Recent Progress on Nucleon Structure with Lattice QCD

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1 Recent Progress on Nucleon Structure with Lattice QCD Huey-Wen Lin University of Washington

2 Outline Lattice gauge theory Nucleon matrix elements on the lattice: systematics Building a picture of nucleons PDFs, proton spin and quark distribution Applications beyond QCD Scalar and tensor contributions to neutron decays

3 LQCD and Nucleon Matrix Elements

4 Lattice QCD QCD observables are calculated from the path integral Strong-coupling regions: expansions no longer converge Lattice QCD is a discrete version of continuum QCD ψ(x+μˆ) U μ (x) ψ(x) Numerical integration to calculate the path integral Take a 0 and V in the continuum limit (a 3D depiction of a time-slice through a 4D lattice)

5 Actions Guided by Symanzik Improvement (order in a) Gauge sector: O(a 2 )-improved Fermion sector: O(a)-improved $$ $$$ $$ $

6 Actions Guided by Symanzik Improvement (order in a) Gauge sector: O(a 2 )-improved Fermion sector: O(a)-improved Complicated matrix elements that may have mixing Spectroscopy Form factors $$ $$ $$$ $ Smaller a and m π Larger V

7 Actions Guided by Symanzik Improvement (order in a) Gauge sector: O(a 2 )-improved Fermion sector: O(a)-improved Needs a lot more computational resources Difficult mixings, renormalization $$ $$ $$$ $ Complex flavor mixing!

8 It s Straightforward, but... Lattice gauge theory was proposed in the 1970s by Wilson Why haven t we solved QCD yet? Progress is limited by computational resources But assisted by advances in algorithms

9 It s Straightforward, but... Lattice gauge theory was proposed in the 1970s by Wilson Why haven t we solved QCD yet? Progress is limited by computational resources But assisted by advances in algorithms Computer power available for gaming in the 1980s:

10 It s Straightforward, but... Lattice gauge theory was proposed in the 1970s by Wilson Why haven t we solved QCD yet? Progress is limited by computational resources But assisted by advances in algorithms Computer power available today: Exciting progress during the last decade

11 Computational Resources USQCD facilities: JLab, Fermilab, BNL Non-lattice resources open to USQCD: ORNL, LLNL, ANL XSEDE Kraken NSF and worldwide increase in computer facilities ALCF Mira

12 LQCD for Nuclear Physics Advanced computing makes it possible! What is the spectrum of QCD? N* resonances and exotic mesons What is the makeup of the nucleon? Quark, gluon and flavor-singlet sea-quark contributions to nucleon structure How does QCD bind (hyper)nuclei? Two- and three-body interactions among baryons and mesons Binding energy of an alpha particle How do nature s symmetries break? Why is there matter and not antimatter? Necessary when experiments are limited

13 Are We There Yet? From quenched to dynamical QCD vacuum Gauge generation costs with the latest algorithms scale as Cost factor (estimation): a (5 6), L 5, M π (2 4) Most major 2+1-flavor gauge ensembles: M π < 200 MeV Including ensembles at physical pion mass (isospin breaking) by PACS-CS Charm dynamics: flavor gauge ensembles MILC (HISQ), ETMC (TMW) Pion-mass extrapolation M π (M π ) phys (Bonus products: Low-Energy Constants)

14 Successful Examples Provide higher precision for known quantities Make a lot of mass predictions Work in progress...

15 Successful Examples Provide higher precision for known quantities Make a lot of mass predictions Charmed-Baryon Spectroscopy Raul Briceno, Huey-Wen Lin, Daniel Bolton Phys. Rev. D86 (2012), Work in progress...

