We resolve subtleties in calculating the post-Minksowskian dynamics of binary systems, as a spin expansion, from massive scattering amplitudes of fixed finite spin. In particular, the apparently ambiguous spin Casimir terms can be fully determined from the gradient of the spin-diagonal part of the amplitudes with respect to = − ( +1) , using an interpolation between massive amplitudes with different spin representations. From two-loop amplitudes of spin-0 and spin-1 particles minimally coupled to gravity, we extract the spin Casimir terms in the conservative scattering angle between a spinless and a spinning black hole at $$ \mathcal{O} $$ ( ), finding agreement with known results in the literature. This completes an earlier study [Phys. Rev. Lett. 130 (2023), 021601] that calculated the non-Casimir terms from amplitudes. We also illustrate our methods using a model of spinning bodies in electrodynamics, finding agreement between scattering amplitude predictions and classical predictions in a electromagnetic background up to $$ \mathcal{O} $$ ( ). For both gravity and electrodynamics, the finite part of the amplitude coincides with the two-body radial action in the aligned spin limit, generalizing the amplitude-action relation beyond the spinless case. Surprisingly, the two-loop amplitude displays a hidden spin-shift symmetry in the probe limit, which was previously observed at one loop. We conjecture that the symmetry holds to all orders in the coupling constant and is a consequence of integrability of Kerr orbits in the probe limit at the first few orders in spin.

United Kingdom

Dogan Akpinar

United States

Fernando Febres Cordero

Mexico

Manfred Kraus

Michael Ruf

Mao Zeng

Spinning black hole scattering at

We compute the far-field time-domain waveform of the gravitational waves produced in the scattering of two spinning massive objects. The results include linear-in-spin (S) couplings and first-order gravitational corrections (G 3), and are valid for encounters in the weak-field regime. Employing a field-theory framework based on the scattering of massive scalar and vector particles coupled to Einstein-Hilbert gravity, we derive results for leading and the next-to-leading spectral waveforms. We provide analytic expressions for the required scattering data, which include trees, one-loop amplitudes and their cuts. The expressions are extracted from numerical amplitude evaluations with the Caravel program, using analytic reconstruction techniques applied in the classical limit. We confirm a recent prediction for infrared physics of the classical observable, and observe the surprising appearance of a ultraviolet singularity, which drops out in the far-field waveform.

Switzerland

Lara Bohnenblust

Harald Ita

Johannes Schlenk

Gravitational Bremsstrahlung in black-hole scattering at   <math> <mi>O</mi> <mfenced> <msup> <mi>G</mi> <mn>3</mn> </msup> </mfenced> </math>  $$ \mathcal{O}\left({G}^3\right) $$ : linear-in-spin effects

In view of the persisting tension between theoretical predictions and the LHC data for the pp →   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> <mi>W</mi> </math>  $$ t\overline{t}W $$   ±  production process, we present the state-of-the-art full off-shell NLO QCD result for pp →   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> <mi>W</mi> </math>  $$ t\overline{t}W $$  + j + X. We concentrate on the multi-lepton decay channel at the LHC with   <math> <msqrt> <mi>s</mi> </msqrt> </math>  $$ \sqrt{s} $$  = 13 TeV. In our calculation off-shell top quarks and gauge bosons are described by Breit-Wigner propagators, furthermore, double-, single- as well as non-resonant top-quark contributions along with all interference effects are consistently incorporated at the matrix element level. We present results for both integrated and differential fiducial cross sections for various renormalisation and factorisation scale settings and different PDF sets. With a fairly inclusive choice of cuts and regardless of the scale and PDF choice, non-flat differential   <math> <mi>K</mi> </math>  $$ \mathcal{K} $$ -factors are obtained for many observables that we have examined. Since from an experimental point of view, both processes pp →   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> <mi>W</mi> </math>  $$ t\overline{t}W $$   ±  j + X and pp →   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> <mi>W</mi> </math>  $$ t\overline{t}W $$   ±  + X consist of similar final states we investigate the effect of additional jet activity on the integrated and differential fiducial cross sections. For this purpose, the normalised differential distributions for pp → e + ν  e  μ  −    <math> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\nu} $$   μ  τ + ν  τ    <math> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ b\overline{b} $$  j + X and pp → e + ν  e  μ  −    <math> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\nu} $$   μ  τ + ν  τ    <math> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ b\overline{b} $$  + X are compared. The theoretical results for the latter process are also recalculated.

