Probing CP violation systematically in differential distributions

Transcription

1 Probing CP violation systematically in differential distributions Gauthier Durieux (DESY Hamburg) Phys.Rev. D9 (15) 7613, [ ] with Yuval Grossman (Cornell) 5 November 15 LHCb implications workshop

2 1 Multibody hadronic decays 1. Large statistics B K + K K ± π 17 candidates [ ] Bs K + K K + K 4 [147.] D K + K π + π 17 [ ] Bs K + π K π + 7 [ ].... Multidimensional phase space Candidates / (11.7 MeV/c ) D (C >) D (C <) (a) m(π + π ) [GeV/c ] D (-C >) D (-C <) LHCb (b) m(π + π ) [GeV/c ] Candidates / (13. MeV/c ) D (C >) D (C <) (c) m(k K ) [GeV/c ] LHCb D (-C >) D (-C <) (d) m(k K ) [GeV/c ] Candidates / D (C >) D (C <) (a) D (-C >) D (-C <) LHCb cos(θ ) K cos(θ K ) (b) Candidates / D (C >) D (C <) (c) D (-C >) D (-C <) LHCb cos(θ π) cos(θ π) (d) Candidates / (.5 rad) D (C >) D (C <) (e) 1 3 Φ [rad] D (-C >) D (-C <) LHCb (f) 1 3 Φ [rad]

3 Multibody hadronic decays 3. Rich variety of interfering contributions Intermediate states in D K + K π + π Br /1 4 (φρ ) S, φ K + K, ρ π + π 9.3 ± 1. D.83 ±.3 (K K ) S, K K ± π 1.48 ±.3 φ(π + π ) S, φ K + K.5 ±.33 (K π + ) P (K + π ) S.6 ±.5 K + 1 K, K + 1 K π ±.5 K 1 K +, K 1 K π. ±.1 K + 1 K, K + 1 ρ K ±.6 K 1 K +, K 1 ρ K 1.46 ±.5 K (141) + K, K (141) + K π + 1. ±.6 K (141) K +, K (141) K π 1.14 ±.5 = Opportunities for CP violation [CLEO 1]

4 Probing CP violation systematically in differential distributions CP-violating distributions With or without strong phases In untagged samples Systematic analysis techniques

5 1 Differential CP violation Compare the CP-conjugate amplitudes (squared) M({ p i }) and M({ p ī}) p ī= p i phase-space point by phase-space point (spinless case). Contributions of definite strong and weak phases ˆ transformation properties M({ p i }) = +a({ p i }) e i(δa+ϕa) +b({ p i }) e i(δ b+ϕ b ) +c({ p i }) e i(δc+[ϕc+π/]) +... M({ p i }) = +a({ p i }) e i(δa ϕa) +b({ p i }) e i(δ b ϕ b ) +c({ p i }) e i(δc [ϕc+π/]) +... where ˆ is motion reversal (flips p and σ).

6 1 Differential CP violation Compare the CP-conjugate amplitudes (squared) M({ p i }) and M({ p ī}) p ī= p i phase-space point by phase-space point (spinless case). Contributions of definite strong and weak phases ˆ transformation properties M({ p i }) = +a({ p i }) e i(δa+ϕa) +b({ p i }) e i(δ b+ϕ b ) +c({ p i }) e i(δc+[ϕc+π/]) +... M({ p i }) = +a({+ p i }) e i(δa ϕa) +b({+ p i }) e i(δ b ϕ b ) c({+ p i }) e i(δc [ϕc+π/]) +... where ˆ is motion reversal (flips p and σ).

7 1 Differential CP violation Compare the CP-conjugate amplitudes (squared) M({ p i }) and M({ p ī}) p ī= p i phase-space point by phase-space point (spinless case). Contributions of definite strong and weak phases ˆ transformation properties M({ p i }) = +a({ p i }) e i(δa+ϕa) +b({ p i }) e i(δ b+ϕ b ) +c({ p i }) e i(δc+[ϕc+π/]) +... M({ p i }) = +a({+ p i }) e i(δa ϕa) +b({+ p i }) e i(δ b ϕ b ) +c({+ p i }) e i(δc ϕc+π/) +... where ˆ is motion reversal (flips p and σ).

8 riple products ˆ oddity arises from antisymmetric ɛ µνρσ p µ q ν r ρ s σ contractions of four independent momenta or spin vectors. in the Lagrangian: i F µν i ɛ µνρσf ρσ in the presence of chiral fermions: γ 5 i 4! ɛ µνρσγ µ γ ν γ ρ γ σ In the p restframe, ɛ µνρσ p µ q ν r ρ s σ = p q ( r s) is a scalar triple product. ˆ-odd quantities are referred to as triple products.

