pi-pi Scattering in Twisted Mass Chiral Perturbation Theory

Abstract

In this report we describe both I=2 and I=0 pi-pi scattering for twisted mass lattice QCD utilizing twisted mass chiral perturbation theory at next-to-leading order. Focusing on the lattice spacing (b) corrections, we demonstrate that in the exotic I=2, I_3=+-2 channels, the leading scaling violations of pi-pi scattering at maximal twist begin at O(m_pi^2 b^2). This is not the case in any other isospin channel, for which the scaling violations at maximal twist begin at O(b^2). Furthermore, we demonstrate the existence of a mixing between the I=2, I_3 = 0 and I=0 scattering channels due to the breaking of isospin symmetry by the twisted mass term. The mixing term, although formally next-to-leading order, is relatively large, thus necessitating the use of a coupled channel analysis. We argue that this mixing likely renders the computation of the I=0 channel impractical with twisted mass lattice QCD.

7 pages, 2 figures, version published in PRD

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Cited by in corpus (10)

• The pi+ pi+ scattering length from maximally twisted mass lattice QCD
• Scattering of two and three physical pions at maximal isospin from lattice QCD
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: isospin-2 $\pi \pi$ scattering length
• Isospin-0 $\pi \pi$ s-wave scattering length from twisted mass lattice QCD
• Chiral logs in twisted mass lattice QCD with large isospin breaking
• Hadron-Hadron Interactions from $N_f=2+1+1$ Lattice QCD: $I=3/2$ $\pi K$ Scattering Length
• Baryon chiral perturbation theory with Wilson fermions up to $\mathcal{O}(a^2)$ and discretization effects of latest $n_f=2+1$ LQCD octet baryon masses
• $\pi \pi$ scattering in partially-quenched twisted-mass chiral perturbation theory
• Study of $a_0^0(980)$-$f_0(980)$ mixing from $a_0(1450)\to a_0^0(980)f_0(500)\to {\pi }^{+}{\pi }^{-}{f}_0(500)$
• Topics in Lattice QCD and Effective Field Theory