The nucleon-nucleon system in chiral effective theory

Size: px

Start display at page:

Download "The nucleon-nucleon system in chiral effective theory"

Norma Powell
6 years ago
Views:

1 The nucleon-nucleon system in chiral effective theory Daniel Phillips Ohio University Research supported by the US Department of Energy

2 Plan χet for nuclear forces: the proposal Leading order for S waves Higher orders and higher partial waves Elastic electron-deuteron scattering

3 χpt for nuclear forces

4 χpt for nuclear forces χpt pion interactions are weak at low energy. Weinberg (1990), apply χpt to V: (E H 0 ) ψ = V ψ V = V (0) + V (2) + V (3) +... Ordonez, Ray, van Kolck (1996); Epelbaum, Meissner, Gloeckle (1999); Entem, Machleidt (2001)

5 χpt for nuclear forces χpt pion interactions are weak at low energy. Weinberg (1990), apply χpt to V: (E H 0 ) ψ = V ψ V = V (0) + V (2) + V (3) +... Ordonez, Ray, van Kolck (1996); Epelbaum, Meissner, Gloeckle (1999); Entem, Machleidt (2001) V (0) = + ;

6 χpt for nuclear forces χpt pion interactions are weak at low energy. Weinberg (1990), apply χpt to V: (E H 0 ) ψ = V ψ V = V (0) + V (2) + V (3) +... Ordonez, Ray, van Kolck (1996); Epelbaum, Meissner, Gloeckle (1999); Entem, Machleidt (2001) V (0) = + ; Requires regularization and renormalization: cutoff Λ, fit C(Λ) to, e.g. deuteron binding energy. Chiral effective theory (χet). Kaplan, Savage, Wise; Beane, Bedaque, Savage, van Kolck; Pavon Valderrama, Ruiz Arriola; Nogga, Timmermans, van Kolck; Birse

7 χpt for nuclear forces χpt pion interactions are weak at low energy. Weinberg (1990), apply χpt to V: (E H 0 ) ψ = V ψ V = V (0) + V (2) + V (3) +... Ordonez, Ray, van Kolck (1996); Epelbaum, Meissner, Gloeckle (1999); Entem, Machleidt (2001) V (0) = + ; Requires regularization and renormalization: cutoff Λ, fit C(Λ) to, e.g. deuteron binding energy. Chiral effective theory (χet). Kaplan, Savage, Wise; Beane, Bedaque, Savage, van Kolck; Pavon Valderrama, Ruiz Arriola; Nogga, Timmermans, van Kolck; Birse Different Λ, different short-distance physics. Different predictions?

8 Results: S waves at leading order Yang, Elster, Phillips, PRC 77, (2007)!( 1 S 0 ) [deg] Subtraction method: LO CD-Bonn!( 3 S 1 ) [deg] " 1 [deg] 1.5 1!( 3 D 1 ) [deg] T lab [MeV] T lab (MeV)

9 Results: S waves at leading order Yang, Elster, Phillips, PRC 77, (2007)!( 1 S 0 ) [deg] Subtraction method: LO CD-Bonn!( 3 S 1 ) [deg] Converges to definite result as Λ Agreement with fitting method Beane, Bedaque, Savage, van Kolck; Pavon Valderrama, Ruiz Arriola 2-2 " 1 [deg] 1.5 1!( 3 D 1 ) [deg] T lab [MeV] T lab (MeV)

10 Results: S waves at leading order Yang, Elster, Phillips, PRC 77, (2007) "!( 1 1 [deg] S 0 ) [deg] Subtraction method: LO CD-Bonn!( 3 S 1 ) [deg]!( 3 D 1 ) [deg] Converges to definite result as Λ Agreement with fitting method Beane, Bedaque, Savage, van Kolck; Pavon Valderrama, Ruiz Arriola Subtractive renormalization makes that easier T lab [MeV] T lab (MeV)

11 Results: S waves at leading order Yang, Elster, Phillips, PRC 77, (2007)!( 1 S 0 ) [deg] " 1 [deg] Subtraction method: LO CD-Bonn T lab [MeV]!( 3 S 1 ) [deg]!( 3 D 1 ) [deg] T lab (MeV) Converges to definite result as Λ Agreement with fitting method Beane, Bedaque, Savage, van Kolck; Pavon Valderrama, Ruiz Arriola Subtractive renormalization makes that easier 2π exchange needed, especially in 1 S0

