V. IV. III. I. - Laboratori Nazionali di FrascatiC)KMModel ∗ discoveryofCPviolationinthe...

Theory of CP Violation in the B System

Matthias Neubert – Cornell University

([email protected])

I. Introduction & CKM Model

II. Determination of sin 2β

III. New Physics: Why? Why not? And maybe...

IV. Rare Hadronic B Decays (γ, α)

V. Outlook

XX International Symposium on Lepton and Photon Interactions at High Energies

(Rome, Italy, 23–28 July 2001)

Introduction

∗ phenomenon of CP violation is one of the most intriguing aspects of physics, with

far-reaching implications:

• fundamental difference between the interactions of matter and anti-matter

CPV+CPT: microscopic violation of time-reversal invariance

• baryon asymmetry in the Universe → our existence

∗ we know how to parameterize CP violation but don’t know its origin

∗ CP violation possible in 3 sectors of Standard Model:

• quark sector → CKM matrix

• strong interactions → θQCD

• lepton sector (neutrinos, Majorana mass terms) → MNS matrix

but only the first sector has been explored in detail

LP01, 23 July 2001, M. Neubert 2 Theory of CP Violation in theB System

The Great Success of the (C)KM Model

∗ discovery of CP violation in the B-meson system is a triumph for Standard Model

∗ pattern of CP-violating effects in mixing and weak decay of kaons, charm and B

mesons is correctly predicted by Kobayashi–Maskawa (KM) mechanism:

• CP violation small in K–K mixing (εK) and K → ππ decay (ε′/ε)

• CP violation large in B → J/ψK (sin 2β) but small in B–B mixing (εB):

sin 2β = 0.62 ± 0.13 SM: 0.68 ± 0.21

Re(εB)1 + |εB |2 = (1.7 ± 3.7) × 10−3 SM: ∼ 10−3

• small CP violation in charm decays, below present experimental sensitivity

∗ now a lot of evidence that KM mechanism is responsible for leading CP violation

effects observed in low-energy weak interactions of hadrons


∗ significance of sin 2β measurement: CP-violating phase is large!

CP is not an approximate symmetry of Nature

⇒ pattern of CP violation effects reflects hierarchy of CKM matrix elements

(powers of λ)

∗ besides describing CP violation, CKM mechanism explains a vast variety of

flavor-changing processes

• semileptonic decays, e.g.:

B →D∗l ν (∼ |Vcb|) D → K l ν (∼ |Vcs|) K → π l ν (∼ |Vus|)B → π l ν (∼ |Vub|) D → π l ν (∼ |Vcd|) n → p l ν (∼ |Vud|)

• leptonic and nonleptonic decays

• rare decays, e.g.: B → Xsγ, B → Xs l+l− (?), K → πνν (?), . . .

• mixing: K–K, Bd–Bd, Bs–Bs (?), D–D (?)


CKM Matrix and the Magic Triangle

∗ VCKM = 3 × 3 unitary matrix connecting mass eigenstates of down-type quarks with

interaction eigenstates

∗ contains 4 physical parameters:

VCKM =

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

=

1 − λ2

2 λ Aλ3(ρ− iη)

−λ 1 − λ2

2 Aλ2

Aλ3(1 − ρ− iη) −Aλ2 1

+ O(λ4)

∗ accurately known: |Vus| and |Vcb| (λ = 0.224 ± 0.003 and A = 0.82 ± 0.04)

∗ more uncertain: |Vub| and |Vtd| (ρ and η)

∗ with standard phase conventions, complex phases appear in smallest matrix elements

(requires ≥ 3 generations)


Unitarity triangle:

V ∗ubVud + V ∗

cbVcd + V ∗tbVtd = 0 td~V

ub*~V

βγ

(ρ,η)

(1,0)(0,0)

CP Violation

α

∗ combining measurements of |Vub| in semileptonic decays, |Vtd| in B–B mixing, and

Im(V 2td) in K–K mixing, the parameters of the unitarity triangle are determined

already with great accuracy:

0

0.2

0.4

0.6

0.8

1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

εK

∆md∆ms/∆md

|Vub||Vcb|

ρ_

η_

βγα


∗ has established existence of a complex phase in the top sector (Im(Vtd) �= 0)

0

0.2

0.4

0.6

0.8

1

-1 -0.5 0 0.5 1

sin 2βWA

|εK|

∆ms/∆md

∆md

|Vub/Vcb|

ρ

η

0

0.2

0.4

0.6

0.8

1

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

εK

∆md

∆ms/∆md

|Vub||Vcb|

ρ_

η_

[Hocker, Lacker, Laplace, Le Diberder] [Ciuchini, Agostini, Franco, Lubicz, Martinelli, ...]

