Massive Spinning Particle Research Articles

Low-virtuality splitting in the Standard Model

When the available collision energy is much above the mass of the particles involved, scattering amplitudes feature kinematic configurations that are enhanced by the much lower virtuality of some intermediate particle. Such configurations generally factorise in terms of a hard scattering amplitude with exactly on-shell intermediate particle, times universal factors. In the case of real radiation emission, such factors are splitting amplitudes that describe the creation or the annihilation — for initial or final state splittings — of the low-virtuality particle and the creation of the real radiation particles. We compute at tree-level the amplitudes describing all the splittings that take place in the Standard Model when the collision energy is much above the electroweak scale. Unlike previous results, our splitting amplitudes fully describe the low-virtuality kinematic regime, which includes the region of collinear splitting, of soft emission, and combinations thereof. The splitting amplitudes are compactly represented as little-group tensors in an improved bi-spinor formalism for massive spin-1 particles that automatically incorporates the Goldstone Boson Equivalence Theorem. Simple explicit expressions are obtained using a suitably defined infinite-momentum helicity basis representation of the spinor variables. Our results, combined with the known virtual contributions, could enable systematic predictions of the leading electroweak radiation effects in high-energy scattering processes, with particularly promising phenomenological applications to the physics of future colliders with very high energy such as a muon collider.

Dark Matter-Dark Energy as Massive Bosons a Quantum Multi-Entanglement System with Dark Matter or Dark Energy as Some Massive Bosons-String Particles of Spin 2

A quantum multi-entanglement system with Dark matter or dark energy as some massive bosons-string particles of spin 2. Dark matter or dark energy are some particles of spin 2 instead of near spin 0 ones.

Gravitational production of completely dark photons with nonminimal couplings to gravity

Dark photons are a theorized massive spin-1 particle which can be produced via various mechanisms, including cosmological gravitational particle production (GPP) in the early universe. In this work, we extend previous results for GPP of dark photons to include nonminimal couplings to gravity. We find that nonminimal couplings can induce a ghost instability or lead to runaway particle production at high momentum and discuss the constraints on the parameter space such that the theory is free of instabilities. Within the instability-free regime we numerically calculate the particle production and find that the inclusion of nonminimal couplings can lead to an enhancement of the particle number. As a result, GPP of nonminimally coupled dark photons can open the parameter space for production of a cosmological relevant relic density (constituting all or part of the dark matter) as compared to the minimally-coupled theory. These results are independent of the choice of inflation model, which we demonstrate by repeating the analysis for a class of rapid-turn multi-field inflation models.

Gravity-matter sum rules in models with a single extra-dimension

We prove a set of sum rules needed for KK-graviton pair production from matter in orbifolded extra-dimensional models. The sum rules can be found in full generality by considering the properties of solutions to the Sturm-Liouville problem, which describes the wave functions and the masses of the KK-gravitons in four dimensions. They ensure cancellations in the amplitudes of the processes mentioned above which considerably reduce their growth with s in the high-energy limit. This protects extra-dimensional theories from the low-scale unitarity problems that plague other theories with massive spin-2 particles. We argue that such relations are valid for a broader category of models thus generalizing our previous results that were limited to the large μ limit of the Randall-Sundrum model.

Bigravity portal dark matter

We consider a model where the interaction between dark matter and the Standard Model particles is mediated by a ghost-free bigravity portal. The bigravity model invokes a massive spin-2 particle coupled to the usual massless graviton as well as generic bimetric matter couplings. The cross sections for dark matter direct detection are computed and confronted with the experimental bounds. The presence of the massive spin-2 mediator resolves the core-cusp problem, which in turn significantly constrains the dark matter coupling in such a bigravity theory. Yet, there remains a window of the parameter space where the model can be tested in the upcoming direct detection experiments such as XENONnT and PandaX-30T. The model also predicts a reheating temperature on the order of 106 GeV. Published by the American Physical Society 2024

Regge growth of isolated massive spin-2 particles and the Swampland

We consider an effective theory with a single massive spin-2 particle and a gap to the cutoff. We couple the spin-2 particle to gravity, and to other lower-spin fields, and study the growth of scattering amplitudes of the particle in the Regge regime: where s is much larger than t and also any mass scales in the effective theory, but still much lower than the cutoff scale of the theory and therefore any further massive spin-2 particles. We include in the effective theory all possible operators, with an arbitrary, but finite, number of derivatives. We prove that the scattering amplitude grows strictly faster than s2 in any such theory. Such fast growth goes against expected bounds on Regge growth. We therefore find further evidence for the Swampland spin-2 conjecture: that a theory with an isolated massive spin-2 particle, coupled to gravity, is in the Swampland.

