[PPT] - Flavor Physics and CP Violation The 2013 European School Zoltan PowerPoint Presentation

SLIDE 1

Flavor Physics and CP Violation

Zoltan Ligeti

(ligeti@lbl.gov) Lawrence Berkeley Laboratory Par´ adf¨ urd˝

, Hungary, June 5–18, 2013

The 2013 European School

f High-Energy

Physics

Parádfürdő, Hungary 5 – 18 June 2013

Deadline for applications: 15 February 2013 http://cern.ch/PhysicSchool/ESHEP

ESHEP2013

CERN - JINR

Standing Committee

T. Donskova, JINR
N. Ellis, CERN
H. Haller, CERN
M. Mulders, CERN
A. Olchevsky, JINR
G. Perez, CERN & Weizmann Inst.
K. Ross, CERN

Enquiries and Correspondence

Kate Ross CERN Schools of Physics CH-1211 Geneva 23 Switzerland Tel +41 22 767 3632 Fax +41 22 766 7690 Email Physics.School@cern.ch Tatyana Donskova International Department JINR RU-141980 Dubna, Russia Tel +7 49621 63448 Fax +7 49621 65891 Email phs@jinr.ru

International Advisors

R. Heuer, CERN
V. Matveev, JINR
J. Pálinkás, Hungarian Academy of Sciences
A. Skrinsky, BINP, Novosibirsk
N. Tyurin, IHEP, Protvino

Scientifjc Programme

Field Theory and the Electro-Weak Standard Model

E. Boos, Moscow State Univ., Russia

Beyond the Standard Model

C. Csaki, Cornell Univ., USA

Higgs Physics

J. Ellis, King’s College London, UK & CERN

Neutrino Physics

B. Gavela, Univ. Autonoma & IFT UAM/CSIC, Madrid,

Spain Cosmology

D. Gorbunov, INR, Russia

Flavour Physics and CP Violation

Z. Ligeti, Berkeley, USA

Practical Statistics for Particle Physicists

H. Prosper, Florida State Univ., USA

Quark–Gluon Plasma and Heavy-Ion Collisions

K. Rajagopal, MIT, USA & CERN

QCD for Collider Experiments

Z. Trócsányi, Univ. Debrecen, Hungary

Highlights from LHC Physics Results

T. Virdee, Imperial College London, UK

Discussion Leaders

A. Arbuzov, JINR
T. Biro, Wigner RCP, Hungary
M. Blanke, CERN
G. Cynolter, Roland Eotvos Univ., Hungary
A. De Simone, SISSA, Italy & CERN
A. Gladyshev, JINR

Local Committee

C. Hajdu, Wigner RCP, Hungary
G. Hamar, Wigner RCP, Hungary
D. Horváth, Wigner RCP, Hungary
J. Karancsi, Univ. Debrecen, Hungary
P. Lévai, Wigner RCP, Hungary
F. Siklér, Wigner RCP, Hungary
B. Ujvári,Univ. Debrecen, Hungary
V. Veszprémi, Wigner RCP, Hungary
A. Zsigmond, Wigner RCP, Hungary

SLIDE 2

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

SLIDE 3

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

SLIDE 4

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

SLIDE 5

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

SLIDE 6

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(photon) ∼ 10−9 ⇒ Nq − Nq Nq + Nq ∼ 10−9 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

SLIDE 7

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

SLIDE 8

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

ǫK: (s ¯ d)2 Λ2 ⇒ Λ> ∼104 TeV, ∆mB: (b ¯ d)2 Λ2 ⇒ Λ> ∼103 TeV, ∆mBs: (b¯ s)2 Λ2 ⇒ Λ> ∼102 TeV

– 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

SLIDE 9

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

SLIDE 10

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

SLIDE 11

Preliminaries

Dictionary:

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

Disclaimers: I will not talk about: the strong CP problem θQCD

16π2 Fµν F µν

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

SLIDE 12

Ancient past

SLIDE 13

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

SLIDE 14

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

Once upon a time, “Tau – Theta puzzle”: θ+ → π+π0

Once upon a time, “Tau – Theta puzzle”: τ + → π+π+π− π : JP = 0− If parity was conserved in decay: P(ππ) = (−1)J(θ+) and P(πππ) = −(−1)J(τ+) Assumed: τ + = 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

SLIDE 15

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

Charge & angular momentum: 4 possibilities

Only νL and ¯ νR participate in weak interaction Weak interaction maximally violates C and P CP was still assumed to be a good symmetry

ZL — p.1/1

SLIDE 16

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

Charge & angular momentum: 4 possibilities
Only νL and ¯

νR participate in weak interaction Weak interactions maximally violate C and P

However, CP could still be a good symmetry

ZL — p.1/1

SLIDE 17

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

SLIDE 18

Aside: the experimental proposal

⇒ Cronin & Fitch, Nobel Prize, 1980 ⇒ 3 generations, Kobayashi & Maskawa, Nobel Prize, 2008

SLIDE 19

Hitchhiker’s guide to the SM

SLIDE 20

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

SLIDE 21

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, ℓR(1, 1)−1 3(+9) Particle content: quarks: u c t d s b

leptons:

νe νµ ντ e µ τ

Symmetry breaking: SU(2)L × U(1)Y → U(1)EM

symmetry breaking: φ(1, 2)1/2 Higgs scalar, φ =

v/

√ 2

2
Strongly interacting particles observed in Nature have no color; quarks confined

mesons: π+ (u ¯ d), K0 (¯ sd), B0 (¯ bd), B0

s (¯

bs); baryons: p (uud), n (udd)

ZL — p.1/4

SLIDE 22

SM: where can CP violation occur?