∗ ranges at 95% CL (without sin 2β): [Hocker et al.]

ρ = 0.21 ± 0.17 η = 0.35 ± 0.14

sin 2β = 0.68±0.21 sin 2α = −0.23±0.73

γ = 58◦ ± 24◦

(γ < 90◦ due to ∆ms/∆md constraint!)

Recent measurements of sin 2β:

BaBar: 0.59 ± 0.14 ± 0.05

Belle: 0.58+0.32+0.09−0.34−0.10

(LP01: ???)


Theory of the sin 2β Determination

∗ in B decays into a CP eigenstate fCP, observable CP asymmetries can arise from

interference of the amplitudes for B–B mixing and decay:

mixing ~ e -2i β

B 0 B 0

fCP

A Aλ = e-2i A

Aβdenote:

∗ resulting time-dependent CP asymmetry:

ACP(t) =Γ(B0 → fCP) − Γ(B0 → fCP)

Γ(B0 → fCP) + Γ(B0 → fCP)=

2 Imλ

1 + |λ|2 sin(∆md t) − 1 − |λ|21 + |λ|2 cos(∆md t)

∗ if the decay amplitude is dominated by a single weak phase φA, then |λ| � 1 and

ACP(t) � ηfCP sin 2(β + φA) · sin(∆md t)


“Golden mode”:

sin 2β from B → J/ψKS decays (b → ccs transitions, ηJ/ψ KS= −1)

g,Z,γ

b bW

tW

c s

c

s c

c

Tree Penguin “Contamination”

VcbV∗

cs ∼ λ2 VtbV∗

ts ∼ λ2, λ4 e−iγ ∆φA ∼ λ2 PT

∼ 1%

⇒ clean measurement:

ACP(t) � −sin 2β · sin(∆md t)


∗ above discussion could be upset if there existed a New Physics contribution to

Bd–Bd mixing, or to b → ccs decays with φNP �= 0

∗ but new contribution to the decay amplitude is unlikely to compete with the large,

tree-level b → ccs transition of the Standard Model, otherwise:

• ... there should be signals of direct CP violation in B± → J/ψK±

• ... there should be other b → qqs New Physics contributions of similar strength

(∼ λ2), which would upset rare decays such as B → πK, ππ, φK, . . .

⇒ appears safe to assume that even in the presence of New Physics

sin 2βψK = sin 2φd

measures Bd–Bd mixing phase φd

∗ excellent agreement of measured sin 2φd with Standard Model prediction suggests

that the Bd–Bd mixing phase is indeed due to the phase of the CKM element Vtd

(caveat: discrete ambiguities)


Much Could Have Happened...

∗ Bd–Bd mixing phase could have been affected by New Physics

[Kagan, MN / Silva, Wolfenstein / Eyal, Nir, Perez / Xing]

∗ some possibilities for potentially large effects:

• models with iso-singlet down-type quarks and tree-level FCNCs [Barenboim, Botella, Vives]

• left-right symmetric models with spontaneous CP violation (now excluded!)

[Ball, Frere, Matias / Ball, Fleischer / Bergmann, Perez]

• SUSY with extended minimal flavor violation [Ali, Lunghi]

∗ on the contrary, only small modifications are allowed in models with minimal flavor

violation: [Buras, Buras / Buras, Fleischer / Bergmann, Perez]

⇒ model-independent bound sin 2β > 0.42; estimate 0.52 < sin 2β < 0.78


Success and Embarrassment

∗ much like the stunning success of Standard Model in explaining EW precision data,

the lack of deviations from KM mechanism gives rise to theoretical puzzles:

• KM does not explain the baryon asymmetry in Universe

• KM does not explain why θQCD = 0

• basically all extensions of Standard Model contain many new CP-violating

parameters (minimal unconstrained SUSY → 43 new CPV phases!)