16 Nucleon Matrix Elements Lattice-QCD calculation of p u Γu p High statistics Often requires multiple computational resources Control all systematic errors: Finite-volume effects Contamination from excited states Chiral extrapolations to physical u and d quark masses Extrapolation to the continuum limit (lattice spacing a 0) Nonperturbative renormalization (e.g. the RI/SMOM scheme)

17 The Trouble with Nucleons Nucleons are more complicated than mesons because Noise Worse signal than mesons Large t sep loses signal Excited-state contamination Nearby excited-state Roper(1440) Hard to extrapolate Δ resonance nearby; multiple expansions, poor convergence May not be an issue in the physical pion-mass era Requires large volume and statistics Ensembles are not always generated with nucleons in mind FV estimation correction sometimes used

18 The Trouble with Nucleons Nucleons are more complicated than mesons because Noise Worse signal than mesons Large t sep loses signal Excited-state contamination Nearby excited-state Roper(1440) Hard to extrapolate Δ resonance nearby; multiple expansions, poor convergence May not be an issue in the physical pion-mass era Requires large volume and statistics Ensembles are not always generated with nucleons in mind FV estimation correction sometimes used Proceed with Caution

19 Excited-State Contamination Trade off: signal-to-noise versus contamination Noise issue (P. Lepage; D. Kaplan) Consider a baryon correlator C= O = qqq(t) qˉ qˉ qˉ(0) Variance (noise squared) of C O O O 2 What you want: Signal falls exponentially as e m N t

20 Excited-State Contamination Trade off: signal-to-noise versus contamination Noise issue (P. Lepage; D. Kaplan) Consider a baryon correlator C= O = qqq(t) qˉ qˉ qˉ(0) Variance (noise squared) of C O O O 2 What you want: What you get: Signal falls exponentially as e m N t Noise falls as e (3/2)m π t Difficulties in Euclidean space True ground state (nucleon in this case) at large Euclidean time

21 Excited-State Contamination For example, g T for a 310-MeV ensemble (PNDME) 0.96 fm t sep 1.20 fm 1.44 fm

22 Excited-State Contamination Including excited-states in the analysis is the way to go In contrast, the single-state ansatz

23 Excited-State Contamination Including excited-states in the analysis is the way to go May still have an optimal t sep but won t lose as much signal

24 Excited-State Contamination Warning! Quantity-dependent! Isoscalar case: Strong t sep dependence when excited states are not taken into account

25 Building a Picture of Nucleons

26 LQCD Status Many lattice calculations of the moments of the PDFs Limited to the lowest few moments Might provide some constraints on models or tests of experiment This also applies to GPDs, limited to 3 rd moment Most progress made in quark contributions Very costly to obtain useful gluon signal Limited by available computational resources

27 How to Slice the Spin Pie Decomposition according to sum rule Xiang-Dong Ji, Phys. Rev. Lett., 78: (1997) quark total angular momentum J q J g total gluonic contribution

28 How to Slice the Spin Pie Decomposition according to sum rule Xiang-Dong Ji, Phys. Rev. Lett., 78: (1997) quark orbital angular momentum quark spin fraction L q ΔΣ/2 J g total gluonic contribution

29 Origin of Proton Spin What is the makeup of the nucleon spin? The origin of the nucleon s spin (the spin crisis ) For example, LHPC + QCDSF dynamical results Renormalized at 2 GeV ΔΣ: spin L: orbital angular momentum M π 2 (GeV 2 ) Ignore disconnected diagram Gluon contribution estimated from sum rule

30 Origin of Proton Spin What is the makeup of the nucleon spin? χqcd, [hep-ph] J total J u+d,ci J u/d J g J s M π 2 (GeV 2 ) Breakdown: ΔΣ q = 50(2)%, L q = 25(12)% (mostly DI), J g = 25(8)% Looking forward to χqcd (overlap/dwf), QCDSF (clover)

31 x n Moments Leading moment x, hypercubic decomposition = : O 44 (O 11 +O 22 +O 33 )/3 O 14 +O 41, (requires p 0) Both operators go to same continuum limit No mixing with operators of same or lower dimension To improve to O(a) Higher moments x : O 111 mixes with q γ 1 q with coefficient ~ 1/a : O {441} (O {221} +O {331} )/2 mixes under renormalization For higher spin (n 4), all ops mix with lower-dim. ops

32 Nucleon Structure Functions Higher moments? Yes Isovector unpolarized moments LHPC (SCRI, SESAM): 2f, Wilson and clover QCDSF: 0f clover, multiple lattice spacings x 2 q Dolgov et al., PRD66, (2002) Göckeler et al. PRD71, (2005) x 3 q

