Prospects for Study of CPV in the Charm Sector

Prospects for Study of CPV in the Charm Sector Brian Meadows 10 November 2012 . TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAAAAAAA

Prologue • “ An important goal in charm physics is not just • to observe CP Violation in D decays • but also to understand its origin” • -- IkarosBigi

Tools available: Hadron: LHCb Charm threshold: BES3 (10 fb-1), SuperB(1 ab-1 with boost) At Y(4S): Belle2, SuperB We are off to a good start: BaBar and Belle, evidence for D0-D0mixing LHCb, observationD0-D0mixing at 9.1 level LHCb, evidence for 3.5 direct CPV in D0h+h- What next ?

Outline Introduction D0 Mixing and evidence for it. Analysis methods, new results Projection to the new generation of experiments Use of threshold data Prospects for searching for CPV in mixing Time-Dependent CP asymmetry Time-integrated and direct CPV Rare decays

Charm was “invented” (GIM mechanism) to account for small FCNC interactions in nature. • In this scenario, for the charm sector, • CP violation (CPV) is expected to be small, mostly because weak phases are small (Arg{Vcd}~ ¸5); • Mixing is greatly suppressed; • Many charm particle decays are also small. • With SM “backgrounds” so small, charm is a good place to look for new physics (NP). • Much of this was discussed almost 40 years ago ! A. Pais and S.B. Treiman, Phys. Rev. D12, 2744 (1975).

NOTE that c is equal to  c+ c~900 cu triangle Weak phases in B and D sectors bd triangle Bevan, Inguglia, BM: Phys.Rev. D83 (2011) 051101

Signals for New Physics would be |x |>>|y | or Evidence for CPV Golowich, Hewett, Pakvasa an Petrov, PR 76, 095009(2007) D0-D0 Oscillations (mixing) are small • Evidence only recently found (2007) • This is the only instance with all down-type quarks. • D0 system exhibits the least mixing among neutral mesons. x and y each ~1%

D0 Mixing Flavour oscillations in the neutral D system arise from the propagation of two mass eigenstates D1 and D2 that comprise the flavour states It is usual to define four mixing parameters: CPV from either mixing, from the decay or their intererence can occur Eigenvaluesare with means: CPV signalled by Define decay amplitudes: mixing Weak decay Strong decay Then we actually measure the quantity

Mixing in SM is hard to compute Off-diagonal mass matrix – two leading terms: Hadronic intermediate states (long-range) C=2 (short-range) (contributes mostly to x ) C=1 C=1 • Difficult to compute (need to know all • the magnitudes and phases, …) • Most computations predict x and y • in the range 10-3–10-2and |x|<|y| • Recent predictions: • (consistent with current observation) • Down-type quarks in loop: • b : CKM-suppressed (|VubVcb|2) • d, s: GIM-suppressed • (almost 2 orders of magnitude less than current sensitivity)

New Physics and Mixing Several extensions to the SM have been considered that can increase the value of x include: Generally agreed that signals for new physics are: EITHER |x|>>|y| ORAny evidence for CPV in mixing W c u c u c u Di Dk H 0 u u u c c W c ~ ~ ~ ~ g q q g Heavy, weak iso-singlet quarks Supersymmetry FCNC [ A survey:Phys. Rev. D76, 095009 (2007), arXiv:0705.3650 ]

Three types of CPV • In the mixing (“indirect CPV”) • In interference between mixing and decay (“indirect CPV” – a.k.a. “mixing-induced CPV”) • In the decay (“direct CPV”) In the last two, CP asymmetry can depend on decay mode

Until now, measurements have generally assumed there is no CPV in mixing, i.e. q = p. and focussed on measurements of x and y., often separately for D0 and D0. • With samples ~100x B factories, we should broaden our view. • No evidence for CPV in D0mixing yet exists, but an order of magnitude in precision for these measurements is possible here.

Mixing Measurements at B Factories Vertex resolution allows measurement of time-dependence of D0 decays, but is a challenge. Distortion from B decays can be removed by cutting low momentumD0 ’s Excellent particle ID (Dirc, Aerogel and dE/dx) allows clean K/ separation • D0’s from D*+ D0+ decays: • Tag flavor of D0 by the sign of the “slow pion” in D* decays • Allow clean rejection of backgrounds • BUT untagged events can be used too !