“CP Problem”

∗ “decoupling” of non-standard CP violation effects may be linked to decoupling of

New Physics in EWSB sector (complementary strategies for probing TeV scale)

⇒ need to keep searching for (probably small) deviations from KM with precision

measurements


Never Stop Dreaming... Potentially Large Effects

∗ Bs–Bs mixing: need to confirm ∆ms ≈ (17 ± 3) ps−1 (SM)

∗ CP-violating phase in bottom sector: γ = arg(V ∗ub)

• not probed yet; could be larger than 90◦ if ∆ms were affected by New Physics

• first opportunity with rare hadronic B → πK, ππ decays

∗ New Physics in rare decays (penguins and boxes)

• sin 2βφK?= sin 2βψK (b → sss penguin) [Grossman, Worah]

• ACP(B → Xsγ)?� 0 (radiative penguin) [Kagan, MN]

• γπK?= γtree (penguin vs. tree) [Grossman, Kagan, MN]

• New Physics in B → K l+l− (zero in AFB) [Burdmann / Ali, Ball, Handoko, Hiller]

∗ New Physics effects in D–D mixing, charm weak decays, rare kaon decays (K → πνν)

∗ CP violation without flavor violation: electric dipole moments


Rare Hadronic B Decays (γ and α)

∗ after obtaining a consistent picture of CP violation in the top sector (Vtd), next

step must be to explore the complex phase γ in the bottom sector (Vub)

∗ several theoretically clean determinations of γ have been suggested, e.g.:

• sin(2β + γ) from B0, B0 → D(∗)±π∓[Dunietz, Sachs / Dunietz]

mixing ~ e -2i β

D π+-

B 0 B 0

b -> c u d b -> u c d∼λ 4

ei γ ∼λ 2 ∼λ 2 ∼λ 4e-i γ

mixing ~ e -2i β

D π-+

B 0 B 0

b -> u c d b -> c u d

• γ from B → DK decays (with discrete ambiguities) [Atwood, Dunietz, Soni]

• γ extracted using various strategies with Bs mesons ⇒ BTeV, LHC-b

∗ all are extremely challenging experimentally!


∗ more accessible: probe γ via sizeable tree–penguin interference in rare hadronic

decays B → πK, ππ, . . .

g,Z,γ

b s,d

u

s,d

bW

t

q

q

W

u

Tree Penguin Ratio

B → πK VubV∗

us ∼ λ4 e−iγ VtbV∗

ts ∼ λ2 |T/P | ∼ 0.2

B → ππ VubV∗

ud ∼ λ3 e−iγ VtbV∗

td ∼ λ3 eiβ |P/T | ∼ 0.3

∗ information about γ from CP asymmetries and CP-averaged branching fractions

BUT: theoretical analysis challenging due to hadronic physics entering T/P ratios

⇒ hadronic matrix elements


∗ different strategies exist for determining the hadronic matrix elements such as

〈πK|Heff |B〉, which range from elementary geometry to complex field-theoretic

calculations:

Maximal Use of Measurements

General Amplitude Parameterizations:Isospin and SU(3) Flavor SymmetryAmplitude Triangles, Quadrangles, ... pQCD, QCD Sum Rules, Lattice

Maximal Use of Theory (ambitious!)

QCD-Based Calculations:QCD Factorization (HQL)

Hadronic Matrix Elements

QCD Factorization

Bounds -> Determinations

+Fleischer-Mannel BoundNeubert-Rosner Bound

+QCD Factorization

Charming Penguins, Fat Penguins, ...

Phenom. Penguin Amplitude

various combinations


Factorization

∗ hadronic weak decays simplify greatly in heavy-quark limit mb � ΛQCD

∗ underlying physical concept:

fast-moving light meson produced by a point-like source decouples from soft QCD

interactions (color transparency) [Bjorken / Dugan, Grinstein]

∗ systematic QCD treatment ⇒ QCD factorization [Beneke, Buchalla, MN, Sachrajda (BBNS)]

⇒ rigorous results in heavy-quark limit, valid to all orders of perturbation theory

[BBNS / Bauer, Pirjol, Stewart]

⇒ dominant power corrections are included in phenomenological analyses and

sometimes lead to sizeable uncertainties [BBNS]

∗ alternative scheme: pQCD [Li / Keum, Li, Sanda]


