Nucleon matrix elements

Transcription

1 Nucleon matrix elements Constantia Alexandrou University of Cyprus and The Cyprus Institute Symposium on Effective Field Theories and Lattice Gauge Theory May 20, 2016 C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

2 Outline 1 Introduction Current status of simulations Computational cost 2 Nucleon observables Nucleon charges: g A, g s, g T Nucleon σ-terms Electromagnetic form factors Parton Distributions Electric Dipole Moment 3 Conclusions C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

3 Quantum ChromoDynamics (QCD) QCD-Gauge theory of the strong interaction Lagrangian: formulated in terms of quarks and gluons L QCD = 1 4 F a µν F a µν + D µ = µ ig λa 2 Aa µ f =u,d,s,c,b,t ψ f ( iγ µ D µ m f ) ψf Choice of fermion discretisation scheme e.g. Clover, Twisted Mass, Staggered, Overlap, Domain Wall Each has its advantages and disadvantages Eventually, all discretization schemes must agree in the continuum limit a 0 observables extrapolated to the infinite volume limit L C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

4 Why nucleon structure? With simulations at the physical value of the pion mass there is a number of interesting questions we want to address: Can we reproduce known quantities? Can we reproduce the excited spectrum of the nucleon and its associated resonances? Can we resolve the long-standing issue of the spin content of the nucleon? Can we determine accurately enough the charge radius of the proton? Can we provide input for experimental searches for new physics? C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

5 Status of simulations Size of the symbols according to the value of m πl: smallest value m πl 3 and largest m πl 6.7. In this talk: Show results from an analysis of N f = 2 simulations with twisted mass Wilson fermions including a clover term at physical values of the light quark masses, (ETMC) A. Abdel-Rehim et al., arxiv: , arxiv: first results at physical point, (ETMC) A. Abdel-Rehim et al., Phys. Rev. D92 (2015), , arxiv: C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

6 Observables at physical quark mass For the analysis of the physical ensemble with a volume of , methods to reduce the statistical error are essential e (mp 3 mπ )ts 2 C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

7 Observables at physical quark mass For the analysis of the physical ensemble with a volume of , methods to reduce the statistical error are essential 10 3 Speed-up over CG ARPACK/CG, nev=1600 Multi-grid, 3-level, original Multi-grid, 3-level, tuned nrhs Speed-up of Inversion (for a lattice of 48 3 x64) C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

8 Observables at physical quark mass For the analysis of the physical ensemble with a volume of , methods to reduce the statistical error are essential Speed-up of Inversion with multi-grid C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

9 The nucleon mn /m Experiment a=0.089 fm, N f =2 a=0.070 fm, N f =2 a=0.091 fm, N f =2, w/ Clover a=0.093 fm, N f = a=0.082 fm, N f = a=0.064 fm, N f = O(p 3 ) fit to N f=2+1+1 and N f= m 2 [GeV 2 ] Cut-off effects small for these lattice spacings LO fit with m π < 375 MeV does not include the physical point Determine lattice spacing using the O(p 3 ) result C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

10 Evaluation of matrix elements Three-point functions: G µν (Γ, q, t s, t ins) = xs, x ins e i x ins q Γ βα J α( x s, t s)o µν Γ ( x ins, t ins)j β ( x 0, t 0 ) OΓ OΓ q = p p q = p p (xs, ts) (xins, tins) (x0, t0) ( xs, ts) ( xins, tins) ( x0, t0) connected contribution disconnected contribution R(t s, t ins, t 0 ) (t ins t 0 ) 1 M[ e (p)(t ins t 0 ) +... e (p )(ts t ins ) ] (ts t ins ) gs ga gt xq ge GM(1) xdq M the desired matrix element t s, t ins, t 0 the sink, insertion and source time-slices (p) the energy gap with the first excited state ts/a To ensure ground state dominance need multiple sink-source time separations ranging from 0.9 fm to 1.5 fm C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

11 Extracting nucleon matrix elements Plateau method: R(t s, t ins, t 0 ) (t ins t 0 ) 1 M[ e (p)(t ins t 0 ) +... e (p )(ts t ins ) ] (ts t ins ) 1 M the desired matrix element t s, t ins, t 0 the sink, insertion and source time-slices (p) the energy gap with the first excited state Excited states contributions are different for different operators and pion mass need to carefully check Need to include disconnected contributions unless shown to be negligible Summation method: Summing over t ins: ts R(t s, t ins, t 0 ) = Const. + M[(t s t 0 ) + O(e (p)(ts t0) ) + O(e (p )(ts t0 ) )]. t ins =t 0 Excited state contributions are suppressed by exponentials decaying with t s t 0, rather than t s t ins and/or t ins t 0 However, one needs to fit the slope rather than to a constant or take differences and then fit to a constant L. Maiani, G. Martinelli, M. L. Paciello, and B. Taglienti, Nucl. Phys. B293, 420 (1987); S. Capitani et al., arxiv: Fit keeping the first excited state, T. Bhattacharya et al., arxiv: All should yield the same answer in the end of the day! C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

