STATES. D. Mark Manley. February 1, Department of Physics Kent State University Kent, OH USA KL 0 P SCATTERING TO 2-BODY FINAL

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1 KL P SCATTERING Department of Physics Kent State University Kent, OH USA February 1, 216 πλ Final πσ Final KΞ Final 1 / 28

2 Outline πλ Final πσ Final KΞ Final πλ Final πσ Final KΞ Final 2 / 28

3 Outline πλ Final πσ Final KΞ Final πλ Final πσ Final KΞ Final 2 / 28

4 Outline πλ Final πσ Final KΞ Final πλ Final πσ Final KΞ Final 2 / 28

5 Outline πλ Final πσ Final KΞ Final πλ Final πσ Final KΞ Final 2 / 28

6 Outline πλ Final πσ Final KΞ Final πλ Final πσ Final KΞ Final 2 / 28

7 Outline πλ Final πσ Final KΞ Final πλ Final πσ Final KΞ Final 2 / 28

8 Outline πλ Final πσ Final KΞ Final πλ Final πσ Final KΞ Final 2 / 28

9 Outline πλ Final πσ Final KΞ Final πλ Final πσ Final KΞ Final 2 / 28

10 Main interest in creating high-quality secondary K L beam is to investigate hyperon spectroscopy. Here we review what can be learned by studying K L p scattering going to two-body final states. Mean lifetime of the K is ns (cτ = 3.7 m) whereas mean lifetime of the KL is ns (cτ = 15.3 m). Thus, it is much easier to perform measurements of KL p scattering at low beam energies than K p scattering due to higher beam flux. πλ Final πσ Final KΞ Final 3 / 28

11 Formalism Here, we summarize some of the physics issues involved with such processes. The differential cross section and polarization for K L p scattering are given by dσ dω = ƛ2 ( f 2 + g 2 ), P dσ dω = 2ƛ2 Im(fg ), πλ Final πσ Final KΞ Final where ƛ = /k, with k the magnitude of c.m. momentum for the incoming meson. Here f = f (W, θ) and g = g(w, θ) are the usual spin-nonflip and spin-flip amplitudes at c.m. energy W and meson c.m. scattering angle θ. 4 / 28

12 Partial-Wave Expansion In terms of partial waves, f and g can be expanded as f (W, θ) = [(l + 1)T l+ + lt l ]P l (cos θ), l= g(w, θ) = [T l+ T l ]P 1 l (cos θ). l=1 Here l is the initial orbital angular momentum, P l (cos θ) is a Legendre polynomial, and P 1 l (cos θ) = sin θ dp l(cos θ)/d(cos θ) is an associated Legendre function. The total angular momentum for T l+ is J = l + 1 2, while that for T l is J = l 1 2. πλ Final πσ Final KΞ Final 5 / 28

13 Isospin Amplitudes We may ignore small CP-violating terms and write KL = 1 (K K ), 2 KS = 1 (K + K ). 2 πλ Final πσ Final KΞ Final We have both I = and I = 1 amplitudes for KN and KN scattering, so that amplitudes T l± can be expanded in isospin amplitudes as T l± = C T l± + C 1T 1 l±, where Tl± I are partial-wave amplitudes with isospin I and total angular momentum J = l ± 1 2, with C I the appropriate isospin Clebsch-Gordon coefficients. 6 / 28

14 T(K p K p) = 1 2 T1 (KN KN) T (KN KN) T(K p K n) = 1 2 T1 (KN KN) 1 2 T (KN KN) T(K + p K + p) = T 1 (KN KN) πλ Final πσ Final KΞ Final T(K + n K + n) = 1 2 T1 (KN KN) T (KN KN) 7 / 28

