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Understanding U-Spin and the Radiative Decay of Strange Baryons in Physics

Explore theoretical predictions, EM transition strengths, and U-spin conservation in radiative decay of baryons. Learn about SU(6) symmetry, lattice calculations, and future research directions to enhance understanding.

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Understanding U-Spin and the Radiative Decay of Strange Baryons in Physics

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  1. U-spin and the Radiative decay of Strange Baryons K. Hicks and D.Keller EM Transition Form Factor Workshop October 13, 2008

  2. Physics Motivation • There is much theoretical interest in the radiative decays of baryons: • Predictions: CQM, Lattice, Chiral-soliton, HBQM, etc. • Radiative decays provide EM transition strength. • For example, the decay S*+ S+g provides a sensitive probe of E2/M1 transitions for Y* decay. • Heavy baryon SU(6) makes precise predictions* for Re(d) with less ambiguity than the CQM. *M. Butler, M. Savage, R. Springer, hep-ph/9302214. K. HIcks, Ohio U.

  3. Lattice Predictions Leinweber, Draper and Woloshyn, Phys. Rev. D 48 (1993) More accurate lattice predictions possible using modern computers. K. HIcks, Ohio U.

  4. S*+ and S*- radiative decays • The difference in magnitude between S*+ and S*- decays can be easily understood: • U-spin conservation (similar to I-spin) • The photon has zero U-spin • The reason that the S*- radiative decay is nearly zero is due to a cancellation in the SU(6) wave functions with a M1 transition operator. • The same principle might suppresses Q+ production from a proton target. Ya.I. Asimov and I. Stakovsky, Phys. Rev. C 70:035210 (2004). K. HIcks, Ohio U.

  5. U-spin symmetry breaking The M1 transition for S*- S- symmetric decay gives: If one could measure this decay, only symmetry-breaking terms remain. Lattice suggests the effect is only a few %. Estimates based on magnetic moments of the quarks gives or about a 1-2 % symmetry breaking effect. K. HIcks, Ohio U.

  6. I-spin representation K. HIcks, Ohio U.

  7. U-spin orientation U-spin forbidden g-decay K. HIcks, Ohio U.

  8. 10 vs 8 g U-spin: pentaquark production From A. Hosaka, LEPS2 Workshop t8 U=3/2 U = 0 p* n* p n U=1/2 S t3 S U=1 U=1 p* –> p is forbidden n* –> n is allowed K. HIcks, Ohio U.

  9. U-spin: Example 1 Let the amplitude for D radiative decay be: M(D- np-) = MD From U-spin conservation, C.-G. coefficients give: M(S*- Lp-) = MD/sqrt(2) Putting in the kinematic factors (p3cm/ MB* EB): Comparing with experiment: K. HIcks, Ohio U.

  10. U-spin: Example 2 Similarly, Putting in the kinematic factors for an M1 transition, (4/3)(1.22) = 1.62 Experiment gives (660 +/- 60) / (470 +/- 120) = 1.4 +/- 0.38 Note: denominator is from a CLAS publication (S. Taylor). K. HIcks, Ohio U.

  11. CLAS data S*0 Lg S. Taylor et al., Phys. Rev. C 71:054609 (2005) Missing mass squared Expanded vertical scale Measured ratio: (g decay)/(p0 decay) = 1.5% g decay p0 decay L(1405) K. HIcks, Ohio U.

  12. Measurement Program • We want to measure the radiative decay of the S*+, the S*0 and, if possible, the S*-. • Start with the S*0, since it has Gg ~ 470 keV. • Reactions: • (g11) gp  K+S*0  K+ (pp-) g • (g11) gp  K0S*+  (p+p-) (np+) g • (g10) gn  K+S*-  K+ (np-) g K. HIcks, Ohio U.

  13. Advantages of g11 and g10 • About 20 times the statistics of g1c (used for the Taylor et al. paper). • Improved calibrations will give better separation of g and p0 peaks. • The EC can be used to reduce the background due to p0 decay. • Analysis being done for PhD thesis (Keller). K. HIcks, Ohio U.

  14. Improved Calculations • The JLab Lattice group recently published the transition form factor for Roper resonance • S* transition form factor should be easier, since there is one strange quark. • Hallway discussions with this group indicates that they can do a similar analysis for the S*. • U-spin is useful to understand the general trend, but lattice calculations are necessary to learn more. K. HIcks, Ohio U.

  15. Possible Future Directions • Further tests of u-spin invariance could be done using Cascade decays. • Need >5 GeV beams to see these resonances • Statistics may be too small to see radiative decays using CLAS data, but perhaps this could be done with CLAS12. • Lattice calculations would be even more reliable for Cascade radiative transitions. K. HIcks, Ohio U.

  16. Summary • U-spin invariance gives predictions of ~5% accuracy for decay ratios, where data exists. • The physics of radiative decays of baryons is interesting, but the experiments are hard. • Direct comparison with lattice is possible. • Tests of heavy baryon SU(6) possible (e.g.S*+) • For S*-, SU(6) symmetry-breaking terms only. • Re-measure at higher statistics S*0 gL. • Initial studies suggest S*+ gS+ is possible. • Improved lattice calculations are needed. K. HIcks, Ohio U.

  17. Backup Slides K. HIcks, Ohio U.

  18. QM predictions for gN  D • Assume that the transition form factor is purely M1. • The naïve quark model couples the photon to the magnetic moment of one of the quarks. • The magnetic moments of the neutron and proton are well known: +2.79 and -1.91 mN. • Naively, one might guess that the cross section ratio for gp  p+n is bigger than for gn  p-p. K. HIcks, Ohio U.

  19. Cross sections: gp  p+n speak = 240 mb. K. HIcks, Ohio U.

  20. Cross sections: gn  p-p speak = 270 mb. K. HIcks, Ohio U.

  21. U-spin prediction for gN  D • Assuming isospin invariance is valid, the ratio (D+ p+n)/(D0  p-p) = 1. • Assuming u-spin invariance holds, the ratio (gp  D+)/(gn  D0) = 1. • The measured cross section ratio is (240)/(270) = 0.89. The ratio of amplitudes is the square root, 0.94. K. HIcks, Ohio U.

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