Kinetic terms: Lkin = −1

4

groups

(F a

µν)2 +

rep′s

ψ iD / ψ

(3 param’s: g, g′, gs) Kinetic terms: always CPC (ignoring F F)

Higgs terms: LHiggs = |Dµφ|2 + µ2φ†φ − λ(φ†φ)2

(2 param’s; v2 = µ2/λ) Higgs terms: CPC for one Higgs doublet; CPV constrains extended Higgs sector

Yukawa couplings in interaction basis:

(where flavor comes from) LY = −Y d

ij QI Li φ dI Rj − Y u ij QI Li

φ uI

Rj − Y ℓ ij LI Li φ ℓI Rj + h.c.

i, j ∼ generations (cannot write such mass term for νi) ց

= 1 −1

φ∗
CPV is related to unremovable phases of Yukawa couplings:

Yij ψLi φ ψRj + Y ∗

ij ψRj φ† ψLi

⇓ CP exchanges fermion bilinears Yij ψRj φ† ψLi + Y ∗

ij ψLi φ ψRj ZL — p.1/5

SLIDE 23

From Yukawa couplings to CKM matrix

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

LY = −Y ij

u QI Li

φ uI

Rj − Y ij d QI Li φ dI Rj

φ =

1 −1

φ∗
Y ij

u,d = 3 × 3 complex matrices ⇒ mass terms after φ acquires VEV

Lmass = −uI

Li M ij u uI Rj − dI Li M ij d dI Rj ,

Mu,d = Yu,d (v/ √ 2)

Diagonalize: M diag

f

≡ VfL Mf V †

fR

(f = u, d; V -s unitary)

Mass eigenstates: fLi ≡ V ij

fL f I Lj ,

fRi ≡ V ij

fR f I Rj

Mass matrices diagonalized by different transformations for uLi and dLi, which

are part of the same SU(2)L doublet, QL, so:

uI

Li

dI

Li

= (V †

uL)ij

uLj

(VuLV †

dL)jk dLk

Charged current weak interactions become off-diagonal:

ւ ր CKM matrix

−g 2 QI

Li γµ W a µ τa QI Li + h.c. ⇒ − g

√ 2

uL, cL, tL
γµ W +

µ (VuLV † dL)

   dL sL bL    + h.c. ZL — p.1/6

SLIDE 24

Weak interaction properties

Only the W ± interactions change the type of quarks

Interaction strength is given by Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix, Vij, 3 × 3 unitary matrix

✁

✂☎✄ ✆ ✆ ✆ ✆ ✝ ✞✠✟ ✡ ✡ ✡ ☛ ☛ ✡ ✡ ✡ ☛ ☛ ☞ ✌✎✍ ✏✒✑ ✓ ✟ ✄

Flavor changing charged currents at tree level

e.g.: K → ππ or K → πℓ¯ ν No flavor changing neutral currents (FCNC) at tree level e.g.: no K0 – K0 mixing, K → µ+µ−, etc.

(Show that Z0 interactions are flavor conserving in the mass basis)

FCNC only at loop level in SM; suppressed by (m2

i −m2 j)/m2 W

e.g.: K0 – K0 mixing used to predict mc before its discovery

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

✂ ✄ ✄ ✄ ✄ ☎ ✆ ✝ ✝ ✝ ✞ ✞ ✝ ✝ ✝ ✞ ✞ ✟

✁✡✠

✄ ✄ ✄ ✄ ☎ ✆

✁

✂ ✄ ✄ ✄ ✄ ☎ ✆ ✝ ✝ ✝ ✞ ✞ ✝ ✝ ✝ ✞ ✞ ✟

✁

✆ ✄ ✄ ✄ ✄ ☎ ✂

×

✁

✂ ✂ ✂ ✂ ✄ ✄ ✄ ✂ ✂ ✂ ✂ ✄ ✄ ✄ ☎ ✆ ✝✟✞✡✠☛✞✌☞ ✄ ✄ ✄ ✄ ✂ ✂ ✂ ✄ ✄ ✄ ✄ ✂ ✂ ✂ ☎ ✍ ✎

✎

✆ ✝✟✞✡✠☛✞✌☞ ✍ ✁

ZL — p.1/7

SLIDE 25

Quark mixing and the unitarity triangle

The (u, c, t) W ± (d, s, b) couplings:

(Wolfenstein parm., λ ∼ 0.23) VCKM =    Vud Vus Vub Vcd Vcs Vcb Vtd Vts Vtb   

CKM matrix

=    1 − 1

2λ2

λ Aλ3(ρ − iη) −λ 1 − 1

2λ2

Aλ2 Aλ3(1 − ρ − iη) −Aλ2 1    + . . .

