Measuring the CKM Angle Γ

Measuring the CKM angle γ

Matthew Kenzie University of Cambridge

Neckarzimmern B Physics Workshop

March 22, 2017 1. Football 2/77 γ as a preamble to this evenings entertainment...?

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 1. Introduction 3/77 1. Introduction

1 Introduction

2 CP violation and the CKM matrix

3 The LHCb Experiment

4 CKM angle γ

5 Combination of Measurements

6 Conclusion and Prospects

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 1. Introduction 4/77 Summary of 2016

March 2016 - Started with such promise

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 1. Introduction 5/77 Summary of 2016

March 2016 - Started with such promise

June 2016 - Brexit

My levels of despair

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 1. Introduction 6/77 Summary of 2016

March 2016 - Started with such promise

June 2016 - Brexit November 2016 - Trump

My levels of despair

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 1. Introduction 7/77 Summary of 2016

March 2016 - Started with such promise

June 2016 - Brexit November 2016 - Trump

End of 2016 - Still no New Physics (NP)

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 1. Introduction 8/77 Don’t despair!

I Direct NP discovery by ATLAS/CMS is still possible

I Flavour sector provides another window of opportunity

I Today I will discuss looking for new sources of CPV by constraining CKM angle γ

I Mainly focused towards LHCb’s searches I Also include information from Belle and BaBar for HFAG / CKM / PDG world average I With some future prospects from Belle II and LHCb

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 1. Introduction 9/77 How does a matter dominated universe arise?

Sakharov:

1. Baryon Number Violation 2. C and CP violation 3. Interactions out of thermal equilibrium

I We live in a matter (and photon) dominated universe I CP violation is a crucial ingredient to this problem 20 I CPV in the SM (∼ 10− ) does not nearly account for the observed baryon-photon 10 ratio (∼ 10− ) Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 2. CP violation and the CKM matrix 10/77 2. CP violation and the CKM matrix

1 Introduction

2 CP violation and the CKM matrix

3 The LHCb Experiment

4 CKM angle γ

5 Combination of Measurements

6 Conclusion and Prospects

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 2. CP violation and the CKM matrix 11/77 CKMCP matrix ViolationCP Violation in the in SM:the SM: CKM CKM matrix matrix

I In the SM quarks can change ﬂavour by emission of a W ± boson I Quark mixing in the SM is described by the 3 × 3 unitary CKM matrix

CKM matrix       d 0 Vud Vus Vub d flavor flavor  s0  =  VcdmassV cs massVcb  ·  s  eigenstates eigenstates b0 Veigenstatestd Veigenstatests Vtb b ﬂavour mass eigenstates eigenstates Cabibbo Cabibbo KobayashiKobayashi MaskawaMaskawa matrixI The matrixelements matrix elements determine determine determine transition the transition transition probabilities: probabilities: probability

Marseille,I ParameterisedMarchMarseille, 2015 March 2015 by three mixingT.M. Karbach anglesT.M. / CERN Karbach (θ12 / LHCb, / θCERN13, θ / 23LHCb) and a CP violating phase12 (δ) 12

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 2. CP violation and the CKM matrix 12/77 CKM matrix

I The CKM matrix exhibits a clear hierachy, sin(θ13) << sin(θ23) << sin(θ12) << 1, so often expressed in Wolfenstein parameterisation (A, λ, ρ, η)

Wolfenstein parametrisation    2 CP Violation3 in the SM: CKM matrix Vud Vus Vub 1 − λ /2 λ Aλ (ρ − iη) 2 2 4 V =  Vcd Vcs Vcb  =  −λ 1 − λ /2 Aλ +O(λ ) 3 2 Vtd Vts Vtb Aλ (1 − ρ − iη) −Aλ 1

I Hierachy gives very distinctive behaviour to the ﬂavour sector of the SM which gives strong constraints on NP I CKM matrix gives the only source of CP violationTriangle in thein the SM complex (mν = plane.θQCD = 0)

Unitarity gives a triangle in the complex plane

Vud Vub∗ + Vcd Vcb∗ + Vtd Vtb∗ = 0 V V V V ⇒ ud ub∗ + 1 + td tb∗ = 0 Area corresponds to the total CP violation Vcd V ∗ Vcd V ∗ cb cb in the Standard Model. I Area corresponds to total CPV in SM

I SM implies that α + β + γ = 180◦

Matthew Kenzie (Cambridge) Neckarzimmern B PhysicsMarseille, Workshop March 2015 MeasuringT.M. Karbach the / CERN CKM / LHCb angle γ 14 2. CP violation and the CKM matrix 13/77 CKM picture is now well veriﬁed

I Any discrepancies would be of great importance I CKM angle γ is the least well known constraint

1995 2016

1.5 excluded at CL > 0.95 excluded area has CL > 0.95 γ 1.0 ∆ ∆ md & ms sin 2β 0.5 ∆ md ε α K γ β

η 0.0 2004 α

Vub α •0.5

ε •1.0 γ K CKM f i t t e r sol. w/ cos 2β < 0 ICHEP 16 (excl. at CL > 0.95) •1.5 •1.0 •0.5 0.0 0.5 1.0 1.5 2.0 ρ

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 2. CP violation and the CKM matrix 14/77 CKM picture is now well veriﬁed

I Any discrepancies would be of great importance

I CKM angle γ is the least well known constraint

1995

2016 - zoom

0.7 m & m CKM ∆ d ∆ s f i t t e r 0.6 γ m ∆ d εK ICHEP 16

0.5 sin 2β sol. w/ cos 2β < 0 (excl. at CL > 0.95) 2004 0.4 excluded area has CL > 0.95 η 0.3 α α 0.2

Vub 0.1 γ β α 0.0 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 ρ

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 2. CP violation and the CKM matrix 15/77 CKM picture is now well veriﬁed

I Any discrepancies would be of great importance

I CKM angle γ is the least well known constraint

1995 Direct γ measurements Indirect γ extrapolation +5.4 +1.0 γ = (72.1 5.8)◦ γ = (65.3 2.5)◦ − − 2015 - zoom

0.7 ∆m & ∆m CKM γ d s f i t t e r 0.6 ∆m ε d K ICHEP 16

0.5 sin 2β 2016 sol. w/ cos 2β < 0 (excl. at CL > 0.95) 2004 0.4 excluded area has CL > 0.95 η 0.3 α α 0.2

Vub 0.1 γ β α 0.0 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 ρ

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ None of the considered models will be presented in detail. We restrict our presentation to what is needed for our purpose and refer the reader to the original literature for any additional information.

5.1 Precision CKM Matrix Next-generation flavor experiments are expected to increase the precision of the determination of SM2. CP flavor violation parameters and the CKM matrix by one order of magnitude. This is a first step16/77 in the quest for NP. Indeed, the high-correlated SM scenario, represented by the overlapping of several CP-conserving and CP- The Ultimate Testviolating constraints in the UT analysis, can easily break down in the presence of new flavor structures. Figure 5 illustrates a conceivable scenarios at the end of next-generation flavor experiments: some of the improved experimental constraints of the UT no longer overlap signaling the presence of source I γ is an excellent probe of new physics Not just via directof flavor- / indirect and disagreement CP-violation beyond but many the constraints CKM matrix. from The new generalized physics in UT analysis, exploiting the I high-precision tree-level constraints, V /V and , can still determine the CKM parameters and, in neutral mixing require input of γ | ub cb| addition, point out the amplitudes deviating from the SM [44].

“The nightmare” - [arXiv:0710.3799] “The dream” - [arXiv:1110.3920]

0.6 0.6 η ∆md η ∆ms ∆m 0.5 0.5 d ∆ms

0.4 0.4 BR(B ντ→ ) α

0.3 εK 0.3 εK 2β+γ

0.2 β 0.2 β

Vub V cb Vub 0.1 ∆md 0.1 γ ∆md Vcb γ α 0 0

-0.1 -0.1 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 ρ ρ

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ Fig. 3: Regions corresponding to 95% probability for the CKM parameters ρ¯ Figureand η¯ selected 5: Extrapolation by different of con- the UT fit using the precisions expected at the next-generation flavor straints, assuming present central values with present errors (left) or with errorsfacilities. expected at Central a SFF tuning values central of all constraints are kept at the present averages. values to have compatible constraints (right). On the other hand, it could happen that the improved UT experimental constraints continue to overlap in one point. This would imply that NP is not showing up in these constraints, mainly coming from mixing amplitudes, even with the increased accuracy. Nonetheless the determination of the CKM 3 Phenomenological Impact parameters would still be improved resulting in a better knowledge of the SM contribution to other FCNC and CP violating processes and increasing in this way their sensitivity to NP. For example, the The power of a SFF to observe NP and to determine the CKM parameterserror precisely on the SM is prediction manifold. of In a golden mode for NP searches in kaon physics, the CP-violating decay the following, we present a few highlights of the phenomenological impactK (for⇡ more0⌫⌫¯, isdetailed presently analyses dominated by the uncertainty of the CKM parameters [45]. L ! see [1, 2, 4–6]). It is worth mentioning that the UT fit extrapolation shown above requires an improved theoretical Precise Determination of CKM Parameters in the SM: Most of the measurementscontrol of the describedhadronic uncertainty. in the Lattice QCD seems able to reach the required accuracy on the previous section can be used to select a region in the ρ–η plane as shown intime Figure scale 3. of The future corresponding experiments [5, 9]. Data-drive methods, based on the heavy quark expansion or on flavor symmetries, are also promising. numerical results are given in Table 2. The results indicate that a precision of a fraction of a percent can be reached, significantly improving the current situation, and providing a generic test of the presence of 5.2 Supersymmetric Models NP at that level of precision. Note that in the right plot of Figure 3 - where the expected precision offered by a SFF is used - the validity of the SM is assumed, so the compatibilityThe of all Minimal constraints Supersymmetric is put in by Standard Model (MSSM) is the supersymmetric extension of the SM hand. In contrast, in Figure 4 we assume that all results take the centralwith values N=1 of supersymmetry their current world (SUSY), minimal particle content and R-parity conservation. The particle averages with the expected precision of a SFF. In this case, the hints of discrepanciesspectrum is doubled present in by today’s the inclusion of supersymmetric partners and the Higgs sector is extended to include a second weak doublet (for a primer on the MSSM see for instance ref. [46]). While addressing data have evolved into fully fledged NP discoveries. most of the SM problems, the MSSM does not contain an explanation for supersymmetry breaking and

Table 2: Uncertainties of the CKM parameters obtained from the Standard Model ﬁt using the experimental and 16 theoretical information available today (left) and at the time of a SFF (right). The precision corresponds to the plots in Figures 3 and 4.

