Charm CP violation & mixing Mat Charles (Oxford & UPMC) !
Overview YES NO Interested in charm? You’ll be You heard this bored by this already at talk CHARM 2013 Take a nap 2 !
Overview • Mixing & time-dependent searches for indirect CPV • Time-integrated searches for direct CPV 3 !
Mixing & indirect CPV • Old news: • LHCb & CDF measurements of mixing in D 0 → K + π − (WS) • BABAR & Belle measurements of mixing & CPV in D 0 → h + h − • New news: • LHCb measurement of CPV in D 0 → h + h − • LHCb measurement of mixing & CPV in D 0 → K + π − (WS) • Belle measurement of mixing & CPV in D 0 → K S h + h − 4 !
Standard mixing formalism Mixing occurs for neutral mesons M 0 = K 0 , D 0 , B 0 , B s0 Decompose into mass eigenstates |M 1,2 〉 : n | q | 2 + | p | 2 = 1 a ! " for ! ! " ! # " ! " ! ! ! " # # ! ! ! ! " ! # " $ # " ! % ! " $ # ! ! " ! " % ! ! " $ #& % ! ! " ! # " $ ! $# " ... and we can invert to get |M 0 (t) 〉 given m 1,2 , ! 1,2 , q/p... General time evolution: 1 � ⇥ e � i ( m 1 � i 2 Γ 1 ) t ( p | M ⇧ + q | M ⇧ ) + e � i ( m 2 � i 2 Γ 2 ) t ( p | M ⇧ � q | M ⇧ ) | M ( t ) ⇧ = 2 p 1 � ⇥ e � i ( m 1 � i 2 Γ 1 ) t ( p | M ⇧ + q | M ⇧ ) � e � i ( m 2 � i 2 Γ 2 ) t ( p | M ⇧ � q | M ⇧ ) | M ( t ) ⇧ = 2 q 5 !
Cartoon of mixing ! " For convenience, define: " x = m 1 − m 2 $ ! " " # " # " ! " " $ " # # #" # Γ R M = x 2 + y 2 # and 2 #$% #$!% !$ ! ! ! ! ! % % & "! " &$%'( &$% # & " !$ ! ! ! ! ! % % & "! " ! ! ! ! % % & "! " !$ ! ! ! ! ! % % & "! " !$ ! 6 !
Mixing in charmed mesons Charm mixing small compared to other mesons in SM: Mixing via box diagram Mixing via hadronic intermediate states (short-range) (long-range) K + K − D 0 π + π − π 0 D 0 D 0 D 0 π + π − K + π − etc Contributes mainly to x Non-perturbative; hard to predict SM contribution. Intermediate b: CKM-suppressed Currently: |x| ≤ 0.01, |y| ≤ 0.01 – less tiny! Intermediate d,s: GIM-suppressed " " # # # ! # # # " $ # " ! !" ! " e.g. PRD 69,114021 (Falk, Grossman, Ligeti, Nir & Petrov) # # # Tiny! 7 !
CP violation Direct • 3 types of CP violation: • In decay: amplitudes for a process and its conjugate differ Indirect • In mixing: rate of D 0 → D 0 and D 0 → D 0 differ • In interference between mixing and decay diagrams • In the SM, indirect CP violation in charm is expected to be very small and universal between CP eigenstates • Perhaps O(10 − 3 ) for CPV parameters => O(10 − 5 ) for observables like A Γ • Direct CP violation can be larger in SM, very dependent on final state (therefore we must search wherever we can) • Negligible in Cabibbo-favoured modes (SM tree dominates everything) • In generic singly-Cabibbo-suppressed modes: up to O(10 − 3 ) plausible • Both can be enhanced by NP , in principle up to O(%) Bianco, Fabbri, Benson & Bigi, Riv. Nuovo. Cim 26N7 (2003) Bobrowski, Lenz, Riedl & Rorhwild, JHEP 03 009 (2010) Grossman, Kagan & Nir, PRD 75, 036008 (2007) Bigi, Blanke, Buras & Recksiegel, JHEP 0907 097 (2009) Bigi, arXiv:0907.2950 CPV in charm not yet discovered 8 !
