Birmingham High Energy Physics Group - Particle Physics Seminar, University of Birmingham, 08.06.2016 Andreas Jüttner Lattice QCD
Outline 1. Lattice QCD (why and what) 2. Precision flavour physics 3. (g-2) μ on the lattice 4. Pushing the frontiers (QED+QCD, rare decays) 2
UK Lattice community • Cambridge (UKQCD, HotQCD, HPQCD, …) • QCD flavour phenomenology • Edinburgh Various collaborations • QCD spectra • Glasgow • BSM models (non-perturbatively) • Liverpool • finite-T, finite- μ • Oxford • Plymouth • developments in quantum field theory, • Southampton algorithms computing and hardware • Swansea http://www.southampton.ac.uk/lattice2016/
Motivation • Standard Model of elementary particle physics describes electromagnetic, weak and strong (QCD) interactions consistently in terms of a renormalisable quantum field theory • but there is substantial phenomenological evidence that it can’t be the whole story: dark matter, CP-violation, … indicate that there must be sth. else • despite decades of experimental and theoretical efforts we have not found a smoking gun 4
Motivation • searches for new physics: direct vs. indirect search: • ‘bump in the spectrum’ • SM provides correlation between processes experiment + theory to over-constrain SM • hadronic (QCD) uncertainties dominating error budget • lattice QCD can in principle provide the relevant input and is becoming increasingly precise in its predictions 5
B s → μ + μ - First observed by LHCb, CMS
B s → μ + μ - Standard Model prediction: • Loop suppressed in the SM (FCNC) → sensitive to non-SM interaction? B s i 2 + . . . s γ µ γ 5 b | ¯ Br / ( PT ) ⇥ h 0 | ¯ very precise and reliable prediction NNLO QCD for the decay constant is needed NLO EW Hermann, Misiak, Steinhauser, JHEP 1312, 097 (2013) Bobeth, Gorbahn. Stamou, PRD 89, 034023 (2014)
QCD asymptotic freedom confinement PDG Necco & Sommer NPB 622 (2002) 8
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 f • quark masses m f = u,d,s,c,b,t • Lagrangian of massless gluons and almost massless quarks • what experiment sees are bound states, e.g. m π ,m P ≫ m u,d • underlying physics non-perturbative Path integral quantisation: R D [ U, ψ , ¯ ψ ] Oe − iS lat [ U, ψ , ¯ 1 ψ ] 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 = Z Boltzmann factor finite volume, space-time grid (IR and UV regulators) ∝ L − 1 ∝ a − 1 → well defined, finite dimensional Euclidean path integral → from first principles 9
Lattice QCD • gauge-invariant regularisation (Wilson 1974) • naively: replace derivatives by finite differences, integrals by sums • finite volume lattice path integral still over large number of degrees of freedom > O(10 10 ) • Evaluate discretised path integral by means of Markov Chain Monte Carlo on state-of-the-art HPC installations • UK computing time via STFC’s DiRAC consortium 10
Euclidean correlation function ψ , ψ , U ] O B s ( t ) O B s (0) † e − S [ ¯ D [ ¯ 1 ψ , ψ ,U ] h 0 |O B s ( t ) O B s (0) † | 0 i R = Z h 0 |O B s ( x ) | n ih n |O † h 0 |O B s ( t ) O B s (0) † | 0 i = P B s (0) | 0 i ~ x,n two-point function | h 0 |O B s (0) | n i | 2 e − E n t x = P n t →∞ | h 0 |O B s (0) | B s i | 2 e − m Bs t x = extract physical properties from fits to simulation data: • normalisation → matrix element (e.g. decay constant) • time-dependence → particle spectrum (e.g. meson mass) π (0) i • stat. errors from MC sampling over N field configurations h O π ( t ) O † N h OO † i = 1 X OO † ⇤ ⇥ n N n =1 (bootstrap, jackknife error analysis, autocorrelation analysis, …)
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: IMPORTANT: = m P DG am π once the QCD-parameters π • tune light quark mass am l such that m P DG are tuned no further am P P parameters need to be fixed = m P DG am π and we can make fully • tune strange quark mass such that π m P DG predictive simulations of am K K af π QCD • determine physical lattice spacing a = f P DG π
