论文标题
在QED中解析带电的HADRON-仪表不变的插值操作员
Resolving Charged Hadrons in QED -- Gauge Invariant Interpolating Operators
论文作者
论文摘要
带电介子的标准插值操作员，例如$ j_ {b} = \ bar biγ_5u $ for $ b^ - $，在QED中不是不变的，因此对于扰动方法而言。我们通过添加辅助电荷标量$φ_b$，$ {\ cal j} _ {b}^{（0）} = j_b \，φ_b$，提出了一个不变的插值操作员，$φ_b$，$ {\ cal j} _ {b}^{（0）} = j_b \，φ_b$。修改后的LSZ因子被证明是红外有限的，这是验证该方法的必要条件。在$ {\ cal o}（α）$时，这等同于带电运营商的特定狄拉克敷料。使用迭代积分的概括性化建立了与所有订单的等价性，并提供了透明的替代观点。该方法由Leptonic Decay $ b^ - \ to \ ell^ - \barν$进行了讨论。形式主义本身对于任何旋转，风味和最终状态集（例如$ b^ - \toπ^0 \ ell^ - \barν$）都是有效的。
Standard interpolating operators for charged mesons, e.g. $J_{B} = \bar b i γ_5 u$ for $B^-$, are not gauge invariant in QED and therefore problematic for perturbative methods. We propose a gauge invariant interpolating operator by adding an auxiliary charged scalar $Φ_B$, ${\cal J}_{B}^{(0)} = J_B \, Φ_B$, which reproduces all the universal soft and collinear logs. The modified LSZ-factor is shown to be infrared finite which is a necessary condition for validating the approach. At ${\cal O}(α)$, this is equivalent to a specific Dirac dressing of charged operators. A generalisation thereof, using iterated integrals, establishes the equivalence to all orders and provides a transparent alternative viewpoint. The method is discussed by the example of the leptonic decay $B^- \to \ell^- \bar ν$ for which a numerical study is to follow. The formalism itself is valid for any spin, flavour and set of final states (e.g. $B^- \to π^0 \ell^- \bar ν$).
