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Parity Violating analogue of GDH sum rule

Parity Violating analogue of GDH sum rule. Leszek Łukaszuk, Nucl.Phys.A 709 (2002) 289-298) Krzysztof Kurek & Leszek Łukaszuk, Phys.Rev.C 70(2004)065204. Frascati, 11 February, 2005. Motivation. The knowledge of p.v. couplings in nucleon-meson

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Parity Violating analogue of GDH sum rule

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  1. Parity Violating analogue of GDH sum rule Leszek Łukaszuk, Nucl.Phys.A 709 (2002) 289-298) Krzysztof Kurek & Leszek Łukaszuk, Phys.Rev.C 70(2004)065204 Frascati,11 February, 2005

  2. Motivation • The knowledge of p.v. couplings in nucleon-meson • (nucleon-nucleon) forces is important for • understanding the non-leptonic, weak hadronic • interactions (p.v. couplings are poorly known). • Polarized photon asymmetry in + photo-production near the threshold can be a good candidate to measure p.v. pion-nucleon couling h1. • Similar is expected for the low energy Compton scattering. • h1 has been measured in nuclear and atomic systems; the disagreement between 18F and 133Cs experiments is seen. • The rising interest in GDH sum rule and its Q2 generalizations has started with the new generation of precise spin experiments. • New experiments based on intense polarized beams of photons give also the opportunity to test a weak part of photon-hadron interactions (parity violating, p.v.)

  3. Asymptotic states in SM and the limitations of considerations concerning the Compton amplitudes Collision theory and SM: • Asymptotic states – stable particles (photons, electrons and neurinos, proton and stable atomic ions) • Existence of unstable particles – source of concern in Quantum Field Theory (Veltman, 1963, Beenakker et al..,2000) • Each stable particle should correspond to an irreducible Poincaré unitary representation – problem with charged particles, QED infrared radiation→ well established procedure exists in perturbative calculus only. (Bloch-Nordsic, Fadeev-Kulish, Frohlich, Buchholz et al.. 1991)

  4. Asymptotic states in SM and the limitations of considerations concerning the Compton amplitudes • Forward amplitudes – no radiation • Strong interactions: no asymptotic states of quarks and gluons in QCD (confinement). Physical states are composite hadrons. • R.Oehme (Int. J. Mod. Phys. A 10 (1995)): „The analytic properties of physical amplitudes are the same as those obtained on the basis of an effective theory involving only the composite, physical fields” The considerations concerning Compton amplitudes will be limited to the order  in p.c. part and to the order 2 in the p.v. part ( they are infrared safe and at low energies are GF order contribution; massive Z0 and W or H bosons) + any order in strong interactions

  5. Dispersion relations and low energy behaviour Let’s consider forward Compton amplitude: For Re() >0 we get the physical Compton amplitude; For Re() <0 the limiting amplitude can be obtained applying complex conjugation and exploiting invariance with respect to rotation :

  6. Dispersion relations and low energy behaviour Coherent amplitudes (related to cross section): crossing Normalization (Optics theorem): We shall not use P, C, T invariance

  7. Dispersion relations and low energy behaviour Analyticity, crossing, unitariry  dispersion relation for amplitude f

  8. Dispersion relations and low energy behaviour Low Energy Theorem (LET) for any spin of target: P, K A.Pais, Nuovo Cimento A53 (1968)433 I.B.Khriplovich et al.., Sov.Phys.JETP 82(1996) 616

  9. Sum rules for p.v. spin polarizabilities and superconvergence hypothesisP.v. analogue of GDH sum rule Subtraction point is taken at  =0 and - due to LET – we get the dispersion formula for fh(-) Unpolarized target Assuming superconvergence: fh(-) () → 0 with → ¯¯¯¯¯¯¯  Parity violating analogue of GDH sum rule

  10. GDH (p.c.) sum rule and p.v. analogue of GDH sum rule For ½ spin target the above formula is equivalent to: Nucl.Phys.B 11(1969)2777 Anomalous magnetic moment Electric dipole moment (2+ 2)

  11. The photon scattering off elementary lepton targets e → Z0e (solid line)  → We (dotted - multiplied by 0.1) e →  W (dashed - multiplied by 5) e → Z0e  → We e → W P.v. sum rule satisfied for every process separately,also separately for left- and right- handed electron target. First time calculations done (for W boson) by Altarelli, Cabibo, Maiami , Phys.lett.B 40 (1972) 415. Also discussed by S. Brodsky and I. Schmidt , Phys.Lett. B 351 (1995) 344. (for details see also: A. Abbasabadi,W.W.Repko hep-ph/0107166v1 (2001), D. Seckel, Phys.Rev.Lett.80 (1998) 900).