Mixing measurements at LHCb Decay time resolution - little issue (D0 momenta ~50 times larger than at B factories) but short lifetime events cut out. Trigger includes D (&/or B) displaced vertex and “slow pion” (¼s). Displaced ¹ from B Prompt D*D¼ Trigger and offline decay length cuts (especially when associated with displacedBD*¹ºdecay) very effective at reducing background. Two RICH’s allow cleanK/separation

Mixing measurements at LHCb Tagging can be from either Charge of ps’s fromD* D0psdecays BD(*)mndecays Any distortion in prompt D decays from B decays must be controlled statistically using “impact parameter” (ln c2(IPD) in D0 point-back. • Efficiency as function of decay length is measured by “swimming”.

Mixing Measurements (D0f) D0 “f”: (D0f) Mix (D0D0) Interference  = f (s1,s2 ) + 0 CPV in Mixing Generally unknown “+” for D0 “ -” for D0 Accessible to D0 or D0 A point in Dalitz Plot (DP), etc Decay through Mixing Direct decay Depends on DP decay model Exploit interference between direct decays D0fand decays through mixing: Time-dependence to 2nd order in x and y.

Analysis Methods • Tag D0flavour at birth (with sign of ¼s or of ¹ from B) and record decay time t. Do this for: • Two body “wrong sign” (WS) decays D0K+p- • Determines y’ and x’2 where y’(coefficient in interference term) is y’ = y cos± - x sin± and x’ = x cos± + y sin± • Mean decay time for decay to CPeigenstate (e.g.K+K-) • Determines yCP (defined as y when CP is conserved) • Depends on range of t over which itis averaged. • Multi-body decays – e.g.D0K+p-p0or D0Ksp-p+ • Fit to ‘DP’ determines y’’=y cos±0- x sin ±0 and x’’=x cos±0+ y sin ±0 • Here, depends on DP coordinates Requires models for and

Method 1: First evidence for mixing in D0K+- decays by BaBar (confirmed by CDF) 400 fb-1 PRL 96,151801 (2006) 1.5 fb-1 PRL 100,121802 (2008) 384 fb-1 PRL 98,211802 (2007) 2.0  3.8  3.9  Fits were made to the time-dependence of the ratio RWS/RRS of rates forD0K+- (WS) andD0K-+ (RS): + No mixing + No mixing An earlier result from Belle was more sensitive, but they were unable to claim observation. Both Babar and CDF obtained central values for x’2~0 and y’~1% + + + RWS/RRS RWS/RRS t/¿ t (ps)

Method 2: Mean decay times (¿) • In the absence of CPV, D1 is CP-even and D2 is CP-odd • Measurement of lifetimes  for D0 decays to CP-even and CP-odd final states lead to a measurement for yin absence of CPV. • Allowing for CPV, measure the D0 and D0 asymmetry Mixed CP. Assumeis mean ofCP-evenandCP -odd K +K –or+- CP -even • PRD 69,114021 (Falk, Grossman, Ligeti, Nir & Petrov)

Belle did find first evidence for mixing in D0h-h- decays, though (confirmed by BaBar) PRL 98 (2007) 211803 PRD 78:011105 (2008) Theorist: Wow – y=1% !! Ratio of K+K- or ¼+¼- to K-¼+ decay vs. time

Method 3: Time-dependent Dalitz plot fit. • Fit time-dependent model for decay amplitude (for D0) and (for D0) to the form where and can have an “isobar model” form with complex coefficients that are allowed to float in the fit. A relative phase d0 between and is introduced and also allowed to fit. For self-conjugate final states (“golden channels”)d0=0 and, if we ignore direct CPV, then D0 from D* D0ps

New BELLE results • (Cho, CKM 2012) • Full sample 920 fb-1 • Improved model • (K-matrix rather • than 2¾’s) • Smaller uncertainties • and IMU Theorist: Wow – x~1% too!! • Third error is irreducible model ( ) uncertainty (IMU): ~10-3 in xD and yD ~8% in |q/p| and ~30 in arg{q/p}.