benchmark - the hadron spectrum Kronfeld, Ann. Rev. of Nucl. Part. Sci 2012 62 13
lattice - systematics In practice one needs to control a number of sources of systematic uncertainties, most notably: • discr. errors (lattice spacing a ) quite crude, in practice more complicated Z d 4 x L 0 ( x ) + a L 1 ( x ) + a 2 L 2 ( x ) + . . . � S e ff = Symanzik 1982,1983 • finite volume errors (box size L ) ∝ e − m π L ∝ O (1%) In QCD for simple ME more complicated for processes with several hadrons in initial or final state Lüscher Commun.Math.Phys. 105 (1986) 153-188, Nucl. Phys. B354, 531 (1991) 14
a state-of-the-art lattice need to keep a -1 ≪ relevant scales ≪ L -1 • for m π =140 MeV the constraint for controlled finite volume effects of m π L ≳ 4 suggests L ≈ 6fm • for charm quarks to be well resolved am c < 1 e.g. a -1 larger than ≈ 2.5GeV needed • lattices with L/a ≳ 80 needed Fulfilling all the constraints is just starting to happen (e.g. first 96 3 × 192 have been generated (MILC)) in the meantime most collaborations • weaken the finite volume effects by simulating unphysically heavy pions • extrapolate from coarser lattices relying on assumptions for functional form of cutoff effects 15
Lattice pheno - what’s possible • Standard: - meson ME with single incoming and/or outgoing pseudo-scalar states , , π , K, D ( s ) , B ( s ) → QCD − vacuum π → π , K → π , D → K, B → π , ... B K , ( B D ) , B B - QCD parameters: quark masses, strong coupling constant - meson/baryon spectroscopy of stable (in QCD) states • Challenging: - two initial/final hadronic states, one channel , … ππ → ππ , K π → K π , K → ππ - elm. effects in spectra - long-distance contributions in e.g. rare Kaon decays, K- mixing • Very challenging - new ideas needed/no clue: - multi-channel final states (hadronic ) D, B (e.g. Hansen, Sharpe PRD86, 016007 (2012)) - transition MEs with unstable in/out states (Briceño et al. arXiv:1406.5965) - electromagnetic effects in hadronic MEs 16
Quark Flavour Physics q 1 d 0 V ud V us V ub d 100GeV s 0 V cd V cs V cb s = b 0 V td V ts V tb b q 2 3x3 unitary matrix 4 unknown parameters 2GeV • quark mixing • CP-violation (one complex phase) • constraints on SM processes • high energy reach • inconsistencies → failure of the SM? 300MeV h had f | H W | had i i h 0 | H W | had i i 17
Quark Flavour Physics e.g tree level leptonic B decay: ??? Assumed factorisation: = V CKM (WEAK)(EM)(STRONG) Γ exp . currently EFT ◆ 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 { { { theory output theory prediction Experimental measurement + theory prediction allows for extraction of CKM MEs 18
Flavour Physics Determine CKM elements (indirect) test of SM: • over-determine elements of V CKM and check consistency of CKM paradigm • unitarity tests: - rows and columns are (in SM) complex unit vectors - rows (columns) are orthogonal to other rows (columns) violation of unitarity would indicate non-SM physics | V ud | 2 + | V us | 2 + | V ub | 2 ? ? X V Ud V ∗ = 0 = 1 Ub row-test triangle-test U = u,c,t • Which channels still allow room for NP? How much NP would be compatible with measurements? What would be the properties of NP? 19
Lattice flavour physics and CKM illustrations from L. Lellouch’s Les Houches Lecture arXiv:1104.5484 leptonic decays semileptonic decays V ud V us V ub V cd V cs V cb V CKM = V td V ts V tb mixing 20
“tree” kaon/pion decays ⌘ 2 m 2 ν µ ) = G 2 ⇣ 8 π f 2 K m 2 | V us | 2 Γ ( K → µ ¯ µ m K 1 − µ F m 2 K meson s/ ¯ ⌦ ↵ 0 | ¯ d γ µ γ 5 u | K/ π ( p ) = if K/ π p µ lepton ⌘ 2 m K (1 − m 2 leptonic decay µ /m 2 K ) 2 ⇣ ν µ ) = | V us | 2 Γ ( K → µ ¯ ν µ ) f K π ) 2 × 0 . 9930(35) Γ ( π → µ ¯ | V ud | 2 f π m π (1 − m 2 µ /m 2 Marciano, Phys.Rev.Lett. 2004 PRELIMINARY 1‰!!! 21
Recommend
More recommend
