Hadron Structure on the Lattice

Transcription

1 Hadron Structure on the Lattice Huey-Wen Lin University of Washington

2 Lattice gauge theory A brief introduction Outline Building a picture of hadrons Recent developments on form factors, EMC effect, etc. Applications beyond QCD Scalar and tensor contributions to neutron decays

3 First Know Thy SM: QCD

4 Strong Force and Lattice QCD Quantum Chromodynamics (QCD) The strong interactions of quarks and gluons (SU(3) gauge) Lattice gauge theory quark field α s (Q) gluon field x, y, z L t a

5 Difficulties at Low Energy Even just the vacuum of QCD is complicated Classical QCD Direct QCD calculation is desired Lattice QCD

6 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

7 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:

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 Computer power available today: Exciting progress during the last decade

9 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

10 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

11 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 Charm dynamics: flavor gauge ensembles MILC (HISQ), ETMC (TMW) Pion-mass extrapolation M π (M π ) phys (Bonus products: Low-Energy Constants)

12 The Trouble with Nucleons Difficulties in Euclidean space Exponentially worse signal-to-noise ratios 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

13 The Trouble with Nucleons Difficulties in Euclidean space Exponentially worse signal-to-noise ratios 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

14 The Trouble with Nucleons Difficulties in Euclidean space Exponentially worse signal-to-noise ratios 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 Problem worsens with: increasing baryon number decreasing quark (pion) mass

15 Extrapolations For example, single-baryon masses Lighter quark simulations require $$$ a fm HWL et al (HSC), l Ξ = m π2 / 4m Ξ 2

16 Extrapolations For example, single-baryon masses Lighter quark simulations require $$$ Mild lattice-spacing dependence a fm a 0.125fm HWL et al (HSC), l Ξ = m π2 / 4m Ξ 2 BMW Collaboration, Science (2008)

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

18 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...

19 M-M N (MeV) Successful Examples Provide higher precision for known quantities Make a lot of mass predictions Highly Excited States Hybrid Baryons Jozef Dudek, Robert Edwards, Phys. Rev. D85, (2012) Phys. Rev. D82, (2010)

20 Properties of N* For example, Roper-N transition form factors 2+1f anisotropic clover with M π 390, 450, 875 MeV (L = 3, 2.5, 2.5 fm) HWL, ;

21 Building a Picture of Hadrons

22 Moments of Structure Structure function/distribution functions Deep inelastic scattering (DIS) x n q, x n Δq, x n δq, x n g

23 Medium Modification Parton structure function in nuclear medium The famous EMC effect Significant deviations between heavy nuclei and deuterium Many models: pion enhancement nucleon expansion multiquark clusters rescaling shadowing local correlations No universal understanding J. J. Aubert et al. Phys. Lett. 123, 275 (1983)

24 Medium Modification Not only significant for heavy nuclei, Hall C E also important for light-nuclear systems J. Seely et al., Phys. Rev. Lett. 103, (2009)

25 Medium Modification Interesting physics with multi-baryon systems Study with nonzero μ B notorious sign problem in Monte Carlo calculation Add nucleons to the system complicated quark contraction and noise/signal issue Number of contractions: (A+Z)! (2A Z)! Triton: He: Signal Quality What you want: What you get: Take a step back and look at nonzero-isospin/multi-meson systems Many studies: QCD at Finite Isospin Density, Son & Stephanov Gain insight and experience for how to deal with nuclear systems

26 Medium-Modification Project William Detmold (MIT) JLab HWL (U. of Washington) UW USQCD W&M NERSC

27 We calculate Pion Structure Function where Contractions Examples from 3-π + system

28 We calculate Pion Structure Function where Wick contractions Use mixed-meson recursion relations W. Detmold, B. Smigielski, Phys.Rev.D84: (2011) Treated as diff. meson spices

29 We calculate Pion Structure Function where Wick contractions Examples from n-π + system Matrix elements extraction (naively),

30 Pion Momentum Fraction x π,n / x π,0 without thermal-state degrees of freedom t sep =T/2 pion medium

31 Thermal Contamination Significant for n-π + system through amplitudes For example, a=0.12 fm ensemble, T=64 a = 0.12 fm, M π = 290 MeV, M π T = 11.6 a = 0.12 fm, M π = 490 MeV, M π T = 19.9 Matrix elements extraction for p=0 (in reality)

32 Medium Modification First lattice-qcd attempt to measure EMC effects Pion momentum fraction in pion medium With m π MeV, 2 lattice spacings x π,n / x π,0 with thermal-state degrees of freedom multiple t sep used Future Plans: Working on light nuclei W. Detmold+HWL; and updated ρ π