China

Huan-Yu Bi

Germany

Minos Reinartz

Malgorzata Worek

NLO QCD predictions for off-shell   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> <mi>W</mi> </math>  $$ t\overline{t}W $$  production in association with a light jet at the LHC

We compute the conservative two-body Hamiltonian of a compact binary system with a spinning black hole through <math><mi>O</mi><mo>(</mo><msup><mi>G</mi><mn>3</mn></msup><mo>)</mo></math> to all orders in velocity, including linear and quadratic spin terms. To obtain our results we calculate the classical limit of the two-loop amplitude for the scattering of a massive scalar particle with a massive spin-1 particle minimally coupled to gravity. We employ modern scattering amplitude and loop integration techniques, in particular numerical unitarity, integration-by-parts identities, and the method of regions. The conservative potential in terms of rest-frame spin vectors is extracted by matching to a nonrelativistic effective field theory. We also apply the Kosower-Maybee-O’Connell (KMOC) formalism to calculate the impulse in the covariant spin formalism directly from the amplitude. We work systematically in conventional dimensional regularization and explicitly evaluate all divergent integrals that appear in full- and effective-theory amplitudes, as well as in the phase-space integrals that arise in the KMOC formalism.

Guanda Lin

Michael S. Ruf

Conservative Binary Dynamics with a Spinning Black Hole at <math><mi>O</mi><mo>(</mo><msup><mi>G</mi><mn>3</mn></msup><mo>)</mo></math> from Scattering Amplitudes

Motivated by ongoing new physics searches in the top-quark sector at the Large Hadron Collider we report on the calculation of NLO QCD corrections to the Standard Model pp →   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> <mi>Z</mi> </math>  $$ t\overline{t}Z $$  + X process in the tetra-lepton decay channel. This calculation is based on the matrix elements for the   <math> <msup> <mi>e</mi> <mo>+</mo> </msup> <msub> <mi>ν</mi> <mi>e</mi> </msub> <msup> <mi>μ</mi> <mo>−</mo> </msup> <msub> <mover> <mi>ν</mi> <mo>¯</mo> </mover> <mi>μ</mi> </msub> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> <msup> <mi>τ</mi> <mo>+</mo> </msup> <msup> <mi>τ</mi> <mo>−</mo> </msup> </math>  $$ {e}^{+}{\nu}_e{\mu}^{-}{\overline{\nu}}_{\mu }b\overline{b}{\tau}^{+}{\tau}^{-} $$  final state and includes all resonant and non-resonant Feynman diagrams, interferences and off-shell effects of the top quark as well as the W and Z gauge bosons. Also incorporated are photon-induced contributions. As it is customary for such studies, we show theoretical predictions for both fixed and dynamical factorisation and renormalisation scale choices and different PDF sets. Furthermore, we study the main theoretical uncertainties that are associated with neglected higher-order terms in the perturbative expansion and with the parameterisation of the PDF sets. In order to investigate the size of off-shell effects and higher-order corrections in top-quark decays, we perform a second computation for this process, which is based on the narrow-width-approximation where the top quarks, W and Z gauge bosons are kept on-shell. Results are given for the integrated and differential fiducial cross sections for the LHC Run II center-of-mass energy of 13 TeV.

