Towards Exploring Parity Violation with Lattice QCD. Towards Exploring Parity Violation with Lattice QCD. Brian Tiburzi 30 July 2014 RIKEN BNL

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1 Towards Exploring Parity Violation with Lattice QCD Brian Tiburzi 30 July 2014 RIKEN BNL Research Center Towards Exploring Parity Violation with Lattice QCD

2 Towards Exploring Parity Violation with Lattice QCD Hadronic Weak Interactions Lattice QCD calculations Hadronic Parity Violation isovector and isotensor Goal: provide a sense of what challenges lattice QCD computations must confront

3 Quark Interactions to Hadronic Couplings Textbook: gauge theories defined in perturbation theory QCD: short distance perturbative, long distance non-perturbative ψ (D/ + m q ) ψ G µνg µν Wilson Lattice Action Wilson Fermions Non-perturbative definition of asymptotically free gauge theories Many Technicalities a M N δ NN (k) Spectrum Interactions b (D) Ken Wilson Strong interaction observables Quarks couple to other fundamental interactions: e.g. weak interaction J(x)D(x, 0)J(0) = i C i (µ)o i (x, µ) Wilson Operator Product Expansion, Wilson Coefficients, Wilson Renormalization Group Hadronic weak (& BSM) interactions require all the Wilson brand names

4 Weak Interactions Leptonic weak interaction Semi-leptonic weak interaction µ ν µ W ν e e µ ν µ W u s K f K Non-leptonic (hadronic) weak interaction ΔS = 1 π u d u W u s K π 10 3 fm

5 Example: K ππ and ΔI = 1/2 Rule Old Puzzle: I = 0 weak decay channel experimentally observed ~500x over I = 2 Amplitude level: A0 / A2 ~ 22.5 pqcd contributes a factor of ~2 Rest non-perturbative? PRL 110, (2013) A = i C i (µ)ππ O i (µ) K Lattice Almost There? A 0 /A 2 (m π = 330 MeV) = 12.0(1.7) Theoretical Challenges ΔS = 1 Processes Usual Suspects: pion mass, lattice spacing, lattice volume underway Additional Challenges: Physical Kinematics Multi-Hadron States and Normalization Operator Renormalization & Scale Invariance underway Statistically Noisy Operator Self-Contractions Can such success carry over to weak nuclear processes?

6 Dirtiest Corner of Standard Model Leptonic weak interaction Semi-leptonic weak interaction ν e µ W e ν µ ν e e W d u p n g A,g V Hadronic weak interaction 5 fm p 1 fm n p n n u W d A PC n d n 10 3 fm n u p A PV

7 Example: N (Nπ)s and ΔI = 1 Parity Violation Old Problem: hadronic neutral weak interaction is the least constrained SM current New experiments: parity violation in few-body systems, map out NN weak interaction? A = C i (µ)(πn) s O i (µ) N Lattice i PRC 85, (2012) Signal Found h 1 πnn =1.1(5) 10 7 ±?? Theoretical Challenges ΔI = 1 Processes Usual Suspects: pion mass, lattice spacing, lattice volume Additional Challenges: Physical Kinematics Multi-Hadron States and Normalization Operator Renormalization & Scale Invariance Statistically Noisy Operator Self-Contractions How many lattice advances carry over to weak nuclear processes? largely solved

8 Particle Physics (B=0) vs. Nuclear Physics (B>0) Statistical nature of lattice QCD two-point correlation functions (Parisi, Lepage) Pion Correlation Function qq(t)qq(0) e m πt Signal Noise^2 {A µ } {A µ } qq(t)qq(t)qq(0)qq(0) e 2m πt Signal/Noise const Nucleon Correlation Function qqq(t)qqq(0) e Mt Signal Noise^2 {A µ } {A µ } qqq(t)qqq(t)qqq(0)qqq(0) e 3m πt Baryons are statistically noisy... nuclear physics has an extra hurdle Signal/Noise e (M 3 2 m π)t Higher statistics Optimal operators

9 (Un)Physical Kinematics in N (Nπ)s Lattice states are created on-shell G(τ) = x e ip x N(x, τ)n (0, 0) = Ze p 2 +M 2 N τ + ground-state saturation Hadronic transition matrix elements have energy insertion E N = M N E (πn)s = M N + m π (πn) s O i (µ) N Lattice = h 1 πnn( E) Partial solution implemented (due to Beane, Bedaque, Parreno, Savage, NUPHA:747, 55 (2005)) p nπ + nπ + p T-invariance h 1 πnn(m π ) h 1 πnn( m π ) h 1 πnn = 1 2 h 1 πnn (m π )+h 1 πnn( m π ) + +O(m 2 π) Consequence: remove via chiral extrapolation but then only can determine chiral limit coupling Likely small: only~10% at 400 MeV pion mass. Precision demands in nuclear physics typically not as great as particle physics Full solution: determine energy dependence, extrapolate to zero, e.g. TwBCs