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

CPV in SM ∝ Area

Vud V ∗

ub + Vcd V ∗ cb + Vtd V ∗ tb = 0

Sides and angles measurable in many ways Goal: overconstrain by many measurements sensitive to different short distance physics

ZL — p.1/8

SLIDE 26

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 = [6 masses] + parameters in VCKM

[3 angles] + [1 phase]
Single source of CP violation in the quark sector in the SM
Lepton sector (if Majorana ν’s): LY = −Y ij

e LI Li φ eI Rj − Y ij ν

M LI

LiLI Lj φ φ

(Y ij

ν

= Y ji

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]

One CPV phase measurable in ν oscillations, others in 0νββ decay

ZL — p.1/9

SLIDE 27

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

SLIDE 28

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

SLIDE 29

Seeking indirect signals of NP

Precision electroweak T parameter (“little hierarchy problem”):

(φDµφ)2 Λ2 ⇒ Λ > few × 103 GeV

Flavor and CP violating operators (“new physics flavor problem”), e.g.:

QQQQ Λ2 ⇒ Λ > ∼ 10(4...7) GeV 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 Λ2 ⇒ Λ > ∼ 1016 GeV

Unique set of dimension-5 terms composed of SM fields:

Ldim-5 = 1 Λ (Lφ)(Lφ) → mν νν , mν ∝ v2 Λ (see-saw mechanism) Suggests very high scales (assuming O(1) couplings) — unless there are “sterile” neutrinos...

ZL — p.1/12

SLIDE 30

Testing the flavor sector

SLIDE 31

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) – ǫK 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

SLIDE 32

The low energy viewpoint

At scale mb, flavor changing pro-

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 weak / NP scale ∼ 5 GeV E.g.: in SM ∆md

∆ms , b → dγ b → sγ , b → dℓ+ℓ− b → sℓ+ℓ− ∝

Vtd

Vts

, but test different short dist. physics
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 = 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

SLIDE 33

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

Operator Bounds on Λ [TeV] (C = 1) Bounds on C (Λ = 1 TeV) Observables Re Im Re Im (¯ sLγµdL)2 9.8 × 102 1.6 × 104 9.0 × 10−7 3.4 × 10−9 ∆mK; ǫK (¯ sR dL)(¯ sLdR) 1.8 × 104 3.2 × 105 6.9 × 10−9 2.6 × 10−11 ∆mK; ǫK (¯ cLγµuL)2 1.2 × 103 2.9 × 103 5.6 × 10−7 1.0 × 10−7 ∆mD; |q/p|, φD (¯ cR uL)(¯ cLuR) 6.2 × 103 1.5 × 104 5.7 × 10−8 1.1 × 10−8 ∆mD; |q/p|, φD (¯ bLγµdL)2 5.1 × 102 9.3 × 102 3.3 × 10−6 1.0 × 10−6 ∆mBd; SψKS (¯ bR dL)(¯ bLdR) 1.9 × 103 3.6 × 103 5.6 × 10−7 1.7 × 10−7 ∆mBd; SψKS (¯ bLγµsL)2 1.1 × 102 2.2 × 102 7.6 × 10−5 1.7 × 10−5 ∆mBs; Sψφ (¯ bR sL)(¯ bLsR) 3.7 × 102 7.4 × 102 1.3 × 10−5 3.0 × 10−6 ∆mBs; Sψφ

Large SM suppressions — excellent probes of NP

ZL — p.1/15

SLIDE 34

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

SLIDE 35

Brief history of CKM constraints

For 35 years (untill 1999), only unambiguous CPV measurement was in K mixing

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 ρ

_

η

_

(BABAR Physics Book, 1998)

γ γ α α

d

m ∆

K

ε

K

ε

s

m ∆ &

d

m ∆

ub

V β sin 2

(excl. at CL > 0.95) < 0 β

sol. w/ cos 2

excluded at CL > 0.95

α β γ

ρ

1.0
0.5

0.0 0.5 1.0 1.5 2.0

η

1.5
1.0
0.5

0.0 0.5 1.0 1.5

excluded area has CL > 0.95 Winter 12

CKM

f i t t e r

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

SLIDE 36

Mixing and CP violation

SLIDE 37

Neutral meson mixing

Quantum mechanical two-level system; flavor eigenstates: |B0=|bd, |B0=|bd
Evolution: i d

dt |B0(t) |B0(t)

=
M − i

2 Γ |B0(t) |B0(t)

Mass eigenstates: |BH,L = p|B0 ∓ q|B0

b d d b t t W W b d d b W W t t

M, Γ: 2 × 2 Hermitian matrices

(CP T implies M11 = M22 and Γ11 = Γ22)

Time dependence involves mixing and decay: |BH,L(t) = e−(iMH,L+ΓH,L/2)t|BH,L

CP violation: |q/p| = 1 ⇔ mass eigenstates = CP eigenstates
GIM mechanism: M12 ∝
i,j

VibV ∗

id VjbV ∗ jd f(mi, mj) →

m2

α − m2 β

m2

W

suppression 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

SLIDE 38

Aside: time evolition

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

cosh ∆Γ t

4 cos ∆m t 2 − i sinh ∆Γ t 4 sin ∆m t 2

g−(t) = e−it(m−iΓ/2)
− sinh ∆Γ t

4 cos ∆m t 2 + i cosh ∆Γ t 4 sin ∆m t 2

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

ZL — p.1/19

SLIDE 39

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

SM contributions to B0 − B0 mixing:

b d d b t t W W b d d b W W t t

⇒

✁

✂ ✄ ☎ ☎ ☎ ☎ ✆ ✝

✁

✂ ✝ ☎ ☎ ☎ ☎ ✆ ✄

Q(µ) = (bL γν dL) (bL γν dL)

New physics can modify coefficients and/or induce new operators

Going from operators to observables is equally important

In SM:

