SU(2) chiral perturbation theory for K(l3) decay amplitudes
Flynn, J.M and Sachrajda, C.T. (2008) SU(2) chiral perturbation theory for K(l3) decay amplitudes Preprint, (0809.1229v1), 20pp. (doi:10.1016/j.nuclphysb.2008.12.001).
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Description/Abstract
We use oneloop \SU(2)_L\times \SU(2)_R chiral perturbation theory (\SU(2) ChPT) to study the behaviour of the formfactors for semileptonic K\to\pi decays with the pion mass at q^2=0 and at q^2_{\textrm{max}}=(m_Km_\pi)^2, where q is the momentum transfer. At q^2=0, the finalstate 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 CallanTreiman 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 semiquantitative 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.
Item Type:  Article  

Digital Object Identifier (DOI):  doi:10.1016/j.nuclphysb.2008.12.001  
Additional Information:  Report number: SHEP0826  
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ePrint ID:  64183  
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Date Deposited:  09 Jan 2009  
Last Modified:  16 Apr 2017 17:21  
Further Information:  Google Scholar  
URI:  http://eprints.soton.ac.uk/id/eprint/64183 
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