RBC/UKQCD ππ scattering, K → ππ , and distillation projects Tom Blum (UCONN/RBRC) USQCD All Hands Meeting, Fermilab April 20, 2018 1 / 27
Outline I 1 ππ scattering and K → ππ 2 QCD + QED studies using twist-averaging 3 Exclusive Study of ( g − 2) µ HVP and Nucleon Form Factors with Distillation 4 Precise scale setting for ( g − 2) µ 5 References 2 / 27
ππ scattering and K → ππ Investigators: Blum (PI), Peter Boyle (Edinburgh), Norman Christ (Columbia), Daniel Hoying (UConn/BNL), Taku Izubuchi (BNL/RBRC), Luchang Jin (UConn/RBRC), Chulwoo Jung (BNL), Christopher Kelly (Columbia), Christoph Lehner (BNL), Robert Mawhinney (Columbia), Chris Sachrajda (Southampton), Amarjit Soni (BNL) compute request: 91.2 M JPsi core-hrs on JLab or BNL KNL clusters storage request: 200 TB disk, 200 TB tape 3 / 27
Motivation and background SM extremely successful, but ... Direct CP violation in kaon decays offers good place to look for breakdown, c . f . single phase in CKM matrix must explain all violation in SM Re ǫ ′ 1 − Γ( K S → π + π − )Γ( K L → π 0 π 0 ) � � 1 = Γ( K L → π + π − )Γ( K S → π 0 π 0 ) ǫ 6 � �� i ω e i ( δ 2 − δ 0 ) � Im A 2 − Im A 0 = Re √ ReA 2 Re A 0 2 ε G F � V ∗ � � H W = √ us V ud z i ( µ ) + τ y i ( µ ) Q i ( µ ) 2 i A ( K 0 → ππ ) I A I e i δ I = � ππ | H W | K � = Experiment: 16 . 6(2 . 3) × 10 − 4 SM: 1 . 38(5 . 15)(4 . 59) × 10 − 4 [1] (RBC/UKQCD G-parity bc project) 4 / 27
�� � ��� Methodology Matrix elements from Euclidean correlation functions � χ ππ ( t ) Q i ( t op ) χ † � � � 0 | χ ππ | n �� n | Q i | m �� m | χ † K | 0 � e − E n ( t − t op ) e − E m t op K (0) � = m n Physical kinematics corresponds to excited state, ground state is pions at rest G-parity bc’s (RBC/UKQCD): ground state is physical (pions at rest not allowed) For periodic bc’s, use A2A[2]+AMA[3]+GEVP analysis to extract excited state 5 / 27
, I0, momtotal000 analysis 24c , I2, momtotal000 analysis 24c I0 24c sigmasigma A 1PLUS Preliminary results with current allocation obius DWF, 1 GeV, 24 3 ensemble 2+1 flavor, physical point, M¨ A2A/AMA measurements on 66 configurations, 2000 low modes, 1 hit for high Good precision on I = 0 excited (physical) state, > ∼ 1 . 5 % 6 / 27
Proposed calculations 2+1 flavor physical point, M¨ obius DWF, Iwasaki gauge action ensembles (RBC/UKQCD) Table: Per-configuration cost of proposed calculations. Costs for propagators (props) are based on (z)M¨ obius DWF with L s = 12. a − 1 type size Cost (KNL node-hours) configs Total props meson fields contractions (M core-hrs) 24 3 × 64 K → ππ 1 72 64 739 100 16.8 32 3 × 64 ππ , K → ππ 1.4 171 470 202+739 100 30.4 32 3 × 64 1 114 1183 1008 100 44.0 ππ Dominated by contractions 7 / 27
Outline I 1 ππ scattering and K → ππ 2 QCD + QED studies using twist-averaging 3 Exclusive Study of ( g − 2) µ HVP and Nucleon Form Factors with Distillation 4 Precise scale setting for ( g − 2) µ 5 References 8 / 27
QCD + QED studies using twist-averaging Investigators: Mattia Bruno (BNL, co-PI), Xu Feng (Peking University), Taku Izubuchi (BNL/RBRC), Luchang Jin (UConn/RBRC), Christoph Lehner (BNL, PI), Aaron Meyer (BNL) Collaborators: Tom Blum (UConn), Norman Christ (CU), Chulwoo Jung (BNL), Chris Sachrajda (Southampton), Amarjit Soni (BNL) compute request: 59 M JPsi core-hrs on JLab or BNL KNL clusters storage request: 80 TB disk 9 / 27
Motivation and background O ( α ) isospin breaking corrections are important for many QCD observables muon g-2 light quark masses f π τ decays (dispersive treatment of muon g-2) 1 st two corrections calculated on 1.73 GeV, 48 3 , physical point M¨ obius DWF ensemble (RBC/UKQCD) goal: take continuum limit 10 / 27
Methodology: perturbative treatment of QED @ O ( α ) HVP f π f π EFT[5] u u u ℓ + ℓ + ℓ + π + π + π + (a) V (b) S (c) T (d) D1 (e) D2 ν ℓ ν ℓ ν ℓ d d d (a) (b) (c) (a) (b) (c) u u u ℓ + ℓ + ℓ + π + π + π + ν ℓ ν ℓ ν ℓ d d d (f) F (g) D3 (d) (e) (f) (d) (e) (f) Sample photon vertex stochastically, using importance sampling strategy C ab 2 ( z ) = � O a ( z ) O b (0) � , C ab ; µ ( x , z ) = � O a ( z ) O b (0) j µ ( x ) � , 3 C ab ; µν ( x , y , z ) = � O a ( z ) O b (0) j µ ( x ) j ν ( y ) � 4 O a ( z ) = ¯ q ( z )Γ a q ( z ) , j µ ( x ) = ¯ q ( x ) γ µ q ( x ) , Use twist averaging for photon to reduce/control FV errors [6] 11 / 27
