Lattice QCD and Proton Structure:

Transcription

1 Lattice QCD and Proton Structure: How can Lattice QCD complement Experiment? Workshop on Future Opportunities in QCD Washington D.C. December 15, 006

2 How can Lattice QCD Complement Experiment? 1. Quantitative calculation of hadron observables from first principles Direct comparison with experiment Credibility for predictions and guiding experiment. Insight into how QCD works Mechanisms Dependence on parameters 3. Example of complementarity: GPD s

3 Quantitative Calculations Current Calculations Fermion determinant - Full QCD Lattice spacing: Quark mass: a ~ 0.15 fm mπ ~ 350 MeV Large lattice volume L ~ 3.5 fm Cost (mπ)-7 - (mπ)-9 Current world sustained Teraflops for lattice US - DOE 8 Europe + UK 0-5 Japan

4 Observables we can calculate now Masses (discussed by David Richards) Matrix elements of twist operators Note - omit disconnected diagrams, so only isovector exact Form factors: em, transition Moments of structure functions Moments of GPD s - generalized form factors Spin structure, transverse structure pion scattering lengths 4

5 Moments of parton distributions Expansion of O(x) = λ/ λ λ dλ iλx ig λ/ dαn A(αn) ψ( n) e ψ ( n) " npe 4π Generates tower of twist- operators Oq{µ1 µ...µn } = ψ q γ {µ1 idµ... id µn } ψq Diagonal matrix element P Oq{µ1 µ...µn } P " dx xn 1 q(x) Off-diagonal matrix element P Oq{µ1 µ...µn } P " Ani (t), Bni (t), Cn0 (t) " n 1 dx x H(x, ξ, t) ξ i Ani (t) + ξ n Cn0 (t) " n 1 dx x E(x, ξ, t) ξ i Bni (t) ξ n Cn0 (t) [ n nγ5 : A ni (t), B ni (t)] 5

6 u d 1" q Nucleon axial charge ga."$."#. /0 "& :;4< =4>8?5@<=4> 9AB+CD'+EF "% "$ "# "# "$ # # "% "& ' ()*+, 6

7 Putting It All Together Chiral Extrapolation of Moments $U $D DU DD X U D X $U $D X DU DD X $U $D 7

8 F1 Isovector Form Factor Dirac isovector charge radius 0.6 p n sqrt[ r ch r ch] (fm) expt 498 mπ = MeV MeV mπ = MeV mπ = 775 mπ = MeV mπ = 775 MeV 0 0 r "u d (1 + 5gA ) log = a0 (4πfπ ) 0. mπ mπ + Λ mπ 0.4 (GeV) 0.6 " 8

9 Form factor ratio: F / F1 4 F (I=1) / F1 (I=1) mπ = 775 MeV mπ = 498 MeV mπ = 359 MeV Expt: κp - κn Q (GeV ) 9

10 Nucleon spin decomposition 5/ /.- 1/.56)/ "$ ", DS+9ê # "# " "# "$ ' #D "% "& 10

11 ' D Nucleon spin decomposition 565)6/)./ // //..--1/1/.. "$ ", "$ ΔΣu/ DS+9ê # "# "# Lqd " ΔΣd/ -"# "# "# "$ "$ # ## Lqu "% "% "& "& 11

12 Transverse size of light-cone wave function xnav = d r dx x xn 1 q(x, r ) d r dxxn 1 q(x, r ) q(x, r ) model (Burkardt hep-ph/007047) 1

13 Future calculations of present observables Precision calculation - few percent errors Chiral sea and valence fermions Smaller lattice spacing - contiuum limit Larger lattice volume - infinite volume limit Smaller pion mass - chiral regime Renormalization - higher loops and/or nonperturbative Nucleon scattering length Examples Domain wall quarks, 30 Tf-yrs a=.09 fm, mπ ~ 50 MeV, L= 4.5fm Staggered quarks, 37 Tf-yrs a=.06 fm, mπ ~ 140 MeV, L= 5fm 13

14 New observables and theoretical issues Disconnected diagrams Flavor singlet matrix elements Strangeness form factors Gluon distributions Mixing of gluon and flavor singlet operators Operator mixing of higher moments of structure functions and generalized form factors Higher twist operators Distribution amplitudes Neutron electric dipole moment - strong CP and theta angle Polarizabilities Changes between free and interacting nucleon Example: difference between moments of structure functions of free n and p and of deuteron 14

15 Insight into how QCD works Mechanisms Origin of confinement Paths that dominate action Role of instantons and zero modes Variational wave functions Diquark correlations - role of diquarks Dependence on topology Nf mq Gauge group C(r1,r) Dependence on parameters Nc HLL correlation function, 0.8 < cos theta <= 1.0 and R (-3.8 <= R <= 4.), as a function of r Plotting C(r1,r) = <rhou(r1) rhod(r)>/(<rho(r1)> <rho(r)>) r C(r1, r ) = ρ(r1 )ρ(r )" ρ(r1 )"ρ(r )" ρ(r1 )"ρ(r )" 15

16 Complementarity of experiment and lattice Once lattice technology is verified by agreement with measured observables, use as tool to calculate unmeasured observables. Example: GPD s Experiment - convolution Lattice - moments Combine for more information than either gives alone Strategy: phenomenological parameterizations 16

17 Comparison with Phenomenology 5 $ ><8) : # ; B61# B?1 5 $ <68) : # ; B61# B?1 6 1#?4 5 $ <68 ) : " ; 1#?34 1#? 1#1>4 1#14 1# #?4 5 $ 4<68 ) : " ; 1#?34 1#? 1#1>4 1#14 1#134 5 $ 4<68) : # ; 5 $ 7<=8 ) : " ; 5 $ 7<=8) : # ; B61#B?1 6 1#?4 5 $ ><8 ) : " ; 1#?34 1#? 1#1>4 1#14 1#134 B61#B?1 *)(C5CDE*F *)G:(@G H*I5 J%-K8LJ-$HI* *E@CIG IH$AMMG 1#?4 1#?34 1#? 1#1>4 1#14 1#134 % 61 O N % 61 O N $ $$P")*) %?1 O N &?1 O N % 61 O N $ # $" " 3 # O " + % $ 1+ N XI5WE*);$@I$WE*E5)@*CVE@CIDK EDGE@V$UF$.C)"(+$M)(;5EDD+ RETIU+$S*I(($QR-$3114 *)5E*TEU()$IY)*E(( E'*))5)D@$E@$5' & 4118)9 Diehl, Feldmann, Jakob, Kroll EPJC 005 # )9 + : " ;1#= 1 5 1#3 1#7+ 311# A)9 3 " "? # )9 + : # ;1#=?#3 15 1#3 1#7+ 311# A)9 3 "??#3 "#$%&'()*+$,-./

18 Resources Computational resources Sustained Petaflops in next 5 years Partnership between NP, HEP, ASCR, SciDAC, NNSA Theorists Innovative ideas Mastery of theoretical physics and computational science As in all nuclear theory, need theory initiatives to attract and mentor outstanding theorists 18