Frontiers of Fundamental Physics 14 CP violation effects in multibody B decays Jeremy Dalseno on behalf of the LHCb collaboration J.Dalseno [at] bristol.ac.uk 18 July 2014 CP violation effects in multibody B decays 1
Outline 1. Motivation 2. LHCb Detector 3. B ± → K ± K + K − and B ± → K ± π + π − (penguin dominated) 4. B ± → π ± K + K − and B ± → π ± π + π − (tree dominated) 5. B ± → K ± p ¯ p and B ± → π ± p ¯ p 6. Summary Dalitz plot contains all kinematic and dynamic information of decay Amplitude analysis one of the most powerful techniques Extract amplitude-level information rather than amplitude-squared information Interference between intermediate states allows measurement of relative magnitudes and phases CP violation effects in multibody B decays 2
Motivation Charmless B → 3 h decay channels provide a rich environment for physics observables Unknown heavy particle in the loop could carry a new CP violating phase - W ? x = u, c, t x b s b s V V * xs xb q q g g q q u u u u � � V ud V ∗ Tree sensitive to γ = φ 3 ≡ − arg ub V cd V ∗ cb α s - V V * V V * W ud ub td tb u b u ∝ γ V ub γ β u u V V * cd cb CP violation effects in multibody B decays 3
Motivation In charged B decays, presence of multiple amplitudes may lead to direct CP violation i | A i | e i ( δ i + φ i ) A ( B → f ) = � A ( ¯ ¯ B → ¯ i | ¯ A i | e i ( δ i − φ i ) f ) = � Strong phase ( δ ) invariant under CP , while weak phase ( φ ) changes sign under CP A | 2 − | A | 2 A CP ( B → f ) ≡ | ¯ � A | 2 + | A | 2 ∝ sin( δ i − δ j ) sin( φ i − φ j ) | ¯ i,j 3 conditions required for direct CP violation At least 2 amplitudes Non-zero strong phase difference, δ i − δ j � = 0 Non-zero weak phase difference, φ i − φ j � = 0 Source of weak phase differences come from different CKM phases of each amplitude CP violation effects in multibody B decays 4
Motivation Direct CP violation more complicated in B → 3 h decay channels compared to 2-body decays There are at least 4 possible sources of strong phase 1. Short-distance contributions (quark level) BSS mechanism, PRL 43 242 (1979) Penguin diagram (b) contains 3 quark generations in loop If gluon in penguin is timelike (on-shell) Momentum transfer q 2 > 4 m 2 i where i = u, c Particle rescattering (c) generates a phase difference Tree contribution (a) carries different strong phase CP violation in 2-body processes caused by this effect eg. B 0 → K + π − CP violation effects in multibody B decays 5
Motivation Remaining sources unique to multibody decays Long-distance contributions ( q ¯ q level) 2. Breit-Wigner phase Represents intermediate resonance states 1 F BW ( s ) = R m 2 R − s − im R Γ R ( s ) Phase varies across the Dalitz plot 3. Relative CP -even phase in the isobar model i | A i | e i ( δ i + φ i ) A ( B → f ) = � A ( ¯ ¯ B → ¯ i | ¯ A i | e i ( δ i − φ i ) f ) = � Related to final state interactions between different resonances CP violation effects in multibody B decays 6
Motivation Each source of strong phase leaves a unique signature in the Dalitz plot Illustrate with series of examples + K Consider B ± → K ± π + π − with only 2 isobars B ± → K ± ρ 0 and non-resonant (NR) component θ π ρ π - 0 + ρ lineshape a Breit-Wigner, F BW ρ ρ 0 is a vector resonance, so angular distribution follows cos θ + e iδ ρ + e iδ NR A + = a ρ + F NR + F BW cos θ + a NR ρ − e iδ ρ − e iδ NR A − = a ρ − F BW cos θ + a NR − F NR ρ | A − | 2 − | A + | 2 A CP ∝ − ) 2 − ( a ρ | 2 cos 2 θ + ... [( a ρ + ) 2 ] | F BW ∝ ρ | 2 | F NR | 2 cos θ... − 2( m 2 ρ − s ) | F BW ρ | 2 | F NR | 2 cos θ... +2 m ρ Γ ρ | F BW ρ CP violation effects in multibody B decays 7
Motivation − ) 2 − ( a ρ | 2 cos 2 θ + ... [( a ρ + ) 2 ] | F BW A CP ∝ ρ | 2 | F NR | 2 cos θ... − 2( m 2 ρ − s ) | F BW ρ | 2 | F NR | 2 cos θ... +2 m ρ Γ ρ | F BW ρ Only depends on ρ resonance, maximum difference at ρ pole, quadratic in helicity + - B 0 - B + -100 K cos θ > 0 -200 -300 θ -400 π ρ π - 0 + 0 0.5 1 1.5 2 2.5 m (GeV) π π + - low + - B 0 + - B K -100 cos < 0 θ -200 -300 θ -400 π ρ π - -500 MC 0 + -600 0 0.5 1 1.5 2 2.5 m (GeV) π + π - low Only short-distance effects can create a ρ + � = a ρ − CP violation effects in multibody B decays 8