Sensitivities depend on decay mode: D0K+¼-¼0vs.D0Ks ¼-¼+ -- D0K +¼-¼0 “HFAG” mixing: x = 6.5 x 10-3 y = 7.4 x 10-3 -- D0K0+¼-¼+ Number of DP bins Colour: Mean decay times Bin sizes: / population Mean decay time (ps) D0K +¼-¼0 D0Ks¼-¼+ Mostly WS Mostly RS

Sensitivity comparison • Pure signal Monte Carlo “toy MC” samples generated according to model for TD Dalitz Plot from BaBar data. • K+p-p0 channel 500 times sensitivity to x and y as Ksp-p+ ! • BUT - experimental factors: • Larger Background and worse time resolution. greatly compensate.

Current World Averages (HFAG) • HFAG combine all current values for observables to obtain: Four main parameters No CPV X X Uncertainties in x and y ~ 20x10-4 No mixing We hope for ~1x10-4 • No evidence yet for CPV in mixing. • Evidence for mixing strong but, until recently, no single observation > 5¾ • But LHCb has now changed this !

New Result from LHCb: Observationof Mixing in “Wrong Sign” (WS) D0K+- decays arXiv:1211.1230v1 [hep-ex] Nov 2012 – 1 fb-1 No Mixing 9.1¾ From no mixing point RWS/RRS % + No Mixing Mixing signal clearin time-dependence of RWS/RRSratio Likelihood contours (expanded to account for systematic uncertainty of ~0.7 xstatistical.)

All Measurements of Mixing in D0 K+-(Method 1) LHCb: arXiv:1208.3355 Right on track for LHCb’s projections

New measurements of yCP and A¡from BaBar and from Belle yCP A¡ New average A¡: • Results: • yCPreduced in value • No evidence for CPV • in mixing

Projections for current and future facilities • As noted, sensitivity toxor toydepends on decay mode, so projections depend on the admixture of channels we plan to use. • The “BaBar x 150” model for projection is chosen, since BaBar has the most modes with evidence for mixing available so far. This works for B factories. • LHCb will differ mostly in a relatively low efficiency in K+¼-¼0 or Ksh+h- modes. • The impact is also considered of the following • Charm threshold machines (1 ab-1SuperB? • Time-dependent CPasymmetry measurements (a la sin2¯).

The BaBar admixture .02 0 -.02 yD -0.02 0 0.02 .04 0 -.04 yD -0.03 0 0.03 .015 .010 .005 yD -0.02 0 0.02 .010 .005 0 yD -.006 +.009 xD • BaBar 1¾ • xDvs.yD • constraints PRL 98,211802 (2007) PRL 100 (2008) 121802 PRL 103:211801 (2009) PRD 78:011105 (2008) PRD 80:071103 (2009) PRL 98 (2007) 211803 PRL 105:081803 (2010) PRL 99 (2007) 131803 PRD 72 (2005) 012001 • WS decays D0 K+-: • f unknown, f2=RDCS – measure (xD’2, yD’ ) • WS decays D0 K+-0: • f unknown, f from decay model – measure (xD’’, yD’’) • “Lifetime” diff for D0 h+h-: • Measure yCP • “Golden” D0 Ksh+h- • = 0 - measure (xD, yD) directly, ALSO measures |q/p| and Arg{q/p}BUT Introducesirreducible model uncertainty, IMU

Project BaBar Average to 75ab-1@(4S): 480 fb-1 75 ab-1 Golden Channels (Ksh+h-) Min. 2 fits (similar to HFAG) Represented by blue contours BaBar average Unofficial!! Uncertainties shrink: but are limited by the IMU(biggest effect on xD ) Strong phase measurements from (3770) can greatly reduce this.

LHCb with ~2.5 fb-1 (2012) Relatively low efficiency for: Ks hh or K+¼-¼0(WS) modes

Irreducible Model Uncertainty (IMU) • The problem - not easy to find a model for • Introduces uncertainty in mixing parameters BaBar: x = (0.16 ± 0.23 ± 0.12 ± 0.08)% y = (0.57 ± 0.20 ± 0.13 ± 0.07)% IMU (our goal ~ 0.01) D0 from D* D0ps Some see poles in Others see it as just a complex number !  They need data from charm threshold. Define bins, measure relative phase fi in each from Ã(3770) decays.