15 (cont d) T(KL p K S p) = 1 ( T1 (KN KN) + 1 ) 2 T (KN KN) 1 2 T1 (KN KN) T(KL p K L p) = 1 ( T1 (KN KN) + 1 ) 2 T (KN KN) T1 (KN KN) ( T(KL p 1 1 K+ n) = 2 2 T1 (KN KN) 1 ) 2 T (KN KN) πλ Final πσ Final KΞ Final 1 2 T1 (KN KN) 8 / 28

16 Data for K L p K S p and K L p K+ n πλ Final πσ Final KΞ Final Figure: Distribution of measured data for K L p K S p and K L p K+ n. dσ/dω data are shown as blue open circles and polarization data are shown as red open circles. σ data are shown on the θ = line. 9 / 28

17 Discussion No dσ/dω data are available for K L p K L p below W 2948 MeV. A fair amount of data are available for the reaction, K + n K p, measured on a deuterium target. Next two slides show a sample of available data for KL p K Sp compared with predictions determined from our previous PWA of KN KN data, combined with KN KN amplitudes from SAID solution. The predictions at lower and higher energies tend to agree less well with the data. πλ Final πσ Final KΞ Final 1 / 28

18 dσ/dω Data for K L p K S p 1.4 W = 166 MeV KL p KS p 1.2 dσ/dω (mb/sr) cos Θ dσ/dω (mb/sr) 2.5 W = 172 MeV KL p KS p cos Θ πλ Final πσ Final KΞ Final Figure: Selected data for KL p K Sp at 166 MeV and 172 MeV. The curves are predictions using amplitudes from our previous PWA of KN KN combined with KN KN amplitudes from SAID solution. 11 / 28

19 dσ/dω Data for K L p K S p dσ/dω (mb/sr) W = 175 MeV KL p KS p cos Θ dσ/dω (mb/sr).8 W = 184 MeV KL p KS p cos Θ πλ Final πσ Final KΞ Final Figure: Selected data for KL p K Sp at 175 MeV and 184 MeV. The curves are predictions using amplitudes from our previous PWA of KN KN combined with KN KN amplitudes from SAID solution. 12 / 28

20 πλ Final T(K p π Λ) = 1 2 T 1 (KN πλ) πλ Final πσ Final KΞ Final T(K L p π+ Λ) = 1 2 T 1 (KN πλ) 13 / 28

21 Data for K L p π+ Λ πλ Final πσ Final KΞ Final Figure: Distribution of measured data for K L p π+ Λ. dσ/dω data are shown as blue open circles and polarization data are shown as red open circles. σ data are shown on the θ = line. 14 / 28

22 Discussion K p π Λ and K L p π+ Λ amplitudes imply that their observables measured at same energy should be identical except for small differences due to isospin-violating mass differences in the hadrons. No dσ/dω data for K p π Λ are available at c.m. energies W < 154 MeV, although data for K L p π+ Λ are available at such energies (next slide). At 154 MeV and higher, dσ/dω and polarization data for the two reactions are in fair agreement, as shown in the following slides. πλ Final πσ Final KΞ Final 15 / 28

23 Low-energy dσ/dω Data for K L p π+ Λ dσ/dω (mb/sr) 1.8 W = 148 MeV KL p π + Λ cos Θ dσ/dω (mb/sr) 1.4 W = 15 MeV KL p π + Λ cos Θ πλ Final πσ Final KΞ Final Figure: Data for K L p π+ Λ at 148 MeV and 15 MeV. No data for K p π Λ are available below 154 MeV. 16 / 28

24 dσ/dω Data for K p π Λ and K L p π+ Λ dσ/dω (mb/sr) W = 154 MeV - K p π Λ KL p π + Λ cos Θ dσ/dω (mb/sr) W = 162 MeV - K p π Λ KL p π + Λ cos Θ πλ Final πσ Final KΞ Final Figure: Comparison of selected dσ/dω data for K p π Λ (red) and K L p π+ Λ (blue) at 154 MeV and 162 MeV. The curves are from our previous PWA of K p π Λ data. 17 / 28

