Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dispersion relations for $\gamma^*\gamma^*\to\pi\pi$: helicity
  amplitudes, subtractions, and anomalous thresholds   We present a comprehensive analysis of the dispersion relations for the
doubly-virtual process $\gamma^*\gamma^*\to\pi\pi$. Starting from the
Bardeen-Tung-Tarrach amplitudes, we first derive the kernel functions that
define the system of Roy-Steiner equations for the partial-wave helicity
amplitudes. We then formulate the solution of these partial-wave dispersion
relations in terms of Omn\`es functions, with special attention paid to the
role of subtraction constants as critical for the application to hadronic
light-by-light scattering. In particular, we explain for the first time why for
some amplitudes the standard Muskhelishvili-Omn\`es solution applies, while for
others a modified approach based on their left-hand cut is required unless
subtractions are introduced. In the doubly-virtual case, the analytic structure
of the vector-resonance partial waves then gives rise to anomalous thresholds,
even for space-like virtualities. We develop a strategy to account for these
effects in the numerical solution, illustrated in terms of the $D$-waves in
$\gamma^*\gamma^*\to\pi\pi$, which allows us to predict the doubly-virtual
responses of the $f_2(1270)$ resonance. In general, our results form the basis
for the incorporation of two-meson intermediate states into hadronic
light-by-light scattering beyond the $S$-wave contribution.

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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
2
The categories of this paper are: math
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: stat