0 mixing 0 D D K.Trabelsi ( KEK ) karim.trabelsi@kek.jp Flavor - PowerPoint PPT Presentation

0 mixing 0 − D D K.Trabelsi ( KEK ) karim.trabelsi@kek.jp Flavor Physics & CP Violation 2013 May 19-24, 2013

Flavour Mixing in the Charm Sector Mass eigenstates ≠ flavour eigenstates m 1, 2 and Γ 1, 2 are mass and width of |D 1, 2 > 0 > ± q|D 0 > |D 1, 2 > = p |D p / q ≠ 1 ⇒ CP violation Long − distance contributions dominant, Short − distance contributions, affected by large theoretical uncertainties GIM and CKM suppressed in SM 0 system 0 − D Time evolution of a D with M and Γ being hermitian −(Γ/ 2 + i m ) t [ cosh ( y + ix p sinh ( y + ix 0 > + q 0 ( t ) > = e Solutions 0 > ] Γ t ) |D Γ t ) |D |D 2 2 q sinh ( y + ix 0 > + cosh ( y + ix −(Γ/ 2 + i m ) t [ p 0 ( t ) > = e 0 > ] Γ t ) |D Γ t ) |D |D 2 2 y = Γ 1 − Γ 2 x = m 1 − m 2 Mixing parameters , Γ D 2 Γ D Γ D = (Γ 1 + Γ 2 )/ 2

0 -D 0 mixing D 0 mixing is small ( |x|, |y | << 1 ) : ∘ Since D q ( y + ix 0 > + p −(Γ/ 2 + i m ) t [ |D 0 ( t ) > = e 0 > ] |D Γ t ) |D 2 0 → f: ∘ Time dependent decay rates of D d N D p ( y + ix 2 = e 0 > + q 0 → f 0 ( t ) >| −Γ t |<f|H |D 0 >| 2 ∝ |<f |H|D Γ t ) |<f |H|D dt 2 ∘ Exponential decay modulated with x and y d N D 0 → f x and y can be obtained from measured time dependence of dt ∘ Shape is final state dependent different final states sensitive to different combinations of x and y

0 -D 0 mixing − SM estimates D ( Joachim Brod ) Can express y = 1 2 Γ D ∑ n ρ n [ <D 0 |H|n ><n |H|D 0 > + < D 0 |H|n ><n|H|D 0 > ] 0 |H|n ><n |H|D 0 > + <D 0 |H|n >< n|H|D 0 > x = 1 <D 0 > + P ∑ n 0 |H|D Γ D [ <D ] 2 − E n 2 M D ''Inclusive approach '': ∘ OPE expansion in powers of '' Λ/ m c '' − 3 [ Georgi 1992; Ohl et al 1993; Bigi et al 2000 ] ∘ x ∼ y < 10 − 2 [ Bobrowski et al 2010 ] ∘ Cannot exclude y ∼ 10 ∘ Violation of quark - hadron duality ''Exclusive approach'': ∘ Sum over on-shell intermediate states − 3 [ Cheng et al 2010 ] ∘ Mainly D → PP, PV leads to x ∼ y < 10 − 2 [ Falk et al 2002 ] ∘ SU ( 3 ) F breaking in phase space alone leads to y ∼ 10 − 2 from a dispersion relation [ Falk et al 2004 ] ∘ Get x ∼ 10

Experimental status at FPCP 2012 ( A.Di Canto ) From HFAG page: 0 → K + π − D E791 0 → h + h − D E791 0 → K + π − π 0 D 0 → K + π + 2 π − D 0 → K S 0 h + h − D 0 → K − ν + l E791 D 0 D 0 ψ ( 3770 ) → D = mixing probability >3 σ

