B physics beyond CKM · Bphysics beyond CKM Zoltan Ligeti Warning: APS/JPS meeting Nov.2; BaBar...

B physics beyond CKMZoltan Ligeti

Warning: APS/JPS meeting Nov.2; BaBar workshop Dec.7

• IntroductionThe flavor problems

• Mixing in the Bd and Bs systemsImplications of the measurement of ∆ms

Bounds on non-SM contributions

• Some topics with interesting progressCP violation (b→ s penguins, angles α and γ)Inclusive decays (|Vxb|, rare decays)Exclusive processes (2-body nonleptonic decays)

• Conclusions

Why is flavor physics and CPV interesting?

– SM flavor problem: hierarchy of masses and mixing angles

– NP flavor problem: TeV scale (hierarchy problem) flavor & CPV scale

εK:(sd)2

Λ2⇒ Λ >∼ 104 TeV, Bd mixing:

Λ2⇒ Λ >∼ 103 TeV

– Almost all extensions of the SM have new sources of CPV & flavor conversion(e.g., 43 new CPV phases in SUSY)

– A major constraint for model building(flavor structure: universality, heavy squarks, squark-quark alignment, ...)

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

ZL — p.1

What are we after?

• At scale mb, flavor changing pro-cesses are mediated by O(100)higher dimension operators

Depend only on a few parametersin the SM⇒ correlations betweens, c, b, t decays

weak / NP scale ∼ 5 GeV

E.g.: in SM∆md

,b→ dγ

b→ sγ,b→ d`+`−

b→ s`+`−∝

˛, 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?

Study SM loops (mixing, rare decays), interference (CPV), tree vs. loop processes

ZL — p.2

Spectacular track record

• Flavor and CP violation have been excellent probes of “new physics”

– Absence of KL → µµ predicted charm

– εK predicted 3rd generation

– ∆mK predicted charm mass

– ∆mB predicted heavy top

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

• Or will the LHC find just a SM-like Higgs?

ZL — p.3

SM tests with K and D mesons

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

• Hadronic uncertainties preclude precision tests (ε′K notoriously hard to calculate)

• K → πνν: Theoretically clean, but rates small B ∼ 10−10(K±), 10−11(KL)

Observation (3 events): B(K+ → π+νν) = (1.5+1.3−0.9)× 10−10 — need more data

• D system: complementary to K and B

Only meson where mixing is generated by down type quarks (SUSY: up squarks)

CPV, FCNC both GIM and CKM suppressed⇒ tiny in SM and not yet observed

yCP =Γ(CP even)− Γ(CP odd)

Γ(CP even) + Γ(CP odd)= (0.9± 0.4)%

No mixing also disfavored by >2σ in

2-d fit to (∆m,∆Γ) at Babar & Belle

• At the present sensitivity, CPV would be the only clean signal of NP in D mixingCould also discover NP via FCNC, e.g., D → π`+`−

ZL — p.4

CKM matrix and unitarity triangle

• Exhibit hierarchical structure of CKM (λ ' 0.23)

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

1− 12λ

2 λ Aλ3(ρ− iη)−λ 1− 1

2λ2 Aλ2

Aλ3(1− ρ− iη) −Aλ2 1

+O(λ4)

• Measurements often shown in (ρ, η) plane — a “language” to compare data

Vud V∗ub + Vcd V

∗cb + Vtd V

∗tb = 0

Angles and sides are directly measur-able in numerous different processes

Goal: overconstraining measurementssensitive to different short dist. phys.

ZL — p.5

Remarkable progress at B factories

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

-1 -0.5 0 0.5 1

sin 2βJ/ΨKs

∆md ∆ms & ∆md

|Vub/Vcb|

C K Mf i t t e r

p a c k a g e

(1998) (2002) K vs. B constraints

ρ-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0.6 BEAUTY 2006

CKMf i t t e r)α(γ

cb/VubV

ρ-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0.6 BEAUTY 2006

CKMf i t t e r

dm∆ dm∆ & sm∆

βsin2 < 0βsol. w/ cos2

(excl. at CL > 0.95)

Tree-level (2006) Loop-dominated

• The CKM picture is verified⇒ looking for corrections rather than alternatives

ZL — p.6

The B factory era

ZL — p.7

The B factory era

• Q: How many CP violating quantities are measured with > 3σ significance?

A: 6? 9? 12? 15? (with different sensitivity to NP)

ZL — p.7

The B factory era

• Q: How many CP violating quantities are measured with > 3σ significance?

A: 12 (with different sensitivity to NP)

εK, ε′K,

SψK, Sη′K, SK+K−K0, SD∗+D∗−, Sπ+π−,

AK−π+, AηK∗0, Aπ+π−, A−+ρπ , aD∗±π∓

• Just because a measurement determines a CP violating quantity, it no longerautomatically implies that it is interesting

(If Sη′K was still consistent with 0, it would be a clear discovery of new physics!)

• It does not matter whether one measures a side or an angle — only experimentalprecision and theoretical cleanliness for interpretation for short distance physics

ZL — p.7

Mixing in the Bd,s systems

BB mixing: matter – antimatter oscillation

• Two flavor eigenstates: |B0〉 = |b d〉, |B0〉 = |b d〉

Time evolution: id

„ |B0(t)〉|B0(t)〉

„M −

«„ |B0(t)〉|B0(t)〉

«M,Γ are 2× 2 Hermitian matrices; CPT ⇒M11 = M22, Γ11 = Γ22

• M12 dominated by box diagrams with top (GIM+ CKM hierarchy) — sensitivity to high scales

Mass eigenstates: |BH,L〉 = p|B0〉 ∓ q|B0〉

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

ZL — p.8

BB mixing: matter – antimatter oscillation

• Two flavor eigenstates: |B0〉 = |b d〉, |B0〉 = |b d〉

Time evolution: id

„ |B0(t)〉|B0(t)〉

„M −

«„ |B0(t)〉|B0(t)〉

«M,Γ are 2× 2 Hermitian matrices; CPT ⇒M11 = M22, Γ11 = Γ22

• M12 dominated by box diagrams with top (GIM+ CKM hierarchy) — sensitivity to high scales

