Anthony W. Thomas UK Annual Theory Meeting Durham : Dec 19 th 2008 - PowerPoint PPT Presentation

New Insights into Hadron Structure Anthony W. Thomas UK Annual Theory Meeting Durham : Dec 19 th 2008 Thomas Jefferson National Accelerator Facility Operated by Jefferson Science Associates for the U.S. Department of Energy

Outline • Octet Masses and Sigma terms • Strangeness in the Nucleon and …. Dark Matter Searches • Solution of the Proton Spin Problem ( Nuclei in the Framework of QCD ) ( Significance for dense matter ) Thomas Jefferson National Accelerator Facility Page 2 Operated by Jefferson Science Associates for the U.S. Department of Energy

Open Questions for Hadron Spectroscopy • Does lattice QCD precisely reproduce the best experimental data - spectroscopy, form factors, DIS, GPDs? • Are some observables more likely to yield interesting constraints than others? • What physical insight can LQCD yield into how QCD works? • Are we able to take the lessons learnt in hadron structure and use them to understand nuclear structure better? Thomas Jefferson National Accelerator Facility Page 3 Operated by Jefferson Science Associates for the U.S. Department of Energy

Formal Chiral Expansion Formal expansion of Hadron mass: 2 + c LNA m  3 + c 4 m  4 + c NLNA m  4 ln m  + O(m π 5 ) M N = c 0 + c 2 m  Another branch cut Mass in from N !   ! N chiral limit - higher order in m  - hence “next -to- leading” First (hence “leading”) non-analytic (NLNA) 3/2 non-analytic term ~ m q No term linear in m  c NLNA MODEL INEPENDENT ( LNA) (in FULL QCD…… Source: N ! N  ! N there is in QQCD) c LNA MODEL INDEPENDENT Convergence? Thomas Jefferson National Accelerator Facility Page 4 Operated by Jefferson Science Associates for the U.S. Department of Energy

Convergence! 2 + γ m  Knowing χ PT , fit with: α + β m  3 (dashed curve) 2 | phys =0.02 m π Best fit with γ as in χ P T Problem: γ = - 0.76 c.f. model independent value -5.6 !! ( From: Leinweber et al ., Phys. Rev., D61 (2000) 074502 ) Thomas Jefferson National Accelerator Facility Page 5 Operated by Jefferson Science Associates for the U.S. Department of Energy

The ―big picture‖ ∆ ρ N Charge radius Spin and L g A Is it believable that smooth behavior for m π above 400 MeV is a result of a different accidental cancellation in every case?? 5 +…. 2 + c m π 3 + d m π 4 ln m π + m π a + b m π Thomas Jefferson National Accelerator Facility Page 6 Operated by Jefferson Science Associates for the U.S. Department of Energy

No: FRR explains this because… • It preserves model independent LNA and NLNA behavior and • For sound physical reasons, FRR suppresses meson loops once m  exceeds about 0.4 GeV • Yields convergent series expansion over mass region covered by lattice data • Form factor naturally yields GT discrepancy of right sign 5 term! and magnitude – and therefore correct m  - i.e. correct NNLNA behavior • N.B. Usual EFT yields this term only at two loops Thomas Jefferson National Accelerator Facility Page 7 Operated by Jefferson Science Associates for the U.S. Department of Energy

Some details of FRR …. 2 /(32  f  2 ) = c LNA I  ; c LNA = -3 g A (with dipole regulator; /// closed forms for other regulators) Thomas Jefferson National Accelerator Facility Page 8 Operated by Jefferson Science Associates for the U.S. Department of Energy

_ _ • Prediction of d – u > 0 from pion cloud 1983 (AWT, Phys. Lett. B126, 97) • Here analysis establishes model independent piece, for b>0.55fm • Inside is ―non - chiral‖ core • m π > 400 MeV : pion cannot be distinguished from ―core‖ • chiral behavior disappears Thomas Jefferson National Accelerator Facility Page 9 Operated by Jefferson Science Associates for the U.S. Department of Energy

χ‘al Extrapolation Under Control when Coefficients Known – e.g. for the nucleon Status in 2004 FRR give same answer to <<1% systematic error! Leinweber et al., PRL 92 (2004) 242002 Thomas Jefferson National Accelerator Facility Page 10 Operated by Jefferson Science Associates for the U.S. Department of Energy

Power Counting Regime Ensure coefficients c 0 , c 2 , c 4 all identical to 0.8 GeV fit Leinweber, Thomas & Young, hep-lat/0501028 Thomas Jefferson National Accelerator Facility Page 11 Operated by Jefferson Science Associates for the U.S. Department of Energy

Now to 2008 2 m π Thomas Jefferson National Accelerator Facility Page 12 Operated by Jefferson Science Associates for the U.S. Department of Energy

We fit using SU(3) expansions plus FRR loops ( π , η and K) Thomas Jefferson National Accelerator Facility Page 13 Operated by Jefferson Science Associates for the U.S. Department of Energy

