Flavor Physics and CP Violation

Zoltan Ligeti The 2013 European School ([email protected]) of High-Energy

Physics 5 – 18 June 2013 Lawrence Berkeley Laboratory Parádfürdő, Hungary

Standing Committee Scientific Programme Discussion Leaders T. Donskova, JINR Field Theory and the Electro-Weak Standard Model A. Arbuzov, JINR N. Ellis, CERN E. Boos, Moscow State Univ., Russia T. Biro, Wigner RCP, Hungary H. Haller, CERN Beyond the Standard Model M. Blanke, CERN M. Mulders, CERN C. Csaki, Cornell Univ., USA G. Cynolter, Roland Eotvos Univ., Hungary A. Olchevsky, JINR Higgs Physics A. De Simone, SISSA, Italy & CERN G. Perez, CERN & Weizmann Inst. J. Ellis, King’s College London, UK & CERN A. Gladyshev, JINR K. Ross, CERN Neutrino Physics B. Gavela, Univ. Autonoma & IFT UAM/CSIC, Madrid, Spain Local Committee Cosmology C. Hajdu, Wigner RCP, Hungary Enquiries and Correspondence D. Gorbunov, INR, Russia G. Hamar, Wigner RCP, Hungary Kate Ross Flavour Physics and CP Violation D. Horváth, Wigner RCP, Hungary CERN Schools of Physics Z. Ligeti, Berkeley, USA J. Karancsi, Univ. Debrecen, Hungary CH-1211 Geneva 23 Practical Statistics for Particle Physicists P. Lévai, Wigner RCP, Hungary Switzerland H. Prosper, Florida State Univ., USA F. Siklér, Wigner RCP, Hungary Tel +41 22 767 3632 Quark–Gluon Plasma and Heavy-Ion Collisions B. Ujvári,Univ. Debrecen, Hungary Fax +41 22 766 7690 K. Rajagopal, MIT, USA & CERN V. Veszprémi, Wigner RCP, Hungary Email [email protected] QCD for Collider Experiments A. Zsigmond, Wigner RCP, Hungary Z. Trócsányi, Univ. Debrecen, Hungary Tatyana Donskova Highlights from LHC Physics Results International Department T. Virdee, Imperial College London, UK JINR RU-141980 Dubna, Russia Tel +7 49621 63448 Fax +7 49621 65891 Email [email protected] Deadline for applications: 15 February 2013 International Advisors http://cern.ch/PhysicSchool/ESHEP R. Heuer, CERN V. Matveev, JINR J. Pálinkás, Hungarian Academy of Sciences A. Skrinsky, BINP, Novosibirsk N. Tyurin, IHEP, Protvino

ESHEP2012 Paradf´ urd¨ o,˝ Hungary, June 5–18, 2013 CERN - JINR

ESHEP2013 CERN - JINR What is particle physics?

• Central question of particle physics: L = ? ... What are the elementary degrees of freedom and how do they interact?

ZL — p.1/i What is particle physics?

• Central question of particle physics: L = ? ... What are the elementary degrees of freedom and how do they interact?

• Most experimentally observed phenomena consistent with standard model (SM)

ZL — p.1/i What is particle physics?

• Central question of particle physics: L = ? ... What are the elementary degrees of freedom and how do they interact?

• Most experimentally observed phenomena consistent with standard model (SM)

• Clearest empirical evidence that SM is incomplete: – Dark matter Maybe at – Baryon asymmetry of the Universe the TeV – Hierarchy problem[ 126 GeV scalar = SM Higgs? why so light?] scale? – Neutrino mass [can add in a straightforward way] – Dark energy [cosmological constant? need to know more to understand?]

ZL — p.1/i The Universe: what is dark matter?

• Homogeneous, isotropic, spatially ﬂat, expanding

• Dark matter: rotation curves, gravitational lensing, cosmology

• DM cannot be a SM particle: Know: non-baryonic, long lived, neutral, abundance Don’t know: interactions, mass, quantum numbers, one/many species

• Maybe thermal relic of early universe: weakly interacting massive particle (WIMP) If so, WIMP mass has to be around the TeV scale — LHC may directly produce it

ZL — p.1/ii The Universe: matter vs. antimatter

• Gravity, electromagnetism, strong interaction are same for matter and antimatter

• Soon after the big bang, quarks and anti- quarks were in thermal equilibrium

N(baryon) N − N ∼ 10−9 ⇒ q q ∼ 10−9 N(photon) Nq + Nq at t < 10−6 s (T > 1 GeV)

• The SM prediction is ∼1010 times smaller

• Solution may lie at the TeV scale, and the LHC may shed light on it

ZL — p.1/iii The matter–antimatter asymmetry

• How could the asymmetry be generated dynamically?

• Sakharov conditions (1967): 1. baryon number violating interactions 2. C and CP violation 3. deviation from thermal equilibrium

• SM contains 1–3, but: i. CP violation is too small ii. deviation from thermal equilibrium too small at electroweak phase transition New TeV-scale physics can enhance both (supersymmetry, 4th generation, etc.)

• What is the microscopic theory of CP violation? How precisely can we test it?

ZL — p.1/iv What is ﬂavor physics?

• Flavor physics (quarks) ≡ what breaks U(3)Q × U(3)u × U(3)d → U(1)Baryon

• SM ﬂavor problem: hierarchy of masses and mixing angles

• NP ﬂavor problem: TeV scale (hierarchy problem) ﬂavor & CPV scale ¯ 2 ¯ 2 2 (sd) 4 (bd) 3 (bs¯) 2 K: ⇒ Λ >10 TeV, ∆mB: ⇒ Λ >10 TeV, ∆mB : ⇒ Λ >10 TeV Λ2 ∼ Λ2 ∼ s Λ2 ∼

– Most TeV-scale new physics models have new sources of CP and ﬂavor violation, which may be observable in ﬂavor physics but not directly at the LHC

– The observed baryon asymmetry of the Universe requires CPV beyond the SM (Not necessarily in ﬂavor changing processes, nor necessarily in quark sector)

• Flavor sector will be tested a lot better, many NP models have observable effects

[Going from: NP ∼< (few × SM) → NP ∼< (0.3 × SM) → NP ∼< (0.05 × SM)]

ZL — p.1/v Outline (1)

• Physics beyond the SM must exist, good reasons to hope it’s at the TeV scale • Brief introduction to the standard model Weak interactions, ﬂavor, CKM