Mass eigenstates: |BH,L〉 = p|B0〉 ∓ q|B0〉

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

• In |Γ12| |M12| limit, which holds for both Bd,s within and beyond the SM

∆m = 2|M12| , ∆Γ = 2|Γ12| cosφ12 , φ12 = arg

„−M12

«⇒ NP cannot enhance ∆Γs

ZL — p.8

Parameterize new physics in 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 = MSM12 r2 e2iθ︸︷︷︸

easy to relate to data

≡ MSM12 (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,sSL , ∆Γs

ZL — p.9

Parameterize new physics in 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 = MSM12 r2 e2iθ︸︷︷︸

easy to relate to data

≡ MSM12 (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,sSL , ∆Γs

∆mBq = r2q ∆mSM

Bq= |1 + hqe

2iσq|∆mSMq

SψK = sin(2β + 2θd) = sin[2β + arg(1 + hde2iσd)] Sρρ = sin(2α− 2θd)

Sψφ = sin(2βs − 2θs) = sin[2βs − arg(1 + hse2iσs)]

AqSL = Im

„Γq12

«= Im

»Γq12

Mq12(1 + hqe2iσq)

–∆Γs = ∆ΓSM

s cos2 2θs

ZL — p.9

Constraining new physics in loops

• B factories determined ρ, η from (effectively) tree-level & loop-induced processes

Tree-dominated Loop-induced

ρ-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0.6 BEAUTY 2006

CKMf i t t e r)α(γ

cb/VubV

ρ-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0.6 BEAUTY 2006

CKMf i t t e r

dm∆ dm∆ & sm∆

• Even in the presence of NP in loops, ρ, η constrained to SM region (caveat: α)

(Was completely unconstrained before B factories turned on!)

• εK, ∆md, ∆ms, etc., can be used to overconstrain the SM and test for NP

Beyond SM: more parameters⇒ independent measurements critical

ZL — p.10

NP parameters r2d, θd and hd, σd

0 1 2 3 4 5 6

C K Mf i t t e r

Lattice 2005

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2hd

σ d (d

C K Mf i t t e r

FPCP 06

shaded areas have exclusion CL < 0.1, 0.68, 0.95

MSM12 r2e2iθ ≡ MSM

12 (1 + he2iσ)

• hd , σd: NP may still be comparable to SM: hd = 0.23 +0.57−0.23, i.e., hd < 1.7 (95% CL)

• Sizable non-SM contributions to most loop-mediated transitions are still allowed

ZL — p.10

The news of 2006: ∆ms

• ∆ms = (17.77± 0.10± 0.07) ps−1

A 5.4σ measurement [CDF, hep-ex/0609040]

]-1 [pssm∆

0 5 10 15 20 25 30 35

2σ 1 ± data

σ 1.645

σ 1.645 ± data (stat. only)σ 1.645 ± data

95% CL limitsensitivity

-117.2 ps-131.3 ps

CDF Run II Preliminary -1L = 1.0 fb

Uncertainty σ(∆ms) = 0.7% is alreadysmaller than σ(∆md) = 0.8% !

• Largest uncertainty: ξ = fBs√Bs

Chiral logs: ξ ∼ 1.2 [Grinstein et al., ’92]

SM CKM fit: ξ = 1.158+0.096−0.064

Using ξLQCD = 1.24± 0.04± 0.06

-1 -0.5 0 0.5 1 1.5 2

sin 2β

sol. w/ cos 2β < 0(excl. at CL > 0.95)

excluded at CL > 0.95

∆ms & ∆md

ξ = 1.24 ± 0.04 ± 0.06

|Vub/Vcb|

sin 2β

excluded area has CL > 0.95

C K Mf i t t e r

EPS05+CDF

ZL — p.11

The news of 2006: ∆ms

• ∆ms = (17.77± 0.10± 0.07) ps−1

A 5.4σ measurement [CDF, hep-ex/0609040]

]-1 [pssm∆

0 5 10 15 20 25 30 35

2σ 1 ± data

σ 1.645

σ 1.645 ± data (stat. only)σ 1.645 ± data

95% CL limitsensitivity

-117.2 ps-131.3 ps

CDF Run II Preliminary -1L = 1.0 fb

Uncertainty σ(∆ms) = 0.7% is alreadysmaller than σ(∆md) = 0.8% !

• Largest uncertainty: ξ = fBs√Bs

Chiral logs: ξ ∼ 1.2 [Grinstein et al., ’92]

SM CKM fit: ξ = 1.158+0.096−0.064

Using ξLQCD = 1.21+0.047−0.035 [HPQCD+JLQCD]

-1 -0.5 0 0.5 1 1.5 2

sin 2β

∆ms & ∆md

ξ = 1.21 +0.047 – 0.035 (hep-lat/0510113)

|Vub/Vcb|

sin 2β

C K Mf i t t e r

EPS05+CDF

ZL — p.11

Some models to enhance ∆ms

• SUSY GUTs: near-maximal νµ − ντ mixing may implylarge mixing between sR and bR, and between sR and bR

Mixing among right-handed quarks drop out from CKMmatrix, but among right-handed squarks it is physical

←→bR

O(1) effects in b→ s possible

−1 −0.5 0 0.5 1

κ= −1.1

−1 −0.5 0 0.5 1

κ= −1.5

−1 −0.5 0 0.5 1

κ= −2.0

−1 −0.5 0 0.5 10

−1 −0.5 0 0.5 1

κ= −0.7

∆ Βs

M vs. SφΚ

−1(ps )

SφΚ[Harnik et al., hep-ph/0212180]

ZL — p.12

Some models to suppress ∆ms

• Neutral Higgs mediated FCNC in the large tanβ region:

Enhancement of B(Bd,s → µ+µ−) ∝ tan6 β up to twoorders of magnitude above the SM

CDF: B(Bs → µ+µ−) < 8× 10−8 (90% CL)SM: 3.4× 10−9 — measurable at LHC

Suppression of ∆ms ∝ tan4 β in a correlated way

[Buras et al., hep-ph/0207241]

ZL — p.13

New physics in B0sB

0s mixing

• Constraints before (left) and after (right) measurement of ∆ms (and ∆Γs)

Recall parameterization: M12 = MSM12 (1 + hs e

2iσs) [ZL, Papucci, Perez, hep-ph/0604112]

sh0 0.5 1 1.5 2 2.5 3 3.5

• To learn more about the Bs system, need data on CP asymmetry in Bs → J/ψ φ

and better constraint on AsSL = Γ[B0s(t)→`

+X]−Γ[B0s(t)→`

Γ[B0s(t)→`+X]+Γ[B0

s(t)→`−X]

[see also: Buras et al., hep-ph/0604057; Grossman, Nir, Raz, hep-ph/0605028]

ZL — p.13

Next milestone for Bs: SBs→ψφ

• 2000: Is sin 2β consistent with εK, |Vub|1999: ∆mB and other constraints?2008: Is sin 2βs consistent with . . . ?

