PHOTO-NUCLEON/NUCLEAR PROCESSES in CHPT/CHIRAL EFT

Transcription

1 1 PHOTO-NUCLEON/NUCLEAR PROCESSES in CHPT/CHIRAL EFT Ulf-G. Meißner, Univ. Bonn & FZ Jülich Supported by DFG, SFB/TR-16 and by EU, I3HP-N5 and by BMBF 06BN411 and by HGF VIQCD VH-VI-231

2 2 CONTENTS Introduction: Towards a unified theory of nucleons and nuclei Lesson I: A true classic pion photoproduction off the nucleon Lesson II: Neutron properties from the deuteron Lesson III: Doubly virtual Compton scattering off protons/neutrons Summary & outlook

3 3 Introduction

4 UNIFIED THEORY of NUCLEONS and NUCLEI 4 seek a unified framework to analyse the structure and dynamics of nucleons and nuclear systems e.g. important for the extraction of neutron properties only available framework: CHPT/chiral EFT Ex.: Interplay of the chiral expansion of nucleon & nuclear form factors in electron scattering off the deuteron Walzl, M., Phys. Lett. B 513 (2001) 37 LO NLO NNLO em nucleon structure

5 5 CHIRAL EFT for NUCLEONS & FEW-NUCLEON SYSTEMS Starting point: CHIRAL LAGRANGIAN Gasser, Leutwyler, Weinberg, van Kolck, Kaplan, Savage, Wise, Bernard, Kaiser, M., Epelbaum,... L QCD L EFF = L ππ + L πn + L NN +... Spontaneous chiral symmetry breaking of QCD pions are Goldstone bosons Systematic expansion in powers of Q/Λ χ & M π /Λ χ, with Λ χ 1 GeV pion and pion-nucleon sectors are perturbative in Q chiral perturbation theory Parameters in L ππ and L πn known from CHPT studies low-energy constants L NN collects short-distance contact terms, to be fitted NN interaction requires non-perturbative resummation chirally expand V NN, use in regularized LS equation [NB: at very low energies, pions are integrated out universal properties Hammer, Bedaque, Braaten, Platter, van Kolck,...]

6 6 Pion photoproduction off protons and neutrons

7 7 THRESHOLD PION PHOTOPRODUCTION T-matrix for γ(k) + p(p 1 ) π 0 (q) + p(p 2 ) in the threshold region m N 4π s T ε = iσ ε (E 0+ + ˆk ˆqP 1 ) + iσ ˆkε ˆq P 2 + iσ (ˆq ˆk) P 3 differential and total XS k q dσ dω cm = A + B cos θ + C cos 2 θ, k q σ tot = 4π ( A C) A = E P P 3 2, B = 2Re (E 0+ P 1 ), C = P P P 3 2, polarized photon asymmetry Σ(θ) = Γ sin θ ( P 3 2 P 2 2) multipoles real between the π 0 p and π + n threshold, otherwise complex [neglect tiny π 0 p phase]

8 8 LOW-ENERGY THEOREMS - S-WAVE Consider threshold neutal pion photoproduction off the nucleon: γn π 0 N Complete one loop (fourth order) chiral perturbation theory calculation BKM, Eur. Phys. J. C 70 (1996) 483 E i 0+ = eg πn 8πm N µ [ C i 1 + µ Ci 2 + µ2 C i 3 + O(µ3 ) ], i = p, n expansion in µ = M π /m N 1/7 triangle graph generates infrared singularities C i 2 BKM, Gasser, Phys. Lett. B 268 (1991) 291 first novel prediction of CHPT in photo-nucleon physics C i 3 contains the combination of LECs ai 1 + ai 2 early years ( ): a i 1 + ai 2 from fit to thr. XS data

9 S-WAVE LETs: A NEW LOOK 9 Bernard, Kubis, M., Eur. Phys. J. A 25 (2005) 419 Fubini-Furlan-Rosetti sum rule (soft pions) κ v,s = R 8m2 N dν eπg πn ν Fubini, Furlan, Rosetti, Nuovo Cim. 40 (1965) 1171 Im A(+,0) 1 (ν, t = 0) Finite pion mass corrections from CHPT p (ν, t) Pasquini, Drechsel, Tiator, Eur. Phys. J. A 23 (2005) 279 Analytic structure covariant calculation LECs from matching to dispersive representation below threshold and data in the threshold region alternative method to fix LECs consistency between sub- & threshold amps most precise description of E 0+ (γp π 0 p) study production off neutrons p (ν,t thr ) Re E 0+ [10-3 /M π ] MAID IR CHPT rel CHPT Schmidt et al ν [MeV] E γ [MeV]

