Lattice QCD Precision Science for Muon g-2 and Running Coupling - PowerPoint PPT Presentation

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary Lattice QCD Precision Science for Muon g-2 and Running Coupling Kohtaroh Miura (GSI Helmholtz-Institut Mainz) Seminar at RIKEN Aug. 19, 2020

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary Muon Anomalous Magnetic Moment a ℓ = e ,µ,τ Dirac Eq. with B: i � ∂ψ � � � � + β c 2 m ℓ + eA 0 − i � c ∇ − e A ∂ t = α · ψ , Nonlelativistic Limit, Pauli Eq.: μ B � ( − i � c ∇ − e A ) 2 i � ∂φ � ∂ t = − M ℓ · B + eA 0 φ , 2 m ℓ c Muon Strorage e � σ Magnetic Moment: M ℓ = g ℓ 2 , 2 m ℓ c In Dirac Theory: p g ℓ = 2 , a ℓ ≡ ( g ℓ − 2 ) / 2 = 0 , ω cyc = ω prec . s In QFT (with Loops) for Electron (M.Knecht ,NPPP2015): = 1 159 652 180 . 07 ( 6 )( 4 )( 77 ) × 10 − 12 ( O ( α 5 )) , a SM e exp = 1 159 652 180 . 73 ( 0 . 28 ) × 10 − 12 a [ 0 . 24 ppb ] . e a exp . = a SM µ ? µ

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary Muon Anomalous Magnetic Moment a ℓ = e ,µ,τ Dirac Eq. with B: i � ∂ψ � � � � + β c 2 m ℓ + eA 0 − i � c ∇ − e A ∂ t = α · ψ , Nonlelativistic Limit, Pauli Eq.: μ B � ( − i � c ∇ − e A ) 2 i � ∂φ � ∂ t = − M ℓ · B + eA 0 φ , 2 m ℓ c Muon Strorage e � σ Magnetic Moment: M ℓ = g ℓ 2 , 2 m ℓ c In Dirac Theory: p g ℓ = 2 , a ℓ ≡ ( g ℓ − 2 ) / 2 = 0 , ω cyc = ω prec . s In QFT (with Loops) for Electron (M.Knecht ,NPPP2015): = 1 159 652 180 . 07 ( 6 )( 4 )( 77 ) × 10 − 12 ( O ( α 5 )) , a SM e exp = 1 159 652 180 . 73 ( 0 . 28 ) × 10 − 12 a [ 0 . 24 ppb ] . e a exp . = a SM µ ? µ

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary a exp . vs. a SM µ µ a contrib . × 10 10 SM contribution Ref. µ QED [5 loops] 11658471 . 8951 ± 0 . 0080 [Aoyama et al ’12] LO-HVP( O ( α 2 ) ) by pheno. 692 . 8 ± 2 . 4 [Keshavarzi et al ’19] 694 . 0 ± 4 . 0 [Davier et al ’19] 687 . 1 ± 3 . 0 [Benayoun et al ’19] 688 . 1 ± 4 . 1 [Jegerlehner ’17] NLO-HVP( O ( α 3 ) ) by pheno. − 9 . 84 ± 0 . 07 [Hagiwara et al ’11] [Kurz et al ’11] − 9 . 83 ± 0 . 04 [KNT19] NNLO-HVP( O ( α 4 ) ) by pheno. 1 . 24 ± 0 . 01 [Kurz et al ’14] HLbyL( O ( α 3 ) ) 10 . 5 ± 2 . 6 [Prades et al ’09] Weak (2 loops) 15 . 36 ± 0 . 10 [Gnendiger et al ’13] SM tot [0.42 ppm] 11659180 . 2 ± 4 . 9 [Davier et al ’11] [0.43 ppm] 11659182 . 8 ± 5 . 0 [Hagiwara et al ’11] 11659184 . 0 ± 5 . 9 [0.51 ppm] [Aoyama et al ’12] Exp [0.54 ppm] 11659208 . 9 ± 6 . 3 [Bennett et al ’06] Exp − SM 28 . 7 ± 8 . 0 [Davier et al ’11] 26 . 1 ± 7 . 8 [Hagiwara et al ’11] 24 . 9 ± 8 . 7 [Aoyama et al ’12] ) ≃ ( 720 ± 7 ) × 10 − 10 , | NoNewPhys = a ex. a LO-HVP µ − ( a QED + a EW µ + a (N)NLO-HVP + a HLbL µ µ µ µ