12 χet deuteron wave functions at leading order Pavon Valderrama, Nogga, Ruiz Arriola,DP, EPJA 36, 315 (2008) u(r) (fm -1/2 ) r-space to r=0 p-space:!=3 fm -1 p-space:!=6 fm -1 p-space:!=12 fm -1 p-space:!=20 fm -1 AV r (fm)

13 χet deuteron wave functions at leading order Pavon Valderrama, Nogga, Ruiz Arriola,DP, EPJA 36, 315 (2008) u(r) (fm -1/2 ) r-space to r=0 p-space:!=3 fm -1 p-space:!=6 fm -1 p-space:!=12 fm -1 p-space:!=20 fm -1 AV r (fm) Converges to definite result NLO: 2π corrections

14 χet deuteron wave functions at leading order Pavon Valderrama, Nogga, Ruiz Arriola,DP, EPJA 36, 315 (2008) u(r) (fm -1/2 ) r-space to r=0 p-space:!=3 fm -1 p-space:!=6 fm -1 p-space:!=12 fm -1 p-space:!=20 fm -1 AV r (fm) Converges to definite result NLO: 2π corrections r < about 1 fm χet invalid. Nodes!

15 χet deuteron wave functions at leading order Pavon Valderrama, Nogga, Ruiz Arriola,DP, EPJA 36, 315 (2008) u(r) (fm -1/2 ) r-space to r=0 p-space:!=3 fm -1 p-space:!=6 fm -1 p-space:!=12 fm -1 p-space:!=20 fm -1 AV r (fm) Converges to definite result NLO: 2π corrections r < about 1 fm χet invalid. Nodes! Good description of deuteron em form factors for q <0.6 GeV at leading order

16 Higher orders in V

17 Higher orders in V Two-pion exchange, additional contact terms at NLO (Ordonez, Ray, van Kolck; Kaiser, Brockmann, Weise; Epelbaum, Meissner, Gloeckle; Entem, Machleidt)

18 Higher orders in V Two-pion exchange, additional contact terms at NLO (Ordonez, Ray, van Kolck; Kaiser, Brockmann, Weise; Epelbaum, Meissner, Gloeckle; Entem, Machleidt) 3NF at NNLO, free parameters fit in A=3: BE, and Consistent 3NFs, 4NFs Courtesy E. Epelbaum

19 State of the Art: O(P 4 )

20 State of the Art: O(P 4 ) Epelbaum, Meissner, Gloeckle, Nucl.Phys.A747, (2005)

21 State of the Art: O(P 4 ) Epelbaum, Meissner, Gloeckle, Nucl.Phys.A747, (2005)

22 State of the Art: O(P 4 ) Epelbaum, Meissner, Gloeckle, Nucl.Phys.A747, (2005) But Limited Range of Cutoffs...

23 Triplet channel at NNLO Yang, Elster, Phillips, PRC 80, (2009) O(P 3 ) [NNLO] χet NN potential: calculated with DR

24 Triplet channel at NNLO Yang, Elster, Phillips, PRC 80, (2009) O(P 3 ) [NNLO] χet NN potential: calculated with DR Increasingly singular potentials as chiral order increases Momentum-dependent short-distance part has limited effect as Λ

25 Issues for other L

26 Issues for other L Eiras, Soto (2002); Nogga, Timmermans, van Kolck (2005)

27 Issues for other L Eiras, Soto (2002); Nogga, Timmermans, van Kolck (2005) Attractive singular potentials need renormalization Pavon Valderrama, Ruiz Arriola

28 Issues for other L Eiras, Soto (2002); Nogga, Timmermans, van Kolck (2005) Attractive singular potentials need renormalization Pavon Valderrama, Ruiz Arriola If Λ>600 MeV need additional contact terms already at LO, to renormalize L>0

29 Issues for other L Eiras, Soto (2002); Nogga, Timmermans, van Kolck (2005) Attractive singular potentials need renormalization Pavon Valderrama, Ruiz Arriola If Λ>600 MeV need additional contact terms already at LO, to renormalize L>0 Or should we consider Λ>1 GeV? Are the appropriate contact terms present at, e.g. NLO? Epelbaum & Meissner

30 Issues for other L Eiras, Soto (2002); Nogga, Timmermans, van Kolck (2005) Attractive singular potentials need renormalization Pavon Valderrama, Ruiz Arriola If Λ>600 MeV need additional contact terms already at LO, to renormalize L>0 Or should we consider Λ>1 GeV? Are the appropriate contact terms present at, e.g. NLO? Epelbaum & Meissner RG analysis indicates which contact terms are promoted Birse