LHPC Data (Walker-Loud et al., arXiv:0806.4549) • Stress: This involves just 4 SU(3) parameters plus Λ , fit to lowest 8 data points • There is a great deal of physics to be extracted from this fit Young & Thomas, in preparation Thomas Jefferson National Accelerator Facility Page 14 Operated by Jefferson Science Associates for the U.S. Department of Energy

PACS-CS Data (Aoki et al., arXiv:0807.1661[hep-lat]) Young & Thomas, in preparation Thomas Jefferson National Accelerator Facility Page 15 Operated by Jefferson Science Associates for the U.S. Department of Energy

Summary of Results of Combined Fits (of 2008 LHPC & PACS-CS data) N. B. Masses are absolute calculations based upon heavy quark potential, which involves no chiral physics Thomas Jefferson National Accelerator Facility Page 16 Operated by Jefferson Science Associates for the U.S. Department of Energy

Strangeness Has Been Widely Believed to Play a Major Role in N Structure – Does It?? • As much as 100 to 300 MeV of proton mass: y=0.2 § 0.2 ? 45 § 8 MeV (or 70?) Hence 110 § 110 MeV (increasing to 180 ± 180 for higher  N ) • Through proton spin crisis: As much as half the deuteron magnetic moment? As much as 10% of the spin of the proton? Thomas Jefferson National Accelerator Facility Page 17 Operated by Jefferson Science Associates for the U.S. Department of Energy

spin σ terms Neutralino (0.3 GeV / cc :WMAP ) Thomas Jefferson National Accelerator Facility Page 18 Operated by Jefferson Science Associates for the U.S. Department of Energy

McGovern & Birse • First to calculate two-loop, dim-reg  PT (hep:lat/0608002) • Major correction is m  dependence of g  NN i.e. origin of GT discrepancy : g  NN  g A /f  • Leads to large Order (m  5 ) term • Agree that convergence of formal chiral expansion is hopeless where current lattice data exists 2 – 5.6m  4 – (50-110)m  5 … 3 + 34 m  M N = 0.885 + 3.20m  c.f. FRR fit required to include physical nucleon mass: 2 – 5.6m  4 – (44 § 18)m  5 … 3 + 22m  M N = 0.897 + 2.83m  Leinweber et al., Lect. Notes in Phys. 663 (2005) 113 Thomas Jefferson National Accelerator Facility Page 19 Operated by Jefferson Science Associates for the U.S. Department of Energy

Sigma Commutator _ _ σ = < N | (m u + m d ) (u u + d d )/2 | N > ≡ m q ∂ M N / ∂ m q = σ val + σ sea δσ = 35 Λ – 23 + 9.6 – 3 + 0.8 +… = 18 MeV (Λ = 1GeV) — — — Λ Λ 2 Λ 3 σ Λ Thomas Jefferson National Accelerator Facility Page 20 Operated by Jefferson Science Associates for the U.S. Department of Energy

Naïve Expansion Traditionally Used to Extract σ Terms is Hopeless! 6 ) to get accurate light quark σ term Need O(m π While for strange condensate expansion is useless ! BUT through FRR have closed expression and can evaluate …. Thomas Jefferson National Accelerator Facility Page 21 Operated by Jefferson Science Associates for the U.S. Department of Energy

Summary of Results of Combined Fits (of 2008 LHPC & PACS-CS data) Of particular interest: σ commutator well determined : σ π N = 51 (6) (2) (2) MeV and strangeness sigma commutator small m s ∂M N / ∂ m s = 18 (10) (6) (3) MeV NOT several 100 MeV ! Profound Consequences for Dark Matter Searches Thomas Jefferson National Accelerator Facility Page 22 Operated by Jefferson Science Associates for the U.S. Department of Energy

Additional Comments • Strangeness content (condensate) is more than an order of magnitude smaller than naively assumed • Strangeness term usually dominates estimates of dark matter cross section - it should NOT! _ _ • In addition, tentatively seems that u u and d d condensates should be approximately equal (c.f. usual assumption of 1 : 1.49 : Chen 1989 ) Thomas Jefferson National Accelerator Facility Page 23 Operated by Jefferson Science Associates for the U.S. Department of Energy

Strangeness & Electromagnetic Form Factors Experiment: Need Parity Violation Theory: Disconnected diagram Thomas Jefferson National Accelerator Facility Page 24 Operated by Jefferson Science Associates for the U.S. Department of Energy

Magnetic Moments within QCD (Leinweber and Thomas, Phys Rev D62 (2000) p = 2/3 u p -1/3 d p + O N 2p +n = u p +3 O N CS n = -1/3 u p +2/3 d p + O N (and p + 2n = d p + 3 O N )  + = 2/3 u  – 1/3 s  + O   + -  - = u   - = -1/3 u  -1/3 s  + O  HENCE : O N = 1/3 [ 2p + n - ( u p / u  ) (  + -  - ) ] Just these ratios from Lattice QCD O N = 1/3 [ n + 2p – ( u n / u  ) (  0 -  - ) ] Thomas Jefferson National Accelerator Facility Page 25 Operated by Jefferson Science Associates for the U.S. Department of Energy