Model independence can be achieved using data from Charm threshold • Decay of Ã(3770) prepares the D(1)D(2) system in a state • Ignore mixing - solve for ci=cos(Ái) and si=sin(Ái) for each bin D0 (Correlation of bins cicj+sisj) Signal (sig tag) (CP=+1) KK, etc. Semi-leptonic K-l+nl , etc. TAG D0

Application for CKM ° 16 bin test of CLEO ci and si values vs. Belle isobar model. ci, si uncertainties should scale as Ã(3770) samples grow? Belle PRD85, 112014 (2012) CLEOc PRD80, 032002 (2009), PRD82, 112006 (2010) 2/NDF=18.6/16 From strong phase measurements Belle IMU for g

Effect of threshold data on mixing We assume that The IMU uncertainties in mixing from CLEO phase measurements (ci and si) will be in similar proportion to those for the Belle test. That these should shrink as the square root of available threshold sample sizes *. The projections are as illustrated … *This last assumption seems not to be so in simulations though this is puzzling. [JHEP 1210 (2012) 85]

Two improvements in mixing precision come from threshold data: Value of strong phase measurements • Dalitz plot model uncertainty shrinks • Information on overall strong phase K()is added BES III SuperD Uncertainty inxDimproves more than that of yD

Prospects for observing CPV in mixing The assumption of no CPV in mixing or decay in measurements should be abandoned as event samples grow. However, asymmetries in measurements of x and y (or x’ and y’) values for D0 and D0 separatelyshould continue to be useful: Dependence on decay mode would indicate direct CPV. Weak mixing phase fM= Arg{q/p} can be measured in Ksh+h- time-dependent Dalitz plot analyses.

CPV Parameters |qD/pD|, M=Arg{q/p} 47 • D0- D0 parameter asymmetries: • az = (z+-z-)/(z++z-) ~ |q|2-|p|2 • where z is x, y, x’, y’, x”, y”, x’2 Decay (|q/p|) (M)0 mode x 100 Global 2 Fit to all modes: ± 18 ±9 (HFAG - direct CPV allowed) Current World Averages (HFAG): Time-dependent amplitude analysis of Golden channels Semi-leptonic asymmetry aSL = BaBar x 150 improves precision by order of magnitude Also allows distinction between decay modes to ~5% 1-|q/p|4 1-|q/p|4 Several strategies:

Another way to obtain fM Bevan, Inguglia, BM, Phys.Rev. D84 (2011) 114009 • Analogous to sin 2¯measurements. • For decays to CPeigenstates, strong phase f in f is zero • If K+K- mode is dominated by a tree diagram, Arg{¸f}=M CP eigenstate or CP self-conjugate state phase = fweak + fstrong D0 “fCP”: CKM phase phase = -fweak + fstrong phase = M So weak phase Arg{¸f} =M– 2fweak

Time-Dependent CP Asymmetry Since D0 and D0 oscillate at different rates, this leads to time-dependent CP asymmetry. • The D0 asymmetry is much smaller than that for B0 • |ACP | is almost linear in t(for B0 it is sinusoidal) • Slope of line / = Arg {} • |ACP |grows with t Any asymmetry at t=0 is from direct CPV

Expected performance A toy MC study was used to estimate precision of measure of Arg{¸f}. Sets of events with expected yields in 3 scenarios generated with asymmetries as predicted for various values for Arg{¸f} Mis-tag rates similar to BaBar’s, and perfect time resolution assumed Unbinned likelihood fits made to obtainArg{¸f}in each case.

Outline Introduction D0 Mixing and evidence for it. Analysis methods, new results Projection to the new generation of experiments Use of threshold data Prospects for searching for CPV in mixing Time-Dependent CP asymmetry Time-integrated and direct CPV

Time-Integrated CPV in D0 Decays • CPV in the charm sector is expected to be small in the SM. If it is measured to be above the 0.1% level, it would signal NP. • Experimentally we measure the decay rate asymmetry which includes both direct and indirect contributions. • New insight on systematics, improve uncertainties  ~(0.2-0.4)%. • Previous asymmetries were~0%with uncertainties~(1-10)% Singly Cabbibbo-suppressed SCS decays allow penguins  can lead to CPV F. Bucella et al., Phys. Rev. D51, 3478 (1995) S. Bianco et al., Riv. NuovoCim. 26N7, 1(2003) S. Bianco, F.L. Fabbri, D. Benson, and I. Bigi, Riv., NuovoCim. 26N7, 1 (2003). A.A. Petrov, Phys. Rev. D69, 111901 (2004) Y. Grossman, A.L. Kagan, and Y. Nir, Phys. Rev. D75,036008 (2007) = -AG~0. 01% TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAAAAAAA

Prospects for Study of CPV in the Charm Sector