Prospects for further Study of CPV in the Charm Sector

Prospects for further Study of CPV in the Charm Sector Brian Meadows 10 November 2012 .

Prologue Tools available: Hadron: LHCb Charm threshold: BES3, SuperB, PANDA At Y(4S): Belle2, SuperB We are off to a good start: BaBar and Belle, evidence for D0-D0mixing LHCb, evidence for 3.5 direct CPV in D0h+h- LHCb, evidence for 3.5 direct CPV in D0h+h- What is next ? • We recall what Ikaros Bigi has often reminded us, • “The goal in charm physics is not just to observe CPV in D decays • - but also to understand its origin !”

Outline Charm, CKM and all that D0 Mixing and why it matters Brief review of evidence for mixing AND projection to the new generation of experiments Recent experimental results Prospects for understanding CPV in mixing TDCPV - CPV in decay ? How about rare decays ?

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 W c u c u c u Di Dk H 0 u u u c c Phase in C=1 transitions tiny: W c Wolfenstein representation ~ ~ ~ ~ q g g q Heavy, weak iso-singlet quarks Supersymmetry FCNC [ A recent survey:Phys. Rev. D76, 095009 (2007), arXiv:0705.3650 ]

Outline D0 Mixing and why it matters Review of evidence for mixing (mostly BaBar) AND projection to the next generation of experiments Prospects for understanding CPV in mixing TDCPV - CPV in decay ?

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 K (WS), point on DP, etc Decay through Mixing Direct decay Depends on DP decay model All current measurements, so far, exploit interference between direct decays D0fand decays through mixing: Time-dependence to 2nd order in x and y.

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 at LHCb Decay time resolution - little issue (D0 momenta ~50 times larger). Trigger includes D (&/or B) displaced vertex and “slow pion”. Two RICH’s and dE/dx allow clean K/ separation Decay length cuts (especially when associated with displaced BD*¹º decay) very effective at reducing background.  Very clean samples !!

Mixing at LHCb Tagging can be from either Charge of ps’s from D* D0ps decays BD(*)mndecays Distortion in prompt D decays from B decays are controlled statistically using “impact parameter” in D0 point-back.

 Very clean samples !!

Evidence for Mixing in (Wrong Sign)D0K+- decays Tagged PRL 98:211802 (2007) – 384 fb-1 No Mixing + No Mixing Point Best Fit RWS/RRS % + 3.9  Mixing signal clearin time-dependence of RWS/RRSratio Likelihood contours (expanded to account for systematic uncertainty of ~0.7 xstatistical.)

Tagged PRL 98:211802 (2007) – 384 fb-1 Observation of Mixing in (Wrong Sign)D0K+- decays No Mixing + No Mixing Point Best Fit RWS/RRS % + 3.9  Mixing signal clearin time-dependence of RWS/RRSratio Likelihood contours (expanded to account for systematic uncertainty of ~0.7 xstatistical.)

Mixing Measurements 2010 .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 • xDvs.yD 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.

DD Threshold Measurements Data from  (3770)DD at charm threshold provide measurement of strong phases such as K. They also provide measured values of  in Dalitz plot bins1 These can be used to significantly reduce uncertainties from the Dalitz plot model used in the golden channel analyses. As basis for projection, we take uncertainties from CLEO-c: N. Lowrey et al, PRD80, 031105 (2009), 0903.4853 Our assumption is that new data from threshold will reduce the uncertainties in model uncertainty IMU: BES III: IMU x 1/3 (Factor 3 improvement) SuperD 500 fb-1 @DD threshold: IMU x 1/10 (Factor 10 improvement) 1Bondar, Poluektov & Vorobiev, Phys. Rev. D82, 034033 (2010)

Model independence The need for a model could be completely by-passed if we had values for ci, si and Ki from elsewhere, preferably data! Ki can simply be taken as the actual number of events in bin i of the Dalitz Plot for the D0 flavour-tagged sample. Measurements of si and ci, from decays of (3770)D(1)D(2), can be obtained without the need for a model. Such pairs of D’s are produced in a Bose-symmetrized state which makes their relative phases observable.

