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:

(bd)2

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

∆ms

,b→ dγ

b→ sγ,b→ d`+`−

b→ s`+`−∝

˛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?

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)

V =

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

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sin 2βJ/ΨKs

∆md ∆ms & ∆md

εK

εK

|Vub/Vcb|

ρ

η

C K Mf i t t e r

p a c k a g e

(1998) (2002) K vs. B constraints

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CKMf i t t e r)α(γ

cb/VubV

excl

uded

are

a ha

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L >

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CKMf i t t e r

dm∆ dm∆ & sm∆

Kε

Kε

βsin2 < 0βsol. w/ cos2

(excl. at CL > 0.95)

excl

uded

are

a ha

s C

L >

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

⇒ B

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

dt

„ |B0(t)〉|B0(t)〉

«=

„M −

i

2Γ

«„ |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〉

b

d

d

b

t

t

W W

b

d

d

b

W

W

t t

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

dt

„ |B0(t)〉|B0(t)〉

«=

„M −

i

2Γ

«„ |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〉

b

d

d

b

t

t

W W

b

d

d

b

W

W

t t

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

Γ12

«⇒ 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

Mq12r

2q e

2iθq

«= 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

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cb/VubV

excl

uded

are

a ha

s C

L >

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CKMf i t t e r

dm∆ dm∆ & sm∆

Kε

Kε

βsin2 < 0βsol. w/ cos2

(excl. at CL > 0.95)

excl

uded

are

a ha

s C

L >

0.95

• 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

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rd 2

2θd

(d

eg)

C K Mf i t t e r

Lattice 2005

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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]

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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

fBd

√Bd

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

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

excluded at CL > 0.95

γ

γ

α

α

∆md

∆ms & ∆md

ξ = 1.24 ± 0.04 ± 0.06

εK

εK

|Vub/Vcb|

sin 2β

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

excluded at CL > 0.95

α

βγ

ρ

η

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]

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itude

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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

fBd

√Bd

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]

-1.5

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0.5

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sin 2β

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

excluded at CL > 0.95

γ

γ

α

α

∆md

∆ms & ∆md

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

εK

εK

|Vub/Vcb|

sin 2β

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

excluded at CL > 0.95

α

βγ

ρ

η

excluded area has CL > 0.95

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

sR

sR

sR

νµ

µ

←→bR

bR

bR

ντ

τ

O(1) effects in b→ s possible

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∆ Βs

∆ Βs

M vs. SφΚ

M

−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]

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sσ

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• 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)→`

−X]

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

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

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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

s

sd

d

W

g

bu, c, t

B

s

K

d

S

φ

d

b qq

ss

q

q

Bd π

Κs

s

φ

KS

d

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)

HFA

GIC

HE

P 2

006

HFA

G

ICH

EP

200

6H

FAG

ICH

EP

200

6

HFA

G

ICH

EP

200

6

HFA

G

ICH

EP

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FAG

ICH

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ICH

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ICH

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b→ccs

φ K

0η′

K0

KS K

S K

S

π0 KS

ω K

S

f 0 K

0

K+ K

- K0

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

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CombinedCKM fit

α (deg)

1 –

CL

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

0.2

0.4

0.6

0.8

1

1.2

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)

1 –

CL

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 +

∑k

(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|

2

192π3

„mΥ

2

«5

(0.534)×»

1

− 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

„T1

(500 MeV)3

«+ 0.002

„T2

(500 MeV)3

«− 0.017

„T3

(500 MeV)3

«− 0.008

„T4

(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

η

0

0.1

0.2

0.3

0.4

0.5

0.6

α

βγ

ρ-0.4 -0.2 0 0.2 0.4 0.6 0.8 1

η

0

0.1

0.2

0.3

0.4

0.5

0.6 BEAUTY 2006

CKMf i t t e r

γ

γ

α

α

dm∆ dm∆ & sm∆

Kε

Kε

cb/VubV

βsin2 < 0βsol. w/ cos2

(excl. at CL > 0.95)

excl

uded

are

a ha

s C

L >

0.95

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]

E.g.:

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

100

200

300

400

500

600

700

800

100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

mh = 114 GeV

m0 (

GeV

)

m1/2 (GeV)

tan β = 10 , µ > 0

mχ± = 104 GeV

100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

100 200 300 400 500 600 700 800 900 10000

100

200

300

400

500

600

700

800

mh = 114 GeV

m0 (

GeV

)

m1/2 (GeV)

tan β = 10 , µ < 0

100 1000 20000

1000

100 1000 20000

1000

m0 (

GeV

)

m1/2 (GeV)

tan β = 35 , µ < 0

mh = 114 GeV

100 1000 2000 30000

1000

1500

100 1000 2000 30000

1000

1500

mh = 114 GeV

m0 (

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

0

1

2

3

4

[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`+`−

d2Γ

ds dz∼ 3Γ0(1− s)

2n

(1 + z2)h“C9 +

2

sC7

”2

+ C210

iHT [Γ = HT +HL]