  12. Proton target

  13. GDH measurement and the saturation: experimental „point of view”

  14. Saturation hypothesis for p.v. sum rule Let’s consider sum rule in the form: And define the F quantity:

  15. Saturation hypothesis for p.v. sum rule • Requirement that F() does not exceed prescribed small value at  = sat determines saturation energy. • The usefulness of such definition of saturation is based on the assumption that there is no large contribution to the sum rule integral from photons with energy higher than sat . • For the GDH on proton – according to experimental data sat and F(sat ) can be estimated as follows: sat  0.5-0.6 GeV and F(sat )  0.1 (10%), respectively.

  16. The pion photoproduction models for γN → pwith weak interactions efects taken into account • HBχPT (J-W,Chen, X.Ji, Phys.Rev.Lett.86 (2001)4239; P.F.Bedaque, M.J.Savage,Phys.Rev.C 62 (2001)018501; J-W.Chen,T.D.Cohen,C.W.Kao, Phys.Rev.C 64 (2001)055206) • Effective lagrangian approach with one particle exchange domination and with vertices structure taken into account. (W-Y.P.Hwang, E.M.Henley, Nucl.Phys.A 356 (1981)365, S-P.Li, E.M.Henley, W-Y.P.Hwang, Ann.Phys. 143 (1982)372) Both approaches give similar results close to threshold. In our paper (KK, LŁ, Phys.Rev.C) the effective lagrangian approach has been used.

  17. Contribution to the p.v. 0 and +production amplitude according to Hwang-Henley pole model Additional contribution for charged pion: a) and b) – nucleon pole, c) - + pole a) , b) - nucleon pole ,c) , d) , e) , f) -  pole, g), h) – vector meson poles

  18. The effective Lagrangians characterizing the couplings among the hadrons (Hwang-Henley) i = 1,2,3 and: 0

  19. Parity violating couplings in Hwang-Henley model • ρNN– (hρ1, hρ2, hρ3) ; izoscalar, izovector, izotensor • ωNN – (hω0, hω1) ; izoscalar and izovector • NN – h1 • N - f , taken 1 (in units 10-7) • γN –μ*, („free” parameter: (-15,15), in units 10-7) • γρ - hE , („free” parameter: (-17,17), in units 10-7) 8 models have been considered (B. Desplanques, Phys.Rep. 297,(1998)1). The values of p.v. couplings (in models) are based on the caclulations of the quark- quark weak interactions with strong interactions corrections, symetry and exprimental data (hyperon’s decays) taken into account.

  20. Parity violating coupling constants The p.v. meson-nucleon coupling constants are calculated from the flavour-conserving part of weak interactions : p.v. Hamiltonian and strong interactions effects from QCD should be accounted for. (K label in table presented on next slide, more details in: B. Desplanques, Phys. Rep. 297 (1998)1. )

  21. Parity violating coupling constants K=1 - absence of strong int. corr.  Ann.Phys.124(80)449  Factorization approximation SU(6)W Nucl.Phys.A335(80)147 N.Kaiser,U.G.Meissner, Nucl.Phys.A 489(88)671, 499(89)699,510(90)759 based on chiral model -7

  22. The cross sections and asymmetriesaccording to Hwang-Henley pole model Cross sections and asymmetries (or polarized cross sections) given by sum of the products of formfactors and relevant couplings The unpolarized cross section for pion photoproduction - good agreement with data. Having couplings calculated for 8 considered models and the formfactors taken from Hwang-Henley pole model the differences of the polarized cross sections are calculated. The saturation hypothesis with saturation energy sat = 0.55 GeV is assumed and „free” parameters hE and * are selected to satisfy condition F (sat) < 0.1 .