“Double-Dalitz: An example of quantum correlations from CLEO c e+e- (3770)  (Ks+-) (Ks+-) There are two Dalitz plots correlated in a time-dependent way: If you select CP-odd Ks0 in one, you see “no”Ks0 in the other. If you select RS K*-+ in one, you see only (opp. sign) RS K*+- in the other. EXCEPT: There will be a small signal arising from MIXING. This has a definite time-dependence, making it more identifiable above background. Backgrounds at (3770) are small ! CLEO data: - It works !! Plots from J. Napolitano http://indico.ihep.ac.cn/conferenceDisplay.py?confId=176

Use of quantum correlations to find c and s Case I: Both D(1) and D(2) decay toKs+-(similar to previous slide). Remembering thatD(1)D(2)are a D0D0 pair, the number of events in bin i of D(1) and bin j of D(2) is the coherent sum where the “interference” term is proportional to the cosine of the difference in phase between these two bins. Case II: D(1)decays, instead, to a CP eigenstate. Then D(2)decays to a CP eigenstate ofKs+- of opposite sign, ie with amplitude (AD  AD)/\/2. So the number of events in bin i in the DP is These observations allow determination of ci, si leaving only a single ambiguity in the sign of ALL the si – ie a complex conjugation of AD. Bondar EPJ C47,347 (2006), EPJ C55,51 (2008)

Implementation The method is implemented by CLEOc tested by Belle. Using 16 bins, ci and si values match the Belle isobar model pleasingly well 2/NDF=18.6/16. CLEOc PRD80, 032002 (2009), PRD82, 112006 (2010)

Belle Test for model independent  test These values for ci and si and bin populations Ki from the tagged D0 sample are used to predict D0DP bin populations in the B+ sample: thereby allowing binned fits to both B samples, each with 3 parameters (hB, x and y). These result in values for , rB and B. The third error is that due to uncertainties in ci and si or due to the model, as appropriate. The first error is statistical and shows that the binned fit introduces some degradation here. We can, however, expect that in the model-independent case, all these uncertainties should decrease as sample sizes grow. Belle PRD80, 032002 (2009)

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 Best strategy may be to improve precision in xD & yD - say to ~1x10-4 D0-D0 asymmetries ~ |q/p|2-1 Several possibilities for this exist. Most likely are: LHCb (or CDF, Atlas, CMS ?) Super B factories For SuperB, a safe estimate for performance can be made by using Babar as basis to project to integrated luminosity of 75 ab-1 at (4S)(Similarly for Belle and Super KEKB) We can also speculate on what “SuperD1” [500 fb-1 at (3770)]might accomplish 1See SuperB white paper:http://arxiv.org/abs/1008.1541 ) Dependence on decay mode would indicate direct CPV? LHC is clearly best candidate now ! Machines are on the way !

CPV Parameters |qD/pD |, M=Arg{q/p} 28 • 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 = Improve present precision by order of magnitude Also improve distinction between decay modes ~ 5% 1-|q/p|4 1-|q/p|4 Several strategies:

What About LHCb (10 fb-1) ? • Clearly has the potential to do very well! • Already seen evidence for direct CPV in D0h+h- channels !! BUT • Must improve trigger rates for “golden channels” • Should try for 0 channels (esp. D0K+-0) Message from Intensity Frontier meeting: Flavour frontier experiments need each other! LHC Guy

ArXiv: 1106.5075v2

A “B factory” for D’s Too ? Bigi and Sanda (hep-ph/9909479v2) pointed out there are six unitarity triangles and that (in addition to ,  and ) two other angles, c and s should be measured if possible. LHCb is already working on s using Bs -> (f0) decays. SuperB and Belle2 should also be able to study Bs  (‘) at Y(5S) We explore the potential to study the “cu” triangle. It is unlikely we can measure c(<0.1 degrees) to high precision However, a larger value would signify new physics. A TDCPV analysis can measure a weak phase, if any exists Perhaps this is how to understand what LHCb is seeing?

CKM Predictions A number of CKM predictions are compared to observables K,  Md,  Ms, BF(B), alpha, sin2, , Vcb, lattice, … Fits to measured values give values for CKM parameters: We take simple averages of two fits to predict cu triangle. It is important to check the CKM paradigm for up-type quarks as it has been in down-quark sector. • Significant discrepancies exist: • sin2 ~3 low • BF(B) 2.7 high • Is CKM model in question? arXiv:1104.2117 [hep-ph]

CPV and CKM CPV requires weak phases - in SM these come from CKM Buras parameters - Ensure unitarity of “bd” triangle at all orders in  For charm decays, most interest is in “cu” triangle. NOTE – phase ofVub is stilldespite5term O(3) OK O(5) Needed [Phys. Rev. D50, 3433 (1994)] qu W qd • Usually use Wolfenstein parameters • =sinC, A, ,  (c=Cabibbo angle) Expand in powers of . There are 6 unitarity triangles – most common is“bd ” Coordinates of apex of bd triangle Phase in Vcd appears at order 5

Unitarity Triangles from CKM Fits NOTE that c is equal to  c+ c~900 bd triangle cu triangle

Constraint on cu Triangle ? • Lengths of sides: • CKMUncertainty • |Vud| 0.022% • |Vcd| 4.8% • |Vub| 11% • |Vcb| 3.2% • |Vus| 1% • |Vcs| 3.5% gc=g ~6.5 x 10-4 c(0.0350) ac Vus*Vcs  1 Might improve SL decays of Ds with run at Ds threshold ?  Some measurement of c is needed to test CKM

Decays to CP Eigenstates For decays to CP eigenstates, strong phase  in f is zero • Several amplitudes could, however, contribute to the decays. • Some information on the magnitude of P, the penguin contribution can be obtained from an isospin analysis if all charge modes have well measured BF’s, including neutralmodes 00, 00 and all the  modes too. • This is best done at the electron machines.