Experimental status at FPCP 2012 [ http://www.slac.stanford.edu/xorg/hfag/charm/March12 ] 0 system is well Mixing in the D established : significance ∼ 10 σ + 0.19 ) % x = ( 0.63 − 0.20 y = ( 0.75 ± 0.12 ) % SM predictions affected by large No mixing point uncertainties: theo ∼ O ( 10 theo , y − 2 -10 − 7 ) x [ see Joachim Brod 's compilation next slide ] Measurements of x and y are at the upper limits of SM, NP contributions (in short - distance diagrams) could at the 1% level e.g. [ Golowich et al ] x ≤ 0 excluded at 2.7 σ y ≤ 0 excluded at 6.0 σ

Results discussed in this talk... From HFAG page: 0 → K + π E791 − D 0 → h + h − D E791 0 → K + π − π 0 D 0 → K + π + 2 π − D 0 → K S 0 h + h − D 0 → K − ν + l D E791 0 D 0 ψ ( 3770 ) → D = mixing probability >3 σ

0 → K + π + K − , π − Decays to CP-even eigenstates D − π + and D 0 → K + K + π − , π − Measurement of lifetime difference between D → K Timing distributions are exponential ( if CP is conserved ) ∘ mixing parameter: y CP = τ( K − π + ) − ) − 1 + h τ( h ∘ if CP conserved : y CP = y + π + K 0 / D 0 → K − , π − If CP is violated → difference in lifetimes of D 0 → h 0 → h − h − h + ) − τ( D + ) ∘ lifetime asymmetry : A Γ = τ( D 0 → h − h 0 → h − h + ) + τ( D + ) τ( D ∘ y CP = y cos ϕ − 1 2 A M x sin ϕ ϕ = arg ( q / p ) 2 ∘ A Γ = 1 A M = 1 − |q / p| 2 A M y cos ϕ − x sin ϕ [ S.Bergmann et al, PLB 486, 418 ( 2000 )]

− 1 ) Experimental method ( update with 976 fb [ arXiv:1212.3478; M.Staric et al, PRL98, 211803 ( 2007 )] *+ → π + D 0 using D ∘ flavor tagging by the charge of π slow ∘ background suppression 0 proper decay time measurement : D p D t = l dec 0 βγ = c βγ , M D extrapolate production vtx 0 ∘ decay time uncertainty σ t ( calculated from vtx err matrices ) CMS > 2.5 ( 3.1 ) GeV / c Υ( 4S ) (Υ( 5S )) *+ from B decays: p D *+ To reject D Observables: ∘ m = m ( K π) ∘ q = m ( K ππ s ) − m ( K π) − m π

0 → K + π + K − , π − Decays to CP-even eigenstates D [ arXiv:1212.3478 ] ∘ Analysis cuts: m, q, σ t optimized on tuned Monte Carlo figure of merit: statistical error on y CP ∘ Background estimated from sidebands in m sideband position optimized ∘ Signal yields ( purities ) entering the measurement: K π π π channel KK Yield 242k 2.61M 114k Purity 98.0% 99.7% 92.9%

0 → K + π + K − , π − Decays to CP-even eigenstates D [ arXiv:1212.3478 ] + π + π + K − samples − , K − , π simultaneous binned fit to K * sum of histograms and fitted function over cos θ 0 CMS angle (θ * ) , fit is performed in bins of cos θ * ] [ as resolution function depends on D SVD1 3- layer SVD − 1 153 fb SVD2 4 -layer SVD − 1 823 fb

0 → K + π + K − , π − Decays to CP-even eigenstates D [ arXiv:1212.3478 ] 0 CMS angle (θ * ) , fit is performed in bins of cos θ * ] [ as resolution function depends on D SVD2 4 -layer SVD − 1 823 fb τ = 408.56 ± 0.54 stat y CP = (+ 1.11 ± 0.22 ± 0.11 ) % Results ( preliminary ) − 1 A Γ = (− 0.03 ± 0.20 ± 0.08 ) % with 976 fb − 1 Belle, 540 fb ∘ y CP is at 4.5 σ when both errors are combined in quadrature y CP = (+ 1.31 ± 0.32 ± 0.25 ) % A Γ = (+ 0.01 ± 0.30 ± 0.15 ) % and at 5.1 σ if only statistical error is considered ∘ A Γ is consistent with no indirect CP violation divide distributions