M12 = (VtbV ∗

td)2 G2 F

8π2 m2

W

mB S m2

t

m2

W

ηB bB(µ) B0|Q(µ)|B0

what we are after calculable perturbatively nonperturbative ηB bB(µ) : Resumming αn

s lnn(mW/µ) is often very important (µ ∼ mb)

B0|Q(µ)|B0 = 2

3 m2 B f 2 B

BB

bB(µ) : hadronic uncertainties enter here ZL — p.1/20

SLIDE 40

The four neutral mesons

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

Order of magnitudes

f SM predictions:

meson x y |q/p| − 1 K 1 1 10−3 D 10−2 10−2 10−2(−3?) Bd 1 10−2 10−3 Bs 101 10−1 10−3

General sol. for eigenvalues is complicated; an important part: q2

p2 = 2M ∗

12 − iΓ∗ 12

2M12 − iΓ12 [CP violation in mixing ↔ Im(Γ12/M12) = 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

SLIDE 41

B0

s mixing and |Vtd/Vts|

B0

s – B0 s oscillate ∼25 times before they decay (first measured by CDF in 2007)

∆ms = (17.768 ± 0.024) ps−1

Uncertainty σ(∆ms) = 0.13% is much

smaller than σ(∆md) = 0.8%

γ γ α α

d

m ∆

K

ε

K

ε

s

m ∆ &

d

m ∆

ub

V β sin 2

(excl. at CL > 0.95) < 0 β

sol. w/ cos 2

excluded at CL > 0.95

α β γ

ρ

1.0
0.5

0.0 0.5 1.0 1.5 2.0

η

1.5
1.0
0.5

0.0 0.5 1.0 1.5

excluded area has CL > 0.95 Winter 12

CKM

f i t t e r

Largest uncertainty: ξ = fBs

√Bs fBd

√

Bd

Lattice QCD: ξ = 1.24±0.03±0.02

ZL — p.1/22

SLIDE 42

Types of CP violation

CP violation: Γ(A → B) = 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

Af = f|H|B =

k Ak eiδk eiφk

Af = f|H|B =

k Ak eiδk e−iφk

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

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

Unambiguously established by ǫ′

K = 0 in 1999, and since 2004 also in B decays

Theoretical understanding for ǫ′

K, AK−π+, etc., insufficient to either prove or to

rule out that NP enters — still, ǫ′

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

SLIDE 43

CPV in mixing

If CP is conserved then |q/p| = 1 and arg(M12/Γ12) = 0

CPV iff (mass eigenstates) = (CP eigenstates) — physical states not orthogonal! |q/p| = 1 ⇔ CPV in mixing implies: BH|BL = |p|2 − |q|2 = 0

Simplest example: decay to “wrong sign” lepton (“dilepton asymmetry”)

ASL = Γ[B0(t) → ℓ+X] − Γ[B0(t) → ℓ−X] Γ[B0(t) → ℓ+X] + Γ[B0(t) → ℓ−X] = |p/q|2 − |q/p|2 |p/q|2 + |q/p|2 = 1 − |q/p|4 1 + |q/p|4 = Im Γ12 M12

Observed in K decay in agreement with SM (CPLEAR @ CERN)

Large hadronic uncertainties in calculation of Γ12, but interesting to look for NP:

|Γ12/M12| = O(m2

b/m2 W) model independently

arg(Γ12/M12) = O(m2

c/m2 b) in SM, maybe O(1) with NP ZL — p.1/24

SLIDE 44

CPV in interference between decay and mixing

Can get theoretically clean information in some

cases when B0 and B0 decay to same final state |BL,H = p|B0 ± q|B0 λfCP = q p AfCP AfCP

B B

CP

f

q/p A A

Time dependent CP asymmetry:

afCP = Γ[B0(t) → f] − Γ[B0(t) → f] Γ[B0(t) → f] + Γ[B0(t) → f] = 2 Im λf 1 + |λf|2

Sf

sin(∆m t) − 1 − |λf|2 1 + |λf|2

Cf (−Af)

cos(∆m t)

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

SLIDE 45

Bits of K and D physics

SLIDE 46

∆mK — built in NP models since 60’s

In the SM: ∆mK ∼ α2

w |VcsVcd|2 m2 c

m4

W

f 2

K mK

(severe suppressions!)

✁

✂ ✂ ✂ ✂ ✄ ✄ ✄ ✂ ✂ ✂ ✂ ✄ ✄ ✄ ☎ ✆ ✝✟✞✡✠☛✞✌☞ ✄ ✄ ✄ ✄ ✂ ✂ ✂ ✄ ✄ ✄ ✄ ✂ ✂ ✂ ☎ ✍ ✎

✎

✆ ✝✟✞✡✠☛✞✌☞ ✍ ✁

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

fraction of the measured value of ∆mK

✁

✂ ✄ ✄ ✄ ✄ ☎ ✆ ✝ ✞ ✞ ✞ ✟ ✟ ✞ ✞ ✞ ✟ ✟ ✠ ✡ ✡ ☛

✁

✝ ✄ ✄ ✄ ✄ ☎ ✆ ✂ ✠

M (X)

12

∆mK

∼
g2 Λ3

QCD

M 2

X ∆mK

⇒ MX >

∼ g × 2 · 103 TeV Similarly, from B0 −B0 mixing: MX > ∼ g ×3·102 TeV

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

SLIDE 47

Precision CKM tests with kaons

CPV in K system is at the right level (ǫK accommodated with O(1) KM phase)
Hadronic uncertainties preclude precision tests (ǫ′