D0 fCPDecay Amplitudes To order 6 these are: Four out of five are complex ! Real Phase is O(6) Phase is -bc Phase is -bcbut ~6 • Phase is c, but only found • in penguin amplitude • unlikely to be able to check thatc= Most promising ? D0  hh (h = , K, , f0, …)

Amplitudes for Decays to CP Eigenstates Dominated by real T Dominated by T with f =  - c

Time-Dependence for D0 Decays (D0f) CP eigenstates are also accessible to D0 or D0 D0 “fCP”: (D0f) Mix (D0D0) Weak decay mixing To measure weak phase f we MUST know M The time-dependences for decay rates () for D0(D0) differ In decays to CP states, strong phase for D0is same as D0 so

Time-Dependent CP Asymmetry Define this as Decay to CP eigenstate dominated by single process, |f|=1 For B decay (if we assume that yB=0and|f|=1) this is Assuming |q/p|=1 Familiar to all B factory practitioners

Time-Dependent CP Asymmetry For D decay we measure CP asymmetry vs. decay time • The D0 asymmetry is much smaller than that for B0 • |ACP | is almost linear in t while, for B0 it is sinusoidal • Slope of line depends upon = Arg {} • |ACP | is largest at large |t| • But as |t| grows larger, the number of events falls off exponentially. Any asymmetry at t~0 is from direct CPV

Mis-Tagging • Effect of mis-tagging probability  is to reduce the D0-D0 asymmetry • Effect of CP asymmetry in  is to shift the asymmetry. • Direct CPV asymmetry is measured at t=0 ! So shift is particularly serious in this case.

Mis-Tagging Effect of mis-tagging probability  is to reduce the D0-D0 asymmetry Effect of CP asymmetry in  is to shift the asymmetry. Direct CPV asymmetry is measured at t=0 ! So shift is particularly serious in this case.

Results – “as good as (they) get” A toy MC study was made to study how well we might measure =Arg{} Events were generated with the distributions ( t) and ( t) Perfect time resolution was assumed Unbinned likelihood fits were made to study (). • Mis-tag assumptions • SuperB (charm thresh.) ==0 • SuperB @ Y(4S) =1%,  = 0 • LHCb  = 6%,  = 0.1% • Numbers of events scaled • from CLEO c to 500 fb-1 • from BaBar to 75 ab-1 • from LHCb 35 pb-1

Results – “as good as (they) get” The K+K- mode is dominated by a tree diagram that is real. So we expect that no direct CPV will be found here Therefore, this mode can be used to find arg (q/p) = M Then +- mode (for which arg(f} = M-2C,eff) can give C,eff

Effect of “yB” on CP Asymmetry In Babar, it was assumed, in the measurement of S = sin2 from B0 decays, that yB = 0.0. The PDG specifies a value of ~0.01 + 0.035 Assuming this is Gaussian we estimate it makes a difference to S = sin2 of ~0.007 + 0.027 This is comparable to the expected statistical precision of measurements from both LHCb and SuperB Part of B 0 oscillation S-sin2 scale factor

Epilogue LHCb, SuperB and Belle2 asymmetries in xD, yD, x’D,yD’, etc. should provide a good probe for CPV in mixing. This should also be possible for a variety of decay modes and maybe provide a clue whether CPV is in mixing alone. A TDCPV “sin2c” measurement will be much harder for D’s than it was for B’s. However, such an analysis brings with it an excellent way to measure the (extremely important) D0 “mixing phase” M using D0K+K- decays. Improved constraints on triangle sides can come from charm threshold runs. This can also be done at charm threshold, at the Y(4S) and at LHCb though the former is cleaner Charm threshold runs will improve our knowledge of strong phases needed for all D0 mixing measurements (and CKM ). We also note that CKM phase measurements for B0 must include better estimates for yB. • We recall what Ikaros Bigi has often reminded us, • “The goal in charm physics is not just to observe CPV in D decays • - but also to understand its origin !”

Backup Here

HFAG Mixing Summary The HFAG collaboration combine 30 “mixing observables” to extract the 8 underlying mixing parameters and their 2 contours: A. Schwartz et al. arXiv:0803.0082 (updated FPCP 2010) X X No Mixing No CPV New D0 Ks+-+ KsK +K - results from BaBar significantly reduce average x Evidence for mixing is >10 No evidence for CPV

Prospects for further Study of CPV in the Charm Sector