Sψφ (sin 2βs for CP -even) analog of SψKCKM fit predicts: sin 2βs = 0.0346+0.0026

−0.0020

• Plot Sψφ = SM value ±0.10 /± 0.03

0.1/1 yr of nominal LHCb data ⇒

• Unless there is an easy-to-find narrowresonance at ATLAS & CMS, this couldbe one of the most interesting earlymeasurements

sh0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

[ZL, Papucci, Perez, hep-ph/0604112]

sh0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

ZL — p.14

Some recent developments

(Go from simpler to theoretically more complex)

Important features of the SM

• The SM flavor structure is very special:

– Single source of CP violation in CC interactions

– Suppressions due to hierarchy of mixing angles

– Suppression of FCNC processes (loops)

– Suppression of FCNC chirality flips by quark masses (e.g., SK∗γ)

Many suppressions that NP might not respect⇒ sensitivity to very high scales

• It is interesting / worthwhile / possible to test all of these

• Need broad program — there isn’t just a single critical measurement

Challenging field theory — many energy scales / expansions

ZL — p.15

CPV in b → s penguin decays

• Measuring same angle in decays sensitive to different short distance physics⇒ Good sensitivity to NP (fs = φKS, η

′KS, etc.)

• Amplitudes with one weak phase dominate — theor. clean:

A = VcbV∗cs︸︷︷︸

O(λ2)

〈“P”〉︸︷︷︸1

+VubV∗us︸︷︷︸

O(λ4)

〈“P + Tu”〉︸︷︷︸O(1)

SM: expect: Sfs − SψK and Cfs(= −Afs) <∼ 0.05SM: How small? Calculate 〈“P”〉/〈“P + Tu”〉

NP: Sfs 6= SψK possible; expect mode-dependent Sf

NP: Depend on size & phase of SM and NP amplitude

bu, c, t

NP could enter SψK mainly in mixing, while Sfs through both mixing and decay

• Interesting to pursue independent of present results — there is room for NP

ZL — p.16

Is there NP in b → s transitions?

sin(2βeff) ≡ sin(2φe1ff)

b→ccs

0η′

π0 KS

0 0.2 0.4 0.6 0.8 1

World Average 0.68 ± 0.03

BaBar 0.12 ± 0.31 ± 0.10

Belle 0.50 ± 0.21 ± 0.06

Average 0.39 ± 0.18

BaBar 0.55 ± 0.11 ± 0.02

Belle 0.64 ± 0.10 ± 0.04

Average 0.59 ± 0.08

BaBar 0.66 ± 0.26 ± 0.08

Belle 0.30 ± 0.32 ± 0.08

Average 0.51 ± 0.21

BaBar 0.33 ± 0.26 ± 0.04

Belle 0.33 ± 0.35 ± 0.08

Average 0.33 ± 0.21

BaBar 0.62 +-00..2350 ± 0.02

Belle 0.11 ± 0.46 ± 0.07

Average 0.48 ± 0.24

BaBar 0.62 ± 0.23

Belle 0.18 ± 0.23 ± 0.11

Average 0.42 ± 0.17

BaBar Q2B 0.41 ± 0.18 ± 0.07 ± 0.11

Belle 0.68 ± 0.15 ± 0.03 +-00..2113

Average 0.58 ± 0.13 +-00..1029

H F A GH F A GICHEP 2006

PRELIMINARY • SM: expect Sfs − SψK <∼ 0.05NP: Sfs 6= SψK possible (mode-dep.)

• Significance of deviations from SψK

decreased — most modes still < SM

Will any of them become significant?

• Smallest exp. errors: η′KS and φKS

All calculations find < few × 0.01 SMpollution [Buchalla et al.; Beneke; Williamson & Zupan]

• Improved theory may allow in futureto constrain specific NP models /parameters via pattern of deviations

ZL — p.16

α from B → ρρ, ππ, ρπ

• Sρ+ρ− = sin[(B-mix = −2β) + (A/A = −2γ + . . .) + . . .] = sin(2α) + small

(1) Longitudinal polarization (CP -even) dominates

(2) Small rate: B(B → ρ0ρ0) = (1.16± 0.46)× 10−6 ⇒ small ∆αB(B→π0π0)B(B→π+π0)

= 0.23± 0.04 vs. B(B→ρ0ρ0)B(B→ρ+ρ0)

= 0.06± 0.03 — observed in 2006

• Before 2006 B → ρρ dominated

All three modes important now

ρρ is more complicated than ππ, I = 1 pos-sible due to Γρ 6= 0; its O(Γ2

ρ/m2ρ) effects can

be constrained with more data [Falk et al.]

• All measurements combined: α =(93+11−9

0 20 40 60 80 100 120 140 160 180

B → ππB → ρπ (Babar)B → ρρ

CombinedCKM fit

α (deg)

WACK Mf i t t e r

Beauty06

ZL — p.17

γ from B± → DK±

• Tree level: interfere b→ c (B− → D0K−) and b→ u (B− → D0K−)NeedD0, D0 → same final state; determineB andD decay amplitudes from data

Sensitivity driven by: rB = |A(B− → D0K−)/A(B− → D0K−)| ∼ 0.1− 0.2

Central value of rB decreased in 2006

• Before 2006 Dalitz plot analysis inD0, D0 →KS π

+π− dominated [Giri et al.; Bondar]

Variants according to D decay; comparableresults now

• All measurements combined: γ =(62+38−24

)⇒ Need a lot more data 0

0 20 40 60 80 100 120 140 160 180

CKM fitno γ meas. in fit

Full frequentist treatment on MC basis

D(*)K(*) GLW + ADSD(*)K(*) GGSZ Combined

γ (deg)

WAC K Mf i t t e r

BEAUTY 06

ZL — p.18

inclusive processes

B physics has been fertile ground for theoretical developments:

HQET, ChPT, SCET, Lattice QCD, ...

