Brian Tiburzi 22 August 2012 RIKEN BNL Research Center

Transcription

1 Anatomy of Hadronic Parity Violation on the Lattice Brian Tiburzi 22 August 2012 RIKEN BNL Research Center

2 The Anatomy of Hadronic Parity Violation Parity Violation, Nuclear Parity Violation, Hadronic Parity Violation Weak interactions between quarks New Experiments, New Motivation Fundamental neutron physics beamline From Quarks to Nuclei Impossibility in non-perturbative QCD Opportunity especially for those interested in multi-hadrons Disclaimer: P odd and CP even processes

3 Historical Introduction Parity Violation in the Weak Interaction ca Maximal violation 100% Parity Violation in Nuclear Interactions

4 55 Years Later: Standard Model Parity Violation in the Weak Interaction G F = 2g 2 8M 2 W = 10 5 /GeV 2 H = G F 2 (u L γ µ d L )(ν L γ µ e L ) p V n g V p A n g A Long-Range Nuclear Force from Strong Interactions ga f π 2 q σ 1 q σ 2 q 2 + m 2 π G F W + Nucleon-Nucleon Weak Interactions G F fπ

5 Nuclear Parity Violation Violate strong interaction symmetries to expose weak nuclear force (Many) Parity Violating Nuclear reactions have been seen starting in From one in ten million to one in ten... Same ideas are being applied in Atomic Parity Violation expts. atoms, molecules, solids 139 La P + P + + P 1 = P + H PV P E/E 10 E + E 6 for E 0.7 kev Parity Violating Nuclear Force Forthcoming: n + 4 He n p dγ h 1 π

6 Panoply of Parity Violation PV nuclear transitions, PV photo-nuclear transitions (anapole moment), PV nucleon-nucleon interaction, PV nucleon-meson couplings,...,... Organize with Effective Theory mindset Weak Scale PV M Z,M W boson exchange between quarks Fermi Theory PV four quark operators m Q below heavy quark thresholds µ QCD Scale PV Λ QCD non-perturbative 0 Few Body

7 Panoply of Parity Violation PV nuclear transitions, PV photo-nuclear transitions (anapole moment), PV nucleon-nucleon interaction, PV nucleon-meson couplings,...,... Organize with Effective Theory mindset Weak Scale PV M Z,M W boson exchange between quarks Fermi Theory PV four quark operators m Q below heavy quark thresholds µ QCD Scale PV Λ QCD non-perturbative -hadronic PV -NN PV -Nuclear PV h γn h πn h NN PV 0 Few Body Many Body

8 Parallel to Parity Violation Lattice QCD: Connect Quarks to Hadrons, Few Body Quantum Many Body: Connect Few Body to Nuclei Organize with Effective Theory mindset -hadronic PC -NN PC -Nuclear PC g V ga d N µ QCD Scale PV Λ QCD non-perturbative -hadronic PV -NN PV -Nuclear PV h γn h πn h NN PV Few Body Many Body

9 Parallels to Parity Violation Organize with Effective Theory mindset Weak Scale PV M Z,M W boson exchange between quarks Fermi Theory PV four quark operators m Q below heavy quark thresholds µ QCD Scale PV Λ QCD non-perturbative -hadronic PV -NN PV -Nuclear PV h γn h πn h NN PV 0 Few Body Many Body

10 Parallels to Parity Violation Perturbative QCD: Connect Standard Model to QCD scale Lattice QCD: Connect Four Quark Ops. to Observables Organize with Effective Theory mindset F =1, 2 Weak Scale PV M Z,M W Weak Scale FC Fermi Theory PV Fermi Theory FC m Q µ QCD Scale PV Λ QCD QCD Scale FC Four-Quark Correlations deep inside hadrons 1/100 fm 0 e.g. K ππ I =1/2... 0

11 Hadronic Parity Violation in QCD Perturbative QCD: Connect Standard Model to QCD scale Lattice QCD: Connect Four Quark Ops. to Observables QCD renormalization of PV (First) Lattice QCD calculation of PV L I=1 PV = i C i (µ)o i (µ) p L I=1 PV πn = h 1 π B Tiburzi, PRD (2012) J Wasem, PRC (R) (2012) In tandem: program to remove model dependence in NN, NNN,... Zhu Maekawa Holstein Ramsey-Musolf van Kolck, Phillips Schindler Springer Grießhammer, Shin Ando Hyun, Vanasse,...

