Spin Kicks Research Articles

Spinning binary dynamics in cubic effective field theories of gravity

We study the binary dynamics of two Kerr black holes with arbitrary spin vectors in the presence of parity-even and parity-odd cubic deformations of gravity. We first derive the tree-level Compton amplitudes for a Kerr black hole in cubic gravity, which we then use to compute the two-to-two amplitudes of the massive bodies to leading order in the deformation and the post-Minkowskian expansion. The required one-loop computations are performed using the leading singularity approach as well as the heavy-mass effective field theory (HEFT) approach. These amplitudes are then used to compute the leading-order momentum and spin kick in cubic gravity in the KMOC formalism. Our results are valid for generic masses and spin vectors, and include all the independent parity-even and parity-odd cubic deformations of Einstein-Hilbert gravity. We also present spin-expanded expressions for the momentum and spin kicks, and the all-order in spin deflection angle in the case of aligned spins.

Massive twistor worldline in electromagnetic fields

We study the (ambi-)twistor model for spinning particles interacting via electromagnetic field, as a toy model for studying classical dynamics of gravitating bodies including effects of both spins to all orders. We compute the momentum kick and spin kick up to one-loop order and show precisely how they are encoded in the classical eikonal. The all-orders-in-spin effects are encoded as a dynamical implementation of the Newman-Janis shift, and we find that the expansion in both spins can be resummed to simple expressions in special kinematic configurations, at least up to one-loop order. We confirm that the classical eikonal can be understood as the generator of canonical transformations that map the in-states of a scattering process to the out-states. We also remark that cut contributions for converting worldline propagators from time-symmetric to retarded amount to the iterated action of the leading eikonal at one-loop order.

Quantum field theory, worldline theory, and spin magnitude change in orbital evolution

A previous paper [Z. Bern , Binary dynamics through the fifth power of spin at O(G2), ] identified a puzzle stemming from the amplitudes-based approach to spinning bodies in general relativity: additional Wilson coefficients appear compared to current worldline approaches to conservative dynamics of generic astrophysical objects, including neutron stars. In this paper we clarify the nature of analogous Wilson coefficients in the simpler theory of electrodynamics. We analyze the original field-theory construction, identifying definite-spin states some of which have negative norms, and relating the additional Wilson coefficients in the classical theory to transitions between different quantum spin states. We produce a new version of the theory which also has additional Wilson coefficients, but no negative-norm states. We match, through O(α2) and O(S2), the Compton amplitudes of these field theories with those of a modified worldline theory with extra degrees of freedom introduced by releasing the spin supplementary condition. We build an effective two-body Hamiltonian that matches the impulse and spin kick of the modified field theory and of the worldline theory, displaying additional Wilson coefficients compared to standard worldline approaches. The results are then compactly expressed in terms of an eikonal formula. Our key conclusion is that, contrary to standard approaches, while the magnitude of the spin tensor is still conserved, the magnitude of the spin vector can change under conserved Hamiltonian dynamics and this change is governed by the additional Wilson coefficients. For specific values of Wilson coefficients the results are equivalent to those from a definite spin obeying the spin supplementary condition, but for generic values they are physically inequivalent. These results warrant detailed studies of the corresponding issues in general relativity. Published by the American Physical Society 2024

Dissipative Scattering of Spinning Black Holes at Fourth Post-Minkowskian Order.

We compute the radiation reacted momentum impulse Δp_{i}^{μ}, spin kick ΔS_{i}^{μ}, and scattering angle θ between two scattered spinning massive bodies (black holes or neutron stars) using the N=1 supersymmetric worldline quantum field theory formalism up to fourth post-Minkowskian (4PM) order. Our calculation confirms the state-of-the-art nonspinning results, and extends them to include spin-orbit effects. Advanced multiloop Feynman integral technology including differential equations and the method of regions are applied and extended to deal with the retarded propagators arising in a causal description of the scattering dynamics. From these results we determine a complete set of radiative fluxes at subleading PM order: the 4PM radiated four-momentum and, via linear response, the 3PM radiated angular momentum, both again including spin-orbit effects.

Conservative Scattering of Spinning Black Holes at Fourth Post-Minkowskian Order.

Using the N=1 supersymmetric, spinning worldline quantum field theory formalism, we compute the conservative spin-orbit part of the momentum impulse Δp_{i}^{μ}, spin kick ΔS_{i}^{μ}, and scattering angle θ from the scattering of two spinning massive bodies (black holes or neutron stars) up to fourth post-Minkowskian (PM) order. These three-loop results extend the state of the art for generically spinning binaries from 3PM to 4PM. They are obtained by employing recursion relations for the integrand construction and advanced multiloop Feynman integral technology in the causal (in-in) worldline quantum field theory framework to directly produce classical observables. We focus on the conservative contribution (including tail effects) and outline the computations for the dissipative contributions as well. Our spin-orbit results agree with next-to-next-to-next-to-leading-order post-Newtonian and test-body data in the respective limits. We also reconfirm the conservative 4PM nonspinning results.

