Observables and anomalies in - ffp14.cpt.univ-mrs.frffp14.cpt.univ-mrs.fr/DOCUMENTS/SLIDES/CUNLIFFE_Sam.pdf · Observables, observables, observables Isospin asymmetry of B! K( ) +

Observables and anomalies inB→ K(∗)`+`− decaysSam Cunliffe on behalf of the LHCb collaboration. [[email protected]]

Frontiers in Fundamental Physics, Aix Marseille Universite 18th July 2014

mailto:[email protected]

Why study rare decays?

The LHCb detector

b→ s`` TheoryThe operator-product expansionObservables, observables, observables

Isospin asymmetry of B→ K(∗)µ+µ−

Angular analysis of B0→ K∗0µ+µ−

Observables from the angular distributionLHCb measurement

InterpretationsGlobal fitsForm factor uncertainties

Lepton universality in B±→ K±`+`−

Something strange from charm

Conclusions

S.Cunliffe (Imperial) FFP14 2/21


I ‘Rare’ Flavour-Changing Neutral Current processesI Forbidden at tree level =⇒ proceed via loops (in SM)

sb

µ−

µ+

W−

Z0, γ

I Searching for new particles via their indirect influence on rare processesI Access to much higher mass scales (particles are virtual)I Able to be model independentI Search for broad classes of new particles at once

I For other flavour observables (and another perspective on b→ s``), see talkby F. Mescia, yesterday

S.Cunliffe (Imperial) FFP14 Why study rare decays? 3/21


I If you want to learn about space...I If you want to find new particles...

χ

χ

q

q

STS-I Launch - NASA/CC [Source]

sb

µ−

µ+

W−

Z0, γ

d d

sb

µ−

µ+

g

H0

d d

d

sb

µ−

µ+

W−

Z ′

d d

sb

µ−

µ+

Z ′

d d

Very Large Array - Image courtesy of NRAO/AUI [Source]


http://en.wikipedia.org/wiki/File:Space_Shuttle_Columbia_launching.jpg

http://images.nrao.edu/304



χ

χ

q

q

CMS Monojet candidate - [Source]

sb

µ−

µ+

W−

Z0, γ

d d

sb

µ−

µ+

g

H0

d d

d

sb

µ−

µ+

W−

Z ′

d d

sb

µ−

µ+

Z ′

d d


https://twiki.cern.ch/twiki/pub/CMSPublic/PhysicsResultsEXO12048



χ

χ

q

q

sb

µ−

µ+

W−

Z0, γ

d d

sb

µ−

µ+

g

H0

d d

d

sb

µ−

µ+

W−

Z ′

d d

sb

µ−

µ+

Z ′

d d




χ

χ

q

q

sb

µ−

µ+

W−

Z0, γ

d d

sb

µ−

µ+

g

H0

d d

d

sb

µ−

µ+

W−

Z ′

d d

sb

µ−

µ+

Z ′

d d




χ

χ

q

q

sb

µ−

µ+

W−

Z0, γ

d d

sb

µ−

µ+

g

H0

d d

d

sb

µ−

µ+

W−

Z ′

d d

sb

µ−

µ+

Z ′

d d




χ

χ

q

q

sb

µ−

µ+

W−

Z0, γ

d d

sb

µ−

µ+

g

H0

d d

d

sb

µ−

µ+

W−

Z ′

d d

sb

µ−

µ+

Z ′

d d



The LHCb detector








Conclusions

The LHCb detectorBeauty Experiment at Small Theta

I Physics reach in other areas than rare b→ s``observables...

I e.g. talks by J. Dalseno on CPV in multibody Bdecaysand B. Couturier on LHCb outreach/education

I 2 < η < 5

I Tracking:0.4 < δp/p < 0.6%

I Vertexing:σIP = 20µm

I Kaon ID = 95%(5% mis-ID)

I Muon ID = 98%(1% mis-ID)

