A lattice study of ππ scattering at large Nc
Abstract We present the first lattice study of pion-pion scattering with varying number of colors, Nc. We use lattice simulations with four degenerate quark flavors, Nf = 4, and Nc = 3 − 6. We focus on two scattering channels that do not involve vacuum diagrams....
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Berlin Heidelberg
2022
|
| Online Access: | https://hdl.handle.net/1721.1/143087 |
| Summary: | Abstract
We present the first lattice study of pion-pion scattering with varying number of colors, Nc. We use lattice simulations with four degenerate quark flavors, Nf = 4, and Nc = 3 − 6. We focus on two scattering channels that do not involve vacuum diagrams. These correspond to two irreducible representations of the SU(4) flavor group: the fully symmetric one, SS, and the fully antisymmetric one, AA. The former is a repulsive channel equivalent to the isospin-2 channel of SU(2). By contrast, the latter is attractive and only exists for Nf ≥ 4. A representative state is
D
s
+
π
+
−
D
+
K
+
/
2
$$ \left(\left.\left|{D}_s^{+}{\pi}^{+}\right.\right\rangle -\left.\left|{D}^{+}{K}^{+}\right.\right\rangle \right)/\sqrt{2} $$
. Using Lüscher’s formalism, we extract the near-threshold scattering amplitude and we match our results to Chiral Perturbation Theory (ChPT) at large Nc. For this, we compute the analytical U(Nf) ChPT prediction for two-pion scattering, and use the lattice results to constrain the Nc scaling of the relevant low-energy couplings. |
|---|