• Testing the ﬂavor sector CP violation and neutral meson mixing The K and D meson systems

• Clean information from B physics Constraining new physics in mixing

ZL — p.1/vi Outline (2–3)

• Heavy quark symmetry and OPE

Spectroscopy, exclusive / inclusive decays, |Vcb|, |Vub|

Rare decays, B → Xsγ, and friends • Isospin and SU(3): α from B → ππ and ρρ • Nonleptonic decays, factorization B decays to ﬁnal states with & without charm

• Flavor symmetries and new physics • Lepton ﬂavor violation

• Flavor physics at high-pT top FCNC, minimal ﬂavor violation, SUSY ﬂavor • Conclusions

ZL — p.1/vii Preliminaries

• Dictionary: SM = standard model NP = new physics Dictionary: CPV = CP violation UT = unitarity triangle

θQCD µν • Disclaimers: I will not talk about: the strong CP problem FµνFe 16π2 Disclaimers: I will not talk about: lattice QCD Disclaimers: I will not talk about: detailed new physics scenarios

• Most importantly: If I do not talk about your favorite process [the one you are Most importantly: working on...], it does not mean that I think it’s not important!

• Many reviews and books, e.g.: Y. Grossman, ZL, Y. Nir, arXiv:0904.4262; A. Hocker, ZL, hep-ph/0605217; ZL, hep-lat/0601022 G. Branco, L. Lavoura and J. Silva, CP Violation, Clarendon Press, Oxford, UK (1999)

ZL — p.1/viii Ancient past Crucial role of symmetries: C, P , and T

• Intimate connection between symmetries and conservation laws C = charge conjugation (particle ↔ antiparticle) P = parity (~x ↔ −~x) T = time reversal (t ↔ −t, initial ↔ ﬁnal states) CPT cannot be violated in a relativistically covariant local quantum ﬁeld theory

ZL — p.1/1 Crucial role of symmetries: C, P , and T

• Once upon a time, “Tau– Theta puzzle”: θ+ → π+π0 Once upon a time, “Tau– Theta puzzle”: τ + → π+π+π− π : J P = 0− + + If parity was conserved in decay: P (ππ) = (−1)J(θ ) and P (πππ) = −(−1)J(τ ) Assumed: τ + 6= θ+ but by 1955 precise mass & lifetime measurements (now: K+)

• Lee and Yang: test if weak interactions violate parity? (Nobel prize, 1957) ⇒ Modern theory of weak interactions

ZL — p.1/1 Crucial role of symmetries: C, P , and T

• Charge & angular momentum: 4 possibilities

Only νL and ν¯R participate in weak interaction Weak interaction maximally violates C and P

CP was still assumed to be a good symmetry

ZL — p.1/1 Crucial role of symmetries: C, P , and T

• Charge & angular momentum: 4 possibilities

• Only νL and ν¯R participate in weak interaction Weak interactions maximally violate C and P

• However, CP could still be a good symmetry

ZL — p.1/1 1964: CP symmetry is also broken

• The CP symmetry was expected to hold

• Two neutral states, nearly equal mass, but lifetime ratio >500 — understood as coming from phase space difference

If CP were conserved: CP eigenstates = mass eigenstates (KL,KS)

ππ in J = 0 state has CP = +1, so only one of the states can decay to it (KS)

• Discovered in 1964: (0.2%) (Nobel prize, 1980)

• A new CP violating interaction? Is CP an approximate symmetry? [Before charm and much of the SM — could involve new particles / new sectors of the theory] Many options... No other independent observation of CP violation until 1999

ZL — p.1/2 Aside: the experimental proposal

⇒ Cronin & Fitch, Nobel Prize, 1980 ⇒ 3 generations, Kobayashi & Maskawa, Nobel Prize, 2008 Hitchhiker’s guide to the SM Ingredients of a model

• Need to specify: (i) gauge (local) symmetries Need to specify: (ii) representations of fermions and scalars Need to specify: (iii) vacuum — spontaneous symmetry breaking

• L = all gauge invariant terms (renormalizable, dim ≤ 4) “Everything” follows, after a ﬁnite number of parameters are ﬁxed from experiment

• Implicit assumptions: Lorentz symmetry and QFT; Implicit No global symmetries imposed; accidental symmetries can arise

• Higher dimension terms are suppressed at low energies (We are modest and don’t worry about details of physics at much higher scales) If higher dimension operators are present ⇒ new physics at high energy

ZL — p.1/3 The standard model

• Gauge symmetry: SU(3)c × SU(2)L × U(1)Y parameters Gauge symmetry: 8 gluons W ±, Z0, γ 3

• Particle content: 3 generations of quarks and leptons

Particle content: QL(3, 2)1/6, uR(3, 1)2/3, dR(3, 1)−1/3 10

Particle content: LL(1, 2)−1/2, `R(1, 1)−1 3(+9) u c t ν ν ν Particle content: quarks: leptons: e µ τ d s b e µ τ

• Symmetry breaking: SU(2)L × U(1)Y → U(1)EM 0 symmetry breaking: φ(1, 2) Higgs scalar, hφi = √ 2 1/2 v/ 2

• Strongly interacting particles observed in Nature have no color; quarks conﬁned + ¯ 0 0 ¯ 0 ¯ mesons: π (ud),K (¯sd),B (bd),Bs (bs); baryons: p (uud), n (udd)

ZL — p.1/4 SM: where can CP violation occur?

1 X a 2 X 0 • Kinetic terms: Lkin = − (F ) + ψ iD/ψ (3 param’s: g, g , gs) 4 µν groups rep0s Kinetic terms: always CPC (ignoring F Fe)

2 2 † † 2 2 2 • Higgs terms: LHiggs = |Dµφ| + µ φ φ − λ(φ φ) (2 param’s; v = µ /λ) Higgs terms: CPC for one Higgs doublet; CPV constrains extended Higgs sector

• Yukawa couplings in interaction basis: (where ﬂavor comes from) d I I u I I ` I I LY = −Yij QLi φ dRj − Yij QLi φe uRj − Yij LLi φ `Rj + h.c.

i, j ∼ generations & 0 1 = φ∗ (cannot write such mass term for νi) −1 0 • CPV is related to unremovable phases of Yukawa couplings: ∗ † Yij ψLi φ ψRj + Yij ψRj φ ψLi ⇓ CP exchanges fermion bilinears † ∗ Yij ψRj φ ψLi + Yij ψLi φ ψRj

