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Resonances in chiral EFT and lattice QCD

Resonances in chiral EFT and lattice QCD. Vladimir Pascalutsa European Centre for Theoretical Studies (ECT*) , Trento, Italy. Supported by. Presented @ Erice School “Quarks and Hadrons in Nuclei” ( Erice, Italy, 17-24 Sep, 2007). Unstable particles (resonances). Muon: Neutron:

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Resonances in chiral EFT and lattice QCD

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  1. Resonances in chiral EFT and lattice QCD Vladimir Pascalutsa European Centre for Theoretical Studies (ECT*) , Trento, Italy Supported by Presented @ Erice School “Quarks and Hadrons in Nuclei” ( Erice, Italy, 17-24 Sep, 2007)

  2. Unstable particles (resonances) • Muon: • Neutron: • 0(1193): • (1116): • (1232): • many more… +p scattering cross-section Bubble chamber events Resonances in ChEFT & LQCD

  3. Low-energy QED (an example of EFT) Resonances in ChEFT & LQCD

  4. Towards low-energy QCD The massless quark Lagrangian, is invariant under “chiral rotations”: Chiral symmetry is an SU(nf )L SU(nf )R symmetry of mq=0 QCD For , SU(nf )isospin symmetry Resonances in ChEFT & LQCD

  5. L R u u d d Chiral Symmetry Breaking goodSU(2)L x SU(2)Rchiral symmetry, : : SU(3)L SU(3)R The symmetry NOT visible in hadron spectrum(no parity doublets), - spontaneously broken down to isospin symmetry, giving rise to (massless) Goldstone bosons: • Spontaneous chiral SB characterized by the • non-zero quark condensate: • Broken explicitly by the quark masses, Goldstone bosons acquire mass: (Gell-Mann – Oakes – Renner) Resonances in ChEFT & LQCD

  6. Chiral Perturbation Theory and Resonances Low-energy QCD ~ ChPT [ Weinberg (1979), Gasser & Leutwyler (1984), …] Lagrangian: S-matrix: However, near a resonance (or a bound state): Resonances in ChEFT & LQCD

  7. Chiral Lagrangians with  (1232)– first nucleon resonance, Include the  as an explicit d.o.f. , [Jenkins & Manohar (1991), …] described by a spin-3/2 (Rarita-Schwinger) isospin-3/2 (isoquartet) field Power counting: Resonances in ChEFT & LQCD

  8. Example: Nucleon mass Leading order pion-nucleon interaction: Power counting index: tells us that a graph is of O(pn) LO nucleon self-energy = prediction renormalization On-mass-shellrenormalization[Gegelia et al. (1999), (2003)], not MS-bar[Gasser et al. (1989)]. LECs Resonances in ChEFT & LQCD

  9. N and Δ masses: pion-mass dependence Lattice : MILC ChEFT: Covariant p3 V.P. & Vanderhaeghen, PLB 636 (2006) physical world Resonances in ChEFT & LQCD

  10. Low-energy QCD in the presence of (1232) Compton scattering on the nucleon Generic features: (i) below  production threshold ( < m), the  is a high-energy degree of freedom – can be integrated out (because / << 1 ) – ChPT with no ’s (ii) above, rapid change with energy, at  -- PT break-down How to obtain this behavior in ChEFT ? Resonances in ChEFT & LQCD

  11. Power countings [Jenkins & Manohar (1991); Hemmert et al. (1998) … (2006)] N and  propagators: [ V.P. & Phillips, PRC (2003) ] OR propagator » = + … = O(p3) = O(3 ) Resonances in ChEFT & LQCD

  12. Pion-nucleon scattering in the resonance region Renormalized NLO propagator Resonances in ChEFT & LQCD

  13. Electromagnetic excitation of the (1232) resonance VP, Vanderhaeghen & S.N. Yang, Phys Rept 427 (2007); “Shape of Hadrons” ed. Bernstein & Papanicolas, AIP 904(2007) * 3 e.m. transitions : N Δ M1, E2, C2 non-zero values of REM =E2/M1, RSM =C2/M1: measure of non-spherical shape G.A. Miller, arXiv:0708.2297;Kvinikhidze & Miller, PRC 76:025203,2007 Resonances in ChEFT & LQCD