33 Light-Cone Observables Consider the properties of nucleon on the light cone

34 Light-Cone Observables Consider the properties of nucleon on the light cone Transform lab coordinates x ± = z±t orthogonal directions unchanged

35 Light-Cone Observables Consider the properties of nucleon on the light cone Transform lab coordinates x ± = z±t orthogonal directions unchanged Massive particles lie on hyperboloids invariant under Lorentz transformation

36 Light-Cone Observables Consider the properties of nucleon on the light cone Transform lab coordinates x ± = z±t orthogonal directions unchanged Massive particles lie on hyperboloids invariant under Lorentz transformation Approach the light cone as momentum goes to infinity Lattice momenta discretized by finite size of volume P z {0,1,2,3} 2π L

37 Quark Distribution Lightcone quark distribution boosted along z direction Renormalization scale µ Light-cone coordinate ξ ± = (t±z)/ 2 Nucleon momentum P µ = {P 0,0,0,P 3 } Gluon potential A +

38 Take the large-p z limit: Quark Distribution x = k z /P z Lattice z coordinate Nucleon momentum P µ = {P 0,0,0,P z } Product of lattice gauge links At P z limit, twist-2 parton distribution is recovered For finite P z, corrections are needed Xiangdong Ji, this Thursday; HWL et al in progress

39 Quark Distribution Exploratory study N f = clover/hisq lattices M π 310 MeV, a 0.12 fm (L 2.88 fm) Isovector only ( disconnected contribution suppressed) P z {0, 1, 2, 3} 2π L

40 Quark Distribution Exploratory study N f = clover/hisq lattices M π 310 MeV, a 0.12 fm (L 2.88 fm) Isovector only ( disconnected contribution suppressed) Preliminary Uncorrected bare lattice results

41 Quark Distribution Exploratory study N f = clover/hisq lattices M π 310 MeV, a 0.12 fm (L 2.88 fm) Isovector only ( disconnected contribution suppressed) Preliminary Corrected to O(P z- 2 ) Gray band shows extrapolation of P z 4 terms No significant finite-momentum effect seen Renormalization needed

42 Helicity Distribution Exploratory study N f = clover/hisq lattices M π 310 MeV, a 0.12 fm (L 2.88 fm) Isovector only ( disconnected contribution suppressed) Preliminary Corrected to O(P z- 2 ) Gray band shows extrapolation of P z 4 terms Large O(P z 4 ) seen but well fit by extrapolation Renormalization needed

43 Transversity Distribution Exploratory study N f = clover/hisq lattices M π 310 MeV, a 0.12 fm (L 2.88 fm) Isovector only ( disconnected contribution suppressed) Preliminary Corrected to O(P z- 2 ) Gray band shows extrapolation of P z 4 terms Large O(P z 4 ) seen and only marginally well fit by extrapolation Renormalization needed

44 Applications beyond QCD

45 A Tale of Two Scales LHC strikes out onto the high-energy frontier (8 TeV) Direct measurement of Higgs and BSM particles Many experiments refine low-energy measurements Discern small discrepancies from the Standard Model Muon g 2, Q weak, CKM matrix Probe small signals that are suppressed in the SM 0νββ, nedm, dark matter, non-v A interactions in β decay

46 Hadronic Physics and BSM Many opportunities to probe BSM with LQCD Dark-matter scattering Certain candidates (e.g. SuSy neutralinos) exchange Higgs Electric dipole moment CP-violating effect Extremely small in SM: e-cm Best SUSY model killer Nucleon beta decay Non-V A (e.g. scalar and tensor) interactions To probe the existence of new particles (mediating new forces) with masses in the multi-tev range Two-photon decay and muon g 2

47 Fermi Theory of Beta Decay Four-fermion interaction explained beta decay before electroweak theory was proposed New operators in effective low-energy theories Electroweak theory adds 3 vector bosons W and Z bosons directly detected later at CERN ~g 2 /Λ 2 Λ m W 80 GeV, m Z 90 GeV

