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Branching ratio and helicity amplitudes for L b  L (pK) g decays ( L spin = 3/2)

Theoretical physics for experimentalists:. Branching ratio and helicity amplitudes for L b  L (pK) g decays ( L spin = 3/2). Combined work of: Gudrun Hiller (Dortmund UNI), the Bearer of the Light Thomas Schietinger (PSI), the Scholar

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Branching ratio and helicity amplitudes for L b  L (pK) g decays ( L spin = 3/2)

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  1. Theoretical physics for experimentalists: Branching ratio and helicity amplitudes for Lb L(pK) g decays (L spin = 3/2) Combined work of: • Gudrun Hiller(Dortmund UNI), the Bearer of the Light • Thomas Schietinger(PSI), the Scholar • Mathias KnechtandFederica Legger (EPFL), the water Carriers

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

  3. u d c s t b 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 ! leptons e ne m nm t nt quarks

  4. The electromagnetic penguin bsg g u,c,t b W s • New physics in the decay rate : • are there any contribution from supersymmetric particles? • the measured bsg branching fraction is compatible with SM prediction • Theory:BF(bsg) [10-6]= 357 ± 30 • Experiment:BF(bsg) [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

  5. The electromagnetic penguin bsg g • The W boson only couples to a left-handed s quark • Left-handed photon (to conserve ang. momentum) u,c,t b W s Photon polarization: “Naïve” SM • pure 2-body decay: right-handed components of the order ofr = ms/mb Atwood, Gronau, Soni, PRL 79, 185 (1997) SM + QCD • when considering bsg + gluons • right-handed components may be up to10-15% • explicit calculations only for BK*g, Brg Grinstein, Grossman, Ligeti, Pirjol, PRD 71, 011504 (2005)

  6. Photon polarization measurements Exp. status Theor. Refs. e+e- conversion First measurements of K* polarization in B->K*l+l- by Belle/Babar Grossman, Pirjol, JHEP06, 029 (2000) Melikov, Nikitin, Simula, PLB 442, 381 (1998) Latest world average sin2b = 0.0 ± 0.3 Atwood, Gronau, Soni, PRL 79, 185 (1997) B-B interference B factories Difficult to disentangle resonance structure (Babar, hep/0507031) Gronau, Pirjol, PRD 66, 054008 (2002) Higher K* resonances Gronau, Grossman, Pirjol, PRL 88, 051802 (2002) Charmonium res. interference No results so far... Knecht, Schietinger, PLB 634, 403 (2006) Mannel, Recksiegel, JPG: NPP 24, 979 (1998) Exploit ang. correlations between polarized initial state and final state. Under study at LHCb (F.Legger, M. Knecht) LHCb b-baryons Hiller, Kagan, PRD 65, 074038 (2002) Legger, Schietinger, PLB 644 (2007) xxx

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

  8. Polarized Lb L(1115) g decays • Angular distributions: depend on photon polarization ag • PB = Lb polarization • ap = weak decay parameter Lb L(1115) g Lb L(1115) g Evtgen ag = 1 PB = 1 ag (fit) = 1.036 ag (theory) = 1 ap (fit) = 0.679 ap(theory) = 0.642 cosqg, Lb rest frame cosqp, L rest frame

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

  10. L(X) resonance spectrum 1520 L spin = 3/2 L spin = 1/2 1690 1670 PDG 2004 • Invariant pK mass spectrum obtained with: • BR(Lb L(X) g ), calculated rescaling BR(Lb L(1115) g ) with a kinematical factor, assuming the same form factors and no spin dependencefor allL(X) resonances. Legger, Schietinger, PLB 644 (2007) xxx

  11. Helicity formalism for Lb L(pK) g JL = 1/2 JL = 3/2 • Photon helicity = ±1, • L helicity = ±1/2 • 2 helicity amplitudes • Photon angular distribution • Proton angular distribution flat because of P conservation • Photon helicity = ±1, • L helicity = ±1/2, ±3/2 • 4 helicity amplitudes • Photon angular distribution Legger, Schietinger, PLB 644 (2007) xxx

  12. Lb L(pK) g decays(JL = 3/2) • ag,3/2 depends on the asymmetry of Lb spin with respect to photon momentum • and can be factorized into the photon helicity parameter ag and the strong parameter  •  can be extracted from the proton angular distribution Legger, Schietinger, PLB 644 (2007) xxx

  13. Open questions • The photon helicity can be probed in decays involving L resonances of spin 3/2 by measuring ag,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 ?

