B meson key measurements at the LHC 85 LHCb Key Measurements B s - PDF document

B meson key measurements at the LHC 85 LHCb – Key Measurements B s mixing phase φ s b → s γ penguins Very rare FCNC proc. μ μ + μ B B s s B − d, s μ 0 ∗ 0 B K A CP (B s → J/ ψ φ ) B d,s → μμ B d → K* γ γ d B d → K* μμ → In addition: Measurement of the CKM angle γ in tree level decays. 86 Probing the High-energy Frontier at the LHC: Probing New Physic with B meson decays 1

Reference Measurements To proof the understanding of the detector a set of reference measurements is necessary: • Lifetime determination in B → J/ ψ ( μμ )X decays. • Measurement of the B s mixing frequency • Determination of sin(2 β ) in the “golden decay” B d → J/ ψ K s 87 Lifetime Measurement B u, B d → J/ ψ ( μμ ) X To reduce backgrounds from prompt g p p J/ ψ production exploit lifetime of “B” by applying impact parameter cut: μ J/ ψ B μ PV SV impact parameter PV = Primary Vertex SV = Secondary Vertex → Lifetime dependent acceptance! 88 Probing the High-energy Frontier at the LHC: Probing New Physic with B meson decays 2

sin(2 β ) in B 0 → J/ ψ K s for 2 fb -1 , 1 yr Time dependent CP asymmetry: = A CP ( t ) 0 → ψ − 0 → ψ N ( B J / K )( t ) N ( B J / K )( t ) s s 0 → ψ + 0 → ψ N ( B J / K )( t ) N ( B J / K )( t ) s s = φ + φ Δ sin ( ) sin( mt ) d J/ ψ K = Δ sin 2 β sin( mt ) e + e - B-factories: LHCb expectation for 2 fb -1 : ~ 200k events, B/S~0.6 sin2 β = 0.670 ± 0.023 ( ± 0.020 stat-only ) Δ (sin2 β ) stat =0.20 … 0.23 89 LHCb – Key Measurements � B s – mixing � B s mixing frequency (reference) B s mixing frequency (reference) � φ s and ΔΓ s with B 0 s → J/ ψφ � Measurement of γ � Radiative (penguin) decays • Exclusive b → s μ μ • Exclusive b → s μ + μ - 0 → μ + μ - • B s 90 Probing the High-energy Frontier at the LHC: Probing New Physic with B meson decays 3

B s – mixing: amplitude and phase Access to the 2 nd A h 2 d Unitarity Triangle 91 2 nd Unitarity triangle ⎛ V V V ⎞ ud us ub ⎜ ⎟ = V V V V ⎜ ⎟ cd cs cb ⎜ ⎜ ⎟ ⎟ V V V ⎝ ⎠ td ts tb ∗ ∗ ∗ + + = V V V V V V 0 „bd“ λ 3 O ( ) ud ub cd cb td tb λ 3 ρ + η − λ 3 + λ 3 − ρ − η = A ( i ) A A ( 1 i ) 0 ∗ ∗ ∗ + + = V V V V V V 0 „tu“ ud td us ts ub tb λ 3 − ρ − η − λ 3 + λ 3 ρ + η = A ( 1 i ) A A ( i ) 0 Same triangle ! 92 Probing the High-energy Frontier at the LHC: Probing New Physic with B meson decays 4

Two different triangles in O( λ 5 ) „tu“ „bd“ ∗ ∗ ∗ ∗ ∗ ∗ + + = + + = V V V V V V 0 V V V V V V 0 ud ub cd cb td tb ud td us ts ub tb λ 3 ρ ρ + η η − λ 3 + λ 3 − ρ ρ − η η = A ( ( i ) ) A A ( ( 1 i ) ) 0 λ λ 3 − ρ ρ − η η − λ λ 3 + + λ λ 3 ρ ρ + + η η = A A ( ( 1 1 i i ) ) A A A A ( ( i i ) ) 0 0 1 1 1 1 − λ 5 ρ + η + λ 5 ρ + η A ( i ) A ( i ) − λ 5 − ρ + η + λ 5 − ρ + η A ( ( i )) A ( ( i )) 2 2 2 2 + λ 7 O ( ) + λ 7 O ( ) * V V Im ud ub Im * V V cd cb η η * V V λ + 2 td tb α α − ρλ ρ 2 α α 1 * V V cd V V 2 2 cb ηλ 2 β′ γ β γ′ Δγ Re Re ρ 0 ρ 0 1 1 ∗ V V λ 2 λ 2 us ts β s = γ − γ ′ = β ′ − β ≈ η = η ⋅ − 0 . ( 1 ) ρ = ρ ⋅ − ( 1 ) 02 λ 3 A 2 2 Very small in SM 93 B s Mixing Phenomenology ∗ V V ts tb ⎛ ⎞ i i b s t ⎜ − Γ * − Γ * ⎟ m m ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ d B B B 0 0 0 0 11 11 12 12 0 B B ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ s = s = 2 2 s i H s s ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ i i dt dt ⎜ ⎜ ⎟ ⎟ B B 0 B B 0 B B 0 ⎝ ⎝ ⎠ ⎠ ⎝ ⎝ ⎠ ⎠ ⎝ ⎝ ⎠ ⎠ b b s s t t − Γ Γ − Γ Γ ⎜ ⎜ m m ⎟ ⎟ s s s ⎝ ⎠ 12 12 22 22 2 2 ∗ V V tb ts Δ − ΔΓ ⎛ i m i / 2 ⎞ Δ = − m m m + φ − Γ − i ⎜ m e ⎟ s H L 2 2 ⎜ ⎟ = ΔΓ = Γ − Γ H Δ − ΔΓ m i / 2 i H L ⎜ ⎟ − φ − i − Γ e m ⎜ ⎟ s q q ⎝ ⎠ 2 2 − i φ = = 1 or e s p p (if CPV in mixing is ignored) B d B s Δ m=m H -m L 0.5 ps -1 17.8 ps -1 In SM ΔΓ = Γ H - Γ L O(0.01)· Γ d O(0.1)· Γ s small: ∗ ∗ ) = β φ s,d = β arg( V tb V arg( V tb V ) 2 2 td ts s 0.04 94 Probing the High-energy Frontier at the LHC: Probing New Physic with B meson decays 5

