Massive Spin Research Articles

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.

Classical limit of higher-spin string amplitudes

It has been shown that a special set of three-point amplitudes between two massive spinning states and a graviton reproduces the linearised stress-energy tensor for a Kerr black hole in the classical limit. In this work we revisit this result and compare it to the analysis of the amplitudes describing the interaction of leading Regge states of the open and closed superstring. We find an all-spin result for the classical limit of two massive spinning states interacting with a photon or graviton. This result differs from Kerr and instead matches the current four-vector and the stress-energy tensor generated by a classical string coupled to electromagnetism and gravity respectively. For the superstring amplitudes, contrary to the black-hole case, we find that the spin to infinity limit is necessary to reproduce the classical spin multipoles.

On-shell supersymmetry and higher-spin amplitudes

We use on-shell Supersymmetry to constrain the three-point function of two massless particles and one massive particle in 3+1 dimensions. We use this information to write down the tree-level four-point function of massless particles for mathcal{N} = 1, 2 and 4 theories. In particular, we derive the expressions for four-photon/gluon amplitudes with massive higher spin exchange in theories with mathcal{N} = 4 Supersymmetry in 3+1 dimensions.

Black hole horizon edge partition functions

We extend a formula for 1-loop black hole determinants by Denef, Hartnoll, and Sachdev (DHS) to spinning fields on any (d + 1)-dimensional static spherically symmetric black hole. By carefully analyzing the regularity condition imposed on the Euclidean eigenfunctions, we reveal an unambiguous bulk-edge split in the 1-loop Euclidean partition function for tensor fields of arbitrary integer spin: the bulk part captures the “renormalized” thermal canonical partition function recently discussed in [1]; the edge part is related to quasinormal modes (QNMs) that fail to analytically continue to a subset of Euclidean modes with enhanced fall-offs near the origin. Since the edge part takes the form of a path integral on Sd−1, this suggests that these are associated with degrees of freedom living on the bifurcation surface in the Lorentzian two-sided black hole geometry. For massive higher spin on static BTZ and massive vector on Nariai black holes, we find that the edge partition function is related to the QNMs with lowest overtone numbers.

Casimir energy for spinor fields with δ-shell potentials

This work analyzes the Casimir energy of a massive spinor field propagating in flat space endowed with a spherically symmetric δ-function potential. By utilizing the spectral zeta function regularization method, the Casimir energy is evaluated after performing a suitable analytic continuation. Explicit numerical results are provided for specific cases in which the Casimir energy is unambiguously defined. The results described in this work represent a generalization of the MIT bag model for spinor fields.

An EFT hunter’s guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes

We derive the contact terms contributing to the four-point amplitudes of the standard model particles, keeping terms with up to quartic energy growth. Imposing just the unbroken low-energy symmetry, and treating the electroweak gauge bosons and the Higgs as independent degrees of freedom, we obtain the most general four-point contact-term amplitudes, corresponding to the Higgs Effective Field Theory (HEFT) framework. The contact terms are spanned by a basis of Stripped Contact Terms, which carry the polarization information, multiplied by polynomials in the Mandelstam invariants. For terms with quadratic energy growth, we also derive the low-energy Standard Model Effective Field Theory (SMEFT) predictions, via on-shell Higgsing of the massless SMEFT contact terms. We discuss several aspects of bottom-up versus top-down on-shell derivations of the HEFT and SMEFT amplitudes, highlighting in particular the simple counting of HEFT dimensions in the on-shell approach and the transparent relation between perturbative unitarity and gauge-invariance in the little-group covariant massive spinor formalism. Our results provide a formulation of Effective Field Theory analyses directly in terms of observable quantities. For terms with quadratic energy growth, we also provide the mapping to the Warsaw basis.

A derivation of the standard model particles from internal spacetime

‘Internal spacetime’ is a modification of general relativity that was recently introduced as an approximate spacetime geometric model of quantum nonlocality. In an internal spacetime, time is stationary along the worldlines of fundamental (dust) particles. Consequently, the dimensions of tangent spaces at different points of spacetime vary, and spin wavefunction collapse is modeled by the projection from one tangent space to another. In this paper, we develop spinors on an internal spacetime, and construct a new Dirac-like Lagrangian [Formula: see text] whose equations of motion describe their couplings and interactions. Furthermore, we show that hidden within [Formula: see text] is the entire standard model: [Formula: see text] contains precisely three generations of quarks and leptons, the electroweak gauge bosons, the Higgs boson, and one new massive spin-[Formula: see text] boson; gluons are considered in a companion paper. Specifically, we are able to derive the correct spin, electric charge, and color charge of each standard model particle, as well as predict the existence of a new boson.