Remark: hadronic uncertainties

• To believe discrepancy = new physics, need model independent predictions:

Quantity of interest = (calculable prefactor)×[1 +

(small parameters)k]

Theoretical uncertainty is parametrically suppressed by ∼ (small parameter)N ,but models may be used to estimate the uncertainty

• Most of the recent progress comes from expanding in powers of Λ/mQ, αs(mQ)

... a priori not known whether Λ ∼ 200MeV or ∼ 2GeV (fπ,mρ,m2K/ms)

... need experimental guidance to see which cases work how well

ZL — p.19

Determination of |Vcb| from B → Xc`ν

• Theoretically cleanest application of heavy quark expansion

νΓ(B → Xc`ν) =G2F |Vcb|

192π3

„mΥ

(0.534)×»

− 0.22

„Λ1S

500 MeV

«−0.011

„Λ1S

500 MeV

«2− 0.052

„λ1

(500 MeV)2

«− 0.071

„λ2

(500 MeV)2

− 0.006

„λ1Λ1S

(500 MeV)3

«+ 0.011

„λ2Λ1S

(500 MeV)3

«− 0.006

„ρ1

(500 MeV)3

«+ 0.008

„ρ2

(500 MeV)3

+ 0.011

(500 MeV)3

«+ 0.002

(500 MeV)3

«− 0.017

(500 MeV)3

«− 0.008

(500 MeV)3

+ 0.096ε− 0.030ε2BLM + 0.015ε

„Λ1S

500 MeV

«+ . . .

–[Bauer, ZL, Luke, Manohar, Trott; Buchmuller & Flacher]

Corrections: O(Λ/m): ∼ 20%, O(Λ2/m2): ∼ 5%, O(Λ3/m3): ∼ 1− 2%,O(αs): ∼ 10%, Unknown terms: < 2%

∼90 observables: consistent fit to hadronic matrix elements and |Vcb|; test theoryClear evidence for power suppressed corrections — measure λ1 with <∼15% error

• |Vcb| = (41.7± 0.7)×10−3, <2% error; also determine mb and mc

ZL — p.20

|Vub| from inclusive B → Xu`ν

• Phase space cuts required to suppress b → c`ν background complicate theory:Lower scales, dependence on nonperturbative functions (rather than numbers)

Renormalization of shape function and structure of subleading terms complicated[Bauer & Manohar; Bosch, Lange, Neubert, Paz; Lee & Stewart; etc.]

“B-beam” technique + use of several kinematic variables: E`, mX, q2, P+

• Inclusive average |Vub| = (4.49± 0.19± 0.27)× 10−3 > CKM fit (3.7± 0.1)× 10−3

ρ-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

0.6 BEAUTY 2006

CKMf i t t e r

dm∆ dm∆ & sm∆

cb/VubV

ZL — p.21

|Vub| from inclusive B → Xu`ν

• Phase space cuts required to suppress b → c`ν background complicate theory:Lower scales, dependence on nonperturbative functions (rather than numbers)

Renormalization of shape function and structure of subleading terms complicated[Bauer & Manohar; Bosch, Lange, Neubert, Paz; Lee & Stewart; etc.]

“B-beam” technique + use of several kinematic variables: E`, mX, q2, P+

• Inclusive average |Vub| = (4.49± 0.19± 0.27)× 10−3 > CKM fit (3.7± 0.1)× 10−3

• Exclusive determinations from B → π`ν lower (larger errors)

– Lattice QCD (q2 > 16 GeV2): |Vub| = (3.7± 0.3+0.6−0.4)× 10−3

[HPQCD & FNAL]

– Lattice & dispersion relation: |Vub| = (4.0± 0.5)× 10−3[Arnesen et al.; Becher & Hill]

– Light-cone SR: |Vub| = (3.4± 0.1+0.6−0.4)× 10−3

[Ball, Zwicky; Braun et al.; Colangelo, Khodjamirian]

• Statistical fluctuation? Inclusive average optimistic? Something more interesting?

Understanding the B → π`ν form factor also important for B → ππ, Kπ decays

ZL — p.21

Inclusive B → Xsγ

• One (if not “the”) most elaborate SM calculationsConstrains many models: 2HDM, SUSY, LRSM, etc.

• NNLO practically completed [Misiak et al., hep-ph/0609232]

4-loop running, 3-loop matching and matrix elements

Scale dependences significantly reduced ⇒

• B(B → Xsγ)∣∣Eγ>1.6GeV

= (3.15± 0.23)× 10−4

measurement: (3.55± 0.26)× 10−4

[1990]

ZL — p.22

B → Xsγ and neutralino dark matter

• Green: excluded by B → Xsγ

Brown: excluded (charged LSP)

Magenta: favored by gµ − 2

Blue: favored by Ωχh2 from WMAP

• Analyses assume constrained MSSM

If either Sη′K 6= sin 2β or SK∗γ 6= 0,then has to be redone

ThenB → Xs`+`− andBs → µµmay

give complementary constraints

100 200 300 400 500 600 700 800 900 10000

mh = 114 GeV

m1/2 (GeV)

tan β = 10 , µ > 0

mχ± = 104 GeV

100 200 300 400 500 600 700 800 900 10000

mh = 114 GeV

m1/2 (GeV)

tan β = 10 , µ < 0

100 1000 20000

m1/2 (GeV)

tan β = 35 , µ < 0

mh = 114 GeV

100 1000 2000 30000

mh = 114 GeV

m1/2 (GeV)

tan β = 50 , µ > 0

[Ellis, Olive, Santoso, Spanos]

ZL — p.23

Inclusive B → Xs`+`−

• Rate depends on

O7 =mb sσµνeFµνPRb,

O9 = e2(sγµPLb)(¯γµ`),

O10 = e2(sγµPLb)(¯γµγ5`)

Theory most precise for 1 GeV2 < q2 < 6 GeV2−→Experiments need additional cut mXs

<∼ 2 GeVto suppress b→ c(→ s`+ν)`−ν background 0 5 10 15 20

[Ghinculov, Hurth, Isidori, Yao]

