Overview of the CP Violation and Mixing in the Charm Sector

Overview of the CP violation and mixing in the charm sector

Evelina Gersabeck Ruprecht-Karls-Universität Heidelberg

on behalf of the LHCb collaboration with results from BELLE, BESIII, BaBar and CLEO-c legacy data

FPCP, Prague June 2017 Outline • Mixing and CP violation basics • Flavour factories • Mixing and CPV in D0→K+π- decays 0 + (‘)- • Indirect CPV in charm (AГ and yCP with D →h h ) • Direct CPV searches in two-body D0→h+h- charm decays • Direct CPV searches in other two- or three-body charm decays • Direct CPV searches in multi-body charm decays (D0→�+�-�+�-) • Conclusions and prospects

2 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Outline • Mixing and CP violation basics • Flavour factories • Mixing and CPV in D0→K+π- decays 0 + (‘)- • Indirect CPV in charm (AГ and yCP with D →h h ) • Direct CPV searches in two-body D0→h+h- charm decays • Direct CPV searches in other two- or three-body charm decays • Direct CPV searches in multi-body charm decays (D0→�+�-�+�-) • Conclusions and prospects

3 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Mixing parameters

Mass eigenstates Flavour eigenstates Assuming CPT symmetry, the physical eigenstates can be expressed as a superposition of the ﬂavour eigenstates

with complex coefﬁcients p,q satisfying

The transition probability

dimensionless

Width difference Mass difference → Lifetime difference 4 → Oscillation E.Gersabeck, Overview of the CP violation and mixing in the charm sector CPV in K,B,D mesons

CP symmetry applies to processes invariant under the combined transformation of charge conjugation (C): exchange of particle and anti-particle and parity (P): spatial inversion CP symmetry conserved in the strong and the EM interaction

• CPV discovered in weak decays of strange and beauty mesons containing quarks from the down sector • What about the up-sector?

5 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Charm • Charm is unique: only bound up-type quark system where mixing and CP violation can occur d s b No CP violation at u ﬁrst order: c imaginary part of Vcd very small t

• Making precise SM predictions in the D-meson sector is difﬁcult • Perturbative QCD valid at energies >> 1 GeV • Chiral perturbation theory valid between 0.1 GeV and 1 GeV 0 • D mass = 1.864 GeV 6 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Types of CPV

The symmetry under CP transformation can be violated in different ways: Present if λf is not equal to 1

CPV in mixing direct CPV CPV in the interference The transition probability of depends on the φ, the CP-violating relative particles to anti-particles compared decay mode phase between q/p and A̅ f ̅/Af , is to the reverse process differs. non-zero

The indirect CP violation is independent of the decay mode. It involves neutral particles

7 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Outline • Mixing and CP violation basics • Flavour factories • Mixing and CPV in D0→K+π- decays 0 + (‘)- • Indirect CPV in charm (AГ and yCP with D →h h ) • Direct CPV searches in two-body D0→h+h- charm decays • Direct CPV searches in other two- or three-body charm decays • Direct CPV searches in multi-body charm decays (D0→�+�-�+�-) • Conclusions and prospects

8 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Nucl. Instrum. Methods Phys. Res. Nucl. Instrum. Meth.A479:1-116,2002 Sect. A 479, 117 (2002) Flavour factories

CLNS-01-1742

JINST 3 (2008) S08005 Nucl. Instrum. Meth. A614, 345 (2010) Int. J. Mod. Phys. A 30 1530022

9 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Outline • Mixing and CP violation basics • Flavour factories • Mixing and CPV in D0→K+π- decays 0 + (‘)- • Indirect CPV in charm (AГ and yCP with D →h h ) • Direct CPV searches in two-body D0→h+h- charm decays • Direct CPV searches in other two- or three-body charm decays • Direct CPV searches in multi-body charm decays (D0→�+�-�+�-) • Conclusions and prospects

10 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Mixing in doubly-tagged D0→K+π- decays (3 fb-1) D0 PV B ratio of WS + Measure the decay rates of to RS decays π μ- X WS to RS events: two paths to reach the ﬁnal state interference mixing

no CF mix RS no DCS mix WS mix DCS mix CF Phys. Rev. D 95, 052004 (2017)

70000 ) ) 2

2 700 LHCb LHCb 60000 Data (a) Data 600 (b) Fit 50000 Fit 500 Background Background 40000 400

30000 300 Events / ( 0.05 MeV/c Events / ( 0.05 MeV/c 20000 200 6.7k WS 10000 1.7M RS 100

20004 2005 2010 2015 2020 2025 20004 2005 2010 2015 2020 2025 0 2 0 2 2 m(D πs) [MeV/c ] 2 m(D πs) [MeV/c ] σ σ / / 0 0 ∆ ∆ −2 −2 −4 −4 2000 2005 2010 2015 2020 2025 2000 2005 2010 2015 2020 2025 0 2 0 2 m(D πs) [MeV/c ] 11 m(D πs) [MeV/c ] E.Gersabeck, Overview of the CP violation and mixing in the charm sector How do we identify the ﬂavour of the neutral D mesons? ± ± h h = π or K D*+ D0 Prompt charm: PV D points to primary vertex Daughters of D don’t in general soft π+ h

The flavour of the initial state (D0, D0 ) is tagged by the charge of the h soft pion or the muon Secondary charm: D doesn’t point to PV B D0 h ~1 cm If B→D*±(→D0π±)μ∓ν: PV doubly-tagged decays IP non-zero impact - low mistag rate parameter μ X lower statistics 12 νμ E.Gersabeck, Overview of the CP violation and mixing in the charm sector Prompt vs secondary decays • Reconstructed prompt D0 decays ≈ 3x muon -tagged D0 decays • More efficient triggering for secondary decays • Small IP parameter for prompt decays; larger for muon-tagged decays • Smaller flight distance for prompt decays; larger for the muon- tagged decays • Different decay-time acceptances LHCb simulation Convolution of (decay time x time resolution) and acceptance