31 Issues for other L Eiras, Soto (2002); Nogga, Timmermans, van Kolck (2005) Attractive singular potentials need renormalization Pavon Valderrama, Ruiz Arriola If Λ>600 MeV need additional contact terms already at LO, to renormalize L>0 Or should we consider Λ>1 GeV? Are the appropriate contact terms present at, e.g. NLO? Epelbaum & Meissner RG analysis indicates which contact terms are promoted Birse Ideas not practically implemented

32 Problems in P waves for large Λ Yang, Elster, Phillips, PRC 80, (2009)

33 Problems in P waves for large Λ Yang, Elster, Phillips, PRC 80, (2009) Limited to 0.6 GeV< Λ< 1 GeV

34 Successes in A=2-4

35 Successes in A=2-4 Epelbaum, Meissner, Gloeckle, NPA 747, 362 (2005) N 3 LO potential, χ 2 /dof good c.f. AV18. Entem, Machleidt (2003) χpt TPE in pp PSA gives ci s, m π =128(9) MeV Rentmeester et al. (1999) Tlab=50 MeV

36 Successes in A=2-4 NLO NNLO Exp. 3 H N 3 LO potential, χ 2 /dof good c.f. AV18. Entem, Machleidt (2003) χpt TPE in pp PSA gives ci s, m π =128(9) MeV Rentmeester et al. (1999) Reproduce A=3 and 4 binding energies Epelbaum, Nogga, et al.(2002) 4 He

37 Successes in A=2-4 E=3 MeV E=10 MeV E=65 MeV Courtesy E. Epelbaum N 3 LO potential, χ 2 /dof good c.f. AV18. Entem, Machleidt (2003) χpt TPE in pp PSA gives ci s, m π =128(9) MeV Rentmeester et al. (1999) Reproduce A=3 and 4 binding energies Epelbaum, Nogga, et al.(2002) nd scattering works well

38 Testing NN forces in elastic electron-deuteron scattering

39 Testing NN forces in elastic electron-deuteron scattering LO QED: electron couples to Jμ

40 Testing NN forces in elastic electron-deuteron scattering LO QED: electron couples to Jμ LO ChiPT: J 0 (r) = e δ (3) (r r p )

41 Testing NN forces in elastic electron-deuteron scattering LO QED: electron couples to Jμ LO ChiPT: J 0 (r) = e δ (3) (r r p ) Deuteron form factor: G C ( q ) = dr j 0 ( q r 2 ) [u 2 (r)+w 2 (r)] Change Q 2 =-q 2 change spatial resolution

42 Testing NN forces in elastic electron-deuteron scattering LO QED: electron couples to Jμ LO ChiPT: J 0 (r) = e δ (3) (r r p ) Deuteron form factor: G C ( q ) = dr j 0 ( q r 2 ) [u 2 (r)+w 2 (r)] Change Q 2 =-q 2 change spatial resolution Prediction of QED and NN force model

43 Predicting A(Q) A(Q) =G 2 C(Q)+ 8 9 η2 G 2 Q(Q)+ 2 3 ηg2 M (Q); η = Q2 4M 2 d JLab Experiment in Hall A 2-3% precision for 0.2< q < 0.8 GeV/c Goal: resolve discrepancy between Mainz and Saclay data Here: 0.2< q <0.5 GeV/c η=1.6%, so A GC We will compute GC to O(eP 4 ), estimate uncertainties Kaiser, Park, DP (2010)

44 Higher orders in J0

45 Higher orders in J0 Use O(P 3 ) [NNLO] χet NN potential, so need J0 to O(eP 3 )

46 Higher orders in J0 Use O(P 3 ) [NNLO] χet NN potential, so need J0 to O(eP 3 ) O(eP 2 ): 1/M 2 effects O(eP 3 ): 2B mechanism enters, but no free parameters DP and Cohen (1999); Park et al. (1999); Meissner and Walzl (2001); DP (2003, 2007)

47 Higher orders in J0 Use O(P 3 ) [NNLO] χet NN potential, so need J0 to O(eP 3 ) O(eP 2 ): 1/M 2 effects O(eP 3 ): 2B mechanism enters, but no free parameters DP and Cohen (1999); Park et al. (1999); Meissner and Walzl (2001); DP (2003, 2007) O(e) O(eP 3 ) O(eP 5 )