The dominating mode of two competing massive modes of quadratic gravity

Over the last two decades, motivations for modified gravity have emerged from both theoretical and observational levels. f(R) and Chern-Simons gravity have received more attention as they are the simplest generalization. However, f(R) and Chern-Simons gravity contain only an additional scalar (spin-0) degree of freedom and, as a result, do not include other modes of modified theories of gravity. In contrast, quadratic gravity (also referred to as Stelle gravity) is the most general second-order modification to 4-D general relativity and contains a massive spin-2 mode that is not present in f(R) and Chern-Simons gravity. Using two different physical settings—the gravitational wave energy-flux measured by the detectors and the backreaction of the emitted gravitational radiation on the spacetime of the remnant black hole—we demonstrate that massive spin-2 mode carries more energy than the spin-0 mode. Our analysis shows that the effects are pronounced for intermediate-mass black holes, which are prime targets for LISA.

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.

Greybody factors emitted by a regular black hole in a non-minimally coupled Einstein–Yang–Mills theory

In this paper, we study the greybody factors (GFs) for fermions with different spins and bosons in the regular black hole (BH) predicted by a non-minimal Einstein–Yang–Mills (EYM) theory. We investigate the effect of magnetic charge on effective potentials and GFs. For this purpose, we consider the Dirac and Rarita–Schwinger, as well as Klein–Gordon equations. First, we study the Dirac equation in curved spacetime for massive and massless spin-1/2 fermions. We then separate the Dirac equation into sets of radial and angular equations. Using the analytical solution of the angular equation, the Schrödinger-like wave equations with potentials are derived by decoupling the radial wave equations via the tortoise coordinate. We also consider the Rarita–Schwinger equation for massless spin-3/2 fermions and derive the one-dimensional Schrödinger wave equation with gauge-invariant effective potential. For bosons, we study the Klein–Gordon equation in the regular non-minimal EYM BH. Afterward, semi-analytic methods were used to calculate the fermionic and bosonic GFs. Finally, we discuss the graphical behavior of the obtained effective potentials and bounds on the GFs. According to graphs, the GF is highly influenced by the potential’s shape, which is determined by the parameterization of the model. This is in line with quantum theory.

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.

Spin-2 dark matter from an anisotropic universe in bigravity

Bigravity is one of the natural extensions of general relativity and contains an additional massive spin-2 field which can be a good candidate for dark matter. To discuss the production of spin-2 dark matter, we study fixed point solutions of the background equations for axisymmetric Bianchi type-I Universes in two bigravity theories without Boulware-Deser ghost, i.e., Hassan-Rosen bigravity and Minimal Theory of Bigravity. We investigate the local and global stability of the fixed points and classify them. Based on the general analysis, we propose a new scenario where spin-2 dark matter is produced by the transition from an anisotropic fixed point solution to isotropic one. The produced spin-2 dark matter can account for all or a part of dark matter and can be directly detected by laser interferometers in the same way as gravitational waves.

Common Features of Free Particle Wave Functions in Curved Space-times

Quantum equations for massless particles of any spin and for massive spin one-half particles are considered in curved space-times. It is demonstrated that in stationary axially symmetric space-times the angular wave functions up to a normalization function are the same as in a Minkowski space-time. The radial wave functions satisfy second order nonhomogeneous differential equations with three nonhomogeneous terms which depend in a unique form on the ratio of time to space curvatures. For a Dirac spin one-half particle, in addition to these three terms a fourth term which depends on the particle rest mass is added.

Pair production in the rainbow dS2 space

The study is devoted to discuss the rate of pair production in a two-dimensional de Sitter (dS2) type manifold with the help of the rainbow gravity formalism and the method of the Bogoliubov transformations. After obtaining exact analytical solutions of the Dirac equation for the selected rainbow metric, we focus on the creation rate of massive spin-1/2 particles.