K notoriously hard to calculate)

We cannot rule out (nor prove) that the measured value of ǫ′

K is dominated by NP

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

With lattice QCD improvements, ǫK has become more sensitive, hopes for ǫ′/ǫ
K → πνν : Theory error ∼ few %, but very small rates 10−10 (K±), 10−11 (KL)

A ∝      (λ5 m2

t) + i(λ5 m2 t)

t : CKM suppressed (λ m2

c) + i(λ5 m2 c)

c : GIM suppressed (λ Λ2

QCD)

u : GIM suppressed

✁

✂ ✄ ☎✝✆✟✞✠✆☛✡ ☞✝✌✟✍✠✌☛✎ ✏ ✑ ✒ ✓ ✔ ✕ ✖ ✗ ✘

So far O(1) uncertainty in K+ → π+ν¯ ν, and O(103) in KL → π0ν¯ ν

⇒ Need much more data to achieve ultimate sensitivity

ZL — p.1/27

SLIDE 48

The quest for K → πν¯ ν

Long history of ingenious experimental progress (huge backgrounds)

E787/E949: 7 events observed, B(K → π+ν¯ ν) = (1.73+1.15

−1.05) × 10−10

SM: B(K+ → π+ν¯

ν) = (0.78 ± 0.08) × 10−10, B(K0

L → π0ν¯

ν) = (0.24 ± 0.04) × 10−10

CERN NA62: expect to get ∼ 100 K+ → π+ν¯ ν events FNAL ORKA proposal: ∼ 1000 K+ → π+ν¯ ν events

[Stage-1 approval]

J-PARC KOTO: observe K0

L → π0ν¯

ν at SM level FNAL w/ project-X: proposal for ∼ 1000 event K0

L → π0ν¯

ν

ZL — p.1/28

SLIDE 49

D0: mixing in up sector

Complementary to K, B: CPV, FCNC both GIM & CKM suppressed ⇒ tiny in SM
2007: observation of mixing, now >

∼10σ [HFAG combination] Only meson mixing generated by down-type quarks (SUSY: up-type squarks) SM suppression: ∆mD, ∆ΓD < ∼ 10−2 Γ, since doubly-Cabibbo-suppressed & vanish in SU(3) limit

y = (0.75 ± 0.12)% and x = (0.63 ± 0.20)%

... suggest long distance dominance

x (%) −0.5 0.5 1 1.5 y (%) −0.5 0.5 1 1.5

CPV allowed σ 1 σ 2 σ 3 σ 4 σ 5

HFAG-charm

March 2012

Don’t known yet if |q/p| is near 1!

ZL — p.1/29

SLIDE 50

D0: mixing in up sector

Complementary to K, B: CPV, FCNC both GIM & CKM suppressed ⇒ tiny in SM
2007: observation of mixing, now >

∼10σ [HFAG combination] Only meson mixing generated by down-type quarks (SUSY: up-type squarks) SM suppression: ∆mD, ∆ΓD < ∼ 10−2 Γ, since doubly-Cabibbo-suppressed & vanish in SU(3) limit

y = (0.75 ± 0.12)% and x = (0.63 ± 0.20)%

... suggest long distance dominance

|q/p| 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Arg(q/p) [deg.] −60 −40 −20 20 40 60

σ 1 σ 2 σ 3 σ 4 σ 5

HFAG-charm

March 2012

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

SLIDE 51

Looking for NP with B decays

CDF

SLIDE 52

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

SLIDE 53

You can “see” B decays

Nch=17 EV1=.935 EV2=.681 EV3=.123 ThT=1.93 Detb= E0FBFF

ALEPH

K

π

D**

π

D*

π µ+ + − + −

Do

−

B+ IP 3 σ ellipses

run = 15419 event = 5991

B −> D

+

**o

__ µ ν +

µ K

π

D**

π

D*

π µ+ + − + −

Do

−

B+ IP 3 σ ellipses

run = 15419 event = 5991

B −> D

+

**o

__ µ ν +

µ

SLIDE 54

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

SLIDE 55

Asymmetric colliders

... to measure time dependence of decay after the collision

SLIDE 56

Hadron colliders — no quantum correlation

Opposite side tagging + same side tagging (at LHCb, both are boosted forward)
Much smaller ǫD2 than at Υ(4S)

(ǫ = tagging efficiency, D = 1 − 2ωmistag = “dilution”)

Need good time resolution, and fully reconstructed B on signal side to know boost

ZL — p.1/32

SLIDE 57

The cleanest case: B → ψKS

Interference of B → ψK0 (b → c¯

cs) with B → B → ψK0 (¯ b → c¯ c¯ s) Amplitudes with one weak phase dominate by far unitarity: VtbV ∗

ts + VcbV ∗ cs + VubV ∗ us = 0

AψKS = VcbV ∗

cs O(λ2)

“T”

“1”

+ VubV ∗

us O(λ4)

“P”

αs(2mc)