ZL — p.1/5 From Yukawa couplings to CKM matrix

• SM is the simplest scenario: Higgs background = single scalar ﬁeld φ

ij I I ij I I 0 1 ∗ LY = −Y Q φ u − Y Q φ d φe = φ u Li e Rj d Li Rj −1 0 ij • Yu,d = 3 × 3 complex matrices ⇒ mass terms after φ acquires VEV √ I ij I I ij I Lmass = −uLi Mu uRj − dLi Md dRj ,Mu,d = Yu,d (v/ 2) diag † Diagonalize: Mf ≡ VfL Mf VfR (f = u, d; V -s unitary) ij I ij I Mass eigenstates: fLi ≡ VfL fLj , fRi ≡ VfR fRj

• Mass matrices diagonalized by different transformations for uLi and dLi, which uI u are part of the same SU(2)L doublet, QL, so: Li † Lj I = (VuL)ij † dLi (VuLVdL)jk dLk % • Charged current weak interactions become off-diagonal: . CKM matrix   dL g I µ a a I g µ + † − Q γ Wµ τ QLi + h.c. ⇒ −√ uL, cL, tL γ Wµ (VuLV )  sL  + h.c. 2 Li 2 dL   bL

ZL — p.1/6

Weak interaction properties ¥

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• Flavor changing charged currents at tree level ¤

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No ﬂavor changing neutral currents (FCNC) at tree level

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• FCNC only at loop level in SM; suppressed by (m2 − m2)/m2

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e.g.: K – K mixing used to predict mc before its discovery ¢

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£ £ £ • FCNCs probe difference between the generations (typically small in the SM)

ZL — p.1/7 Quark mixing and the unitarity triangle

• The (u, c, t) W ± (d, s, b) couplings: (Wolfenstein parm., λ ∼ 0.23)    1 2 3  Vud Vus Vub 1 − 2λ λAλ (ρ − iη) V =  V V V  =  −λ 1 − 1λ2 Aλ2  + ... CKM  cd cs cb   2  3 2 Vtd Vts Vtb Aλ (1 − ρ − iη) −Aλ 1 | {z } CKM matrix

One complex phase in VCKM: only source of CP violation in quark sector 9 complex couplings depend on 4 real parameters ⇒ many testable relations

• Unitarity triangles (6): visualize SM constraints and compare measurements

∗ ∗ ∗ Vud Vub + Vcd Vcb + Vtd Vtb = 0 Sides and angles measurable in many ways

CPV in SM ∝ Area Goal: overconstrain by many measurements sensitive to different short distance physics

ZL — p.1/8 Aside: counting ﬂavor parameters

• Nonzero Yukawa couplings break ﬂavor symmetries — pattern of masses and mixings are inherited from the interactions of fermions with the Higgs background

• Quark sector: U(3)Q × U(3)u × U(3)d → U(1) quark (baryon) number

[36 couplings in Yu,d] − [26 broken generators] = 10 parameters with physical meaning parameters in VCKM z }| { = [6 masses] + [3 angles] + [1 phase] | {z } Single source of CP violation in the quark sector in the SM

ij ij I I Yν I I ij ji • Lepton sector (if Majorana ν’s): LY = −Y L φ e − L L φ φ (Y = Y ) e Li Rj M Li Lj ν ν Lepton sector (if Majorana ν’s): U(3)L × U(3)e completely broken

[30 couplings in Ye,ν] − [18 broken generators] = 12 parameters with physical meaning = [6 masses] + [3 angles] + [3 phases] | {z } One CPV phase measurable in ν oscillations, others in 0νββ decay

ZL — p.1/9 Determinations of CKM elements

• Magnitudes of CKM elements (sides of UT): semileptonic decays; Bd,s oscillation

• Relative phases of CKM elements (angles of UT-s): CP violation (Any physical CP violating quantity must depend on at least 4 CKM elements)

Measure hadrons, but interested in quark properties, parameters in Lagrangian

Need to deal with strong interactions, at scales at which perturbation theory is of limited use

• The name of the game: do “redundant” / “overconstraining” measurements using processes sensitive to different short-distance physics — if inconsistent ⇒ NP

Lincoln Wolfenstein: ‘I do not care what the values of the Wolfenstein parameters are, so you should not either; the only thing that matters is if their independent determinations are consistent’

• Combination of experimental feasibility and theoretical cleanliness is the key

ZL — p.1/10 Summary — standard model

• The SM is consistent with a vast amount of particle physics phenomena – special relativity + quantum mechanics – local symmetry + spontaneous breaking

• “Electroweak symmetry breaking” breaking of SU(2)L × U(1)Y → U(1)EM What is the physics of Higgs condensate? What generates it? What else is there? ⇒ The LHC started to directly address this (produce h and test its couplings)

• “Flavor physics” breaking of U(3)Q × U(3)u × U(3)d → U(1)Baryon Which interactions distinguish generations (e.g., d, s, b identical if massless)? How do the fermions see the condensate and the physics associated with it? ⇒ CP violation and ﬂavor changing neutral currents are very sensitive probes

ZL — p.1/11 Seeking indirect signals of NP

• Precision electroweak T parameter (“little hierarchy problem”): (φDµφ)2 ⇒ Λ > few × 103 GeV Λ2 • Flavor and CP violating operators (“new physics ﬂavor problem”), e.g.: QQQQ ⇒ Λ > 10(4...7) GeV Λ2 ∼ Flavor and custodial symmetry broken in SM already, so cannot forbid NP to generate these op’s

• Baryon and lepton number violating operators (lack of proton decay), e.g.: QQQL ⇒ Λ > 1016 GeV Λ2 ∼ • Unique set of dimension-5 terms composed of SM ﬁelds: 1 v2 L 5 = (Lφ)(Lφ) → mν νν , mν ∝ (see-saw mechanism) dim- Λ Λ Suggests very high scales (assuming O(1) couplings) — unless there are “sterile” neutrinos...