Parameter SMFittoday SMFitataSFF ρ 0.163 0.028 0.0028 ± ± η 0.344 0.016 0.0024 ± ± α ( ) 92.7 4.2 0.45 ◦ ± ± β ( ) 22.2 0.9 0.17 ◦ ± ± γ ( ) 64.6 4.2 0.38 ◦ ± ±

Of course, many of the measurements used for the SM determination of ρ–η can be affected by the presence of NP. Thus, unambiguous NP searches require a determination of ρ and η in the presence of arbitrary NP contributions, which can be done using ∆F =2processes.

10 2. CP violation and the CKM matrix 17/77 The Ultimate Test

I LHCb expected precision in 2019 (end of Run 2) ∼ ±3-4◦

I LHCb expected precision in 2024 (end of Run 3) ∼ ±1.5◦

I Belle II expected precision in 2023 (end of Run) ∼ ±1.5◦

I LHCb expected precision in 2029 (end of Run 4) < 1◦

0.7 ∆m & ∆m CKM γ d s f i t t e r 0.6 ∆m ε d K ICHEP 16

0.5 sin 2β sol. w/ cos 2β < 0 (excl. at CL > 0.95) 0.4 excluded area has CL > 0.95 η 0.3 α α 0.2

Vub 0.1 γ β α 0.0 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 World Average ~2025 ρ World Average ~2030

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 2. CP violation and the CKM matrix 18/77 CP violation

I CKM matrix is the only place in the SM with CP violation (mν = θQCD = 0)

I Given CPV in SM is ten orders of magnitude to small to explain baryon-photon ratio

I New sources of CP violation would be a clear indiction of NP

LHCb - [PRD 90 (2014) 112004]

+ + + + B K K⇡ B K K⇡ )

2 400 ! !

c Model − 350 LHCb B±→π±K+K 300 CP Combinatorial BS→4-body 250 B→4-body − 200 B±→K±K+K ± ± + − 150 B →K π π 100 50 3 3 0 ×10 ×10 Candidates / (0.01 GeV/ 5.1 5.2 5.3 5.4 5.5 5.1 5.2 5.3 5.4 5.5 m(π−K+K−) [GeV/c2] m(π+K+K−) [GeV/c2]

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 2. CP violation and the CKM matrix 19/77 CPV recap

I Phenomenology of quark mixing → neutral meson osciallation 0 0 0 0 0 0 2 2 BH = qB + qB and BL = pB − qB where p + q = 1 (1) I Define decay amplitudes to final state f as ¯ ¯ ¯ ¯ Af = Γ(B → f ) , Af = Γ(B → f ) , Af¯ = Γ(B → f ) , Af¯ = Γ(B → f ) (2) I For any hadron carrying conserved quantum numbers (any charged meson and all baryons) then B and B cannot decay to same final state I Only possible manifestiation of CPV is: ¯ I CPV in decay: Af = Af¯ | | 6 | | ¯ q Af I For neutral mesons (consider f as a CP eigenstate) define λf = p Af ¯ I CPV in decay: Af /Af = 1 (as for charged mesons) | | 6 I CPV in mixing: q/p = 1 | | 6 I CPV in mixing/decay interference: arg(λf ) = 0 6 Summary of observed CPV effects - [arXiv:1607.06746]

0 + 0 + + + 0 + 0 0 K K Λ D D Ds Λc B B Bs Λb Mixing -- --- - - Mixing/Decay Int. -- --- - - Decay

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 3. The LHCb Experiment 20/77 3. The LHCb Experiment

1 Introduction

2 CP violation and the CKM matrix

3 The LHCb Experiment

4 CKM angle γ

5 Combination of Measurements

6 Conclusion and Prospects

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 3. The LHCb Experiment 21/77 LHC, CERN, Geneva

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 3. The LHCb Experiment 22/77 LHCb Detector

I A single arm forward spectrometer

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 3. The LHCb Experiment 23/77 LHCb Detector

I A single arm forward spectrometerLHCb I A factory for beauty and charm decays

I Acceptance● one range arm 2 forward< η < 5 spectrometer 100K bb pairs produced per second (104× B I ● b pair production angles factories) strongly correlated I σ(bb) = 284 ± 54µb ● covers 1.9 < η < 4.9 I σ(cc) ≈ 20 × σ(bb) ● 100'000 bb pairs produced per 4 second (10 x B factories) LHCb acceptance LHCb performance paper - [arXiv:1412.6352] ATLAS/CMS acceptance [PLB 694 (2010) 209] I IP resolution ≈ 20µm

I p resolution ≈ 0.5% [LHCb-CONF-2010-013]

I τ resolution ≈ 45 fs 0 I Calorimeter ID for γ, e, π

I Particle ID (K) ∼ 95% with 5% π → K mis-id

I Muons (µ) ∼ 97% with (1 − 3)%π → µ mis-id Marseille, March 2015 T.M. Karbach / CERN / LHCb 8

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 3. The LHCb Experiment 24/77 LHCb Trigger

LHCb 2015 Trigger Diagram

40 MHz bunch crossing rate

I The detector is complimented with an incredibly sophisticated and versatile trigger system L0 Hardware Trigger : 1 MHz readout, high ET/PT signatures I Allow detector alignment and calibration in real time! 450 kHz 400 kHz 150 kHz h± µ/µµ e/γ I In turn means online and oﬄine reconstruction

are identical Software High Level Trigger

I Allows performing of many analyses online Partial event reconstruction, select displaced tracks/vertices and dimuons I Allows high readout rate

I High eﬃciency for a broad range of topics Buffer events to disk, perform online detector calibration and alignment I Larger gains expected in the future (full software readout) Full offline-like event selection, mixture of inclusive and exclusive triggers

12.5 kHz Rate to storage

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 25/77 4. CKM angle γ

1 Introduction

2 CP violation and the CKM matrix

3 The LHCb Experiment

4 CKM angle γ

5 Combination of Measurements

6 Conclusion and Prospects

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 26/77 Measuring γ

I γ is the phase between Vub∗ Vud and Vcb∗ Vcd I Require interference between b cW and b uW to access it → → ∗ I No dependence on CKM elements involving the top Vud Vub γ = arg − V V ∗ I Can be measured using tree level B decays cd cb I Makes it a benchmark of the SM (no loops) ( ) 0 I The “textbook” case is B± → D K ±: 0 0 I Transitions themselvesfirst havemethod different finalto measure states (D and γD ) 0 0 I Interference occurs when D and D decay to the same final state f Reconstruct the D0/D0 in a final state accesible to both to acheievefirst interference method to measure γ

0 I The crucial feature of these (and similar) decays is that the D can be reconstructedWe need to in reconstruct several diﬀerent the ﬁnal meson states in a final state accessible to both Matthew Kenzie (Cambridge)to achieve interference. Neckarzimmern B Physics Workshop Measuring the CKM angle γ

Marseille, March 2015 T.M. Karbach / CERN / LHCb 34 We need to reconstruct the meson in a final state accessible to both to achieve interference.

Marseille, March 2015 T.M. Karbach / CERN / LHCb 34 4. CKM angle γ 27/77 γ from theory

∗ Vud Vub γ = arg − ∗ Vcd Vcb

I γ is known very well I Can be determined entirely from tree decays

I Unique property among all CP violation parameters I Hadronic parameters can be determined from data

I Neglible theoretical uncertainty (Zupan and Brod 2013)

Theory uncertainty on γ 7 δγ/γ ≈ O(10− )- [arXiv:1308.5663]

I γ can probe for new physics at extrememly high energy scales (Zupan) 2 I (N)MFV new physics scenarios: (10 ) TeV ∼ O 3 I gen. FV new physics scenarios: (10 ) TeV ∼ O I NP contributions to C1,2 can cause sizeable shifts( O(4◦)) in γ (Brod, Lenz et. al 2014) - [arXiv:1412.1446]

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 28/77 γ from experiment

I γ is NOT known very well

I It is quite challenging to measure

I The decay rates are small

Branching ratio for suppressed γ mode 7 BR(B− → DK −, D → πK) ≈ 2 × 10−

I Small interference eﬀect typically ∼ 10%

I Fully hadronic decays - hard to trigger on 0 I Many channels have a KS in the final state - low efficiency 0 I Many channels have a π in the final state - very hard at LHCb

I Many diﬀerent decay channels, many observables and many hadronic unknowns make it statistically challenging

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 29/77 Methods to measurefirstγ method to measure γ Reconstruct the D0/D0 in a ﬁnal state accesible to both to acheieve interferencefirst method to measure γ

I GLW method I CP eigenstatesWe need to reconstruct e.g. D → theKK meson in aI final[Phys. state Lett. accessible B253 (1991) to both 483] I Gronau,to achieve London, interference. Wyler (1991) I [Phys. Lett. B265 (1991) 172]

I ADS method Marseille, March 2015 T.M. Karbach / CERN / LHCb 34 I CF or DCS decays e.g. D → Kπ I [Phys. Rev. D63 (2001) 036005] I Atwood, Dunietz, Soni (1997,2001) WeI [Phys. need Rev.to reconstruct Lett. 78 (1997) the 3257] meson in a final state accessible to both to achieve interference. I GGSZ method 0 I 3-body ﬁnal states e.g. D → KS ππ Marseille, March 2015 T.M. Karbach / CERN / LHCb 34 I [Phys. Rev. D68 (2003) 054018] I Giri, Grossman, Soﬀer, Zupan (2003)

