Bootstrapping gauge theories

Journal Article · 03 November 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.110.096001 · OSTI ID:2476074

He, Yifei ; Kruczenski, Martin

We consider asymptotically free gauge theories with gauge group $SU\left(N_c\right)$ and $N_f$ quarks with mass $m_q\ll {\mathrm{\Lambda }}_{\mathrm{QCD}}$ 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 ( $N_c$ , $N_f$ , $m_q$ , ${\mathrm{\Lambda }}_{\mathrm{QCD}}$ ) by using the form-factor bootstrap recently proposed by Karateev, Kuhn and Penedones together with a finite energy version of the Shifman-Vainshtein-Zakharov (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. Published by the American Physical Society 2024

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0007884
• OSTI ID: 2476074
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 9 Vol. 110; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English