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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.19764 |
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| _version_ | 1866914580416954368 |
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| author | Kozameh, Carlos Depaola, Gerardo |
| author_facet | Kozameh, Carlos Depaola, Gerardo |
| contents | We compute the third-order Bondi shear $σ^+_3$ in the null
surface formulation (NSF) of general relativity with definite
graviton helicities. The quantum operator $\daout{3,\pm}$ is
derived explicitly in terms of the four helicity channels
(I)--(IV) of the scattering equation, and compared with the
helicity-summed result of Ref.~\cite{PRL2026}.
Applied to two-graviton scattering, the contribution
$\langle\daout{3,+}\,\daout{3,-}\rangle$ for the process
$h^+(K_1)+h^-(K_2)\to h^+(K'_3)+h^-(K'_4)$ generates
simultaneously the $t$- and $u$-channel poles of the
tree-level graviton amplitude. An explicit Wick-contraction
calculation (Appendix~\ref{app:Wick}) shows that the NSF
kernels yield
\begin{equation*}
\mathcal{M}^{(33)}\big|_{(+,-\to+,-)}
= 16πG\,\frac{s^3}{tu},
\end{equation*}
from first principles, with the angular integration over $S^2$
manifestly finite and no propagator introduced. The pole
structure $1/(tu)$ and the $s^3$ dependence are exact
consequences of the null-cone geometry; the coefficient
$16πG$ follows from the Ashtekar normalization of the
asymptotic modes, in analogy with Ref.~\cite{PRD2026partI}. Both $t$- and $u$-channel poles
arise simultaneously from a single Wick contraction; in
covariant perturbation theory they arise from
two separate Feynman diagrams. The completion of the tree-level amplitude
via $\mathcal{M}^{(24)}=\langle\daout{2}\cdot\daout{4}\rangle$
is carried out in Part~III~\cite{PRD2026partIII}.
Unitarity at order $\varepsilon^2$ is verified; the operators
$\daout{n,\pm}$ are identified as the terms of the
Baker-Campbell-Hausdorff expansion of $S^\dagger\ain{\pm}S$,
establishing unitarity as a structural consequence of the
recursive NSF equations~\cite{SmatrixNSF}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19764 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum graviton scattering with definite helicities in the null surface formulation, Part II: Third-order scattering and the exchange channels \author{C.~N.~Kozameh \and G.~O.~Depaola} Kozameh, Carlos Depaola, Gerardo High Energy Physics - Theory We compute the third-order Bondi shear $σ^+_3$ in the null surface formulation (NSF) of general relativity with definite graviton helicities. The quantum operator $\daout{3,\pm}$ is derived explicitly in terms of the four helicity channels (I)--(IV) of the scattering equation, and compared with the helicity-summed result of Ref.~\cite{PRL2026}. Applied to two-graviton scattering, the contribution $\langle\daout{3,+}\,\daout{3,-}\rangle$ for the process $h^+(K_1)+h^-(K_2)\to h^+(K'_3)+h^-(K'_4)$ generates simultaneously the $t$- and $u$-channel poles of the tree-level graviton amplitude. An explicit Wick-contraction calculation (Appendix~\ref{app:Wick}) shows that the NSF kernels yield \begin{equation*} \mathcal{M}^{(33)}\big|_{(+,-\to+,-)} = 16πG\,\frac{s^3}{tu}, \end{equation*} from first principles, with the angular integration over $S^2$ manifestly finite and no propagator introduced. The pole structure $1/(tu)$ and the $s^3$ dependence are exact consequences of the null-cone geometry; the coefficient $16πG$ follows from the Ashtekar normalization of the asymptotic modes, in analogy with Ref.~\cite{PRD2026partI}. Both $t$- and $u$-channel poles arise simultaneously from a single Wick contraction; in covariant perturbation theory they arise from two separate Feynman diagrams. The completion of the tree-level amplitude via $\mathcal{M}^{(24)}=\langle\daout{2}\cdot\daout{4}\rangle$ is carried out in Part~III~\cite{PRD2026partIII}. Unitarity at order $\varepsilon^2$ is verified; the operators $\daout{n,\pm}$ are identified as the terms of the Baker-Campbell-Hausdorff expansion of $S^\dagger\ain{\pm}S$, establishing unitarity as a structural consequence of the recursive NSF equations~\cite{SmatrixNSF}. |
| title | Quantum graviton scattering with definite helicities in the null surface formulation, Part II: Third-order scattering and the exchange channels \author{C.~N.~Kozameh \and G.~O.~Depaola} |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.19764 |