Mixing and indirect CPV • D 0 mesons undergo mixing like K 0 , B 0 , B s0 • But unlike the others, D 0 mixing is small. • Mixing parameters x, y order of 10 − 2 • First seen by BABAR & Belle in 2007 • Now well-established: multiple results exclude no-mixing hypothesis by > 5 σ • Smallness of mixing parameters makes CP asymmetries doubly small, e.g. CP-violating terms < 10 − 2 in SM 2 A Γ = ( | q/p | − | p/q | ) y cos φ − ( | q/p | + | p/q | ) x sin φ (neglecting direct CPV) Mixing parameters O(10 − 2 ) Observable asymmetry < 10 − 4 in SM 9 !
Mixing via CP eigenstates D 0 → K − π + : Mixture of CP states y CP = τ ( K − π + ) Define τ ( K + K − ) − 1 D 0 → K − K + : CP-even eigenstate y CP related to y and CP parameters by: h y CP = y cos φ − 1 2 A M x sin φ A M ≠ 0: CPV in mixing (asymmetry in R M between D 0 and D 0 ) cos ϕ≠ 1: CPV in interference between mixing and decay CP observable A Γ defined as: 0 → K − K + ) − τ ( D 0 → K − K + ) A Γ = τ ( D 0 → K − K + ) + τ ( D 0 → K − K + ) τ ( D 2 A Γ = ( | q/p | − | p/q | ) y cos φ − ( | q/p | + | p/q | ) x sin φ (neglecting direct CPV) 10 !
BABAR & Belle measurements τ D PDG (±1 σ region) PRD 87, 012004 (2013) 468 fb -1 Phys. Rev. D 87, 012004 (2013) � � ‣ no mixing hypothesis excluded at 3.3 σ level ‣ no CPV observed � � � � � = (+1 . 11 ± 0 . 22 ± 0 . 11)% y CP Be 977 fb − 1 preliminary A Γ = ( − 0 . 03 ± 0 . 20 ± 0 . 08)% arXiv:1212.3478 11 ! � � � � � � �
New LHCb measurement • New result at CHARM on 2011 data (1fb − 1 ) • Uses two complementary methods: • Multidimensional fit to { m(h + h − ), Δ m, t, ln(IP χ 2 ) } floating A Γ directly • Divide into bins of t, fit D 0 /D ̅ 0 ratio in each bin separately • First method is more sophisticated (uses swimming) and ultimately has better precision -- but more moving parts • Second method simpler ) 2 Data c 4 10 Entries / (0.02 MeV/ LHCb Fit Signal 1fb − 1 preliminary Rnd. π s - 0 + 0 D K → π π - + + + D K K → π s Comb. bkg A Γ ( K + K − ) = ( − 0 . 35 ± 0 . 62 ± 0 . 12) × 10 − 3 3 10 A Γ ( π + π − ) = (+0 . 33 ± 1 . 06 ± 0 . 14) × 10 − 3 1fb − 1 preliminary 2 10 No sign of indirect 5 2 KK deltam [MeV/c ] CPV in this analysis. Pull 0 -5 140 145 150 2 m [MeV/ c ] Δ LHCB-PAPER-2013-054-001 12 !
Mixing via wrong-sign decays DCS K + π − D 0 δ: strong phase between DCS and CF amplitudes MIX CF D 0 ! ' " #$ % (+ % * ' # ! ! ' ! ! ! "#$% ' ! ! & + ! " ( % * ! & " " # (+ % * ! ' $ ' $ , " #$ % [Limit of |x| ≪ 1, |y| ≪ 1, and no CPV.] 234 8%)(".("(%/( 7#A#%B ! • D 0 → K + π − simplest, but can also use K ππ 0 , K πππ , etc • different strong phases; also coherence term for multi-body final states 13 !