Regge constraints on local four-point scattering amplitudes of massive particles with spin

In this work, we classify all the possible local four-point couplings relevant for tree-level flat space 2 → 2 scattering of external massive particles of spin one and spin two which do not grow faster than s2 at large s and fixed t. This kinematic constraint on local growth of tree-level S-matrices is known as Classical Regge Growth criteria or CRG [1]. We first construct the spin one and spin two tree-level contact S-matrices as modules of polarisation tensors and momenta over the ring of polynomials generated by Mandelstam invariants. We then consider a general scattering process where the external scattering particles are of different masses but of same spin and constrain this space to obtain a finite number of CRG allowed local Lagrangians. Our concrete results are primarily for D ≥ 8 but the process outlined is easily generalised to lower dimensions to include low dimensional parity violating structures. The space of CRG allowed structures reduces when we specialise to identical scattering and restrict to parity even couplings in D = 4. We show that tree-level scattering amplitudes involving exchange diagrams and contact terms in de Rham-Gabadadze-Tolley massive gravity (dRGT) violate CRG unless the parameters of the theory take special values. The CRG allowed S-matrices, in the context of large N conformal field theories (CFTs), can also be interpreted as bulk AdS counterterms consistent with Chaos bound. Our classified structures therefore can be thought of as ambiguities arising in the context of conformal field theory inversion formula for four point functions of unconserved spin one and spin two operators in large N CFTs.

Hunting for hypercharge anapole dark matter in all spin scenarios

We conduct a combined analysis to investigate dark matter (DM) with hypercharge anapole moments, focusing on scenarios where Majorana DM particles with spin 1/2, 1, 3/2, and 2 interact exclusively with Standard Model particles through U(1)Y hypercharge anapole terms for the first time. For completeness, we construct general effective U(1) gauge-invariant three-point vertices. These enable the generation of hypercharge gauge-invariant interaction vertices for both a virtual photon γ and a virtual Z boson with two identical massive Majorana particles of any nonzero spin s, after the spontaneous breaking of electroweak gauge symmetry. For complementarity, we adopt effective operators tailored to each dark matter spin allowing crossing symmetry. We calculate the relic abundance, analyze current constraints and future sensitivities from dark matter direct detection and collider experiments, and apply the conceptual naive perturbativity bound. Our estimations based on a generalized vertex calculation demonstrate that the scenario with a higher-spin DM is more stringently constrained than a lower-spin DM, primarily due to the reduced annihilation cross section and/or the enhanced rate of LHC monojet events. As a remarkable outcome, the spin-2 anapole DM scenario is almost entirely excluded, while the high-luminosity LHC exhibits high sensitivities in probing spin-1 and -3/2 scenarios, except for a tiny parameter range of DM mass around 1 TeV. A significant portion of the remaining parameter space in the spin-1/2 DM scenario can be explored through upcoming Xenon experiments, with more than 20 ton-yr exposure equivalent to approximately 5 years of running the XENONnT experiment. Published by the American Physical Society 2024

Unitarity bounds on the massive spin-2 particle explanation of muon g-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g-2$$\\end{document} anomaly

Motivated by the long-standing discrepancy between the Standard Model prediction and the experimental measurement of the muon magnetic dipole moment, we have recently proposed to interpret this muon g-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g-2$$\\end{document} anomaly in terms of the loop effect induced by a new massive spin-2 field G. In the present paper, we investigate the unitarity bounds on this scenario. We calculate the s-wave projected amplitudes for two-body elastic scatterings of charged leptons and photons mediated by G at high energies for all possible initial and final helicity states. By imposing the condition of the perturbative unitarity, we obtain the analytic constraints on the charged-lepton-G and photon-G couplings. We then apply our results to constrain the parameter space relevant to the explanation of the muon g-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g-2$$\\end{document} anomaly.