9 3 CP violation and strong phases Distributions of definite CP and ˆ transformation properties d{ p i} d{ p i} d{ p i} d{ p i} ˆ-even CP-even ˆ-even ˆ-odd ˆ-odd CP-even d{ p i } ˆ- even odd CP- even odd a a + b b + c c I ± ˆ I ± CP + a b cos(δ a δ b ) cos(ϕ a ϕ b ) a b sin(δ a δ b ) sin(ϕ a ϕ b ) a c cos(δ a δ c) sin(ϕ a ϕ c) + b c cos(δ b δ c) sin(ϕ b ϕ c) a c sin(δ a δ c) cos(ϕ a ϕ c) + b c sin(δ b δ c) cos(ϕ b ϕ c) d{ p i }

10 4 CP-violating distributions D K + K π + π Candidates / (13. MeV/c ) Candidates / (13. MeV/c ) 1 9 (c) 8 D (C >) 7 6 D (C <) (c) m(k K ) [GeV/c ] 9 (d) (c) LHCb 18 D (C >) 16 D (-C (C >) D (C <) D (-C (C <) Candidates / (.5 rad) LHCb Candidates / (.5 rad) D (C >) (d) D (-C >) D (C <) D (-C <) [ ] m(k K ) [GeV/c (d) ] Φ [rad] LHCb (e) 18 (f) (e) D (-C (C >) LHCb D (-C >) 16 D (-C >) D (-C (C D (-C <) <) D (-C <) Candidates / (.5 rad) (e) D (-C >) D (-C <) D (C >) D (C <) m(k K ) [GeV/c ] m(k K ) [GeV/c ] Φ [rad] m(k K ) [GeV/c ] Φ [rad] 1

11 CP-violating distributions D K + K π + π events/13. MeV ˆ-even CP-even /1 ˆ-odd CP-even events/ π 63 rad ˆ-even CP-even ˆ-odd CP-even events/13. MeV ˆ-even events/ π 63 rad ˆ-even events/13. MeV ˆ-odd mkk [GeV] events/ π 63 rad ˆ-odd π 4 π φ [rad] 3π 4 π 4

12 Probing CP violation systematically in differential distributions CP-violating distributions With or without strong phases In untagged samples Systematic analysis techniques

13 5 CP violation and untagged samples agging CP conjugate processes may cost efficiency. An untagged sample [as in ] e.g. Bs K + (+ p 1 ) π (+ p ) K (+ p 3 ) π + (+ p 4 ) B s K ( p 1 ) π + ( p ) K + ( p 3 ) π ( p 4 ) I + CP d{ p i }

14 5 CP violation and untagged samples agging CP conjugate processes may cost efficiency. An untagged sample [as in ] e.g. Bs K + (+ p 1 ) π (+ p ) K (+ p 3 ) π + (+ p 4 ) B s K (+ p 1 ) π + (+ p ) K + (+ p 3 ) π (+ p 4 ) I + CPˆ d{ p i }

15 5 CP violation and untagged samples agging CP conjugate processes may cost efficiency. An untagged sample [as in ] e.g. Bs K + (+ p 1 ) π (+ p ) K (+ p 3 ) π + (+ p 4 ) B s K (+ p 3 ) π + (+ p 4 ) K + (+ p 1 ) π (+ p ) I + CPˆE d{ p i }

16 5 CP violation and untagged samples agging CP conjugate processes may cost efficiency. An untagged sample [as in ] e.g. Bs K + (+ p 1 ) π (+ p ) K (+ p 3 ) π + (+ p 4 ) B s K (+ p 3 ) π + (+ p 4 ) K + (+ p 1 ) π (+ p ) I + CPˆE d{ p i } has two distributions, of opposite ˆ and E parities I ± ˆ I E ( I + CPˆE ) d{ p i} = I ± ˆ I E I CP d{ p i}

17 CP violation and untagged samples D K + K π + π [ ] events/ ˆ-odd E -odd CP-even ˆ-even E -even /1 CP-even events/ ˆ-odd E -odd CP-even ˆ-even E -even /1 CP-even ˆ-even E -odd 4 ˆ-even E -odd events/.4 events/ ˆ-odd E -even 4 ˆ-odd E -even events/.4 events/ cos θ K + cos θ π + 6

18 Probing CP violation systematically in differential distributions CP-violating distributions With or without strong phases In untagged samples Systematic analysis techniques

19 7 Analysis techniques Based on phenomenological parametrisations Full unbinned likelyhood fits Measurement of expected asymmetries may miss unexpected manifestations of CP violation More systematic, relying some milder dynamical assumptions Phase-space binnings [ ] Decomposition in moments [Dighe et al 98, Beaujean et al 15, Gratrex et al 15] Series of asymmetries i.e. integrated observables d{ p i } f({ p i }) d{ p i } ˆ-odd

20 8 4 6 Systematic analysis techniques D K + K π + π events/ π 63 rad ˆ-odd 16 1.σ 6 π 4 π φ [rad] 3π 4 π n 8.6σ 4.σ A n ˆ-odd d{ p i } sign{sin nφ} d{ p i }

21 Generalized triple-product asymmetries 1. Fix a phase-space parametrisation 4 θ b b 3 φ a. Angular asymmetries from partial-wave expansion For spinless external particles: M = 4π A ja,j b λ (m a, mb) Yj λ a (θ a, φ) Yj λ b (θ b, ) j a,j b,λ 3. he invariant masses can also induce change of signs { } 1 ma M R ma M = + iγm (ma M ) + Γ M { d{ p i} sign f l ( cθ a ) f m( cθ b ) sin nφ } (ma Mi ) (mb Mj ) d{ p i} i j 1 θ a ˆ-odd 9

22 Probing CP violation systematically in differential distributions High statistics allows for the accurate measurement of rich multidimensional differential distributions. Symmetries characterize distributions measurable in the presence or absence of strong phases, in untagged samples. Systematic procedures should be used to assess the departure from zero of CP-violating ones. [Phys.Rev. D9 (15) 7613]