D 0 -mixing and CP Violation in Charm at Belle

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1 D 0 -mixing and CP Violation in Charm at Belle Marko Starič Belle collaboration Jožef Stefan Institute, Ljubljana Xth Rencontres du Vietnam M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

2 Outline Introduction Updates of D 0 -mixing with our final data set ( 1 ab 1 ) D 0 K + π D 0 K + K, π + π D 0 K 0 s π + π Time-integrated CPV searches D 0 π 0 π 0 (latest one) many more... Conclusions M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

3 D 0 D 0 mixing Mass eigenstates differ from flavor eigenstates D 0 1,2 = p D0 ± q D 0 D 0 1,2 with masses m 1, m 2 and partial widths Γ 1, Γ 2 Mixing parameters: x = m Γ y = Γ 2Γ Time dependent decay rates of D 0 f (since mixing is small): dn D 0 f dt e Γt f H D 0 + q p + ix (y Γt) f H D exponential time dependency modulated with x and y, and q/p modulation is final state dependent different final states sensitive to different combinations of x and y M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

4 CP violation dn D 0 f dt e Γt f H D 0 + q p ( y+ix 2 Γt) f H D0 2 q/p 1 indirect CP violation q/p = q/p e iφ : q/p 1 CP violation in mixing φ 0(π) CP violation in interference of decays w/ and w/o mixing A(D 0 f ) 2 A( D 0 f ) 2 direct CP violation Experimental techniques Time-dependent analysis: difference in proper decay time distributions of D 0 f and D 0 f measure indirect CPV Time-integrated analysis: difference in time-integrated decay rates of D 0 f and D 0 f measure direct+indirect CPV M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

5 Experimental method at B-factories Usually using D + D 0 π + slow flavor tagging by π slow charge background suppression Observables: D 0 invariant mass: M m(kπ) D + mass difference: M m(kππ slow ) m(kπ) or Q M m π Measurements performed mainly at Υ(4S) D + from B decays can be completely rejected with π K pd CMS + > 2.5 GeV /c D 0 proper decay time measurement: t = l dec cβγ, βγ = p D 0 M D 0 π s D 0 ldec fit D 0 decay vtx e - D * Beamspot e + extrapolate production vtx M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

6 Wrong sign decays D 0 K + π (976 fb 1 ) PRL 112, (2014) Wrong sign (WS) final state: via DCS decays or via mixing D 0 MIX DCSD D 0 CF K + π Proper decay time distribution RS events Γ WS [R D +y R D (t/τ)+ x 2 + y 2 (t/τ) 2 ]e t/τ 4 WS events DCS interference mixing R D ratio of DCS/CF decay rates x = x cos δ + y sin δ y = y cos δ x sin δ δ strong phase between DCS and CF M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

7 D 0 K + π : Method Fit of WS to RS decay rate ratio in bins of measured proper decay time t WS to RS ratio R(t) = ΓWS (t )R(t t )dt ΓRS (t )R(t t )dt WS and RS signal yields in bins of t determined from fit to M distributions Resolution function parameterized as a sum of four Gaussians RS time distribution R(t) = 4 f i G i (t; µ i, σ i ), i=1 µ i = µ 1 + aσ i Parameters f i, µ 1, a, σ i determined from fit to sideband subtracted RS time distribution τ = (408.5 ± 0.9) fs consistent with W.A. M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

8 D 0 K + π : Results systematics less that 1/10 of statistical error Best fit point and 1, 3, 5 σ contours no-mixing point at 5.1σ observation of D 0 mixing M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

9 Decays to CP states D 0 K + K, π + π (976 fb 1 ) Measurement of lifetime difference between flavor specific and decays into CP final states choice of flavor specific: kinematically similar D 0 K π + Timing distributions are exponential mixing parameter: y CP = τ(k π + ) τ(k + K ) 1 y CP = y, if CP conserved If CP violated difference in lifetimes of D 0 /D 0 K + K, π + π asymmetry in lifetimes: A Γ = τ(d0 K K + ) τ(d 0 K + K ) τ(d 0 K K + )+τ(d 0 K + K ) If direct CPV negligible: y CP = y cos φ 1 2 A Mx sin φ A Γ = 1 2 A My cos φ x sin φ A M = 2( q/p 1) M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