48 What You See/How You Look LHC L SM + L BSM SLC L SM + UCN LANSCE

49 BSM Interactions Neutron beta decay could be related to new interactions: the scalar and tensor ε S and ε T are related to the masses of the new TeV-scale particles but the unknown coupling constants g S,T are needed Given precision g S,T and O BSM, predict new-physics scales Precision LQCD input Experiment O BSM = fo(εs,t gs,t) (m π 140 MeV, a 0) ε S,T Λ 2 S,T

50 UCNs by 2013 Physics Program Given precision g S,T and b, B 1, we can predict possible new particles b = fb (εs,t gs,t) B1 = fb (εs,t gs,t) Precision LQCD input (m π 140 MeV, a 0) εs and εt Gives the scale of particles mediating new forces With exp t precision of B 1 b BSM < 10 3 b BSM < 10 3 T. Bhattacharya et al., Phys. Rev. D (2012)

51 Tensor and Scalar Charges Tensor charge: the zeroth moment of the transversity g T = δu δd Experimentally, probed through SIDIS (HERMES and COMPASS) M. Anselmino et al., Phys. Rev. D75, (2007) Model-dependent extractions Combined with other experiments g T (Q 2 =0.8 GeV 2 )= x

52 Tensor and Scalar Charges Tensor charge: the zeroth moment of the transversity g T = δu δd Experimentally, probed through SIDIS: g T (Q 2 =0.8 GeV 2 )= Model estimate: 0.8(4) Scalar charge n u d p Prior model estimate: 1 g S 0.25 g T LQCD =0.988(42)(?) g S LQCD =0.761(88)(?)

53 Combined with Experiments Given precision g S,T and O BSM, predict new-physics scales Nuclear Exp. Model input O BSM = fo(εs,t gs,t) ε S,T Λ 2 S,T Nuclear beta decays transitions β asym in Gamow-Teller 60 Co polarization ratio between Fermi and GT in 114 In positron polarization in polarized 107 In β-ν correlation parameter a

54 Combined with Experiments Given precision g S,T and O BSM, predict new-physics scales New UCN Exp. Model input O BSM = fo(εs,t gs,t) ε S,T Λ 2 S,T LANL UCN neutron decay exp t Expect by 2013: B 1 b BSM < 10 3 b BSM < 10 3 Similar proposal at ORNL by 2015

55 Combined with Experiments Given precision g S,T and O BSM, predict new-physics scales New UCN Exp. Precision LQCD input O BSM = fo(εs,t gs,t) (m π 140 MeV, a 0) ε S,T Λ 2 S,T LANL UCN neutron decay exp t Expect by 2013: B 1 b BSM < 10 3 b BSM < 10 3 Similar proposal at ORNL by 2015

56 High-Energy Constraints Constraints from high-energy experiments? LHC current bounds and near-term expectation Estimated though effective L Looking at high transverse mass in e ν + X channel Compare with W background Estimated 90% C.L. constraints on ε S,T Λ 2 S,T HWL, ; T. Bhattacharya et al,

57 Summary Exciting time to explore QCD LQCD is building a picture of hadrons Controlling systematic uncertainty in nucleon matrix elements Techniques to reveal proton spin composition New idea for studying full x dependence of PDFs (can be expanded to TMDs, GPDs, and gluons) Applications of LQCD to probe beyond the Standard Model Opportunities combining high- (TeV) and low- (GeV) energies Vital input when experiment is limited (e.g. g S ) Aim at high precision and understand/quote systematics!

58 Outlook Welcome more ideas and discussions

59 Outlook Welcome more ideas and discussions A wide variety of experiments of this type, including improved measurements of neutron beta decay, as well as searches for proton decay, neutron-antineutron oscillations, dark matter, and permanent electric dipole moments (EDMs) would benefit from a renewed look at the QCD inputs required to set limits on models of BSM physics. Our plan is to collect a group of phenomenologists, lattice gauge theorists and a few key experimentalists, to discuss the constraints on theories probed by the experiments we consider and the manner in which these constraints are entwined with QCD physics, both perturbative and nonperturbative.