1. Branching ratio and helicity amplitudes for  b   (pK)  decays (  spin = 3/2) Combined work of: Gudrun Hiller (Dortmund UNI), the Bearer of the Light Thomas Schietinger (PSI), the Scholar Mathias Knecht and Federica Legger (EPFL), the water Carriers Theoretical physics for experimentalists:

2. 2 Outline  Once upon a time:  the electromagnetic penguin b  s   the photon polarization (theory and experiment)  my thesis results & open questions  The mighty quest for  spin = 3/2:  Branching ratio for  b   (pK)   the tools: Mathematica  Helicity amplitudes  Sensitivity to photon polarization  Summary and outlook

3. 3 Motivations  Standard Model (SM): best description of known elementary particles and their interactions:  passed all experimental tests up to now;  still one missing particle, the Higgs boson. However...  19 (!!!) free parameters;  gravity is not included.  Quest for new physics in the quark sector:  CKM picture is very successful  but we still know little about b  s, d transitions ! quarks leptons udud cscs tbtb e  

4. 4 The electromagnetic penguin b  s   New physics in the decay rate :  are there any contribution from supersymmetric particles?  the measured b  s  branching fraction is compatible with SM prediction  Theory: BF(b  s  ) [10 -6 ]= 357 ± 30  Experiment: BF(b  s  ) [10 -6 ]= 355 ± 24 +9 -10 ± 3  from HFAG (combined measurements by Belle, BaBar, CLEO)  Need other observables to test the SM... Gambino, Misiak, NPB 611 (2001) 338 http://www.slac.stanford.edu/xorg/hfag/rare b s u,c,t W 

5. 5 b s W   The W boson only couples to a left-handed s quark  Left-handed photon (to conserve ang. momentum) “Naïve” SM Atwood, Gronau, Soni, PRL 79, 185 (1997) Photon polarization:  pure 2-body decay: right-handed components of the order of r = m s /m b Grinstein, Grossman, Ligeti, Pirjol, PRD 71, 011504 (2005) SM + QCD  when considering b  s  + gluons  right-handed components may be up to 10-15%  explicit calculations only for B  K*  B  The electromagnetic penguin b  s 

6. 6 Photon polarization measurements Melikov, Nikitin, Simula, PLB 442, 381 (1998) Grossman, Pirjol, JHEP06, 029 (2000) Atwood, Gronau, Soni, PRL 79, 185 (1997) Mannel, Recksiegel, JPG: NPP 24, 979 (1998) LHCb B factories Knecht, Schietinger, PLB 634, 403 (2006) Gronau, Pirjol, PRD 66, 054008 (2002) B-B interference First measurements of K* polarization in B->K*l+l- by Belle/Babar e + e - conversion Exp. statusTheor. Refs. Latest world average sin2  = 0.0 ± 0.3 Higher K* resonances Difficult to disentangle resonance structure (Babar, hep/0507031) Gronau, Grossman, Pirjol, PRL 88, 051802 (2002) Charmonium res. interference No results so far... b-baryons Hiller, Kagan, PRD 65, 074038 (2002) Exploit ang. correlations between polarized initial state and final state. Under study at LHCb (F.Legger, M. Knecht) Legger, Schietinger, PLB 644 (2007) xxx

7. 7 Polarized b baryons decays s d  u b d u bb  Hiller, Kagan, PRD 65, 074038 (2002)  If initial state is polarized:  exploit angular correlations between initial and final states  only possible with b baryons  feasible at hadron colliders Mannel, Recksiegel, JPG: NPP 24, 979 (1998) Case study:  b  (  (1115)  p  )  Long distance contributions from internal W exchange, or vector meson cc contributions are expected to be small

8. 8 Polarized  b   (1115)  decays  Angular distributions  depend on photon polarization    P B =  b polarization   p = weak decay parameter Evtgen   = 1 P B = 1 cos  ,  b rest framecos  p,  rest frame  b   (1115)    (fit) = 1.036   (theory) = 1  p (fit) = 0.679  p (theory) = 0.642  b   (1115) 

9. 9 However...  From the experimental point of view the decay  b   (1115)  is quite hard to observe (c  = 7.89 cm)  Can we probe the photon polarization in heavier  resonance decays?   b  (  (X)  pK)   what do we need?  Branching ratios for  b   (X)   Angular distributions for  spin = 1/2, 3/2  spin > 3/2: helicity states > observables s d u b d u bb  u u p K

10. 10  (X) resonance spectrum 1690 1670  spin = 1/2  spin = 3/2 1520  Invariant pK mass spectrum obtained with:  BR(  b   (X)  ), calculated rescaling BR(  b   (1115)  ) with a kinematical factor, assuming the same form factors and no spin dependence for all  (X) resonances. PDG 2004 Legger, Schietinger, PLB 644 (2007) xxx

11. 11 Helicity formalism for  b   (pK)   Photon helicity = ±1,   helicity = ±1/2  2 helicity amplitudes  Photon angular distribution  Proton angular distribution flat because of P conservation J  = 1/2  Photon helicity = ±1,   helicity = ±1/2, ±3/2  4 helicity amplitudes  Photon angular distribution J  = 3/2 Legger, Schietinger, PLB 644 (2007) xxx

12. 12    depends on the asymmetry of  b spin with respect to photon momentum  and can be factorized into the photon helicity parameter   and the strong parameter    can be extracted from the proton angular distribution  b   (pK)  decays  (J  = 3/2) Legger, Schietinger, PLB 644 (2007) xxx