Linear response, Hamiltonian, and radiative spinning two-body dynamics

Using the spinning, supersymmetric worldline quantum field theory formalism we compute the momentum impulse and spin kick from a scattering of two spinning black holes or neutron stars up to quadratic order in spin at third post-Minkowskian (PM) order, including radiation-reaction effects and with arbitrarily misaligned spin directions. Parts of these observables, both conservative and radiative, are also inferred from lower-PM scattering data by extending Bini and Damour's linear response formula to include misaligned spins. By solving Hamilton's equations of motion we also use a conservative scattering angle to infer a complete 3PM two-body Hamiltonian including finite-size corrections and misaligned spin-spin interactions. Finally, we describe mappings to the bound two-body dynamics for aligned spin vectors: including a numerical plot of the binding energy for circular orbits compared with numerical relativity, analytic confirmation of the NNLO PN binding energy, and the energy loss over successive orbits.

The 2PM Hamiltonian for binary Kerr to quartic in spin

From the S-matrix of spinning particles, we extract the 2 PM conservative potential for binary spinning black holes up to quartic order in spin operators. An important ingredient is the exponentiated gravitational Compton amplitude in the classical spin-limit for all graviton helicity sectors. The validity of the resulting Hamiltonian is verified by matching to known lower spin order results, as well as direct computation of the 2PM impulse and spin kicks from the eikonal phase and that from the test black hole scattering based on Mathisson-Papapetrou-Dixon equations.

Conservative and Radiative Dynamics of Spinning Bodies at Third Post-Minkowskian Order Using Worldline Quantum Field Theory.

Using the spinning worldline quantum field theory formalism we calculate the quadratic-in-spin momentum impulse Δp_{i}^{μ} and spin kick Δa_{i}^{μ} from a scattering of two arbitrarily oriented spinning massive bodies (black holes or neutron stars) in a weak gravitational background up to third post-Minkowskian (PM) order (G^{3}). Two-loop Feynman integrals are performed in the potential region, yielding conservative results. For spins aligned to the orbital angular momentum we find a conservative scattering angle that is fully consistent with state-of-the-art post-Newtonian results. Using the 2PM radiated angular momentum previously obtained by Plefka, Steinhoff, and the present authors, we generalize the angle to include radiation-reaction effects, in which case it avoids divergences in the high-energy limit.

SUSY in the sky with gravitons

Picture yourself in the wave zone of a gravitational scattering event of two massive, spinning compact bodies (black holes, neutron stars or stars). We show that this system of genuine astrophysical interest enjoys a hidden mathcal{N} = 2 supersymmetry, at least to the order of spin-squared (quadrupole) interactions in arbitrary D spacetime dimensions. Using the mathcal{N} = 2 supersymmetric worldline action, augmented by finite-size corrections for the non-Kerr black hole case, we build a quadratic-in-spin extension to the worldline quantum field theory (WQFT) formalism introduced in our previous work, and calculate the two bodies’ deflection and spin kick to sub-leading order in the post-Minkowskian expansion in Newton’s constant G. For spins aligned to the normal vector of the scattering plane we also obtain the scattering angle. All D-dimensional observables are derived from an eikonal phase given as the free energy of the WQFT that is invariant under the mathcal{N} = 2 supersymmetry transformations.

Classical observables from coherent-spin amplitudes

The quantum field-theoretic approach to classical observables due to Kosower, Maybee and O’Connell provides a rigorous pathway from on-shell scattering amplitudes to classical perturbation theory. In this paper, we promote this formalism to describe general classical spinning objects by using coherent spin states. Our approach is fully covariant with respect to the massive little group SU(2) and is therefore completely synergistic with the massive spinor-helicity formalism. We apply this approach to classical two-body scattering due gravitational interaction. Starting from the coherent-spin elastic-scattering amplitude, we derive the classical impulse and spin kick observables to first post-Minkowskian order but to all orders in the angular momenta of the massive spinning objects. From the same amplitude, we also extract an effective two-body Hamiltonian, which can be used beyond the scattering setting. As a cross-check, we rederive the classical observables in the center-of-mass frame by integrating the Hamiltonian equations of motion to the leading order in Newton’s constant.