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 30/77 Methods to measure γ

Reconstruct the D0/Dfirst0 in a ﬁnal method state accesible to to both measure to acheieve interference γ

I GLW method I CP eigenstates e.g. D → KK I [Phys. Lett. B253 (1991) 483] Depending on the final state fD the method is called: I Gronau, London, Wyler (1991) I [Phys. Lett. B265 (1991) 172] I ADS method “GLW” “ADS” I CF orGronau, DCS London, decays Wyler e.g. D (1991)→ Kπ Atwood,I [Phys. Dunietz, Rev. Soni D63 (1997, (2001) 2001) 036005] I Atwood, Dunietz, Soni (1997,2001) I [Phys. Rev. Lett. 78 (1997) 3257] I GGSZ methodPhys. Lett. B253 (1991) 483 Phys. Rev. D63 (2001) 036005 Phys. Lett. B265 (1991) 172 0 Phys. Rev. Lett. 78 (1997) 3257 I 3-body ﬁnal states e.g. D → KS ππ I [Phys. Rev. D68 (2003) 054018] Marseille,I Giri, March Grossman, 2015 Soﬀer, ZupanT.M.(2003) Karbach / CERN / LHCb 35 Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 31/77 γ with CP eigenstates (GLW)

( ) 0 I Use the B± → D K ± case as an example: I Consider only D decays to CP eigenstates, fCP I Favoured: b c with strong phase δF and weak phase φF → I Supressed: b u with strong phase δS and weak phase φS → Favoured: Supressed: u b u

− 0 K D → [f]D s c B− b c s − 0 B ¡ D → [f]D ¡ K− u u u u

Subsequent amplitude to ﬁnal state fCP is:

i(δF φF ) i(δS φS ) Af = |F |e − + |S|e − (3)

i(δF +φF ) i(δS +φS ) A¯f = |F |e + |S|e (4)

because strong phases (δ) don’t change sign under CP while weak phases (φ) do

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 32/77 γ with CP eigenstates (GLW)

I Deﬁne the CP asymmetry as the rate diﬀerence between meson with b (B) and b (B)

¯ 2 2 |Af¯| − |Af | ACP = (experimental observable) ¯ 2 2 |Af¯| + |Af | 2|F ||S| sin(δF − δS ) sin(φF − φS ) = 2 2 |F | + |S| + 2|F ||S| cos(δF − δS ) cos(φF − φS )

S I Choose rB = |F| (so that r < 1) and use strong phase diﬀerence δB = δF − δS | | I γ is the weak phase diﬀerence φF − φS I Subsequently the CP asymmetry becomes

GLW CP asymmetry

±2rB sin(δB ) sin(γ) ACP = 2 1 + rB ± 2rB cos(δB ) cos(γ)

I The +(−) sign corresponds to CP-even (-odd) final states I Note that rB and δB (ratio and strong phase difference of favoured and supressed modes) are different for each B decay I The value of γ is shared by all such decays

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 33/77

) 400 400 2 c LHCb LHCb An example300 GLW analysis 300

200 B−→[K+K−] K− 200 B+→[K+K−] K+ D + D I GLW analysis of B± → DK ± with D → K K − - [arXiv:1603.08993] 100 100

IEvents / ( 10 MeV/ CP asymmetry can be seen by eye

5100 5200 5300 5400 5500 5100 5200 5300 5400 5500

) 400 400 2 c 6000 LHCbLHCb 6000 LHCbLHCb 300 300 4000 4000 − − − − 200 B →−→[K++K ]− Kπ− 200 B++→→[K++K ]− Kπ++ B [K K D]D B [K K D]D 2000100 2000100 Events / ( 10 MeV/

5100 5200 5300 5400 5500 5100 5200 5300 5400 5500 m(Dh±) [MeV/c2] 6000 LHCb 6000 LHCb + 4000 GLW asymmetry for B± DK4000± and D K K − −→ + −→π− → +→ + − π+ B [K K ]D B [K K ]D 2000 + 2000 + + + DK,KK Γ(B− → [K K −]D K −) − Γ(B → [K K −]D K ) ACP = + + + + Γ(B− → [K K −]D K −) + Γ(B → [K K −]D K ) 5100 5200 5300 5400 5500 5100 5200 5300 5400 5500 = 0.087 ± 0.020 ± 0.008 m(Dh±) [MeV/c2]

∼ 4σ from zero

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 34/77 150

) 150 2 Anc example GLW analysis LHCb LHCb 100 100

B−→[π+π−] K− B+→[π+π−] K+ D + D I Same50 story with the B± → DK ± and D →50 π π− CP asymmetry can be seen by eye IEvents / ( 10 MeV/

5100 5200 5300 5400 5500 2000150 5100 5200 5300 5400 5500 ) 2000150 2 c LHCb LHCb 1500 1500 100 100

− − − + − + 1000 −→ π++π − − 1000 +→ π++π − + BB →[[π π ]]DKπ BB →[[π π ]]DKπ 50 D 50 D 500 500 Events / ( 10 MeV/

200051005100 52005200 53005300 54005400 55005500 200051005100 52005200 53005300 54005400 55005500 m(Dh±) [MeV/c2] LHCb LHCb 1500 1500 + GLW asymmetry for B± DK ± and D K K − 1000 − 1000 → π+π−→π− → +→ π+π− π+ B [ ]D B [ ]D 500 + 500 + + + DK,ππ Γ(B− → [π π−]D K −) − Γ(B → [π π−]D K ) ACP = + + + + Γ(B− → [π π−]D K −) + Γ(B → [π π−]D K ) 5100 5200 5300 5400 5500 5100 5200 5300 5400 5500 = 0.128 ± 0.037 ± 0.012 m(Dh±) [MeV/c2]

∼ 3σ from zero

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 35/77 γ with CF and DCS decays (ADS)

0 0 I A 2-body D decay to final state f accesible to both D and D can be 0 + I Cabibbo-favoured (CF)- D π−K → 0 + I Doubly-Cabibbo-supressed (DCS)- D π K → − I Introduces 2 new hadronic parameters: 0 0 I rD - ratio of magnitudes for D and D decay to f 0 0 I δD - relative phase for D and D decay to f I Leads to an additional (modified) asymmetry defintion and an additional ratio observable

ADS asymmetry

2rD rB sin(δB + δD ) sin(γ) AADS = 2 2 rD + rB + 2rB rD cos(δB + δD ) cos(γ)

ADS ratio ¯ 2 2 |Af¯| + |Af | 2 2 RADS = = r + r + 2rB rD cos(δB + δD ) cos(γ) ¯ 2 2 B D |Af | + |Af¯|

I Hadronic parameters rD and δD can be de independently determined (using CLEO data and HFAG averages) I Combining all information for various decays allows determination of γ, rB and

Matthewδ KenzieB (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 36/77 150

) 150 2 Anc example ADS analysis LHCb LHCb 100 100 I ADS analysis of B± → DK ± with D → K ±π∓ which has two asymmetries 1. “Favoured:” B−→[π+π−] K− B+→[π+π−] K+ − 0 − + − D − 0 − + − D I B [D K π ]K AND B [D K π ]K 50 → → 50→ → I (fav. B with fav. D) AND (sup. B with sup. D)

Events / ( 10 MeV/ | {z } Dominated by doubly favoured 2000 5100 5200 5300 5400 5500 20003000 5100 5200 5300 5400 5500 ) 3000 2 c LHCb LHCb 1500 1500 2000 2000

1000 −− − + − 1000 + + − + B →→[Kπ+ππ−] Kπ− B +→→[Kπ+ππ−] Kπ+ B [ ]DD B [ ]DD 1000 1000 500 500 Events / ( 10 MeV/

51005100 52005200 53005300 54005400 55005500 51005100 52005200 53005300 54005400 55005500 m(Dh±) [MeV/c2] 40000 LHCb 40000 LHCb Favoured ADS asymmetry for B± DK ± and D K ±π∓ → → B−→[K−π+] π− B+→[K+π−] π+ 20000 +D 20000 + + + D DK,Kπ Γ(B− → [K −π ]D K −) − Γ(B → [K π−]D K ) ACP = + + + + Γ(B− → [K −π ]D K −) + Γ(B → [K π−]D K )

5100 5200 =5300−0.01945400± 0.00725500 ± 0.00605100 5200 5300 5400 5500 m(Dh±) [MeV/c2] ∼ 2σ from zero

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 37/77

150

) 150 2

Anc example ADS analysis LHCb LHCb 100 100 I ADS analysis of B± → DK ± with D → K ±π∓ which has two asymmetries 2. Supressed: B−→[π+π−] K− B+→[π+π−] K+ − 0 + − − D − 0 + − − D I B [D K π ]K AND B [D K π ]K 50 → → 50→ → I (fav. B with sup. D) AND (sup. B with fav. D)

Events / ( 10 MeV/ | {z } Both of similar size so large CP eﬀect 2000 5100 5200 5300 5400 5500 2000 5100 5200 5300 5400 5500 ) 2 c 100 LHCb 100 LHCb 1500 1500

1000 −− − + − 1000 + + − + B →→[ππK+π−] Kπ− 50 B +→→[ππ+Kπ−] Kπ+ 50 B [ ]DD B [ ]DD 500 500 Events / ( 10 MeV/

51005100 52005200 53005300 54005400 55005500 51005100 52005200 53005300 54005400 55005500 m(Dh±) [MeV/c2] LHCb LHCb 400 Favoured ADS asymmetry for B400± DK ± and D K ∓π± → → −→ π− + π− +→ π+ − π+ B [ +K ]D + + + B [ K ]D 200 DK,πK Γ(B− → [K π−]D K200−) − Γ(B → [K −π ]D K ) AADS = + + + + Γ(B− → [K π−]D K −) + Γ(B → [K −π ]D K )