0/4π

/2π/4π3

π

0

/4π

/2π

/4π3

π [rad]1θ

[rad]2θ

1θ

2θ

b

b

z

LHCb MC = 8 TeVs

S.Cunliffe (Imperial) FFP14 The LHCb detector 5/21


The LHCb detector








Conclusions

The operator-product expansionOr: how to be model independent

sb

µ−

µ+

W−

Z0, γ

d d

sb

µ−

µ+

W−

W+

νµ

dd

S.Cunliffe (Imperial) FFP14 b→ s`` Theory 6/21


sb

γ

“O7”“C7”

sb

ℓ+

ℓ−“O9”, “O10”“C9”, “C10”

I “Effective operators” OiI “Wilson Coefficients” Ci

I c.f. GF from 4 point β decay modelI Can predict Ci’s for SM and NP scenarios

I Have an effective Hamiltonian =⇒ can calculate things

Heff = −4GF√2

e2

16π2VtbV

∗ts

∑i=7,9,10

(CiOi + C′iO′i

)+ h.c.



sb

γ

“O7”“C7”

sb

ℓ+

ℓ−“O9”, “O10”“C9”, “C10”




Heff = −4GF√2

e2

16π2VtbV

∗ts

∑i=7,9,10

(CiOi + C′iO′i

)+ h.c.



sb

γ

“O7”“C7”

sb

ℓ+

ℓ−“O9”, “O10”“C9”, “C10”




Heff = −4GF√2

e2

16π2VtbV

∗ts

∑i=7,9,10

(CiOi + C′iO′i

)+ h.c.



sb

γ

“O7”“C7”

sb

ℓ+

ℓ−“O9”, “O10”“C9”, “C10”




Heff = −4GF√2

e2

16π2VtbV

∗ts

∑i=7,9,10

(CiOi + C′iO′i

)+ h.c.


A word on QCDEnter form factor uncertainty

I Observables also contain contributions Hadronic Form Factors.I Different theorists use different versions/approximations.

O = f (Ci, {form factors})

sb

µ−

µ+

W−

Z0, γ

d d


A word on QCDEnter form factor uncertainty

I Observables also contain contributions Hadronic Form Factors.I Different theorists use different versions/approximations.

O = f (Ci, {form factors})

sb

µ−

µ+

W−

Z0, γ

d d

sb

µ−

µ+

d d


O7

b→ s``cos θK

q2

V (q2)

T3(q2)

AL⊥

A2(q2)ξ⊥C9

S6

P ′5C7

CNP9

AFB

|AR‖ |2

P ′4

b→ sγ Jc1

ξ‖Js2

Nomenclature

O7

b→ s``cos θK

q2

V (q2)

T3(q2)

AL⊥

A2(q2)ξ⊥C9

S6

P ′5C7

CNP9

AFB

|AR‖ |2

P ′4

b→ sγ Jc1

ξ‖Js2

Nomenclature

q2 = m2``

Squared dileptoninvariant mass

Observables, observables, observables

I Need to find measurable quantities that...I ...are sensitive to the Wilson CoefficientsI ...cancel the QCD uncertainty (hadronic form factors) wherever possible

Lepton-universality

RK =B[B±→ K±µ+µ−

]B[B±→ K±e+e−

]

Isospin asymmetry (spectator-model-asymmetry)

AI =B[B0→ K(∗)0µ+µ−

]− τ

B0

τB+B[B±→ K(∗)±µ+µ−

]B[B0→ K(∗)0µ+µ−

]+

τB0

τB+B[B±→ K(∗)±µ+µ−

]



The LHCb detector








Conclusions


[J. High Energy Phys. 06 (2014) 133]

I Measure asymmetry in ratebetween neutral and chargedmodes

I B0→ K∗0(→ K±π∓)µ+µ−

I B±→ K∗±(→ K0Sπ±)µ+µ−

I B0→ K0Sµ

+µ−

I B±→ K±µ+µ−

I Asymmetry v.close to zero in SMI Experimental challenge:

I K0S → π+π− reconstruction

I Normalise toB→ J/ψ (→ µ+µ−)K(∗)

