LOW-ENERGY QCD and STRANGENESS in the NUCLEON

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1 PAVI 09 Bar Harbor, Maine, June 009 LOW-ENERGY QCD and STRANGENESS in the NUCLEON Wolfram Weise Strategies in Low-Energy QCD: Lattice QCD and Chiral Effective Field Theory Scalar Sector: Nucleon Mass and Sigma Term Vector Currents: Role of Strangeness in e.m. Form Factors

2 enough observables to determine all polarized PDFs. These polar polarized PDFs. These polarized PDFs may be fully accessed via flavor tagging in accessed viaat flavor tagging in semi-inclusive deep inelastic scatt mi-inclusive deep inelastic scattering. Fig shows several global analyses a scale several global analyses at a scale of.5 GeV along with the da.5 GeV along with the data from semi-inclusive DIS. DIS. 0.6 uv g 0.5 *+,-*. 0.7 *+,-*. x f(x) Prelude: STRANGE SEA in Deep Inelastic Scattering '"$ '"# 0.4 u ' '"# g ' dv 0.3!"& 0.!"& d s s u '"$ c uv!"% !"$ c x Strange quark-antiquark pairs!"# from (perturbative) evolution Figure 16.4: Distributions of x times the QCD unpolarized parton distributions f (x) (where f = uv, dv,at! u, high d, s, c, Q g) using MRST001 parameterization [9,13](with and the small Bjorken-x '! '! ($ uncertainties for uv, dv, and g) at a scale µ = 10 GeV.!"%!"$ dv d () '! (# '!!"# (' *! ($ '! '! () Figure 16.4: Distributions of xsystem times the unpolarized parto Lab frame picture: highly excited interacting photon-nucleon June 16, 004 Q x= Mν 14:04 q γ q large (where f = uv, dv, u, d, s, c, b, g) and their associated uncertain MRST006 parameterization [13] at a scale µ = 0 GeV and Comprehensive sets of PDFs available as program-callable fun from several sources e.g., Refs.1[55,56]. As a result of a Les Ho [57] which facilitates the inclusion of coherence length! package (LHAPDF) exists Mx Carlo/Matrix Element programs in a very compact and efficient f NOT representative of sea quarks in the nucleon ground state DIS determinations of αs

3 1. LOW-Energy QCD: Concepts and Strategies Lattice QCD Chiral Effective Field Theory

4 LATTICE QCD n quarks ψ(x) = (u(x), d(x), s(x),...) T on nodes gauge fields (gluons) U µ (x y) = P exp on links for any operator : Ô ( y ) dx A µ (x ) x Ô = Dψ D ψ DA Ô e S Dψ D ψ DA e S DU Ô eff [U] e S g[u] detm[u] limits / extrapolations required: lattice spacing: lattice volume: quark masses: a 0 L m q m phys q

5 Hierarchy of QUARK MASSES and SCALES in QCD light quarks L QCD = ψ (iγ µ D µ m) ψ 1 4 G µνg µν heavy quarks separation of scales 0 u, d s 1 GeV c mass m d 3 7 MeV m u /m d m s MeV (µ GeV) LOW-ENERGY QCD: realized as EFFECTIVE FIELD THEORY with spontaneously broken CHIRAL SYMMETRY SU(N f ) L SU(N f ) R SU(N f ) V Expansion in powers of and low momentum m q m c 1.5 GeV m b 4. GeV m t 174 GeV Non-Relativistic QCD: HEAVY QUARK EFFECTIVE THEORY Expansion in powers of 1/m Q

6 Spontaneously Broken CHIRAL SYMMETRY ORDER PARAMETERS: DECAY CONSTANTS axial current f π = 9.4 MeV chiral limit: π µ K ν f K = ± 1.3 MeV Symmetry Breaking: explicit SB m π f π = m q ψψ + O(m q) spontaneous SB f = 86. MeV Gell-Mann, Oakes, Renner D D mass [GeV] K K mass [GeV] K K mesons a ρ ω π c d s d s d u d u d Change of MASS GAP SYMMETRY BREAKING SCALE Spontaneous CHIRAL SY K a Nambu- Goldstone 0 Bosons 0 0 VACUUM ρ π Goldstone baryons Boson Goldstone Boson + Axial 3 Dipole 1 + Axial Dipole+ 1 Dipole N 1 Dipole Goldstone 0 Goldstone Boson Boson condensates Gap GAP Gap 4π f π 4π f π MASS GAP Λ χ = 4π f 1 GeV 3

