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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 Knecht and Federica Legger (EPFL), the water Carriers Outline Once upon a time: the electromagnetic penguin bsg 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 2 Motivations Standard Model (SM): best description of known elementary particles and their interactions: e m t ne nm nt passed all experimental tests up to now; still one missing particle, the Higgs boson. However... leptons 19 (!!!) free parameters; gravity is not included. quarks Quest for new physics in the quark sector: CKM picture is very successful but we still know little about b s, d transitions ! u d c s t b 3 The electromagnetic penguin bsg u,c,t g b W s New physics in the decay rate : are there any contribution from supersymmetric particles? the measured bsg branching fraction is compatible with SM prediction Theory: BF(bsg) [10-6]= 357 ± 30 Gambino, Misiak, NPB 611 (2001) 338 Experiment: BF(bsg) [10-6]= 355 ± 24 +9-10 ± 3 http://www.slac.stanford.edu/xorg/hfag/rare from HFAG (combined measurements by Belle, BaBar, CLEO) Need other observables to test the SM... 4 The electromagnetic penguin bsg u,c,t g b W s The W boson only couples to a left-handed s quark Left-handed photon (to conserve ang. momentum) Photon polarization: pure 2-body decay: right-handed components of the order of r = ms/mb when considering bsg + gluons right-handed components may be up to 10-15% explicit calculations only for BK*g, Brg “Naïve” SM Atwood, Gronau, Soni, PRL 79, 185 (1997) SM + QCD Grinstein, Grossman, Ligeti, Pirjol, PRD 71, 011504 (2005) 5 Photon polarization measurements LHCb B factories Exp. status Theor. Refs. e+e- conversion First measurements of K* polarization in B->K*l+lby Belle/Babar Grossman, Pirjol, JHEP06, 029 (2000) Melikov, Nikitin, Simula, PLB 442, 381 (1998) B-B interference Latest world average sin2b = 0.0 ± 0.3 Atwood, Gronau, Soni, PRL 79, 185 (1997) Higher K* resonances Difficult to disentangle resonance structure (Babar, hep/0507031) Gronau, Pirjol, PRD 66, 054008 (2002) Gronau, Grossman, Pirjol, PRL 88, 051802 (2002) Charmonium res. interference No results so far... b-baryons Exploit ang. correlations between polarized initial state and final state. Under study at LHCb (F.Legger, M. Knecht) Knecht, Schietinger, PLB 634, 403 (2006) Mannel, Recksiegel, JPG: NPP 24, 979 (1998) Hiller, Kagan, PRD 65, 074038 (2002) Legger, Schietinger, PLB 644 (2007) xxx 6 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 Lb b s d d u u L Long distance contributions from internal W exchange, or vector meson cc contributions are expected to be small Mannel, Recksiegel, JPG: NPP 24, 979 (1998) Hiller, Kagan, PRD 65, 074038 (2002) 7 Polarized Lb L(1115) g decays Angular distributions: PB = Lb polarization ap = weak decay parameter depend on photon polarization ag 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 8 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? g Lb (L(X) pK) g b s Lb d u u u d u K p 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 9 L(X) resonance spectrum 1520 L spin = 3/2 L spin = 1/2 1670 1690 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 dependence for all L(X) resonances. Legger, Schietinger, PLB 644 (2007) xxx 10 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 11 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 12 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 ? 13 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) 14 Decay amplitude for Lb L(1520) g The effective hamiltonian: The matrix element: g (q, e) L(1520) (p´,s´) Lb (p, s) 15 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) Rarita, Schwinger, The matrix element: Phys Rev 60(1941) 61 Dirac spinor Find Gan and G(5)an!! Polarization vector 1/2 1 = 3/2 16 Conditions Equations of motion (EOM) On-shell photon RS spinors Gauge invariance Main actors: 17 Gan and G(5)an We define the tensor Gamn(antisymmetric in m and n): Ansatz: 18 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 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 Contracting with qm 20 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) : 21 Spin averaged matrix element To evaluate the BR we need: Writing explicitely the spinor indices! where 22 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 23 Trace evaluation 24 Trace evaluation 25 Branching Ratio In the limit BR (Lb L0g ) ~ 7·10-5 f2 26 HFAG ICHEP 2006 K*(892) = vector K1(1270) = axial vector K1(1400) = axial vector K2*(1430) = tensor From B+ and B0 radiative decays, and dedicated form factors studies, BR should have the same order of magnitude S. Veseli, M.G. Olsson, Z. Phys. C 71 (1996) 287 27 Helicity amplitudes We use the Lb rest frame: g q=(E,0,0,-E) Lb L(1520) z p´=(E´,0,0,E) 28 Helicity amplitudes The amplitudes A3/2 (A1/2 ) result from a Lb-baryon with h = 1/2 (h = +1/2) and a photon with Jz = +1 RS spinor Dirac spinor Photon polarization vectors: Jz in Lb rest frame: L polarization vectors: L helicity 29 Helicity amplitudes: results Right-handed photon In the limit and f1~f2 30 Helicity amplitudes: naïve picture b Quark level: g Left-handed photon = SM Spin flip b vs s s b Lb Spin flip Lb vs L s L(1520) g b Opposed b and Lb spin -> suppressed ~ O(1/mb) Lb g s L(1520) M. Suzuki, J. Phys. G: Nucl. Part. Phys. 31 (2005) 755 31 Sensitivity to the photon polarization Lb Polarization = 20% 10k L(1520) events (~3 yrs LHCb running) 3s significance Photon polarization: 32 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! 33 Backup slides 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 n p1 Lb p2 Expectations are PB ~ 20% Ajaltouni, Conte, Leitner, PLB, 614 (2005) 165 ATLAS plans to measure it with a statistical precision better than 1% Feasibility of Beauty Baryon Polarization Measurement in Lb J/Y L decay channel by ATLAS – Atlas note 94-036 PHYS 35 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 36 Sensitivity on |r| measurement 1 year, 3s SM naive SM + QCD 5 years, 3s SM naive SM + QCD Values of |r| that can be probed from single measurements Getting close to the SM expected range, becomes interesting if NP! Lb Polarization = 20% 37 Combined measurements 1 year, 3s SM + QCD SM naive 5 years, 3s SM + QCD SM naive 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) Lb Polarization = 20% 38 Dependence on Lb polarization Lb L(X) g Lb L(1115) g 1 year If only the photon asymmetry is measured, a polarization of at least 20% is needed to have good sensitivity 39