25 dσ/dω Data for K p π Λ and K L p π+ Λ dσ/dω (mb/sr) W = 176 MeV - K p π Λ KL p π + Λ cos Θ dσ/dω (mb/sr) W = 184 MeV - K p π Λ KL p π + Λ cos Θ πλ Final πσ Final KΞ Final Figure: Comparison of selected dσ/dω data for K p π Λ (red) and K L p π+ Λ (blue) at 176 MeV and 184 MeV. The curves are from our previous PWA of K p π Λ data. 18 / 28

26 Polarization Data for K p π Λ and K L p π+ Λ 2 W = 176 MeV - K p π + Λ 1.5 KL p π + Λ W = 188 MeV - K p π + Λ KL p π + Λ P P πλ Final πσ Final KΞ Final cos Θ cos Θ Figure: Comparison of selected polarization data for K p π Λ (red) and K L p π+ Λ (blue) at 176 MeV and 188 MeV. The curves are from our previous PWA of K p π Λ data. 19 / 28

27 πσ Final T(K p π Σ + ) = 1 2 T1 (KN πσ) 1 6 T (KN πσ) T(K p π + Σ ) = 1 2 T1 (KN πσ) 1 6 T (KN πσ) T(K p π Σ ) = 1 6 T (KN πσ) πλ Final πσ Final KΞ Final T(K L p π+ Σ ) = 1 2 T1 (KN πσ) T(K L p π Σ + ) = 1 2 T1 (KN πσ) 2 / 28

28 Data for K L p π Σ + and K L p π+ Σ πλ Final πσ Final KΞ Final Figure: Distribution of measured data for K L p π Σ + and K L p π+ Σ. dσ/dω data are shown as blue open circles and polarization data are shown as red open circles. σ data are shown on the θ = line. 21 / 28

29 Discussion Reactions KL p π+ Σ and KL p π Σ + are isospin selective (only I = 1 amplitudes are involved) whereas reactions K p π Σ + and K p π + Σ are not. New measurements with a KL beam would lead to better understanding of Σ states and help constrain amplitudes for K p πσ reactions No dσ/dω data are available for K L p π Σ + Next two slides compare dσ/dω data for K p and K L p reactions leading to πσ final states at W = 166 MeV (or P lab = 716 MeV/c) Quality of KL p data is comparable to that for K p data. It would be advantageous to combine KL p data in a new coupled-channel PWA with available K p data πλ Final πσ Final KΞ Final 22 / 28

30 dσ/dω Data for K p π Σ + and K p π + Σ 1.4 W = 166 MeV 1.4 W = 166 MeV dσ/dω (mb/sr) K + p Σ π - dσ/dω (mb/sr) K - p Σ π + πλ Final πσ Final KΞ Final cos Θ cos Θ Figure: Comparison of selected dσ/dω data for K p π Σ + and K p π + Σ at 166 MeV. The curves are from our previous PWA of K p πσ data. 23 / 28

31 dσ/dω Data for K p π Σ and K L p π+ Σ dσ/dω (mb/sr) W = 166 MeV - K p π Σ cos Θ dσ/dω (mb/sr) W = 166 MeV KL p π + Σ cos Θ πλ Final πσ Final KΞ Final Figure: Comparison of selected dσ/dω data for K p π Σ and K L p π+ Σ at 166 MeV. The curves are from our previous PWA of K p πσ data. 24 / 28

32 KΞ Final T(K p K Ξ ) = 1 2 T1 (KN KΞ) T (KN KΞ) T(K p K + Ξ ) = 1 2 T1 (KN KΞ) 1 2 T (KN KΞ) T(K L p K+ Ξ ) = 1 2 T 1 (KN KΞ) πλ Final πσ Final KΞ Final 25 / 28

