The KN KΞ reac*on in a chiral NLO model

The KN KΞ reac*on in a chiral NLO model Àngels Ramos A. Feijoo, V.K. Magas, A. Ramos, Phys. Rev. C92 (2015) 1, 015206

Outline Introduc*on State- of- the art of chiral unitary models for the meson- baryon interac*on in the S=- 1 sector The KN KΞ reac*on ( important for NLO terms) Reac*ons providing I=0 or I=1 filters for the KN KΞ reac*on Conclusions

Chiral unitary approach Describing the dynamics of hadrons at low energies from the QCD Lagrangian (quarks and gluons d.o.f.) is a highly non- perturba*ve problem One may address this problem through the modern perspec*ve of Chiral Perturba*on Theory (χpt): effec*ve theory with hadron degrees of freedom which respects the symmetries of QCD, in par*cular the (spontaneously broken) chiral symmetry. In ordinary χpt: à convergence restricted to low energy physics à not adequate close to bound- states (pole in the T- matrix) Unitarized non- perturba*ve schemes (UχPT ) allow to extend the predic*ve power of the chiral theories. With these non- perturba*ve methods several known resonances have been generated as poles in the scatering amplitude (quasi- bound states) and many hadron reac*on cross sec*ons have been nicely reproduced.

The case of the Λ(1405) (a nice example of the success of non- perturba*ve chiral approaches) Kbar- N scatering in the isospin I=0 channel is dominated by the presence of the Λ(1405), located only 27 MeV below the Kbar- N threshold Back in 1950, Dalitz and Tuan already proposed that the Kbar- N interac*on is atrac*ve enough to generate a quasi- bound state, the Λ(1405), below the Kbar- N threshold and embedded in the πσ con*nuum. R. H. Dalitz and S. F. Tuan, Phys. Rev. LeM. 2 (1959) 425. R. H. Dalitz and S. F. Tuan, Annals of Phys. 10 (1960) 307

In 1995 Kaiser, Siegel and Weise reformulated the problem in terms of the effec*ve chiral unitary theory in coupled channels. N. Kaiser, P. B. Siegel, and W. Weise, Nucl. Phys. A594 (1995) 325 For the next 10 years (up to 2006) much work was devoted to this subject with various degrees of sophis*ca*on: more channels, NLO Lagrangian, s- channel and u- channel Born terms, all of them obtaining in general similar features. E. Oset and A. Ramos, Nucl. Phys. A635 (1998) 99 J.A. Oller and U.G. Meissner, Phys. LeM. B500 (2001) 263 M.F.M. Lutz, E.E. Kolomeitsev, Nucl. Phys. A700 (2002) 193 C. Garcia- Recio et al., Phys. Rev. D (2003) 07009 B. Borasoy, R. Nissler, and W. Weise, Phys. Rev. LeM. 94, 213401 (2005); Eur. Phys. J. A25,79 (2005) J.A. Oller, J. Prades, and M. Verbeni, Phys. Rev. LeM. 95, 172502 (2005) B. Borasoy, U. G. Meissner and R. Nissler, Phys. Rev. C74, 055201 (2006)

Essence of the non- perturba^ve chiral approach 1. Meson- baryon effec^ve chiral Lagrangian: Lowest order (LO), O(q) LO meson- baryon poten*al in s- wave (contact term): One parameter: f

Next to leading order (NLO), O(q 2 ) deriva*ve terms: d 1,d 2,d 3,d 4 explicit chiral symmetry breaking terms: b D, b F, b 0 NLO contribu*on to the meson- baryon poten*al: D ij, L ij : matrices which depend on the 7 NLO parameters: b D, b F, b 0,d 1,d 2,d 3,d 4

2. Unitariza^on: N/D, Bethe- Salpeter = + T ij = V ij + V il G l T lj Coupled channels in S=- 1 meson- baryon sector: 3. Regulariza^on of loop func^on: Dimensional regulariza*on : subtrac*on constants (to be fited): a l natural size (µ~700 MeV) J.A. Oller and U.G. Meissner, Phys. LeM. B500 (2001) 263

Parameters - 1 decay constant: f - 7 parameters of the NLO Lagrangian: b D, b F, b 0,d 1,d 2,d 3,d 4-6 subtrac*on constants (isospin symmetry):

( ) Threshold observables γ = Γ ( K p π + Σ ) Γ ( K p π Σ +) ( + (( Γ ( K p π 0 Λ ) R n = Γ ( ) K p neutral states ) = ( = + +) = ) R c = Γ ( K p π + Σ, π Σ +) Γ ( K p all inelastic channels )

