U-spin and the Radiative decay of Strange Baryons

K. Hicks and D.Keller

EM Transition Form Factor Workshop

October 13, 2008

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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 *+ provides a sensitive probe of E2/M1 transitions for Y* decay.– Heavy baryon SU(6) makes precise predictions* for

Re() with less ambiguity than the CQM.*M. Butler, M. Savage, R. Springer, hep-ph/9302214.

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Lattice Predictions

Decay BR (Lattice) BR (Exp.) MeV

N 0.43 +/- 0.15 0.66 +/- 0.05

*+ + 0.100 +/- 0.026

*0 0 0.017 +/- 0.004 < 0.18

*- - 0.003 +/- 0.001

*0 0 0.129 +/- 0.029 < 0.38

More accurate lattice predictions possible using modern computers.

Leinweber, Draper and Woloshyn, Phys. Rev. D 48 (1993)

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*+ and *- radiative decays

• The difference in magnitude between *+ and *- decays can be easily understood:– U-spin conservation (similar to I-spin)– The photon has zero U-spin– The reason that the *- 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 + production from a proton target.

Ya.I. Asimov and I. Stakovsky, Phys. Rev. C 70:035210 (2004).

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U-spin symmetry breaking

The M1 transition for *- - 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.

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I-spin representation

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U-spin orientation

U-spin forbidden -decay

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t3

t8

U-spin: pentaquark production

pp*

nn*

U(p*) 3 / 2 ° U(p) 1 / 2 p* –> p is forbidden n* –> n is allowed

U=3/2

U(n*) = U(n) 1

U=1/2

U=1 U=1

U = 0

10 vs 8

From A. Hosaka, LEPS2 Workshop

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U-spin: Example 1Let the amplitude for radiative decay be:

M(- n-) = M

From U-spin conservation, C.-G. coefficients give:M(*- -) = M/sqrt(2)

Putting in the kinematic factors (p3cm/ MB* EB):

Comparing with experiment:

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U-spin: Example 2

Similarly,

Putting in the kinematic factors for an M1 transition,

Experiment gives (660 +/- 60) / (470 +/- 120) = 1.4 +/- 0.38

Note: denominator is from a CLAS publication (S. Taylor).

(4/3)(1.22) = 1.62

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CLAS data *0 S. Taylor et al., Phys. Rev. C 71:054609 (2005)

Missing mass squared Expanded vertical scale

decay 0 decay L(1405)Measured ratio:( decay)/(0 decay) = 1.5%

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Measurement Program

• We want to measure the radiative decay of the *+, the *0 and, if possible, the *-.– Start with the *0, since it has ~ 470 keV.

• Reactions:– (g11) p K+*0 K+ (p-) – (g11) p K0*+ (+-) (n+) – (g10) n K+*- K+ (n-)

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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 and 0 peaks.

• The EC can be used to reduce the background due to 0 decay.

• Analysis being done for PhD thesis (Keller).

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Improved Calculations• The JLab Lattice group recently published the

transition form factor for Roper resonance– * 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 *.

– U-spin is useful to understand the general trend, but lattice calculations are necessary to learn more.

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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.

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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. *+)– For *-, SU(6) symmetry-breaking terms only.

• Re-measure at higher statistics *0 .• Initial studies suggest *+ + is possible.• Improved lattice calculations are needed.

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Backup Slides

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QM predictions for N

• 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 N.

– Naively, one might guess that the cross section ratio for p +n is bigger than for n -p.

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Cross sections: p +n

peak = 240 b.

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Cross sections: n -p

peak = 270 b.

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U-spin prediction for N

• Assuming isospin invariance is valid, the ratio (+ +n)/(0 -p) = 1.

• Assuming u-spin invariance holds, the ratio (p +)/(n 0) = 1.

• The measured cross section ratio is (240)/(270) = 0.89. The ratio of amplitudes is the square root, 0.94.