Bootstrapping gauge theories

Abstract

We consider asymptotically free gauge theories with gauge group $SU(N_c)$ and $N_f$ quarks with mass $m_q\ll {\Lambda }_{\text{QCD}}$ that undergo chiral symmetry breaking and confinement. We propose a bootstrap method to compute the S-matrix of the pseudo-Goldstone bosons (pions) that dominate the low energy physics. For the important case of $N_c=3$, $N_f=2$, a numerical implementation of the method gives the phase shifts of the $S0$, $P1$ and $S2$ waves in good agreement with experimental results. The method incorporates gauge theory information ($N_c$, $N_f$, $m_q$, ${\Lambda }_{\text{QCD}}$) by using the form-factor bootstrap recently proposed by Karateev, Kuhn and Penedones together with a finite energy version of the SVZ sum rules. At low energy we impose constraints from chiral symmetry breaking. The only low energy numerical inputs are the pion mass $m_{\pi }$ and the quark and gluon condensates.

v3: 43 pages, 11 figures, appendix added testing numerical parameters; Joint publications in Phys. Rev. Lett. (short version) and Phys. Rev. D (this version)

References in corpus (11)

• ππscattering
• The S-matrix Bootstrap I: QFT in AdS
• The S-matrix Bootstrap II: Two Dimensional Amplitudes
• The pion-pion scattering amplitude
• Recent Progress in QCD Condensate Evaluations and Sum Rules
• Bootstrapping QCD: the Lake, the Peninsula and the Kink
• Scalar form factors of light mesons
• Bootstrapping Massive Quantum Field Theories
• Cornering Large-$N_c$ QCD with Positivity Bounds
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• Unitarized Chiral Perturbation Theory and the meson spectrum

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