Manifestly covariant worldline actions from coadjoint orbits. Part I. Generalities and vectorial descriptions

We derive manifestly covariant actions of spinning particles starting from coadjoint orbits of isometry groups, by using Hamiltonian reductions. We show that the defining conditions of a classical Lie group can be treated as Hamiltonian constraints which generate the coadjoint orbits of another, dual, Lie group. In case of (inhomogeneous) orthogonal groups, the dual groups are (centrally-extended inhomogeneous) symplectic groups. This defines a symplectic dual pair correspondence between the coadjoint orbits of the isometry group and those of the dual Lie group, whose quantum version is the reductive dual pair correspondence à la Howe. We show explicitly how various particle species arise from the classification of coadjoint orbits of Poincaré and (A)dS symmetry. In the Poincaré case, we recover the data of the Wigner classification, which includes continuous spin particles, (spinning) tachyons and null particles with vanishing momenta, besides the usual massive and massless spinning particles. In (A)dS case, our classification results are not only consistent with the pattern of the corresponding unitary irreducible representations observed in the literature, but also contain novel information. In dS, we find the presence of partially massless spinning particles, but continuous spin particles, spinning tachyons and null particles are absent. The AdS case shows the largest diversity of particle species. It has all particles species of Poincaré symmetry except for the null particle, but allows in addition various exotic entities such as one parameter extension of continuous particles and conformal particles living on the boundary of AdS. Notably, we also find a large class of particles living in “bitemporal” AdS space, including ones where mass and spin play an interchanged role. We also discuss the relative inclusion structure of the corresponding orbits.

Reconciling absence of vDVZ discontinuity with absence of ghosts in nonlocal linearized gravity

The modern massive gravity theories resolve a historical tension between the absence of the so called vDVZ mass discontinuity and the absence of ghosts via a fine tuned gravitational potential and a sophisticated screening mechanism. Those theories have originated the modern covariant bimetric models which are local, ghost free and cosmologically viable apparently, they contain a massive plus a massless graviton in the spectrum. It seems hard to solve the mentioned tension if we do insist in a model with a minimal number of degrees of freedom, with only one massive spin-2 particle in the spectrum, even if we allow nonlocal theories. Here we show that this problem can be circumvented in linearized nonlocal theories by the introduction of exponential terms with infinite derivatives. The model admits non linear completions via nonlocal quadratic terms in curvatures. We also investigate the role of the exponential factors in linearized models where the graviton remains massless and a mass scale is introduced via nonlocal terms, they are also ghost free and approach the Einstein–Hilbert theory as we go much above the introduced mass scale.

Collider constraints on massive gravitons coupling to photons

We study the discovery potential of massive graviton-like spin-2 particles coupled to standard model fields, produced in photon-photon collisions at the Large Hadron Collider (LHC) as well as in electron-positron (e+e−) collisions, within an effective theory with and without universal couplings. Our focus is on a massive graviton G coupled to the electromagnetic field, which decays via G→γγ and leads to a resonant excess of diphotons over the light-by-light scattering continuum at the LHC, and of triphoton final states at e+e− colliders. Based on similar searches performed for pseudoscalar axion-like particles (ALPs), and taking into account the different cross sections, γγ partial widths, and decay kinematics of the pseudoscalar and tensor particles, we reinterpret existing experimental bounds on the ALP-γ coupling into G-γ ones. Using the available data, exclusion limits on the graviton-photon coupling are set down to gGγ≈1–0.05 TeV−1 for masses mG≈100 MeV–2 TeV. Such bounds can be improved by factors of 100 at Belle II in the low-mass region, and of 4 at the HL-LHC at high masses, with their expected full integrated luminosities.

Violation of the Landau-Yang theorem from infrared Lorentz symmetry breaking

Lorentz symmetry forbids decays of massive spin-1 particle like the Z0 into two massless photons, a result known as the Landau-Yang theorem. But it is known that infrared effects can break Lorentz invariance. Employing the construction of Mund et al. [1] which incorporated this Lorentz violation, we propose an interaction leading to the decay Z0→ 2γ and study the dependence of the decay on the parameter of this Lorentz violation.

A braneworld model in a massive gravity

A Randall–Sundrum-like braneworld scenario is constructed in a 5D extension of the Lorentz-violating massive gravity. The gauge hierarchy problem is solved in current model. The linear perturbations are calculated, and it is found that the tensor and vector perturbations are robust and free from the ghost and tachyonic instabilities, however, the scalar perturbation is a ghost filed. After Kaluza–Klein reduction, all the tensor, vector and scalar modes are massive and possess the mass splitting of order of TeV in their respective mass spectra. The massive ground states of tensor and scalar modes propagate only along the brane, however, the vector ground state is absent in the mass spectrum. By introducing the Goldberger-Wise mechanism to stabilize the extra dimension, the 4D effective theory on the brane includes a nearly massless graviton plus three towers of very massive spin-2, spin-1 and ghost spin-0 particles.