ZL — p.1/12 Testing the ﬂavor sector Spectacular track record

• Most parameters of the SM (and in many of its extensions) are related to ﬂavor

• Flavor physics was crucial to ﬁgure out LSM:

– β-decay predicted neutrino (Pauli)

– Absence of KL → µµ predicted charm (Glashow, Iliopoulos, Maiani)

– K predicted 3rd generation (Kobayashi & Maskawa)

– ∆mK predicted mc (Gaillard & Lee)

– ∆mB predicted large mt

• Likely to be important to ﬁgure out LLHC as well

If there is NP at the TEV scale, it must have a very special ﬂavor & CP structure

ZL — p.1/13 The low energy viewpoint

• At scale mb, ﬂavor changing pro- weak / NP scale ∼ 5 GeV cesses are mediated by dozens of higher dimension operators

Depend only on a few parameters in the SM ⇒ correlations between s, c, b, t decays + − ∆md b → dγ b → d` ` Vtd , , ∝ E.g.: in SM + − , but test different short dist. physics ∆ms b → sγ b → s` ` Vts

• Does the SM (i.e., integrating out virtual W , Z, and quarks in tree and loop dia- grams) explain all ﬂavor changing interactions? Right coefﬁcients and operators?

– Changes in correlations (B vs. K constraints, SψKS 6= SφKS , etc.)

– Enhanced or suppressed CP violation (sizable SBs→ψφ or Ab→sγ, etc.) – Compare tree and loop processes — FCNC’s at unexpected level

ZL — p.1/14 Constraints on ∆F = 2 operators

• Neutral meson mixings: dimension-6 operators, come with coefﬁcients C/Λ2

• If Λ = O(1 TeV) then C 1; alternatively, if C = O(1) then Λ 1 TeV

Bounds on Λ [TeV] (C = 1) Bounds on C (Λ = 1 TeV) Operator Observables Re Im Re Im µ 2 2 4 −7 −9 (¯sLγ dL) 9.8 × 10 1.6 × 10 9.0 × 10 3.4 × 10 ∆mK; K 4 5 −9 −11 (s¯R dL)(¯sLdR) 1.8 × 10 3.2 × 10 6.9 × 10 2.6 × 10 ∆mK; K µ 2 3 3 −7 −7 (¯cLγ uL) 1.2 × 10 2.9 × 10 5.6 × 10 1.0 × 10 ∆mD; |q/p|, φD 3 4 −8 −8 (c¯R uL)(¯cLuR) 6.2 × 10 1.5 × 10 5.7 × 10 1.1 × 10 ∆mD; |q/p|, φD (¯b γµd )2 5.1 × 102 9.3 × 102 3.3 × 10−6 1.0 × 10−6 ∆m ; S L L Bd ψKS (¯b d )(¯b d ) 1.9 × 103 3.6 × 103 5.6 × 10−7 1.7 × 10−7 ∆m ; S R L L R Bd ψKS ¯ µ 2 2 2 −5 −5 (bLγ sL) 1.1 × 10 2.2 × 10 7.6 × 10 1.7 × 10 ∆mBs; Sψφ ¯ ¯ 2 2 −5 −6 (bR sL)(bLsR) 3.7 × 10 7.4 × 10 1.3 × 10 3.0 × 10 ∆mBs; Sψφ

• Large SM suppressions — excellent probes of NP

ZL — p.1/15 Important features of SM-ﬂavor

• All ﬂavor changing processes depend only on a few parameters in the SM ⇒ correlations between large number of s, c, b, t decays

• The SM ﬂavor structure is very special:

– Single source of CP violation in CC interactions – Suppressions due to hierarchy of CKM elements – Suppression of FCNC processes (loops) – Suppression of FCNC chirality ﬂips by quark masses (e.g., B → K∗γ)

Many suppressions that NP might not respect ⇒ probe very high scales

• It is interesting and possible to look for NP contributions with better sensitivity

ZL — p.1/16 Brief history of CKM constraints

• For 35 years (untill 1999), only unambiguous CPV measurement was in K mixing 1.5 excluded at CL > 0.95 excluded area has CL > 0.95 γ 1.0 ∆md & ∆ms _

η 1 0.9 sin 2β 0.8 0.5 ∆md 0.7 εK α 0.6 γ β

η 0.0 0.5 α 0.4 V 0.3 ub α •0.5 0.2 0.1 0 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 •1.0 ε _ K ρ CKM (BABAR Physics Book, 1998) f i t t e r γ sol. w/ cos 2β < 0 Winter 12 (excl. at CL > 0.95) •1.5 •1.0 •0.5 0.0 0.5 1.0 1.5 2.0 ρ • CP vioaltion used to be interesting in itself; by now dozens of measurements ⇒ In which cases can both theory and experiment be precise?

ZL — p.1/17 Mixing and CP violation Neutral meson mixing

• Quantum mechanical two-level system; ﬂavor eigenstates: |B0i=|bdi, |B0i=|bdi d |B0(t)i i |B0(t)i • Evolution: i = M − Γ b t d b W d dt |B0(t)i 2 |B0(t)i W W t t 0 0 W Mass eigenstates: |BH,Li = p|B i ∓ q|B i d t b d b

M, Γ: 2 × 2 Hermitian matrices (CPT implies M11 = M22 and Γ11 = Γ22)

−(iM +Γ /2)t Time dependence involves mixing and decay: |BH,L(t)i = e H,L H,L |BH,Li

• CP violation: |q/p|= 6 1 ⇔ mass eigenstates 6= CP eigenstates 2 2 X mα − mβ • GIM mechanism: M ∝ V V ∗ V V ∗ f(m , m ) → suppression 12 ib id jb jd i j m2 i,j W GIM mechanism: since m-independent terms in f cancel due to CKM unitarity

• Hadronic uncertainties in ∆m (LQCD helps) and especially |q/p|, but not arg(q/p)

ZL — p.1/18 Aside: time evolition

• If you like to calculate things, maybe derive (start with ∆Γ = 0)

0 0 q 0 |B (t)i = g+(t) |B i + g−(t) |B i p

0 p 0 0 |B (t)i = g−(t) |B i + g+(t) |B i q −it(m−iΓ/2) ∆Γ t ∆m t ∆Γ t ∆m t g+(t) = e cosh cos − i sinh sin 4 2 4 2 −it(m−iΓ/2) ∆Γ t ∆m t ∆Γ t ∆m t g−(t) = e − sinh cos + i cosh sin 4 2 4 2

(We deﬁned ∆m > 0, but the sign of ∆Γ is physical)

ZL — p.1/19 Aside: Effective Hamiltonians (M12 in B mixing)

• Interactions at high scale (weak or new physics) produce local operators at lower

scales (hadron masses) — mixing dominated by intermediate top quarks

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SM contributions to B − B mixing: ¤