13. 13  The photon helicity can be probed in decays involving  resonances of spin 3/2 by measuring   3/2 and   Can we get a better estimate of the BR ?  Include at least the spin dependence  Form factors will have to be measured  Can we get an estimation of  ? Open questions

14. 14  Electromagnetic dipole operators:  long distance effects  non perturbative approach (HQET)  Wilson coefficients: C 7, C 7 ’  short distance  Fermi theory (point-like interactions) The effective hamiltonian: Decay amplitude for  b   (1520) 

15. 15 The effective hamiltonian: Decay amplitude for  b   (1520)  The matrix element:  bb  (p, s) (q,  ) (p´,s´)

16. 16 The effective hamiltonian: Decay amplitude for  b   (1520)  The matrix element: Find   and   !! u(p,s) = Dirac spinor to describe the  b (spin 1/2) Rarita-Schwinger (RS) spinor to describe the  (spin 3/2) Dirac spinor Polarization vector 1/2  1 = 3/2 Rarita, Schwinger, Phys Rev 60(1941) 61

17. 17 Conditions Gauge invariance On-shell photon Equations of motion (EOM) RS spinors Main actors:

18. 18   and   Ansatz: We define the tensor   (antisymmetric in  and ):

19. 19   and   Ansatz: On-shell photon! Reabsorbed in B and C using EOM We define the tensor   (antisymmetric in  and ):

20. 20   and   We define the tensor   (antisymmetric in  and ): Ansatz: On-shell photon! Reabsorbed in B and C using EOM Contracting with q 

21. 21   and   Form factors  (5)  is related to  (5)  through the identity: it is straightforward to obtain (ask Mathias) :

22. 22 Spin averaged matrix element To evaluate the BR we need: where Writing explicitely the spinor indices!

23. 23 Spin averaged matrix element Sum over spins: Aliev, Ozpineci, hep-ph/0406331 We finally obtain: To calculate the trace we use: with the TRACER package

24. 24 Trace evaluation

25. 25 Trace evaluation

26. 26 Branching Ratio In the limit f2f2 BR (  b   0  ~ 7·10 -5

27. 27 HFAG ICHEP 2006 From B + and B 0 radiative decays, and dedicated form factors studies, BR should have the same order of magnitude K*(892) = vector K 1 (1270) = axial vector K 1 (1400) = axial vector K 2 *(1430) = tensor S. Veseli, M.G. Olsson, Z. Phys. C 71 (1996) 287

28. 28 Helicity amplitudes We use the  b rest frame:  bb  p´=(E´,0,0,E) q=(E,0,0,-E) z

29. 29 Helicity amplitudes The amplitudes A  3/2 (A  1/2 ) result from a  b -baryon with h =  1/2 (h = +1/2) and a photon with J z = +1 Photon polarization vectors: JzJz in  b rest frame:  polarization vectors:  helicity RS spinor Dirac spinor

30. 30 Helicity amplitudes: results In the limit and f 1 ~f 2 Right-handed photon

31. 31 Helicity amplitudes: naïve picture  bb  Opposed b and  b spin -> suppressed ~ O(1/m b ) Left-handed photon = SM b s M. Suzuki, J. Phys. G: Nucl. Part. Phys. 31 (2005) 755  bb  b s Spin flip b vs s Quark level:  b s Spin flip  b vs 

32. 32 Sensitivity to the photon polarization Photon polarization:  b Polarization = 20% 10k  (1520) events (~3 yrs LHCb running ) 3  significance

33. 33 Conclusions and outlook  The BR(  b   ) has been calculated in the framework of HQET  form factors will need to be measured  Helicity amplitudes for the decay  b   have been evaluated  straightforward extension to decay involving J P = 3/2 + resonances, by replacing C ’ 7 -> -C ’ 7  Still to do: work out a better estimate of the Lb polarization  (Some) theoretical models and calculations are (also) accessible to experimentalists!

34. Backup slides

35. 35  b production at LHC:  bb cross section in pp collision = 500  b   10% of produced bb hadronize in baryons   b dominates (  90%)   b produced with transversal polarization  Expectations are P B ~ 20%  ATLAS plans to measure it with a statistical precision better than 1% p1p1 p2p2 bb n Ajaltouni, Conte, Leitner, PLB, 614 (2005) 165 Feasibility of Beauty Baryon Polarization Measurement in  b  J  decay channel by ATLAS – Atlas note 94-036 PHYS

36. 36 Photon polarization   b   (1670)  selected evts.  transversally polarized  b )  efficiency corrected (from unpolarized decays)  from data, the correction can be obtained from B  K*  decays 

37. 37 Sensitivity on |r| measurement  Values of |r| that can be probed from single measurements  Getting close to the SM expected range, becomes interesting if NP! 1 year, 3  5 years, 3  SM naive SM + QCD SM naive SM + QCD  b Polarization = 20%

38. 38 Combined measurements 1 year, 3  5 years, 3  SM naive SM + QCD  Combining measurement increases range by a few percent at most   (X) measurements have good sensitivity (in case  (1115) turns out to be difficult)  b Polarization = 20% SM naive SM + QCD

39. 39 Dependence on  b polarization  If only the photon asymmetry is measured, a polarization of at least 20% is needed to have good sensitivity  b   (X)  b   (1115)  1 year