Dualisation of free fields

We consider the general free field theory such that system of equations of motion includes a subsystem with a special property. If the subsystem is considered by itself, it would be a topological field theory having no local degrees of freedom. Various well-known field theories admit such a subsystem, including Einstein’s gravity. As the subsystem is a topological theory, the general solution is a pure gauge, modulo global degrees of freedom. Gauge symmetry of the subsystem of linear theory can be explicitly found, providing the general solution to the subsystem. Substituting this solution into entire system, we arrive at an equivalent field theory where the role of the field variables is played by the gauge parameters of the topological subsystem. These fields can be viewed as the potentials for the original ones. A general procedure is proposed for constructing a “parent action” which includes the fields of both dual formulations. At the level of this action, one can switch between dual formulations by imposing appropriate gauge fixing conditions. This general dualisation procedure is exemplified by massless and massive spin two fields. For the massless case, the hook type tensor serves as a potential for the metric, while for the massive case it is the fourth rank tensor with window Young diagram.

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.

Classical double copy of spinning worldline quantum field theory

We study the classical double copy of massive spinning objects in the worldline quantum field theories (WQFT) formalism. We couple the mathcal{N} = 1 supersymmetric model to a Yang-Mills background to describe the propagation of a spin-half particle interacting with gluons. At the classical level, this model captures physical effects up to linear order in spin. We propose a double copy relation to map the spin tensors to the gravitation side. Enforcing R-symmetry and supersymmetry (SUSY) on the double copy integrands, we find that the gravitational theory is the mathcal{N} = 2 particle coupled to dilaton-gravity (DG). We check the double copy prescription for the eikonal phase up to next-to-leading order and for radiation at leading order in coupling constants, finding that the Grassmann nature of the spin tensor in WQFT plays a crucial role in finding full agreement with direct calculation in the mathcal{N} = 2 model. We show how to deform the SUSY charges of the free theory to include DG. Since the constraints algebra is first class, the worldline model can be quantized, describing the propagation of a massive vector field coupled to DG, in agreement with the literature. In addition, we investigate the double copy without preserving SUSY and R-symmetry, finding that the B-field also couples to the worldline.

Next-to-leading-order solution to Kerr-Newman black hole superradiance

The superradiant instabilities of Kerr-Newman black holes with charged or uncharged massive spin-0 fields are calculated analytically to the next-to-leading order in the limit of $\alpha\sim r_g \mu \ll 1$. A missing factor of $1/2$ in the previous leading-order result is identified. The next-to-leading order result has a compact form and is in good agreement with existing numerical calculations. The percentage error increases with $\alpha$, from a few percent for $\alpha\sim 0.1$ to about $50\%$ for $\alpha\sim 0.4$. Massive neutral scalars too heavy to be produced with Kerr black hole superradiance may exist in the superradiant region of Kerr-Newman black holes.

Generating tensor polarization from shear stress

We derive an expression for the tensor polarization of a system of massive spin-1 particles in a hydrodynamic framework. Starting from quantum kinetic theory based on the Wigner-function formalism, we employ a modified method of moments which also takes into account all spin degrees of freedom. It is shown that the tensor polarization of an uncharged fluid is determined by the shear-stress tensor. In order to quantify this novel polarization effect, we provide a formula which can be used for numerical calculations of vector-meson spin alignment in relativistic heavy-ion collisions.

The dark universe: Primordial black hole ⇋ dark graviton gas connection

We study the possible correspondence between 5-dimensional primordial black holes and massive 5-dimensional KK gravitons as dark matter candidate within the recently proposed dark dimension scenario that addresses the cosmological hierarchy problem. First, we show that in the local universe a population of 5-dimensional black holes with MBH∼7×1013g would be practically indistinguishable from a KK tower of dark gravitons with mDM∼50keV. Second, we connect the mass increase of 5-dimensional black holes and the related temperature decrease with the cooling of the tower of massive spin-2 KK excitations of the graviton. The dark gravitons are produced at a mass ∼1−50GeV and the bulk of their mass shifts down to roughly 1−100keV today. The cooling of the system proceeds via decay to lighter gravitons without losing much total mass density, resembling the intra-tower decays that characterize the cosmological evolution of the dynamical dark matter framework. We associate the intra-tower decays of the graviton gas with the black hole growth through accretion. We also discuss that the primordial black hole ⇋ dark graviton gas connection can be nicely explained by the bound state picture of black holes in terms of gravitons.