12 Nucleon charges: g A, g s, g T axial-vector operator: O a A = ψ(x)γ µ γ 5 τ a 2 ψ(x) scalar operator: O a S tensor operator: O a T = ψ(x) τa 2 ψ(x) = ψ(x)σ µν τa 2 ψ(x) = extract from ratio: N( p )O X N( p) q 2 =0 Axial charge g A Scalar charge g S Tensor charge g T (i) isovector combination has no disconnect contributions; (ii) g A well known experimentally, g T to be measured at JLab C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

13 Nucleon charges: g A, g s, g T N f = 2 TMF with clover term a = 0.093(2) fm with m π = 133 MeV; Connected part with 6800 statistics First results with 1500 statistics, A. Abdel-Rehim et al. Phys.Rev. D92 (2015) no.11, , Erratum: Phys.Rev. D93 (2016) no.3, C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

14 Nucleon axial charge g A A previous study using N F = TM with m π = 373 MeV and a = 0.08 fm Vary source- sink separation: ga fixed sink method, tsink = 12a PDG open sink method tsink/a < x >u d fixed sink method, tsink = 12a ABMK fit open sink method tsink/a g A unaffected, x u d 10% lower = Excited contributions are operator dependent S. Dinter, C.A., M. Constantinou, V. Drach, K. Jansen and D. Renner, arxiv: C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

15 Nucleon Axial-vector charge g A Comparison of lattice results Axial-vector FFs: A 3 µ = τ ψγ µγ ψ(x) = 1 2 ūn ( p [ ] ) γ µγ 5G A (q 2 ) + qµ γ 5 2m Gp(q2 ) u N ( p) q 2 =0 yields G A (0) g A : i) well known experimentally, & ii) no quark loop contributions Isovector 1.4 g u d A Nf =2 TMF : a =0.089, 0.07, fm Nf =2+1+1 TMF : a=0.082, fm Nf =2 TMF/Clover : a=0.093 fm Nf =2+1 MILC/DWF : a=0.124 fm m 2 [GeV 2 ] Nf =2 clover : a =0.08, 0.07, 0.06 fm Nf =2+1 clover : a=0.116, fm Nf =2+1+1 HISQ/clover : a=0.12, fm experiment g A at the physical point using 6800 at sink-source time separation 1.3 fm slightly below the physical value important to increase sink-source time separation at constant statistical error but also volume effects should also be checked - compute g A on a volume at the same light quark masses many results from other collaborations, e.g. N f = Clover, J. R. Green et al., arxiv: N f = 2 Clover, R.Hosley et al., arxiv: N f = 2 Clover, S. Capitani et al. arxiv: N f = Clover, B. J. Owen et al., arxiv: N f = Mixed action (HISQ/Clover), T. Bhattacharya et al., arxiv: C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

16 Nucleon tensor g T, g S Isovector 1.2 scalar operator: O a S = ψ(x) τa 2 ψ(x) tensor operator: O a T = µν τa ψ(x)σ 2 ψ(x) 1.1 g u d T Nf =2+1+1 TMF : a=0.082, fm Nf =2+1+1 TMF : a=0.064 fm Nf =2 TMF/clover : a=0.093 fm Nf =2+1 clover : a=0.116, fm Nf =2+1 clover : a=0.09, fm Nf =2 +1 DWF : a =0.084 fm Nf =2+1 MILC/DWF : a=0.124 fm Nf =2+1+1 HISQ/clover : a=0.09, fm Nf =2 clover : a=0.08,fm Nf =2 clover : a=0.07,fm Nf =2 clover : a=0.06,fm m 2 [GeV 2 ] Experimental value of g u d T 0.13 from global analysis of HERMES, COMPASS and Belle e+ e data, M. Anselmino et al. (2013). New analysis of COMPASS and Belle data :g u d = 0.81(44), M. R. A. Courtoy, A. Bacchettad, M. Guagnellia, arxiv: T g u d s is very noisy. Currently g u d S 1 ± 0.5 C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