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary a ℓ in QFT QFT Def. for a ℓ : � ¯ ℓ − ( p ) |J µ | ℓ − ( p ′ ) � = ¯ u ( p )Γ µ ( p , p ′ ) u ( p ′ ) = (1) Γ µ ( q = p − p ′ ) = γ µ F 1 ( q 2 ) + i σ µν q ν 2 m µ F 2 ( q 2 ) + · · · , (2) F 2 ( 0 ) = a ℓ = ( g ℓ − 2 ) / 2 . (3) Standard Model, Loop Corr.: a ℓ = α/ ( 2 π ) + · · · . BSM = MSSM (Padley et.al.’15) or TC (Kurachi et.al. ’13) etc.: γ ∝ ( m ℓ / Λ BSM ) 2 . µ µ Technicolor

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary Whitepaper (WP): Lattice QCD Consensus HVP,LO . 10 10 a µ ETM-18/19 Mainz/CLS-19 FHM-19 PACS-19 RBC/UKQCD-18 BMW-17 Mainz/CLS-17 HPQCD-16 ETM-13 KNT-19 DHMZ-19 BDJ-19 Jegerlehner-18 RBC/UKQCD-18 LQCD No New Physics No New Physics Pheno. Pheno+LQCD 600 650 700 750 Muon g-2 Theory Initiative Whitepaper, arXiv:2006.04822. = 711 . 6 ( 18 . 4 ) · 10 − 10 , BMW-2020 Not Yet Included. LQCD Concensus: a LO-HVP µ

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary Hadronic Light-by-Light (HLbL) k ρ O ( α 3 ) Contributions. HAD . Need investigate Π µνλρ ( q 1 , q 2 , q 3 , k ) . q 1 µ q 3 λ q 2 ν Not full related to experimental observables. µ ( p ) µ ( p ′ ) Current Status = 7 . 87 ( 3 . 06 ) stat ( 1 . 77 sys ) × 10 − 10 . [RBC/UKQCD PRL2020.] LQCD: a HLbL µ = 9 . 2 ( 1 . 9 ) × 10 − 10 . [Whitepaper 2006.04822.] Pheno.: a HLbL µ LQCD and Phenomenology are consistent. HLbL seems not to be a source of the muon g-2 discrepancy.

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary Motivation Questions Really a ex . � = a SM µ ? µ HVP � = ( 720 ± 7 ) × 10 − 10 ? More specifically, a LO-HVP µ Impact for ∆ had α ( Q 2 ) at EW scale? [c.f. Crivellin et.al.(2003.04886), Keshavarzi et.al.(2006.12666).] New Experiments a ex . µ : FNAL-E989 0 . 14 ppm (soon 0 . 5 ppm ), J-PARC-E34 0 . 1 ppm (2024). ∆ had α ( Q 2 ) : MUonE, ILC. THIS TALK Investigate a LO-HVP by Lattice QCD (BMW-2020, arXiv:2002.12347). µ Discuss ∆ had α ( Q 2 ) by Lattice QCD (Manz/CLS) compared with Data-Driven Dispersion (Jegerlehner et.al.).