I 3 fb−1 2011+2012 data

]2c) [MeV/−µ+µ−π+K(m5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

200

400 LHCb

−µ+µ *0K → 0B

]2c) [MeV/−µ+µ+πS0K(m

5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

20

40

60

LHCb

−µ+µ *+K → +B

S.Cunliffe (Imperial) FFP14 Isospin asymmetry ofB→ K(∗)µ+µ− 11/21

http://dx.doi.org/10.1007/JHEP06(2014)133


AI =B[B0→ K(∗)0µ+µ−

]− τ

B0

τB+B[B±→ K(∗)±µ+µ−

]B[B0→ K(∗)0µ+µ−

]+

τB0

τB+B[B±→ K(∗)±µ+µ−

]

]4c/2 [GeV2q0 5 10 15 20

IA

-1

-0.5

0

0.5

1

LHCb −µ+µ K →B *

]4c/2 [GeV2q0 5 10 15 20

IA

-1

-0.5

0

0.5

1

LHCb −µ+µ K →B

I Consistent with SM. (AI ≈ 0)

S.Cunliffe (Imperial) FFP14 Isospin asymmetry ofB→ K(∗)µ+µ− 12/21


The LHCb detector








Conclusions

Observables from the angular distribtionForB0 → K∗(892)0(→ K±π∓)µ+µ− decays...

I P → V V ′ (pseudoscalar to vector-vector)I Vector K∗(892) =⇒ angular distribution, as well as rate, is interesting

B0

K* 0

K+

π - μ -

μ+

θKθℓ

φ

I 3 angles, and q2{θK , θ`, φ, q

2}

I Angular distribution −→ Sets of observables:{FL, AFB, A

2T, S9

} {P ′4, P ′5, P ′6, P ′8}

I ...Clever ratios of angular terms

S.Cunliffe (Imperial) FFP14 Angular analysis ofB0→ K∗0µ+µ− 13/21

Observables from the angular distribtionForB0 → K∗(892)0(→ K±π∓)µ+µ− decays...

I P → V V ′ (pseudoscalar to vector-vector)I Vector K∗(892) =⇒ angular distribution, as well as rate, is interesting

B0

K* 0

K+

π - μ -

μ+

θKθℓ

φ

I 3 angles, and q2{θK , θ`, φ, q

2}

I Angular distribution −→ Sets of observables:{FL, AFB, A

2T, S9

} {P ′4, P ′5, P ′6, P ′8}

I ...Clever ratios of angular terms



[Phys. Rev. Lett. 111 (2013) 191801]

I Fit a reduced angular distributionI 3D fit, binned in q2{

P ′4, P′5, P

′6, P

′8

}I Correct for detector acceptance

I Observe local 3.7σ deviationfrom SM [JHEP 1305 (2013) 137]

I Prob. for 24 independentobservations (4P ’s × 6q2 bins) is0.5%

I 1 fb−1 2011 data

]4c/2 [GeV2q0 5 10 15 20

'4

P

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

SM Predictions

Data

LHCb

]4c/2 [GeV2q0 5 10 15 20

'5

P

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

SM Predictions

Data

LHCb


http://dx.doi.org/10.1103/PhysRevLett.111.191801



The LHCb detector








Conclusions

Global fitsP ′5 ⇒ tension inC9

Descotes-Genon, Matias & Virto[Phys. Rev. D 88, 074002 (2013)]

I Global fit including {P ′4, P ′5, P ′6, P ′8}I Fit includes b→ s`` and b→ sγ inputsI 4.5σ discrepancy from SM pointI Favours CNP

9 ≈ −1.5

68.3% C.L

95.5% C.L

99.7% C.L

Includes Low Recoil data

Only @1,6D bins

SM

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15

-4

-2

0

2

4

C7NP

C9N

P

Altmannshofer & Straub[Eur. Phys. J. C (2013) 73: 2646]

I 3σ discrepancyI Differences:

I Definitions of observablesI Different q2 rangesI Theory assumptions

I Best fit is modified C9

I Data described by additional Z′ at ∼ 7TeV

I Hard to reconcile with MSSM-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

ReHC9NPL

ReHC

9' LFL

S4

S5

AFB

B®K

ΜΜ

S.Cunliffe (Imperial) FFP14 Interpretations 15/21

http://link.aps.org/doi/10.1103/PhysRevD.88.074002

http://dx.doi.org/10.1140/epjc/s10052-013-2646-9

A hint of new physics?Contributions from new Z′ vector?