10 D 0 K + K, π + π : Method Simultaneous binned maximum likelihood fit of KK, Kπ and ππ performed in bins of cosθ, than weighted average to obtain y CP, A Γ Background estimated from sidebands in M parameterized with two lifetime components (zero and non-zero τ) Resolution function: decay mode, run period, cosθ dependent χ 2 /ndf= 792.9/684 (CL= 0.2%) KK (+) KK (-) Kπ ππ (+) ππ (-) t (bins) M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

11 D 0 K + K, π + π : Results (preliminary) arxiv: (2012) y CP = (+1.11 ± 0.22 ± 0.11)% A Γ = ( 0.03 ± 0.20 ± 0.08)% 4.5σ evidence consistent with zero events/bin events/bin D 0 K + K -,π + π - D 0 K - π + divide distributions (N KK +N ππ )/N Kπ Belle preliminary (976 fb -1 ) t (fs) t (fs) M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

12 Self-conjugate decays: D 0 K 0 s π + π (921 fb 1 ) PRD 89, (R) (2014) This three body decay proceeds via many intermediate states, like CF: D 0 K π + DCS: D 0 K + π CP: D 0 ρ 0 Ks 0 Matrix element is Dalitz space dependent, so also time distribution is dn D 0 f dt e Γt A(m 2, m 2 +) + q p + ix (y Γt)A(m 2 2, m+) 2 2 Total amplitude A parametrized as a sum of quasi two-body amplitudes of resonances A r A(m 2, m 2 +) = r a r e iφr A r (m 2, m 2 +) Both mixing parameters, x and y as well as CPV parameters φ and q/p can be measured Requires 3D fit in (m 2, m 2 +, t); many free parameters M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

13 D 0 K 0 s π + π : Method Unbinned maximum likelihood fit in 3D Dalitz model with 16 resonances Background estimated from sidebans combinatorial: M-sideband random π slow : Q-sideband Resolution function: 3 Gaussians M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

14 D 0 K 0 s π + π : Results error order: statistics, systematics, Dalitz model τ = (410.3 ± 0.6) fs consistent with W.A. Best fit point, 68.3% and 95% contours no-mixing point at 2.5σ no evidence for CPV M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

15 Time-integrated measurements (A CP ) Asymmetry in time-integrated decay rates of D 0 f and D 0 f A f CP = Γ(D0 f ) Γ(D 0 f ) Γ(D 0 f )+Γ(D 0 f ) Raw asymmetry A raw = N N N+N = A D + A f ɛ + A f CP A D production asymmetry A f ɛ asymmetry in efficiencies Production asymmetry at B-factory odd function of CMS polar angle A D A FB (cosθ ) can easily be disentangled A CP = Acor raw (cosθ )+A cor raw ( cosθ ) 2 A FB = Acor raw (cosθ ) A cor raw ( cosθ ) 2 M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

16 Detection asymmetries A f ɛ Asymmetries in detection efficiencies can be measured with sufficient precision using CF decays (CPV is very unlikely) must be performed in bins of relevant phase-spaces requires production asymmetries to be known at B-factory: A D A FB (cosθ ) Slow pions: from tagged and untagged D 0 K π + decays Kaons: from decays D 0 K π + and D + s φπ + Pions: from decays D + K π + π + and D 0 K π + π 0 Slow pion asymmetry Kaon asymmetry M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

17 A CP in D 0 π 0 π 0 and D 0 K 0 S π0 (966 fb 1 ) PRL 112, (2014) Flavor tag with D + D 0 π + Raw asymmetry: A raw = A CP + A FB + A π slow ɛ (+ A K mat) 0 Last term due to different strong interactions of K 0 / K 0 in detector material A K 0 mat = 0.11%, PRD 84, (2011) D 0 / D 0 yields from fit to M distributions in bins of (cos θ, p πs T, cos θπs ) Results consistent with no CPV: A π0 π 0 CP = ( 0.03 ± 0.64 ± 0.10)% A K S 0π0 CP = ( 0.21 ± 0.16 ± 0.07)% Modes with KS 0: CPV due to K 0 -mixing: 0.34%, D 0 π 0 π 0 D 0 K 0 S π0 PRL 109, (2012); 109, (E) (2012) M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