33 Form Factors Structure function/distribution functions Deep inelastic scattering (DIS) x n q, x n Δq, x n δq Form factors Elastic scattering F 1 (Q 2 ), F 2 (Q 2 ), G A (Q 2 ), G P (Q 2 )

34 Higher-Q 2 Form Factors Higher-Q 2 data will help us to understand hadrons and challenge QCD-based models Electromagnetic probes are a common exp. approach Nucleon form factors Recent progress on precision data for proton up to 8.5 GeV 2 Experimentally more challenging for neutron (more from JLab 12-GeV) Little is known in the axial form-factor channels Q 2 (GeV 2 )

35 Why Nonperturbative? At higher energies, perturbative QCD should work better However, the range of validity is unclear For example, recent BaBar data for γ * γ π 0 Disagreement with pqcd over a wide range: 4 GeV 2 < Q 2 < 40 GeV 2 Nonperturbative QCD will provide a direct test Lattice QCD

36 Higher-Q 2 Form Factors Challenge for lattice-qcd calculations Typical Q 2 range for nucleon form factors is < 3.0 GeV 2 Higher-Q 2 calculations suffer from poor noise-to-signal ratios 2+1 dynamical example: RBC/UKQCD Dirac FF LHPC, Q 2 F π

37 Source Selection Problem: traditional approach fails at large Q 2 Simplify to a one-state problem J N J N = Σ n J n n J e E nt Nucleon effective mass log[c(t)/c(t+1)] 0 t Solution: confront excited states directly and allow operators to couple to excited states t

38 High-Momentum Sources Phenomenological choice with dimensionless parameter HWL et al., arxiv: N f = 2+1 anisotropic lattices, M π 450, 580, 875 MeV F 1 u d F 2 u d

39 Transverse Charge Density Infinite-momentum frame G. A. Miller, arxiv: How does high-q 2 affect charge density? Red band uses lattice data 2.0 GeV 2 Blue band uses lattice data 4.0 GeV 2

40 Transverse Charge Density Fourier transform using large-q 2 form factors to reveal transverse charge densities in a polarized nucleon HWL, National Academies Press

41 Higher-Q 2 Pion Form Factors Less is known about the pion form factor Precision data up to 2.5 GeV 2 Disagreement among model calculations at large Q 2 12-GeV Project E (Huber and Gaskell) Work in progress Q 2 F π New Proposal

42 Nucleon Axial Form Factors N f = 2+1 anisotropic lattices, M π 450, 580, 875 MeV G A u d (Q 2 )

43 Generalized Parton Distribution Structure function/distribution functions Deep inelastic scattering (DIS) x n q, x n Δq, x n δq Form factors Elastic scattering F 1 (Q 2 ), F 2 (Q 2 ), G A (Q 2 ), G P (Q 2 ) Generalized Parton Distribution Deeply virtual Compton scattering (DVCS) x n 1 q = A n0 (0), x n 1 Δq = A ~ n0(0), x n δq = A Tn0 (0) F 1 (Q 2 ) = A 10 (Q 2 ), F 2 (Q 2 ) = B 10 (Q 2 ), G A (Q 2 ) = A ~ 10(Q 2 ), G P (Q 2 ) = B ~ 10(Q 2 ) Nucleon spin A 20 (0), B 20 (0)

44 Generalized Parton Distribution 2 ) Generalized Parton Distribution Deeply virtual Compton scattering (DVCS) x n 1 q = A n0 (0), x n 1 Δq = A ~ n0(0), x n δq = A Tn0 (0) F 1 (Q 2 ) = A 10 (Q 2 ), F 2 (Q 2 ) = B 10 (Q 2 ), G A (Q 2 ) = A ~ 10(Q 2 ), G P (Q 2 ) = B ~ 10(Q 2 ) Nucleon spin A 20 (0), B 20 (0)

45 Origin of Proton Spin What is the makeup of the nucleon? 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

46 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)

47 Applications beyond QCD

48 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

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

50 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

51 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)

52 Tanmoy Bhattacharya Rajan Gupta PNDME Precision Neutron-Decay Matrix Elements (2011 ) HWL (PI) Saul Cohen Anosh Joseph N f = Lightest pion mass 220 MeV a min = 0.06 fm Physical pion mass planned

53 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

54 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

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

56 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

57 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)(?)

58 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

59 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

60 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

61 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,

62 Exciting time to explore Summary LQCD is building a picture of hadrons Revealed proton spin components, transverse distribution New techniques for gluonic, disconnected and in-medium quantities shine new light for more calculations 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!

63 Outlook Welcome more ideas and discussions

64 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.