Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2008-09-07
Nucl.Phys.B812:64-80,2009
Physics
High Energy Physics
High Energy Physics - Phenomenology
20 pages, 4 figures
Scientific paper
10.1016/j.nuclphysb.2008.12.001
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 $K\to\pi$ decays with the pion mass at $q^2=0$ and at $q^2_{\textrm{max}}=(m_K-m_\pi)^2$, where $q$ is the momentum transfer. At $q^2=0$, the final-state pion has an energy of approximately $m_K/2$ (for $m_K\gg m_\pi$) and so is not soft, nevertheless it is possible to compute the chiral logarithms, i.e. the corrections of $O(m_\pi^2\log(m_\pi^2))$. 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 $f^0_{P\to\pi}(\qsqmax)=f^{(P)}/f$ 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.
Flynn Jonathan M.
Sachrajda Chris T.
No associations
LandOfFree
SU(2) chiral perturbation theory for Kl3 decay amplitudes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with SU(2) chiral perturbation theory for Kl3 decay amplitudes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and SU(2) chiral perturbation theory for Kl3 decay amplitudes will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-322323