13 E.Gersabeck, Overview of the CP violation and mixing in the charm sector D*+ D0 Combined LHCb results PV + soft π+ D0 • Combined ﬁt using two independent data PV B samples (no CPV, no direct CPV, CPV)

+ - Double-tagged (DT) sample π μ X • 6 LHCb 5.5 D0 Prompt sample PRL 111, 251801 (2013) ] 5 • -3

[10 4.5 + • Precision improves by 10-20% when adding DT R 4 Prompt data (2.5% of signal) 3.5 Doubly Tagged 3 0 5 10 6 0 0 D D t/τ 5.5

] 5 -3

[10 4.5 - R 4 No CPV No Direct CPV 3.5 All CPV allowed 3 0.8 0 5 10 0 0.6 0 0 D t/τ ] D − D -3 0.4 0.2 [10 - 0

- R −0.2 • Gain from complementary decay-time coverage, + −0.4 R and higher signal purity. −0.6 −0.8 0 5 10 No evidence for CPV in mixing or decay t/τ 14 Phys. Rev. D 95, 052004 (2017) E.Gersabeck, Overview of the CP violation and mixing in the charm sector Mixing parameters with D0→h0π+π-

0 0 + - 0 + - D →π π π BaBar D →KSπ π BESIII PhysRevD 93 (2016) 112014 preliminary at CHARM & others • Time-dependent Dalitz plot analysis: • Quantum correlations in unbinned logL ﬁt to (t, s(π-π0), s(π+π0)) ψ(3370) to tag D ﬂavour and CP x = (1.5±1.2±0.6)% • Obtain ci = cos(ΔδD,i) and y = (0.2±0.9±0.5)% si = sin(ΔδD,i) • 4x Cleo-c statistics • Fundamental for the GGSZ 0 + - method for γ - uncertainty due D →KSπ π LHCb (1fb-1) to ci, s i can be halved with the JHEP 04 (2016) 033 existing statistics • Model independent technique: uses info from Cleo-c: yields Ti and strong phase differences ΔδD,i in Dalitz bins x = (-0.86±0.53±0.17)% y = (0.03±0.46±0.13)% • The way to go in the future!

Dalitz modelling adds irreducible systematics! BaBar 2008 optimal binning 15 CLEO, PRD 82 (2010) 112006 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Outline • Mixing and CP violation basics • Flavour factories • Mixing and CPV in D0→K+π- decays 0 + (‘)- • Indirect CPV in charm (AГ and yCP with D →h h ) • Direct CPV searches in two-body D0→h+h- charm decays • Direct CPV searches in other two- or three-body charm decays • Direct CPV searches in multi-body charm decays (D0→�+�-�+�-) • Conclusions and prospects

16 E.Gersabeck, Overview of the CP violation and mixing in the charm sector 0 + - AГ: Indirect CPV in D →h h decays D*+ D0 PV Comprises CPV in mixing and in the interference soft π+

ind AГ ≈ ηCP[1/2(AM +Ad)y cosϕ + x sinϕ] ≡ -aCP

AM - CPV from mixing Ad - direct CPV CPV phase ϕ x,y - mixing parameters Time dependent: Measure asymmetries of effective lifetimes of decays to CP eigenstates

0 + − 0 + − 0 + − 0 + − A Γ ≡ [τ(D̅ → h h ) − τ(D → h h )] / [τ(D̅ → h h ) + τ(D → h h )] Universal: does not depend on the decay mode -4 SM predicts AГ < 10 Enhancements up to 1 order of magnitude are possible in BSM models Large AГ or ﬁnal state dependence will indicate NP

2 independent analyses using different approaches 0 Pseudo AГ (using CF D →Kπ decays) is a null test of the methodology 17 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Indirect CP violation in D0→h+h- (1fb-1+2fb-1)(unbinned)

Measurements use prompt D0→K+K- and D0→π+π- decays (1 fb-1+2 fb-1) Fit the asymmetries between the decay times in 2 two-stages ﬁt involving 0 *+ 0 0 2 0 m(D ) and Δm (= m(D ) - m(D )); then ﬁt D decay time and ln(IP� D )

+ - -3 AГ(K K ) = (-0.14±0.37±0.10)×10 Largest source of systematic + - -3 uncertainty: modelling of AГ(π π ) = (0.14±0.63±0.15)×10 secondary backgrounds

PRL 112 (2014) 041801 ) ) t t ( ( Data 0.02 Data

0.01 A A Fit Fit Prompt signal LHCb Prompt signal LHCb 0 0 −0.01 −0.02 −0.02 K+K- π+π- 1 2 3 t [ps] 1 2 3 t [ps] 5 5 0 0 Pull −5 Pull −5

Asymmetry between D0/D̅0 data overlaid by the total unbinned maximum likelihood ﬁt E.Gersabeck, Overview of the CP violation and mixing in the charm sector 18 Indirect CP violation in D0→h+h- (3 fb-1)(binned) • Correct for detector non-uniformities and presence of secondary decays • Split data in bins of D0 decay time; extract yield by ﬁtting Δm (=m(D*+) - m(D0))

• Extract AГ via a linear ﬁt for background subtracted events

• Direct CPV, production and detection asymmetry are not time-dependent

Largest source of systematic uncertainty: peaking backgrounds

19 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Overview of AГ

Combination with statistically independent muon-tagged charm decays results on 3fb-1 available in JHEP 04 (2015) 043

Best precision asymmetry measured in the charm system done by LHCb!

