The K 3 form factor from four-flavor lattice QCD and | V us | Aida - PowerPoint PPT Presentation

The K ℓ 3 form factor from four-flavor lattice QCD and | V us | Aida X. El-Khadra (University of Illinois and Fermilab) HC2NP workshop Puerto de la Cruz, Tenerife, 26-30 Sep 2016

Outline A Fermilab Lattice and MILC collaborations project Introduction Set-up Analysis Chiral-continuum fit Systematic error analysis Result in comparison Implications Summary and Outlook A. El-Khadra Lattice 2018, 23-28 July 2018 � 2

Introduction µ + V us example: K 0 → ⇡ − ` + ⌫ ` ν µ W ¯ s ¯ u K 0 π − d ✓ ◆ phase SU(2) ) × | V us | 2 × | f K 0 ⇡ − (0) | 2 × (1 + δ K ` EM + δ K ⇡ Γ K ` 3 = (known) × + space A. El-Khadra Lattice 2018, 23-28 July 2018 3 �

Introduction µ + V us example: K 0 → ⇡ − ` + ⌫ ` ν µ W ¯ s ¯ u K 0 π − d ✓ ◆ phase SU(2) ) × | V us | 2 × | f K 0 ⇡ − (0) | 2 × (1 + δ K ` EM + δ K ⇡ Γ K ` 3 = (known) × + space Needed to include charged kaon decay Needed to relate pure QCD form factor in the experimental average. to experiment. Mode dependent. Both are currently estimated phenomenologically. [Cirigliano et al, arXiv:1107.6001, RMP 2012] . A. El-Khadra Lattice 2018, 23-28 July 2018 � 3

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Moulson @ CKM 2016, arXiv:1704.04104) | V us | f K 0 π − All modes: 0.19% uncertainty (0) = 0 . 21654 (41) + | V us | f K 0 π − K 0 only: (0) = 0 . 21633 (44) exp (24) δ K 0 ` + EM | V us | f K 0 π − K ± only: (0) = 0 . 21710 (51) exp (24) δ K ± ` EM (42) δ K ± ⇡ 0 + SU(2) A. El-Khadra Lattice 2018, 23-28 July 2018 4 �

Set-up •MILC HISQ ensembles with N f = 2+1+1 sea ✦ Size of disk: # of configurations ✦ Black circles: new ensembles or increased # confs since 2014 
 (see table in appendix for more details) A. El-Khadra Lattice 2018, 23-28 July 2018 � 5