Isospin mixing in the 4 He ground state and the nucleon strange form factor

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Dedicated to Adelchi. Isospin mixing in the 4 He ground state and the nucleon strange form factor. XI Convegno di Cortona M.Viviani INFN - Pisa (Italy). In collaboration with A. Kievsky, L.E. Marcucci, S. Rosati , L. Girlanda R. Schiavilla (Jlab). 2. g. g. Z 0. - PowerPoint PPT Presentation

Text of Isospin mixing in the 4 He ground state and the nucleon strange form factor

  • Isospin mixing in the 4He ground state and the nucleon strange form factorXI Convegno di Cortona

    M.Viviani INFN - Pisa (Italy)In collaboration withA. Kievsky, L.E. Marcucci, S. Rosati, L. GirlandaR. Schiavilla (Jlab)Dedicated to Adelchi

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    Parity violating scattering e-4HeElectron-nucleus scattering

    The parity violating left-right asymmetry ALR

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    Strange quark contribution

    EM & neutral-weak currents

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    Nucleon Strange Form FactorsDirac-Pauli

    Sachs

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    The experimentsExperiments on nucleon:Jefferson Lab (USA): HAPPEX & G0 MIT-Bates (USA): SAMPLEMainz: A4Sensitive to an admixture of GE(s) and GM(s) HAPPEX 2005; G0 2005; SAMPLE 2004; A4 2004Experiments on 4He:HAPPEX-He @ JlabIn the case of a target (J,T)=(0+,0), at low Q2:Musolf et al, 1994

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    World Data at Q2 ~ 0.1 GeV2

    HAPPEX-He @ Jlab (2006-preliminary, K.Aniol QNP06) ALR = +6.43 0.23 (stat) 0.22 (syst) ppmExtrapolated from G0 Q2=[0.12,0.16] GeV22005 world data

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    4He LR asymmetry (1)Currents

    Three contributions

    Left-right asymmetry

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    4He LR asymmetry (2)Charge density operators

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    4He LR asymmetry (3)

    At low Q2: MEC and spin-orbit contribution in J=0 are small and then

    One needs to know:

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    NN interactionRealistic (phenomenological) potentialsArgonne V18 [Wiringa et al, 1995]CD Bonn [Machleidt, 2001]Nijmegen [Stoks et al, 1994]Doleshall [Doleshall et al, 2000]

    Effective field theory based on chiral symmetry[Weinberg 1991, van Kolck 1994]N3LO potential [review: Epelbaum, 2005] Julich [Epelbaum et al, 2005]N3LO [Emtem & Machleidt, 2003 ]

    Effective potentials Vlow-k [Bogner, Kuo & Schwenk, 2003, Coraggio et al, 2005]JISP [Shirokov et al, 2005]UCOM [Roth et al, 2004]

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    NN potentials in p-space very long tailCD BONNVN3LO(k,k)0 for k,k>5 fm-1Vlow-kVlow-k(k,k)=0 for k,k>2.1 fm-1

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    CSB NN interactionIsospin symmetry breakingnp singlet scattering length 23.740.02 fmpp singlet scattering length 17.30.4 fm (Coulomb corrected)nn singlet scattering length 18.50.4 fm

    They come ultimately from u-d different charge & mass

    In the modern Hamiltonians:CoulombNuclear effects (mass difference between +, - and 0,)Other e.m. interactions (magnetic moments,)n-p mass difference

    Important forStrange FF of 4HeReaction d+d 4He+ 0[Gardestig & Phillips, 2005]CSB from PT: [Epelbaum & Meissner, 2005][Miller et al, nucl-ex/0602021]

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    3N forceOld models Brazil & Tucson Melbourne [Friar et al, 1999] Urbana [Pudliner et al, 1997] New proposed modelsIllinois (3 exchanges) [Pieper et al, 2001] Chiral symmetry [Friar et al, 1999] [Epelbaum et al, 2002] N3LO: work in progress

    CSB: and exchange (effects unknown)[Kaiser, 2006]4NF from PT: [Epelbaum, 2006, Rozpedzik et al., 2006]

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    HH method (1)Hyperspherical coordinates

    HH functions

    Grand angular q.n.Fabre de la Ripelle, 1983

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    HH method (2)Expansion of the wave function

    Rainal-Revai coefficients

    Matrix elements of the interaction

    Fabre de la Ripelle, 1983

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    HH method (3)

    Fourier transform

    Usual choice: Lagrange polynomials

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    HH method (4)Bound state

    Rayleigh-Ritz variational principleBoundary conditions:

    Scattering states

    Kohn variational principleBoundary conditions:

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    Convergence

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    3H binding energyBinding energy (MeV)

    F: Nogga et al, PRC65, 054003 (2002); Deltuva et al, PRC68, 024005 (2003)NCSM: Navratil & Barret, PRC59, 014311 (2004)

    BE (MeV)PD (%)PT=3/2 (%)MethodHHFNCSMHHFHHFAV187.6187.6218.5118.510.002.002CD-Bonn7.9987.9977.997.027.02.005.005N3LO7.8547.8547.85(1)6.316.32.001.001