20 E.Gersabeck, Overview of the CP violation and mixing in the charm sector AГ and yCP from BELLE and BESIII

D*+ D0 PV soft π+

BES III PLB 744 (2015) 339 Belle PLB 753 (2016) 412 Quantum-entangled pairs Final data set CP-tagging technique: Simultaneous ﬁt to D0 → K−π+, + - + - 0 0 0 0 − + 0 − + • CP tags(K K , π π ,KSπ π ,KSπ ,KSη, D →K K and D → π π KSω) vs ﬂavour tags Keν and Kμν Fits in bins of cosθ*

yCP = (1.11±0.22±0.09)%

AΓ = (-0.03±0.20±0.07)%

Assuming no direct CP violation, yCP = (-2.0±1.3±0.7)%

New preliminary results 0 0 CP tags(KLπ , K Sπ ) vs ﬂavour tags Keν yCP = (-0.98±2.43(stat.))%

θ* polar angle of D0 in CMS with respect to the direction of e+ See the talk of in case of no CPV y=yCP Xiaokang Zhou for details 21 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Outline • Mixing and CP violation basics • Flavour factories • Mixing and CPV in D0→K+π- decays 0 + (‘)- • Indirect CPV in charm (AГ and yCP with D →h h ) • Direct CPV searches in two-body D0→h+h- charm decays • Direct CPV searches in other two- or three-body charm decays • Direct CPV searches in multi-body charm decays (D0→�+�-�+�-) • Conclusions and prospects

22 E.Gersabeck, Overview of the CP violation and mixing in the charm sector The CP asymmetries

Measure the time integrated asymmetry in the SCS decays D0→hh decays (h=K or π)

Γ(D0 → f ) − Γ(D0 → f ) ACP ( f ) = Γ(D0 → f ) + Γ(D0 → f )

But ACP this is not what we measure. We measure

+ − *+ 0 + *− 0 − f = f = K K N (D → D ( f )π s ) − N D → D ( f )π s A f = ( ) or raw ( ) *+ 0 + *− 0 − N D D f N D D f + − ( → ( )π s ) + ( → ( )π s ) f = f = π π where N(X) refers to the number of reconstructed events of decay X after background subtraction

We measure the physical CP asymmetry plus asymmetries due to detection effects and production

Araw =ACP + Aproduction + Adetection 23 E.Gersabeck, Overview of the CP violation and mixing in the charm sector ΔACP

Main experimental challenge: separate the asymmetries nuisance asymmetries ~O(1%)

Araw =ACP + Aproduction + Adetection if we take the raw asymmetry difference: experimentally more robust 1st order

ΔACP ≡ Araw (KK) − Araw (ππ ) = ACP (KK) − ACP (ππ ) D0 PV B ΔACP muon-tagged = (+0.14 ± 0.16 ± 0.08)% μ- X JHEP 1407 (2014) 041

D*+ D0 PV ΔACP prompt = (-0.10 ± 0.08 ± 0.03) % soft π+

24 Phys. Rev. Lett. 116, 191601 (2016) E.Gersabeck, Overview of the CP violation and mixing in the charm sector Individual asymmetries: use CF decay control channels

D*+ D0 PV soft π+

Phys. Lett. B 767 177-187 25 E.Gersabeck, Overview of the CP violation and mixing in the charm sector - + ACP(h h ) results with LHCb Run 1 data

A prompt(K-K+) = (0.14 ± 0.15(stat) ± 0.10(syst))% D*+ D0 CP PV + Combination with the prompt ΔACP measurement soft π - + - + ΔACP = ACP(K K ) - ACP(π π ) dir ind ≈ΔaCP (1+yCP❬t❭/�) + aCP Δ❬t❭/� Phys. Lett. B 767 177-187

prompt - +

)[%] LHCb ACP (π π ) = (0.24 ± 0.15(stat) ± 0.11(syst))% 0.5 muon tagged LHCb + LHCb K

− LHCbpion tagged K ( LHCbcomb 0 CP

+ 0 D A D* D HFAG PV PV B + + soft π 0 μ- X Combination with the LHCb muon-tagged results

comb - + ACP (K K ) = (0.04 ± 0.12(stat) ± 0.10(syst))% comb - + ACP (π π ) = (0.07 ± 0.14(stat) ± 0.11(syst))% −0.5

Most precise measurement of charm time-integrated −0.5 0 0.5 − + CP asymmetry ACP(π π )[%]

26 E.Gersabeck, Overview of the CP violation and mixing in the charm sector HFLAV averages including the latest results Compatible with no-CPV in the charm sector at 9.3% CL

ind AΓ≈-aCP aCPind = (0.030 ± 0.026)% ΔaCPdir = (-0.134 ± 0.070)% ΔACP ≡ ACP(KK) - ACP(ππ) dir ind ≈ ΔaCP (1 + yCP t/τ ) + aCP Δt/τ 27 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Outline • Mixing and CP violation basics • Flavour factories • Mixing and CPV in D0→K+π- decays 0 + (‘)- • Indirect CPV in charm (AГ and yCP with D →h h ) • Direct CPV searches in two-body D0→h+h- charm decays • Direct CPV searches in other two- or three-body charm decays • Direct CPV searches in multi-body charm decays (D0→�+�-�+�-) • Conclusions and prospects

28 E.Gersabeck, Overview of the CP violation and mixing in the charm sector + + -1 Direct CPV search in D (s)→�’� (3fb ) ± ± arXiv: 1701.01871 submitted to PLB Data sample: 63k D and 152k D s

Yes, we can do γ ! • Usual strategy: Subtract detector asymmetries using control channels

Fit m(η‘�±) to extract Control channel External input raw asymmetry asymmetry (D0, Belle)

