N and (1232) masses and the γn transition. Marc Vanderhaeghen College of William & Mary / Jefferson Lab

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1 N and (1232) masses and the γn transition Marc Vanderhaeghen College of William & Mary / Jefferson Lab Hadron Structure using lattice QCD, INT, April 4, 2006

2 Outline 1) N and masses : relativistic chiral EFT calculation chiral extrapolation of lattice data 2) γn transition form factors chiral EFT used in dual role : as a framework to predict e p -> e p π observables (extraction of γn form factors) and to perform chiral extrapolation of lattice data work done in coll. with V. Pascalutsa -> N and masses : PLB 635 (2006), in press -> γn transition : PRL 95 (2005) and PRD 73 (2006)

3 spin 3/2 field The Isospin-3/2 Spin-3/2 -isobar is described in EFT by an isoquartet Rarita-Schwinger field ψ µ i = ( µ ++, µ+, µ0, µ - ). The free Lagrangian is given by The couplings of these field are also required to be gauge symmetric, to ensure the decoupling of the spin-1/2 components of the Rarita-Schwinger field.

4 N and chiral Lagrangians πnn π πn part is such that # spin d.o.f. is constrained to physical number Couplings involving are consistent : respect spin-3/2 gauge symmetry Pascalutsa (1998) Chiral behavior of masses

5 N and masses : LEC (fit parameters) Chiral loops : depend on 2 light scales

6 2 (free) low-energy constants renormalizes M B (0) nucleon mass in chiral limit M N (0) = GeV c 1B quark mass contribution to nucleon mass ( πn sigma-term ) -4c 1N m π2 = GeV

7 N and masses : relativistic chiral loops renormalizes M B (0) c 1B 2 light scales : µ and δ

8 N and masses : relativistic chiral loops (contd.) in an expansion to third power in ( m π, = M M N ) m π < m π >

9 πn N and π chiral loops : leading non-analytic behavior LNA terms agree with : Banerjee, Milana (1995) Young, Leinweber, Thomas, Wright (2002) Bernard, Hemmert, Meissner (2003)

10 N mass : m π dependence Lattice : MILC (2001) πn : relativistic M N (0) = GeV, c 1N = GeV -1, c 2N = 0 πn : m π 3 term (HBChPT) πn + π : relativistic M N (0) = GeV, c 1N = GeV -1, c 2N = 3 GeV -3 πn + π : relativistic c 2N = 0

11 mass : m π dependence Lattice : MILC (2001) πn : relativistic M (0) = 1.20 GeV, c 1 = GeV -1, c 2 = 0 πn + π : relativistic M (0) = GeV, c 1 = GeV -1, c 2 = 2 GeV -3 πn + π : relativistic c 2 = 0 π : m π 3 term (HBChPT)

12 electromagnetic N -> (1232) transition in chiral effective field theory J P =3/2 + (P33), M ' 1232 MeV, Γ ' 115 MeV N! transition: π N! (99%), γ N! (<1%) non-zero values for E2 and C2 : measure of non-spherical distribution of charges spin 3/2 Sphere: Q 20 =0 Oblate Q 20 /R 2 < 0 Prolate: Q 20 /R 2 > 0 : Role of quark core (quark spin flip) versus pion cloud

13 Effective field theory calculation of the e p -> > e p π 0 process in (1232) region Power counting : in region, treat parameters δ = (M M N )/M N and m π on different footing ( m π ~ δ 2 ) in threshold region : momentum p ~ m π / in region : p ~ M -M N calculation to NLO in δ expansion (powers of δ) LO (a) (b) (c) Pascalutsa, Vdh (2005) ρ (d) (e) (f) vertex corrections : unitarity & gauge invariance exactly preserved to NLO

14 N and masses : m π dependence Lattice : MILC (2001)

15 γ * N vertex γ * 3 electromagnetic transitions : M1 -> G M * N E2 -> G E * C2 -> G C * q : momentum in rest frame vertex corrections : fully relativistic loop calculation : equivalent to a sideways dispersion relation imaginary part is model independent prediction in chiral EFT framework

16 Effective field theory calculation of the magnetic (M1) & electric (E2) N transition 2 free parameters! pole + Born pole + Born + vertex corr. pole MAID (2003) SAID (2003) G * M = 2.97 G * E = 0.07 (E2/M1 = -2.3 %)

17 e p -> > e p π 0 in (1232) region : observables W = GeV, Q 2 = GeV 2 EFT calculation error bands due to NNLO, estimated as data : MIT-BATES (2001, 2003, 2005)

18 Q 2 dependence of E2/M1 and C2/M1 ratios data points : MIT-Bates (Sparveris et al., 2005) MAMI : R EM (Beck et al., 2000) R SM (Pospischil et al., 2001; Elsner et al., 2005) EFT calculation error bands due to NNLO, estimated as : EFT calculation predicts the Q 2 dependence

19 5 m π dependence of G * M ( Jones-Scadron convention ) Q 2 = 0 Re G M (Q 2 ) m 2 π (GeV 2 ) data points : MAMI, MIT-Bates quenched lattice QCD results at m π = 0.37, 0.45, 0.51 GeV Q 2 = 0.1 GeV 2 m π dependence of M N and M included Q 2 = 0.1 GeV 2 m π dependence of M N and M NOT included Lattice : Nicosia MIT group (2005)

20 m π dependence of E2/M1 and C2/M1 ratios Q 2 = 0.1 GeV 2 quenched lattice QCD results : linear extrapolation in m q ~ m π 2 at m π = 0.37, 0.45, 0.51 GeV Nicosia MIT group Alexandrou et al., PRL 94 (2005) discrepancy with lattice explained by chiral loops (pion cloud)! EFT calculation Pascalutsa, Vdh PRL 95 (2005) data points : MAMI, MIT-Bates

21 New (preliminary) MAMI data Q 2 =0.127 (GeV/c) 2 Data: Bates & Mainz V. Pascalutsa and M. Vdh, PRL 95 (2005) Lattice Results: Alexandrou et al PRL 94 (2005)

22 Summary 1) N and masses : relativistic chiral EFT calculation improved convergence (for πn loops) special situation : interplay of 2 light scales 2) γn transition form factors chiral EFT (δ-expansion) plays a dual role : both extract low energy quantity from observables and provide chiral extrapolation to connect lattice QCD results to the real world 3) (1232) magnetic dipole moment (MDM) -> see previous talk chiral EFT framework for γ p -> γ + -> γ p π 0 process dedicated experiment performed in , results forthcoming