Hungary

Giuseppe Bevilacqua

Heribertus Hartanto

Jasmina Nasufi

NLO QCD corrections to full off-shell production of   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> <mi>Z</mi> </math>  $$ t\overline{t}Z $$  including leptonic decays

We present a new Monte Carlo event generator for the hadronic production of four top quarks in the powheg box framework. Besides the dominant next-to-leading order QCD corrections at <math><mi>O</mi><mo>(</mo><msubsup><mi>α</mi><mi>s</mi><mn>5</mn></msubsup><mo>)</mo></math> we also include all subleading electroweak productions channels at leading-order accuracy. We validate our theoretical predictions by comparing to parton-shower matched predictions obtained within the mc@nlo framework for stable top quarks. Furthermore, we investigate in detail the various sources of theoretical uncertainties. Finally, we investigate a single lepton plus jets signature to study for the first time the impact of the electroweak production modes as well as spin-correlation effects at the fiducial level.

Tomáš Ježo

Hadroproduction of four top quarks in the powheg box

We study a “heavy” QCD axion whose coupling to the standard model is dominated by <math><mi>a</mi><mi>G</mi><mover><mi>G</mi><mo>˜</mo></mover></math> but with <math><msub><mi>m</mi><mi>a</mi></msub><mo>≫</mo><msub><mi>m</mi><mi>π</mi></msub><msub><mi>f</mi><mi>π</mi></msub><mo>/</mo><msub><mi>f</mi><mi>a</mi></msub></math>. This is well motivated as it can solve the strong <math><mi>C</mi><mi>P</mi></math> problem while evading the axion quality problem. It also poses interesting challenges for its experimental search due to its suppressed couplings to photons and leptons. Such axion with mass around a GeV is kinematically inaccessible or poorly constrained by most experimental probes except <math><mi>B</mi></math>-factories. We study <math><mi>B</mi><mo>→</mo><mi>K</mi><mi>a</mi></math> transitions as a powerful probe of the heavy QCD axion by performing necessary 2-loop calculations for the first time, together with some improvement on the existing analysis strategy. We find some of the existing limits are enhanced by at least an order of magnitude. We also demonstrate that the bounds are robust against unknown UV physics. For forthcoming data sets of the Belle II experiment, we provide a projection that <math><msub><mi>f</mi><mi>a</mi></msub></math> of a few TeV is within its future reach, which is relevant to the quality problem.

Sabyasachi Chakraborty

Vazha Loladze

Japan

Takemichi Okui

Kohsaku Tobioka

Heavy QCD axion in <math><mi>b</mi><mo>→</mo><mi>s</mi></math> transition: Enhanced limits and projections

We report on the calculation of the next-to-leading order QCD corrections to the production of a   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> </math>  $$ t\overline{t} $$  pair in association with two heavy-flavour jets. We concentrate on the di-lepton   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> </math>  $$ t\overline{t} $$  decay channel at the LHC with   <math> <msqrt> <mi>s</mi> </msqrt> </math>  $$ \sqrt{s} $$  = 13 TeV. The computation is based on pp → e + ν  e  μ  −    <math> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\nu} $$   μ    <math> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ b\overline{b}b\overline{b} $$  matrix elements and includes all resonant and non-resonant diagrams, interferences and off-shell effects of the top quark and the W gauge boson. As it is customary for such studies, results are presented in the form of inclusive and differential fiducial cross sections. We extensively investigate the dependence of our results upon variation of renormalisation and factorisation scales and parton distribution functions in the quest for an accurate estimate of the theoretical uncertainties. We additionally study the impact of the contributions induced by the bottom-quark parton density. Results presented here are particularly relevant for measurements of   <math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> <mi>H</mi> </math>  $$ t\overline{t}H $$ (H →   <math> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ b\overline{b} $$ ) and the determination of the Higgs coupling to the top quark. In addition, they might be used for precise measurements of the top-quark fiducial cross sections and to investigate top-quark decay modelling at the LHC.