10 Example: N (Nπ)s and ΔI = 1 Parity Violation Old Problem: hadronic neutral weak interaction is the least constrained SM current New experiments: parity violation in few-body systems, map out NN weak interaction? A = C i (µ)(πn) s O i (µ) N Lattice i PRC 85, (2012) Signal Found h 1 πnn =1.1(5) 10 7 ±?? Theoretical Challenges ΔI = 1 Processes Usual Suspects: pion mass, lattice spacing, lattice volume Additional Challenges: Physical Kinematics Multi-Hadron States and Normalization Operator Renormalization & Scale Invariance Statistically Noisy Operator Self-Contractions How many lattice advances carry over to weak nuclear processes? largely solved

11 Multi-Hadron States and Normalization Multi-Hadron operator not used... Matrix element evaluated by a trick G (τ) =0 N (τ)n (0) 0 = Ze E (Nπ)s τ + M N >M N + m π ground-state saturation (Nπ) s three-quark operator for odd-parity N four-quarks + antiquark = Ze E (Nπ)s τ + Z e E τ + Method requires this condition to hold for lattice parameters Unfortunately likely Z << Z... requires extremely long time to resolve ground state Finite volume and infinite volume states have different normalizations Lellouch, Lüscher, Commun. Math. Phys. 291, 31 (2001) 1 = N 1 1 V n n = Nn 2 V n n V = Nne 2 Enτ + Not needed for spectrum 2 = N 2 2 V 2 O 1 = N 2 N 1 V 2 O 1 V = N 2 N 1 (h 1 πnn) V Lellouch-Lüscher factor requires two-particle energy Not Computed Computed

12 Lellouch-Lüscher Factor Single Particle Energy Quantization: E = p 2 + M 2 p = 2π L n Two Particle Energy Quantization: E total = k 2 + M 2 + k 2 + m 2 P =0 nπ δ 0 (k) =φ(k) ρ V (E) = dn de = φ (k)+δ (k) E 4πk (known function for a torus) One-to-Two Particle Amplitude: 2 =4π VEρV (E) k 2 V M 2 = 8πV 2 ME 2 total k 2 [δ (k)+φ (k)] M V 2 Not Computed Computed (h 1 πnn) V 2 Generalization for energy insertion: Lin, Martinelli, Pallante, Sachrajda, Villadoro NuPhB:650, 301 (2003) Kim, Sachrajda, Sharpe NuPhB:727, 218 (2005)

13 Example: N (Nπ)s and ΔI = 1 Parity Violation Old Problem: hadronic neutral weak interaction is the least constrained SM current New experiments: parity violation in few-body systems, map out NN weak interaction? A = C i (µ)(πn) s O i (µ) N Lattice i PRC 85, (2012) Signal Found h 1 πnn =1.1(5) 10 7 ±?? Theoretical Challenges ΔI = 1 Processes Usual Suspects: pion mass, lattice spacing, lattice volume Additional Challenges: Physical Kinematics Multi-Hadron States and Normalization Operator Renormalization & Scale Invariance Statistically Noisy Operator Self-Contractions How many lattice advances carry over to weak nuclear processes? largely solved

14 Operator Renormalization and Scale Invariance A = i C i (µ)(πn) s O i (µ) N µ = 90 GeV µ =1 2 GeV computable in pqcd at high scale computable on lattice at low scale Tree Level M Z,M W O i m Q Λ QCD

15 Operator Renormalization and Scale Invariance A = i C i (µ)(πn) s O i (µ) N µ = 90 GeV µ =1 2 GeV computable in pqcd at high scale computable on lattice at low scale Tree Level One Loop M Z,M W log M 2 Z p 2 O i m Q Λ QCD log µ2 p 2 log M Z 2 µ2 µ2 = log log p2 p2 M 2 Z δc(µ) α s (µ) log µ2 M 2 Z 70 s Donoghue, McKellar,..., 90 s Dia Savage Liu Springer

16 Operator Renormalization and Scale Invariance Tree Level L I=1 PV = i C i (µ)o i (µ) sin 2 θ W Non-Strange 1 vs. Strange One Loop Results C i (µ =1GeV) /C Tree 1 Discrepancies DSLS provide only ratios α s (m c )/α s (m b )=1.44 O 5 =(uu dd) A (ss) V O 6 =(uu dd] A [ss) V O 7 =(uu dd) V (ss) A O 8 =(uu dd] V [ss) A (Fierz) **Using their ratios, I get their values** No heavy quark masses quoted in 1990 PDG Dia, Savage, Liu, Springer PLB 271, 403 (1991) Tiburzi, PRD (2012)