Consistent with CP conservation

Most precise measurements to date of these variables E.Gersabeck, Overview of the CP violation and mixing in the charm sector Complementary searches in two- or three-body decays D*+ D0 PV soft π+ + + D → KL e νe BESIII 0 D → KSKS Belle PRD 92 (2015) 112008 + CONF-1609 ArXiv 1609.06393 ACP(D ) = (-0.59 ±0.60 ±1.48)% • Interference with NP amplitudes could lead to large nonzero CPV. Upper SM limit See the talk of 1.1% @ Nierste & Schach Phys. Rev. D92, Xiaokang Zhou for details 054036 (2015) + + 0 D → KS,LK (π ) BESIII arXiv:1611.01256 ACP = (-0.02 ±1.53 ±0.17)% • To be compared to the recent LHCb JHEP 10 (2015) 055 ACP = (2.9 ±5.2 ±2.2)% See the talk of 0 Varghese Babu D →Vγ Belle for details Phys. Rev. Lett. 118, 051801 (2017) •Radiative decays sensitive to NP (chromomagnetic dipole operators) 0 ACP(D →φγ)= (-9.4 ±6.6 ±0.1)% Most uncertainties still O (%) 0 ACP(D →K*γ)= (-0.3 ±2.0 ±0.0)% Still room for NP ACP(D0→ργ)= (5.6 ±15.2 ±0.6)% 30 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Outline • Mixing and CP violation basics • Flavour factories • Mixing and CPV in D0→K+π- decays 0 + (‘)- • Indirect CPV in charm (AГ and yCP with D →h h ) • Direct CPV searches in two-body D0→h+h- charm decays • Direct CPV searches in other two- or three-body charm decays • Direct CPV searches in multi-body charm decays (D0→�+�-�+�-) • Conclusions and prospects

31 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Multi-body decays and local asymmetries • Many ways to reach multi-body ﬁnal states through intermediate resonances • Local asymmetries potentially larger than the phase space integrated ones Discover CPV •Model-independent: Look for asymmetries in regions of phase space by “counting” binned (χ2 difference method) • Stat. Comp. Simul. 75, Issue 2 109-119 (2004), Nucl. Instrum. Methods A537, 626-636 (2005) •unbinned (Energy test, kNN)

•Model-dependent: Origin of CPV Fit all contributing amplitudes and look for differences in ﬁt

parameters 32 E.Gersabeck, Overview of the CP violation and mixing in the charm sector LHCb signal sample of DSearches0→� for +CPV� in- D�0 decays+� at- LHCbdecays

D*+ D0 PV soft π+ Pion tagged D0 decays • Phys. Lett. B 769 345-356 + 0 + • D* →D πs • ~1M signal candidates • Purity ~96% • Use all LHCb Run 1 sample • 2011+2012

•Previous LHCb D0→π+π−π+π- analysis using 2011 data, with binned approach, and P-even observables PLB726 (2013) 623

33 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Unbinned method: Energy test

Energy test: unbinned sample comparison used to assign p-value for hypothesis of identical distributions (= no CPV) Test statistic

• Compare average pair-wise distance in Dalitz plot between: all D0 events; all D̅0 events; all D0 to D̅0 events

• no CP violation → T≈0 First application of the method for a CPV search in D0→π-π+π0 PLB 740 (2015) 158-167 • CP asymmetry → T > 0 • For 4-body decays, introduce triple product CT as parity sensitive variable

Analyse different ﬂavours and signs of CT regions • 34 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Direct CPV searches in D0→�+�-�+�- decays (LHCb)

90 90 (a) (b) 80 LHCb 80 LHCb P-even Entries 70 Entries 70 P-odd 60 60 50 50 p-value: 40 40 p-value: 30 30 (4.6±0.5)% 20 20 (0.6±0.2)% 10 10 2.7σ 0 0 -2 0 2 4 6 -2 0 2 4 6 T value [10−6] T value [10−6]

3 3 ×10 ×10 ) 1 ] 2 ) 1 ] 2 c

σ c

σ 16

3 16 LHCb (c) LHCb (d) 14 P-even test 14 2 2 P-odd test only marginally 12 12 1 1 consistent with CP 10 10 consistent with no-CPV 0 0 8 Significance [

8 Significance [ symmetry -1 hypothesis 6 -1 6 4

4 Candidates / (0.03 GeV/ -2

Candidates / (0.03 GeV/ -2 2 2 -3 -3 0 0 0.5 1 1.5 0.5 1 1.5

2 m(π π π )[GeV/c2] m(π1π2π3)[GeV/c ] 1 2 3 3 3 ×10 ) 1 ] ×10 2 18 )

1 c

18 ] 2

3 c

σ 3 16 LHCb (f) 16 LHCb (e) 2 14 2 14 12 12 1 1 10 10 0 0

8 Significance [ 8 Significance [ -1 6 -1 6 4

4 Candidates / (0.02 GeV/ -2

Candidates / (0.02 GeV/ -2 2 2 -3 -3 0 0 0 1 Phys. Lett. B 769 345-356 0 0.4 0.6 0.8 1 1.21 0.4 0.6 0.8 1 1.2 2 2 m(π1π2)[GeV/c ] m(π1π2)[GeV/c ] 35 E.Gersabeck, Overview of the CP violation and mixing in the charm sector

0 1 0 1 D→4π and D→KKππ with CLEOc legacy data

+ - • Quantum-entangled states e e →Ψ(3770)→DaDb ± - + 0 • Tagging: K e.g. Db→K e ν then Da = D̅ CLEO-c legacy data

• 7k ﬂavoured tagged Db→4π candidates

P. d’Argent,... EG et al. arXiv:1703.08505 36 accepted for publication by JHEP E.Gersabeck, Overview of the CP violation and mixing in the charm sector Amplitude model and CPV search (CLEO-c legacy data)

P. d’Argent,... EG et al. arXiv:1703.08505 accepted for publication by JHEP

Check the backup for D→KKππ amplitude model and CP fractions results CLEO-c legacy data