33 Discussion Threshold for K p and KL p reactions leading to KΞ final states is fairly high (W thresh = 1816 MeV) There are no dσ/dω data available for K L p K+ Ξ and very few (none recent) for K p K Ξ or K p K + Ξ Measurements for these reactions would be very helpful, especially for comparing with predictions from dynamical coupled-channel (DCC) models K L p K+ Ξ is isospin-1 selective, whereas the reactions K p K Ξ and K p K + Ξ involve both I = and I = 1 amplitudes The Review of Particle Physics lists only two states with branching fractions (BF) to KΞ, namely, Λ(21) 7 2 (BF < 3%) and Σ(23) (BF < 2%) πλ Final πσ Final KΞ Final 26 / 28

34 New data for KL p scattering could significantly improve our knowledge of Λ and Σ Resonances Very few polarization data are available for any K L p reactions Several KL p reactions are isospin selective, so would help constrain PWAs of K p scattering Long lifetime of KL would allow measurements to be made at lower energies than can be done easily with K beams πλ Final πσ Final KΞ Final 27 / 28

35 New data for KL p scattering could significantly improve our knowledge of Λ and Σ Resonances Very few polarization data are available for any K L p reactions Several KL p reactions are isospin selective, so would help constrain PWAs of K p scattering Long lifetime of KL would allow measurements to be made at lower energies than can be done easily with K beams πλ Final πσ Final KΞ Final 27 / 28

36 New data for KL p scattering could significantly improve our knowledge of Λ and Σ Resonances Very few polarization data are available for any K L p reactions Several KL p reactions are isospin selective, so would help constrain PWAs of K p scattering Long lifetime of KL would allow measurements to be made at lower energies than can be done easily with K beams πλ Final πσ Final KΞ Final 27 / 28

37 New data for KL p scattering could significantly improve our knowledge of Λ and Σ Resonances Very few polarization data are available for any K L p reactions Several KL p reactions are isospin selective, so would help constrain PWAs of K p scattering Long lifetime of KL would allow measurements to be made at lower energies than can be done easily with K beams πλ Final πσ Final KΞ Final 27 / 28

38 Thanks to Igor Strakovsky and the other organizers for inviting me to talk at this workshop Thanks also to Igor for providing the data distribution plots shown in this talk Thanks to my Ph.D. student, Brian Hunt, who prepared all the figures of observables in this talk This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Medium Energy Nuclear Physics, under Award No. DE-SC14323 Thank YOU for your attention! πλ Final πσ Final KΞ Final 28 / 28

39 Thanks to Igor Strakovsky and the other organizers for inviting me to talk at this workshop Thanks also to Igor for providing the data distribution plots shown in this talk Thanks to my Ph.D. student, Brian Hunt, who prepared all the figures of observables in this talk This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Medium Energy Nuclear Physics, under Award No. DE-SC14323 Thank YOU for your attention! πλ Final πσ Final KΞ Final 28 / 28

40 Thanks to Igor Strakovsky and the other organizers for inviting me to talk at this workshop Thanks also to Igor for providing the data distribution plots shown in this talk Thanks to my Ph.D. student, Brian Hunt, who prepared all the figures of observables in this talk This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Medium Energy Nuclear Physics, under Award No. DE-SC14323 Thank YOU for your attention! πλ Final πσ Final KΞ Final 28 / 28

41 Thanks to Igor Strakovsky and the other organizers for inviting me to talk at this workshop Thanks also to Igor for providing the data distribution plots shown in this talk Thanks to my Ph.D. student, Brian Hunt, who prepared all the figures of observables in this talk This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Medium Energy Nuclear Physics, under Award No. DE-SC14323 Thank YOU for your attention! πλ Final πσ Final KΞ Final 28 / 28

42 Thanks to Igor Strakovsky and the other organizers for inviting me to talk at this workshop Thanks also to Igor for providing the data distribution plots shown in this talk Thanks to my Ph.D. student, Brian Hunt, who prepared all the figures of observables in this talk This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Medium Energy Nuclear Physics, under Award No. DE-SC14323 Thank YOU for your attention! πλ Final πσ Final KΞ Final 28 / 28