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A particle physicist lacing their shoes

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arxiv 2503.18935 v1 pith:3PHJFY6M submitted 2025-03-24 hep-th math-phmath.MP

A particle physicist lacing their shoes

classification hep-th math-phmath.MP
keywords tensorsamplitudesanswerbestbosoncoefficientsconnectedconstraints
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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This letter presents the solution to a counting problem, to the best of our knowledge not known in full generality, which can be mapped to both (i) ways to lace a $N$-holes-per-side shoe with $\ell$ shoestrings and (ii) a sum over the indexes of $2N$-tensors made of symmetric 2-tensors. The coefficients that answer this question are then connected to spin $J=N$ boson exchange amplitudes and perturbative unitarity constraints, deriving relations with Legendre polynomials and sum rules.

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Cited by 1 Pith paper

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  1. The Potential of HEFT and the scale of New Physics

    hep-ph 2025-12 conditional novelty 6.0

    From a geometric recursion, the authors compute leading high-energy amplitudes with arbitrary multiplicities, resum them into unitarity bounds and cut-offs, and show that a dilaton HEFT reaches the SM as Δ→2 without p...