37 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Outline • Mixing and CP violation basics • Flavour factories • Mixing and CPV in D0→K+π- decays 0 + (‘)- • Indirect CPV in charm (AГ and yCP with D →h h ) • Direct CPV searches in two-body D0→h+h- charm decays • Direct CPV searches in other two- or three-body charm decays • Direct CPV searches in multi-body charm decays (D0→�+�-�+�-) • Conclusions and prospects

38 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Conclusions

• Latest precision measurements in the charm sector at LHCb, BELLE, BESIII, BaBar, CLEO-c legacy data presented • CPV in charm not yet observed: All searches consistent with no direct or indirect CPV - some only marginally • 10-3 precision reached in direct CPV searches and 10-4 in the indirect CPV searches • no-mixing hypothesis excluded at >10σ already with LHCb Run I prompt data; different results agree well • measurement of the mixing parameters x and y is urgent: BESIII input is critical for precision measurements • The key measurements are still statistically limited; systematics reduces with statistics

39 E.Gersabeck, Overview of the CP violation and mixing in the charm sector What comes next? • Several key LHCb Run 1 analyses still ongoing; LHCb Run II analyses ongoing • Factor two gain in statistics seen with Run II LHCb data due to trigger optimisation, and even more with the upgraded LHCb experiment is expected • More data from LHCb and BESIII • BELLE2 will start taking data soon

upgrade of inner tracker plan 40 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Backup Charm Physics Marco Gersabeck

CP violation CP symmetry applies to processes invariant under the combined transformation of charge conjugation (C): exchange of particle and anti-particle and parity (P): spatial inversion

+ W W

b CP b Vub Vub⇤

u u CP violation discovered in 1964 in weak interactions of neutral Kaon decays by Cronin and Fitch CP symmetry conserved in the strong and the EM interaction The symmetry under CP transformation can be violated in different ways 42 E.Gersabeck, Overview of the CP violation and mixing in the charm sector

2 Types of CPV: direct CPV

The decay rate of a particle to a ﬁnal state f, Af, is different to the rate of the anti-particle decay to the

CP conjugate ﬁnal state f, ̅ A̅ f.̅

Direct CPV occurs for non-zero Ad

This type of CPV depends on decay mode.

43 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Types of CPV: indirect CPV CPV in mixing (involves neutral particles)

The transition probability of particles to anti- particles compared to the reverse process differs.

Occurs if:

Where p,q - complex coefﬁcients relating the mass and the ﬂavour eigenstates

44 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Types of CPV: indirect CPV CPV in interference (mixing and decay amplitudes can interfere)

Present if the imaginary part of λf is non-zero

φ is the CP violating relative phase between q/p and A̅ f ̅/Af

It involves neutral particles

The indirect CP violation is independent of the decay mode.

45 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Neutral D mesons

The neutral mesons can mix into each other via:

Short distance process Long distance process • Mixing box contains down-type quarks • No dominance of top mass as in B sector • CKM-suppression balances the GIM suppression ➡ Long-distance effects are important (but difﬁcult to calculate)

For neutral mesons, the mass eigenstates, i.e. the physical particles, do not a priori coincide with the ﬂavour eigenstates 46 E.Gersabeck, Overview of the CP violation and mixing in the charm sector The mass and width differences for the neutral

Δm negligible: very slow mixing

KS KL D1 D2

-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 -10 -8 -6 -4 -2 0 2 4 6 8 10 Δpsm-1 ps-1

Bd,L Bd,H Bs,L Bs,H

-3 -2 -1 0 1 2 3 -15 -10 -5 0 5 10 15 ps-1 ps-1

Δm large: very fast mixing 47 E.Gersabeck, Overview of the CP violation and mixing in the charm sector • Over 1000 lifetimes for 1 full oscillation • Difﬁcult to measure ➡ CP violation even more tricky to discover

48 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Mixing in D0→K+π- decays

Measure the decay rates of WS to RS events: two paths to reach the ﬁnal state no CF mix RS interference mix DCS

mixing no DCS ratio of WS mix to RS decays WS mix CF Mixing parameters

delta is the strong phase between CF and DCS

49 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Yield extraction of doubly-tagged D0→K+π- decays

• Use Run 1 data • Doubly-tagged candidates • 1.7M RS and 6.7k DCS candidates • Fit m(D*) in 5 different decay-time bins

) 70000 ) 2 700 2 LHCb LHCb Data 60000 Data 600 (b) (a) Fit 50000 Fit 500 Background 40000 Background 400

300 30000 Events / ( 0.05 MeV/c Events / ( 0.05 MeV/c 200 20000

100 10000

20004 2005 2010 2015 2020 2025 20004 2005 2010 2015 2020 2025 0 2 0 2 2 m(D πs) [MeV/c ] 2 m(D πs) [MeV/c ] σ σ / / 0 0 ∆ ∆ −2 −2 −4 −4 2000 2005 2010 2015 2020 2025 2000 2005 2010 2015 2020 2025 0 2 m(D0π ) [MeV/c2] m(D πs) [MeV/c ] s 50 Phys. Rev. D 95, 052004 (2017) E.Gersabeck, Overview of the CP violation and mixing in the charm sector 4.8 LHCb 4.6 Mixing in doubly-tagged 4.4 D0

] 4.2 -3 0 + - 4 [10

D →K π decays + 3.8 R 3.6 Measure R(t) in bins of decay time:(*separate 3.4 • 3.2 signal and background) 3 4.8 0 1 2 3 4 0 D0 t/τ ﬂat: no mixing 4.6 D • 4.4