17 Nucleon charges: g q A, gq T, gq S Include disconnected contributions, 202, 000 statistics Disconnected contribution to g u+d A Disconnected contribution to g u+d T Disconnected contribution to g u+d S cannot be neglected, 10% of connected negligible are 25% of the connected. C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

18 The quark content of the nucleon or nucleon σ-terms σ f m f N q f q f N : measures the explicit breaking of chiral symmetry Largest uncertainty in interpreting experiments for dark matter searches - Higgs-nucleon coupling depends on σ, J. Ellis, K. Olive, C. Savage, arxiv: In lattice QCD: m i) Feynman-Hellmann theorem: σ l = m N l m l m Similarly σ s = m N s ms ii) Direct computation of the scalar matrix element, A. Abdel-Rehim et al. arxiv: R(ts, tins) N [MeV] Connected Summation Two-state Disconnected Summation Two-state ts=1.1 fm ts=1.3 fm ts=1.5 fm ts=1.6 fm ts=1.7 fm tins ts/2 [fm] R(ts, tins) s [MeV] R(ts, tins) c [MeV] Summation Two-state Two-state Summation ts=0.9 fm ts=1.1 fm ts=1.3 fm ts=1.5 fm ts=1.7 fm tins ts/2 [fm] C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

19 The quark content of the nucleon or nucleon σ-terms σ f m f N q f q f N : measures the explicit breaking of chiral symmetry Largest uncertainty in interpreting experiments for dark matter searches - Higgs-nucleon coupling depends on σ, J. Ellis, K. Olive, C. Savage, arxiv: In lattice QCD: m i) Feynman-Hellmann theorem: σ l = m N l m l m Similarly σ s = m N s ms ii) Direct computation of the scalar matrix element, A. Abdel-Rehim et al. arxiv: Pavan '02 Alarcón '11 Hoferichter '15 QCDSF-UKQCD '11 ETMC '14 BMWc '15 QCDSF '12 QCD '15 This work N [MeV] c s QCD '13 BMWc '15 QCDSF '12 QCD '13 QCD '15 This work This work QCDSF-UKQCD ' s, c [MeV] C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

20 Electromagnetic form factors [ ] N(p, s ) j µ (0) N(p, s) = ū N (p, s ) γ µ F 1 (q 2 ) + iσµν qν 2m F 2 (q 2 ) u N (p, s) Proton radius extracted from muonic hydrogen is 7.7 σ different from the one extracted from electron scattering, R. Pohl et al., Nature 466 (2010) 213 Muonic measurement is ten times more accurate C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

21 Dirac and Pauli radii Dipole fits: G 0 (1+Q 2 /M 2 ) 2 r 2 i = 6 F i Need better accuracy at the physical point df i dq 2 Q 2 =0 = 12 M 2 i Using results from summation method, J. M. Green et al., C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

22 Position methods Avoid model dependence-fits Application to Sachs form factors nucleon isovector magnetic moment G iso M (0) Isovector rms charge radius of the nucleon Neutron electric dipole moment As a first step we calculated G M (0) (equivalently F 2 (0)) at m π = 373 MeV. C.A., G. Koutsou, K. Ottnad, M. Petschlies, PoS(Lattice2014), 144 C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

23 Magnetic moment G iso M (0) 6 5 y-summation y-summation G iso M (Q2 = 0) sequential method In principle, values at larger Q 2 have very little influence Value for G iso M = 4.45(15)stat larger than result from dipole fit 3.99(9) stat Closer to exp. value (4.71) G iso M (Q2 ) Q 2 [GeV 2 ] G iso M (0) from O(4700) gauge confs of B55; ts/a = C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

24 Results for r iso E 0.8 direct computation CODATA re,iso 2 muonic atoms r 2 E,iso 6(G iso E (Q2 ) G iso E (0))/Q2 [fm 2 ] direct computation r 2 E,iso standard method We use an ETMC , N f = 2 ensemble with physical pion mass Data shown in plot are for O(1400) confs t s/a = 14 compatible with experiment! Unfortunately errors are still not small enough to distinguish the two experimental values Q 2 [GeV 2 ] C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

25 Strange Electromagnetic form factors New methods for disconnected fermion loops: hierarchical probing, A. Stathopoulos, J. Laeuchli, K. Orginos, arxiv: N f = clover fermions, m π 320 MeV, J. Green et al., Phys.Rev. D92 (2015) 3, , arxiv: Sampling of the fermion propagator using site colouring schemes C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