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W d t b d b ν Q(µ) = (bL γν dL)(bL γ dL) New physics can modify coefﬁcients and/or induce new operators • Going from operators to observables is equally important G2 m2 m2 M =( V V ∗)2 F W S t η b (µ) hB0|Q(µ)|B0i In SM: 12 tb td 2 2 B B 8π mB mW what we are after calculable perturbatively nonperturbative

n n ηB bB(µ) : Resumming αs ln (mW /µ) is often very important (µ ∼ mb) hB0|Q(µ)|B0i = 2 m2 f 2 BbB : hadronic uncertainties enter here 3 B B bB(µ)

ZL — p.1/20 The four neutral mesons

• Physical observables: x = ∆m/Γ, y = ∆Γ/(2Γ), |q/p| − 1

Order of magnitudes meson x y |q/p| − 1 of SM predictions: K 1 1 10−3 D 10−2 10−2 10−2(−3?) −2 −3 Bd 1 10 10 1 −1 −3 Bs 10 10 10

q2 2M ∗ − iΓ∗ = 12 12 • General sol. for eigenvalues is complicated; an important part: 2 p 2M12 − iΓ12 [CP violation in mixing ↔ Im(Γ12/M12) 6= 0]

• In the absence of CP violation: ∆m = 2|M12|, ∆Γ = 2|Γ12|

• If |M12| |Γ12|, valid for Bd and Bs mixing:

∆m = 2|M12|, ∆Γ = 2|Γ12| cos φ12, φ12 = arg(−M12/Γ12) q/p = pure phase — a key to allow model independent measurements from CPV

ZL — p.1/21 0 Bs mixing and |Vtd/Vts|

0 0 • Bs – Bs oscillate ∼25 times before they decay (ﬁrst measured by CDF in 2007)

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

η 0.0 α

Vub α •0.5

•1.0 εK CKM f i t t e r γ sol. w/ cos 2β < 0 Winter 12 (excl. at CL > 0.95) •1.5 •1.0 •0.5 0.0 0.5 1.0 1.5 2.0 −1 ∆ms = (17.768 ± 0.024) ps ρ √ f B Uncertainty σ(∆m ) = 0.13% is much Largest uncertainty: ξ = Bs√ s • s f B Bd d smaller than σ(∆md) = 0.8% Lattice QCD: ξ = 1.24±0.03±0.02

ZL — p.1/22 Types of CP violation

• CP violation: Γ(A → B) 6= Γ(A¯ → B¯) Requires interference of amplitudes with ≥ 2 different weak and strong phases

• CPV in decay: simplest, possible for charged and neutral mesons, and baryons

P iδk iφk P iδk −iφk Af = hf|H|Bi = k Ak e e Af = hf|H|Bi = k Ak e e

weak phases φk from Lagrangian, CP -odd — strong phases δk from rescattering, CP -even

2 2 In case of two amplitudes: |A| − |A| = 4A1A2 sin(φ1 − φ2) sin(δ1 − δ2)

0 • Unambiguously established by K 6= 0 in 1999, and since 2004 also in B decays

0 Theoretical understanding for K, AK−π+, etc., insufﬁcient to either prove or to 0 rule out that NP enters — still, K is a very strong constraint on NP

• Two other ways for CP violation in neutral mesons — can be theoretically cleaner

ZL — p.1/23 CPV in mixing

• If CP is conserved then |q/p| = 1 and arg(M12/Γ12) = 0 CPV iff (mass eigenstates) 6= (CP eigenstates) — physical states not orthogonal!

2 2 |q/p|= 6 1 ⇔ CPV in mixing implies: hBH|BLi = |p| − |q| 6= 0

• Simplest example: decay to “wrong sign” lepton (“dilepton asymmetry”) Γ[B0(t) → `+X] − Γ[B0(t) → `−X] |p/q|2 − |q/p|2 1 − |q/p|4 Γ A = = = = Im 12 SL 2 2 4 Γ[B0(t) → `+X] + Γ[B0(t) → `−X] |p/q| + |q/p| 1 + |q/p| M12 Observed in K decay in agreement with SM (CPLEAR @ CERN)

• Large hadronic uncertainties in calculation of Γ12, but interesting to look for NP: 2 2 |Γ12/M12| = O(mb/mW ) model independently 2 2 arg(Γ12/M12) = O(mc/mb) in SM, maybe O(1) with NP

ZL — p.1/24 CPV in interference between decay and mixing

• Can get theoretically clean information in some 0 A cases when B0 and B0 decay to same ﬁnal state B fCP

q A q/p 0 0 fCP B0 A |BL,Hi = p|B i ± q|B i λfCP = p AfCP

• Time dependent CP asymmetry: Γ[B0(t) → f] − Γ[B0(t) → f] 2 Im λ 1 − |λ |2 a = = f sin(∆m t) − f cos(∆m t) fCP 0 0 2 2 Γ[B (t) → f] + Γ[B (t) → f] 1 + |λf | 1 + |λf | | {z } | {z } Sf Cf (−Af ) • If amplitudes with one weak phase dominate a decay, hadronic physics drops out • Measure a phase in the Lagrangian theoretically cleanly:

afCP = ηfCP sin(phase difference between decay paths) sin(∆m t)

ZL — p.1/25 Bits of K and D physics

∆mK — built in NP models since 60’s

¢ ¢ ¢

£ £ £ £

2 ¤ 2 2 mc 2

• In the SM: ∆mK ∼ α |VcsVcd| f mK

¥ ¥ ¦¨§ © § w 4 K ¦¨§ © §

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• If tree-level exchange of a heavy gauge boson was responsible for a signiﬁcant

fraction of the measured value of ∆mK

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• Or new particles at TeV scale can have large contributions in loops [g ∼ O(10−2)]

(In many scenarios the constraits from kaons are the strongest, since so is the SM suppression, and these are built into models since the 70’s)

ZL — p.1/26 Precision CKM tests with kaons

• CPV in K system is at the right level (K accommodated with O(1) KM phase)

0 • Hadronic uncertainties preclude precision tests (K notoriously hard to calculate) 0 We cannot rule out (nor prove) that the measured value of K is dominated by NP

(N.B.: bad luck in part — heavy mt enhanced hadronic uncertainties, but helps for B physics)

0 • With lattice QCD improvements, K has become more sensitive, hopes for /

−10 ± −11

• K → πνν : Theory error ∼ few %, but very small rates 10 (K ), 10 (KL)