48 Higher orders in J0 Use O(P 3 ) [NNLO] χet NN potential, so need J0 to O(eP 3 ) O(eP 2 ): 1/M 2 effects O(eP 3 ): 2B mechanism enters, but no free parameters O(eP 4 ): Two-pion exchange pieces of J0, and corrections to one-pion exchange piece from LπN (3) O(e) O(eP 3 ) O(eP 5 )

49 Higher orders in J0 Use O(P 3 ) [NNLO] χet NN potential, so need J0 to O(eP 3 ) O(eP 2 ): 1/M 2 effects O(eP 3 ): 2B mechanism enters, but no free parameters O(eP 4 ): Two-pion exchange pieces of J0, and corrections to one-pion exchange piece from LπN (3) Vanishes! Kölling et al. (2009) Kaiser, Park, DP (2010) O(e) O(eP 3 ) O(eP 5 )

50 χet for GC to NNLO, O(eP 3 ) G C 10-2 NNLO: NLO: OPEP + R=1.5 fm CD-Bonn Nijm93 Good J0 convergence GC insensitive to r 1/Λ physics GM more sensitive to r 1/Λ; only NLO calculation exists q (MeV) DP, J. Phys. G 34, 365 (2007)

51 GC/GC fit

52 GC/GC fit More data: only some Abbott et al. data here Role of nucleon ffs; here Mergell et al.

53 GC/GC fit More data: only some Abbott et al. data here Role of nucleon ffs; here Mergell et al. <rpt 2 > 1/2 =1.975(1) at NNLO Hydrogen level shift: <rpt 2 > 1/2 =1.9753(10)

54 GC/GC fit More data: only some Abbott et al. data here Role of nucleon ffs; here Mergell et al. <rpt 2 > 1/2 =1.975(1) at NNLO Hydrogen level shift: <rpt 2 > 1/2 =1.9753(10) At most 0.6% shift in ratio at Q=0.5 GeV/c

55 Conclusion

56 Conclusion χet for nuclear forces has had impressive phenomenological success in describing NN data up to Tlab=200 MeV see also Pastore et al., PRC 80, (2009)

57 Conclusion χet for nuclear forces has had impressive phenomenological success in describing NN data up to Tlab=200 MeV see also Pastore et al., PRC 80, (2009) Also success for 3N and 4N systems, and spectra of light nuclei

58 Conclusion χet for nuclear forces has had impressive phenomenological success in describing NN data up to Tlab=200 MeV see also Pastore et al., PRC 80, (2009) Also success for 3N and 4N systems, and spectra of light nuclei But, theory as originally proposed not cutoff independent at Λ>1 GeV. Also issues with renormalization of m π -dependent effects. Restricted to using χet in a narrow cutoff range

59 Conclusion χet for nuclear forces has had impressive phenomenological success in describing NN data up to Tlab=200 MeV see also Pastore et al., PRC 80, (2009) Also success for 3N and 4N systems, and spectra of light nuclei But, theory as originally proposed not cutoff independent at Λ>1 GeV. Also issues with renormalization of m π -dependent effects. Restricted to using χet in a narrow cutoff range Successes for elastic electron-deuteron scattering DP, JPG 34, 365 (2007); Kaiser, Park, DP (2010)

60 Conclusion χet for nuclear forces has had impressive phenomenological success in describing NN data up to Tlab=200 MeV see also Pastore et al., PRC 80, (2009) Also success for 3N and 4N systems, and spectra of light nuclei But, theory as originally proposed not cutoff independent at Λ>1 GeV. Also issues with renormalization of m π -dependent effects. Restricted to using χet in a narrow cutoff range Successes for elastic electron-deuteron scattering DP, JPG 34, 365 (2007); Kaiser, Park, DP (2010) Magnetic moments of light nuclei, plus capture, e.g. nd tγ, n 3 He 4 Heγ. Hierarchy of mechanisms there not necessarily in accord with counting a la Weinberg. Pastore et al., PRC 80, (2009); Lazauskas, Song, Park, arxiv:

61 Electron-deuteron observables G C = 1 ( 1 J J J 0 1 ), 3 e G Q = 1 ( 0 2 e ηmd 2 J J 0 1 ) G M = 1 1 J + 0 ; η = Q2 2η e 4Md 2 THEORY

