1. Weak Coherent Kaon Production L. Alvarez-Ruso 1, J. Nieves 1, I. Ruiz Simo 2, M. Valverde 3, M. Vicente Vacas 1 1.IFIC, Universidad de Valencia 2.Universidad de Granada 3.RCNP, Osaka TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAA A A A

5. 1.IFIC, Universidad de Valencia 2.Universidad de Granada 3.RCNP, Osaka L. Alvarez-Ruso 1, J. Nieves 1, I. Ruiz Simo 2, M. Valverde 3, M. Vicente Vacas 1 Weak Coherent Kaon Production

6. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Introduction QE and 1 ¼ are the most important (large and relevant for oscillations) (anti) º interaction channels in the few-GeV region, but there are others… Strangeness production: ¢ S = 0 e.g. ¢ S = 1 : Cabibbo suppressed but with lower thresholds than ¢ S = 0 Hyperon e.g. Kaon: Background for proton decay p ! º K + Accessible by Miner º a but also MiniBooNE, T2K, … There is a coherent channel

7. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Introduction QE and 1 ¼ are the most important (large and relevant for oscillations) (anti) º interaction channels in the few-GeV region, but there are others… Strangeness production: ¢ S = 0 e.g. ¢ S = -1 : Cabibbo suppressed but with lower thresholds than ¢ S = 0 antiKaon: Accessible by Miner º a but also MiniBooNE, T2K, … Potentially interesting for anti º beams There is a coherent channel

8. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski The model 1.Microscopic kaon production on the nucleon 2.The coherent reaction 3.Kaon distortion

9. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski The model 1.Microscopic kaon production on the nucleon Rafi Alam et al., PRD82 Includes all terms in SU(3) chiral Lagrangians at leading order Parameters: f ¼, ¹ p and ¹ n, D and F (from semileptonic decays) A global dipole form factor : F(q 2 )=(1-q 2 /M 2 F ) -2, M F = 1 GeV Absence of S=1 baryon resonances ) Extended validity of model CTKP Cr §, Cr ¤ ¼ F, ´ F

10. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski The model 1.Microscopic kaon production on the nucleon Rafi Alam et al., PRD82 Includes all terms in SU(3) chiral Lagrangians at leading order A global dipole form factor : F(q 2 )=(1-q 2 /M 2 F ) -2, M F = 1 GeV ( § 10%)

11. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski The model 1.Microscopic kaon production on the nucleon Rafi Alam et al., PRD82 vs ¢ S = 0 from GENIE

12. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski The model 2. The coherent reaction Amplitude: Nuclear current: ¼ F, ´ F vanish with the sum initial and final nucleons taken on-shell with averaged momenta:

13. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski The model 3. Kaon distortion (with DWBA) or in the eikonal approximation: The optical potential: C=0.13 or 0.114 Ã Klein-Gordon eq. Cabrera, Vicente Vacas, PRC69

14. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results In the Impulse Approximation: Very small cross section…

15. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results In the Impulse Approximation: Very small cross section… Compare to Coh ¼ + (on 12 C): ¾ (Coh ¼ +,1 GeV)~ 0.05-0.1 >> ¾ (Coh K +,1.35 GeV)~ 0.00014

16. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results In the Impulse Approximation: Very small cross section… why?

17. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results In the Impulse Approximation: Very small cross section… why? because K is heavy

18. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results In the Impulse Approximation: Very small cross section… why? because K is heavy

19. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results In the Impulse Approximation: Very small cross section… why? because K is heavy ) Sensitive to the nuclear density distribution

20. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results In the Impulse Approximation. Contribution from different mechanisms: CT is the largest contribution, followed by Cr ¤ Interference stronger than in the free case Rafi Alam et al., PRD82 (2010)

21. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results In the Impulse Approximation. Contribution from different mechanisms: CT is the largest contribution, followed by Cr ¤ Interference stronger than in the free case

22. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results With Kaon distortion. Kaon momentum distributions:

23. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results With Kaon distortion. Kaon momentum distributions: Eikonal approximation breaks down at low |p K |

24. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results With Kaon distortion. Kaon momentum distributions: Eikonal approximation breaks down at low |p K |, unlike in Coh ¼ LAR et al., PRC

25. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results With Kaon distortion. Angular distributions:

26. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results With Kaon distortion. Angular distributions:

27. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski The model Coherent K - production with antineutrinos Elementary interaction: Rafi Alam et al., PRD 85 Direct terms with strange baryons ( ¤, §, § *(1385)) in the intermediate state

28. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski The model Coherent K - production with antineutrinos Elementary interaction: Rafi Alam et al., PRD 85 N- § *(1385) transition: C3V, C4V, C5V, C3A, C4A, C5A, C6A ff related to those of N- ¢ (1232) using SU(3) symmetry In particular: C5A(0) Ã off-diagonal G-T

29. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski The model Coherent K - production with antineutrinos Elementary interaction: Rafi Alam et al., PRD 85 Small contribution from § *(1385): it is below K production threshold

30. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results Coherent K - production with antineutrinos In the Impulse Approximation. Contribution from different mechanisms: Rafi Alam et al., PRD85 (2012) Largest contribution from CT Strong destructive interference (Relatively) large § *

31. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski The model 3. antiKaon distortion (with DWBA) The optical potential: K - p interaction dominated by ¤ (1405) resonance ¤ (1405) dynamically generated by s-wave meson-baryon rescattering in coupled channels Dressing of meson propagators (1p1h, ¢ h) Self consistent treatment of antiK Ã Klein-Gordon eq. Ramos, Oset, NPA 671 (2000)

32. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski The model 3. antiKaon distortion (with DWBA) The optical potential: Very different interaction vs Kaon case: Ã Klein-Gordon eq. Ramos, Oset, NPA 671 (2000)

33. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Results With antiKaon distortion. Momentum distributions:

34. March 19, 2012 Zakład Fizyki Neutrin, Uniwersytet Wrocławski Conclusions (anti)Neutrino induced coherent (anti)kaon production has been studied Microscopic production mechanism based on SU(3)chiral Lagrangians Coherent sum over all (noninteracting) nucleons DWIA for the outgoing (anti)kaon by solving the KG eq. with a realistic density-dependent potential Small cross sections are obtained due to: Small (Cabibbo suppressed) c. s. on nucleons Large momentum transferred to the nucleus because of the large kaon mass Destructive interference Kaon distortion (stronger for K - as expected) Eikonal approximation is wrong at low momenta