Quadratic-in-spin Hamiltonian at mathcal{O} (G2) from scattering amplitudes

We obtain the quadratic-in-spin terms of the conservative Hamiltonian describing the interactions of a binary of spinning bodies in General Relativity through mathcal{O} (G2) and to all orders in velocity. Our calculation extends a recently-introduced framework based on scattering amplitudes and effective field theory to consider non-minimal coupling of the spinning objects to gravity. At the order that we consider, we establish the validity of the formula proposed in [1] that relates the impulse and spin kick in a scattering event to the eikonal phase.

Biomechanical Analysis of SPIN KICKS for Establishing the Technical Difficulty of Free style Poomsae in Taekwondo

Purpose: Quantitative grounds for the difficulty distinction and clear evaluation criteria of Taekwondo free style Poomsae spin kick are required. The purpose of this research is to conduct a kinematic analysis of 540°Dwihuryochagi(540D), 720°Dollyochagi(720D) and 900°Dwihuryochagi(900D) and provide a quantitative basis for spin kick difficulty classification. Method: 13 athletes(age: 20.6±0.7 years, height: 171.3±4.2 cm, weight: 65.4±6.2 kg, experience: 8.3±4.5 years) were selected for this study. The analysis variables were the interval-specific time required for the spin kick, the displacement and velocity of the center of mass(COM), and the rotation angle and rotation angular velocity of the trunk. Results: First, as the rotation angle increased, the time to kick(E2-E4) increased and the height of kick-off(E4) COM decreased(p<.05). Second, it has been shown that the time to land(E4-E5) is shortened(p<.05). The 900D was followed by kick after the landing was completed. Third, for the rotational angular velocity of the torso, rapid angular velocity was shown in the order of 900D > 720D > 540D in the air rotation interval(Phase 2-5). Conclusion: Based on the results of this study, the difficulty of 900D should be allocated higher than that of 540D and 720D. In addition, Video Assistant Referee(VAR) techniques need to be applied to evaluate the suc-cess of 900D.

Tidal effects for spinning particles

Expanding on the recent derivation of tidal actions for scalar particles, we present here the action for a tidally deformed spin-1/2 particle. Focusing on operators containing two powers of the Weyl tensor, we combine the Hilbert series with an on-shell amplitude basis to construct the tidal action. With the tidal action in hand, we compute the leading-post-Minkowskian tidal contributions to the spin-1/2–spin-1/2 amplitude, arising at mathcal{O} (G2). Our amplitudes provide evidence that the observed long range spin-universality for the scattering of two point particles extends to the scattering of tidally deformed objects. From the scattering amplitude we find the conservative two-body Hamiltonian, linear and angular impulses, eikonal phase, spin kick, and aligned-spin scattering angle. We present analogous results in the electromagnetic case along the way.

Studies of Systematic Limitations in the EDM Searches at Storage Rings

Searches of the electric dipole moment (EDM) at a pure magnetic ring, like COSY, encounter strong background coming from magnetic dipole moment (MDM). The most troubling issue is the MDM spin rotation in the so-called imperfection, radial and longitudinal, B-fields. To study the systematic effects of the imperfection fields at COSY we proposed the original method which makes use of the two static solenoids acting as artificial imperfections. Perturbation of the spin tune caused by the spin kicks in the solenoids probes the systematic effect of cumulative spin rotation in the imperfection fields all over the ring. The spin tune is one of the most precise quantities measured presently at COSY at [Formula: see text] level. The method has been successfully tested in September 2014 run at COSY, unravelling strength of spin kicks in the ring’s imperfection fields at the level of [Formula: see text].

Forhend spin i vežbe razvoja u treningu stonotenisera

Modern table tennis is unimaginable without the use of spin kick, which after his appearance in the 60s of the last century became one of the most common strokes in table tennis game. Role of forehand spinkick is multifunctional. In the game it can be applied as a basic attack hit when you want to make points and as a preparatory kick for starting the attack phase. The Paper presents exercises that can be used in the phase of basic training, exercising and improving of different variants of forehand spins. Selection and implementation of these exercises is conditioned with individual characteristics and abilities of table tennis players.

Kinematics Analysis on 720° Spin Kick Followed by Horse Stance of Fukui Li in Southern Fist

720°spin kick followed by horse stance is among one of the high difficulty movements of C level in the southern fist in martial art, it was formed on the basis of 360°tornado kick, because of its complex technical details and action links, it values a lot in the competition. The possibility of athletes who can successfully complete the action during training and competition is rather low. Modern three-dimension picture analysis will become the main method on technique diagnosis of kinematics parameter at game site. We took up Fukui Li’s 720°spin kick followed by horse stance in 2012 National Nanquan competition and also made three-dimension analysis on it. The aim of the paper is to get the kinematics parameters and then summarize his skill features, explore its internal kinematic characteristics and laws thus to provide some scientific basis for martial arts training

