论文标题
在大$ n_c $上解剖$ΔI= 1/2 $规则
Dissecting the $ΔI= 1/2$ rule at large $N_c$
论文作者
论文摘要
我们研究了带有四种简并风味的理论，研究颜色$ n_c $的kaon衰变振幅的缩放尺寸，$ n_f = 4 $。在这种情况下，两个电流运算符，$ q^\ pm $，中介$δs= 1 $过渡，例如，非leptonic kaon的两个isospin振幅，以$ k \ to（ππ）_ {i = 0,2} $，$ a_0 $和$ a_0 $和$ a_0 $和$ a_0 $和$ a_0 $和$ a_0 $和$ a_0 $。特别是，我们专注于这两个操作员介导的简单$ k \toπ$振幅，$ a^\ pm $。提出了对这些可观察到的大型缩放的大$ n_c $缩放的图表分析，这证明了领先的$ {\ Mathcal O}（1/n_c）$和$ {\ Mathcal O}（N_F/N_C^2）$校正的$ {\ Mathcal O}（1/N_C）$。使用我们的新$ n_f = 4 $和以前的淬火数据，我们确认了这一期望，并表明这些更正是$自然$大，并且可能是$ΔI= 1/2 $规则的起源。后者的证据是间接的，基于振幅与手性扰动理论预测的匹配，从中可以确定手性弱的汉密尔顿人的低能耦合，$ g^\ pm $。然后可以得出$ k \ to（ππ）_ {i = 0,2} $ isospin振幅的NLO估计值，然后可以得出与实验值一致。
We study the scaling of kaon decay amplitudes with the number of colours, $N_c$, in a theory with four degenerate flavours, $N_f=4$. In this scenario, two current-current operators, $Q^\pm$, mediate $ΔS=1$ transitions, such as the two isospin amplitudes of non-leptonic kaon decays for $K\to (ππ)_{I=0,2}$, $A_0$ and $A_2$. In particular, we concentrate on the simpler $K\toπ$ amplitudes, $A^\pm$, mediated by these two operators. A diagrammatic analysis of the large-$N_c$ scaling of these observables is presented, which demonstrates the anticorrelation of the leading ${\mathcal O}(1/N_c)$ and ${\mathcal O}(N_f/N_c^2)$ corrections in both amplitudes. Using our new $N_f=4$ and previous quenched data, we confirm this expectation and show that these corrections are $naturally$ large and may be at the origin of the $ΔI=1/2$ rule. The evidence for the latter is indirect, based on the matching of the amplitudes to their prediction in Chiral Perturbation Theory, from which the LO low-energy couplings of the chiral weak Hamiltonian, $g^\pm$, can be determined. A NLO estimate of the $K \to (ππ)_{I=0,2}$ isospin amplitudes can then be derived, which is in good agreement with the experimental value.