5100 5200 =5300−0.4035400± 0.0565500± 0.0115100 5200 5300 5400 5500 m(Dh±) [MeV/c2] ∼ 7σ from zero

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 38/77 Aside: Multibody ﬁnal states

I The GLW/ADS formalisms are fairly trivally extended to multibody ﬁnal states GLW ADS

I Multibody quasi-CP states I Multibody DCS decys + 0 + 0 I D → K K −π I D → K π−π + 0 + + I D → π π−π I D → K π−π π− + + I D → π π−π π− I Account for the dilution, κ, from + I Account for the fraction, F of interference between resonances CP-even content quasi-GLW asymmetry quasi-ADS asymmetry

±2(2F ++1)r sin(δ ) sin(γ) 2κr r sin(δ + δ ) sin(γ) B B A = D B B D ACP= 2 + CP 2 2 1+rB ±2(2F +1)rB cos(δB ) cos(γ) rD +rB +2κrB rD cos(δB + δD ) cos(γ)

I We can also construct partial rate ratios as additional observables

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 39/77 γ with 3-body self-conjugate states (GGSZ)

I Now get additional sensitivity over the 3-body phase space

I Idea is to perform a GLW/ADS type analysis across the D decay phase space 0 0 + I For example D → KS π π− has contributions from 0 0 0 I Singly-Cabibbo-suppressed decay D KS ρ 0→ + I Doubly-Cabibbo-suppressed decay D K π → ∗ − I Interference between them enhances sensitivity and resolves amiguities in γ determination

Partial B rate as function of Dalitz position (+, ) = (mK 0 π+ , mK 0 π− ) − S S

2 2 2 dΓB± (x) = A( , ) + rB A( , ) ± ∓ ∓ ± + 2A( , )A( , ) rB cos(δB ± γ) cos(δD( , )) + rB sin(δB ± γ) sin(δD( , )) ± ∓ ∓ ± | {z } ± ∓ | {z } ± ∓ x± y±

I Model-dependent - Fit Dalitz plot with full amplitude model for (x , y ) ± ± I Model-independent - Choose binning scheme in Dalitz plane to minimize δD variation across bin and ﬁt simultaneously in each bin for (x , y ) ± ±

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 40/77 Examples of the D0 K 0π+π Dalitz distribution → S − ] 4 3 c / 2 LHCb 102 2.5 ρ(770)

) [GeV ω(782) + 2 2

π f (980) 0 s 0 10

(K 1.5 2 m 1 – K*(892) 1 0.5

1 2 3 2 0 - 2 4 m (Ksπ1) [GeV /c ]

I In other words CP asymmetry in bins of Dalitz space

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 41/77 The cartesian coordinates

y (x+,y+) Cartesian deﬁnition

i(δB γ) x + iy = rB e ± rB ± ± y+ = rB sin(B + ) x = rB cos(δB ± γ) ± x = rB cos(B ) B + y = rB sin(δB ± γ) x+ = rB cos(B + ) ± y = rB sin(B ) x rB

I Use these for ﬁt stability 1 (x ,y ) Ease of combianation I ⇠ rB I Good statistical behaviour

Uncertainty on γ is inversely proportional to central value of hadronic unknown!!

I Fluctuation in nuisance parameter = ﬂuctuation in error on parameter of interest!

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 42/77 An example GGSZ analysis - B DK , D K 0π+π ± → ± → S − ) ) 2 2

c c 6000 I First ﬁt invariant B mass distrbution 400 LHCb LHCb

± ± I Project (cut) signal candidates into Dalitz plane DK 4000 DK Dπ ± Dπ ± I Requires experimental eﬃciency and background 200 Combinatorial Combinatorial Part. reco. 2000 Part. reco. distributions in DP Candidates / (10 MeV/ Candidates / (10 MeV/ 0 0 I Control channels used are B± → Dπ± and B− → Dµ−ν 5200 5400 5600 5800 5200 5400 5600 5800 m(DK±) [MeV/c2] m(Dπ ±) [MeV/c2] Compare bin by bin diﬀerences for signal candidates in the Dalitz plane ] ] 4 4 c 3 c 3 / / 2 LHCb 2 LHCb

– + B B [GeV [GeV 2 + 2 2 −

m 2 m

1 1

1 2 3 1 2 3 2 2 4 2 2 4 m− [GeV /c ] m+ [GeV /c ]

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 43/77 An example GGSZ analysis

I GGSZ analyses have excellent standalone sensitivity with a single solution

B D0( K 0hh)K ± → → S ±

y 0.3 LHCb preliminary −1 “Third” uncertainty arises from: 0.2 ∫ L dt = 3.0 fb − B I MD: - amplitude model uncertainty 0.1 I MI: - knowledge of strong phase in DP bins 0 x = −0.077 ± 0.024 ± 0.010 ± 0.004 -0.1 + + B y+ = −0.022 ± 0.025 ± 0.004 ± 0.010 -0.2 x = 0.025 ± 0.025 ± 0.010 ± 0.005 − -0.3 y = 0.075 ± 0.029 ± 0.005 ± 0.014 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 − x

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 44/77 Extensions to other decays Extension for many other decays with inclusion of relevant coherence factors, κ 1. Obvious extensions to higher resonant final states 0 0 I B± D K ∗± (K ∗± KS π±) → 0 0 → 0 0 0 0 I B D K (D D γ or D D π ) ± → ∗ ± ∗ → ∗ → I mainly just the B factories so far - LHCb starting for Run 2 0 I Similar hadronic parameters as B± D K ± but lower yields 2. Extensions to other B decays (swapping→ spectator quark) 0 0 0 0 + I B D K ∗ (K ∗ K π− tags initial B flavour) 0 → 0 0 → I B D KS (not self tagging) 0 → 0 I Bs D φ (not self tagging and low rate) → 0 I Bc± D D± (very low rate - favoured mode not yet seen) → 0 0 0 I under exploration at LHCb with some B D K published → ∗ I Typically enhanced rB because favoured diagram is colour supressed 3. Extension into baryon sector (add/swap spectators) 0 0 I Λ D Λ (Λ pπ ) b → → − I Difficult - either long lived final state or dominated by strong interaction 4. Swap final state K ± for π± 0 I B D π ± → ± I Tried at LHCb - problematic as rB is very small - statistical difficulties 5. Other methods 0 I Time-dependent method (Bs Ds∓K ± etc.) → 0 0 I Dalitz method (multibody B decays e.g. B D K π ) → ± ∓ I Both tried at LHCb

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 45/77 The time-dependent method with B0 D K s → s∓ ±

0 0 I Bs and Bs can both decay to same ﬁnal state Ds∓K ± (one via b → cW , the other via b → uW ) 0 I Intereference acheived by neutral Bs mixing (requires knowledge of −2βs ≡ φs ) I Weak phase diﬀerence is (γ 2βs ) − u, c, t s s b s

0 + B0 ± ± − Bs Ds s W W K u, c, t b b c s u

u c 3 − V × V ≈ λ3 D+ ¡Vcb × Vus ≈ λ K ¡ub cs s s s

0 I Requires tagging the initial Bs ﬂavour

I Requires a time-dependent analysis to observe the meson oscillations

I Fit the decay-time-dependent decay rates

I Also requires knowledge of Γs , ∆Γs , ∆ms

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 46/77 The time-dependent method with B0 D K s → s∓ ±

0 0 Time-dependent decay rate for initial Bs or Bs at t = 0

dΓ 0 (t) Bs f Γs t ∆Γs t ∆Γs ∆Γs t → ∝ e− cosh + A sinh dt 2 f 2 + Cf cos (∆ms t) − Sf sin (∆ms t)

dΓ 0 (t) Bs f Γs t ∆Γs t ∆Γs ∆Γs t → ∝ e− cosh + A sinh dt 2 f 2 − Cf cos (∆ms t) + Sf sin (∆ms t)

Time-dependent rate asymmetry

Γ 0 (t) − Γ 0 (t) Bs f Bs f Sf sin(∆ms t) − Cf cos(∆ms t) ACP (t) = → → = ∆Γ t ∆Γs ∆Γ t Γ 0 (t) + Γ 0 (t) s s B f Bs f cosh( ) + Af sinh( ) s → → 2 2

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 47/77 The time-dependent method with B0 D K s → s∓ ± I Fit for decay-time-dependent asymmetry - + K K + s 0.4 LHCb Preliminary - s 0.4 LHCb Preliminary D D mix mix

A 0.2 0.2 A

0 0

-0.2 -0.2

-0.4 -0.4

0 0.1 0.2 0.3 0 0.1 0.2 0.3 τ modulo (2π/∆m ) [ps] τ modulo (2π/∆m ) [ps] s s

LHCb prel, 3 fb− 1, B → D K 1.5 s s λ λ 2 − -iγ 2 f / (1+| | ) = ( A ∆Γ, S)~ e 2 +iγ 2λ / (1+|λ| ) = (− A ∆Γ,− S)~e Variable deﬁnitions Im 1 f

0.5 1 − r 2 C = −C = B f f¯ 2 0 1 + rB

∆Γ −2rB cos(γ − 2βs ∓ δB ) −0.5 γ − A s = ( A ∆Γ,S) f (f¯) 2 − 1 + rB ( A ∆Γ,S) −1 radius = 1 − C2 ±2rB sin(γ − 2βs ∓ δB ) S ¯ = f (f ) 2 −1.5 1 + rB −1 0 1 Re

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 4. CKM angle γ 48/77 Dalitz methods

0 + I Study Dalitz structure of 3-body B decays with B →DK π−

I In principle has excellent sensitivity to γ I “GW method”? (Gershon-Williams - [arXiv:0909.1495])

I Get multiple interfering resonances which increase sensitivity to γ 0 0 0 I D∗0(2400)−, D∗2(2460)−, K ∗(892) , K ∗(1410) , K ∗2(1430) I Fit B decay Dalitz Plot for cartesian parameters (similar to GGSZ except for the B not the D) + + I D K K −, D π π− - GLW-Dalitz (done by LHCb - [arXiv:1602.03455]) → → 0 I D K ±π∓ - ADS-Dalitz (problematic backgrounds from Bs DK ±π∓) → 0 + → I D K π π - GGSZ-Dalitz (double Dalitz!) → S − ± y 1 ] ] 12 12

