# Solitons in an effective theory of CP violation

Research paper by **N. Chandra, M. B. Paranjape, R. Srivastava**

Indexed on: **06 Jan '16**Published on: **06 Jan '16**Published in: **High Energy Physics - Theory**

Join Sparrho today to stay on top of science

Discover, organise and share research that matters to you

Join Sparrho today to stay on top of science

Discover, organise and share research that matters to you

Join for free

#### Abstract

We study an effective field theory describing CP-violation in a scalar meson
sector. We write the simplest interaction that we can imagine, $${\cal L}\sim
\epsilon_{i_1\cdots
i_5}\epsilon^{\mu_1\cdots\mu_4}\phi_{i_1}\partial_{\mu_1}\phi_{i_2}\partial_{\mu_2}\phi_{i_3}\partial_{\mu_3}\phi_{i_4}\partial_{\mu_4}\phi_{i_5}$$
which involves 5 scalar fields. The theory describes CP-violation only when it
contains scalar fields representing mesons such as the $K^*_0$, sigma, $f_0$ or
$a_0$. If the fields represent pseudo-scalar mesons, such as B, K and $\pi$
mesons then the Lagrangian describes anomalous processes such as $KK\to
\pi\pi\pi$. We speculate that the field theory contains long lived excitations
corresponding to $Q$-ball type domain walls expanding through space-time. In an
1+1 dimensional, analogous, field theory we find an exact, analytic solution
corresponding to such solitons. The solitons have a U(1) charge $Q$, which can
be arbitrarily high, but oddly, the energy behaves as $Q^{2/3}$ for large
charge, thus the configurations are stable under disintegration into elementary
charged particles of mass $m$ with $Q=1$. We also find analytic complex
instanton solutions which have finite, positive Euclidean action.