¢ £ ¡ 5 2 5 2  (λ m ) + i(λ m ) t ¦ ¨©  t t : CKM suppressed

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A ∝ (λ mc) + i(λ mc) c : GIM suppressed

 (λ Λ2 ) u : GIM suppressed

QCD

+ + 3 0 So far O(1) uncertainty in K → π νν¯, and O(10 ) in KL → π νν¯ • ⇒ Need much more data to achieve ultimate sensitivity

ZL — p.1/27 The quest for K → πνν¯

• Long history of ingenious experimental progress (huge backgrounds)

+ +1.15 −10 E787/E949: 7 events observed, B(K → π νν¯) = (1.73−1.05) × 10

+ + −10 0 0 −10 SM: B(K → π νν¯) = (0.78 ± 0.08) × 10 , B(KL → π νν¯) = (0.24 ± 0.04) × 10

CERN NA62: expect to get ∼ 100 K+ → π+νν¯ events

FNAL ORKA proposal: ∼ 1000 K+ → π+νν¯ events [Stage-1 approval]

0 0 J-PARC KOTO: observe KL → π νν¯ at SM level

FNAL w/ project-X: proposal for ∼ 0 0 1000 event KL → π νν¯

ZL — p.1/28 D0: mixing in up sector

• Complementary to K,B: CPV, FCNC both GIM & CKM suppressed ⇒ tiny in SM

HFAG- charm CPV allowed 1.5 March 2012

> y (%) • 2007: observation of mixing, now ∼10σ [HFAG combination] Only meson mixing generated by down-type quarks 1 (SUSY: up-type squarks) 0.5

−2 SM suppression: ∆mD, ∆ΓD < 10 Γ, since ∼ 0 1 σ doubly-Cabibbo-suppressed & vanish in SU(3) limit 2 σ 3 σ 4 σ −0.5 5 σ • y = (0.75 ± 0.12)% and x = (0.63 ± 0.20)% −0.5 0 0.5 1 1.5 x (%) ... suggest long distance dominance Don’t known yet if |q/p| is near 1!

ZL — p.1/29 D0: mixing in up sector

• Complementary to K,B: CPV, FCNC both GIM & CKM suppressed ⇒ tiny in SM

HFAG- charm 1 σ > March 2012 2 σ • 2007: observation of mixing, now 10σ [HFAG combination] 60 3 σ ∼ 4 σ 5 σ 40

Only meson mixing generated by down-type quarks Arg(q/p) [deg.] 20 (SUSY: up-type squarks) 0 < −2 −20 SM suppression: ∆mD, ∆ΓD ∼ 10 Γ, since doubly-Cabibbo-suppressed & vanish in SU(3) limit −40 −60

• y = (0.75 ± 0.12)% and x = (0.63 ± 0.20)% 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 |q/p| ... suggest long distance dominance Don’t known yet if |q/p| is near 1! • How small CPV would unambiguously establish NP?

• Interesting inerplay in SUSY between ∆mD and ∆mK constraints Possible connections to top FCNC top decays

ZL — p.1/29 Looking for NP with B decays

CDF What’s special about B’s?

• Large variety of interesting processes: – Top quark loops neither GIM nor CKM suppressed – Large CP violating effects possible, some with clean interpretation

– Some of the hadronic physics understood model independently( mb ΛQCD)

• Experimentally feasible to study: – Υ(4S) resonance is clean source of B mesons – Long B meson lifetime

If |Vcb| were as large as |Vus|, probably BaBar, Belle, LHCb would not have been built, these lectures would not take place, etc. – Timescale of oscillation and decay comparable: ∆m/Γ ' 0.77 [= O(1)] (and ∆Γ Γ)

ZL — p.1/30 You can “see” B decays

Nch=17 EV1=.935 EV2=.681 EV3=.123 ThT=1.93 Detb= E0FBFF ALEPH run = 15419 event = 5991 .40Gev EC 1.6Gev HC Y’ 0 |−8cm 8cm|

|−10cm 0 X’ 10cm| Z0<4 __ YX o + B+ −> D** µ ν µ π− + π ** − D π *

Y’ D 0 µ+ IP −o B+ D +

|−0.1cm 0.1cm| K

|−1cm 0 X’ 1cm| Z0<4 3 σ ellipses YX Quantum entanglement in Υ(4S) → B0B0

• B0B0 pair created in a p-wave (L = 1) evolve coherently and undergo oscillations

Two identical bosons cannot be in an antisymmetric state — if one B decays as a B0 (B0), then at the same time the other B must be B0 (B0) • EPR effect used for precision physics:

Measure B decays and ∆z

• First decay ends quantum correlation and tags the ﬂavor of the other B at t = t1

ZL — p.1/31 Asymmetric colliders

... to measure time dependence of decay after the collision Hadron colliders — no quantum correlation

• Opposite side tagging + same side tagging (at LHCb, both are boosted forward)

2 • Much smaller D than at Υ(4S) ( = tagging efﬁciency, D = 1 − 2ωmistag = “dilution”) Need good time resolution, and fully reconstructed B on signal side to know boost

ZL — p.1/32 The cleanest case: B → ψKS

• Interference of B → ψK0 (b → ccs¯ ) with B → B → ψK0 (¯b → cc¯s¯) £¡£

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• World average: sin 2β = ±SψKS,L = 0.677 ± 0.020 — a 3% uncertainty! • Large deviations from CKM excluded; CPV is not small in general, only in K

ZL — p.1/33 CP violation in B → J/ψ KS by the naked eye

• CP violation is an O(1) effect: sin 2β = 0.677 ± 0.020

Γ[B0(t) → ψK] − Γ[B0(t) → ψK] af = = sin2 β sin(∆m t) CP Γ[B0(t) → ψK] + Γ[B0(t) → ψK] • CP violation is large in some B decays — in K decays it is small due to small CKM elements, not because CP violation is generically small

ZL — p.1/34 Similarly: βs from Bs → ψφ

• Analog in B → ψ K: time dependent CP asymmetry in Bs → ψφ

∗ ∗ 2 In SM: βs = arg(−VtsVtb/VcsVcb) = 0.019 ± 0.001 (λ suppressed compared to β)

• LHCb 2013: φs ≡ −2βs = 0.01 ± 0.07 The Bs “squashed” UT: 0.10 excluded at CL > 0.95 εK excluded area has CL > 0.95

0.05 ∆md & ∆ms

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Bs 0.00

η β s

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ρBs • Uncertainty of the SM prediction current experimental error( ⇒ LHCb upgrade)

ZL — p.1/35 B → φK and Bs → φφ — window to NP?

