Hadron structure from lattice QCD

Transcription

1 Hadron structure from lattice QCD Giannis Koutsou Computation-based Science and Technology Research Centre () The Cyprus Institute EINN2015, 5th Nov. 2015, Pafos

2 Outline Short introduction to lattice calculations Challenges and current landscape Nucleon charges Nucleon sigma-terms Electromagnetic matrix elements Form factors and radii Strange form factor New directions: Neutron EDM Direct calculation of PDFs Summary and outlook

3 Lattice QCD ab initio simulation of QCD Freedom in choice of: quark masses (heavier is cheaper) lattice spacing a (larger is cheaper) lattice volume L 3 T (smaller is cheaper) Choice of discretisation scheme e.g. Clover, Twisted Mass, Staggered, Overlap, Domain Wall Trade offs and advantages for each differ Eventually, all schemes must agree: At the continuum limit: a 0 At infinite volume limit L At physical quark mass

4 Simulations landscape Selected lattice simulation points used for hadron structure Multiple collabs. simulating at physical pion mass Size of points indicates m π L

5 Sources of uncertainty Statistical error: 1 p, with MC samples N Correlation functions: exponentially decay with timeseparation Disconnected contributions: stochastic error Systematic uncertainties Extrapolations a, L, mπ Contamination from higher energy states

6 Sources of uncertainty Statistical error: 1 p, with MC samples N Correlation functions: exponentially decay with timeseparation Disconnected contributions: stochastic error Systematic uncertainties Extrapolations a, L, mπ Contamination from higher energy states

7 Multi-petascale to exa-scale requirements Indicative computer time requirements for nucleon structure

8 Reproduction of light baryon masses Agreement between lattice discretisation schemes Reproduction of experiment Prediction of yet-to-be-observed charmed baryons Confidence through agreement between lattice schemes Nucleon structure

9 Benchmark Axial charge Agreement towards experiment Simulations very close to or at the physical quark mass

10 g S = hn ūu dd Ni gt = h1i u d Scalar and tensor charges Isovector charges General agreement between calculations Different dependence on excited states between lattice actions

11 ū 5 µ u + d 5 µ d Axial charge light disconnected Required for individual u- and d- contributions Requires dedicated calculations for disconnected quark loop Large statistical fluctuations in correlation functions Sign is negative: brings connected result down About 10% of connected value

12 s 5 µ s Axial charge strange contribution Contribution exclusively by disconnected quark loop More by M. Constantinou s winning poster talk: Orbital and gluon contribution to proton spin

13 Nucleon sigma terms Pion nucleon σ-term: Strange σ-term: N = m ud hn ūu + dd Ni s = m s hn ss Ni Enter super-symmetric candidate particle scattering cross sections with nucleon (e.g. neutralino through Higgs) 1.Direct calculation of matrix elements Involves disconnected contributions 2.Through Feynman - Hellmann theorem: N = m ud s = m s Reliance on effective theories for dependence on mπ Weak dependence on ms

14 Nucleon sigma terms More results coming from the lattice using direct evaluation of the matrix element First results from simulations directly at the physical point

15 Electromagnetic form factors Dirac (F1) and Pauli (F2): hn(p 0,s 0 ) j µ N(p, s)i = s MN 2 E N (p 0,s 0 )O µ u(p, s) )E N (p)ū(p0 O µ = µ F 1 (q 2 )+ i µ q 2M N F 2 (q 2 ), q = p 0 p Isovector and isoscalar combinations: j v µ =ū µ u d µ d, j s µ =ū µ u + d µ d F p F n =F u F d F p + F n = 1 3 (F u + F d ) assuming flavour SU(2) isospin symmetry, i.e.: p n when u d

16 J µ =ū µ u d µ d Electromagnetic form factors General agreement between calculations Two physical point lattices: Twisted Mass PoS LATTICE2014 (2015) 148 Clover improved Phys.Rev. D90 (2014)

17 EM form factors Radii from fits to dipole form F 1 (Q 2 )= F 2 (Q 2 )= 1 (1 + Q 2 /M1 2)2 F 2 (0) (1 + Q 2 /M2 2)2 hr 2 i i = 12 M 2 i m [GeV] Curvature towards physical point Increasing sink-source separation Need 1% error for contact to experiment [fm 2 ] V r m [GeV]

18 EM form factors New methods for disconnected fermion loops hierarchical probing [arxiv: ] Sampling of the fermion propagator using site colouring schemes J. Green et al., Phys.Rev. D92 (2015) 3, , arxiv:

19 nedm CP-breaking term in action: / i µ Tr[G µ G ] θ new bare parameter of action Gives rise to dipole form factor: C. Alexandrou et al., arxiv: M N F 3 (q 2 )ū(p 0 ) µ 5u(p)F µ ~ d N = F 3(0) 2m N leading order in θ Topological charge Lattice: 1. Re-weight lattice configs. with e i Q expanded to leading order in θ 2. Include an external electric field 3. Simulate with modified action which includes a Wick rotated e i Q

20 nedm from the lattice F3(0) from O( ) External ~E θ in action Using latest experimental bound:. O( ) Poster by A. Athenodorou Phys. Rev. D 78, (2008) Phys. Rev. Lett. 115, 6, (2015) arxiv: [hep-lat] Phys. Lett. B (2010), [arxiv: ]

21 Direct calculation of PDFs on the lattice Would in principle require higher order Mellin moments, calculated on the lattice: For larger n: Z 1 Noisier correlation functions x n q(x)dx Complicated renormalisation 1 Mixing at high derivatives hx n i q = Proposal by X. Ji [Phys.Rev.Lett. 110 (2013) 26] for the calculation of quasi-pdfs on a Euclidean lattice: q(x, P 3 )= Z dz 4 e ixp 3z hn(p 3 ) (z) z A z (z,0) (0) N(P 3 )i Three-point correlation function Boosted nucleon Line of glue connecting quark lines Match using PT

22 Direct calculation of PDFs on the lattice Two pilot, promising calculations in lattice QCD Phys. Rev. D91 (2015) Clover on HISQ, mπ=310 MeV q q q (0) MSTW CJ12 ABM q q q (0) MSTW CJ12 ABM11 Talk by Fernanda Steffens, Tue Phys.Rev. D92 (2015) PDF u d twisted mass, mπ=370 MeV x x

23 Algebraic multi-grid: A. Frommer et al. SIAM J. Sci. Comput. 36 (2014) A1581-A1608 Exact eigenvalue deflation At physical quark masses Mathematical algorithms for alleviating critical slowing down Multiple right-hand-side methods for efficient multiplication of statistics

24 Summary and outlook Lattice QCD converging on benchmark quantities Physical pion mass simulations from a number of collaborations Systematic uncertainties coming under control Huge effort in algorithmic improvements for boosting statistical accuracy Exciting new directions Reliable calculation of disconnected contributions Individual quark contributions to nucleon structure Contact to new physics searches: σ-terms, scalar and tensor charges Initial, promising pilot calculations of PDFs on the lattice Future directions/challenges Effects of isospin breaking, Nf=1+1+1(+1) Electromagnetic effect