Cross sec*ons

The two- pole structure of the Λ(1405) T- matrix poles and couplings to physical states with I=0 T -matrix will be as T ij = g i g j s MR + iγ/2, z R 1390-66i 1426-16i (I=0) g i g i πσ 2.9 1.5 ΚΝ 2.1 2.7 ηλ 0.77 1.4 ΚΞ 0.61 0.35 Experimental evidence Magas, Oset, Ramos, PRL 95 (2005) 052301 π - pà K 0 πσ D.W.Thomas et al. Nucl. Phys. B56, 15 (1973) K - p à π 0 π 0 Σ 0 S. Prakhov et al., Phys.Rev. C70,034605 (2004) à The Λ(1405) resonance shows different proper*es (posi*on, width) in different reac*ons à Success of meson- baryon coupled- channel models!

Recently, the more precise SIDDHARTA measurement of the energy shim ΔE and width Γ of the 1s state in kaonic hydrogen, clarifying the inconsistency between earlier KEK and DEAR experiments, has injected a renovated interest in the field M. Bazzi et al. Phys. LeM. B704 (2011) 113 the parameters of the NLO meson- baryon Lagrangian can be beter constrained beter knowledge of the KbarN interac*on Y. Ikeda, T. Hyodo, W. Weise, Nucl.Phys. A881 (2012) 98 Z- H. Guo, J.A. Oller, Phys.Rev. C87 (2013) 3, 035202 M. Mai, U- G. Meissner, Nucl.Phys. A900 (2013) 51; Eur. Phys. J. A51 (2015) 3, 30 V.K. Magas, A. Feijoo, A. Ramos, Phys. Rev. C92 (2015) 1, 015206

K - p K Ξ channels V.K. Magas, A. Feijoo, A. Ramos, Phys. Rev. C92 (2015) 1, 015206 Differently than the other chiral unitary fits, we incorporate the data on the Κ - p Κ + Ξ -, Κ 0 Ξ 0 reac*ons These transi*ons are par*cularly interes*ng because the LO (Weinberg- Tomozawa) terms are zero Therefore, these channels are especially sensi*ve to NLO parameters!!

NLO coefficients

Results (K - p --> K - p) [mb] 150 120 90 60 30 WT (no ) NLO (no ) WT NLO (K - p --> K 0 n) [mb] 60 45 30 15 WT (no ) NLO (no ) WT NLO (K - p --> + ) [mb] (K - p --> 0 0 ) [mb] 0 50 100 150 200 250 300 P lab [MeV/c] 100 80 60 40 20 WT (no ) NLO (no ) WT NLO 0 50 100 150 200 250 300 P lab [MeV/c] 150 120 90 60 30 WT (no ) NLO (no ) WT NLO 0 50 100 150 200 250 300 P lab [MeV/c] (K - p --> + ) [mb] (K - p --> 0 ) [mb] 250 200 150 100 0 50 100 150 200 250 300 P lab [MeV/c] 50 WT (no ) NLO (no ) WT NLO 0 50 100 150 200 250 300 P lab [MeV/c] 50 40 30 20 10 WT (no ) NLO (no ) WT NLO 0 50 100 150 200 250 300 P lab [MeV/c] 2 models do not use KΞ data: WT(no Ξ) NLO (no Ξ) 2 models include KΞ data: WT NLO

Results 0.15 (K - p --> K 0 0 ) [mb] 0.12 0.09 0.06 0.03 WT (no ) NLO (no ) WT NLO 0 1.8 2 2.2 2.4 2.6 E CM [GeV] 2 models do not use KΞ data: WT(no Ξ) NLO (no Ξ) 2 models include KΞ data: WT NLO (K - p --> K + ) [mb] 0.2 0.1 WT (no ) NLO (no ) WT NLO ü The NLO terms are determinant for a reasonable descrip*on of data! ü There are s*ll some resonant structures not accounted for! 0 1.8 2 2.2 2.4 2.6 E CM [GeV] Explore the addi*onal effect of resonances!