7 CHIRAL SU(3) EFFECTIVE FIELD THEORY Interacting systems of NAMBU-GOLDSTONE BOSONS (pions, kaons) coupled to BARYONS L eff = L mesons (Φ) + L B (Φ, Ψ B ) Leading DERIVATIVE couplings (involving ) µ Φ determined by spontaneously broken CHIRAL SYMMETRY Φ : pseudoscalar meson octet B : baryon octet + Φ Φ Φ B Φ B Low-Energy Expansion: CHIRAL PERTURBATION THEORY p energy / momentum / quark mass small parameter: 4π f π chiral s.b. scale of order 1 GeV

8 CHIRAL EFFECTIVE FIELD THEORY... works quantitatively for low-energy pion-pion interactions, also quite well for processes involving kaons and for pion-nucleon interactions Precision measurements of ππ scattering lengths a 0, a K ± π + π e ± ν NA48/ Ke4 ( ) δ = δ0 0 δ1 1 EPJ C54 (008) 411 [rad] PRELIMINARY NA48/ Ke4 (prel.) sππ [GeV] ()*#+, ' "$&% "$% "$!% "!$&%!$%!$!%! #$&% Precision measurement of K S γγ (new KLOE result)!?@ie! 0 I6./5J./01KLL./01K45 CDEF a 0 a Theory (ChPT) 0.0 ± Exp (NA48/) 0.18 ± ± ± (in units of m 1 π ) G. Colangelo et al., Nucl. Phys. B 603 (001) 15 #$% #$!% # M. Martini et al. (008) B(K S γγ) = (.6 ± 0.1 ± 0.06) 10 6 in perfect agreement with ChPT

9 . NUCLEON MASS and SIGMA TERMS Determination of PION-NUCLEON SIGMA TERM Contribution of STRANGE SEA to SCALAR qq DENSITY in the nucleon Headline News: Hadronic Uncertainties in the Elastic Scattering of Supersymmetric Dark Matter John Ellis, 1, Keith A. Olive,, and Christopher Savage, ignorance of the N qq N matrix elements linked to the π-nucleon σ term, already... impacting impacting the the interpretations of experimental of experimental searches for cold dark matter. We plead for an experimental campaign to determine better the π-nucleon σ term. Phys. Rev. D77 (008) 06506

10 MASS of the NUCLEON: LATTICE QCD + CHIRAL PERTURBATION THEORY M N = N β(g) g Tr(G µνg µν ) + i m i q i q i N = M 0 + M(m π ) M N = M 0 4 c 1 m π + " 3 3π f π p 3 4 e r 1(λ) + 3 c 18π f π " 3 g A 3πf π g A M 0 8 c 1 + c + 4 c 3 3 g A m 3 π 64π fπ M 0! ln m π λ # m 4 π... five years ago: nucleon mass [GeV] Masse des Nukleons [GeV] ChPT lattice QCD (CP-PACS, JLQCD, QCDSF) + p 4 3 g A 56πf π M 0 m5 π + O(m 6 π) physical point physical point Quarkmasse [MeV] quark mass [MeV] M. Procura, T. Hemmert, W.W.: Phys. Rev. D69(004)034505

11 MASS of the NUCLEON: LATTICE QCD + CHIRAL PERTURBATION THEORY 1.6 LHP N f = + 1 Full QCD simulations 1.4 MN GeV 1. Pion masses now down to ~ 300 MeV 1.0 A. Walker-Loud et al. Phys. Rev. D79 (009) JLQCD N f = m Π Π f ChPT at NNLO used for chiral extrapolation Finite volume corrections included M N [GeV] H. Ohki et al. arxiv: [hep-lat] m π [GeV ]