First term ≫ second term ⇒ theoretically very clean

λψKS,L = ∓ V ∗

tbVtd

VtbV ∗

td

B−mixing

VcbV ∗

cs

V ∗

cbVcs

decay

VcsV ∗

cd

V ∗

csVcd

K−mixing

= ∓e−2iβ

Corrections: |A/A| = 1 (main uncertainty), ǫK = 0, ∆ΓB = 0 Corrections: all are few ×10−3 ⇒ accuracy < 1%

d

d d s b

W

c c

ψ K B

S

✁ ✁ ✁ ✁ ✁ ✂✁✂ ✂✁✂ ✂✁✂ ✂✁✂ ✂✁✂ ✄✁✄ ✄✁✄ ✄✁✄ ✄✁✄ ✄✁✄ ☎✁☎ ☎✁☎ ☎✁☎ ☎✁☎ ☎✁☎ ✆✁✆ ✆✁✆ ✆✁✆ ✆✁✆ ✆✁✆ ✝✁✝ ✝✁✝ ✝✁✝ ✝✁✝ ✝✁✝

d

d d s

✁✁✁ ✁✁✁ ✁✁✁ ✁✁✁ ✁✁✁ ✁✁✁ ✁✁✁ ✁✁✁ ✁✁✁ ✂✁✂✁✂✁✂ ✂✁✂✁✂✁✂ ✂✁✂✁✂✁✂ ✂✁✂✁✂✁✂ ✂✁✂✁✂✁✂ ✂✁✂✁✂✁✂ ✂✁✂✁✂✁✂ ✂✁✂✁✂✁✂ ✂✁✂✁✂✁✂ ✄✁✄✁✄ ✄✁✄✁✄ ✄✁✄✁✄ ✄✁✄✁✄ ✄✁✄✁✄ ✄✁✄✁✄ ✄✁✄✁✄ ☎✁☎✁☎ ☎✁☎✁☎ ☎✁☎✁☎ ☎✁☎✁☎ ☎✁☎✁☎ ☎✁☎✁☎ ☎✁☎✁☎

b

ψ W

u,c,t c c

K B

S

g

✆✁✆ ✆✁✆ ✆✁✆ ✆✁✆ ✆✁✆ ✝✁✝ ✝✁✝ ✝✁✝ ✝✁✝ ✝✁✝ ✞✁✞ ✞✁✞ ✞✁✞ ✞✁✞ ✞✁✞ ✟✁✟ ✟✁✟ ✟✁✟ ✟✁✟ ✟✁✟ ✠✁✠ ✠✁✠ ✠✁✠ ✠✁✠ ✠✁✠ ✡✁✡ ✡✁✡ ✡✁✡ ✡✁✡ ✡✁✡

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

SLIDE 58

CP violation in B → J/ψ KS by the naked eye

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

afCP = Γ[B0(t) → ψK] − Γ[B0(t) → ψK] Γ[B0(t) → ψK] + Γ[B0(t) → ψK] = sin 2β sin(∆m t)

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

SLIDE 59

Similarly: βs from Bs → ψφ

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

In SM: βs = arg(−VtsV ∗

tb/VcsV ∗ cb) = 0.019 ± 0.001

(λ2 suppressed compared to β)

LHCb 2013: φs ≡ −2βs = 0.01 ± 0.07

The Bs “squashed” UT:

s

β γ γ α α

d

m ∆

K

ε

K

ε

s

m ∆ &

d

m ∆

ub

V β sin 2

s

β excluded at CL > 0.95

Bs

ρ

0.10
0.05

0.00 0.05 0.10

Bs

η

0.10
0.05

0.00 0.05 0.10

excluded area has CL > 0.95 Winter 12

CKM

f i t t e r

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

ZL — p.1/35

SLIDE 60

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) Amplitudes with one weak phase expected to dominate: A = VcbV ∗

cs O(λ2)

[Pc − Pt + Tc]

“1”

+ VubV ∗

us O(λ4)

[Pu − Pt + Tu]

O(1)

SM: SφKS − SψK and CφKS < 0.05 NP: SφKS = SψK possible NP: Expect different Sf for each b → s mode

s s d d

W g

b u, c, t

B

s

K

d

S

✁ ✁ ✁ ✁ ✁ ✂✁✂ ✂✁✂ ✂✁✂ ✂✁✂ ✂✁✂ ✄✁✄ ✄✁✄ ✄✁✄ ✄✁✄ ✄✁✄ ☎✁☎ ☎✁☎ ☎✁☎ ☎✁☎ ☎✁☎ ✆✁✆ ✆✁✆ ✆✁✆ ✆✁✆ ✆✁✆ ✝✁✝ ✝✁✝ ✝✁✝ ✝✁✝ ✝✁✝

φ

✁ ✁ ✁ ✁ ✁ ✂✁✂ ✂✁✂ ✂✁✂ ✂✁✂ ✂✁✂ ✄✁✄ ✄✁✄ ✄✁✄ ✄✁✄ ✄✁✄ ☎✁☎ ☎✁☎ ☎✁☎ ☎✁☎ ☎✁☎ ✆✁✆ ✆✁✆ ✆✁✆ ✆✁✆ ✆✁✆ ✝✁✝ ✝✁✝ ✝✁✝ ✝✁✝ ✝✁✝ ✞✁✞ ✞✁✞ ✞✁✞ ✞✁✞ ✞✁✞ ✟✁✟ ✟✁✟ ✟✁✟ ✟✁✟ ✟✁✟ ✠✁✠ ✠✁✠ ✠✁✠ ✠✁✠ ✠✁✠ ✡✁✡ ✡✁✡ ✡✁✡ ✡✁✡ ✡✁✡ ☛✁☛ ☛✁☛ ☛✁☛ ☛✁☛ ☛✁☛ ☞✁☞ ☞✁☞ ☞✁☞ ☞✁☞ ☞✁☞ ✌✁✌ ✌✁✌ ✌✁✌ ✌✁✌ ✌✁✌ ✍✁✍ ✍✁✍ ✍✁✍ ✍✁✍ ✍✁✍ ✎✁✎ ✎✁✎ ✏✁✏ ✏✁✏

d

✑ ✑✒ ✒

b q q s s q q

Bd π Κ

s s

φ KS

d

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

SLIDE 61

Status of sin 2βeff measurements

sin(2βeff) ≡ sin(2φe

1 ff)

