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arXiv 0809.1229hep-phhep-lat
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Kl3衰变振幅的SU(2)手征微扰理论

SU(2) chiral perturbation theory for Kl3 decay amplitudes

J. M. Flynn, C. T. Sachrajda

摘要:

本文用单圈$\SU(2)_L\times \SU(2)_R$手征微扰理论($\SU(2)$ ChPT)研究了半轻子$K\toπ$随π介子质量在$q^2=0$和$q^2_{\textrm{max}}=(m_K-m_π)^2$衰变的形状因子的行为,其中$q$是动量转移.在$q^2=0$,最终态π介子的能量约为$m_K/2$(对于$m_K\gg m_π$),因此不是软的,但是可以计算手征介子,即$O(m_π^2\log(m_π^2))$的修正。我们设想,我们在$q^2=0$的结果将是有用的外推晶格QCD结果的物理质量。Callan-Treiman关系的一个结果是,在$\SU(2)$手征极限($m_u=m_d=0$)中,$\qsqmax$处的标量形状因子$f^0$等于$f^{(K)}/f$,手征极限中K介子和π介子轻子衰变常数的比值。在$\qsqmax$上获得的标量形状因子的晶格结果具有很好的精度,但是在进行模拟的质量下,结果比$f^{(K)}/f$低约25%,并且仅非常缓慢地增加。我们调查的手征行为的$f^0(\qsqmax)$,并找到大的修正,提供了一个半定量的解释之间的差异晶格结果和$f^{(K)}/f$。我们强调的一般性关系$f^0_{P\toπ}(\qsqmax)=f^{(P)}/f$在$\SU(2)$手征极限,其中$P=K,D$或$B$和简要评论的潜在价值,使用这个定理在获得物理结果从晶格模拟。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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