Descotes-Genon, et al.[JHEP 1305 (2013) 137)]

I Originally motivated {Pi}observables

I Simplification (assumption) inchoice of form factors

]4c/2 [GeV2q0 5 10 15 20

'5

P

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

SM Predictions

Data

LHCb

3.7σ

Jager & Camlich[JHEP 1305 (2013) 043]

I Uncertainty due to simplifiedchoice of form factors(factorisable corrections areunderestimated)




A hint of new physics?...or underestimated errors

Descotes-Genon, et al.[JHEP 1305 (2013) 137)]

I Originally motivated {Pi}observables

I Simplification (assumption) inchoice of form factors

]4c/2 [GeV2q0 5 10 15 20

'5

P

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

SM Predictions

Data

LHCb

3.7σ

Jager & Camlich[JHEP 1305 (2013) 043]

I Uncertainty due to simplifiedchoice of form factors(factorisable corrections areunderestimated)

B0→K*0µµ : interpretation

∃∀

•  Global fits → 2-4σ tension

•  Views from the theory community:

–  P5’ tension correlated with other

(smaller) tensions and NP explanation consistent with all

measurements is possible [1,2]

–  Theory errors underestimated,

tension is reduced [3]

•  Difficult to explain with SUSY [1]

•  Consistent with a Z’ with mass ~ 7 TeV (!) [4]

→ Measure other B→Kµµ decays!

∀%&∋()∗+,#,−.#//01∀

]4c/2 [GeV2q

0 5 10 15 20

'5

P

-1

0

1

SM arXiv:1303.5794

SM arXiv:1212.2263

-1LHCb 1fb

%,1∀2345&66789:;∋∀;4∀&3.<∀&∋()∗+,#−/.,=−,>∀%!1∀?;7≅94;7ΑΒ;696∀;4∀&3.<∀Χ8∆7.∀Ε;∗.∀?∀//<∀−0∃−−!∀Φ!−,#Γ<∀Η9∋Ι&6∀

;4∀&3.<∀&∋()∗+,#,−.#//0>∀%#1∀ϑ;&ΚΛ;&6∀;4∀&3.<∀&∋()∗+,#,−.!∃0/<∀Μ&;Ι;∋∀;4∀&3.<∀&∋()∗+,!,!.!!Ν#>∀%∃1∀Β&Κ3Ο∀;4∀&3.<∀

ΜΗΠΧ∀,∃−,∀Φ!−,∃Γ∀−ΝΘ<∀ϑΚ∋&7∀;4∀&3.<∀&∋()∗+,#,,.Ν0!Θ∀





The LHCb detector








Conclusions


[arXiv:1406.6482] submitted: Phys.Rev.Lett

RK =B[B±→ K±µ+µ−

]B[B±→ K±e+e−]

I If a Z′ is responsible for P ′5 does itcouple equally to lepton flavours?

I Altmannshofer et al.[Phys. Rev. D89 (2014) 095033]

I Kruger & Hiller[Phys.Rev. D69 (2004) 074020]

I Experimental challenge:I Selection of B±→ K±e+e−

I Bremsstrahlung → q2 movementI Correct for bremsstrahlung with

calorimeter photonsI Migration in q2 corrected with

simulationI 3 fb−1 2011+2012 data

]2c) [MeV/−e+e

+K(m

5000 5200 5400 5600

)2c

Can

did

ate

s /

( 4

0 M

eV

/

0

5

10

310×

LHCb

(a)B±→ J/ψK±

]2c) [MeV/−

e+e+

K(m

5000 5200 5400 5600

)2c

Can

did

ate

s /

( 4

0 M

eV

/

0

10

20

30

40 LHCb

(d)B±→ K±e+e−

S.Cunliffe (Imperial) FFP14 Lepton universality inB±→ K±`+`− 17/21

http://arxiv.org/abs/arXiv:1406.6482

http://dx.doi.org/10.1103/PhysRevD.89.095033



I Experimentally, use double ratio with B±→ J/ψK± decaysI Cancels systematic biases

RK =NK±µ+µ−

NJ/ψ (µ+µ−)K±

NJ/ψ (e+e−)K±

NK±e+e−×εJ/ψ (µ+µ−)K±

εK±µ+µ−

εK±e+e−

εJ/ψ (e+e−)K±

where Nf is the observed yield for B±→ f and εf is the corresponding efficiency

I RK = 1.000 in SM (argue aboutthe 4th s.f.)

