Kaons and long-distance meson mixing from lattice QCD Stephen R. Sharpe University of Washington S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 1 /34 Friday, March 7, 14
Based partly on 2013 white paper www.usqcd.org/documents/13flavor.pdf S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 2 /34 Friday, March 7, 14
Based partly on 2013 white paper Very helpful input from experimentalists and phenomenologists! S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 3 /34 Friday, March 7, 14
Master Formula Expt = (CKM)(pQCD)(non-pert QCD) + BSM(non-pert QCD) LQCD provides first-principles method to calculate (some) non-perturbative QCD matrix elements S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 4 /34 Friday, March 7, 14
Outline Standard vs non-standard/novel/new lattice calculations Results for standard quantities Results & prospects for new quantities K →ππ decays Δ M K (long distance) K →πνν and other rare decays D →ππ , D → KK and D-Dbar mixing Summary & Outlook S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 5 /34 Friday, March 7, 14
Standard vs non - standard quantities Standard means matrix elements involving single particles d ⇒ f K2 (similarly f π , f D , f B ) A μ A μ s d ⇒ K →π form factor A μ A μ s u (similarly B → D, etc) J μ S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 6 /34 Friday, March 7, 14
Standard vs non - standard quantities Standard means matrix elements involving single particles d H W ⇒ B K (similarly B D , B B ) A μ A μ s Nearly 20 standard matrix elements are fully controlled with small errors Decay constants: f π , f K , f D , f Ds , f B , f Bs Form factors: K →π , D → K, D →π , B → D, B → D * , B s → D s & B →π Mixing matrix elements: B K , B B , B Bs S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 7 /34 Friday, March 7, 14
Standard vs non - standard quantities Non-standard: matrix elements involving two or more particles A μ ⇒ K →ππ (I=2) u d A μ d s u H W A μ S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 8 /34 Friday, March 7, 14
Standard vs non - standard quantities Non-standard: matrix elements involving two or more particles and/or quark-disconnected contributions A μ ⇒ K →ππ (I=0) u d H W d A μ s u A μ S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 9 /34 Friday, March 7, 14
Standard vs non - standard quantities Non-standard: matrix elements involving two or more particles and/or quark-disconnected contributions A μ ⇒ K →ππ (I=0) d H W d A μ s u u A μ S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 10 /34 Friday, March 7, 14
Standard vs non - standard quantities Non-standard: matrix elements involving two or more particles and/or quark-disconnected contributions and/or two insertions of H W u d H W d H W A μ A μ s ⇒ Long distance part of Δ M K S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 11 /34 Friday, March 7, 14
Standard vs non - standard quantities Non-standard: matrix elements involving two or more particles and/or quark-disconnected contributions and/or two insertions of H W u u H W d H W A μ A μ s ⇒ Long distance part of Δ M K S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 12 /34 Friday, March 7, 14
Outline Standard vs non-standard/novel/new lattice calculations Results for standard quantities Results & prospects for new quantities K →ππ decays Δ M K (long distance) K →πνν and other rare decays D →ππ , D → KK and D-Dbar mixing Summary & Outlook S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 13 /34 Friday, March 7, 14
Status of f K /f π FLAG 2013 (arXiv:1310.8555) 0.4% error (really 2% on difference from 1) ⇒ | V us | = 0 . 2256(3) exp (2 − 4) EM (10) lat (1) V ud Further lattice improvement underway, but will eventually require inclusion of EM effects. This is not easy since axial current not EM gauge invariant. S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 14 /34 Friday, March 7, 14
Status of K → π form factor FLAG 2014 (preliminary) f + (0) = 0 . 9661(32) ( N f = 2 + 1) 0.3% error [really 10% on f + (0) − 1] ⇒ | V us | = 0 . 2239(5) exp (2) EM (7) lat Lattice errors will be reduced using physical light-quark masses (underway) “EM wall” not far away S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 15 /34 Friday, March 7, 14
Status of B K FLAG 2013 (arXiv:1310.8555) 1.3% error Can be further improved, but already other errors dominate when using B K in unitarity triangle analysis (V cb , long distance in ε K , PT errors) S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 16 /34 Friday, March 7, 14
Reasons for future improvement Steadily improve calculations of standard matrix elements, in particular using: Physical light-quark masses Isospin breaking & EM effects Charmed sea Finer lattice spacings & improved actions (heavy quarks) Improved statistical errors Improved methods of normalizing operators (e.g. SMOM) Already in use for some quantities, will soon become widespread S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 17 /34 Friday, March 7, 14
Expanding portfolio of standard quantities Contributions of BSM physics to K (and D & B) mixing B → K l + l - , Λ b →Λ l + l - and related form factors Tensor form factors for K →π ; needed to constrain BSM theories Others? Can achieve few-10% accuracy on few year timescale, which is commensurate with experimental program, and significantly enhances search for BSM physics S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 18 /34 Friday, March 7, 14
Outline Standard vs non-standard/novel/new lattice calculations Results for standard quantities Results & prospects for new quantities K →ππ decays Δ M K (long distance) K →πνν and other rare decays D →ππ , D → KK and D-Dbar mixing Summary & Outlook S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 19 /34 Friday, March 7, 14
K → ππ (I =2 ) decay amplitudes [RBC/UKQCD arXiv:1111.1699, 1206.5142, 1311.3844(Lattice 2013) ] First controlled result for an amplitude involving two particles Isospin 2 ⇒ no quark-disconnected contributions Uses physical kinematics (physical quark masses, moving pions so M K =2E π ) which requires box with L ≈ 5.5 fm Original result at a ≈ 0.14 fm; two new (prelim.) results at a ≈ 0.12 & 0.9 fm, allowing continuum extrapolation Systematic error now ≈ 11% (down from 19%); statistical errors 1-2% A μ u d A μ d s u H W A μ S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 20 /34 Friday, March 7, 14
ππ (I =2 ) phase shi fu [RBC/UKQCD arXiv:1111.1699, 1206.5142] Auxiliary calculation needed to make finite volume correction (few % effect) First calculation of phase shift with physical quark masses u Lattice I=2 Experiment phase shift S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 21 /34 Friday, March 7, 14
Comparison with experiment Lattice Results (2012) [RBC/UKQCD arXiv:1111.1699, 1206.5142] expt. 1.479(4) 10 − 8 [K + ] Re A 2 =1.38 (5) stat (26) syst 10 − 8 GeV 1.57(6) 10 − 8 [K S ] New information! Im A 2 = − 6.5 (5) stat (12) syst 10 − 13 GeV Can use with expt result for ε ’ to determine Im A 0 Present lattice errors about half this size [arXiv:1311.3844; RBC/UKQCD article in progress] S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 22 /34 Friday, March 7, 14
K → ππ (I =0 ) amplitude & Δ I =1 / 2 rule I=0 involves disconnected contractions ⇒ numerics much more challenging Several other technical challenges too. Fermions with chiral symmetry essential. Pilot calculation in 2012: decay at threshold for M K ~660, 880MeV [RBC/UKQCD arXiv:1212.1474] Demonstrates that technology (& related theory) exists. Statistical errors ~ 15%. u A μ A μ d d H W H W d d A μ A μ s s u u u A μ A μ S. Sharpe, “Kaons & long-distance meson mixing” 3/7/14 @ Lattice meets Experiment 2014, FNAL 23 /34 Friday, March 7, 14
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