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary Table of Contents Introduction 1 Lattice QCD for HVP and Muon g-2 2 BMW Highlight for Muon g-2 3 Discussion: ∆ had α ( Q 2 ) 4 Running α ( s ) BMW Results Mainz/CLS Results Summary 5

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary Table of Contents Introduction 1 Lattice QCD for HVP and Muon g-2 2 BMW Highlight for Muon g-2 3 Discussion: ∆ had α ( Q 2 ) 4 Running α ( s ) BMW Results Mainz/CLS Results Summary 5

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary Lattice Gauge Theory I ψ ] e − S G [ U ] − ¯ D [ U , ψ, ¯ ψ · D [ U , M ] · ψ O [ U , ψ, ¯ � O � = 1 � ψ ] , Z = 1 D U e − S G [ U ] Det � � � D [ U , M ] O [ U ] wick , Z = � N i = 1 O [ U ( i ) ] wick + O ( N − 1 / 2 ) , { U ( i ) } created w. P = e − S G · Det [ D ] / Z . Hybrid Monte Carlo (HMC) ↔ Heat-Bath. Regulalization: UV cutoff a , IR cutoff L 3 × T . Gauge Fields: U µ ∈ SU ( N c ) . Action: S LatGT = S G [ U ] − ¯ ψ · D [ U , M ] · ψ possesses exact gauge symm. Formally taking a → 0 reproduces the continuum theory action. M π, K , ··· Renormalization: µ = a → 0 w. fixed around the physical values. M Ω

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary Lattice Gauge Theory II ψ ] e − S G [ U ] − ¯ D [ U , ψ, ¯ ψ · D [ U , M ] · ψ O [ U , ψ, ¯ � O � = 1 � ψ ] , Z = 1 � D U e − S G [ U ] Det � � D [ U , M ] O [ U ] wick , Z = � N i = 1 O [ U ( i ) ] wick + O ( N − 1 / 2 ) , { U ( i ) } created w. P = e − S G · Det [ D ] / Z . Hybrid Monte Carlo (HMC) ↔ Heat-Bath. Lattice Gauge Theory Non-Perturbative Definition of asymptotic-free gauge theory. Regulalization: UV cutoff a , IR cutoff L 3 × T . 1 M π, K , ··· 2 Renormalization: µ = a → 0 keeping M Ω With a mass gap Λ ∼ F π , M ρ , ... , a Λ → 0 and L Λ → ∞ under controlled. 3 First-Principle Calculations, i.e., No Approximation.

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary LQCD Meas. of HVP and a LO-HVP µ { U ( i ) } : HMC ↓ D f [ U ] ≡ D [ U , m f ] : Dirac Op. η ( r ) X η ( r ) ↓ D XY φ X = η ( r ) , � N r Y | N r →∞ = δ XY X r = 1 N r ↓ with Conjugate Gradient Method, ↓ Low-Mode Averaging (Lanczos, No η ( r ) X ). D − 1 [ U ] : Quark Propagator. f

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary LQCD Meas. of HVP and a LO-HVP µ { U ( i ) } : HMC ↓ D f [ U ] ≡ D [ U , m f ] : Dirac Op. η ( r ) X η ( r ) ↓ D XY φ X = η ( r ) , � N r Y | N r →∞ = δ XY X r = 1 N r ↓ with Conjugate Gradient Method, ↓ Low-Mode Averaging (Lanczos, No η ( r ) X ). D − 1 [ U ] : Quark Propagator. f

Discussion: ∆ had α ( Q 2 ) Introduction Lattice QCD for HVP and Muon g-2 BMW Highlight for Muon g-2 Summary LQCD Meas. of HVP and a LO-HVP µ { U ( i ) } : HMC ↓ D f [ U ] ≡ D [ U , m f ] : Dirac Op. η ( r ) X η ( r ) ↓ D XY φ X = η ( r ) , � N r Y | N r →∞ = δ XY r = 1 X N r ↓ with Conjugate Gradient Method, ↓ Low-Mode Averaging (Lanczos, No η ( r ) X ). eγ µ eγ ν D − 1 [ U ] : Quark Propagator. f ↓ Vector Current Correlator µν ( x ) = � ( ¯ ψγ µ ψ ) x ( ¯ G f ψγ ν ψ ) y = 0 � − − → wick C f ReTr [ γ µ D − 1 ( x , 0 ) γ ν D − 1 � � µν ( x ) = − ( 0 , x )] , eγ µ f f eγ ν D f Tr [ γ µ D − 1 ( x , x )] Tr [ γ ν D − 1 � � �� µν ( x ) = Re ( y , y )] y = 0 , f f