10 LOW-ENERGY THEOREMS - S-WAVE continued 10 How about the neutron amplitude at threshold? apply isospin invariance and resonance saturation E π0 n 0+ 2 p Eπ0 0+ stunning prediction, counter-intuitive, cf dipole picture in text books need EFT for light nuclei to test this later chiral corrections to the Kroll-Ruderman theorem have also been worked out ] E ( ) 0+ = eg πn 8πm N [1 µ + µ 2 C 2 + µ 3 C 3 + O(µ 4 ) E 0+ (γp π + n) = (27.6 ± 0.6) 10 3 /M π E 0+ (γn π p) = (32.0 ± 0.6) 10 3 /M π precise predictions, more accurate tests desired but consistent with data and dispersion relations table BKM, Phys. Lett. B 383 (1996) 116

11 RESULTS for CHARGED PION PHOTOPRODUCTION 11 reaction CHPT [1] disp. rel. [2] experiment γp π + n 27.6 ± ± ± 0.5 [3] 28.8 ± 0.5 [4] 27.8 ± 0.6 [5] ± 0.27 [6] γn π p 32.0 ± ± ± 0.3 [5] 32.2 ± 1.2 [7] 31.5 ± 0.8 [8] [1] V. Bernard, N. Kaiser, UGM, Phys. Lett. B 383 (1996) 116 [2] O. Hanstein, D. Drechsel, L. Tiator, Nucl. Phys. A 632 (1998) 561 [3] J.P. Burg, Ann. Phys. (Paris) 10 (1965) 363 [4] M.J. Adamovitch et al., Sov. J. Nucl. Phys. 2 (1965) 95 [5] J.C. Bergstroem et al., Phys. Rev. C 55 (1997) 2016 [6] E. Korkmaz et al., Phys. Rev. Lett. 83 (1999) 3609 [7] E.L. Goldwasser, Proc. XII Int. Conf. on High-Energy Physics (Dubna, 1964) [8] M.A. Kovash et al. [E643 Coll.], pin Newsletter 12 (1997) 51

12 P-WAVE LOW-ENERGY THEOREMS 12 Even more stunning: LETs for the P-waves P 1,2 in γp π 0 p 1 q P π0 p i ] = eg πn 8πm N [1 + κ p + µ C p 1,i + µ2 C p 2,i + O(µ3 ), i = 1, 2 remember: P 1 = 3E 1+ + M 1+ M 1 & P 2 = 3E 1+ M 1+ + M 1 C p 1,i only depends on κ p and g πn C p 2,i contains the effect of the these effects turn out ot be small, see BKM, Eur. Phys. J. A 11 (2001) 209 Comparison to experiment ( γ + p π 0 + p): A. Schmidt et al.,, Phys. Rev. Lett. 87 (2001) P π0 p 1 /q = 9.1 ± 0.5 [9.5 ± 0.3] P π0 p 2 /q = 9.7 ± 0.5 [ 9.5 ± 0.3]

13 13 Photoproduction off the deuteron

14 CALCULATION of DEUTERON MATRIX ELEMENTS 14 Various calc s of photo/electroproduction off the deuteron Interplay of nucleon & nuclear dynamics (impulse approx. & MECs) Most done in Weinberg s hybrid approach: Weinberg, Phys. Lett. B 295 (1992) 114 γ π kernel K from chiral expansion w.f. Ψ from high-precision potential a few utilizing chiral EFT w.f. s First success: Neutron amplitude in γd π 0 d predicted E π0 n 0+ = 2.13 E d = ( 1.8 ± 0.2) Beane et al., Nucl. Phys. A 618 (1997) 381 Ψ K Ψ dominated by three-body terms (exchange curr s) CHPT uncertainty largely from choice of potentials agrees well with SAL data E d = ( 1.7 ± 0.2) Bergstrom et al., Phys. Rev. C 57 (1998) 3203