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    4He binding energy

    FY: Nogga et al, PRC 65, 054003 (2002)NCSM: Navratil & Barret, PRC 59, 014311 (2004)

    BE (MeV)PD (%)R (fm)MethodHHFYNCSMHHFYHHFYAV1824.2224.2513.7413.781.512 1.516CD-Bonn26.1326.1610.7410.771.454N3LO25.3825.3725.369.299.291.516

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    T>0 components (1)Previous estimates of PT=1:[Ramavataram et al, 1994] based on an approx 4He w.f.PT=10.0007% : RT=1 was estimated to be negligible

    Current estimates of PT=1 3 to 5 times larger

    Pot.PT=1 (%)PT=2 (%)AV180.00280.0052NIJ-II0.00160.0074CD Bonn0.00290.0108N3LO0.00350.0024

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    T>0 components (2)

    Origin of the T>0 components

    Hamilt.103xPT=1 (%)103xPT=2 (%)H000 +Coulomb1.50.1 +CSB3.04.9 +e.m. +m2.85.2

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    4He FF (1) Q2=0.0772 GeV2 q1.4 fm-1PRELIMINARY

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    4He FF (2)Preliminary HAPPEX estimate @ Q2=0.0772 GeV2 (q1.4fm-1):ALR = +6.43 0.23 (stat) 0.22 (syst) ppmRs-1.08 RT=1= 0.009 0.03K. Aniol, QNP06 Madrid June 2006PRELIMINARYIn agreement with recent lattice calculations GEs= 0.001 0.004[Leinweber et al, hep-lat/0601025]

    HamiltonianRT=1(q1.4fm-1)GEs-00.0040.02AV18UIX-0.00170.0030.02CDBonn+3N-0.00170.0030.02N3LO+3N-0.00230.0030.02

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    SummaryCurrent models predict a non-negligible contribution of the T>0 components to the LR asymmetry

    GEs is currently predicted (at low Q2) to be very small

    The next generation of the HAPPEX-He experiment could measure RT=1

    CSB in NN interaction is of maior interestd+d 4He+0 at IUCF

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    Wed like to invite everybody to theEUROPEAN FEW BODY CONFERENCE XX PISA (Italy) preregistration: http://www.pi.infn.it/efb20 10-15 September 2007

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    NN potentials in p-space

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    NN potentials in p-space CD BONN very long tail

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    NN potentials in p-space CD BONNVN3LO(k,k)0 for k,k>5 fm-1 very long tailCD BONN

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    NN potentials in p-space very long tailCD BONNVN3LO(k,k)0 for k,k>5 fm-1Vlow-kVlow-k(k,k)=0 for k,k>2.1 fm-1

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    Deuton wave functionIn r-space:3S1 wave0 2.5 5.0 7.5 10.0 12.5 15.0 r (fm)

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    Deuton wave functionIn p-space:3S1 wave

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    NN potentials in r-space

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    NN potentials in r-space: N3LO V(r,r)=

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    NN potentials in r-space: Vlow-k V(r,r)=

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    A=4 scatteringp-3He, p-3H, d-d,3N force effect?Fusion

    Theoretical methods still under developmentFaddeev-Yakubovsky [Lazauskas & Carbonell, 2004] [Fonseca, 1999, Deltuva & Fonseca, work in progress]Variational HH [MV et al, 2006]

    Resonating Group Model [Pfitzinger, Hofmann & Hale, 2001]

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    A=4 scattering with the N3LO potentialn-t scattering lenghts [fm]Experimental situation

    Theoretical calculations

    FY: Lazauskas & Carbonell, 2004PRELIMINARY

    Experimentas (singlet)at (triplet)Rauch et al, 1985 (I)4.980.123.130.11Hale et al, 19904.450.103.320.02

    HHFYPot.SingletTripletSingletTripletAV184.303.804.283.80AV18UIX4.053.584.043.60N3LO4.213.70

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    n-t scattering lengths (expt) =1.700.03 b[Phillips et al, 1980]Coherent scattering lengthac=3.590.02 fm[Rauch et al, 1985]ac=3.6070.017 fm[Hale et al, 1990]

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    n-t scattering lengths (expt) =1.700.03 b[Phillips et al, 1980]Coherent scattering lengthac=3.590.02 fm[Rauch et al, 1985]ac=3.6070.017 fm[Hale et al, 1990]

    AV18UIX

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    n-t scattering lengths Rauch et al, 1985 (I)Hale et al, 1990PRELIMINARY

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    n-t scattering lengths Rauch et al, 1985 (I)Hale et al, 1990PRELIMINARY

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    p-t scattering at low energies (1)

    Isospin state T=1/2,Tz=-1/2rp3HIsospin state T=1/2,Tz=+1/2The internal part contains T=0 and T=1 isospin channels

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    p-t scattering at low energies (2)Triplet phase shift [deg]Ecm=0.1 MeV

    FY: Lazauskas & Carbonell, 2004N3LOPRELIMINARYPRELIMINARY

    Pot.3S1HHFYAV14-3.56-3.536N3LO-3.40

    K [deg]2-3.546-3.5110-3.4414-3.4118-3.40