• Measuring same angle in decays sensitive to different short distance physics give

good sensitivity to NP (sensitive to NP–SM interference)

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NP could enter SψK mainly in mixing, while SφKS through both mixing and decay • Interesting to pursue independent of present results — plenty of room left for NP

ZL — p.1/36 Status of sin 2βeﬀ measurements

eff eff HFAGHFAG eff eff sin(2 ) sin(2 ) sin(2β ) ≡ sin(2φ1 ) vs CCP ≡ -ACP HFAGHFAG β ≡ φ1 Moriond 2012 Moriond 2012 PRELIMINARY CCP ≡ -ACP PRELIMINARY b→ccs World Average 0.68 ± 0.02

0 BaBar 0.66 ± 0.17 ± 0.07 0.8 Belle HFAG 0.90 +0.09 K +-0.119 φ Average Moriond 2012 0.74 -0.13 HFAG

0 BaBar 0.57 ± 0.08 ± 0.02 Moriond 2012 K Belle 0.64 ± 0.10 ± 0.04 0.6 η′ S Average 0.59 ± 0.07

HFAG +0.21

K BaBar 0.94 -0.24 ± 0.06 S

Belle Moriond 2012 0.30 ± 0.32 ± 0.08 K Average 0.72 ± 0.19 S 0.4 HFAG 0 K BaBar 0.55 ± 0.20 ± 0.03 K Belle Moriond 2012 0.67 ± 0.31 ± 0.08 0

π Average 0.57 ± 0.17

HFAG +0.26

S BaBar 0.35 -0.31 ± 0.06 ± 0.03 +0.19 0.2 Moriond 2012 K Belle 0.64 -0.25 ± 0.09 ± 0.10 0 +0.18

ρ Average 0.54 -0.21

HFAG +0.26

S BaBar 0.55 -0.29 ± 0.02 Moriond 2012

K Belle 0.11 ± 0.46 ± 0.07 0

ω Average 0.45 ± 0.24

HFAG +0.12

S BaBar 0.74 +-0.165 b→ccs

Moriond 2012 0.63 K Belle -0.19

0 +0.10 0 f Average 0.69 -0.12 -0.2 φ K HFAG S BaBar 0.48 ± 0.52 ± 0.06 ± 0.10 0

K η′ K Moriond 2012

2 Average 0.48 ± 0.53 f S

BaBar HFAG 0.20 ± 0.52 ± 0.07 ± 0.07 K K K K S -0.4 S S S X Average 0.20 ± 0.53 0 f Moriond 2012

K π K BaBar HFAG -0.72 ± 0.71 ± 0.08 0 S

π 0 0 0 S -0.72 ± 0.71

Average

Moriond 2012 +0.03 K K 0 ρ S π π S K BaBar HFAG 0.97

π -0.52 0 +0.03 -0.6 π Average 0.97 -0.52 ω K f K NR

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φ 0 BaBar HFAG 0.01 ± 0.31 ± 0.05 ± 0.09 f K f K K 0 X S

- 0.01 ± 0.33

0 Average

Moriond 2012 + - 0 + - 0 π

BaBar HFAG 0.65 ± 0.12 ± 0.03 K K K K π π K NR - + +0.14 S K -0.8 - π Belle 0.76 -0.18 Moriond 2012 K +0.09 + K Average 0.68 -0.10 + HFAG K -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Average HFAG 0.68 ± 0.07 K eff eff

Moriond 2012 sin(2β ) ≡ sin(2φ )

Moriond 2012 1 -2 -1 0 1 2 Contours give -2∆(ln L) = ∆χ2 = 1, corresponding to 60.7% CL for 2 dof

• Earlier hints of deviations reduced, e.g., in SφK and Sη0K It is still interesting to signiﬁcantly reduce these experimental uncertainties

ZL — p.1/37 γ from B± → DK±

• Tree level: interference of b → cus¯ (B− → D0K−) and b → ucs¯ (B− → D0K−) Extract B & D decay amplitudes from data; many variants depending on D decay

• Problem: large ratio of interfering amplitudes, CKM D(*) K(*) GLW + ADS WA f i t t e r Winter 12 D(*) K(*) GGSZ Combined

sensitivity crucially depends on: Full Frequentist treatment on MC basis CKM fit 1.0 − 0 − − 0 − rB = |A(B → D K )/A(B → D K )| ≈ 0.1 0.8

0.6 0 0 + − • Best measurement so far: D , D → KS π π p•value 0.4 – Both amplitudes Cabibbo allowed; 0.2 0.0 0 20 40 60 80 100 120 140 160 180 – Can integrate over regions in Dalitz plot γ (deg) Other variants: GLW (Gronau–London–Wyler), ADS (Atwood–Dunietz–Soni)

• Measurement will not be theory limited at any conceived future experiment

ZL — p.1/38 ± ∓ Only LHCb: γ from Bs → Ds K

± ∓ • Same weak phase in each Bs, Bs → Ds K decay ⇒ the 4 time dependent rates determine 2 amplitudes, a strong, and a weak phase (clean, although |fi= 6 |fCP i)

A1 + − A2 + − Four amplitudes: Bs → Ds K (b → cus) , Bs → K Ds (b → ucs) A1 − + A2 − + Four amplitudes: Bs → Ds K (b → cus) ,Bs → K Ds (b → ucs)

A + − ∗ A − + ∗ Ds K A1 VcbVus Ds K A2 VubVcs = ∗ , = ∗ A + − A2 V Vcs A − + A1 V Vus Ds K ub Ds K cb

Magnitudes and relative strong phase of A1 and A2 drop out if four time dependent rates are measured ⇒ no hadronic uncertainty: V ∗V 2V V ∗ V V ∗ tb ts cb us ub cs −2i(γ−2βs−βK) λ + − λ − + = = e Ds K Ds K ∗ ∗ ∗ VtbVts VubVcs VcbVus

(∗)± ∓ −2i(γ+2β) • Similarly, Bd → D π determines γ + 2β, since λD+π− λD−π+ = e ... ratio of amplitudes O(λ2) ⇒ small asymmetries (tag side interference)

ZL — p.1/39 New physics in B mixing The standard model CKM ﬁt

1.5 excluded at CL > 0.95 • Looks impressive... excluded area has CL > 0.95 γ 1.0 • Level of agreement between the ∆md & ∆ms measurements often misinterpreted sin 2β 0.5 ∆md ε α • Increasing the number of parame- K γ β