15 COHERENT NEUTRAL PION PROD. off the DEUTERON Bernard, Krebs, M., Eur. Phys. J. A 22 (2004) Complete one-loop calculation of γ d π 0 d, employs chiral EFT w.f.s data from MAMI-B at Q 2 = 0.1 GeV 2 Ewald et al., Phys. Lett. B 499 (2001) 238 Epelbaum, Glöckle, M.,, Eur. Phys. J. A 19 (2004) 401 two LECs from the n amplitude two methods to fix them (uncertainty) p amplitude fixed from MAMI and NIKHEF data for γ p π 0 p at Q 2 = 0.1 GeV 2 decent description of the (not very precise) data ε=0.364, W=0.5 MeV ε=0.364, W=1.5 MeV ε=0.364, W=2.5 MeV dσ/dω [nb/sr] fit 1 fit dσ/dω [nb/sr] dσ/dω [nb/sr] cos(θ) cos(θ) cos(θ)

16 PRECISION CALCULATION of γd π + nn 16 Lensky, Baru, Haidenbauer, Hanhart, Kudryatsev, M., Eur. Phys. J. A 26 (2005) 107 Small parameters: χ m = M π /m N, χ Q = k π /M π organized as: χ χ m χ 2 Q Leading order (LO) χ 0 : Kroll-Ruderman vertex (a1) (b1) (c1) (d1) NN NNπ Next-to-leading order (NLO) χ 1,2 : parameter-free s, p, d pion partial waves; S, P NN partial waves (a2) (b2) (c2) (d2) corrections to the KR vertex from CHPT χ, χ, χ χ, χ /2 Bernard, Kaiser, M., Phys. Lett. B 383 (1996) 116 Leading recoil (3-particle cut) χ 5/2 : parameter-free precise and convergent description Booth et al, Phys. Rev. C 20 (1979) 1217 accuracy 3% for E γ 5 MeV strong suppression of pionic rescattering more data! & use of EFT wave functions σ tot [µb] LO, NLO, χ 5/ E γ [MeV]

17 γd π + nn & the nn SCATTERING LENGTH 17 Lensky, Baru, Epelbaum, Haidenbauer, Hanhart, Kudryatsev, M., Eur. Phys. J. A 33 (2007) 339 Puzzle of the neutron-neutron scattering length π + 2 H n + n + γ a nn = 18.5 ± 0.5 fm Howell et al n + 2 H n + n + p a nn = 18.7 ± 0.6 fm Gonzales Trotter et al n + 2 H n + n + p a nn = 16.3 ± 0.4 fm Huhn et al large sensitivity to a nn at the FSI peak for properly chosen kinematics, a nn can be extracted with a very small uncertainty a nn 0.1 fm d 5 σ/dω pr dω Kπ dp r 2 [a.u.] fm -19 fm -18 fm p r [MeV] similar proposal to determine a nn from π d nnγ Gardestig, Phillips, Phys. Rev. C 73 (2006)

18 18 Lessons from doubly virtual Compton scattering (V 2 CS)

19 SPIN STRUCTURE OF THE NUCLEON 19 Consider doubly virtual Compton scattering off the nucleon γ (q, ε) + N(p, s) γ (q, ε ) + N(p, s ) γ* γ* in forward direction related to spin-dependent structure functions I 1 (Q 2 ) = 2m2 Q 2 I 1 (0) = Γ 1 (Q 2 ) = x0 0 g 1 (x, Q 2 )dx κ 2 /4 GDH sum rule Q2 2m 2 I 1(Q 2 ) Γ p n 1 (Q 2 ) Bjorken sum rule of DIS N N for more details see e.g. Filippone and Ji, Adv. Nucl. Phys. 26 (2002) 1 Drechsel, Kamalov and Tiator, Phys. Rev. D 63 (2001)

20 20 LOW-ENERGY ANALYSIS complete one-loop calculation free of parameters (only dependent on g A, m N, κ N ) 3a 3b 3c 3d 3e heavy-baryon calculations Ji, Kao, Osborne, Phys. Lett. B 472 (2000) 1 3f 3g 3h 3i Kao, Spitzenberg, Vanderhaeghen, Phys. Rev. D 67 (2003) calculations using IR Bernard, Hemmert, M., Phys. Lett. B 545 (2002) 105 Bernard, Hemmert, M., Phys. Rev. D 67 (2003) j 3k 3l 3m 3n resonances (esp. ) important phenomenological inclusion in BHM drop out in Γ p n 1 (Q 2 ) (isospin inv.) analysis with explicit using IR in progress Bernard, Dorati, Krebs, M., forthcoming 4a 4b 4c 4d 4e 4f 4g 4h 4i 4j 4k 4l 4m 4n 4o

