SU(2) chiral perturbation theory for Kl3 decay amplitudes

Abstract

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 $q_{\text{max}}^2=(m_K-m_{\pi }{)}^2$, 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 $f^0_{P\toπ}(\qsqmax)=f^{(P)}/f$ 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.

20 pages, 4 figures

References in corpus (17)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• New Results on B->pi, K, eta Decay Formfactors from Light-Cone Sum Rules
• Chiral perturbation theory
• Twisted Boundary Conditions in Lattice Simulations
• B Meson Semileptonic Form Factors from Unquenched Lattice QCD
• $K_{\ell 3}$ decays in Chiral Perturbation Theory
• The K -> pi vector form factor at zero momentum transfer on the lattice
• Twisted valence quarks and hadron interactions on the lattice
• Kl3 semileptonic form factor from 2+1 flavour lattice QCD
• The Decay $B\to \pi \ell \nu$ in Heavy Quark Effective Theory
• Pion-Kaon Scattering near the Threshold in Chiral SU(2) Perturbation Theory
• Hadronic form factors in Lattice QCD at small and vanishing momentum transfer
• $\bar B\to\bar K\e^+\e^-$ in Chiral Perturbation Theory
• Vector form factor in K_l3 semileptonic decay with two flavors of dynamical domain-wall quarks
• B-->pi and B-->K transitions in standard and quenched chiral perturbation theory
• Full CKM matrix with lattice QCD
• B --> pi and B --> K transitions in partially quenched chiral perturbation theory

Cited by in corpus (28)

• FLAG Review 2019
• FLAG Review 2021
• QCD and strongly coupled gauge theories: challenges and perspectives
• Review of lattice results concerning low energy particle physics
• Flavor Physics in the Quark Sector
• $B\to \pi \ell \nu$ and $B_s\to K\ell \nu$ form factors and $|V_{ub}|$ from 2+1-flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks
• FLAG Review 2024
• $K\to \pi$ semileptonic form factors with $N_f=2+1+1$ Twisted Mass fermions
• K -> pion Semileptonic Form Factors from Two-Flavor Lattice QCD
• Hard Pion Chiral Perturbation Theory for $B\to \pi$ and $D\to \pi$ Formfactors
• Vector Formfactors in Hard Pion Chiral Perturbation Theory
• Chiral Extrapolation of the Strangeness Changing K pi Form Factor
• D-meson semileptonic decays to pseudoscalars from four-flavor lattice QCD
• Chiral dynamics with strange quarks in the light of recent lattice simulations
• Hyperon Axial Charges in Two-Flavor Chiral Perturbation Theory
• $K\to \pi \pi$ Decays in SU(2) Chiral Perturbation Theory
• Exclusive semileptonic $B_s\to K\ell \nu$ decays on the lattice
• Hyperon Electromagnetic Properties in Two-Flavor Chiral Perturbation Theory
• On the factorization of chiral logarithms in the pion form factors
• Kaon Thresholds and Two-Flavor Chiral Expansions for Hyperons
• Kl3 and pion form factors using partially twisted boundary conditions
• Possible lattice approach to B to D pi (K) matrix elements
• Momentum dependence of kaon semileptonic form factors with Nf=2+1+1 Twisted Mass fermions
• Chiral perturbation theory in the meson sector
• Lattice Kaon Physics
• Chiral Symmetry and Charmonium Decays to Two Pseudoscalars
• Next to Leading Order Chiral Perturbation theory of $K\pi \to \pi$ and $K\to \pi \pi$ amplitudes
• Kaon semileptonic vector form factor with $N_f=2+1+1$ Twisted Mass fermions