Motivation − ) 2 − ( a ρ | 2 cos 2 θ + ... [( a ρ + ) 2 ] | F BW A CP ∝ ρ | 2 | F NR | 2 cos θ... − 2( m 2 ρ − s ) | F BW ρ | 2 | F NR | 2 cos θ... +2 m ρ Γ ρ | F BW ρ Interference term from real part of Breit-Wigner, zero at ρ pole, linear in helicity + - B 400 - B + 200 K 0 cos > 0 θ -200 θ -400 π - ρ π 0 + 0 0.5 1 1.5 2 2.5 m (GeV) π + π - low + - B 800 + - K B 600 400 200 θ 0 cos < 0 θ -200 π ρ π - MC 0 + -400 -600 0 0.5 1 1.5 2 2.5 m (GeV) π + π - low Caused by long distance effects from final state interactions CP violation effects in multibody B decays 9
Motivation − ) 2 − ( a ρ | 2 cos 2 θ + ... [( a ρ + ) 2 ] | F BW A CP ∝ ρ | 2 | F NR | 2 cos θ... − 2( m 2 ρ − s ) | F BW ρ | 2 | F NR | 2 cos θ... +2 m ρ Γ ρ | F BW ρ Interference term from imaginary part of Breit-Wigner, maximum at ρ pole, linear in helicity + - B 0 - B + -100 K cos > 0 θ -200 -300 θ -400 π - ρ π 0 + 0 0.5 1 1.5 2 2.5 m (GeV) π + π - low + - B 700 + - K B 600 500 400 300 MC θ cos < 0 θ 200 π ρ π 100 - 0 + 0 0 0.5 1 1.5 2 2.5 m (GeV) π + π - low Caused by long distance effects from Breit-Wigner phase and final state interactions CP violation effects in multibody B decays 10
Motivation Last source of strong phase 4. Final state KK ↔ ππ rescattering Can occur between decay channels with the same flavour quantum numbers eg. B ± → K ± K + K − and B ± → K ± π + π − CPT conservation constrains hadron rescattering For given quantum numbers, sum of partial widths equal for charge-conjugate decays KK ↔ ππ rescattering generates a strong phase Look into rescattering region If rescattering phase in one decay channel generates direct CP violation in this region, Rescattering phase should generate opposite sign direct CP violation in partner decay channel CP violation effects in multibody B decays 11
LHCb Detector pp collisions Forward spectrometer b quark tends to foward/backward direction Vertex Locater (VeLo) Precision tracking Tracker Turicensis (TT) Tracking, p measurement Ring Imaging Cherenkov (RICH) Particle identification Electromagnetic Calorimeter (ECAL) e , γ ID Hadronic Calorimeter (HCL) Hadronic showers Muon Detector Magnet polarity reversal Data set: 1 fb − 1 @ 7 TeV and 2 fb − 1 @ 8 TeV CP violation effects in multibody B decays 12
B ± → K ± h + h − , π ± h + h − B − → K − π + π − B + → K + π + π − B − → K − K + K − B + → K + K + K − N Sig = 181069 ± 404 (stat) N Sig = 109240 ± 354 (stat) × × 3 3 10 10 ) ) 2 2 c c 18 Candidates / (0.01 GeV/ Candidates / (0.01 GeV/ LHCb model 12 LHCb model − ± ± − ± ± + → π + π → B K B K K K 16 combinatorial combinatorial 10 14 → → B 4-body B 4-body − ± → η ρ γ ± ± → + π 0 ± B ’( )K B K K 12 8 − − ± → π + π π ± → ± π π ± + B B K Penguin 10 6 8 6 4 4 4 y 4 0 2 r - 2 a 4 × × × × 1 n 0 0 0 i 5.1 5.2 5.3 5.4 5.5 5.1 5.2 5.3 5.4 5.5 5.1 5.2 5.3 5.4 5.5 5.1 5.2 5.3 5.4 5.5 2 m - m c m c m c m c R [GeV/ 2 ] [GeV/ 2 ] [GeV/ 2 ] [GeV/ 2 ] − − − − − + − π + π π + π i + + + K K K K K K K K l E e P × × 3 3 10 10 r A P 1 ) ) P 3 2 2 c c - Candidates / (0.01 GeV/ b Candidates / (0.01 GeV/ model LHCb LHCb model − ± + → π ± C B K K ± − → π + π π ± 2.5 0.8 B combinatorial H → B 4-body combinatorial L S → B 4-body → 2 B 4-body − ± ± + → B K K K 0.6 − ± → ± π π − + ± → ± π π + B K B K 1.5 Tree 0.4 1 0.2 0.5 × × × × 0 0 5.1 5.2 5.3 5.4 5.5 5.1 5.2 5.3 5.4 5.5 5.1 5.2 5.3 5.4 5.5 5.1 5.2 5.3 5.4 5.5 m c m c m c m c 2 2 [GeV/ 2 ] [GeV/ 2 ] [GeV/ ] [GeV/ ] π π π π π π - π π - - - + - + + - + + + K K K K B − → π − π + π − B + → π + π + π − B − → π − K + K − B + → π + K + K − N Sig = 24907 ± 222 (stat) N Sig = 6161 ± 172 (stat) CP violation effects in multibody B decays 13
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