4 LHCb 4 c c / / 2 2 LHCb (b) LHCb (a) 0.5 10 + − 10 0 − B0→DK π B →DK π+ 8 8 ) [GeV

) [GeV 0 + − π π − + 6 6 K K ( ( 2

2 -0.5

4 m 4 m

2 2 -1 0 0 5 10 15 20 5 10 15 20 -1 -0.5 0 0.5 1 − m2(Dπ ) [GeV2/c4] m2(Dπ +) [GeV2/c4] x±

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 5. Combination of Measurements 49/77 5. Combination of Measurements

1 Introduction

2 CP violation and the CKM matrix

3 The LHCb Experiment

4 CKM angle γ

5 Combination of Measurements

6 Conclusion and Prospects

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 5. Combination of Measurements 50/77 Combining measurements to determine γ

I The diﬀerent methods mentioned previously are complimentary in determining γ I GLW - excellent sensitivty but multiple solutions I ADS - poorer sensitivty but fewer solutions I GGSZ - a single unambigous solution

I Best precision can only be obtained by combining several measurements together I Requires knowledge of external parameters I Particularly in the D system (e.g. rD , δD , κD ) I Extracted from charm data obtained elsewhere (HFAG, CLEO, LHCb) 0 0 0 I Should also account for D -D mixing (and K mixing) I Although impact is small for most B DK-like systems (as rD << rB ) → I Will discuss here the LHCb combination and world average for HFAG/CKMﬁtter/PDG 1 0.2 B-→DK-, D→hhπ0/h3π DK B - - HFAG HFAG r → → B DK , D KShh CKM 2016 CKM 2016 - - - 1-CL → → + π0 ω φ 0.8 B DK , D h h' /KS /KS /KS GLW All B-→DK- modes ADS 0.15 World Average 0.6 GGSZ Combined

0.4 68.3% 0.1

0.2 95.5% 0.05 0 0 50 100 150 0 50 100 150 γ [°] γ [°]

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 5. Combination of Measurements 51/77 ASIDE: GammaCombo

I Software plug! I GammaCombo is a statistical software originally designed for averaging I https://github.com/gammacombo/gammacombo I http://gammacombo.hepforge.org I Also in development (almost ﬁnished) as limit setting software 1 HFAG CKM 2016 1-CL Most common statistical methods available 0.8 0→ - + I Bs DsK B-→DK*- * B-→D K- I Proﬁle Likelihood 0→ *0 0.6 Bd DK B-→DK- I Feldman-Cousins (Plugin, Highland-Cousins) Combined 0.4 I CLs (Asymptotic, Hybrid) 68.3% I Bayesian MC (on the wish-list) 0.2 95.5% 0 I Contributors and users are welcome! 0 50 100 150 γ [°] s 3 3 8 6

Γ 0.25 inclusive PDG 2014 + CP-odd ∆ 10 10 CKM fitter + CP-even LHCb Preliminary × × 7 B→πlν Λ →pµν (LHCb) b exclusive inclusive Flavour Specific cb cb | | Λ → µν 0.2

p (LHCb) V V b 5 Bs→J/ψKK ub L ub 6 combined LHCb Combined |V |V V ub inclusive Comb. incl. 0.15 5 4

V exclusive 0.1 4 ub Comb. excl. 3 Indirect (CKM fitter) 0.05 3 /V LHCb V ub cb contours hold 39%, 87% CL 2 2 0 −0.4 −0.2 0 0.2 0.4 36 38 40 42 44 0.62 0.64 0.66 0.68 0.7 0.72 0.74 ε × 3 Γ R |Vcb| 10 s

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 5. Combination of Measurements 52/77 LHCb γ combination inputs

B decay D decay Type R Ref. L B+ DK + D hh GLW/ADS 3 fb−1 [arXiv:1603.08993] → → B+ DK + D hπππ GLW/ADS 3 fb−1 [arXiv:1603.08993] → → B+ DK + D hhπ0 GLW/ADS 3 fb−1 [arXiv:1504.05442] B+ → DK + D → K 0 hh GGSZ 3 fb−1 [arXiv:1405.2797] → → S B+ DK + D K 0 Kπ GLS 3 fb−1 [arXiv:1402.2982] → → S B0 D0K ∗0 D Kπ ADS 3 fb−1 [arXiv:1407.3186] + → + → −1

LHCb Inputs B DK ππ D hh GLW/ADS 3 fb [arXiv:1505.07044] → → B0 D∓K ± D+ hhh TD 1 fb−1 [arXiv:1407.6127] * s → s s → B0 D0K +π− D hh GLW-Dalitz 3 fb−1 [arXiv:1602.03455] → → B0 D0K ∗0 D K 0 ππ GGSZ 3 fb−1 [arXiv:1604.01525] → → S Decay Parameters Source Ref. D0–D0 mixing HFAG - [arXiv:1412.7515] D Kπππ (δD , κD , rD ) CLEO+LHCb - [arXiv:1602.07430] * → + D ππππ (F ) CLEO - [arXiv:1504.05878] → 0 D Kππ (δD , κD , rD ) CLEO+LHCb - [arXiv:1602.07430] → 0 + D hhπ (F ) CLEO - [arXiv:1504.05878] → 0 D KSKπ (δD , κD ) CLEO - [arXiv:1203.3804] * → 0 D KSKπ (rD ) CLEO - [arXiv:1203.3804]

Auxilliary Inputs → 0 D KSKπ (rD ) LHCb - [arXiv:1509.06628] 0→ 0 ∗0 B D K (κB , R¯B , ∆¯ B ) LHCb - [arXiv:1602.03455] 0 → + − B D K (φs ) LHCb - [arXiv:1411.3104] s → s Combination: [arXiv:1611.03076] New or updated since last combination Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 5. Combination of Measurements 53/77 LHCb γ Combination

I Combination of all B → DK-like modes

I 71 observables and 32 free parameters

I Frequentist Feldman-Cousins “plugin” procedure 2 I p(χ , Ndof ) = 91.5% I p(toys) = (90.5 0.2)% ± I Also perform a Bayesian implementation

I Uncertainty < 10◦ is better than combined B factories

I The most precise single experiment measurement of γ

+6.8 +7.1 Frequentist - γ = (72.2 7.3)◦ Bayesian - γ = (70.3 7.9)◦ − − 1 LHCb 0.05 LHCb 1-CL 0.8 0.04 0.6 68.3% 0.03 0.4 68.3% 0.02 Probability Density 0.2 0.01 95.5% 95.5% 0 0 50 60 70 80 90 50 60 70 80 90 γ [°] γ [°]

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 5. Combination of Measurements 54/77 LHCb γ Combination

Naive statistical treatement (proﬁle likelihood method) - plots for demonstrative purposes only

Comparison split by initial B ﬂavour Comparison split by analysis method

1 1 LHCb LHCb 1-CL 0.8 1-CL 0.8

0.6 0.6

0.4 0.4 68.3% 68.3%

0.2 0.2 95.5% 95.5% 0 0 0 50 100 150 0 50 100 150 γ [°] γ [°]

0 Bs decays GGSZ B0 decays GLW/ADS B+ decays Others Combination Combination

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 5. Combination of Measurements 55/77 LHCb γ Combination

Naive statistical treatement (proﬁle likelihood method) - plots for demonstrative purposes only

B+ D0K + system B0 D0K 0 system → → ∗

0.2 0 0.8 * DK B r DK B

LHCb r LHCb 0.15 0.6

0.1 0.4

0.05 0.2

0 0 0 50 100 150 0 50 100 150 γ [°] γ [°]

+ + 0 B →DK , D→h3π/hh'π B0→DK *0, D→KK/Kπ/ ππ +→ + → 0 B DK , D KShh 0→ *0 → 0ππ B DK , D KS B+→DK +, D→KK/Kπ/ ππ All B0 modes All B+ modes

Full LHCb Combination Full LHCb Combination

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ

+→ 0 + → ππ0 πππ 0→ 0 0 → π ππ BAllCombination BDu modesK D hhKShh/KK//h3 BAllCombination BDd modesK* D KSKK/KK/ 5. Combination of Measurements 56/77 On inclusion of B Dπ-like modes → Dπ I r expectation 0.005 (favoured enhanced by Vud /Vus , suppressed reduced by Vcd /Vcs ) B ∼ Frequentist Bayesian

1 LHCb 0.05 LHCb 1-CL 0.8 0.04 0.6 68.3% 0.03 0.4 68.3% 0.02 Probability Density 0.2 0.01 95.5% 95.5% 0 0 50 60 70 80 90 50 60 70 80 90 γ [°] γ [°]

0.25 68.3% − LHCb 10 1 LHCb 1-CL 0.8 LHCb 0.2 −2

Probability Density 10 0.6 95.5% 0.15 −3 10 0 0.01 0.02 0.03 0.04 0.05 rD π 0.4 68.3% B 68.3% 0.1 Probability Density 0.2 0.05 95.5% 95.5% 0 0 0 0.01 0.02 0.03 0.04 0.05 0 0.01 0.02 0.03 0.04 0.05 Dπ Dπ rB rB

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 5. Combination of Measurements 57/77 On inclusion of B Dπ-like modes →

I The a priori sensitivity gain is rather minimal Dπ Dπ I Enforcing a constraint on rB using a theory prediction rB = 0.0053 ± 0.0007 ( [arXiv:1606.09129] - Kenzie, Martinelli, Tuning)

I Recovers similar results to DK-mode combination

Dπ Using external constraint on rB : +7.2 γ = (71.8 8.6)◦ − 1 LHCb 1-CL 0.8 Preliminary

0.6

0.4 68.3%

0.2 95.5% 0 50 60 70 80 90 γ [°]

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 0 + with D K h h the model-dependent results, as listed in Table 55, are used for the BABAR ! S and Belle experiments, whilst the model-independent results, as listed in Table 57 are used for LHCb. This choice is made in order to maintain consistency of the approach across experiments whilst maximising the size of the samples used to obtain inputs for the combination. The result of the GLS analysis of B DK with D K⇤±K⌥ from LHCb (Table 58) are used. The ! 0 ! 0 results of the LHCb ADS analysis of B DK⇤ (Table 54) are included. The GLW equiva- ! lent is not used because of the overlap with the GLW-Dalitz analysis (Table 50) which is used 0 0 0 + instead. For GGSZ analyses of B DK⇤ with D K h h the model-independent result ! ! S from LHCb (Table 57) is used for consistency with the treatment of the LHCb B DK 0 ! GGSZ result. Finally, results from the time-dependent analysis of Bs Ds⌥K± from LHCb 0 (!) (Table 47) are used. Results from time-dependent analyses of B D ⇤ ⌥⇡± and D⌥⇢± (Ta- ! ble 46) are not used as there are insuﬃcient constraints on the associated hadronic parameters. 5. Combination0 of Measurements0 58/77 Similarly, results from B D⌥KS ⇡± (Sec. 4.13) are not used. HFAG γ combination inputs! (1/4) Table 61: List of measurements used in the combination.