I SM Higgs v.suppressedI LHCb measuresRK = 0.745+0.090

−0.074 ± 0.036

I In range q2 ∈ [1, 6]GeV2/c4

I Only agrees with SM within 2.6σ ]4c/2 [GeV2q0 5 10 15 20

KR

0

0.5

1

1.5

2

SM

LHCbLHCb

LHCb BaBar Belle

BaBar: [Phys. Rev. D86 (2012) 032012]

Belle: [Phys.Rev.Lett. 103 (2009) 171801]

S.Cunliffe (Imperial) FFP14 Lepton universality inB±→ K±`+`− 18/21


http://dx.doi.org/10.1103/PhysRevLett.103.171801


The LHCb detector








Conclusions


3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

Rexp

Rthe

Rcon

Rint

Rres

RBW

R

Ecm(GeV)

χ2/d.o.f=1.05

BESII e+e−→ hadrons/e+e−→ µ+µ−

0

0.5

1

1.5

2

2.5

3

3.5

3.6 3.8 4 4.2 4.4 4.6

dB

r

d√

q2[B

+→

K+µµ]/

10−

7G

eV−

1

!q2/GeV

Ψ(3770)

Ψ(4040)

Ψ(4160)

Ψ(4400)

a) afacb) ηcafacc) ρr ∈ Rd) ρr ∈ CLHCb

(4415)

(2S)

LHCb data: B±→ K±µ+µ−, L&Z fits

Lyon & Zwicky[arXiv:1406.0566]

I Fit BESII and LHCb dataI Necessary to add in large corrections (fudge factors) to get good fitI Are we underestimating the non-factorisable effects in Ceff

9 ?I Could explain P ′5 effectI And/or motivate new physics studies in b→ ccs operators

S.Cunliffe (Imperial) FFP14 Something strange from charm 19/21

http://arxiv.org/abs/1406.0566

Something strange from charm (loops)

ℓ

cc

O1,2

ℓℓ

γ(q)

b s

(a) (b)ℓ

O1,2

ℓℓ

γ(q)

b s

ℓ

J/Ψ, Ψ′..

O1,2

ℓℓ

γ(q)

b s

ℓ

O1,2

ℓℓ

γ(q)

b s

ℓ

O1,2b s

cc

O1,2b s OG

b sg

ℓℓℓ

γ(q)ℓ ℓ

(c)

I Massively underestimated terms like (a) at low q2

I The green gluons can’t account for this

S.Cunliffe (Imperial) FFP14 Something strange from charm 20/21


The LHCb detector








Conclusions

Conclusions

I FCNC processes probe higher mass scales for NPI Formalism gives model-independenceI Observables!

I Interesting results in b→ s`` processesI Isospin asymmetry in B→ K(∗)µ+µ−

I Angular analyses of B0→ K∗0µ+µ−

I Lepton universality in B±→ K±`+`−

I Interest from our theory/phenomenology friends

I LHCb data-taking in 2015...I Belle-II physics runs late 2016...

S.Cunliffe (Imperial) FFP14 Conclusions 21/21

[Backup Slides]

The actual definitions of the Wilson Operators

Heff = −4GF√2

e2

16π2VtbV

∗ts

∑i=7,9,10

(CiOi + C′iO′i

)+ h.c.

O7 =e

g2mb(sσµνPRb)F

µν , O′7 =e

g2mb(sσµνPLb)F

µν ,

O9 =e2

g2(sγµPLb)(¯γµ`), O′9 =

e2

g2(sγµPRb)(¯γµ`),

O10 =e2

g2(sγµPLb)(¯γµγ5`), O′10 =

e2

g2(sγµPRb)(¯γµγ5`),

S.Cunliffe (Imperial) FFP14 Backup 23/21

The actual definitions of the Wilson Operators

Ci = CSMi + CNP

i , C′i = C′ SMi + C′NP

i .