  23. Results

  24. Results: „non-saturated” models • Models 2 and 3 do not satisfy the quick saturation hypothesis for any hE and * additional structure should be seen above 0.55 GeV to satisfy sum rule; • If saturation energy shifted to 1 GeV then 100 pb is expected for  in energy of photon between 0.55-1 GeV – quite large. • This might indicate that it is desirable to look for p.v. effects in this region • Remaining considered models satisfy hypothesis; additional measurements of asymmetries can help to distinguish between different models 

  25. The asymmetries for different „saturated” models. Model 4 Model 5 (A in 10-7 units, E in GeV)

  26. Results: „saturated” models • Combining the measurements of 0 and + asymmetries together would allow to select models or group of models. • Let’s define: A0sat , A+sat , A0th , A+th are 0 and + asymmetries for saturation and threshold energy region, respectively. Then: A+sat >0 selects models 1 and 8; in addition A0th > 0 (and/or A0sat < 0) → 1 A0th < 0 (and/or A0sat > 0) → 8

  27. Results: „saturated” models A+sat <-6*10-7 (large) selects 4 and 5; in addition A0th  -2*10-7 → 5 A0th  0 → 4 -6*10-7 < A+sat <0 selects 1,4,6,7,8; in addition A0th < 0(  -1*10-7) → 7 A0th  0→ 1,4,6,8 - then combinnig with A+th and A0sat: A+th>1 and A0th <0 select (4 and 6) and (1 and 8)

  28. Experimental feasibility • The intensity and polarization of the electron beam at JLab allow to produce an intense, circularly polarized beams of photons from the bremsstrahlung process. • Ch.Sinclair et al.. Letter of intent 00-002, JLab. • B. Wojtsekhowski, W.T.H. van Oers, (DGNP collaboration),PHY01-05, • JLab, AIP Conference proceedings SPIN 2000, 14 –th International Spin • Physiscs Symposium, Osaka, Japan, October 16-21, 2000; • published June 2001, ISBN 0-7354-3. • The 12 GeV upgrade of CEBAF, White Paper prepared for the NSAC • Long Range Planning Exercise, 2000, L.S. Cardman et al..,editors, • Kees de Jager, PHY02-51, JLab.

  29. Experimental feasibility Taking 60 A current at 12 GeV electron beam and 1mm Au plate target we calculate the photon bremsstrahlung spectrum as follows: For energy range from 0.137 GeV (threshold) to 0.55 GeV (saturation) it reads 1.9*109 events/sec.; 0.137 – 0.3 GeV → 7*108 events/sec 0.4 – 0.55 GeV → 2.7*108 events/sec Spectrum of photons  1/ - „bremsstrahlung” sum rule type. For 1cm long liquid hydrogen target the number of events /sec. is 108 -109 events/sec seems to be large but the same rate 109is expected in LHC and the relevant detection techniques are feasible (E.Longo, Nucl.Inst. and Meth.A 486 (2002)7)

  30. Experimental feasibility • To verify quick saturation hypothesis: sum rule ntegral • should be measured up to 0.55 GeV and: • if the results comes 40 -110 pb – the hypothesis is not satisfied - in this case one needs 1013 – 1014 events which correspond to 6*103 - 6* 104 sec. of beam time; • much smaller results would indicate the possibility of quick • saturation. • example: model 5: • low energy contribution (up to 0.3 GeV) is positive: 20-28 pb, • saturation region (0.4-0.55 GeV) is negative: (-10)–(-14) pb, • It demands 4*1013 – 6*1013 and 1.5*1012 – 4.5*1012 events, • respectively. Corresponding beam time: • 6*104 – 8.5*104 and 6*103 - 1.7*104 sec. To overcome statistics the large number of events is needed (signal higher than fluctuation of total production):

  31. Concluding remarks • The sum rule has been checked within lowest order of the electroweak theory for the photon-induced processes with elementary lepton targets.It would be interesting to check this sum rule in higher perturbative orders. • In analogy with observed feature of GDH sum rule on proton the quick saturation hypothesis has been formulated. • 8 models with different sets of p.v. couplings have been analyzed in the frame of effective lagrangian and pole model approach

  32. Concluding remarks • Models with the largest p.v.pion couplings h1 do not saturate below 0.55 GeV and the contribution from higher energies cross sections are needed • It is argued that the measurements of the 0 and + asymmetries at the threshold and close to saturation point allow to distinguish between „saturated” models (p.v. couplings) • The verification of our predictions seems to be experimentally feasible with the beam time of the order of 105 sec. in the near future experimental facilities (JLab)

  33. SU(6)W Bałachandram, Phys.Rev. 153 (1967) 1553 S.Pakwasa, S.P.Rosen, Phys.Rev. 147 (1966)1166 • SU(6)W – subgroup of SU(12), all transformations which leave untouched 0 and 3 • Decomposition: SU(3)XSU(2)W • SU(2)W – weak isospin • Generators: ik 5 (SU(2)W) • SU(6)W – symmetry related to fixed direction; useful in description of two-body decays Factorization: matrix element factorizes into two parts: Matrix element of current between vacuum and meson and Matrix element of another currents between nucleons

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