62 Electron-deuteron observables G C = 1 ( 1 J J J 0 1 ), 3 e G Q = 1 ( 0 2 e ηmd 2 J J 0 1 ) G M = 1 1 J + 0 ; η = Q2 2η e 4Md 2 THEORY EXPERIMENT dσ dω = ( dσ dω ) Mott [ A(Q 2 )+B(Q 2 ) tan 2 ( θe 2 )] ; T 20 (Q 2 ; θ e )

63 Electron-deuteron observables G C = 1 ( 1 J J J 0 1 ), 3 e G Q = 1 ( 0 2 e ηmd 2 J J 0 1 ) G M = 1 1 J + 0 ; η = Q2 2η e 4Md 2 THEORY A = G 2 C ηg2 M η2 M 4 d G 2 Q, B = 4 3 η(1 + η)g2 M, T 20 = A(Q 2 )+B(Q 2 ) tan 2 ( θ e2 ) η { 1 + 2(1 + η) tan 2 ( θe 2 [ 8 3 ηg C(Q 2 )G Q (Q 2 )+ 8 9 η2 G 2 Q(Q 2 ) )} ] G 2 M (Q 2 ). EXPERIMENT dσ dω = ( dσ dω ) Mott [ A(Q 2 )+B(Q 2 ) tan 2 ( θe 2 )] ; T 20 (Q 2 ; θ e )

64 GC/GQ at NNLO and beyond G C /G Q (fm -2 ) NLO: NNLO: N 3 LO:225 Nijm93 CD-Bonn OPEP + R=1.5 fm OPEP + R=2.5 fm q (MeV)

65 GC/GQ at NNLO and beyond G C /G Q (fm -2 ) NLO: NNLO: N 3 LO:225 Nijm93 CD-Bonn OPEP + R=1.5 fm OPEP + R=2.5 fm Adjust O(eP 5 ) contact term to reproduce Qd: predict ratio q (MeV)

66 GC/GQ at NNLO and beyond G C /G Q (fm -2 ) Natural Contact Term NLO: NNLO: N 3 LO:225 3 Nijm93 CD-Bonn OPEP + + R=1.5 fm fm OPEP + + R=2.5 fm fm Adjust O(eP 5 ) contact term to reproduce Qd: predict ratio q (MeV)

67 GC/GQ at NNLO and beyond G C /G Q (fm -2 ) Natural Contact Term NLO: NNLO: N 3 LO:225 3 Nijm93 CD-Bonn OPEP + + R=1.5 fm fm OPEP + + R=2.5 fm fm q (MeV) Adjust O(eP 5 ) contact term to reproduce Qd: predict ratio Ratio largely independent of short-distance physics for q<600 MeV GC/GQ to 3% at q= 0.39 GeV

68 BLAST data on t20 first two points give normalization PRELIMINARY Courtesy M. Garcon t 20 R = 3 t 20 2Qd Q 2 GC/GQ

69 Results for GC and GQ at LO 10 0 Pavon Valderrama, Ruiz Arriola, Nogga, DP, arxiv: G C r-space: r= p-space:!=3 fm p-space:!=20 fm -1 Data: Abbott et al., EPJA 7, 421(2000) G C G (s) E Nucleon form factors included via: = ψ e ψ + O(P 2 ) Including TPE in ψ> improves description

70 Successes in A=2

71 Successes in A=2 Example at Elab=50 MeV Epelbaum, Meissner, Gloeckle, Nucl.Phys.A747, (2005)

72 Successes in A=2 Example at Elab=50 MeV Entem/Machleidt: N 3 LO potential, χ 2 /dof comparable to AV18. Epelbaum, Meissner, Gloeckle, Nucl.Phys.A747, (2005)

73 Successes in A=2 Example at Elab=50 MeV Entem/Machleidt: N 3 LO potential, χ 2 /dof comparable to AV18. Nijmegen phase-shift analysis + NN data gives: f 2 πnn=0.0750(9), mπ+=139.6(1.3) MeV χpt TPE in pp PSA gives ci s, m π =128(9) MeV Epelbaum, Meissner, Gloeckle, Nucl.Phys.A747, (2005) Rentmeester et al., 1999

The NN system: why and how we iterate

The NN system: why and how we iterate Daniel Phillips Ohio University Research supported by the US department of energy Plan Why we iterate I: contact interactions Why we iterate II: pion exchange How