B s Mixing Measurement Signal B K - (flavor specific decay) K + - π + B s → D s π - D s - + π - B s → D s B s π + PV B flavor tagging B − N ( B ) ( t ) N ( B ) ( t ) ( ) = Δ unmixed mixed A ( t ) ~ sin m t mix + s N ( B ) ( t ) N ( B ) ( t ) unmixed mixed 95 Necessary Tool: B Flavor Tagging π + Signal B (same side tagging) π − B 0 • Fragmentation kaon near B s B 0 Tagging B (opposite tagging) D Dilution • lepton l t form K - • kaon oscillation + l if B 0 • Vertex charge b B s Mistag rate s b Tag ε Tag (%) w (%) ε eff (%) s Κ + u Muon Muon 11 11 35 35 1.0 1.0 u Electron 5 36 0.4 Kaon 17 31 2.4 Vertex Charge 24 40 1.0 Dilution D=(1-2 w ) Frag. kaon (B s ) 18 33 2.1 Effective Tagging Power Combined B 0 (decay dependent: ~4 ε eff = ε Tag D 2 Combined B s trigger + select.) ~6 96 Probing the High-energy Frontier at the LHC: Probing New Physic with B meson decays 6

Effect of mistag rate on mixing − N ( B )( t ) N ( B )( t ) = ) = B ( t B 0 = A ( t ) + N ( B )( t ) N ( B )( t ) ω ω Observed asymmetry w/ wrong tag fraction Observed asymmetry w/ wrong tag fraction ′ ′ − N ( B )( t ) N ( B )( t ) = A meas ( t ) ′ ′ + N ( B )( t ) N ( B )( t ) − ω + ω − − ω − ω N ( B )( t )( 1 ) N ( B )( t ) N ( B )( t )( 1 ) N ( B )( t ) = − ω + ω + − ω + ω N ( B )( t )( 1 ) N ( B )( t ) N ( B )( t )( 1 ) N ( B )( t ) − N N ( ( B B )( )( t t ) ) N N ( ( B B )( )( t t ) ) = − ω = − ω = ( 1 2 ) ( 1 2 ) A ( t ) D A ( t ) − N ( B )( t ) N ( B )( t ) ′ ′ N ( B ), N ( B ) Observed number of events of given flavor = − ω D ( 1 2 ) ω =50% → D=0 Tagging “dilution”: no measurement possible Dilution ω × (1-2 ω ) Probing the High-energy Frontier at the LHC: Probing New Physic with B meson decays 7

Sensitivity and Tagging Power = N qN , B − N ( B ) N ( B ) = − = = N ( 1 q ) N pN A Statistical error of asymmetry B + N ( B ) N ( B ) N = B q N = + + N N N N ( ( B B ) ) N N ( ( B B ) ) fixed fixed T t l Total event number t b σ 2 = − ( qN ) N ( 1 q ) q Statistical error calculated according binominal distribution (A or notA): 1 2 ) 1 / 2 Δ = − A ( 1 A N 1 Δ = − 2 ) 1 / 2 A ( 1 ( A ) meas meas ε N → → ′ = = ε ε N N N N N N Tagging efficiency: Tagging efficiency: A meas = D A 1 Wrong tag fraction: Δ A stat ~ ε 2 D N 1 We are interested in A and Δ = Δ A A meas therefore also in the error of A D = effective tagging power B s Mixing B s → D s π Perfect reconstruction Perfect reconstruction Perfect reconstruction Perfect reconstruction Perfect reconstruction B s oscillates about 26 times until it decays: 1000 1000 1000 + flavour tagging + flavour tagging 1000 1000 + flavour tagging + flavour tagging need excellent proper time resolution to + proper time resolution + proper time resolution + proper time resolution resolve the mixing (LHCb ~40 fs) + background 800 800 800 + background 800 800 800 + acceptance + acceptance Observation of B s mixing is basis for time dependent CP asymmetry measurements. Events Events Events 600 600 Events 600 Events 600 2 fb -1 (1 yr) of data 600 Δ m s =20 ps -1 400 400 400 400 400 200 200 200 200 200 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 0 1 2 3 4 5 0 1 2 3 4 5 Proper time (ps) Proper time (ps) Proper time (ps) Proper time (ps) Proper time (ps) CDF: LHCb expects 80k B s → D s π events in 1 yr ± ± . ( stat. ) . ( syst. ) ps -1 0 10 0 07 100 Probing the High-energy Frontier at the LHC: Probing New Physic with B meson decays 8