12 SIGMA TERMS Pion-nucleon sigma term: σ N = m N ūu + dd N = m M N m m π M N m π ( m = m ) u + m d Previous status: from chiral interpolation using older lattice data M. Procura et al. Phys. Rev. D73 (006) σ N = 49 ± 3 MeV Σ N MeV Strangeness content: y = N ss N N ūu + dd N Gasser, Leutwyler, Sainio (1991) m Π GeV σ N = N ūu + dd ss N 1 y σ emp N = 45 ± 8 MeV m π [GeV ] 1 m M Ξ + M Σ M N m s σ N... but with large uncertainties assuming flavour SU(3) mass relations B. Borasoy, U.-G. Meißner Ann. of Phys. 54 (1997) 19

13 SIGMA TERMS... today From most recent dynamical QCD simulations + chiral extrapolations (+1 flavors) LHP A. Walker-Loud et al., Phys. Rev. D79 (009) PACS-CS S. Aoki et al., arxiv: [hep-lat] HSC H.W. Lin et al., arxiv: [hep-lat] S. Dürr et al., Science 3 (008) 14 Combined analysis of baryon octet (and decuplet) σ N = 47 (9)(1)(3) MeV (statist.) (chiral extrap.) (lattice artifacts) consistent with earlier results, with recent JLQCD ( flavors) and with phenomenology Strange quark contribution σ Ns = m s N ss N = m s M N m s σ Ns = 31 (15)(4)() MeV mb GeV much smaller than previously expected! Ξ Σ Λ N R.D. Young, A.W. Thomas arxiv: [hep-lat] m Π GeV m π [GeV ] m Π GeV y (5 ± 4) 10

14 3. STRANGENESS VECTOR CURRENT N sγ µ s N Strangeness el. - mag. Form Factors and Magnetic Moments of the Nucleon u,d s s kaon cloud First systematic study of G s M(0) : D. Leinweber, A.W. Thomas; Phys. Rev. D6 (000)

15 ISOVECTOR ANOMALOUS MAGNETIC MOMENT Lattice QCD combined with Chiral Perturbation Theory κ V V Pion cloud effects in κ V = lim Q 0 F (Q ) Chiral extrapolations (with update - right - including information from Q dependence of magnetic form factor) Th. Hemmert, W.W.; Eur. Phys. J. A15 (00) 487 κ V = 3.71 lattice results: QCDSF M. Göckeler et al. Phys. Rev. D71 κ V V lattice results: C. Alexandrou et al. Phys. Rev. D74 (006) O(p 4 ) m! [GeV] 1 T. Gail, Th. Hemmert (007) O(p 3 ) m! [GeV]

16 G s M (Q ) STRANGENESS EM FORM FACTORS Lattice QCD + chiral extrapolations (+1 flavors) T. Loi et al. ( QCD Collaboration); arxiv: 0903:33 [hep-ph] χ κ ud = κ ud = κ ud = Q (GeV ) G s E (Q ) 0.06 G s M(Q )/µ N G s E(Q ) κ ud = κ ud = κ ud = Q (GeV ) G s M(Q = 0) = (5)(07) µ N Indirect results: sea quark effects from Lattice QCD + charge symmetry D.B. Leinweber et al. (Adelaide - JLAB) G s M (0) = ± µ N G s E(0.1 GeV ) = ± PRL 94 (005) 1001 PRL 97 (006) 0001 G s M (Q = 0.3 GeV ) = ± 0.01 µ N P. Wang et al. arxiv: [hep-ph]

17 THEORY status summary in comparison with EXPERIMENTS JLab Q = 0.1 GeV Leinweber et al Courtesy of R. McKeown, R. Young, J. Liu Global analysis Q = 0. GeV R.D. Young et al., PRL 99 (007) 1003 PVA4 (Mainz) G Ms = ± 0.11 ± 0.11 µ N ; G Es = ± ± S. Baunack et al., arxiv: [nucl-ex]

18 SUMMARY LATTICE QCD and CHIRAL EFFECTIVE FIELD THEORY in combination have reached the level of quantitatively accurate tools for LOW-ENERGY QCD full QCD with almost physical quark masses reliable chiral extrapolations now feasible STRANGENESS CONTENT of the NUCLEON GROUND STATE turns out to be unexpectedly SMALL (few %) not only in VECTOR (electromagnetic) currents but also in SCALAR densities (sigma terms) Special thanks to Philipp Hägler and Tony Thomas