Michele Lupattelli

<math> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ t\overline{t}b\overline{b} $$  at the LHC: on the size of corrections and b-jet definitions

Recent discrepancies between theoretical predictions and experimental data in multi-lepton plus b-jets analyses for the  $$t{\bar{t}}W^\pm $$  <math> <mrow> <mi>t</mi> <mover> <mrow> <mi>t</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <msup> <mi>W</mi> <mo>±</mo> </msup> </mrow> </math>   process, as reported by the ATLAS collaboration, have indicated that more accurate theoretical predictions and high precision observables are needed to constrain numerous new physics scenarios in this channel. To this end we employ NLO QCD computations with full off-shell top quark effects included to provide theoretical predictions for the  $$\mathcal{R}= \sigma _{t{\bar{t}}W^+}/\sigma _{t{\bar{t}}W^-}$$  <math> <mrow> <mi>R</mi> <mo>=</mo> <msub> <mi>σ</mi> <mrow> <mi>t</mi> <mover> <mrow> <mi>t</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <msup> <mi>W</mi> <mo>+</mo> </msup> </mrow> </msub> <mo>/</mo> <msub> <mi>σ</mi> <mrow> <mi>t</mi> <mover> <mrow> <mi>t</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <msup> <mi>W</mi> <mo>-</mo> </msup> </mrow> </msub> </mrow> </math>   cross section ratio at the LHC with  $$\sqrt{s}=13$$  <math> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>13</mn> </mrow> </math>   TeV. Depending on the transverse momentum cut on the b-jet we obtain 2–3% theoretical precision on  $$\mathcal{R}$$  <math> <mi>R</mi> </math>  , which should help to shed some light on new physics effects that can reveal themselves only once sufficiently precise Standard Model theoretical predictions are available. Furthermore, triggered by these discrepancies we reexamine the charge asymmetry of the top quark and its decay products in the  $$t{\bar{t}}W^\pm $$  <math> <mrow> <mi>t</mi> <mover> <mrow> <mi>t</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <msup> <mi>W</mi> <mo>±</mo> </msup> </mrow> </math>   production process. In the case of charge asymmetries, that are uniquely sensitive to the chiral nature of possible new physics in this channel, theoretical uncertainties below 15% are obtained. Additionally, the impact of the top quark decay modelling is scrutinised by explicit comparison with predictions in the narrow-width approximation.

NLO QCD corrections to off-shell  $${t{\bar{t}}W^\pm }$$  <math> <mrow> <mi>t</mi> <mover> <mrow> <mi>t</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <msup> <mi>W</mi> <mo>±</mo> </msup> </mrow> </math>   production at the LHC: correlations and asymmetries

Recent measurements of the $$ t\overline{t}{W}^{\pm } $$ process in multi-lepton final states, as performed by the ATLAS collaboration in the context of the Higgs boson studies in the $$ t\overline{t}H $$ channel, have shown discrepancies between theoretical predictions and experimental data. Such discrepancies have been observed both in the overall normalisation as well as in the modelling of the $$ t\overline{t}{W}^{\pm } $$ process. With the goal of understanding and resolving the modelling issues within the SM $$ t\overline{t}{W}^{\pm } $$ process we report on the state-of-the-art NLO QCD computation for this process. Specifically, we calculate higher-order corrections to the $$ {e}^{+}{\nu}_e{\mu}^{-}{\overline{\nu}}_{\mu }{e}^{+}{\nu}_eb\overline{b} $$ and $$ {e}^{-}{\overline{\nu}}_e{\mu}^{+}{\nu}_{\mu }{e}^{-}{\overline{\nu}}_eb\overline{b} $$ final state at the LHC with $$ \sqrt{s} $$ = 13 TeV. In the computation off-shell top quarks are described by Breit-Wigner propagators, furthermore, double-, single- as well as non-resonant top-quark contributions along with all interference effects are consistently incorporated at the matrix element level. Results at NLO QCD accuracy are presented in the form of fiducial integrated and differential cross sections for two selected renormalisation and factorisation scale choices and three different PDF sets. The impact of the top quark off-shell effects on the $$ t\overline{t}{W}^{\pm } $$ cross section is also examined by an explicit comparison to the narrow-width approximation.

The simplest of them all: