasons. First,with every new field included in the low-energy EFT, comes the `knowledge' ofan extra pole to be subtracted, hence strengthening the positivity bounds.Second, while adding new fields increases the number of free parameters fromthe new interactions, this is rapidly overcome by the increased number ofpositivity bounds for different possible scattering processes. We also discusshow positivity bounds appear to favour relations between operators thateffectively raise the cutoff of the EFT.
Rham CD, Tolley AJ, 2019, The speed of gravity
Within the standard effective field theory of General Relativity, we showthat the speed of gravitational waves deviates, ever so slightly, fromluminality on cosmological and other spontaneously Lorentz-breakingbackgrounds. This effect results from loop contributions from massive fields ofany spin, including Standard Model fields, or from tree level effects frommassive higher spins $s \ge 2$. We show that for the choice of interactionsigns implied by S-matrix and spectral density positivity bounds suggested byanalyticity and causality, the speed of gravitational waves is in generalsuperluminal at low-energies on NEC preserving backgrounds, meaninggravitational waves travel faster than allowed by the metric to which photonsand Standard Model fields are minimally coupled. We show that departure of thespeed from unity increases in the IR and argue that the speed inevitablyreturns to luminal at high energies as required by Lorentz invariance.Performing a special tuning of the EFT so that renormalization sensitivecurvature-squared terms are set to zero, we find that finite loop correctionsfrom Standard Model fields still lead to an epoch dependent modification of thespeed of gravitational waves which is determined by the precise field contentof the lightest particles with masses larger than the Hubble parameter today.Depending on interpretation, such considerations could potentially havefar-reaching implications on light scalar models, such as axionic or fuzzy colddark matter.
de Rham C, Melville S, Tolley AJ, et al., 2019, Positivity bounds for massive spin-1 and spin-2 fields, The Journal of High Energy Physics, Vol: 2019, ISSN: 1029-8479
We apply the recently developed positivity bounds for particles with spin, applied away from the forward limit, to the low energy effective theories of massive spin-1 and spin-2 theories. For spin-1 theories, we consider the generic Proca EFT which arises at low energies from a heavy Higgs mechanism, and the special case of a charged Galileon for which the EFT is reorganized by the Galileon symmetry. For spin-2, we consider generic Λ5 massive gravity theories and the special ‘ghost-free’ Λ3 theories. Remarkably we find that at the level of 2-2 scattering, the positivity bounds applied to Λ5 massive gravity theories, impose the special tunings which generate the Λ3 structure. For Λ3 massive gravity theories, the island of positivity derived in the forward limit appears relatively stable against further bounds.
Dar F, de Rham C, Deskins JT, et al., 2019, Scalar gravitational radiation from binaries: Vainshtein mechanism in time-dependent systems, Classical and Quantum Gravity, Vol: 36, ISSN: 0264-9381
We develop a full four-dimensional numerical code to study scalar gravitational radiation emitted from binary systems and probe the Vainshtein mechanism in situations that break the static and spherical symmetry, relevant for binary pulsars as well as black holes and neutron stars binaries. The present study focuses on the cubic Galileon which arises as the decoupling limit of massive theories of gravity. Limitations associated with the numerical methods prevent us from reaching a physically realistic hierarchy of scales; nevertheless, within this context we observe the same power law scaling of the radiated power as previous analytic estimates, and confirm a strong suppression of the power emitted in the monopole and dipole as compared with quadrupole radiation. Following the trend to more physically realistic parameters, we confirm the suppression of the power emitted in scalar gravitational radiation and the recovery of general relativity with good accuracy. This paves the way for future numerical work, probing more generic, physically relevant situations and sets of interactions that may exhibit the Vainshtein mechanism.
Ondo NA, Tolley AJ, 2018, Deconstructing supergravity: massive supermultiplets, Journal of High Energy Physics, Vol: 2018, ISSN: 1029-8479
Given the success of the deconstruction program in obtaining ghost-free massive gravity from 5-D Einstein gravity, we propose a modification of the deconstruction procedure that incorporates supersymmetry at the linear level. We discuss the relevant limits of a conjectured interacting theory of a massive spin 2 supermultiplet, and determine the linear theory to be the N=1 Zinoviev theory, a supersymmetric extension of Fierz-Pauli theory. We develop a family of 1-site deconstruction procedures for fermionic fields (yielding Dirac and Majorana mass terms). The deconstruction procedure appropriate for giving fermions a Dirac mass is found to preserve half of the supersymmetry of the 5-D theory. We explicitly check this by deconstructing 5-D N=2 super-Maxwell theory down to 4-D N=1 super-Proca theory, and deconstructing linear 5-D N=2 supergravity down to 4-D N=1 Zinoviev theory, and derive the full 4-D supersymmetry algebras and Stückelberg symmetries from the 5-D superalgebras and gauge symmetries, respectively. We conjecture that this procedure should admit a generalization to fully non-linear theories.
de Rham C, Melville S, Tolley AJ, 2018, Improved positivity bounds and massive gravity, Journal of High Energy Physics, Vol: 2018, ISSN: 1029-8479
Theories such as massive Galileons and massive gravity can satisfy the presently known improved positivity bounds provided they are weakly coupled. We discuss the form of the EFT Lagrangian for a weakly coupled UV completion of massive gravity which closely parallels the massive Galileon, and perform the power counting of corrections to the scattering amplitude and the positivity bounds. The Vainshtein mechanism which is central to the phenomenological viability of massive gravity is entirely consistent with weak coupling since it is classical in nature. We highlight that the only implication of the improved positivity constraints is that the EFT cutoff is lower than previous assumed, and discuss the observable implications, emphasizing that these bounds are not capable of ruling out the model contrary to previous statements in the literature.
de Rham C, Melville S, Tolley AJ, et al., 2018, UV complete me: positivity bounds for particles with spin, Journal of High Energy Physics, Vol: 2018, ISSN: 1029-8479
For a low energy effective theory to admit a standard local, unitary, analytic and Lorentz-invariant UV completion, its scattering amplitudes must satisfy certain inequalities. While these bounds are known in the forward limit for real polarizations, any extension beyond this for particles with nonzero spin is subtle due to their non-trivial crossing relations. Using the transversity formalism (i.e. spin projections orthogonal to the scattering plane), in which the crossing relations become diagonal, these inequalities can be derived for 2-to-2 scattering between any pair of massive particles, for a complete set of polarizations at and away from the forward scattering limit. This provides a set of powerful criteria which can be used to restrict the parameter space of any effective field theory, often considerably more so than its forward limit subset alone.
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