Lattice Nuclear Physics Investigations of Fundamental Symmetries Advisor: Tom Luu | Begin of Work: November 2014 31. July 2015 | Christopher Körber | Forschungszentrum Jülich & University of Bonn ECT* Talent — Training in Advanced Low Energy Nuclear Theory Mitglied der Helmholtz-Gemeinschaft 1 Asymmetry of Matter and Antimatter Symmetry of baryonic matter and antimatter after beginning of universe? Pair annihilation and radiation Observed asymmetry of matter Images by TED-Ed original: What happened to antimatter? Rolf Landua Mitglied der Helmholtz-Gemeinschaft Christopher Körber — ECT* Talent — 31. July 2015 2 2 Need for Charge-Parity Violation Sakharov conditions for explaining asymmetry Processes violate Processes violate Charge Generation of baryon or lepton and Charge-Parity symmetry antisymmetry outside number conservation (Weak interactions violate both) of thermal equilibrium X ‘æ B + Y ‘æ X ‘æ B + Y N = N ‘æC-Symmetry B B¯ T-Symmetry‘æ ¯ ¯ ¯ CP:CP Phase space X ‘æ B + Y cancellations Y + B ‘æ X Weak Standard Model interactions (CKM matrix) not sufficient to explain amount of asymmetry Mitglied der Helmholtz-Gemeinschaft Christopher Körber — ECT* Talent — 31. July 2015 3 3 Hadronic Hints for CP Violations: Electric Dipole Moment Electric Dipole Moment as a CP violating quantity S˛ 3 d˛ := d r ˛r fl(˛r )=d S˛ d˛ ⁄ Charge distribution Total nucleus spin P Magnetic Dipole Moment ˛ ˛ ˛ ˛ H = −B · (µ S) − E · (d S) T ˛ ˛ ˛ ˛ = −(−B) · (µ (−S)) − (+E) · (d (−S)) EDM violates CP CPT Mitglied der Helmholtz-Gemeinschaft Christopher Körber — ECT* Talent — 31. July 2015 4 4 EDMs and Matter Asymmetry? Analysis of EDMs Sources of CP violating interactions Weak Strong New Analysis of CP violating interactions Interactions Interactions Physics (CKM matrix) (QCD, theta) (SUSY,…) Experimental Status if θ =1 • Background free • Complementary to LHC (order of magnitudes?) • Less expensive than high energy physics • Non-vanishing measurement: Nobel price? Current Bounds: −25 199 dp ∼ 7.9 · 10 Hg, UWash −26 dn ∼ 2.9 · 10 ultracold neutrons, ILL −29 de ∼ 8.7 · 10 ThO, ACME Planned Bounds: d ∼ 10−29 proton & deuteron, p Storage Ring EDM, JEDI −29 Source: “NEDM limit history" by dn ∼ 10 CryoEDM, ILL Andreas Knecht - Wikipedia: Neutron electric dipole moment Mitglied der Helmholtz-Gemeinschaft Christopher Körber — ECT* Talent — 31. July 2015 5 5 Computation of EDMs… … is essential for understanding CP violating structure on fundamental level … on fundamental level is important for controlled model-independent predictions Nuclear Level Hadronic Level SM/QCD Level BSM Level Currently large Nucleon EDMs Quark EDMs SUSY uncontrolled uncertainties Nuclear EDMs Pion Int. Gluon Int. Multi-Higgs Nuclear Models Chiral Perturbation Theory & Lattice QCD Pion Nucleon Int. Quark-Gluon Int. LR Symmetric Effective Field Theories Mitglied der Helmholtz-Gemeinschaft Theta Term QCD Christopher Körber — ECT* Talent — 31. July 2015 6 6 Chiral Perturbation Theory: An Effective Field Theory for QCD E q q g g g g q q g g g g CP violating CP conserving q g g g g q q q Perturbative treatment of QCD in low energy sector not possible 1 GeV (confinement) and Lattice QCD not able to access light nuclear systems yet Chiral Perturbation Theory: Most general Lagrangian which respects the symmetries of QCD in chiral limit and has hadrons as degrees of freedom L χ = L + L + L + L χ ··· Compute bound states 100 MeV Nπ π NN ¨CP¨ (non perturbative) Final Objective P 2π N NN + NN +NN + NN + EDM operator 3 2π γ Nπ + Nπ + 3P + ··· + ··· + ··· d˛ e - - Âf - - - - NN + NN +NN + NN + Mitglied der Helmholtz-Gemeinschaft Nucleus wave function Christopher Körber — ECT* Talent — 31. July 2015 7 7 Nuclear Lattice Effective Field Theory: The Transfer Matrix Transfer matrix evolves states by accounting all possible paths and interactions (path Transfer Matrix Interpretation (Triton) integral of chiral Lagrangian) Èψ(t + δt) | Mδt | ψ(t)Í Eigenstates of transfer matrix correspond to wave function of physical state N t t M t N 3 P Èψ( + δ ) | δt | ψ( )Í & 1 L2 Path integral identities and stochastically methods Greatly reduced Statistical errors dimensionality Nucleon Number Scaling for L = 6, L = 8, L = 8 tin tout 6000 2014 Code A A2 5000 79.7 + 7.11 4000 3000 2000 1000 Time for 100 HMC traj. per process [s] Mitglied der Helmholtz-Gemeinschaft 0 0 4 8 12 16 20 Christopher Körber — ECT* Talent — 31. July 2015 A 8 8 Why NLEFT for EDMs? Nuclear Models Theta Term QCD NLEFT Nucleon EDMs Quark EDMs SUSY ChPT + LQCD EFT Nuclear EDMs Pion Int. Gluon Int. Multi-Higgs Improvement Pion Nucleon Int. Quark-Gluon Int. LR Symmetric of precision and accessibility Nuclear EDM calculations systematically connected to fundamental theory Why NLEFT Extend calculations to uncharted territories for EDMs? Crucial to interpret experimental signal Crucial to interpret matter-antimatter Mitglied der Helmholtz-Gemeinschaft asymmetry… Christopher Körber — ECT* Talent — 31. July 2015 9 9.