Recent LHCb & CDF mixing results • Divide data into bins of time • Fit D 0 /D ̅ 0 ratio in each bin separately • Beautiful, clean method -- v. robust against systematics -3 -1 10 CDF Run II preliminary L= 9.6 fb × -1 3 -1 9 CDF Run II preliminary L= 9.6 fb CDF Run II preliminary L= 9.6 fb × 10 m 2 R 2 per 0.5 MeV/c Data per 0.5 MeV/c 2500 Data Data 8 35000 Mixing fit Fit total Fit total No-mixing fit D* signal 30000 D* signal 2000 7 Background Background Prompt fit projection 25000 6 0 0 1500 D D 20000 5 15000 1000 10000 4 500 5000 3 0 0 0 0.005 0.01 0.015 0.02 0.025 0.03 0 0.005 0.01 0.015 0.02 0.025 0.03 0 2 4 6 8 10 2 2 Right-Sign M [GeV/c ] Wrong-Sign M [GeV/c ] � � t/ τ y 0 (10 � 3 ) x 0 2 (10 � 3 ) R D (10 � 3 ) Expt. σ no mixing (preliminary) 3 . 51 ± 0 . 35 4 . 3 ± 4 . 3 0 . 08 ± 0 . 18 CDF (now) 6.1 0.6 +4 . 0 0.18 +0 . 21 3.64 ± 0.17 Belle [11] 2.0 � 3 . 9 � 0 . 23 B A B AR [2] 3.03 ± 0.19 9.7 ± 5.4 − 0 . 22 ± 0.37 3.9 CDF [4] 3.04 ± 0.55 8.5 ± 7.6 -0.12 ± 0.35 3.8 3.52 ± 0.15 7.2 ± 2.4 -0.09 ± 0.13 LHCb [6] 9.1 LHCb: PRL 110, 101802 (2013) 14 CDF Note 10990 !
Brand new LHCb result • New at CHARM: full 2011+2012 prompt D *+ sample (3/fb) • Adds CPV search (fit D *+ , D * − separately) No CP violation 3 6 10 10 × × R D [10 � 3 ] 3 . 568 ± 0 . 058 ± 0 . 033 ) ) 60 2 2 3 y 0 [10 � 3 ] RS 2012 TOS c c 4 . 81 ± 0 . 85 ± 0 . 53 LHCb Data Candidates/(0.1 MeV/ Candidates/(0.1 MeV/ LHCb x 0 2 [10 � 5 ] Fit 5 . 5 ± 4 . 2 ± 2 . 6 50 Fit 2.5 Background χ 2 / ndf 87 . 45 / 101 Background 40 2 No direct CP violation R D [10 � 3 ] 3 . 568 ± 0 . 058 ± 0 . 033 30 1.5 y 0 + [10 � 3 ] 4 . 46 ± 0 . 89 ± 0 . 57 x 0 2+ [10 � 5 ] 20 1 7 . 7 ± 4 . 6 ± 2 . 9 y 0� [10 � 3 ] 5 . 17 ± 0 . 89 ± 0 . 58 10 0.5 x 0 2 � [10 � 5 ] 3 . 2 ± 4 . 7 ± 3 . 0 χ 2 / ndf 86 . 32 / 99 0 0 2.005 2.01 2.015 2.02 2.005 2.01 2.015 2.02 Direct and indirect CP violation 0 0 + + M ( D ) [GeV/ c 2 ] 2 π M ( D ) [GeV/ c ] π s s R D [10 � 3 ] 3 . 568 ± 0 . 058 ± 0 . 033 A D [10 � 2 ] − 1 . 3 ± 1 . 6 ± 0 . 9 y 0 + [10 � 3 ] 10 10 5 . 1 ± 1 . 2 ± 0 . 7 10 LHCb CPV allowed No direct CPV No CPV x 0 2+ [10 � 5 ] 4 . 9 ± 6 . 0 ± 3 . 6 y 0� [10 � 3 ] 4 . 5 ± 1 . 2 ± 0 . 7 ] x 0 2 � [10 � 5 ] -3 6 . 0 ± 5 . 8 ± 3 . 6 [10 5 5 5 χ 2 / ndf 85 . 87 / 98 y' 99.7% C.L. No sign of indirect 2 2 − − − − ( x' , y' ) 68.27% C.L. ( x' , y' ) 68.3% C.L. 95.5% C.L. 2+ + 2+ + ( x' , y' ) 68.27% C.L. ( x' , y' ) 68.3% C.L. 68.3% C.L. 0 0 0 CPV in this analysis. -0.2 0 0.2 -0.2 0 0.2 -0.2 0 0.2 -3 2 x' [10 ] 15 LHCb-PAPER-2013-053 (preliminary) [10 !
New HFAG averages CPV-allowed plot, no mixing (x,y) = (0,0) point: Δ χ 2 > 300 No CPV (|q/p|, φ ) = (1,0) point: Δ χ 2 = 1.479, CL = 0.48 , consistent with no CPV Alan Schwartz, CHARM 2013 16 !
Before & after CHARM Last week Now Same scale for both plots. New LHCb results greatly shrink allowed region. 17 !
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