HFAG

Moriond 2012

HFAG

Moriond 2012

HFAG

Moriond 2012

HFAG

Moriond 2012

HFAG

Moriond 2012

HFAG

Moriond 2012

HFAG

Moriond 2012

HFAG

Moriond 2012

HFAG

Moriond 2012

HFAG

Moriond 2012

HFAG

Moriond 2012

HFAG

Moriond 2012

HFAG

Moriond 2012

HFAG

Moriond 2012

HFAG

Moriond 2012 b→ccs φ K0 η′ K0 KS KS KS π0 K0 ρ0 KS ω KS f0 KS f2 KS fX KS π0 π0 KS φ π0 KS π+ π- KS NR K+ K- K0 K+ K- K0

2
1

1 2

World Average

0.68 ± 0.02

BaBar

0.66 ± 0.17 ± 0.07

Belle

0.90 +

.

. 1 9 9

Average

0.74 +

.

. 1 1 1 3

BaBar

0.57 ± 0.08 ± 0.02

Belle

0.64 ± 0.10 ± 0.04

Average

0.59 ± 0.07

BaBar

0.94 +

.

. 2 2 1 4 ± 0.06

Belle

0.30 ± 0.32 ± 0.08

Average

0.72 ± 0.19

BaBar

0.55 ± 0.20 ± 0.03

Belle

0.67 ± 0.31 ± 0.08

Average

0.57 ± 0.17

BaBar

0.35 +

.

. 2 3 6 1 ± 0.06 ± 0.03

Belle

0.64 +

.

. 1 2 9 5 ± 0.09 ± 0.10

Average

0.54 +

.

. 1 2 8 1

BaBar

0.55 +

.

. 2 2 6 9 ± 0.02

Belle

0.11 ± 0.46 ± 0.07

Average

0.45 ± 0.24

BaBar

0.74 +

.

. 1 1 2 5

Belle

0.63 +

.

. 1 1 6 9

Average

0.69 +

.

. 1 1 2

BaBar

0.48 ± 0.52 ± 0.06 ± 0.10

Average

0.48 ± 0.53

BaBar

0.20 ± 0.52 ± 0.07 ± 0.07

Average

0.20 ± 0.53

BaBar

0.72 ± 0.71 ± 0.08

Average

0.72 ± 0.71

BaBar

0.97 +

.

. 5 3 2

Average

0.97 +

.

. 5 3 2

BaBar

0.01 ± 0.31 ± 0.05 ± 0.09

Average

0.01 ± 0.33

BaBar

0.65 ± 0.12 ± 0.03

Belle

0.76 +

.

. 1 1 4 8

Average

0.68 +

.

. 1 9

Average

0.68 ± 0.07

H F AG H F A G

Moriond 2012 PRELIMINARY

sin(2βeff) ≡ sin(2φe

1 ff) vs CCP ≡ -ACP

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

0.4
0.2

0.2 0.4 0.6 0.8 1

0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 sin(2βeff) ≡ sin(2φe

1 ff)

CCP ≡ -ACP

b→ccs φ K0 η′ K0 KS KS KS π0 KS ρ0 KS ω KS f0 K0 f2 KS fX KS π0 π0 KS π+ π- KS NR K+ K- K0

H F AG H F A G

Moriond 2012 PRELIMINARY

Earlier hints of deviations reduced, e.g., in SφK and Sη′K

It is still interesting to significantly reduce these experimental uncertainties

ZL — p.1/37

SLIDE 62

γ from B± → DK±

Tree level: interference of b → c¯

us (B− → D0K−) and b → u¯ cs (B− → D0K−) Extract B & D decay amplitudes from data; many variants depending on D decay

Problem: large ratio of interfering amplitudes,

sensitivity crucially depends on: rB = |A(B− → D0K−)/A(B− → D0K−)| ≈ 0.1

Best measurement so far: D0, D0 → KS π+π−

– Both amplitudes Cabibbo allowed; – Can integrate over regions in Dalitz plot

(deg) γ

20 40 60 80 100 120 140 160 180

p-value

0.0 0.2 0.4 0.6 0.8 1.0

Winter 12

CKM

f i t t e r

Full Frequentist treatment on MC basis

D(*) K(*) GLW + ADS D(*) K(*) GGSZ Combined CKM fit

WA

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

SLIDE 63

Only LHCb: γ from Bs → D±

s K∓

Same weak phase in each Bs, Bs → D±

s K∓ decay ⇒ the 4 time dependent rates

determine 2 amplitudes, a strong, and a weak phase (clean, although |f = |fCP) Four amplitudes: Bs