0 → K + π + K − , π − Decays to CP-even eigenstates D [ J.P. Lees et al, PRD87, 012004 ( 2013 ) , arXiv:1209.3896 ] Simultaneous fit to 7 signal channels: 0 π 0 π + , D + K + K − ;D − , D − ; *+ → D 0 → K *- → D 0 → K ∘ flavour tagged: D 0 π + π 0 π + π + , D − ;D − , D − ; D ± π ∓ *+ → D 0 →π *- → D 0 →π * → D π , D → K D ± π + K flavour untagged − , D → K ∓ ∘ flavour untagged : D → K 500k 74.4 % flavour tagged 2 × 32k 2 × 65k 1.5M 5.8M 94.4 % 99.3% 99.8% 84.7%

0 → K + π + K − , π − Decays to CP-even eigenstates D [ J.P. Lees et al, PRD87, 012004 ( 2013 ) , arXiv:1209.3896 ] ∘ Charm background: Small component ( < 0.7% ) , misreconstructed charm decays, not separated in the mass fit Lifetime fit PDFs and yields extracted from MC in the signal region flavour untagged ∘ Combinatorial background : Main component, random tracks 500k Lifetime fit PDFs extracted from data outside the signal region 74.4 % + K − ) are extracted from Lifetime fit yields ( not for untagged K data in the signal region ( integral of bkg PDF minus the charm bkg yields from MC) flavour tagged 2 × 32k 2 × 65k 1.5M 5.8M 94.4 % 99.3% 99.8% 84.7%

0 → K + π + K − , π − Decays to CP-even eigenstates D [ J.P. Lees et al, PRD87, 012004 ( 2013 ) , arXiv:1209.3896 ] ∘ Signal: properly normalized 2d conditional PDF ( t , σ t ) ∘ Lifetime 2d fit in the signal region only CP + eigenstates CP mixed states CP + lifetimes + = ( 405.69 ± 1.25 ) fs τ + = ( 406.40 ± 1.25 ) fs τ 0 lifetime D τ K π = ( 408.97 ± 0.24 ) fs

0 → K + π + K − , π − Decays to CP-even eigenstates D [ J.P. Lees et al, PRD87, 012004 ( 2013 ) , arXiv:1209.3896 ] 0 lifetime D τ K π = ( 408.97 ± 0.24 ) fs CP + lifetimes + = ( 405.69 ± 1.25 ) fs τ + = ( 406.40 ± 1.25 ) fs τ − 1 Results with 468 fb y CP = (+ 0.72 ± 0.18 ± 0.12 ) % A Γ = (+ 0.09 ± 0.26 ± 0.06 ) % Exclude no mixing at 3.3 σ − 1 BaBar , 384 fb y CP = (+ 1.16 ± 0.22 ± 0.18 ) % ( 0.866 ± 0.155 ) % A Γ = (+ 0.26 ± 0.36 ± 0.08 ) % previous value: ( 1.064 ± 0.209 ) %

0 π + π − time-dependent Daliz analysis D → K S 0 3 body self -conjugated decays, Dalitz analysis can be performed: ∘ For D 0 → K S 0 π + π 2 , m + − , decay amplitude A ( m − 2 ) e.g. in D 2 ≡ m K S 2 ≡ m K S where m − 0 π − , m + 0 π + ∘ In CP conservation assumption, A = A and q / p = 1 BaBar Distribution of events across Dalitz 0 ) space vs t ( D Variation → signature of mixing sensitivity to x and y comes mainly from regions with: − interferences of CF and DCS − CP eigenstates Simultaneous determination Example of mean lifetime in different regions of the DP of x and y