• Rate in this region is determined by B light-cone distribution function (“shape fn”)Theory similar to measurement of |Vub| from B → Xu`ν (and related to B → Xsγ)

[Lee, ZL, Stewart, Tackmann]

• Sensitivity to NP survives after taking into account hadronic effects

ZL — p.24

A “new” observable in B → Xs`+`−

ds dz∼ 3Γ0(1− s)

(1 + z2)h“C9 +

+ C210

iHT [Γ = HT +HL]

− 4 z s C10

“C9 +

”HA [≡ (4/3)AFB]

+ (1− z2)h(C9 + 2C7)

ioHL [no C7/s pole]

z = cos[ 6 (~p`+, ~pB0, B−)] [or (~p`−, ~pB0, B+)] in `+`− center of mass frame

• Inclusive, with “guessed” errors for ∼1 ab−1

Define: Hi(q21, q

dq2Hi(q

• Small q2-dependence ⇒ splitting Γ into tworegions not useful (splitting HA ≡ AFB is!)

SeparatingHT andHL (q2-indept) very powerful

Can extract all info from a few integrated rates[Lee, ZL, Stewart, Tackmann, hep-ph/0612156] -6 -4 -2 0 2 4 6 8 10

GH1,3.5L

GH3.5,6L

HAH1,3.5LHAH3.5,6L

-6 -4 -2 0 2 4 6 8 10C9

ZL — p.25

ds dz∼ 3Γ0(1− s)

(1 + z2)h“C9 +

+ C210

iHT [Γ = HT +HL]

− 4 z s C10

“C9 +

”HA [≡ (4/3)AFB]

+ (1− z2)h(C9 + 2C7)

ioHL [no C7/s pole]

Define: Hi(q21, q

dq2Hi(q

• SeparatingHT and HL (q2-indept) very powerful

Can extract all info from a few integrated rates[Lee, ZL, Stewart, Tackmann, hep-ph/0612156] -6 -4 -2 0 2 4 6 8 10

HLH1,6L HTH1,6L

HAH1,3.5LHAH3.5,6L

-6 -4 -2 0 2 4 6 8 10C9

ZL — p.25

ds dz∼ 3Γ0(1− s)

(1 + z2)h“C9 +

+ C210

iHT [Γ = HT +HL]

− 4 z s C10

“C9 +

”HA [≡ (4/3)AFB]

+ (1− z2)h(C9 + 2C7)

ioHL [no C7/s pole]

Define: Hi(q21, q

dq2Hi(q

• SeparatingHT and HL (q2-indept) very powerful

• Can extract all info from a few integrated rates[Lee, ZL, Stewart, Tackmann, hep-ph/0612156] -6 -4 -2 0 2 4 6 8 10

HTH3.5,6L

HLH1,6LHTH1,3.5L

HAH1,3.5LHAH3.5,6L

-6 -4 -2 0 2 4 6 8 10C9

ZL — p.25

Many other interesting rare B decays

• Important probes of new physics

– B → K∗γ or Xsγ: Best mH± limits in 2HDM — in SUSY many param’s

– B → K(∗)`+`− or Xs`+`−: bsZ penguins, SUSY, right handed couplings

A crude guide (` = e or µ)Decay ∼SM rate physics examples

B → sγ 3× 10−4 |Vts|, H±, SUSY

B → τν 1× 10−4 fB|Vub|, H±

B → sνν 4× 10−5 new physics

B → s`+`− 5× 10−6 new physics

Bs → τ+τ− 1× 10−6

B → sτ+τ− 5× 10−7 ...

B → µν 5× 10−7

Bs → µ+µ− 4× 10−9

B → µ+µ− 2× 10−10

Replacing b → s by b → d costs afactor∼20 (in SM); interesting to testin both: rates, CP asymmetries, etc.

In B → q l1 l2 decays expect 10–20%K∗/ρ, and 5–10% K/π (model dept)

Many of these (cleanest inclusiveones) impossible at hadron colliders

ZL — p.26

Nonleptonic decays: the Λb lifetime

• OPE has been thought to be less reliable in non-leptonic than semileptonic decay (local duality)

Prediction Data (PDG)τΛb

τB0= 1 +O

„Λ2

, 16π2 Λ3

«= 0.80± 0.05

Hard to accommodate τΛb/τB0 much below 0.9[Bigi et al.; Neubert & Sachrajda; Gabbiani, Onishchenko, Petrov, ...]

Recent CDF measurement ∼3σ from PDG lifetime [ps]bΛ

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

l cΛALEPH (91-95)

0.03± -0.12+0.131.18

-l+ l0ΛALEPH (91-95)

0.04± -0.21+0.261.30

l cΛOPAL (90-95)

0.06± -0.22+0.241.29

l cΛDELPHI (91-95)

0.05± -0.18+0.191.11

l cΛCDF (92-95)

0.06± 0.15 ±1.32

µ cΛD0 (02-06)-11.3 fb

0.09± -0.11+0.121.28

0Λ ψD0 J/ (02-06) -11.2 fb

0.05± 0.14 ±1.30

0Λ ψCDF J/ (02-06)-11 fb

0.03± 0.08 ±1.59

PDG 2006

Lifetime MeasurementsbΛ PDG0B

τ/bΛτ 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

• How this settles will affect our estimate of the uncertainty of the calculation of ∆Γs

(In addition to perturbative uncertainty and that in matrix elements [from LQCD])

ZL — p.27

Aside: measurement of B → τν

• A new operator not previously constrained

Sensitive to tree-level charged Higgs contribution

Data: B(B+ → τ+ν) = (1.34± 0.48)× 10−4

To constrain SM, need much more precise Γ(B → τν)

• If experimental error small: Γ(B → τν)/∆md deter-mines |Vub/Vtd| independent of fB (left with Bd error)

• If error of fB small: two circles that intersect at α ∼ 90

• With a super-B-factory (+LHCb+CLEO-c), a Grinstein-type double ratio can minimize uncertainties:

B(B → `ν)

B(Bs → `+`−)×B(Ds → `ν)

B(D → `ν)= calculable to few %

[Browder@ICHEP]

ρ-1 -0.5 0 0.5 1 1.5 2

η-1.5

CKM fit

ρ-1 -0.5 0 0.5 1 1.5 2

η-1.5

τν +τ → +B

dm∆ and τν +τ → +Constraint from BBEAUTY 2006

CKMf i t t e r

ZL — p.28

exclusive processes

Two-body nonleptonic B decays

• Huge field: some successes of factorization, some unexplained phenomena

• B → Dπ,Dρ: a testing ground (important also for measuring “2β + γ”)B(B− → D(∗)0π−)/B(B0 → D(∗)+π−) ∼ 1.8± 0.2 ... also for ρ

• B → ππ: measure α — rates and CPV not easy to explain (are exp’s consistent?)Cπ+π− = −0.39± 0.07 , B(B → π0π0)/B(B → π+π0) = 0.23± 0.04

• B → Kπ: P–T interference sensitive to γ — data looked puzzling (disappearing?)