] 4.2 -3 non-flat: mixing 4 [10 • - 3.8 R 3.6 No CPV • Efficiency-corrected data fitted to extract 3.4 No Direct CPV under three hypotheses: 3.2 All CPV allowed 3 0.8 0 1 2 3 4 0 No CPV 0.6 0 0 D t/τ ] D − D • -3 0.4 0.2

+ − [10 • No direct CPV (RD = RD ) - 0

- R −0.2 + −0.4 All CPV allowed R • −0.6 −0.8 0 1 2 3 4 • No evidence for CPV in mixing or decay t/τ • Statistical uncertainties dominate • Inconsistent with no-mixing hypothesis at 4.6σ (Reminder: Results exclude the no-mixing hypothesis at 9.1σ already with 2011 LHCb prompt data) Phys. Rev. D 95, 052004 (2017) 51 E.Gersabeck, Overview of the CP violation and mixing in the charm sector LHC & LHCb

52 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Forward spectrometer at LHC LHCb is optimised for heavy ﬂavour physics bb ̅ (and cc)̅ production angles strongly correlated: heavily boosted in the forward or backward direction

JINST 3 (2008) S08005 Int. J. Mod. Phys. A 30 1530022 • Forward acceptance 2<η<5 • Precise vertex reconstruction • Precise & efﬁcient tracking • Excellent decay time resolution ~0.1τD • Hadron identiﬁcation: RICHes • Dipole magnet with reversible polarity 53 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Run 1 performance

Instantaneous Luminosity levelling unlike ATLAS and CMS: uniform operating conditions

• In total: • 2010: 37 pb-1 @ 7 TeV • 2011: 1 fb-1 @ 7 TeV • 2012: 2 fb-1@ 8 TeV

54 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Charm production cross-sections @ 7TeV in LHCb acceptance

All c species produced at LHCb D0

• Cross section for cc ̅ in LHCb acceptance 2010 data Nucl.Phys. B871 (2013) 1-20

• ~5x1012 D0 mesons produced in LHCb acceptance in run1 • Huge statistics of prompt and secondary charm: worlds’ best sensitivity to very small CP asymmetries 55 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Direct CPV

• Condition for direct CPV: |A/A̅|≠1 • Need A and A̅ to consist of (at least) two parts: with different weak (φ) and strong (δ) phases • Divide amplitudes into leading and sub-leading parts:

A(D→f) = C(1+rei(δ+ϕ)) • C is the leading amplitude A̅(D̅→f) = C(1+re̅ i(δ−ϕ)) • r is the ratio of sub-leading over leading amplitude

• CP violation requires difference in strong (δ) and weak phase (ϕ): 2 2) 2 2 aCP ≡ ( | A| -| A̅| )/ (| A| +| A̅| ) = 2 r sin(δ) sin(ϕ)

56 E.Gersabeck, Overview of the CP violation and mixing in the charm sector CPV in decay: SCS D0→h+h- decays

Often realised by “tree” and “penguin” diagrams

Vud,Vus Tree-level weak decay amplitude. • involves the CKM matrix elements 0 + - • Vus and Vcs for D → K K Vcd, Vcs 0 + - • Vud and Vcd for D → π π Vuq One-loop amplitude (“penguin”) * V • b-loop involves Vub V cb : tiny cq s and d loops: similar magnitude, • q=d,s,b opposite sign

Vus ≈ -Vcd ≈ 0.22 gives the Cabbibo suppression 57 E.Gersabeck, Overview of the CP violation and mixing in the charm sector What to expect?

Individual asymmetries are expected to have opposite sign due to CKM structure

Direct CP violation depends on the decay mode: can be different for different ﬁnal states

Expect non-zero ΔACP = ACP(KK)-ACP(ππ) result in presence of direct CP violation

58 E.Gersabeck, Overview of the CP violation and mixing in the charm sector ΔACP

where

Mostly a measure of direct CPV The indirect CPV is expected to cancel but a small amount could be present due to the different decay time acceptance of the two decays

59 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Theoretical expectations

dir -2 aCP <10 within the SM Enhancements up to 1 order of magnitude possible in some BSM models

SU3 limit

Global ﬁt of D->hh branching ratios to topological amplitudes including linear SU(3)F breaking and 1/Nc-counting

Müller, Nieste, Schacht, Phys. Rev. Lett. 115, 251802 (2015)

60 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Production asymmetries Production rates of B0 and B0̅ (or D0 and D̅0) are not the same gluon fusion, quarks combine with valence quark from the beam protons, valence quark scattering, etc.

61 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Detection asymmetries (1) • Detector asymmetries

• Cancel left-right asymmetries by swapping dipole ﬁeld • But do not rely only on it (detectors move, alignment changes etc. )

62 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Detection asymmetries (11) • Interaction asymmetries: e.g. K+ cross-section for Introductioninteraction with matter differs from K- cross-section

PDG

If we want to measure CP asymmetries63 in modes with an odd number • E.Gersabeck, Overview of the CP violation and mixing in the charm sector of kaons*, then we need to measure the kaon detection asymmetry.

0 The updated RS/WS D → Kπ analysis will ﬁt for RD+ and RD-, + - which requires external input for the K π detection asymmetry.