I @ right-handed interactions i = 9, 10 operators in SM

C′ SM9,10 = 0

I ∃ helicity-suppressed right-handed SM contributions to O′7 so

C′7 =ms

mb(CSM

7 + CNP7 ) + C′NP

7 .


Angular distribution of B0→ K∗0µ+µ−

The distribution of for vectorK∗0(892)

d4Γ

d cos θKd cos θldφdq2=

9

32π

(Js1 sin2 θK + Jc1 cos2 θK

+ (Js2 sin2 θK + Jc2 cos2 θK) cos 2θ`

+ J3 sin2 θK sin2 θ` cos 2φ

+ J4 sin 2θK sin 2θ` cosφ

+ J5 sin 2θK sin θ` cosφ

+ J6 sin2 θK cos θ`

+ J7 sin 2θK sin θ` sinφ

+ J8 sin 2θK sin 2θ` sinφ

+ J9 sin2 θK sin2 θ` sin 2φ

)


Angular distribution of B0→ K∗0µ+µ−

The principle moments

J1s =3

4

[|AL⊥|2 + |AL‖ |2 + |AR⊥|2 + |AR‖ |2

]J1c = |AL0 |2 + |AR0 |2

J2s =1

4

[|AL⊥|2 + |AL‖ |2 + |AR⊥|2 + |AR‖ |2

]J2c = −

[|AL0 |2 + |AR0 |2

]J3 =

1

2

[|AL⊥|2 − |AL‖ |2 + |AR⊥|2 − |AR‖ |2

]J4 =

1√2

[<(AL0A

L∗‖ +AR0 A

R∗‖ )]

J5 =√

2[<(AL0A

L∗⊥ −AR0 AR∗⊥ )

]J6 = 2

[<(AL‖A

L∗⊥ −AR‖ AR∗⊥ )

]J7 =

√2[=(AL0A

L∗‖ −AR0 AR∗‖ )

]J8 =

1√2

[=(AL0A

L∗⊥ −AR0 AR∗⊥ )

]J9 = =(AL∗‖ AL⊥ +AR∗‖ AR⊥).

(1)


The AmplitudesCalculated in the effective field theory

AL,R⊥ = N√

2λ1/2

[ [(Ceff

9 + Ceff′9 )∓ (Ceff

10 + Ceff′10 )] V (q2)

mB +mK∗

+2mb

q2(Ceff

7 + Ceff′7 )T1(q2)

],

AL,R‖ = −N√

2(m2B −m2

K∗)

[ [(Ceff

9 − Ceff′9 )∓ (Ceff

10 − Ceff′10 )] A1(q2)

mB −mK∗

+2mb

q2(Ceff

7 − Ceff′7 )T2(q2)

],

AL,R0 = − N

2mK∗∗√q2

{[(Ceff

9 − Ceff′9 )∓ (Ceff

10 − Ceff′10 )]

×[(m2

B −m2K∗∗ − q2)(mB +mK∗∗)A1(q2)− λ A2(q2)

mB +mK∗∗

]+ 2mb(C

eff7 − Ceff′

7 )

[(m2

B + 3m2K∗∗ − q2)T2(q2)− λ

m2B −m2

K∗∗T3(q2)

]},


The AmplitudesCalculated in the effective field theory

...where

N = VtbV∗ts

[G2Fα

2

3 · 210π5m3B

q2λ1/2βµ

]1/2

,

with λ = m4B +m4

K∗ + q4 − 2(m2Bm

2K∗ +m2

K∗q2 +m2

Bq2) and

βµ =√

1− 4m2µ/q2.


What are the Pi observables?

P ′i ≡Si√

FL(1− FL)=

1

2

1

dΓ/dq2

Ji + Ji√FL(1− FL)

P ′5 ≡1

2

1

dΓ/dq2

√2[<(AL0A

L∗⊥ −AR0 AR∗⊥ )

]√FL(1− FL)

I The asymmetry of the cross term between the longitudinal andperpendicularly polarised amplitudes.


Documents

Observables and anomalies in - ffp14.cpt.univ-mrs.frffp14.cpt.univ-mrs.fr/DOCUMENTS/SLIDES/CUNLIFFE_Sam.pdf · Observables, observables, observables Isospin asymmetry of B! K( ) +