B decay D decay Method Experiment Ref. + + B DK D K K, D ⇡ ⇡,GLWBABAR [419] ! ! 0 0 ! 0 0 D KS ⇡ , D KS !, D KS ! + ! + ! B DK D K K, D ⇡ ⇡,GLWBelle[420] ! ! 0 0 ! 0 0 D KS ⇡ , D KS !, D KS ! + ! + ! B DK D K K, D ⇡ ⇡ GLW CDF [421] ! ! + ! + B DK D K K, D ⇡ ⇡ GLW LHCb [422] ! ! + ! + B D⇤K D K K, D ⇡ ⇡,GLWBABAR [423] ! 0 ! 0 0 ! 0 0 D⇤ D (⇡ ) D KS ⇡ , D KS !, D KS ! ! + ! + ! B D⇤K D K K, D ⇡ ⇡,GLWBelle[420] ! 0 ! 0 0 ! 0 0 D⇤ D (⇡ ) D KS ⇡ , D KS !, D KS ! ! + ! + ! B DK⇤ D K K, D ⇡ ⇡,GLWBABAR [424] ! ! 0 0 ! 0 0 D KS ⇡ , D KS !, D KS ! + ! + ! B DK⇤ D K K, D ⇡ ⇡, GLW LHCb [425] ! + ! + ! + B DK⇡ ⇡ D K K, D ⇡ ⇡ GLW LHCb [426] ! ! + 0 ! B DK D ⇡ ⇡⇡ GLW-like BABAR [309] ! ! + 0 B DK D h h⇡ GLW-like LHCb [430] ! ! + + B DK D ⇡ ⇡⇡ ⇡ GLW-like LHCb [422] ! ! B DK D K±⇡⌥ ADS BABAR [431] ! ! MatthewB KenzieDK (Cambridge) D K±⇡ Neckarzimmern⌥ B Physics WorkshopADS Measuring Belle the CKM angle γ [432] ! ! B DK D K±⇡⌥ ADS CDF [433] ! ! B DK D K±⇡⌥ ADS LHCb [422] ! ! 0 B DK D K±⇡⌥⇡ ADS BABAR [434] ! ! 0 B DK D K±⇡⌥⇡ ADS Belle [435] ! ! 0 B DK D K±⇡⌥⇡ ADS LHCb [430] ! ! + B DK D K±⇡⌥⇡ ⇡ ADS LHCb [422] ! ! B D⇤K D K±⇡⌥ ADS BABAR [431] ! ! D⇤ D ! B D⇤K D K±⇡⌥ ADS BABAR [431] ! 0 ! D⇤ D⇡ !

129 0 + with D K h h the model-dependent results, as listed in Table 55, are used for the BABAR ! S and Belle experiments, whilst the model-independent results, as listed in Table 57 are used for LHCb. This choice is made in order to maintain consistency of the approach across experiments whilst maximising the size of the samples used to obtain inputs for the combination. The result of the GLS analysis of B DK with D K⇤±K⌥ from LHCb (Table 58) are used. The ! 0 ! 0 results of the LHCb ADS analysis of B DK⇤ (Table 54) are included. The GLW equiva- ! lent is not used because of the overlap with the GLW-Dalitz analysis (Table 50) which is used 0 0 0 + instead. For GGSZ analyses of B DK⇤ with D K h h the model-independent result ! ! S from LHCb (Table 57) is used for consistency with the treatment of the LHCb B DK 0 ! GGSZ result. Finally, results from the time-dependent analysis of Bs Ds⌥K± from LHCb 0 (!) (Table 47) are used. Results from time-dependent analyses of B D ⇤ ⌥⇡± and D⌥⇢± (Ta- ! ble 46) are not used as there are insuﬃcient constraints on the associated hadronic parameters. 0 0 Similarly, results from B D⌥K ⇡± (Sec. 4.13) are not used. ! S Table 61: List of measurements used in the combination.

B decay D decay Method Experiment Ref. + + B DK D K K, D ⇡ ⇡,GLWBABAR [419] ! ! 0 0 ! 0 0 D KS ⇡ , D KS !, D KS ! + ! + ! B DK D K K, D ⇡ ⇡,GLWBelle[420] ! ! 0 0 ! 0 0 D KS ⇡ , D KS !, D KS ! + ! + ! B DK D K K, D ⇡ ⇡ GLW CDF [421] ! ! + ! + B DK D K K, D ⇡ ⇡ GLW LHCb [422] ! ! + ! + B D⇤K D K K, D ⇡ ⇡,GLWBABAR [423] ! 0 ! 0 0 ! 0 0 D⇤ D (⇡ ) D KS ⇡ , D KS !, D KS ! ! + ! + ! B D⇤K D K K, D ⇡ ⇡,GLWBelle[420] ! 0 ! 0 0 ! 0 0 D⇤ D (⇡ ) D5. CombinationKS ⇡ of, MeasurementsD KS !, D KS 59/77 ! ! + ! + ! B DK⇤ D K K, D ⇡ ⇡,GLWBABAR [424] HFAG!γ combination! inputs0 0 (2/4)! 0 0 D KS ⇡ , D KS !, D KS ! + ! + ! B DK⇤ D K K, D ⇡ ⇡, GLW LHCb [425] ! + ! + ! + B DK⇡ ⇡ D K K, D ⇡ ⇡ GLW LHCb [426] ! ! + 0 ! B DK D ⇡ ⇡⇡ GLW-like BABAR [309] ! ! + 0 B DK D h h⇡ GLW-like LHCb [430] ! ! + + B DK D ⇡ ⇡⇡ ⇡ GLW-like LHCb [422] ! ! B DK D K±⇡⌥ ADS BABAR [431] ! ! B DK D K±⇡⌥ ADS Belle [432] ! ! B DK D K±⇡⌥ ADS CDF [433] ! ! B DK D K±⇡⌥ ADS LHCb [422] ! ! 0 B DK D K±⇡⌥⇡ ADS BABAR [434] ! ! 0 B DK D K±⇡⌥⇡ ADS Belle [435] ! ! 0 B DK D K±⇡⌥⇡ ADS LHCb [430] ! ! + B DK D K±⇡⌥⇡ ⇡ ADS LHCb [422] ! ! B D⇤K D K±⇡⌥ ADS BABAR [431] ! ! D⇤ D ! B D⇤K D K±⇡⌥ ADS BABAR [431] ! 0 ! D⇤ D⇡ !

129

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 5. Combination of Measurements 60/77 HFAG γ combination inputs (3/4) List of measurements used in the combination – continued from previous page. B DK⇤ D K±⇡⌥ ADS BABAR [424] ! ! B DK⇤ D K±⇡⌥ ADS LHCb [425] ! + ! B DK⇡ ⇡ D K±⇡⌥ ADS LHCb [426] ! ! 0 + B DK D KS ⇡ ⇡ GGSZ MD BABAR [441] ! ! 0 + B DK D KS ⇡ ⇡ GGSZ MD Belle [440] ! ! 0 + B D⇤K D KS ⇡ ⇡ GGSZ MD BABAR [441] ! 0 ! D⇤ D (⇡ ) ! 0 + B D⇤K D KS ⇡ ⇡ GGSZ MD Belle [440] ! 0 ! D⇤ D (⇡ ) ! 0 + B DK⇤ D KS ⇡ ⇡ GGSZ MD BABAR [441] ! ! 0 + B DK⇤ D KS ⇡ ⇡ GGSZ MD Belle [443] ! ! 0 + B DK D KS ⇡ ⇡ GGSZ MI LHCb [448] ! ! 0 + B DK D KS K ⇡ GLS LHCb [451] 0 ! 0 ! B DK⇤ D K±⇡⌥ ADS LHCb [427] 0 ! + ! + B DK ⇡ D h h GLW-Dalitz LHCb [428] 0 ! + ! 0 + B DK ⇡ D KS h h GGSZ MI LHCb [450] 0 ! +! + + B D⌥K± D h h⇡ TD LHCb [417] s ! s s ! Auxiliary inputs are used in the combination in order to constrain the D system parameters and subsequently improve the determination of 3. These include the ratio of suppressed Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop⌘ Measuring the CKM angle γ to favoured decay amplitudes and the strong phase difference for D K±⇡⌥ decays, taken ! from the HFAG Charm Physics subgroup global fits (see Sec. 8). The amplitude ratios, strong 0 + 0 phase differences and coherence factors of D K±⇡⌥⇡ , D K±⇡⌥⇡ ⇡ and D K K±⇡± ! ! ! S decays are taken from CLEO-c and LHCb measurements [452,458,459]. The fraction of CP -even + + + 0 + 0 content for quasi-GLW D ⇡ ⇡⇡ ⇡, D K K⇡ and D ⇡ ⇡⇡ decays are taken ! ! ! from CLEO-c measurements [429]. Constraints required to relate the hadronic parameters of 0 0 the B DK⇤ GLW-Dalitz analysis to the effective hadronic parameters of the quasi-two- ! body approaches are taken from LHCb measurements [428]. Finally, the value of 2s is taken from the HFAG Lifetimes and Oscillations subgroup (see Sec. 3); this is required to obtain 0 sensitivity to 3 from the time-dependent analysis of B D⌥K± decays. A summary of ⌘ s ! s

Table 62: List of the auxiliary inputs used in the combinations.