26 Moments of Generalized Parton Distributions Factorization leads to matrix elements of local operators: vector operator O µ 1 µn V a = ψ(x)γ {µ 1 i D µ 2... i D µn} τ a 2 ψ(x) axial-vector operator O µ 1 µn A a = ψ(x)γ {µ 1 i D µ 2... i D µn} γ 5 τ a 2 ψ(x) tensor operator O µ 1 µn T a = ψ(x)σ {µ 1,µ 2 i D µ 3... i D µn} τ a 2 ψ(x) Special cases: no-derivative nucleon form factors For Q 2 = 0 parton distribution functions one-derivative first moments e.g. average momentum fraction x Generalized form factor decomposition: N(p, s ) O µν V 3 N(p, s) = ū N (p, s ) Nucleon spin J q = 1 2 [ A 20 (q 2 )γ {µ P ν} +B 20 (q 2 ) iσ{µα q αp ν} +C 20 (q 2 ) q{µ q ν} 2m m [ ] A 20 (0) + B 20 (0) and x q = A 20 (0) ] 1 2 u N (p, s) C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

27 Momentum fraction and the nucleon spin What is the distribution of the nucleon momentum among the nucleon constituents? x obtained in the MS scheme at µ = 2 GeV. x u d approach physical value for bigger source-sink separations need an equivalent high statistics study e.g. t s 1.5 fm we used statistics Can provide a prediction for x δu δd Experimental value: x u d from S. Alekhin et al. arxiv: C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

28 Momentum fraction and the nucleon spin What is the distribution of the nucleon momentum among the nucleon constituents? x obtained in the MS scheme at µ = 2 GeV x u d Nf =2 TMF : a =0.089, 0.07, fm Nf =2+1+1, TMF : a=0.082,0.064 fm Nf =2 TMF/clover : a=0.093 fm Nf =2+1 clover : a=0.116 fm Nf =2 Clover : a =0.07 fm m 2 [GeV 2 ] Nf =2 +1 DWF : a =0.114 fm Nf =2+1 MILC/DWF : a=0.124 fm Nf =2 clover : a =0.075 fm experiment Near the physical point we show results from: N f = 2 twisted mass plus clover-impoved from ETMC fermions, A. Abdel-Rehim et al N f = clover fermions with 2-HEX smearing from LHPC, J. Green et al., N f = 2 clover fermions, G. Bali et al., N f = 2 clover fermions from QCDSF/UKQCD, D. Pleiter et al., x u d approach physical value for bigger source-sink separations need an equivalent high statistics study e.g. t s 1.5 fm we used statistics Can provide a prediction for x δu δd Experimental value: x u d from S. Alekhin et al. arxiv: C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

29 Nucleon gluon moment N f = twisted mass, a = fm, m π = 373 MeV, 34,470 statistics N f = 2 twisted mass plus clover, a = fm, m π = 132 MeV, 155,800 statistics Matrix element of the gluon operator O µν = Tr[G µρg νρ] We consider N O O jj N at zero momentum, which yields directly x g HYP-smearing to reduce noise Perturbative renormalization C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

30 Nucleon gluon moment-renormalization Mixing with x u+d = Perturbation theory - M. Constantinou and H. Panagopoulos C. Millions Alexandrou of(univ. terms of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

31 Nucleon gluon moment-renormalization Mixing with x u+d = Perturbation theory - M. Constantinou and H. Panagopoulos Preliminary value: x g = 0.282(39) for the physical ensemble in MS at µ = 2 GeV Momentum conservation: q x q + x g = x CI u+d + x DI u+d+s + x g = 0.929(64) C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

32 C Nucleon spin? m 2 (GeV 2 ) Spin sum: 1 2 = ( ) 1 q 2 Σq + L q +J G }{{} J q J q = A q 20 (0) + Bq 20 (0) and Σq = g q A Disconnected contribution using O(150, 000) statistics for m π = 373 MeV and for m π = 133 MeV Contributions to nucleon spin m 2 (GeV 2 ) = Total spin for u-quarks J u < 0.25 and for d-quark J d 0 J u J d C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

33 Nucleon spin? m 2 (GeV 2 ) Spin sum: 1 2 = ( ) 1 q 2 Σq + L q +J G }{{} J q J q = A q 20 (0) + Bq 20 (0) and Σq = g q A Disconnected contribution using O(150, 000) statistics for m π = 373 MeV and for m π = 133 MeV Contributions to nucleon spin s 1 2 u 1 2 d m 2 (GeV 2 ) Σ u,d consistent with experimental values C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