From the PDG we see many 3* and 4* resonances in the region of interest! Resonances in KΞ channels K R K N Ξ In the resonant model of Sharov, Korotkikh, Lanskoy, EPJA 47 (2011) 109 for the KN KΞ reac*on several combina*ons were tested Σ(2030) and Σ(2250) were the more relevant! The Σ(2030) also plays a relevant role in the γ p K + K + Σ - reac*on K. Nakayama, Y. Oh, H. HabertzeMl, Phys. Rev. C74, 035205 (2006) K. Shing Man, Y. Oh, K. Nakayama,, Phys. Rev. C83, 055201 (2011)

We suplement the LO+NLO Lagrangian with two resonances: J P =7/2 + M R ~ 2030 MeV the fit determines their masses, widths and couplings J P =5/2 - M R ~ 2250 MeV 0.15 (K - p --> K 0 0 ) [mb] 0.12 0.09 0.06 0.03 NLO* NLO+RES 0 1.8 2 2.2 2.4 2.6 E CM [GeV] 0.25 (K - p --> K + ) [mb] 0.2 0.15 0.1 0.05 NLO* NLO+RES 0 1.8 2 2.2 2.4 2.6 E CM [GeV]

Differen*al cross sec*ons d /d (µb/sr) 30 20 10 NLO* NLO+RES s 1/2 =1.97 GeV 40 30 s 1/2 =2.07 GeV 20 10 40 30 s 1/2 =2.14 GeV 20 10 10 8 6 s 1/2 =2.28 GeV 4 2 0-1 -0.5 0 0.5 1 cos s 1/2 =2.02 GeV s 1/2 =2.11 GeV s 1/2 =2.15 GeV s 1/2 =2.47 GeV -0.5 0 0.5 1 cos d /d (µb/sr) 40 30 s 1/2 =1.95 GeV 20 10 80 60 s 1/2 =2.07 GeV 40 20 60 45 s 1/2 =2.14 GeV 30 15 50 40 s 1/2 =2.28 GeV 30 20 10 40 30 s 1/2 =2.42 GeV 20 10 08 6 s 1/2 =2.79 GeV 4 2 0-1 -0.5 0 0.5 1 cos 40 s 1/2 =1.97 GeV 30 20 10 80 s 1/2 =2.11 GeV 60 40 20 40 s 1/2 =2.24 GeV 30 20 10 40 s 1/2 =2.33 GeV 30 20 10 40 s 1/2 =2.48 GeV 30 20 10-0.5 0 0.5 0 1 cos

Parameters

NLO* Analysis of isospin contribu*ons NLO* NLO+RES ü Our unitarized calcula*ons produce stronger I=1 amplitudes than I=0 ones ü This tendency is enhanced when I=1 resonances are included (NLO+RES) Different theore*cal models predict different isospin decomposi*ons, see e.g.. C. Jackson, Y. Oh, H. HaberzeMl, and K. Nakayama, Phys. Rev. C 91, 065208 (2015)

An I=0 filter for KΞ amplitudes: the decay Λ b J/Ψ K Ξ A. Feijoo, V.K. Magas, A. Ramos, E. Oset, Phys.Rev. D92 (2015) 076015 + FSI: P c + states: R. Aaij et al. LHCb coll. PRL 115, 072001 (2015)

W. H. Liang and E. Oset, Phys. LeM. B 737, 70 (2014) L. Roca, M. Mai, E. Oset and U. G. Meissner, Eur. Phys. J. C75, 218 (2015) Meson- Baryon in I=0! +

K+Ξ - invariant mass distribu*on from the decay Λ b J/Ψ K + Ξ - (I=0 filter)! Different models fited to K- p K + Ξ -, K 0 Ξ 0 scatering data predict different I=0 distribu*ons The NLO terms of the Lagrangian are dominant

I=1 filter from the Secondary K 0 L beam at Jlab (S=- 1, I=1) _ It proceeds through the K 0 component of the K 0 L (K 0 L p --> K+ 0 ) [mb] 0.25 0.2 0.15 0.1 0.05 NLO+RES NLO* WT 0 1.8 2 2.2 2.4 2.6 E CM [GeV]

I=1 reac*on: K - n K 0 Ξ - J. P. Berge et al. Phys. Rev. 147, 945 (1966). S.A.B.R.E. Collabora^on, J. C. Scheuer et al. Nucl. Phys. B 33, 61 (1971). Data from the secondary K 0 L beam at Jlab will be very valuable to constrain the models of the S=- 1 meson- baryon interac*on!

Conclusions Chiral Perturba*on Theory with unitariza*on in coupled channels is a very powerful technique to describe low energy hadron dynamics. More precise data has become available in K - p scatering NLO calcula*ons become more meaningful The K - p K + Ξ -, K 0 Ξ 0 reac*ons are very sensi*ve to the NLO parameters Explicit inclusion of resonances improves the precision of the fited parameters _ An isospin decomposi*on of the KN KΞ reac*ons would help constrain beter the S=- 1 meson- baryon interac*on Data from the secondary K 0 L beam at Jlab will be very valuable!