η 0.0 ters can alter the ﬁt completely α

Vub α • Plausible TeV scale NP scenarios, •0.5 consistent with all low energy data,

•1.0 εK w/o minimal ﬂavor violation (MFV) CKM f i t t e r γ sol. w/ cos 2β < 0 Winter 12 (excl. at CL > 0.95) •1.5 • CKM is inevitable; the question is •1.0 •0.5 0.0 0.5 1.0 1.5 2.0 not if it’s correct, but is it sufﬁcient? ρ

ZL — p.1/40 New physics in B0–B0 mixing

• Assume: (i) 3 × 3 CKM matrix is unitary; (ii) Tree-level decays dominated by SM

Concentrate on NP in mixing amplitude; two parameters for each neutral meson:

SM 2 2iθ SM 2iσ M12 = M12 r e ≡ M12 (1 + h e ) easy| to relate{z to data} easy| to relate{z to models}

• Tree-level CKM constraints unaffected: |Vub/Vcb| and γ (or π − β − α)

d,s • BB mixing dependent observables sensitive to NP: ∆md,s, Sfi, ASL , ∆Γs

ZL — p.1/41 New physics in B0–B0 mixing

• Assume: (i) 3 × 3 CKM matrix is unitary; (ii) Tree-level decays dominated by SM

Concentrate on NP in mixing amplitude; two parameters for each neutral meson:

SM 2 2iθ SM 2iσ M12 = M12 r e ≡ M12 (1 + h e ) easy| to relate{z to data} easy| to relate{z to models}

• Tree-level CKM constraints unaffected: |Vub/Vcb| and γ (or π − β − α)

d,s • BB mixing dependent observables sensitive to NP: ∆md,s, Sfi, ASL , ∆Γs

2 SM 2iσq SM ∆mBq = rq ∆mBq = |1 + hqe |∆mq 2iσ SψK = sin(2β +2 θd) = sin[2β + arg(1 + hde d)] Sρρ = sin(2α − 2θd)

2iσs Sψφ = sin(2βs − 2θs) = sin[2βs − arg(1 + hse )] q q q Γ12 Γ12 CP SM 2 A = Im = Im ∆Γ = ∆Γ cos 2θs SL q 2 2iθq q 2iσq s s M12rq e M12(1 + hqe )

ZL — p.1/41 New physics in B meson mixing

• Tree-dominated measurements: Until 2004, hd ∼ 10 was allowed 0.7 CKM f i t t e r 0.6 γ γ(α) Winter 12 Better tree-level measurements crucial 1-CL 0.5 1.0 3.0 excluded area has CL > 0.95 0.4 w/o B-> ντ , A SL 0.9 excluded area has CL > 0.95 > areaexcludedhas CL η 0.3 α 2.5 0.8 0.2 0.7 0.1 Vub γ β 2.0 0.0 0.6 •0.4 •0.2 0.0 0.2 0.4 0.6 0.8 1.0

ρ d 0.5

σ 1.5 • Loop-dominated measurements: 0.4 1.0 0.7 0.3 ∆m & ∆m CKM d s f i t t e r 0.6 ∆md εK Winter 12 0.2 0.5 0.5 sin 2β CKM sol. w/ cos 2β < 0 f i t t e r 0.1 (excl. at CL > 0.95) 0.4 LP 11 excluded area has CL > 0.95 > areaexcludedhas CL η 0.0 0.0 0.3 0.0 0.2 0.4 0.6 0.8 1.0 εK α h 0.2 d

0.1 2 γ β A goal: assume h ∼ (4πv/Λﬂav.) 0.0 •0.4 •0.2 0.0 0.2 0.4 0.6 0.8 1.0 > ρ Can we probe Λﬂav. ∼ ΛEWSB ?

ZL — p.1/42 Preliminary — sensitivity in ∼10 years?

• Rough predictions to illustrate increased sensitivity

1-CL p•value 1.0 1.0 3.0 excluded area has CL > 0.95 excluded area has CL > 0.95 w/o B-> ντ , A 3.0 CKM SL 0.9 f i t t e r 0.9 2020 (?)

2.5 0.8 2.5 0.8

0.7 0.7 2.0 2.0 0.6 0.6 d d 0.5 0.5 σ σ 1.5 1.5 0.4 0.4 1.0 0.3 1.0 0.3

0.2 0.2 0.5 0.5 CKM f i t t e r 0.1 •1 0.1 LP 11 Belle II+LHCb 50 fb 0.0 0.0 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 h d hd

Hot off the press (computers), since I gave the slides to Kate yesterday

[Thanks to S. Descotes-Genon and K. Trabelsi, CKMﬁtter]

ZL — p.1/43 Preliminary — sensitivity in ∼10 years?

• Rough predictions to illustrate increased sensitivity

p•value p•value 1.0 1.0 3.0 excluded area has CL > 0.95 3.0 excluded area has CL > 0.95 CKM 0.9 f i t t e r 0.9 2020 (?)

2.5 0.8 2.5 0.8

0.7 0.7 2.0 2.0 0.6 0.6

s 0.5 s 0.5 σ 1.5 σ 1.5 0.4 0.4

1.0 0.3 1.0 0.3

0.2 0.2 0.5 0.5 CKM f i t t e r 0.1 •1 0.1 LP 11 Belle II+LHCb 50 fb 0.0 0.0 0.0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.2 0.4 0.6 0.8 1.0

hs hs

Hot off the press (computers), since I gave the slides to Kate yesterday

[Thanks to S. Descotes-Genon and K. Trabelsi, CKMﬁtter]

ZL — p.1/44 Summary (1)

• Flavor physics ≡ what distinguishes generations (break U(3)5 global symmetry)

• Flavor changing neutral currents and neutral meson mixing probe high scales ... strong constraints on TeV-scale NP, many synergies (hard to avoid)

• CP violation is always the result of interference phenomena; no classical analog

• Past: Ten years ago O(1) deviations from the SM predictions were possible Present: O(20%) corrections to most FCNC processes are still allowed Future: Few % sensitivities. Corrections to SM? What can we learn about NP?

• KM phase is the dominant source of CP violation in ﬂavor changing processes

• The point is not measuring CKM elements, but to overconstrain ﬂavor many ways

• Measurements probe scales 1 TeV; sensitivity limited by statistics, not theory

ZL — p.1/45