21 RESULTS from JLAB 21 J.-P. Chen, arxiv: v1 [nucl-ex] emerging data at (very) low Q 2 sizeable difference in (p-n) for HB vs IR clearly visible in Γ p 1 and Γn 1 EFT calculation with explicit s called for Γ 1 p (no elastic) Γ 1 n (no elastic) Q 2 (GeV 2 ) SLAC E143 CLAS EG1a CLAS EG1b (preliminary) Soffer-Teryaev (2004) Burkert-Ioffe HERMES GDH slope CLAS EG1b preliminary JLab Hall A E CLAS EG1a SLAC E143 HERMES GDH slope Burkert-Ioffe Soffer- Teryaev (2004) Ji et al, Χpt Bernard et al, Χpt Bernard et al, Χpt Ji et al, Χpt Γ 1 d (no elastic) Γ 1 p-n Q 2 (GeV 2 ) CLAS EG1a CLAS EG1b SLAC E143 Soffer-Teryaev (2004) GDH slope Burkert-Ioffe HERMES EG1b JLab Hall A E94010/CLAS EG1a CLAS EG1a HERMES E143 E155 pqcd leading twist ΧpT Bernard et al Ji et al, Χpt Burkert -Ioffe Soffer- Teryaev (2004) GDH slope Q 2 (GeV 2 ) Q 2 (GeV 2 )

22 22 SUMMARY & OUTLOOK Towards a unified theory of nucleons and nuclei systematic and precise approach based on chiral L eff good progress in electromagnetic pion production off N and d threshold region: ideal testing ground (π, N, γ, A) more work on pion production off light nuclei needed Epelbaum, Hammer, Lenkewitz,... Compton scattering: real, virtual and doubly virtual many talks this workshop sensitive to the nucleon spin sector more important (esp. V 2 CS) more work on nucleons and light nuclei needed higher precision, larger A and more data

23 23 SPARES etc.

24 SCALES IN NUCLEAR PHYSICS 24 Natural scales Long-range one-pion-exchange interaction: λ π = 1/M π 1.5 fm But: nuclei exhibit UNNATURAL scales Large S-wave scattering lengths: a np ( 1 S 0 ) = 23.8 fm, a np ( 3 S 1 ) = 5.4 fm 1/M π NB: effective ranges are of natural size Shallow nuclear binding: γ = E D m N = 45 MeV M π (E D = 2.22 MeV) the corresponding EFT requires a non-perturbative resummation

25 CHIRAL EFT FOR FEW-NUCLEON SYSTEMS 25 Starting point: CHIRAL LAGRANGIAN Gasser, Leutwyler, Weinberg, van Kolck, Kaplan, Savage, Wise, Bernard, Kaiser, M.,... L QCD L EFF = L ππ + L πn + L NN +... Spontaneous chiral symmetry breaking of QCD pions are Goldstone bosons Systematic expansion in powers of Q/Λ χ & M π /Λ χ, with Λ χ 1 GeV pion and pion-nucleon sectors are perturbative in Q chiral perturbation theory Parameters in L ππ and L πn known from CHPT studies low-energy constants L NN collects short-distance contact terms, to be fitted NN interaction requires non-perturbative resummation chirally expand V NN, use in regularized LS equation [NB: at very low energies, pions are integrated out universal properties Hammer, Bedaque, Braaten, Platter, van Kolck,...]

26 CALCULATIONAL SCHEME S. Weinberg, Nucl. Phys. B 363 (1991) 3 26 No perturbative description for bound states V V NN cuts violate perturbative power counting Effective potential can be constructed perturbatively V = Solve non-perturbative Lippmann-Schwinger eq. (requires regularization) T = V + V T

27 HIERARCHY OF NUCLEAR FORCES 27 O((Q/Λ χ ) 0 ) O((Q/Λ χ ) 2 ) O((Q/Λ χ ) 3 ) O((Q/Λ χ ) 4 ) 2N 3N 4N

28