Rc ≡ 2B(B+ → π0K+) + B(B− → π0K−)

B(B+ → π+K0) + B(B− → π−K0)= 1.11± 0.07, Rn ≡

B(B0 → π−K+) + B(B0 → π+K−)

B(B0 → π0K0) + B(B0 → π0K0)= 0.99± 0.07

RL ≡ 2Γ(B− → π0K−) + Γ(B0 → π0K0)

Γ(B− → π−K0) + Γ(B0 → π+K−)= 1.06± 0.05

• Another topic: B → V V polarization (won’t talk about)

• Literally, hundreds of papers on each... SM and NP “explanations”

ZL — p.29

Factorization in charmless B → M1M2

• BBNS (QCDF) proposal [Beneke, Buchalla, Neubert, Sachrajda]

〈ππ|Oi|B〉 ∼ FB→π T (x)⊗ φπ(x)

〈ππ|Oi|B〉 ∼+ T (ξ, x, y)⊗ φB(ξ)⊗ φπ(x)⊗ φπ(y)

• KLS (pQCD) proposal involve only φB & φM1,2, with k⊥ dependence [Keum, Li, Sanda]

• SCET: 〈ππ|Oi|B〉 ∼ Acc +P

ij T (x, y)⊗hJij(x, zk, k

+` )⊗ φiπ(zk)φ

` )i⊗ φπ(y)

• In practice, relate some convolutions to the measurable B →M1,2 form factorsSelfconsistency between many nonleptonic (and/or semileptonic) rates

Open issues — theoretical challenges:

– Is the second term suppressed by αs compared to the first one?

– Are charm penguins perturbatively calculable?

– Role and regularization of certain seemingly divergent convolutions?

ZL — p.30

SCET in a nutshell

• Effective field theory for processes involving energetic hadrons, E Λ[Bauer, Fleming, Luke, Pirjol, Stewart, + . . . ]

• Expand in Λ2 ΛE E2, separate scales[light-cone variables: (p−, p+, p⊥)]

Introduce distinct fields for relevant degreesof freedom; power counting in λ

SCETI: λ =√

Λ/E — jets (m ∼ ΛE)

SCETII: λ = Λ/E — hadrons (m ∼ Λ)

New symmetries: collinear / soft gauge inv.

• Simplified / new (B → Dπ, π`ν) proofs of factorization theorems [Bauer, Pirjol, Stewart]

• Subleading order untractable before: factorization in B → D0π0[Mantry, Pirjol, Stewart],

CPV parameter SK∗γ [Grossman, Grinstein, ZL, Pirjol], weak annihilation, etc.

ZL — p.31

A breakthrough in nonleptonic B decays

• SCET: factorization proven in B → DM (light) to all orders in αs & leading in Λ/mD+π−, D0π− D0π−, D0π0 D+π−, D0π0

SCET: O(1) O(ΛQCD/mb,c) O(ΛQCD/mb,c)

• D∗π/Dπ ratios: the 4 = 1 relations follow fromnaive factorization and heavy quark symmetry

The • = 1 relations do not — a prediction ofSCET not foreseen by any model calculations

• Also predicts equal strong phases betweenI = 1/2 and 3/2 amplitudes in Dπ and D∗π

Data: δ(Dπ) = (28± 3), δ(D∗π) = (32± 5)

D0π0 0η0 0K

0η’

DD0ρ0

D+π-D0π-

D+ρ-D0ρ-D+Κ-

D0 -Κ

A(D*M)A(D M)

2.0color allowedcolor suppressed

SCET prediction

* ω + ω

[Mantry, Pirjol, Stewart, Blechman]

ZL — p.32

Semileptonic B → π, ρ form factors

• At leading order in Λ/Q, to all orders in αs, two contri-butions at q2 m2

B: soft form factor & hard scattering

(Separation scheme dependent; Q = E,mb, omit µ’s)[Beneke & Feldmann; Bauer, Pirjol, Stewart; Becher, Hill, Lange, Neubert]

Λ~p 22 Λ~p 22Λ~p2 Q

~p2 Q2

F (Q) = Ci(Q) ζi(Q) +mBfBfM

Zdzdxdk+ T (z,Q) J(z, x, k+, Q)φM(x)φB(k+)

• Symmetries⇒ nonfactorizable (1st) term obey form factor relations [Charles et al.]

Symmetries⇒ 3B → P and 7B → V form factors related to 3 universal functions

• Relative size? QCDF: 2nd ∼ αs×(1st), PQCD: 1st 2nd, SCET: 1st ∼ 2nd

• Whether first term factorizes (involves αs(µi), as 2nd term does) involves samephysics issues as hard scattering, annihilation, etc., contributions to B →M1M2

ZL — p.33

An application: B → ργ

• Determines |Vtd/Vts| independent of BB mixing (a new operator!)

Hadronic physics: form factor at q2 = 0 [Bosch, Buchalla; Beneke, Feldman, Seidel; Ali, Lunghi, Parkhomenko]

B(B → ργ)

B(B → K∗γ)=

˛2„mB −mρ

mB −mK∗

12(ξV 0γ)

(ξV±γ)−2

No weak annihilation inB0, cleaner thanB±

(Please don’t average ργ and ωγ!)

