Polarized radiative Lb decays Lb Lx g

1
Polarized radiative Lb decaysLb ? L(x) g

• A first look

2
Outline

• Channel description
• Theoretical motivations
• Observables
• Angular distributions
• See talk at next Production and Decay models WG
  for more details
• LHCb expectations
• Simulation with EvtGen
• Status and perspectives

3
Lb ? L(px) g xp,k

• Lb ? L(1115) g
• ? p p

• Lb ? L(X) g
• ? p k

g
g
s
b
k
s
b
u
Lb
L
d
d
Lb
u
p
u
u
d
d
u
u

• Electromagnetic penguin b ? s g

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LO Effective hamiltonian b?sg
g
OPE (Operator Product expansion)
s
b

• Electromagnetic dipole operators

• Wilson coefficients
• C7, C7
• BR(B ? Xs g) constrains C72 C72

left
right
5
Observables at LO

• Angular asymmetries (with respect to Lb spin)
• constrain
• 2 indipendent measurements for r, or
• PB measurement
• a discrepancy with the value measured in
  semileptonic Lb?cl?lX decays would indicate the
  presence of non-standard right-handed b ? c
  currents.

• PB Lb polarization
• ap weak decay parameter

sensitive to NP
Hiller et al., Phys Rev D65, 404 (2001)
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NLO Effective hamiltonian b?sg

• Wilson coefficients
• CP violation in C7, C8
• Direct CP violation interference between the
  weak and strong phases in the decay amplitudes
• O(1) in SM
• ?10 if NP!

left
right
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Observables at NLO

• Angular asymmetries
• where
• Ratio of CP even quantities
• Expected small in SM ? ms/ mb

Lb
Lb
probe chirality
sensitive to NP
Hiller et al., Phys Rev D65, 404 (2001)
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Helicity formalism for Lb ? L(px) g

• Lb polarization
• Polarization density matrix
• Helicity amplitudes
• Lb ? Lg
• L ? px

More details at next Production Decay WG
 Weak radiative decays of beauty baryons 
LHCb note 2004-009 Jacob, Wick, Ann Phys 7, 404
(1959)
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Results JL 1/2

• Angular distributions
• Lb ? L(pp) g

• Lb ? L(pk) g

• Photon asymmetry
• Proton asymmetry

Only 2 helicity states

• agap 0.639 L? pp
• ap 0 L? pk (P cons)
• ag ? -1 in SM

More details at next Production Decay WG
10
Results JL 3/2

• L helicity can now assume the values 1/2, 3/2
• 8 helicity amplitudes
• no theoretical calculations
• Too complicated!!

More details at next Production Decay WG
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Lb production at LHC

• ?10 of produced bb hadronize in B hadrons
• Lb dominates (?90)
• Lb produced with transversal polarization
• PB usually greater than 20
• At LHC luminosity 104pb-1 the Lb polarization can
  be measured with the statistical precision better
  than 0.01

Lb
n
p1
p2
Bourrely, Leader, Soffer, Phys Reports 59, 2
(1980)
Ajaltouni, Conte, Leitner, ?b into ?-vector
decays, Phys Lett B, 614 (2005) Leader, Spin
in particle Physics, Cambridge University Press
(2001)
Feasibility of Beauty Baryon Polarization
Measurement in Lb ? J/Y L decay channel by ATLAS
Atlas note
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Lb ? L(1115) g in LHCb

• BR (Lb ? L(1115) g ) 4.15 10-5
• At LHCb
• etrigger 20 ? estimate low
• esel 5 ? as B ? K g
• edet, rec edet, rec (B ? K g)
• ratio B ? J/? Ks / B ? J/? K

Exp. annual signal yeald ? 5k evts
Optimization TDR numbers
etot 0.1
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LHCb sensitivity to r
Depending on PB measurement
Ag only
Ag and Ap combined
CP averaged

• dPB 0.01
• ap 0.639 0.005
• 1 year 2500 evts

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LHCb sensitivity to r
Ag only
Ap only

• PB 0.20.01
• ap 0.639 0.005
• 2500 evts/year

Ag and Ap combined
CP averaged
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EvtGen

• Lb polarization
• Now it is possible to produce polarized Lb in
  Gauss (from v15r17)
• Thanks to Patrick Robbe!
• Fully polarized Lb PB 1
• HELAMP model for Lb ? Lg decay
• Helicity amplitudes and phases as input
• L fully polarized ag -1
• HELAMP model for L ? px decay
• agap 0.639 L? pp
• ap 0 L? pk (P cons)
• Decay files for Lb ? Lg
• m(L) 1115,1520,1600,1670
• Both phase space and helamp models
• Bug in EvtGen code was preventing correct
  generation of Lb

More details at next Production Decay WG
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Lb ? L(1115) g