+ - * * Or modes with a kinematically asymmetric K K pair (e.g. asl with Bs → Ds (→K K)μνX)

Wednesday, February 13, 13 2 Cancellation of nuisance asymmetries

The detection asymmetries as well as the production asymmetries depend on the kinematics of the decay

JHEP 07 (2014) 041 JHEP 1407 (2014) 041

AD, A P (~1%) cancel to 1st order but if the decays are kinematically very different there would be a residual nuisance asymmetry: equalise the KK and ππ kinematical distributions by re-weighting

64 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Strategy D*+ D0 PV soft π+ • 2 independent analyses using different approaches • Binned analysis using 3fb-1 • Unbinned analysis using 2fb-1@ 8TeV, and a statistical combination with the previous measurement using 1fb-1 @ 7 TeV • Both analyses use pion-tagged D0 • Both methods have different systematic uncertainties • Both methods have been validated by measuring a value for pseudo AГ compatible with 0 • Muon-tagged charm decays results on 3fb-1 available in JHEP 04 (2015) 043

65 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Unbined method: strategy

• Analyse 2012 data only, 2011 data have been analysed using the same approach PRL 112 (2014) 041801 • Blind analysis 0 0 • Measure the effective lifetimes of D and D̅ decays • Empirically evaluating the per-event proper-time acceptance • Two stage fit: first fit m(D0) and Δm (= m(D*+) - 0 0 2 m(D )); then fit D decay time and ln(IP� D0)

66 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Example of the two-staged ﬁt using D0→ππ decays

0 PRL 112 (2014) 041801 m(D ) Δm ) )

5000 2 2 c c Data LHCb 5000 LHCb 4000 Fit Signal 4000

3000 Random πs 1 3000 Comb. bkg

2000 2000 Candidates / ( 0.04 MeV/

Candidates / ( 0.33 MeV/ 1000 1000

0 1840 1860 1880 1900 140 145 150 m(π+ π-) [MeV/c2] ∆ m [MeV/c2] 0 2 D decay time ln(IP� D0) ×103 8 Data LHCb 7 LHCb Fit Prompt Signal 6 103 Secondary 5 Prompt random πs

2 Candidates / 0.04

Candidates / ( 0.02 ps ) 4 Sec. random πs 3 Comb. bkg 102 2 1 0 1 2 3 −5 0 5 t [ps] ln(χ2 (D0)) 67 IP E.Gersabeck, Overview of the CP violation and mixing in the charm sector Example of the two-staged ﬁt using D0→ππ decays

m(D0) Δm PRL 112 (2014) 041801 ) )

5000 2 2 c c Data 5000 LHCb Fit LHCb 4000Separation between signal, random slow pion Signal 4000

3000 Random πs 1 background and combinatoric/speciﬁc3000 backgrounds Comb. bkg

2000 2000 Candidates / ( 0.04 MeV/

Candidates / ( 0.33 MeV/ 1000 1000

0 1840 1860 1880 1900 140 145 150 m(π+ π-) [MeV/c2] ∆ m [MeV/c2] 0 2 D decay time ln(IP� D0) ×103 8 Data LHCb 7 LHCb Fit Prompt Signal Separation between prompt 6 103 Secondary 5 and secondary decays Prompt random πs

2 Candidates / 0.04

Candidates / ( 0.02 ps ) 4 Sec. random πs 3 Comb. bkg 102 2 1 0 1 2 3 −5 0 5 t [ps] ln(χ2 (D0)) 68 IP E.Gersabeck, Overview of the CP violation and mixing in the charm sector Indirect CP violation in D0→h+h- (3 fb-1)(binned) • Analyse 2011+2012 data, blind analysis • Flavour tagged using the sign of the pion in the strong decay D*+→D0π • Split data in bins of D0 decay time; extract yield by ﬁtting Δm (= m(D*+) - m(D0))

• Correct for detector non-uniformities and presence of secondary decays PRL 112 (2014) 041801 35000 Data LHCb 30000 Fit ( 2/ndf = 22) χ D0 → K−π+ Assuming only indirect contribution 25000 Prompt Secondary assumed to be universal, the average 20000 15000 Candidates / 0.20 10000 5000 0 −10 −5 0 5 10 ln(χ2 (D0)) E.Gersabeck, Overview of the CP violation69 and mixing in the charm sector IP AΓ measurement

70 E.Gersabeck, Overview of the CP violation and mixing in the charm sector YCP

● Mixing parameter, if no CPV

yCP=y

71 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Phys. Lett. B 767 177-187 + + Direct CPV search in D (s)→�’�

• No CPV yet observed in any charm decays • Can strongly depend on ﬁnal state • ⇒ investigate more channels • CP asymmetries in decays to η’ poorly constrained – not yet measured at hadron collider. • Small (<0.1%) in SM • Usual strategy: Subtract detector asymmetries using control channels • Main challenge: Background modelling.Main physics BG from D(s)+➝π+ (φ➝π+π−π0)

E.Gersabeck, Overview of the CP violation and mixing in the charm sector + + Direct CPV search in D (s)→�’� : Method

Fit m(η‘�±) to Control channel External input extract raw asymmetry (D0, Belle) arXiv:1701.01871 asymmetry submitted to PLB ± ± Data sample: 63k D and 152k D s

Separate by magnet polarity and collision energy.

Bin in η(π), pT(π) to improve cancellation of detector asymmetries

74 E.Gersabeck, Overview of the CP violation and mixing in the charm sector + + Direct CPV search in D (s)→�’�

arXiv:1701.01871• Main challenge: Background Bin in η(π), pT(π) to improve submittedmodelling. to PLB Main physics BG from cancellation of detector asymmetries D(s)+➝π+(φ➝π+π−π0) arXiv:1701.01871 submitted to PLB • Also gives largest systematic uncertainty • Statistically limited • Additional uncertainty from external ACP(control) inputs Consistent with CP conservation

Most precise measurements to date of these variables

75 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Multi-body decays and local asymmetries

• Many ways to reach multi-body ﬁnal states through intermediate resonances • Resonances interfere and can carry different strong phases: Superb playground for CP violation

Local asymmetries • potentially larger than the phase space integrated ones • may change sign across the phase space • additional information about the dynamics

76 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Shanzhen Chen @ CHARM 2016 Energy testSearches for CPV in D0 decays at LHCb

• Compare two distributions statistically • Idea comes from the calculation of electric potential energy