SU(3) breaking: ξ = 1.2± 0.1 (CKM ’05)[Ball, Zwicky; Becirevic; Mescia]

Conservative? ξ − 1 is model dependent

Could LQCD help? Moving NRQCD? -1.5

-1 -0.5 0 0.5 1 1.5 20

αβγ

CKM fit

ηC K M

f i t t e rICHEP 06

1 – CL

BR(B → ργ) / BR(B → K*γ)

• More data: control some theoretical errors by comparing ratios inB0 vs.B± decay

ZL — p.34

Meet the “zero-bin”

• Encounter singular integrals∫ 1

0dxφπ(x)/x2 ∼

∫dx/x in several calculations

e.g., B → π form factor, weak annihilation, “chirally enhanced” terms, etc.

Divergences ∼ one of the quarks become soft near x = 0 or 1 (p−i small), butderivations use that they are collinear (p−i large)

• Zero-bin: simple way to eliminate double counting between collinear & soft modes(collinear quark with p−i = 0 is not a collinear quark) [Manohar & Stewart, hep-ph/0605001]

Understand which singularities are physical, and how confinement effects them

• Zero-bin ensures there is no contribution from xi = p−i /(n · pπ) ∼ 0

Subtractions implied by zero-bin depend on the singularity of integrals, e.g.:Z 1

x2φπ(x, µ) ⇒

dxφπ(x, µ)− xφ′π(0, µ)

x2+ φ

′π(0, µ) ln

„n · pπµ−

«+ . . .

= finite and real

ZL — p.35

Weak annihilation

• Power suppressed,order Λ/E corrections

Yields convolution integrals of the form:∫ 1

0dxφπ(x)/x2 , φπ(x) ∼ 6x(1− x)

Singularity if gluon near on-shell — one of the pions near endpoint configuration

• KLS: first emphasized importance for strong phases and CPV [Keum, Li, Sanda]

Divergence rendered finite by k⊥, still sizable and complex contributions

• BBNS: interpret as IR sensitivity⇒ model by complex parameters“XA” =

0dx/x = (1 + ρAe

iϕA) ln(mB/Λ) [Beneke, Buchalla, Neubert, Sachrajda]

• SCET: Match onto six-quark operators of the formO

(ann)1d =

ˆdsΓs bv

˜| z gives fB

ˆun,ω2

Γn qn,ω3

˜| z π in n direction

ˆqn,ω1

Γn un,ω4

˜| z π in n direction

[Arnesen, ZL, Rothstein, Stewart]

At leading nonvanishing order in Λ/mb and αs: real and calculable

ZL — p.36

What the B → ππ data tell us

• Theory predicts suppression of strong phase: arg(T/C) = O(αs,Λ/mb)

• Use theory to extract weak phase [Bauer, Stewart, Rothstein]

SCET fit to data: γ ∼ 80, about 2σ from CKM fit

Statistics? Power corrections? New physics?

0.6SCET allowed region isospin

bound0.2

Flat triangle0.4

• Use CKM fit to learn about theory [Grossman, Hocker, ZL, Pirjol; Feldmann & Hurth]

– large power corrections to T,C?– large u penguins?– large weak annihilation?– conspiracy between several smaller effects?

Need to better understand B → ππ, B → π`ν, αρρ, γDK 0

-60 -40 -20 0 20 40 60

τ (deg)

t-conventionc-convention

t-conventionfit without using C00

• Kπ: hard to accommodate AK+π0 = 0.047±0.026, given AK+π− = −0.093±0.015

ZL — p.37

More hints of possible surprises

• Theory of heavy-to-light decays is rapidly developing

More work and data needed to understand behavior of expansionsWhy some predictions work at<∼10% level, while others receive∼30% corrections

Open issues: role of charming penguins, chirally enhanced terms, annihilation, ...

We have the tools to try to address the questions

• Hope to clarify in the next 2–3 years (better data + refined theory)

• B → ππ, Kπ rates and CP asymmetries

• α from B → ππ using SCET vs. α from CKM fit

• B → V V polarization

• Robustness of predictions for SK∗γ and zero of AFB in B → K∗`+`−

ZL — p.38

Final comments

Shall we see new physics in flavor physics?

Do we just need to look with higher resolution?

A diamond field in Namibia

Outlook

• If there are new particles at TeV scale, new flavor physics could show up any time

• Goal for flavor physics experiments:

If NP is seen in flavor physics: study it in as many different operators as possible

If NP is not seen in flavor physics: achieve what is theoretically possibleIf NP is not seen in flavor physics: could teach us a lot about the NP seen at LHC

The program as a whole is a lot more interesting than any single measurement

• Try to distinguish: One / many sources of CPV?

Try to distinguish: CPV only in CC interactions?

Try to distinguish: NP couples mostly to up / down sector?

Try to distinguish: . . . to 3rd or all generations? ∆(F ) = 2 or / and 1?

• Many interesting measurements, complementarity with high energy frontier

ZL — p.39

Theoretical limitations (continuum methods)

• Many interesting decay modes will not be theory limited for a long time

Measurement (in SM) Theoretical limit Present error

SψK (β) ∼ 0.2 1.0

Sη′K, SφK (β) ∼ 2 6, 11

SKSπ0γ (related to β) ∼ 5 ∼ 15

B → ρρ, ρπ, ππ (α) ∼ 1 ∼ 15

B → DK (γ) 1 ∼ 25

Bs → ψφ (βs) ∼ 0.2 —

Bs → DsK (γ − 2βs) 1 —

|Vcb| ∼ 1% ∼ 2%

|Vub| ∼ 5% ∼ 10%

B → Xsγ ∼ 5% ∼ 10%

B → Xs`+`− ∼ 5% ∼ 20%

B → K(∗)νν ∼ 5% —

For some entries, the shown theoretical limits require more complicated analyses

ZL — p.40

Conclusions

• Our knowledge of the flavor sector and CPV improved tremendously

CKM phase is the dominant source of CPV in flavor changing processes

• Deviations from SM in Bd mixing, b→ s and even in b→ d decays are constrained

NP in loop-induced transitions may still be ∼0.3×SM (sensitive to scalesLHC)

• Progress in theory toward model independently understanding more observables:

Precision calculations for inclusive semileptonic and rare decays

Zero-bin⇒ no divergent convolutions, annihilation real (novel ideas)

• Flavor physics may provide clues to model building in the LHC era

ZL — p.41

Backup l slides

Aside: statistics

0 20 40 60 80 100 120 140 160 180

B → ππB → ρπ (Babar)B → ρρ

CombinedCKM fit

α (deg)