• PB 1
• ag -1
• ap 0.642

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Lb ? L(1670) g

• PB 1
• ag -1
• ap 0

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Status report

• Gauss ready for production of polarized Lb decays
• Asked for 300K events of both (in March!!)
• Lb ? L(1115) g
• Lb ? L(1670) g
• Still waiting

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Backup slides
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Helicity formalism for Lb ? L(px) g

• z spin quantization axis
• parallel to Lb spin
• z' parallel to L momentum
• (qL,fL) and (qg,fg)
• Lb rest frame
• (qp,fp) and (qx,fx)
• L rest frame
• x k,p
• f the same in both frames

Jacob, Wick, Ann Phys 7, 404 (1959)
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Decay probability for Lb ? L(px) g

• Lb polarization
• Polarization density matrix
• Amplitude probability
• Decay probability

? ½ - ? -½
No correlation production/decays

• C,E helicity amplitudes
• If P E(lp) E(-lp)

We dont measure the final helicities
Jacob, Wick, Ann Phys 7, 404 (1959)
22
Results JL 1/2

• g helicity can only assume the values 1
• only 2 helicity states are possible
• Decay probability

23
Results JL 1/2

• Angular distributions
• Lb ? L(pp) g

• Lb ? L(pk) g

• Proton asymmetry
• agap 0.639 L? pp
• ap 0 L? pk (P cons)
• ag ? -1 in SM

• Beam asymmetry
• Photon asymmetry

24
Results JL 3/2

• L helicity can now assume the values 1/2, 3/2
• 8 helicity amplitudes!!
• no theoretical calculations
• Decay probability
• Too complicated!!

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Lambda baryons
PDG 2004
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Lambda baryons
Existence is certain. Existence ranges
from very likely to certain.
Below NK threshold
PDG 2004
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Lambda baryons
JL ½
PDG 2004

• Most promising L(1115), L(1670)

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BR (Lb ? L(x) g )
Hiller et al., Phys Rev D65, 404 (2001)
Dependance on mL

• HQET, LEET ? form factors,
• SM values for C7, C7
• PDG 2004 values for L(x) ?NK

• BR (Lb ? L(1115) g ) 4.15 10-5
• BR (Lb ? L(1520) g ) 1.30 10-5
• BR (Lb ? L(1600) g ) 0.65 10-5
• BR (Lb ? L(1670) g ) 0.70 10-5

BR ? 10-5 ? 10-6
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Observables for Lb ? L(1115) g
Helicity formalism
HQET
Measuring the angular asymmetries

• 2 indipendent measurements for r
• PB measurement
• a discrepancy with the value measured in
  semileptonic Lb?cl?lX decays would indicate the
  presence of non-standard right-handed b ? c
  currents.
• Lb ? L(1670) g only Ag

30
LHCb sensitivity to r
Depending on PB measurement
Ag only
Ag and Ap combined
CP averaged

• PB 0.5
• ap 0.639 0.005
• 1 year 2500 evts

31
LHCb sensitivity to r
Ag only
Ap only

• PB 0.50.01
• ap 0.639 0.005
• 2500 evts/year

Ag and Ap combined
CP averaged
32
EvtGen

• Lb polarization
• Polarization density matrix
• Now it is possible to produce polarized Lb in
  Gauss (from v15r17)
• Thanks to Patrick Robbe
• GeneratorModules EvtGenTool.cpp

1 0 0 0
r
Fully polarized Lb PB 1
// sets diagonal polarization matrix for
unpolarized decays // or generate Polarized
Lambda_b if requested if ( ( m_generatePolLambdab
) ( abs( theHepMCPart -gt pdg_id() )
5122 ) ) EvtSpinDensity rho
rho.SetDim( 2 ) rho.Set( 0
, 0 , 1.0 ) rho.Set( 0 , 1 , 0.0 )
rho.Set( 1 , 0 , 0.0 )
rho.Set( 1 , 1 , 0.0 ) thePart
-gt setSpinDensityForwardHelicityBasis( rho )
else thePart -gt setDiagonalSpinDensity( )
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EvtGen

• HELAMP model for Lb ? Lg decay
• Helicity amplitudes and phases as input
• L fully polarized ag -1
• HELAMP model for L ? px decay
• agap 0.639 L? pp
• ap 0 L? pk (P cons)
• Decay files for Lb ? Lg
• m(L) 1115,1520,1600,1670
• Both phase space and helamp models
• Bug in EvtGen code was preventing correct
  generation of Lb

Decay Lambda_b0sig 1.000 MyLambda0 gamma
HELAMP 1. 0. 0. 0. Decay
anti-Lambda_b0sig 1.000 Myanti-Lambda0 gamma
HELAMP 0. 0. 1. 0. Decay MyLambda0
1.000 p pi- HELAMP
.906 0. .423 0. Decay Myanti-Lambda0 1.000
anti-p- pi HELAMP .423 0.
.906 0.
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Lb ? L(1115) g EvtGen Bug

• PB 1
• ag -1
• ap 0.642

WRONG !!