Graviton-photon production with a massive spin-2 particle

Graviton-photon production with a massive spin-2 particle

Space-time origin of gauge symmetry

In this work, by a first principles calculation, we show that quantum states describing massive relativistic free spinning particles obey kinematical conditions whose origin can be traced to parity as a good quantum number. These conditions are at the root of the equations of motion and of the constraints satisfied by the corresponding fields. In the massless limit, well defined parity is lost but a symmetry emerges related to arbitrary changes in the unphysical parity components. It is shown that this emergent symmetry is the celebrated gauge symmetry.

Spin supplementary condition in quantum field theory: covariant SSC and physical state projection

The spin supplementary conditions are constraints on spin degrees of freedom in classical relativity which restricts physical degrees of freedom to rotations. It is argued that the equivalent constraints in quantum field theory are the projection conditions on polarisation tensors, which remove timelike/longitudinal polarisations from the physical spectrum. The claim is supported by three examples of massive spinning particles coupled to electromagnetism: Dirac and Proca fields in quantum field theory, and \U0001d4a9 = 1 worldline QFT for classical worldline theory. This suggests a resolution to the apparent discrepancy between effective field theory description of massive higher-spin fields [1, 2] and post-Newtonian effective field theory of spinning classical particles [3], where the former admits more unfixed parameters compared to the latter; the additional parameters are fixed by projection conditions and therefore are not tunable parameters.

Cosmological gravitational particle production of massive spin-2 particles

The phenomenon of cosmological gravitational particle production (CGPP) is expected to occur during the period of inflation and the transition into a hot big bang cosmology. Particles may be produced even if they only couple directly to gravity, and so CGPP provides a natural explanation for the origin of dark matter. In this work we study the gravitational production of massive spin-2 particles assuming two different couplings to matter. We evaluate the full system of mode equations, including the helicity-0 modes, and by solving them numerically we calculate the spectrum and abundance of massive spin-2 particles that results from inflation on a hilltop potential. We conclude that CGPP might provide a viable mechanism for the generation of massive spin-2 particle dark matter during inflation, and we identify the favorable region of parameter space in terms of the spin-2 particle’s mass and the reheating temperature. As a secondary product of our work, we identify the conditions under which such theories admit ghost or gradient instabilities, and we thereby derive a generalization of the Higuchi bound to Friedmann-Robertson-Walker (FRW) spacetimes.

Bimetric-affine quadratic gravity

Bimetric gravity is a theory of gravity that posits the existence of two interacting and dynamical metric tensors. The spectrum of bimetric gravity consists of a massless and a massive spin-2 particle. The form of the interactions between the two metrics ${g}_{\ensuremath{\mu}\ensuremath{\nu}}$ and ${f}_{\ensuremath{\mu}\ensuremath{\nu}}$ is constrained by requiring absence of the so-called Boulware-Deser ghost. In this work we extend the original bimetric theory to its bimetric-affine counterpart, in which the two connections, associated with the Ricci scalars, are treated as independent variables. We examine in detail the case of an additional quadratic in the Ricci scalar curvature term ${\mathcal{R}}^{2}(g,\mathrm{\ensuremath{\Gamma}})$ and we find that this theory is free of ghosts for a wide range of the interaction parameters, not excluding the possibility of a dark matter interpretation of the massive spin-2 particle.

Helical inflation correlators: partial Mellin-Barnes and bootstrap equations

Massive spinning particles acquire helicity-dependent chemical potentials during the inflation from axion-type couplings. Such spinning fields can mediate sizable inflaton correlators which we call the helical inflation correlators. Helical inflaton correlators are approximately scale invariant, dS boost breaking, parity violating, and are promising observables of cosmological collider physics. In this work, we present complete and analytical results for 4-point helical inflation correlators with tree-level exchanges of massive spinning particles, including both the smooth background and the oscillatory signals. We compute the bulk Schwinger-Keldysh integrals in two independent ways, including the partial Mellin-Barnes representation and solving bootstrap equations. We also present new closed-form analytical results for 3-point functions with massive scalar or helical spinning exchanges. The analytical results allow us to concretely and efficiently explore the phenomenological consequences of helicity-dependent chemical potentials. In particular, we show that the chemical potential can exponentially enhance oscillatory signals of both local and nonlocal types, but only affects the background in a rather mild way. Our results extend the de Sitter bootstrap program to include nonperturbative breaking of de Sitter boosts. Our results also explicitly verify the recently proposed cutting rule for cosmological collider signals.