Decay Parameters Source Ref. K⇡ K⇡ D K±⇡⌥ rD , D HFAG Sec. 8 ! + K3⇡ K3⇡ K3⇡ D K±⇡⌥⇡ ⇡ D , D , rD CLEO+LHCb [458] ! + + D ⇡ ⇡⇡ ⇡ F⇡⇡⇡⇡ CLEO [429] ! 0 K2⇡ K2⇡ K2⇡ D K±⇡⌥⇡ D , D , rD CLEO+LHCb [458] ! + 0 D h h⇡ F⇡⇡⇡0 , FKK⇡0 CLEO [429] ! KS K⇡ KS K⇡ KS K⇡ 0 + D , D , rD CLEO [452] D KS K ⇡ KS K⇡ ! rD LHCb [459] 0 0 0 0 0 DK⇤ DK⇤ B DK⇤ B(DK⇤ ), RB , B LHCb [428] 0 ! B D⌥K± s HFAG Sec. 3 s ! s

130 List of measurements used in the combination – continued from previous page. B DK⇤ D K±⇡⌥ ADS BABAR [424] ! ! B DK⇤ D K±⇡⌥ ADS LHCb [425] ! + ! B DK⇡ ⇡ D K±⇡⌥ ADS LHCb [426] ! ! 0 + B DK D KS ⇡ ⇡ GGSZ MD BABAR [441] ! ! 0 + B DK D KS ⇡ ⇡ GGSZ MD Belle [440] ! ! 0 + B D⇤K D KS ⇡ ⇡ GGSZ MD BABAR [441] ! 0 ! D⇤ D (⇡ ) ! 0 + B D⇤K D KS ⇡ ⇡ GGSZ MD Belle [440] ! 0 ! D⇤ D (⇡ ) ! 0 + B DK⇤ D KS ⇡ ⇡ GGSZ MD BABAR [441] ! ! 0 + B DK⇤ D KS ⇡ ⇡ GGSZ MD Belle [443] ! ! 0 + B DK D KS ⇡ ⇡ GGSZ MI LHCb [448] ! ! 0 + B DK D KS K ⇡ GLS LHCb [451] 0 ! 0 ! B DK⇤ D K±⇡⌥ ADS LHCb [427] 0 ! + ! + B DK ⇡ D h h GLW-Dalitz LHCb [428] 0 ! + ! 0 + B DK ⇡ D KS h h GGSZ MI LHCb [450] 0 ! +! + + B D⌥K± D h h⇡ TD LHCb [417] s ! s s ! Auxiliary inputs are used in the combination in order to constrain the D system parameters and subsequently improve the determination of 3. These include the ratio of suppressed ⌘ to favoured decay amplitudes and the strong phase difference for D K±⇡⌥ decays, taken ! from the HFAG Charm Physics subgroup global fits (see Sec. 8). The amplitude ratios, strong 0 + 0 phase differences and coherence factors of D K±⇡⌥⇡ , D K±⇡⌥⇡ ⇡ and D K K±⇡± ! ! ! S decays are taken from CLEO-c and LHCb measurements [452,458,459]. The fraction of CP -even + + + 0 + 0 content for quasi-GLW D ⇡ ⇡⇡ ⇡, D K K⇡ and D ⇡ ⇡⇡ decays are taken ! ! ! from CLEO-c measurements [429]. Constraints required to relate the hadronic parameters of 0 0 the B DK⇤ GLW-Dalitz analysis to the effective hadronic parameters of the quasi-two- ! body approaches are taken from LHCb measurements [428]. Finally, the value of 2s is taken from the HFAG Lifetimes and Oscillations subgroup (see Sec. 3); this is required to obtain 0 sensitivity to 3 from the time-dependent analysis of Bs Ds⌥K± decays. A summary of ⌘ 5. Combination of Measurements ! 61/77 HFAG γ combination inputs (4/4) Table 62: List of the auxiliary inputs used in the combinations.

130

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 5. Combination of Measurements 62/77 The World Average

I World average performed for HFAG ([arXiv:1612.07233]) - soon also to be CKMfitter and PDG I Add to LHCb results from Belle, BaBar and CDF I Plus a few of the latest additions I Always the most up to date result I A few minor differences (simplifications) I 116 observables and 33 free parameters - global fit p-value=16.4% World Average +5.8 γ = (74.0 6.4)◦ − 1 1 HFAG HFAG CKM 2016 CKM 2016 1-CL 1-CL 0.8 0.8 0→ - + GLW Bs DsK B-→DK*- ADS * B-→D K- GGSZ 0.6 0.6 B0→DK*0 Combined d B-→DK- Combined 0.4 0.4 68.3% 68.3%

0.2 0.2 95.5% 95.5% 0 0 0 50 100 150 0 50 100 150 γ [°] γ [°]

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 6. Conclusion and Prospects 63/77 6. Conclusion and Prospects

1 Introduction

2 CP violation and the CKM matrix

3 The LHCb Experiment

4 CKM angle γ

5 Combination of Measurements

6 Conclusion and Prospects

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 6. Conclusion and Prospects 64/77 Prospects

I With Run II of the LHC underway and Belle II starting soon the prospects look good I LHCb and Belle II compliment each other for many measurements I We can reasonably expect to half the experimental uncertainty on γ in the next 3 years I We can reasonably expect to have ∼ 1◦ precision in the next 5-8 years I In 10-12 years we should be < 1◦ I Current systematic eﬀects are relatively small: 1 − ° I GLW/ADS Belle 20 LHCb +20°

I instrumental charge asymmetries 1-CL 0.8 Comb 2016 Comb ~2019 I PID calibration Comb ~2023 I GGSZ 0.6 I eﬃciency correction over the Dalitz plane 0.4 68.3% I amplitude model uncertainties I Time-dependent 0.2 I Decay time resolution 95.5% I Decay time acceptance 0 Knowledge of ∆m , ∆Γ ,Γ 40 60 80 100 120 I s s s γ [°]

I Tree measurements of γ will not be systematically limited for a little while yet

This does not include smart new ideas which people often have

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 6. Conclusion and Prospects 65/77 Prospects

I There are several established methods / channels that LHCb haven’t exploited yet 0 I B± D∗ K ± - work is underway on both GGSZ and GLW/ADS methods → 0 I B± D K ∗± - ﬁrst GLW/ADS results shown at CKM (other methods expect inclusion for Moriond→ or Summer) 0 0 0 0 0 I Any CP-odd GLW decays (D K π , D K ω) - neutrals are very hard for LHCb → S → S I There are also ideas for new methods / channels

I ADS-Dalitz and GGSZ-Dalitz (double Dalitz) I Simultaneous GGSZ analysis (reduce systematic uncertainties) 0 +?+ I TD analyses with Bs Ds K − 0 →0 + I Use decays from B , Bs , Bc (low branching fractions and production rates but topology means larger values of rB ) 0 I Use decays from Λb (diﬃcult ﬁnal state Λ) I We anyway struggle to keep up with our data 0 + 1 I The TD Bs Ds−K analysis was only just updated to full 3 fb− (still only a CONF and not yet a→ PAPER) I This wasn’t included for the last LHCb combination but now we already have at least an equivalent size dataset for 2015+2016 and will soon have a much bigger dataset with 2017

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 3

1.5 1.5 excluded area has CL > 0.95 excluded area has CL > 0.95 CKM CKM f i t t e r f i t t e r 2003 γ 2013 1.0 1.0 γ(α)

0.5 0.5 Vub Vub

α α 6. Conclusion and Prospects 66/77 γ β γ β

η 0.0 η 0.0 Prospects -0.5 -0.5 γ & γ(α) & Vub

I -1.0We are approaching the ﬁrst tree-level precision-1.0 measurementγ(α) of the CKM triangle γ I Direct measurements of Vub play a crucial role in this as well -1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 [arXiv:1309.2293] ρ ρ 1.5 1.5 1.5 excluded area has CL > 0.95 excluded area has CL > 0.95 CKM excluded area has CL > 0.95 CKMf i t t e r a CKM γ f i t t2013 e r f i t t e r a Stage I Stage II 1.0 ( ) 1.0 aγ(_α) 1.0 a(_) LHCb Upgrade 0.5 0.5 Vub 2013 0.5 + Belle II Vub Vub α _ _ 2023 γ β a ` a ` η 0.0 d d 0.0 0.0 0.45 0.45

0.40 0.40 -0.5-0.5 a & a(_) & Vub -0.5 a & a(_) & Vub γ & γ(α) & Vub 0.35 0.35

-1.0-1.0 a(_γ)(α) 0.30 -1.0 a(_) 0.30

0.25 0.25 _ aγ 0.05 0.10 0.15_ 0.20 0.25 a 0.05 0.10 0.15 0.20 0.25 -1.5-1.5 -1.5 -1.0-1.0 -0.5 -0.5 0.0 0.0 0.5 0.5 1.0 1.0 1.5 1.5 2.0 2.0 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 l ρ l

