Prof. Jonathan Flynn The Lattice QFT Group Dr. Andreas Jüttner Prof. Chris Sachrajda
Who Is Who Staff: Jonathan Flynn Andreas Jüttner Chris Sachrajda Postdoc: Nils Asmussen Masanori Hanada Postgrads: Ryan Hill Ben Kitching-Morley James Richings
Motivation • Standard Model - Electroweak and Strong interaction consistently described in terms of renormalisable Quantum Field Theory • It works incredibly well • But there is evidence that it’s not the whole story: dark matter, dark energy, matter-anti-matter asymmetry, … indicate that there must be sth. else • So far no smoking gun
Motivation • SM tests / search for new physics • Direct: new particles in spectra • Indirect: SM provides correlations between processes experiment + theory to over constrain SM → precision physics • Hadronic uncertainties very often dominating error budget • Lattice QCD is the tool of choice to compute hadronic matrix elements and is becoming increasingly precise in its predictions
SM coupling constants typical SM-sector mediator coupling 10 -5 GeV -2 Z, W ± WEAK EM 1/137 γ QCD 0- O(1) gluons PDG
non-perturbative physics - proton mass and hadron decays Proton Neutron Illustrations from slides by Laurent Lellouch
non-perturbative physics - proton mass and hadron decays Decays ν ? meson leptonic decay l QCD EM EM WEAK WEAK π ? meson π hadronic decay experimental and theoretical study of decays furthers understanding QCD QCD of Standard Model’s flavour sector EM EM WEAK WEAK
Lattice QCD Free parameters: L QCD = − 1 µ ν F a µ ν + ¯ X 4 F a ψ f ( i γ µ D µ − m f ) ψ f • gauge coupling g → α s =g 2 /4 π • quark masses m f = u,d,s,c,b,t f • Lagrangian of massless gluons and almost massless quarks • W hat experiment sees are bound states, e.g. m π ,m P ≫ m u,d • Underlying physics non-perturbative Path integral quantisation: ψ ] Oe − iS lat [ U, ψ , ¯ D [ U, ψ , ¯ 1 ψ ] R h 0 | O | 0 i = Z Euclidean space-time ψ ] Oe − S lat [ U, ψ , ¯ D [ U, ψ , ¯ 1 ψ ] R h 0 | O | 0 i = Boltzmann factor Z finite volume, space-time grid (IR and UV regulators) ∝ L − 1 ∝ a − 1 → Well defined, finite dimensional Euclidean path integral → From first principles, solve via MCMC � 8
Lattice QCD • Evaluate discretised path integral in finite volume by means of Monte Carlo simulation • even on the most powerful high-performance computers a set of simulation can easily take months if not years
State of the art of lattice QCD simulations What we can do • simulations of QCD with dynamical (sea) u,d,s,c quarks with masses as found in nature N f = 2 , 2 + 1 , 2 + 1 + 1 • bottom only as valence quark a − 1 ≤ 4GeV • cut-off • volume L ≤ 6 fm action density of RBC/UKQCD physical point DWF ensemble Parameter tuning start from educated guesses and compute IMPORTANT: = m P DG am π once the QCD-parameters • tune light quark mass am l such that π m P DG are tuned no further am P P parameters need to be fixed = m P DG and we can make fully am π • tune strange quark mass such that π predictive simulations of m P DG am K K QCD af π • determine physical lattice spacing a = f P DG π
works well for some quantities - e.g. spectrum from LQCD vs. experiment BMW Science 322 (2008) 1224
Lattice QFT — wide range of skills Quantum Field Theory • many fundamental questions open: peculiarities of Euclidean Field Theory — understand how to ask the question (QED+QED, renormalisation, finite volume effects, finite density, phase diagram of QCD, …) Computing Algorithms • exascale computing • development of new simulation algorithms • using hardware efficiently use physics intuition/knowledge of dynamics • data analysis • address fundamental questions: • developing purpose built hardware • critical slowing down • renormalisability of algorithms
Some of the questions we are addressing: Are there any other particles out there? CP Why is there something rather than nothing? How to make sense out of LHCb data? Are cosmology and particle physics intimately related?