34 Direct evaluation of parton distribution functions - an exploratory study + ã n(x, Λ, P 3 ) = dx x n 1 q(x, Λ, P 3 ), + dz q(x, Λ, P 3 ) = 4π e izxp 3 P ψ(z, 0) γ 3 W (z)ψ(0, 0) P }{{} h(p 3,z) canbecomputedinlqcd is the quasi-distribution defined by X. Ji Phys.Rev.Lett. 110 (2013) , arxiv: Exploratory calculations: Huey-Wen Lin et al. Phys. Rev. D91 (2015) , Clover on N f = HISQ, m π = 310MeV and Jiunn-Wei Chen et al., arxiv: C.A., K. Cichy, E. G. Ramos, V. Drach, K. Hadjiyiannakou, K. Jansen, F. Steffens, C. Wiese, Phys.Rev. D92 (2015) We used the N f = TMF ensemble with m π = 373 MeV Perform HYP-smearing on the gauge links Use the stochastic all-to-all propagator in the three-point function Extract quasi-distribution for 2π L, 4π L, 6π L C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

35 Comments Our starting point is ( q(x, µ) = q(x, Λ, P 3 ) αs 2π q(x, Λ, P 3)δZ (1) µ, Λ ) αs 1 ( dy x F P 3 P 3 2π 1 y Z (1) y, µ, Λ ) q(y, Λ, P 3 )+O(α 2 s P 3 P ) 3 The calculation of the leading UV divergences in q in PT are done keeping P 3 fixed while taking Λ (in contrast to first taking P 3 for the renormalization of q) We still do not have a renormalization procedure identify the UV regulator as µ for q and as Λ for the case of the quasi-distribution. The dependence on the UV regulator Λ will be translated, in the end, into a renormalization scale µ after proper renormalization Single pole terms cancel when combining the vertex and wave function corrections, and double poles are reduced to a single pole that are taken care via the principal value prescription C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

36 Preliminary results Results for 5-HYP steps, P 3 = 4π/L P 3 = 6π/L, Jiunn-Wei Chen et al., arxiv: Work in progress for the renormalization C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

37 Neutron Electric Dipole Moment (nedm) Probe for beyond the standard model physics Current best upper limit : d n < e cm (90% C.L. from ILL Grenoble) C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

38 Lattice determination of Neutron Electric Dipole Moment (nedm) Add θ-term to the Langragian complex action Measure neutron energy in an external electric field Simulate with imaginary θ, see e.g. QCDSF, Guo et al Assume θ is small and expand to first order: Compute the CP-violating form factor F 3 (0) d n = lim q 2 0 F 3 (q 2 ) 2m N But F 3 (0) cannot be determined directly use: Fit the q 2 -dependence Use space methods to extract it C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

39 Results on nedm N f = twisted mass, a = fm, m π = 373 MeV Use gradient flow to define the topological charge Comparison of results Shintani et al. '13 (Nf=2+1) F3(0) F3(0)/ 2mN [e fm] TMF Nf=2 Nf=0 Shintani et al. '08 (Nf=2) External electric field m 2 π [GeV 2 ] ETMC, C. Alexandrou et al.x, arxiv: Computation at the physical point under study C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

40 Conclusions Future Perspectives Confirm g A, x u d, etc, at the physical point using N f = 2 at a larger volume and with N f = Provide predictions for g s, g T, tensor moment, sigma-terms, etc. Compute hadron GPDs using new techniques Increase statistics on the proton radius using position methods Compute gluonic observables Nucleon excited states and resonance properties C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34

41 European Twisted Mass Collaboration European Twisted Mass Collaboration (ETMC) Cyprus (Univ. of Cyprus, Cyprus Inst.), France (Orsay, Grenoble), Germany (Berlin/Zeuthen, Bonn, Frankfurt, Hamburg, Münster), Italy (Rome I, II, III, Trento), Netherlands (Groningen), Poland (Poznan), Spain (Valencia), Switzerland (Bern), UK (Liverpool) Collaborators: A. Abdel-Rehim, S. Bacchio, K. Cichy, M. Constantinou, V. Drach, E. Garcia Ramos, J. Finkenrath, K. Hadjiyiannakou, K.Jansen, Ch. Kallidonis, G. Koutsou, K. Ottnad, M. Petschlies, F. Steffens, A. Vaquero, C. Wiese C. Alexandrou (Univ. of Cyprus & Cyprus Inst.) Nucleon from LQCD May 20, / 34