12 Isovector Parity Violation in QCD Why Isovector? QCD renormalization of PV (First) Lattice QCD calculation of PV L I=1 PV = i C i (µ)o i (µ) p L I=1 PV πn = h 1 π h1 π g A f 2 π σ q q 2 + m 2 π Alleged: Longest range piece of PV NN interaction

13 Isovector Parity Violation in QCD Why Isovector? QCD renormalization of PV (First) Lattice QCD calculation of PV L I=1 PV = i C i (µ)o i (µ) p L I=1 PV πn = h 1 π W ± : I =0, 2 V ud 2 I =1 V us 2 Z 0 : I =0, 1, 2 J W µ = U L γ µ VD L J Z0 µ = 1 c W ΨL γ µ T 3 Ψ L s 2 W Ψγ µ QΨ Alleged: 95% probe of hadronic neutral current

14 QCD Renormalization of Isovector Parity Violation Alleged: 95% probe of hadronic neutral current Tree Level One Loop M Z,M W log M 2 Z p 2 m Q Λ QCD log µ2 p 2 L I=1 PV = G F s2 W (uu dd) A (uu + dd) V log M Z 2 µ2 µ2 = log log p2 p2 M 2 Z L I=1 PV = i Sum leading logs C i (µ)o i (µ) µ d dµ C = α s 4π γt C C(µ) log µ2 M 2 Z 70 s Donoghue, McKellar,..., 90 s Dia Savage Liu Springer

15 QCD Renormalization of Isovector Parity Violation α s (1 GeV) 0.4 Sum NLL... renormalization scheme dependence (Good!)

16 QCD Renormalization of Isovector Parity Violation Renormalization scheme: dimensional regularization γ µ γ 5 γ µ γ ν γ ρ γ µ γ 5 γ ν γ ρ γ µ Four dimensions affords simplification γ ν γ ρ γ µ = g νρ γ µ g νµ γ ρ + g ρµ γ ν iε νρµσ γ σ γ 5 Enlarge operator basis to include mixing with evanescent operators F = 0 Experts: Buras Jamin Lautenbacher Weisz, Ciuchini Franco Lubicz Martinelli Reina Scimemi Silvestrini (PV in Lattice QCD requires different scheme than dim. reg.... one-loop matching = bookkeeping)

17 QCD Renormalization of Isovector Parity Violation E.g. S =1 W-exchange I =1 Z-exchange Renormalization scheme: dimensional regularization Q 1 =(sd) V A (uu) V A U-spin (ss dd) V A (uu) V A V-spin (uu dd) V A (ss) V A Mass independent scheme & QCD flavor blind! Parity invariance O =(uγ µ u dγ µ d) L (sγ µ s) L (uγ µ u dγ µ d) R (sγ µ s) R I =1 follows from S =1 including QED penguins, and BSM operators... just different initial conditions in evolution

18 QCD Renormalization of Isovector Parity Violation Results ( t Hooft-Veltman scheme) L I=1 PV = i C i (µ)o i (µ) Non-Strange vs. Strange Fierz constraint Alleged: 95% probe of hadronic neutral current C i (µ =1GeV) - 2 ops in chiral basis L L R R L R R L sin 2 θ W Non-Strange vs. 1 Strange % Dynamical Question! [18] Kaplan Savage, NuPhA 556 (1993) B Tiburzi, PRD (2012)

19 First Lattice Computation (J Wasem) PRC (R) (2012) p O p (x) (πn) s-wave γ 5 O p (x) p L I=1 PV πn = h 1 π Easy to pick on a first calculation (much harder to have done it, or improve it!) Multi-hadron overlap? No Lellouch-Lüscher factor Ignores regularization scheme Inexact kinematics 2 τ vs. m 2 π Noisy operator self-contractions Wilson coefficients of strange operators are enhanced 5 Strangeness not-so suppressed N 1/2 c

20 Auxiliary Fields for Isovector Parity Violation Perhaps only a Gedankenexperiment until exascale computers materialize E.g. O = qγ µ γ 5 τ 3 q (qγ µ q) qγ µ γ5 τ 3 1 q 2 P τ 1 τ 3 chiral symmetry Integrate in auxiliary field Introduces PC and PV four-quark operators L = σ 2 + iσ qγ µ γ5 τ 3 1 q No sign problem γ 5 τ 1 Hermiticity Can implement all isovector PV operators in sign-problem-free ways Continuum limit (!?!?) p L I=1 PV πn = h 1 π p π + (x) n σ Bodies buried in gauge field generation Nucleon anapole moment: just calculate anapole form factor PV NN interactions from PV two-point functions

21 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) Renormalization by bookkeeping B Tiburzi, arxiv: 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 two hadrons (... bound states currently!) πn interactions L ππn + L πγn External fields could ``substitute for hadrons [15] Kaplan Savage, NuPhA 556 (1993) πpv Isotensor three-pion vertex exists (πpv very suppressed in other channels)

22 Anatomy of Parity Violation New neutron experiments will constrain PV in few-body systems Connecting few-body PV to many-body PV stringent test of methods NMB/NNEFT Connecting PV four quark operators to PV couplings between hadrons: test of non-pqcd Connection of nuclear PV to Standard Model