FIG. 1. The past (2003, top left) and present (top right) status of the unitarity triangle in the presence of NP in neutral-meson mixing. The lower plots show future sensitivities for Stage IandStageIIdescribedinthetext,assumingdataconsistentwith theMatthew SM. The Kenzie combination (Cambridge) of all constraints in Table Neckarzimmern I yields theB red-hatchedPhysics Workshop regions, yellow regions, and Measuring dashed the red CKM cont angleoursγ at 68.3% CL, 95.5% CL, and 99.7% CL, respectively. tal and theoretical sides. Our Stage I projection refers systematic (treated through the Rfit model [8]). Consid- to a time around or soon after the end of LHCb Phase I, ering the difficulty to ascertain the breakdown between 1 corresponding to an anticipated 7 fb− LHCb data and statistical and systematic uncertainties in lattice QCD 1 5ab− Belle II data, towards the end of this decade. The inputs for the future projections, for simplicity, we treat 1 1 Stage II projection assumes 50fb− LHCb and 50 ab− all such future uncertainties as Gaussian. Belle II data, and probably corresponds to the middle The fits include the constraints from the measurements of the 2020s, at the earliest. Estimates of future experi- d,s of ASL [10, 11], but not their linear combination [23], mental uncertainties are taken from Refs. [17, 18, 21, 22]. nor from ∆Γ ,whoseeffects on the future constraints (Note that we display the units as given in the LHCb and s on NP studied in this paper are small. While ∆Γs is in Belle II projections, even if it makes some comparisons agreement with the CKM fit [10], there are tensions for less straightforward; e.g., the uncertainties of both β and ASL [23]. The large values of hs allowed until recently, βs will be 0.2◦ by Stage II.) For the entries in Ta- corresponding to (M s ) 2(M s ) , are excluded ble I where∼ two uncertainties are given, the first one is 12 NP ∼− 12 SM by the LHCb measurement of the sign of ∆Γs [24]. We do statistical (treated as Gaussian) and the second one is not consider K mixing for the fits shown in this Section, 6. Conclusion and Prospects 67/77 Conclusions

I CKM matrix is incredibly successful description of the quark sector in the SM

I Measurements of CKM elements are becoming increasingly precise

I Finding new sources of CP violation can lead us to New Physics I CKM angle γ is one of the only CP measurements accesible with tree-level decays I Theoretically very clean

I Experimentally challenging I LHCb has the worlds most precise single experiment measurement and dominates the world average +6.8 +5.8 I γ = (72.2 7.3)◦ (LHCb), γ = (74.0 6.4)◦ (HFAG WA) − − I The future looks incredibly bright with the prospect of reducing the direct measurement uncertainty by a factor of ∼ 8 I This will compete with the indirect precision (which assumes the SM)

Thank You

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 7. Back Up 68/77 Back Up

BACK UP

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 7. Back Up 69/77 DK frequentist 1D

1 1 1 LHCb LHCb LHCb 1-CL 0.8 1-CL 0.8 1-CL 0.8

0.6 0.6 0.6

0.4 0.4 0.4 68.3% 68.3% 68.3%

0.2 0.2 0.2 95.5% 95.5% 95.5% 0 0 0 0.08 0.09 0.1 0.11 0.12 120 130 140 150 160 0 0.1 0.2 0.3 0.4 0 rDK δ DK ° DK* B B [ ] rB 1 1 LHCb LHCb 1-CL 0.8 1-CL 0.8

0.6 0.6

0.4 0.4 68.3% 68.3%

0.2 0.2 95.5% 95.5% 0 0 150 200 250 50 60 70 80 90 δ DK*0 ° γ [°] B [ ]

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 7. Back Up 70/77 DK frequentist 2D

] 160 ° DK B DK B [ r 0.12 LHCb LHCb r 0.12 LHCb DK B δ 150 0.11 0.11 140 0.1 0.1 130 0.09 0.09 120 0.08 0.08 50 60 70 80 90 50 60 70 80 90 120 130 140 150 160 γ ° γ ° δ DK ° [ ] [ ] B [ ]

0 0.4 ] 0 0.4 * * ° [ 0 DK B DK B * r LHCb LHCb r LHCb

0.3 DK B 250 0.3 δ

0.2 200 0.2

0.1 150 0.1

0 0 50 60 70 80 90 50 60 70 80 90 150 200 250 γ [°] γ [°] δ DK*0 ° B [ ]

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ

DK CKM 2016 DK CKM 2016 DK CKM 2016

DK CKM 2016 DK CKM 2016 DK CKM 2016 7. Back Up 71/77 DK Bayesian 1D

0.06 0.08 LHCb LHCb LHCb 0.06 0.05 0.06 68.3% 0.04 68.3% 68.3% 0.04 0.03 0.04

0.02 Probability Density 0.02 Probability Density Probability Density 0.02 95.5% 0.01 95.5% 95.5% 0 0 0 0.08 0.09 0.1 0.11 0.12 120 130 140 150 160 0 0.1 0.2 0.3 0.4 0 rDK δ DK ° DK* B B [ ] rB

0.015 LHCb 0.05 LHCb 0.04 0.01 68.3% 68.3% 0.03

0.02

Probability Density 0.005 Probability Density 0.01 95.5% 95.5% 0 0 150 200 250 50 60 70 80 90 δ DK*0 ° γ [°] B [ ]

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 7. Back Up 72/77 DK Bayesian 2D

] 160 ° DK B DK B [ r 0.12 LHCb LHCb r 0.12 LHCb DK B δ 150 0.11 0.11 140 0.1 0.1 130 0.09 0.09 120 0.08 0.08 50 60 70 80 90 50 60 70 80 90 120 130 140 150 160 170 γ ° γ ° δ DK ° [ ] [ ] B [ ]

0 0.4 ] 0 0.4 * * ° [ 0 DK B DK B * r LHCb LHCb r LHCb

0.3 DK B 250 0.3 δ

0.2 200 0.2

0.1 150 0.1

0 0 50 60 70 80 90 50 60 70 80 90 150 200 250 γ [°] γ [°] δ DK*0 ° B [ ]

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 7. Back Up 73/77 Dh frequentist 1D

1 1 1 1 LHCb LHCb LHCb LHCb 1-CL 0.8 1-CL 0.8 1-CL 0.8 1-CL 0.8

0.6 0.6 0.6 0.6

0.4 0.4 0.4 0.4 68.3% 68.3% 68.3% 68.3%

0.2 0.2 0.2 0.2 95.5% 95.5% 95.5% 95.5% 0 0 0 0 0.08 0.09 0.1 0.11 0.12 120 130 140 150 160 0 0.1 0.2 0.3 0.4 150 200 250 0 *0 rDK δ DK ° DK* δ DK ° B B [ ] rB B [ ] 1 1 1 LHCb LHCb LHCb 1-CL 0.8 1-CL 0.8 1-CL 0.8

0.6 0.6 0.6

0.4 0.4 0.4 68.3% 68.3% 68.3%

0.2 0.2 0.2 95.5% 95.5% 95.5% 0 0 0 0 0.01 0.02 0.03 0.04 0.05 200 250 300 350 50 60 70 80 90 Dπ δ Dπ ° γ ° rB B [ ] [ ]

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 7. Back Up 74/77 Dh frequentist 2D

] 0 0.4 160 * ° DK B DK B [ r r 0.12 0.12 DK B

LHCb LHCb LHCb r LHCb DK B δ 150 0.3 0.11 0.11 140 0.2 0.1 0.1 130 0.09 0.09 0.1 120 0.08 0.08 0 50 60 70 80 90 50 60 70 80 90 120 130 140 150 160 50 60 70 80 90 γ ° γ ° δ DK ° γ ° [ ] [ ] B [ ] [ ] ] 0 ] 0.4 π 0.05 * ° °

D B 350 [ [ r 0 DK B π * LHCb r LHCb LHCb LHCb 0.04 D B DK B 250 0.3 δ δ 300 0.03 200 0.2 0.02 250 150 0.1 0.01 200 0 0 50 60 70 80 90 150 200 250 50 60 70 80 90 50 60 70 80 90 γ [°] δ DK*0 ° γ [°] γ [°] B [ ]

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ

Dh CKM 2016 Dh CKM 2016 Dh CKM 2016 Dh CKM 2016

Dh CKM 2016 Dh CKM 2016 Dh CKM 2016 Dh CKM 2016 7. Back Up 75/77 Dh Bayesian 1D

0.06 0.08

LHCb 0.05 LHCb LHCb 0.015 LHCb 0.06 0.06 0.04 68.3% 68.3% 68.3% 0.01 68.3% 0.04 0.03 0.04

0.02

Probability Density Probability Density Probability Density Probability Density 0.005 0.02 0.02 95.5% 0.01 95.5% 95.5% 95.5% 0 0 0 0 0.08 0.09 0.1 0.11 0.12 120 130 140 150 160 0 0.1 0.2 0.3 0.4 150 200 250 0 *0 rDK δ DK ° DK* δ DK ° B B [ ] rB B [ ]

0.012

0.25 68.3% − 0.05 10 1 LHCb LHCb LHCb LHCb 0.01 0.2 −2 0.04 Probability Density 10 0.008 95.5% 68.3% 0.15 68.3% −3 0.03 10 0 0.01 0.02 0.03 0.04 0.05 rD π 0.006 68.3% B 0.1 0.004 0.02 Probability Density Probability Density 95.5% Probability Density 0.05 0.002 0.01 95.5% 95.5% 0 0 0 0 0.01 0.02 0.03 0.04 0.05 200 250 300 350 50 60 70 80 90 Dπ δ Dπ ° γ ° rB B [ ] [ ]

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 7. Back Up 76/77 Dh Bayesian 2D

] 0 0.4 160 * ° DK B DK B [ r r 0.12 0.12 DK B

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ 7. Back Up 77/77 Coverage studies

) 0.75 ) 0.75 σ LHCb σ LHCb 0.7 0.7

0.65 0.65

Coverage (1 0.6 Coverage (1 0.6 Profile likelihood Profile likelihood

0.55 PLUGIN (µ) method 0.55 PLUGIN (µ) method

0.5 0.5 0.05 0.1 0 0.01 0.02 0.03 DK Dπ rB rB

Matthew Kenzie (Cambridge) Neckarzimmern B Physics Workshop Measuring the CKM angle γ