WACK Mf i t t e r

Beauty06

α =(93+11−9

]o[α0 50 100 150

Favored sol’n:α = (168±6)

SM region:α = (92± 7)

0 20 40 60 80 100 120 140 160 180

CKM fitno γ meas. in fit

Full frequentist treatment on MC basis

D(*)K(*) GLW + ADSD(*)K(*) GGSZ Combined

γ (deg)

WAC K Mf i t t e r

BEAUTY 06

γ =(62+38−24

]o[γ-100 0 100

0.0005

]o[γ-100 0 100

0.0005

]o[γ-100 0 100

0.0005

γ = (82±20)

• Both Babar and Belle use the frequentist method to quote the results — so shall I

ZL — p.i

CP violation in Bs mixing: AsSL

• Difference of B → B vs. B → B transition probabilities

ASL =Γ[B0

phys(t) → `+X]− Γ[B0phys(t) → `−X]

Γ[B0phys(t) → `+X] + Γ[B0

phys(t) → `−X]= −2

„˛q

˛− 1

sh0 0.5 1 1.5 2 2.5 3

• Can be 3 orders of magnitude above SM; |AsSL| > |AdSL| possible, contrary to SM

ZL — p.ii

Correlation between Sψφ and AsSL

• In hs, σs βs region AsSL and Sψφ are highly correlated

AsSL = −

˛Γs12Ms

Sψφ +O„h

2s,m2c

φ ψS-1 -0.5 0 0.5 1

• Deviation would indicate violation of 3× 3 unitarity or NP at tree level

ZL — p.iii

One-page introduction to SCET

• Effective theory for processes involving energetic hadrons, E Λ[Bauer, Fleming, Luke, Pirjol, Stewart, + . . . ]

Introduce distinct fields for relevant degrees of freedom, power counting in λ

modes fields p = (+,−,⊥) p2

collinear ξn,p, Aµn,q E(λ2, 1, λ) E2λ2

soft qq, Aµs E(λ, λ, λ) E2λ2

usoft qus, Aµus E(λ2, λ2, λ2) E2λ4

SCETI: λ =√

Λ/E — jets (m∼ΛE)

SCETII: λ = Λ/E — hadrons (m∼Λ)

Match QCD→ SCETI → SCETII

• Can decouple ultrasoft gluons from collinear Lagrangian at leading order in λ

ξn,p = Yn ξ(0)n,p An,q = YnA

(0)n,q Y †n Yn = Pexp

∫ x−∞ ds n ·Aus(ns)

]Nonperturbative usoft effects made explicit through factors of Yn in operators

New symmetries: collinear / soft gauge invariance

• Simplified / new (B → Dπ, π`ν) proofs of factorization theorems [Bauer, Pirjol, Stewart]

ZL — p.iv

Photon polarization in B → Xsγ

• Is B → Xsγ due to O7 ∼ s σµνFµν(mbPR+msPL)b or s σµνFµν(mbPL+msPR)b?

SM: In ms → 0 limit, γ must be left-handed to conserve Jz

O7 ∼ s (mbFLµν +msF

Rµν) b , therefore b→ sLγL dominates

Inclusive B → Xsγγ sb

Assumption: 2-body decayDoes not apply for b→ sγg

Exclusive B → K∗γγ KB *

... quark model (sL implies JK∗

z = −1)... higher K∗ Fock states

• One measurement so far; had been expected to give SK∗γ = −2 (ms/mb) sin 2β[Atwood, Gronau, Soni]

Γ[B0(t) → K∗γ]− Γ[B0(t) → K∗γ]

Γ[B0(t) → K∗γ] + Γ[B0(t) → K∗γ]= SK∗γ sin(∆mt)− CK∗γ cos(∆mt)

• What is the SM prediction? What limits the sensitivity to new physics?

ZL — p.v

Right-handed photons in the SM

• Dominant source of “wrong-helicity” photons in the SM is O2

Equal b→ sγL, sγR rates at O(αs); calculated to O(α2sβ0)

Inclusively only rates are calculable: Γ(brem)22 /Γ0 ' 0.025

Suggests: A(b→ sγR)/A(b→ sγL) ∼√

0.025/2 = 0.11

[Grinstein, Grossman, ZL, Pirjol]

• Exclusive B → K∗γ: factorizable part contains an operator that could contributeat leading order in ΛQCD/mb, but its B → K∗γ matrix element vanishes

Subleading order: several contributions to B0 → K0∗γR, no complete study yet

We estimate:A(B0 → K0∗γR)

A(B0 → K0∗γL)= O

«∼ 0.1

• Data: SK∗γ = −0.28±0.26 — both the measurement and the theory can progress

ZL — p.vi

CPV in interference between decay and mixing

• Can get theoretically clean information in somecases whenB0 andB0 decay to same final state

|BL,H〉 = p|B0〉 ± q|B0〉 λfCP =q

AfCPAfCP

Time dependent CP asymmetry:

afCP =Γ[B0(t)→ f ]− Γ[B0(t)→ f ]Γ[B0(t)→ f ] + Γ[B0(t)→ f ]

=2 Imλf

1 + |λf |2︸︷︷︸Sf

sin(∆mt)− 1− |λf |2

1 + |λf |2︸︷︷︸Cf (−Af)

cos(∆mt)

• If amplitudes with one weak phase dominate a decay, hadronic physics drops outMeasure a phase in the Lagrangian theoretically cleanly:

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

ZL — p.vii

The cleanest case: B → J/ψKS

• Interference of B → ψK0 (b→ ccs) with B → B → ψK0 (b→ ccs)

Amplitudes with a second weak phase strongly suppressed(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

SψKS = − sin[(B-mix = −2β) + (decay = 0) + (K-mix = 0)]

Corrections: |A/A| 6= 1 (main uncertainty), εK 6= 0, ∆ΓB 6= 0Corrections: all are few×10−3 ⇒ accuracy < 1%

Wu,c,t

• World average: sin 2β = 0.675± 0.026 — a 4% measurement!

• Large deviations from CKM excluded (e.g., approximate CP in the sense that allCPV phases are small)⇒ Look for corrections, rather than alternatives to CKM

ZL — p.viii

B physics beyond CKM · Bphysics beyond CKM Zoltan Ligeti Warning: APS/JPS meeting Nov.2; BaBar...

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