Any other particles out there? Example - the muon g-2 There is a persistent 2.5-3.5 σ tension between experiment and theory and there are many potential BSM candidates that could explain the discrepancy non-perturbative contributions PDG contribution value error QED (4-loop, LO 5-loops) 11658471.895 0.2 Weak incl. 2-loops 15.4 1.8 q q QCD leading VP 692.3 4.2 q QCD light-by-light 10.5 2.6 SM TOTAL 11659181.5 4.9 Experiment 11659209.1 6.3 Fermilab 1.6 J-PARC 4.3 (later ~1) An ab initio prediction of the hadronic contributions is still missing
Any other particles out there? We are computing the leading order contribution q The aim is to provide the first real SM prediction, match current q experiment-based prediction and go beyond Computing it in Lattice QCD is basically understood The current challenge is to include QED and strong isospin breaking corrections There are many conceptual issues in QFT which we have to deal with in parallel with understanding how to do the computation itself
Why is there something rather than nothing? CP violation needed to explain why there is matter in the universe assuming symmetric beginning Sakharov 1967: • C and CP violation • baryon number violation • thermal inequilibrium SM does not provide sufficient CP violation to account for observed amount of matter Precision physics study of SM CP violation in search of new physics s very sensitive to New Physics d CP violation in Kaons: direct and indirect CP violation both observed and measured experimentally (after decades of efforts)
Why is there something rather than nothing? Direct CP-violation: predictions of decay amplitudes K → ππ η ij = A ( K L → π i π j ) weak K L mainly CP odd, 3 π CP odd eigenstates K S mainly CP even, 2 π CP even A ( K S → π i π j ) Gino Isidori at Kaon 2016, Birmingham ( ε/ε ) exp ( ε/ε ) exp “This is by far the most complicated project that Lattice QCD studies of K → ππ I have ever been could be awarded a Nobel Prize ! involved with.”
Why is there something rather than nothing? Indirect CP violation — K L -K S Mass difference: K K • experimentally Δ M K =3.483(6) ⨉ 10 -12 MeV (PDG) • suppressed by 14 orders of magnitude with respect to QCD → poses strong BSM constraints (e.g. (1/ Λ ) 2 BSM contribution) knowing sd ¯ sd ¯ Δ M K at 10%-level → Λ≥ 10 4 TeV • SD about 70% of experimental value - rest LD? We are computing the mass difference from first principles — the results could have tremendous impact on searches for new physics
How to make sense out of LHCb data? First observed by LHCb, CMS
Quark Flavour Physics e.g tree level leptonic B decay: ??? Assumed factorisation: = V CKM (WEAK)(EM)(STRONG) Γ exp . ◆ 2 1 − m 2 ✓ Γ ( B → l ν l ) = | V ub | 2 m B 8 π G 2 F m 2 l f 2 l B m 2 B { { { experiment output theory prediction Experimental measurement + theory prediction allows for extraction of CKM MEs � 20
� Cosmology ↔ Particle Physics CMB provides a unique view on the very early (Planck-Scale) Universe where quantum gravity becomes relevant 6000 3000 ● � CDM 2500 5000 * Holographic d-1 QFT(no gravity) is holographic dual of QG Cosmology 2000 Planck l(l+1)C l /2 � [ µK 2 ] 1500 4000 l(l+1)C l /2 � [ µK 2 ] Idea: study 3d QFT and use holography to make 1000 500 3000 predictions for QG 0 10 20 30 40 l 2000 1000 ● ● ● ● * ● * 500 1000 1500 2000 * 0.04 0.04 ● [C a (l) - C Planck (l)]/C ave (l) ● l * * * ● * ● ● ● * ● * * * l * * * ● ● l � C ave � * ● ● 0.02 0.02 ● ● ● * ** ● ● * * * ** ● * ● ● ● * * * ● * ** ● * * * ● ● ● * ● ● ** *** *** ● ● ● ● ● * ● ● ● ● * * ** ****** ****** * * ● ● ● ● ● ** ● * ** ● * ● ● ● ● *** ● ● * ● * * ● ● ● * * ● ● ● ● * ● * * * ** * ● ** * * ● ** ** ● ● ● ● ● ** ● ● *** ● ● ● * ● ● * ● ● ● ● ● ** ● * ● ● * *** ** ● ● ● 0.00 0.00 * ● * * ● ● * ● * ● ● ● ** * ● ● ● ● ● ● ● * ● ● * ● ** * ● l - C b � ● ● ● * * ** ● ● ● ● * ● * ● ● * ● ● ● *** * ● ** ● ● ● * * ● ● ● ● ● ● * ● ● ● ● * ● ● ● ● * ● ** * ● ● ● ● ● * * ● ** * * ● ● ● * * ● ● ● ● * * ● ● ● ● * * ● - 0.02 - 0.02 ● * * ● ● ● ● ● * * * * ● C a � ● ● ● * * ● * * ● ● * ● ● * - 0.04 ● ● - 0.04 * * ● * * ● ● ● ● 0 0 500 500 1000 1000 1500 1500 2000 2000 l l Perturbatively this has shown successful but PT breaks down → lattice simulations
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