Results from current allocation O ( α ) corrections to HVP, 1.73 GeV, physical point M¨ obius DWF ensemble (RBC/UKQCD) [4] Isospin breaking corrections in τ decays (Bruno, KEK workshop on HVP) 4 2 Cirigliano et al . 2002 , w / o S EW 0 ∆ a µ V Davier et al . 2009 , w / o S EW F − 2 Jegerlehner et al . 2011 Total This work preliminary − 4 − 6 − 6 − 4 − 2 0 0 1 2 3 4 5 ∆ a µ T [fm] 12 / 27
Proposed calculations obius DWF, 2.38 GeV, 64 3 ensemble (RBC/UKQCD) 2+1 flavor, physical point M¨ 12 sloppy 64 3 solves on 64 KNL nodes 600 seconds 12 exact 64 3 solves on 64 KNL nodes 2580 seconds Number of configurations 30 Number of sloppy solves per configuration 900 × 12 Number of exact solves per configuration 15 × 12 Total computational cost on 64 3 for sloppy solves in M Jpsi-core hours 55 Total computational cost on 64 3 for exact solves in M Jpsi-core hours 4 Total request 59 M Jpsi-core hours Table: Cost estimates for the proposed computation. We intend to use an AMA [3] setup with parameters described in this table. 13 / 27
Outline I 1 ππ scattering and K → ππ 2 QCD + QED studies using twist-averaging 3 Exclusive Study of ( g − 2) µ HVP and Nucleon Form Factors with Distillation 4 Precise scale setting for ( g − 2) µ 5 References 14 / 27
Exclusive Study of ( g − 2) µ HVP and Nucleon Form Factors with Distillation Investigators: A. S. Meyer (PI), M. Bruno, T. Izubuchi, Y. C. Jang, C. Jung, and C. Lehner compute request: 46.7 M JPsi core-hrs on JLab or BNL KNL clusters storage request: 50 TB disk 15 / 27
Motivation and background muon g-2 experiment E989 at Fermilab Error on HVP contribution to g − 2 desired at sub-percent level Long distance part of correlation function is noisy, dominates error use exclusive ππ channel(s) to improve“bounding method” [4], significantly reduce statistical error ν oscillation experiments NO ν A, DUNE, and HyperK precision measurements of mass-squared splittings, mixing angles, CP-violating angle in the lepton sector need accurate/precise nucleon axial-vector form factor calculations 16 / 27
Distillation Method (JLab/Trinity [7]) Eigenvectors of 3D laplacian act as a projection that smears quark fields in space 1.0 0.014 0.8 0.012 0.010 0.6 0.008 0.4 0.006 0.004 0.2 = ⇒ 0.002 0.0 20 20 15 15 0 0 10 10 5 5 10 10 5 5 15 15 20 0 20 0 i p 2 9 evecs (57 equiv), � i ≤ 2 Eigenvectors used as sources, contracted at sink to create “perambulators” yx ,βα ) − 1 | i a M ji � � � j b t ; y | ( D ba t ,βα = 0; x � xy ab Meson correlation functions constructed from tracing over perambulators C ( t ) = tr [Γ M ( t , t ′ )Γ ′ M ( t ′ , t ′′ )Γ ′′ M ( t ′′ , t ′′′ ) . . . ] 17 / 27
Generalized EigenValue Problem Vector current operator: x ¯ Local O 0 = � ψ ( x ) γ µ ψ ( x ) Two 2 π operators with different momenta 2 � � xyz ¯ ψ ( x ) f ( x − z ) e − i � p π · � z γ 5 f ( z − y ) ψ ( y ) �� O n = : � � � L L O 1 : p π = (1 , 0 , 0) O 2 : p π = (1 , 1 , 0) 2 π � 2 π � Correlators arranged in a 3 × 3 symmetric matrix: O 0 O 1 O 2 C (2) C (3) C (3) O 0 ρ ρ → ππ ρ → ππ C (4) C (4) O 1 ππ → ππ ππ → ππ C (4) O 2 ππ → ππ Analyze with Generalized EigenValue Problem (GEVP) method: Λ nn ( δ t ) ∼ e + E n δ t C ( t ) V = C ( t + δ t ) V Λ( δ t ) , 18 / 27
Results - HVP Bounding Method 350 800 local-local 1 state reconstruction 700 300 2 state reconstruction 600 3 state reconstruction 250 scalar QED 500 w t C ( t ) 200 10 10 400 t = 1.5fm 150 t max a 300 100 200 50 upper bound 100 lower bound 0 0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 t max [fm] t [fm] a − 1 = 1 . 015 GeV 24 3 × 64 physical mass ensemble Precise reconstruction of long-distance contribution to HVP down to 1 . 5 fm a HVP No bounding method (purple band): = 516(51) µ a HVP Start bounding method at t = 1 . 6 fm , 1 state reconstruction: = 570 . 2(8 . 3) µ Factor > 5 improvement in statistical precision 19 / 27
Results - Nucleon Two-Point 10 1 1.4 10 2 10 3 log[ C ( t )/ C ( t + 1)] 1.2 10 4 10 5 C ( t ) 1.0 10 6 10 7 0.8 10 8 0.6 10 9 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 t t Can compute nucleon form factors = ⇒ g A , F A ( Q 2 ) F V ( Q 2 ) F N → ∆ ( Q 2 ) Useful for neutrino physics: Axial form factor a dominant source of systematic uncertainty in ν oscillation experiments 20 / 27
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