1. hard gluon effects with µ � mb can be calculated and factorized into the Wilson

coefficients Ci(µ) of an effective weak Hamiltonian

2. hard gluon effects with µ ∼ mb can be calculated and factorized into hard-scattering

kernels Tij(µ)

Oi (µ)

+ O(1/M )W

Ci (µ)

µ ∼ m> b

π+

π-

0Bi=1...10

π+0B

π-

C i (µ)i,j=1...10

π-

0B

Ojfact(µ)

T (µ)ijI

+ O(1/m )b

jfact(µ)Q

T (µ)ijII+

µ m b<

π+


How Heavy is Heavy Enough?

∗ importance of heavy-quark limit evident from comparison of nonfactorizable effects

seen in kaon, charm and beauty decays

∗ crucial to address issue of power corrections ∼ ΛQCD/mb:

• “chirally-enhanced” corrections [BBNS]

• weak annihilation [Keum, Li, Sanda / Cheng, Yang / BBNS]

• soft nonfactorizable gluon exchange:

QCD sum rules [Khodjamirian], renormalons [Burrell, Williamson / Becher, MN, Pecjak]

∗ important that QCD factorization makes many testable predictions

⇒ data will teach us about importance of power-suppressed effects


Tests of QCD Factorization

∗ factorization works at the level of 10% in B0 → D(∗)+L− decays, but more precise

data are necessary for a firm conclusion; related ideas:

• “designer mesons”, for which factorizable amplitudes are suppressed [Diehl, Hiller]

• quasi two-body decays with variable invariant mass of light jet [Ligeti, Luke, Wise]

∗ factorization in decays B → two light mesons can be probed using B± → π±π0

(� pure tree) and B± → π±K0 (� pure penguin), which have negligible amplitude

interference

∗ crucial properties:

magnitude of tree amplitude, magnitude and strong phase of T/P ratio

∗ once these tests are conclusive, factorization can be used to constrain the unitarity

triangle

⇒ alternative schemes (pQCD, charming penguins, ...) must pass the same tests


Test 1: Magnitude of the Tree Amplitude

∗ absolute prediction for B± → π±π0 branching ratio: [BBNS]

Br(B± → π±π0) =[5.3+0.8

−0.4 (pars.) ± 0.3 (power)]· 10−6 ×

[|Vub|

0.0035

F B→π0 (0)

0.28

]2

Exp.: (5.6 ± 1.5) × 10−6

∗ sensitivity to semileptonic form factor and |Vub| is eliminated in the ratio [Bjorken]

Γ(B± → π±π0)

dΓ(B0 → π+l−ν)/dq2|q2=0

= 3π2f2π |a(ππ)

1 + a(ππ)2 |2︸︷︷︸

1.33 +0.20−0.11 (pars.)±0.07 (power)

= (0.68+0.11−0.06)GeV

2


Test 2: Magnitude of the T/P Ratio

∗ tree-to-penguin ratio can be experimentally determined via

εexp =∣∣∣∣TP

∣∣∣∣ = tanθCfK

fπ

[2Br(B± → π±π0)Br(B± → π±K0)

] 12

= 0.223 ± 0.034

⇒ independent of form factors, but ∝ |Vub/Vcb|∗ agrees well with theoretical prediction: [BBNS]

εth = 0.24 ± 0.04 (pars.) ± 0.04 (power) ± 0.05 (Vub)

∗ problematic for approaches with large, dynamically enhanced penguin amplitudes

(“fat penguins” [Keum, Li, Sanda], “charming penguins” [Ciuchini, Franco, Martinelli, Pierini,

Silvestrini])


Test 3: Strong Phase of the T/P Ratio

∗ QCD factorization predicts that (most) strong phases are parametrically suppressed

in heavy-quark limit:

sinφst = O[αs(mb);

ΛQCD

mb

]⇒ small direct CP asymmetries:

ACP(π+K−) � −2 | TP| sin γ sin φst

∗ in many other schemes these phases are predicted to be much larger

∗ first experimental data show no evidence for large asymmetries:

Experiment Theory

(CLEO, BaBar∗, Belle) BBNS Keum, Li, Sanda Ciuchini et al.