  14. Decay amplitude for Lb L(1520) g The effective hamiltonian: • Electromagnetic dipole operators: • long distance effects • non perturbative approach (HQET) • Wilson coefficients: C7, C7’ • short distance • Fermi theory (point-like interactions)

  15. Decay amplitude for Lb L(1520) g The effective hamiltonian: The matrix element: (q, e) g L(1520) (p´,s´) Lb (p, s)

  16. Decay amplitude for Lb L(1520) g The effective hamiltonian: u(p,s) = Dirac spinor to describe the Lb (spin 1/2) Rarita-Schwinger (RS) spinor to describe the L (spin 3/2) The matrix element: Rarita, Schwinger, Phys Rev 60(1941) 61 Dirac spinor Polarization vector 1/2  1 = 3/2 Find Gan and G(5)an!!

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

  18. Gan and G(5)an We define the tensor Gamn(antisymmetric in m and n): Ansatz:

  19. Gan and G(5)an We define the tensor Gamn(antisymmetric in m and n): Ansatz: On-shell photon! Reabsorbed in B and C using EOM

  20. Gan and G(5)an We define the tensor Gamn(antisymmetric in m and n): Ansatz: On-shell photon! Reabsorbed in B and C using EOM Contracting with qm

  21. Gan and G(5)an Form factors G(5)an is related to G(5)an through the identity: it is straightforward to obtain (ask Mathias) :

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

  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. Trace evaluation

  25. Trace evaluation

  26. Branching Ratio In the limit BR (Lb L0g ) ~ 7·10-5 f2

  27. HFAG ICHEP 2006 From B+ and B0 radiative decays, and dedicated form factors studies, BR should have the same order of magnitude K*(892) = vector K1(1270) = axial vectorK1(1400) = axial vector K2*(1430) = tensor S. Veseli, M.G. Olsson, Z. Phys. C 71 (1996) 287

  28. Helicity amplitudes We use the Lb rest frame: Lb L(1520) z g p´=(E´,0,0,E) q=(E,0,0,-E)

  29. Helicity amplitudes The amplitudes A3/2 (A1/2 ) result from aLb-baryon with h = 1/2 (h = +1/2) and a photon with Jz= +1 Dirac spinor RS spinor L polarization vectors: Photon polarization vectors: Jz in Lb rest frame: L helicity

  30. Helicity amplitudes: results Right-handed photon In the limit and f1~f2

  31. Helicity amplitudes: naïve picture b Left-handed photon = SM Quark level: g Spin flip b vs s s b Lb Spin flip Lb vs L s g L(1520) b Opposed b and Lb spin -> suppressed ~ O(1/mb) Lb s g L(1520) M. Suzuki, J. Phys. G: Nucl. Part. Phys. 31 (2005) 755

  32. Sensitivity to the photon polarization LbPolarization = 20% 10k L(1520) events (~3 yrs LHCb running) 3ssignificance Photon polarization:

  33. Conclusions and outlook • The BR(Lb L(1520) g) has been calculated in the framework of HQET • form factors will need to be measured • Helicity amplitudes for the decay Lb L(1520) g have been evaluated • straightforward extension to decay involving JP = 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. Lb production at LHC: • bb cross section in pp collision =500 mb • 10% of produced bb hadronize in baryons • Lb dominates (90%) • Lb produced with transversal polarization • Expectations are PB~ 20% • ATLAS plans to measure it with a statistical precision better than 1% n Lb p1 p2 Ajaltouni, Conte, Leitner,PLB, 614 (2005) 165 Feasibility of Beauty Baryon Polarization Measurement in Lb J/Y L decay channel by ATLAS – Atlas note 94-036 PHYS

  36. Photon polarization • Lb L(1670) g selected evts. (transversally polarized Lb) • efficiency corrected (from unpolarized decays) • from data, the correction can be obtained from B  K*g decays ag

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

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

  39. Dependence on Lb polarization 1 year Lb L(X) g Lb L(1115) g • If only the photon asymmetry is measured, a polarization of at least 20% is needed to have good sensitivity

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