A1

→ D+

s K−

(b → cus) , Bs

A2

→ K+D−

s

(b → ucs) Four amplitudes: Bs

A1

→ D−

s K+

(b → cus) , Bs

A2

→ K−D+

s

(b → ucs) AD+

s K−

AD+

s K−

= A1 A2 VcbV ∗

us

V ∗

ubVcs

,

AD−

s K+

AD−

s K+

= A2 A1 VubV ∗

cs

V ∗

cbVus

Magnitudes and relative strong phase of A1 and A2 drop out if four time depen-

dent rates are measured ⇒ no hadronic uncertainty: λD+

s K− λD− s K+ =

V ∗

tbVts

VtbV ∗

ts

2VcbV ∗

us

V ∗

ubVcs

VubV ∗

cs

V ∗

cbVus

= e−2i(γ−2βs−βK)
Similarly, Bd → D(∗)±π∓ determines γ + 2β, since λD+π− λD−π+ = e−2i(γ+2β)

... ratio of amplitudes O(λ2) ⇒ small asymmetries (tag side interference)

ZL — p.1/39

SLIDE 64

New physics in B mixing

SLIDE 65

The standard model CKM fit

Looks impressive...
Level of agreement between the

measurements often misinterpreted

Increasing the number of parame-

ters can alter the fit completely

Plausible TeV scale NP scenarios,

consistent with all low energy data, w/o minimal flavor violation (MFV)

CKM is inevitable; the question is

not if it’s correct, but is it sufficient?

γ γ α α

d

m ∆

K

ε

K

ε

s

m ∆ &

d

m ∆

ub

V β sin 2

(excl. at CL > 0.95) < 0 β

sol. w/ cos 2

e x c l u d e d a t C L > . 9 5

α β γ

ρ

1.0
0.5

0.0 0.5 1.0 1.5 2.0

η

1.5
1.0
0.5

0.0 0.5 1.0 1.5

excluded area has CL > 0.95 Winter 12

CKM

f i t t e r

ZL — p.1/40

SLIDE 66

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: M12 = M SM

12 r2 e2iθ

easy to relate to data

≡ M SM

12 (1 + h e2iσ)

easy to relate to models
Tree-level CKM constraints unaffected: |Vub/Vcb| and γ (or π − β − α)
BB mixing dependent observables sensitive to NP: ∆md,s, Sfi, Ad,s

SL, ∆Γs ZL — p.1/41

SLIDE 67

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: M12 = M SM

12 r2 e2iθ

easy to relate to data

≡ M SM

12 (1 + h e2iσ)

easy to relate to models
Tree-level CKM constraints unaffected: |Vub/Vcb| and γ (or π − β − α)
BB mixing dependent observables sensitive to NP: ∆md,s, Sfi, Ad,s

SL, ∆Γs

∆mBq = r2

q ∆mSM Bq = |1 + hqe2iσq|∆mSM q

SψK = sin(2β + 2θd) = sin[2β + arg(1 + hde2iσd)] Sρρ = sin(2α − 2θd) Sψφ = sin(2βs − 2θs) = sin[2βs − arg(1 + hse2iσs)] Aq

SL = Im

Γq

12

M q

12r2 q e2iθq

= Im
Γq

12

M q

12(1 + hqe2iσq)

∆ΓCP

s

= ∆ΓSM

s

cos2 2θs

ZL — p.1/41

SLIDE 68

New physics in B meson mixing

Tree-dominated measurements:

γ ) α ( γ

ub

V

α β γ

ρ

0.4
0.2

0.0 0.2 0.4 0.6 0.8 1.0

η

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

excluded area has CL > 0.95

Winter 12

CKM

f i t t e r

Loop-dominated measurements:

d

m ∆

K

ε

K

ε

s

m ∆ &

d

m ∆ β sin 2

(excl. at CL > 0.95) < 0 β

sol. w/ cos 2

α β γ

ρ

0.4
0.2

0.0 0.2 0.4 0.6 0.8 1.0

η

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

excluded area has CL > 0.95

Winter 12

CKM

f i t t e r

Until 2004, hd ∼ 10 was allowed Better tree-level measurements crucial

d

h

0.0 0.2 0.4 0.6 0.8 1.0

d

σ

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1-CL

excluded area has CL > 0.95 LP 11

CKM

f i t t e r SL

, A ν τ w/o B->

A goal: assume h ∼ (4πv/Λflav.)2 Can we probe Λflav. > ∼ ΛEWSB ?

ZL — p.1/42

SLIDE 69

Preliminary — sensitivity in ∼10 years?

Rough predictions to illustrate increased sensitivity

d

h

0.0 0.2 0.4 0.6 0.8 1.0

d

σ

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1-CL

excluded area has CL > 0.95 LP 11

CKM

f i t t e r SL

, A ν τ w/o B-> d

h

0.0 0.2 0.4 0.6 0.8 1.0

d

σ

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

p-value

excluded area has CL > 0.95 2020 (?)

CKM

f i t t e r

1

Belle II+LHCb 50 fb

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

SLIDE 70

Preliminary — sensitivity in ∼10 years?

Rough predictions to illustrate increased sensitivity

s

h

0.0 0.5 1.0 1.5 2.0 2.5

s

σ

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

p-value

excluded area has CL > 0.95

LP 11

CKM

f i t t e r

s

h

0.0 0.2 0.4 0.6 0.8 1.0

s

σ

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

p-value

excluded area has CL > 0.95 2020 (?)

CKM

f i t t e r

1

Belle II+LHCb 50 fb

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

SLIDE 71

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