ACP(π+K−) (%) −4.8 ± 6.8 5 ± 9 |ACP| ∼ 15 |ACP| = 17 ± 6BaBar: −7± 8± 2

ACP(π0K−) (%) −9.6 ± 11.9 7 ± 9 |ACP| ∼ 15 |ACP| = 18 ± 6

ACP(π−K0) (%) −4.7 ± 13.9 1 ± 1 |ACP| ∼ 1 |ACP| = 3 ± 3

ACP(π−π+) (%) −25 ± 48 −6 ± 12 |ACP| ∼ 30 |ACP| = 58 ± 29


New Constraints on the Unitarity Triangle

Determination of “sin 2α”:

∗ possible to control the “penguin pollution” in the time-dependent CP asymmetry

Sππ = sin 2α · [1 + O(P/T )]in B → π+π− decays (→ “penguin enchantment”)

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1-1

-0.5

0

0.5

1

sin 2αsin 2α

Sππ

Sππ

-0.6 -0.4 -0.2 0 0.2 0.4 0.6-0.6

-0.4

-0.2

0

0.2

0.4

0.60

-0.3-0.6-0.9

ρ

η

Sππ:

⇒ even a result for Sππ with large experimental errors would imply a useful constraint

on the unitarity triangle (BaBar at LP01: Sππ = 0.03+0.53−0.56 ± 0.11)


Global Fit to B → πK, ππ Branching Ratios:

∗ various ratios of CP-averaged B → πK, ππ branching fractions have a strong

dependence on γ and |Vub|, e.g.:

0 25 50 75 100 125 150 1750

0.5

1

1.5

2

2.5

3

0 25 50 75 100 125 150 1750

0.5

1

1.5

2

2.5

3

γ (deg)γ (deg)

2Br(π0K±)/Br(π±K0)

0 25 50 75 100 125 150 1750

0.5

1

1.5

2

2.5

0 25 50 75 100 125 150 1750

0.5

1

1.5

2

2.5

γ (deg)γ (deg)

Br(π+π−)/Br(π∓K±)

⇒ possible to derive constraints on (ρ, η) from a global analysis of the data using QCD

factorization


∗ results are compatible with the standard CKM fit using semileptonic decays, K–K

mixing and B–B mixing (|Vub|, |Vcb|, εK , ∆md, ∆ms, sin 2β): [BBNS]

-0.6 -0.4 -0.2 0 0.2 0.4 0.60

0.10.20.30.40.50.6

��

��

95%, 90% and 68% confidence level contours in the (ρ, η) plane obtained

from rare hadronic B decays (green dot = overall best fit; gray dot = best fit

for default parameter set). The (yellow region) shows the standard CKM fit.

∗ best fit (χ2/dof = 0.7) prefers larger γ and/or smaller |Vub|∗ combination of results from rare hadronic B decays with |Vub| from semileptonic

decays excludes η = 0 at 95% CL, establishing the existence of a

CP-violating phase in the bottom sector


Outlook

∗ B physics is more fascinating that ever!

∗ discovery of CP violation in the B system (2001), and of direct CP violation in kaon

decays (1999), are outstanding achievements and a triumph for the Standard Model

⇒ compelling evidence that KM is dominant source of CP violation in weak decays

∗ yet, searches for deviations from CKM are well motivated and must be continued

∗ key measurements in the near future:

• ∆ms in Bs–Bs mixing

• CP-violating phase in the bottom sector: γ = arg(V ∗ub)

• time-dependent CP violation in B → π+π−

• systematic study of penguins: B → φKS , B → Xsγ, B → K l+l−, etc.


∗ QCD factorization will be tested with a variety of experimental measurements, which

are able to distinguish between different theoretical schemes (BBNS, pQCD)

∗ ultimately, this may provide theoretical control over a vast variety of hadronic decays,

yielding new constraints on the unitarity triangle


∗ QCD factorization will be tested with a variety of experimental measurements, which

are able to distinguish between different theoretical schemes (BBNS, pQCD)

∗ ultimately, this may provide theoretical control over a vast variety of hadronic decays,

yielding new constraints on the unitarity triangle

∗ if CKM mechanism remains to stand ever more precise experimental tests, we will

face a new decoupling problem, whose explanation may be linked to the decoupling

of New Physics in the electroweak sector

EWSB ProblemCP Problem???


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