Gauge Theory Bootstrap: Pion amplitudes and low energy parameters
arxiv(2024)
摘要
Following the Gauge Theory Bootstrap method proposed in our previous work
[arXiv:2309.12402], we compute pion scattering phase shifts for all partial
waves with angular momentum ℓ≤ 3 up to 2 GeV and calculate the low
energy χPT coefficients ℓ̅_1,2,4,6. The method looks for the
most general S-matrix that matches at low energy the tree level amplitudes of
the non-linear sigma model and at high energy, QCD sum rules and form factors.
This is a theoretical/numerical calculation that uses as only data the pion
mass m_π, pion decay constant f_π and the QCD parameters N_c=3,
N_f=2, m_q and α_s. All results are in reasonable agreement with
experiment. In particular, we find the ρ(770), f_2(1270) and
ρ(1450) resonances and some initial indication of particle production near
the resonances. The interplay between the UV gauge theory and low energy pion
physics is an example of a general situation where we know the microscopic
theory as well as the effective theory of long wavelength fluctuations but we
want to solve the strongly coupled dynamics at intermediate energies. The
bootstrap builds a bridge between the low and high energy by determining the
consistent S-matrix that matches both and provides, in this case, a new
direction to understand the strongly coupled physics of gauge theories.
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