− 4 z s C10

“C9 +

2

sC7

”HA [≡ (4/3)AFB]

+ (1− z2)h(C9 + 2C7)

2+ C2

10

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

22) =

Z q22

q21

dq2Hi(q

2)

• 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

C9

-8

-6

-4

-2

0

2

4

6

8

C10

GH1,3.5L

GH3.5,6L

HAH1,3.5LHAH3.5,6L

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

-8

-6

-4

-2

0

2

4

6

8

C10

↑SM

ZL — p.25

A “new” observable in B → Xs`+`−

d2Γ

ds dz∼ 3Γ0(1− s)

2n

(1 + z2)h“C9 +

2

sC7

”2

+ C210

iHT [Γ = HT +HL]

− 4 z s C10

“C9 +

2

sC7

”HA [≡ (4/3)AFB]

+ (1− z2)h(C9 + 2C7)

2+ C2

10

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

22) =

Z q22

q21

dq2Hi(q

2)

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

• 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

C9

-8

-6

-4

-2

0

2

4

6

8

C10

HLH1,6L HTH1,6L

HAH1,3.5LHAH3.5,6L

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

-8

-6

-4

-2

0

2

4

6

8

C10

↑SM

ZL — p.25

A “new” observable in B → Xs`+`−

d2Γ

ds dz∼ 3Γ0(1− s)

2n

(1 + z2)h“C9 +

2

sC7

”2

+ C210

iHT [Γ = HT +HL]

− 4 z s C10

“C9 +

2

sC7

”HA [≡ (4/3)AFB]

+ (1− z2)h(C9 + 2C7)

2+ C2

10

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

22) =

Z q22

q21

dq2Hi(q

2)

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

• 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

C9

-8

-6

-4

-2

0

2

4

6

8

C10

HTH3.5,6L

HLH1,6LHTH1,3.5L

HAH1,3.5LHAH3.5,6L

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

-8

-6

-4

-2

0

2

4

6

8

C10

↑SM

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

m2b

, 16π2 Λ3

m3b

«= 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

-1

-0.5

0

0.5

1

1.5

CKM fit

α

βγ

ρ-1 -0.5 0 0.5 1 1.5 2

η-1.5

-1

-0.5

0

0.5

1

1.5

dm∆

τν +τ → +B

excluded area has CL > 0.95

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 ≡

1

2

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

jB(k+

` )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’

0ω

DD D

DD0ρ0

D+π-D0π-

D+ρ-D0ρ-D+Κ-

D0 -Κ

A(D*M)A(D M)

0.0

0.5

1.0

1.5

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]

B M

Λ~p 22 Λ~p 22Λ~p2 Q

~p2 Q2

F (Q) = Ci(Q) ζi(Q) +mBfBfM

4E2

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)=

˛Vtd

Vts

˛2„mB −mρ

mB −mK∗

«3(

12(ξV 0γ)

−2

(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

-1 -0.5 0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

αβγ

CKM fit

ρ

ηC K M

f i t t e rICHEP 06

1 – CL

BR(B → ργ) / BR(B → K*γ)

WA

• 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

0

dx

x2φπ(x, µ) ⇒

Z 1

0

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” =

∫ 1

0dx/x = (1 + ρAe

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

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

(ann)1d =

Pq

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?

70 75

80

-0.8

-0.6

-0.4

-0.2

0.2

0.4

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

0.2

0.4

0.6

0.8

1

1.2

-60 -40 -20 0 20 40 60

τ (deg)

1 –

CL

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

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0 20 40 60 80 100 120 140 160 180

B → ππB → ρπ (Babar)B → ρρ

CombinedCKM fit

α (deg)

1 –

CL

WACK Mf i t t e r

Beauty06

α =(93+11−9

)

]o[α0 50 100 150

Prob

abili

ty d

ensi

ty

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0.004

0.006

0.008

]o[α0 50 100 150

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0.008

]o[α0 50 100 150

Prob

abili

ty d

ensi

ty

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0.002

0.004

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0.008

Favored sol’n:α = (168±6)

SM region:α = (92± 7)

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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)

1 –

CL

WAC K Mf i t t e r

BEAUTY 06

γ =(62+38−24

)

]o[γ-100 0 100

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abili

ty d

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ty

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0.001

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]o[γ-100 0 100

Prob

abili

ty d

ensi

ty

0

0.0005

0.001

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

p

˛− 1

«

sh0 0.5 1 1.5 2 2.5 3

s SLA

-0.02

-0.01

-0

0.01

0.02

• 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

12

˛SM

Sψφ +O„h

2s,m2c

m2b

«

φ ψS-1 -0.5 0 0.5 1

s SLA

-0.02

-0.01

0

0.01

0.02

• 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

[ig

∫ 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]

b s

cO2

gγ

• 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

„C2

3C7

ΛQCD

mb

«∼ 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

p

AfCPAfCP

0B

0B

CPf

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 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%

d

d

d

s

b

W c

cψ

K

B

S

d

d

d

s

b

ψ

Wu,c,t

c

c

K

B

S

g

• 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