+q and −q equally distributed, electric potential energy = 0

77 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Shanzhen Chen @ CHARM 2016 Energy testSearches for CPV in D0 decays at LHCb

• Compare two distributions statistically • Idea comes from the calculation of electric potential energy

+q and −q equally distributed, electric potential energy = 0 +q and −q distributions different, electric potential energy > 0

78 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Shanzhen Chen @ CHARM 2016 Energy testSearches for CPV in D0 decays at LHCb

System → phase space +q /−q → opposite flavoured decays

2 −dij /2δ ψ(dij ) = e : interaction potential 0 n, n: number of D0, D candidates

dij : distance in phase space δ - tunable parameter: effectively, radius in the phase space in which a local asymmetry is measured _ _ _ D0-D0 D0-D0 D0-D0 1 n 1 n 1 n,n Test statistic: T = ψ(dij )+ ψ(dij )− ψ(dij ) n(n−1) ∑ n(n−1) ∑ nn∑ i, j>i 79 i, j>i i, j E.Gersabeck, Overview of the CP violation and mixing in the charm sector Energy test Searchesp-value for CPV in D0 decays at LHCb

Phys. Lett. B 769 345-356

Calculate p-value for no CPV s • e

r LHCb preliminary hypothesis t 60

E • Compare T-value from tested 50 sample (T0) with T-values from no- 40 T0 CPV samples 30 • No-CPV sample from permutation 20 of data: randomly assign ﬂavour 10

tags 0 -2 0 2 4 6 • p-value: fraction of permutation T value [10−6] T-values above T0 Large p-value, no-CPV

80 E.Gersabeck, Overview of the CP violation and mixing in the charm sector New P-odd observablesSearches for CPV in D0 decays at LHCb

• In decays to four or more pseudo-scalars, there is the possibility of using P-parity-odd observables for CP violation searches • Four-body-decay kinematics cannot be described unambiguously using only invariant-mass-squared variables, as these are all parity even

• Introduce triple product CT as parity sensitive variable

• Analyse different ﬂavours and signs of CT regions

81 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Detection / tracking / productionSearches for CPV asymmetriesin D0 decays at LHCb

• Cancellations occur due to method • Veriﬁed with a control sample of Cabibbo-favoured D0→K-π+π+π- decays • Split into ten sub-samples equal in size to signal mode • Sensitive with neither P-even nor P-odd tests • p-value distributions for reference sample

82 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Sensitivity tests withSearches Monte for CPV in D 0 Carlodecays at LHCb

• Performed for both P-even and P-odd tests Phys. Lett. B 769 345-356 Insert CP violation to simulated samples*, apply energy • R (partial wave) (A,) p-value (ﬁt) test, determine the sensitivity 0 +3.4 4 a1 ⇢ ⇡ (S) (5%, 0)2.6 1.7 10 ! 0 +3 .6 ⇥ 6 a1 ⇢ ⇡ (S) (0%, 3)1.2 1.2 10 0 !0 +2 .9 ⇥ 3 Visualise signiﬁcance of asymmetries by assigning per- ⇢ ⇢ (D)P (5%-even, 0)3.8 10 • 1.9 0 0 +24 ⇥ 6 event T-values ⇢ ⇢ (D) (0%, 4)9.6 7.2 10 0 0 +1 .2 ⇥ 3 ⇢ ⇢ (P) (4%, 0)3.0 0.9 10 0 0 +4 .4 ⇥ 4 Highlight those >1,2,3σ positive in pink, negative in ⇢ ⇢ (P) (0%, 3)9.8 3.8 10 • P-odd ⇥ blue ×103 3 ) 1 ×10 ) ] 2 1 ] 2

c 18

σ c

16 σ (c) 3 16 LHCb LHCb (e) 2 14 14 simulation simulation 2 12 12 1 1 Example: 10 10 0 0 3° phase difference

Significance [ 8 8 Significance [ 0 + - in D →a1(1260) π -1 6 -1 6 Amplitude 4 4 Candidates / (0.03 GeV/ -2

Candidates / (0.02 GeV/ -2 2 2 (P-even test) -3 -3 0 0 0.5 1 1.5 0.4 0.6 0.8 1 1.2

m(π π π )[GeV/c2] 2 1 2 3 m(π1π2)[GeV/c ] *Amplitude model taken from P. d’Argent, N. Skidmore ... E.Gersabeck et al. arXiv:1703.08505 83 E.Gersabeck, Overview of the CP violation and mixing in the charm sector

0 1 0 1 D→KKππ amplitude model and CPV search

P. d’Argent,... EG et al. arXiv:1703.08505 accepted for publication by JHEP

84 E.Gersabeck, Overview of the CP violation and mixing in the charm sector but before that

Prospects Run11 and beyond Improved trigger strategies for Run11

• Turbo stream of the trigger: • Data are ready for analysis directly after the trigger • Smaller size of raw events: reduce pre-scaling • More efﬁcient exclusive charm triggers • Split high level trigger in 2 stages: gain CPU power • Events from lower trigger levels can be buffered on disk while performing real-time alignment and calibration • Improved speed of the algorithms

86 E.Gersabeck, Overview of the CP violation and mixing in the charm sector Run 2 cross-sections & estimated integrated luminosity • More data!!! Higher cross-sections in LHCb acceptance x2 @ 13TeV JHEP03(2016)159; JHEP09(2016)013; JHEP05(2017)074

compare to Run 1 @ 7TeV 2010 data Nucl.Phys. B871 (2013) 1-20

Run1 Run2 Run3 Run4 Run5

100 3 fb-1 8 fb-1 23 fb-1 46 fb-1 fb-1 -4 ΔaCP: uncertainty 10 at 50 fb-1 upgrade; gain more data by removing the L0 thresholds 87 E.Gersabeck, Overview of the CP violation and mixing in the charm sector