10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 1 Hyperon polarization in a quark-quark scattering model Eduard De La Cruz Burelo Homer A. Neal

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 2 Outline  Hyperon polarization remains a major open question even at energies of hundreds of GeV  Extraordinary behavior of hyperon polarization has no simple explanation  Polarization in pp  pp and pp  H + X : could both be the result of simple quark- quark scattering?  A proposed model based on quark-quark scattering.  The qualitative explanation of the hyperon polarization for a variety of processes

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 3 Hyperon polarization  An unresolved question:  What causes the large polarization in inclusive hyperon production in p-p collisions?  Vanishingly small polarizations are predicted in QCD.  No model is now able to explain all features of Hyperon polarization at the same time.

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 4 Particle Quark content*Polarization pN  H+X Λ0Λ0Λ0Λ0 (ud) 0 sNegative Σ0Σ0Σ0Σ0 (ud) 1 sPositive Σ+Σ+Σ+Σ+ (uu) 1 sPositive Σ-Σ-Σ-Σ- (dd) 1 sPositive Ξ-Ξ-Ξ-Ξ- (ss) 1 dNegative Ξ0Ξ0Ξ0Ξ0 (ss) 1 uNegative Ω-Ω-Ω-Ω- s s s~Zero Λ0Λ0Λ0Λ0 (u d) 0 s Zero Ξ+Ξ+Ξ+Ξ+ (s s) 1 dNegative Σ-Σ-Σ-Σ- (ūū) 1 s Positive ΛbΛbΛbΛb (ud) 0 b ? Hyperon polarization characteristics Particle Quark content*Polarization pN  H+X Λ0Λ0Λ0Λ0 (ud) 0 sNegative Σ0Σ0Σ0Σ0 (ud) 1 sPositive Σ+Σ+Σ+Σ+ (uu) 1 sPositive Σ-Σ-Σ-Σ- (dd) 1 sPositive Ξ-Ξ-Ξ-Ξ- (ss) 1 dNegative Ξ0Ξ0Ξ0Ξ0 (ss) 1 uNegative Ω-Ω-Ω-Ω- s s s~Zero Λ0Λ0Λ0Λ0 (u d) 0 s Zero Ξ+Ξ+Ξ+Ξ+ (s s) 1 dNegative Σ-Σ-Σ-Σ- (ūū) 1 s Positive * (Diquark) J state J=0 : Negative J = 1 + s quark: Positive 2 s-quarks: Negative Plans to measure it (LHC)

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 5 Λ 0 : Lowest mass hyperon … more intriguing  Very little dependence on the initial proton energy and in the target material.  Grows negative linearly with p T until a plateau is reached around 1 GeV/c.  For constant x F (=p L /p max ) value, the plateau extends from 1 GeV/c to the highest measured p T.

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 6 Intriguing questions: Why do the Λ 0 and Ξ polarizations look similar? Why is the Σ polarization positive? Why is the Ω polarization almost ~zero? Why is there a plateau in the Λ 0 polarization?

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 7 Features we would like to explain:  The shape and magnitude of the Λ 0 polarization  The different signs in the Λ 0 and Σ polarization  The similarity of the polarization for the Λ 0 and Ξ  The small value of the Ω polarization

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 8 q-q scattering: relating pp  pp to pp  Λ + X process  Is there any connection between the observed polarization in these two processes? –They could come from the same source: quark-quark scattering. u d u u d s Λ0Λ0 proton u d u u d u u d u u d s u d u u d u u Λ0Λ0

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 9 pp  pp in a quark-quark scattering model   Neal et al. proposed a q-q scattering model to explain the polarization in elastic p-p scattering:   First region is due to q-q scattering   Second region is due to 2q-2q or q-2q   Subsequent data is consistent with 3q-3q scattering*.  Can we apply the same idea to pp  Λ + X process? H.A. Neal et al. Phys. Lett. B 51 (1974) 79 *) H.A. Neal et al. Phys. Lett. B 439 (1998) 407

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 10 pp  Λ + X in a quark-quark scattering model  From a preexisting pair in the incoming proton, the s quark scatters, get highly polarized, and end up in the hyperon.  Hyperon polarization: P H =P q (x,p T ). P q (x F,p T ) : quark polarization effect due to a q-q scattering process.

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 11 Λ 0 polarization from polarization in pp  pp (1)  Model: P H =P q (x,p T ) –In a multiple quark scattering* P –In a multiple quark scattering* P ~ m q P q (p T ) *) J. Szwed, Phys. Lett. B 105 (1981) 403. Assuming m s ~2m u

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 12 Λ 0 polarization from polarization in pp  pp (2)  What p T (Λ 0 ) vs. p T (p) should we compare? – –For a elastic p-p scattering in a q-q region (Neal et al.): – –For pp  Λ + X in q-q region:  We should compare at: Assuming s-quark account for half of the Λ 0 mass.

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 13 Comparison of proton and Λ 0 polarization Proton polarization multiplied by 2 Proton p T multiplied by 2/3 If we let proton data to tell us what values prefer to match Λ 0 data, selected values are around to 2 and 2/3.

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 14 What about the plateau?   The plateau in the Λ 0 polarization can be understood as the saturation of the s quark polarization (P=100%). Polarization

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 15 Explaining the other features  Why the similar polarization for the Λ 0 and Ξ? If the polarization of both hyperons is due to one s quark becoming highly polarized from the scattering process, then we expect the polarization of both hyperons to be similar.

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 16 Why the different sign in the Λ 0 and Σ polarization? u d s u d s  Beam quarks does not contributed to the Λ 0 polarization  s quark is responsible for the large polarization of the Λ 0.  s quark polarization is negative.  s quark polarization is negative which force the polarization of the u and d quarks to be positive, so overall polarization is positive.  If we assume the s quark being responsible of the polarization, it can be showed that the sign of the Σ polarization is opposite to that of the Λ polarization.

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 17 Why Ω polarization is ~0?  One of 3 s quarks get polarized in the scattering, setting a maximum of 33% to the polarization of the Ω.  Should be similar to the Λ 0 polarization in the one quark scattering region. Λ 0 polarization compared to the Ω polarization. Statistics too low to make strong conclusions.

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 18 Future tests/Implications  Λ b polarization is planned to be measured in LHC (ATLAS & LHCb)  Polarization could be huge if the q-q contribution to production is important and the Szwed mass scaling holds.  Simple relation should exist between Λ and Λ b polarization is our q-q idea is correct.

10/6/2006 E. De La Cruz Burelo, SPIN 2006, Kyoto Japan 19 Conclusions:  A model based in a simple q-q scattering process is proposed:  Polarization due the scattering process P q (p T ) is the same for all quark species.  s quark scatters from the incoming proton is the responsible for the large hyperon polarization.  Λ and proton polarization seems to have a common source.  The model is able to qualitatively address all of the main observed features of hyperon polarization.