  14. Pion Electroproduction in Chiral EFT [V.P. & Vanderhaeghen, PRL 95 (2005); PRD 73 (2006)] Calculation of e N -> e N πto NLO in theδ expansion: LO 4 free parameters – LECs corresponding to GM, GE, GC at Q2=0, and GM radius chiral loop corrections: unitarity & e.m. gauge-invariance exact to NLO Resonances in ChEFT & LQCD

  15. e N -> e N π in Δ(1232) region: observables data points : W = 1.232 GeV , Q2 = 0.127 GeV2 MIT-Bates (Sparveris et al., 2005) NLO ChEFT (4 LECs) theory error bands due to NNLO Resonances in ChEFT & LQCD

  16. Prediction of the Q2 dependence of E2/M1 and C2/M1 data points : MIT-Bates [Sparveris et al. (2005) ] MAMI : [Beck et al.(2000), Pospischil et al. (2001), Elsner et al. (2005), Stave et al (2006), Sparveris et al (2006) ] curves : NLO (LECs fixed from observables) “Bare” N->Delta (no chiral corr.’s) MAID SAID Resonances in ChEFT & LQCD

  17. Prediction of the mq dependence of E2/M1 and C2/M1 W=1.232 GeV, Q2 = 0.1 GeV2 Nicosia – MIT group [Alexandrou et al., PRL 94 (2005)] quenched lattice QCD results : mπ= 0.37, 0.45, 0.51 GeV linear extrapolation in mq ~ mπ2 ChEFT prediction data points : MAMI, MIT-Bates m =  Resonances in ChEFT & LQCD

  18. Radiative Pion Photoproduction (N -> Nπ ’ ) V.P. & Vanderhaeghen, PRL 94 (2005) Machavariani, Faessler & Buchmann, NPA (1999), Erratum-ibid (2001). Drechsel et al, PLB (2000) Drechsel & Vanderhaeghen, PRC (2001) Chiang, Vanderhaeghen, Yang & Drechsel, PRC (2005). Calculation to NLO in theδ expansion 2 free LECs –(s)andm(v) • First observations of the magnetic moment of a very unstable particle. • High-precision experiment at MAMI (Mainz) using Crystal Ball and TAPS detectors, see M. Kotulla’s talk. • Theory input needed Resonances in ChEFT & LQCD

  19. Circular beam asymmetry VP & Vanderhaeghen, in prep. Resonances in ChEFT & LQCD

  20. Chiral behavior of the  magnetic moment quenched lattice points : Leinweber (1992) Cloet,Leinweber,Thomas (2003) Lee et.al. (2004) – revised (2006) p m =  Real parts Curves - chiral EFT calculations V.P & Vanderhaeghen PRL (2005) Imag. parts Resonances in ChEFT & LQCD

  21. New quenched lattice results Leinweber et al. (to be publ.) Wrong trend [Young, Leinweber, Thomas (2006)] Quenching pathology – full QCD needed Resonances in ChEFT & LQCD

  22. Resonance properties from lattice QCD • Lattice QCD, an Euclidean field theory (real numbers) • A method to compute a resonant phase-shift on the lattice [ Luscher, NPB364 (1991) ] – study the volume dependence of the energy spectrum • NPLQCD:  scattering length; QCDSF: -meson • Rusetsky, Bernard, Lage, Meissner: -resonance volume dependence in ChPT, hep-lat/0702012 Resonances in ChEFT & LQCD

  23. Conclusion and challenges • -resonance in ChEFT 1. Effective fields, require resummations (strict low-energy expansion fails), which must make sense within the power-counting scheme; acquire width via the absorptive part of the self-energy… 2. Successful description of both the momentum dependence of scattering amplitudes (connection to experiment) and the pion-mass dependence of static quantities (connection to lattice) • Higher resonances in ChEFT ? • Resonances in LQCD impossible in quenched tough in full Resonances in ChEFT & LQCD

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