Match Analysis in a University Taekwondo Championship

The aim of this study was to analyze the performance of medallists’ taekwondo athletes in University level Championship. Kicking actions were grouped into three categories; circular, linear and with a previous spin kicks. Performance was evaluated based on 1) the type and height of the kicks employed, 2) the attacking and counterattacking nature of the kicking actions and 3) the scoring profiles of these. Forty-five matches from the four Olympic weight categories were notationally analyzed in male and female populations. Kruskal-Wallis tests revealed that the reading scores in the four weight categories differed significantly in males for linear kicks, and in circular kicks to the chest, attacking kicks and total actions (p < 0.05) for females. A greater number of circular kicks was recorded in male and female taekwondo athletes; this was followed by linear kicks and those with a previous spin. Kicks to the chest were also more common than kicks to the head as well as attacking kicks were used more frequently than counterattacking kicks. Given the new competition rules, coaches are encouraged to induce athletes to increase the frequency of kicks to the head and with a previous spin to maximise the point scoring rate per kicks delivered.

태권도 6주간 훈련 프로그램에 따른 스텝 돌려차기 동작의 운동역학적 분석

The purpose of this study is to analyze the characteristics of the spin kick moves in Taekwondo and provide necessary information to the university athletes in correcting their moves. It is also a goal of this study to quantify the forms of the kicks in training to maximize the efficiency. Four national varsity players of Taekwondo and four beginners with no award histories from K Univ. were given 6 weeks of training and motor mechanic analysis have been performed with the spin kicks. The conclusions of this study are as follows. 1. The total elapsed time of performing a spin kick move in each group differed significantly. The beginner group`s elapsed time for a spin kick was an average of 0.415±0.158, while the national varsity group`s spin kick took only 0.283±0.044. Therefore, the national varsity group turned out to show much more speed in spin kicks. Also, the procedures within individual moves of the varsity group appeared to shorten the entire elapsed time of a move compared to those of the beginner group. 2. In performing Step-and-Spin kicks, the two groups showed significant differences in the angles of joints such as the coxa, knee, and ankle. In case of the beginners, they failed to reduce the angle of the coxa joints, and the knee joint were not fully stretched out in the associated movement of Step-and-Spin kicks. Also at the impact, the dorsification of the ankle joint denied that accurate hits on the desired positions. But, as the training went on, the beginners showed improvements in narrowing down the angles. 3. The angular velocity of the coxa joints in both groups while performing a Step-and-Spin kick move, the angular velocities of each joint turned out to be rather higher. Such an outcome with the beginner group might be due to the lack of practices and thereby failure in controlling effective distances while associating each phase of the Step-and-Spin kick. 4. The surface recoil of the beginner group appeared to increase in its value as the training progressed in comparison with the national varsity group. Such a result was found to allow bigger motions when stamping, adding to the force directed upward from the ground. It can contribute to make faster and wider expansion angle movement. 5. In this study, while the Step phase in a Step-and-Spin kick is a precedent but a very important movement before the spin kick is performed, the beginners were found to fail in utilizing this phase efficiently due to lack of techniques.

Recoiling from a kick in the head-on collision of spinning black holes

Recoil ``kicks'' induced by gravitational radiation are expected in the inspiral and merger of black holes. Recently the numerical relativity community has begun to measure the significant kicks found when both unequal masses and spins are considered. Because understanding the cause and magnitude of each component of this kick may be complicated in inspiral simulations, we consider these effects in the context of a simple test problem. We study recoils from collisions of binaries with initially head-on trajectories, starting with the simplest case of equal masses with no spin and then adding spin and varying the mass ratio, both separately and jointly. We find spin-induced recoils to be significant relative to unequal-mass recoils even in head-on configurations. Additionally, it appears that the scaling of transverse kicks with spins is consistent with post-Newtonian theory, even though the kick is generated in the nonlinear merger interaction, where post-Newtonian theory should not apply. This suggests that a simple heuristic description might be effective in the estimation of spin kicks.

Neutron star spin–kick velocity correlation effect on binary neutron star coalescence rates and spin–orbit misalignment of the components

We study the effect of the neutron star spin-kick velocity alignment observed in young radio pulsars on the coalescence rate of binary neutron stars. Two scenarios are considered for neutron star formation: when the kick is always present, and when it is small or absent if a neutron star is formed in a binary system as a result of electron-capture degenerate core collapse. The effect is shown to be especially strong for large kick amplitudes and tight alignments, reducing the expected galactic rate of binary neutron star coalescence compared to calculations with randomly directed kicks. The spin-kick correlation also leads to a much narrower neutron star spin-orbit misalignment.