18 Time-integrated measurements: Summary mode L (fb 1 ) A CP (%) paper D 0 K + K ± 0.21 ± 0.09 arxiv: (2012) D 0 π + π ± 0.36 ± 0.09 arxiv: (2012) D 0 π 0 π ± 0.64 ± 0.10 PRL 112, (2014) D 0 Ks 0 π ± 0.16 ± 0.07 PRL 112, (2014) D 0 Ks 0 η ± 0.51 ± 0.16 PRL 106, (2011) D 0 Ks 0 η ± 0.67 ± 0.14 PRL 106, (2011) D 0 π + π π ± 1.30 PLB 662, 102 (2008) D 0 K + π π ± 5.30 PRL 95, (2005) D 0 K + π π + π ± 4.40 PRL 95, (2005) D + φπ ± 0.28 ± 0.05 PRL 108, (2012) D + ηπ ± 1.13 ± 0.19 PRL 107, (2011) D + η π ± 1.12 ± 0.17 PRL 107, (2011) D + Ks 0 π ± 0.09 ± 0.07 PRL 109, (2012) D + Ks 0 K ± 0.28 ± 0.14 JHEP 02, 98 (2013) D s + Ks 0 π ± 2.50 ± 0.33 PRL 104, (2010) D s + Ks 0 K ± 0.36 ± 0.22 PRL 104, (2010) M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

19 Conclusions D 0 -mixing measurements in the three most sensitive decay modes were updated with the Belle final data set ( 1 ab 1 ) D 0 K + π : 5.1σ observation D 0 K + K, π + π : 4.5σ evidence in y CP D 0 K 0 s π + π : most stringent limits on x No evidence for indirect CP violation. CP violation was searched in many decay modes using time-integrated approach no evidence found for CPV in the charm sector can see CPV due to K 0 -mixing in D + K 0 S π+ decay M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

20 backup: HFAG averages BaBar, Belle, CDF, CLEO, E791, FOCUS, LHCb y (%) HFAG-charm FPCP 2014 CPV allowed Arg(q/p) [deg.] HFAG-charm FPCP σ 2 σ 3 σ 4 σ 5 σ σ 2 σ σ 4 σ σ x = ( )% y = ( )% x (%) q/p = φ = ( )o q/p M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

21 backup: D 0 K + K, π + π : Resolution function Resolution function (for binned fit) Constructed from normalized distribution of σ t Using 2 or 3 Gaussian PDF for each σ t bin PDF parameters determined in each cos θ bin by fitting the distribution of pulls (t t gen )/σ t widths σ pull k, fractions w k n bin n g R(t) = w k G(t; µ i, σ ik ) f i i=1 k=1 σ ik = s k σ pull k σ i µ i = t 0 + a(σ i n f j σ j ) j=1 n bin = 50 σ i f i σ t /τ PDG Free parameters: width scaling factors: s k, k = 1,..., n g (n g = 2 or 3) resolution function offset: t 0 slope to model asymmetry: a M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22

22 backup: Measurement strategies dn D 0 f dt e Γt f H D 0 + q p ( y+ix 2 Γt) f H D0 2 Wrong-sign semileptonic decays (D 0 K + l ν) WS only via mixing: f H D 0 = 0 measures time integrated mixing rate R M = x 2 +y 2 2 = N WS N RS Wrong-sign hadronic decays (D 0 K + π ) WS via doubly Cabibbo suppressed (DCS) decays or mixing interference between DCS and mixing (strong phase δ) measures x = x cos δ + y sin δ, y = y cos δ x sin δ Decays to CP eigenstates (D 0 K + K, π + π ) if no direct CPV: f H D 0 = f H D 0 measures y Decays to self-conjugate states (D 0 K 0 s π + π ) time dependent Dalitz plot analysis measures x and y M. Starič (IJS) D 0 -mixing and CPV in Charm at Belle Quy Nhon, , / 22