SU(2) chiral perturbation theory for Kl3 decay amplitudes
| dc.creator | Flynn, J. M. | |
| dc.creator | Sachrajda, C. T. | |
| dc.date | 2008-09-07 | |
| dc.date.accessioned | 2026-07-07T12:40:17Z | |
| dc.date.available | 2026-07-07T12:40:17Z | |
| dc.description | We use one-loop $\SU(2)_L\times \SU(2)_R$ chiral perturbation theory ($\SU(2)$ ChPT) to study the behaviour of the form-factors for semileptonic $K\toπ$ decays with the pion mass at $q^2=0$ and at $q^2_{\textrm{max}}=(m_K-m_π)^2$, where $q$ is the momentum transfer. At $q^2=0$, the final-state pion has an energy of approximately $m_K/2$ (for $m_K\gg m_π$) and so is not soft, nevertheless it is possible to compute the chiral logarithms, i.e. the corrections of $O(m_π^2\log(m_π^2))$. We envisage that our results at $q^2=0$ will be useful in extrapolating lattice QCD results to physical masses. A consequence of the Callan-Treiman relation is that in the $\SU(2)$ chiral limit ($m_u=m_d=0$), the scalar form factor $f^0$ at $\qsqmax$ is equal to $f^{(K)}/f$, the ratio of the kaon and pion leptonic decay constants in the chiral limit. Lattice results for the scalar form factor at $\qsqmax$ are obtained with excellent precision, but at the masses at which the simulations are performed the results are about 25% below $f^{(K)}/f$ and are increasing only very slowly. We investigate the chiral behaviour of $f^0(\qsqmax)$ and find large corrections which provide a semi-quantitative explanation of the difference between the lattice results and $f^{(K)}/f$. We stress the generality of the relation $f^0_{P\toπ}(\qsqmax)=f^{(P)}/f$ in the $\SU(2)$ chiral limit, where $P=K,D$ or $B$ and briefly comment on the potential value of using this theorem in obtaining physical results from lattice simulations. | |
| dc.description | 20 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0809.1229 | |
| dc.identifier | http://arxiv.org/abs/0809.1229 | |
| dc.identifier | Nucl.Phys.B812:64-80,2009 | |
| dc.identifier | doi:10.1016/j.nuclphysb.2008.12.001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219397 | |
| dc.subject | High Energy Physics - Phenomenology | |
| dc.subject | High Energy Physics - Lattice | |
| dc.title | SU(2) chiral perturbation theory for Kl3 decay amplitudes | |
| dc.type | text |