17 Operator Renormalization and Scale Invariance Tree Level L I=1 PV = i C i (µ)o i (µ) sin 2 θ W Non-Strange 1 vs. Strange One Loop Results O 5 =(uu dd) A (ss) V O 6 =(uu dd] A [ss) V O 7 =(uu dd) V (ss) A O 8 =(uu dd] V [ss) A C i (µ =1GeV) /C Tree 1 (Fierz) LO: 1992 PDG 0.54(4) 0.55(6) 0.35(3) (7) 1.57(10) 4.45(8) 2.12(15) Dia, Savage, Liu, Springer PLB 271, 403 (1991) Tiburzi, PRD (2012)

18 Operator Renormalization and Scale Invariance A = i C i (µ)(πn) s O i (µ) N µ = 90 GeV µ =1 2 GeV computable in pqcd at high scale computable on lattice at low scale Tree Level One Loop log M 2 Z p 2 O i log µ2 p 2 Two Loop α s (1 GeV) 0.4

19 QCD Renormalization of Isovector Parity Violation Results ( t Hooft-Veltman scheme) L I=1 PV = i C i (µ)o i (µ) ΔI = 1 Alleged: 95% probe of hadronic neutral current C i (µ =1GeV) /C Tree 1 sin 2 θ W Non-Strange vs. (Fierz) (Fierz) (Fierz) 1 Strange % Dynamical Question! Tiburzi, PRD (2012)

20 QCD Renormalization of Isovector Parity Violation Results ( t Hooft-Veltman scheme) L I=1 PV = i C i (µ)o i (µ) ΔI = 1 Alleged: 95% probe of hadronic neutral current Additional finding: chiral basis reveals only 5 independent operators (consequence of non-singlet chiral symmetry) C i (µ =1GeV) /C Tree 1 L L R R L R R L sin 2 θ W Non-Strange vs. (Fierz) (Fierz) (Fierz) 1 Strange % Dynamical Question! Tiburzi, PRD (2012)

21 Operator Renormalization and Scale Invariance A = i C i (µ)(πn) s O i (µ) N µ = 90 GeV µ =1 2 GeV computable in pqcd at high scale computable on lattice at low scale Scale Invariance: requires same renormalization scheme pqcd t Hooft-Veltman scheme Anisotropic Lattice Regularization + Wilson Fermions 5 independent PV operators in chiral basis 14 independent PV operators Unphysical + unphysical chiral mixing Matching calculation required...

22 Example: N (Nπ)s and ΔI = 1 Parity Violation Old Problem: hadronic neutral weak interaction is the least constrained SM current New experiments: parity violation in few-body systems, map out NN weak interaction? A = C i (µ)(πn) s O i (µ) N Lattice i PRC 85, (2012) Signal Found h 1 πnn =1.1(5) 10 7 ±?? Theoretical Challenges ΔI = 1 Processes Usual Suspects: pion mass, lattice spacing, lattice volume Additional Challenges: Physical Kinematics Multi-Hadron States and Normalization Operator Renormalization & Scale Invariance Statistically Noisy Operator Self-Contractions How many lattice advances carry over to weak nuclear processes? largely solved

23 Statistically Noisy Operator Self-Contractions G(τ, τ) =0 N(τ )O i (τ)n (0) 0 Another notorious difficulty quark disconnected diagrams sin 2 θ W Vector and Axial-Vector self-contractions (a)+(b) Flavor dependence? ~m q Extend to SU(3) + chiral corrections? Utilize Fierz redundancy? 1 O 5 =(uu dd) A (ss) V O 6 =(uu dd] A [ss) V O 7 =(uu dd) V (ss) A (b) ss sγ µ s small nucleon strangeness sγ µ sqγ µ q? Wilson coeffs. O 8 =(uu dd] V [ss) A 0.16 from Adelaide

24 Isotensor Parity Violation O =(qτ 3 q) A (qτ 3 q) V 1 3 (qτ q) A (qτ q) V Only one operator & without self-contractions L I=2 PV = G F 2 C(µ)O(µ) Operator Renormalization Tiburzi, PRD86: (2012) 1992 PDG 0.78(1) Better proving ground for Lattice QCD? L NN =[ p σ σ 2 p ] [n T σ 2 n]+... s- to p-wave NN interaction Operator matrix element between 2 hadrons (one step beyond multi-hadron calculations done) πn interactions L ππn + L πγn External fields could ``substitute for pions πpv Isotensor 3 pion interaction exists [15] Kaplan Savage, NuPhA 556 (1993) Wilson fermions still to do... Easier for lattice compute parameters in DDH model?

25 Summary Lattice QCD: Wilsonian machinery turns high-scale interactions (both SM & Beyond) into QCD-scale hadronic couplings After decades of dedicated work, trustworthy results emerging e.g. K ππ Some of this success will carry over to weak nuclear processes! Challenges = Opportunity Hadronic Parity Violation: πn-coupling more or less challenging than K ππ? Use external axial fields for coupling to pions? Develop technology for isotensor NN-interaction? Isovector parity-violating lattices from auxiliary fields?