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NP in B decays B physics Tool-Box Theory: B K * μ + μ - Prospects at LHCb: B K * μ + μ - Constraints Finding New Physics with B decays: Prospects for B K * μ + μ - Aoife Bharucha with W. Altmannshofer, Patricia Ball, A.J. Buras, D. Straub and M. Wick (arXiv:0811.1214 [hep-ph]) also with William Reece IPPP Seminar, Liverpool, 17th February 2010 Aoife Bharucha (IPPP) B K * μ + μ - February 18, 2010 1 / 32

Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

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Page 1: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Finding New Physics with B decays:

Prospects for B → K∗µ+µ−

Aoife Bharucha with W. Altmannshofer, Patricia Ball,A.J. Buras, D. Straub and M. Wick (arXiv:0811.1214 [hep-ph])

also with William Reece

IPPP

Seminar, Liverpool, 17th February 2010

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 1 / 32

Page 2: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Just launched expedition to 14 TeV

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 2 / 32

Page 3: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Just launched expedition to 14 TeV

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 2 / 32

Page 4: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Some Structure

New sources of Flavour in B decays

Theoretical Predictions for B → K∗µ+µ−

Prospects at LHCb for B → K∗µ+µ−

Constraints on NP at LHCb

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 3 / 32

Page 5: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Source of all Flavour in the SM

Lkinetic+gauge + LHiggs

respects the Flavour Symmetry SU(3)3q × SU(3)2

` , under which

QL → VQQL, UR → VUUR, DR → VDDR,

andLL → VLLL, ER → VEER,

where the Vi are unitary matrices.The Yukawa interactions

−LYukawa = Y dij QLiφDRj + Y u

ij QLiφURj + Y eij LLiφERj + h.c..

BREAK the global symmetry, resulting in Flavour Violation...

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 4 / 32

Page 6: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

CP Violation via the CKM Matrix

ChoosingY d = λd, Y u = V †λu,

where λd,u are diagonal,

CKM matrix V using the Wolfenstein Parameterization

1− 12λ

2 − 18λ

4 λ Aλ3(ρ− iη)−λ+ 1

2A2λ5[1− 2(ρ+ iη)] 1− 1

2λ2 − 1

8λ4(1 + 4A2) Aλ2

Aλ3[1− (1− 12λ

2)(ρ+ iη)] −Aλ2 + 12Aλ

4[1− 2(ρ+ iη)] 1− 12A

2λ4

λ = 0.2257± 0.001 and A = 0.814± 0.022

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 5 / 32

Page 7: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

γ

γ

α

α

dm∆Kε

sm∆ & dm∆

SLubV

ν τubV

βsin 2

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

excluded at CL > 0.95

α

βγ

ρ−1.0 −0.5 0.0 0.5 1.0 1.5 2.0

η

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5excluded area has CL > 0.95

Moriond 09

CKMf i t t e r

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 6 / 32

Page 8: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Current status of B decays and prospects at future colliders1

SM Theory Present Future FutureObservable prediction error result error Facility

|Vcb| [B → Xc`ν] input 1% (41.54± 0.73)× 10−3 1% Super-B

|Vub| [B → π`ν] input 10%→ 5%Latt (3.38± 0.36)× 10−3 4% Super-B

γ [B → DK] input < 1 (70+27−30) 3 LHCb

SBd→ψK sin(2β) ∼< 0.01 0.671± 0.023 0.01 LHCb

SBs→ψφ 0.036 ∼< 0.01 0.81+0.12

−0.32 0.01 LHCb

SBd→φK sin(2β) ∼< 0.05 0.44± 0.18 0.1 LHCb

SBs→φφ 0.036 ∼< 0.05 — 0.05 LHCb

SBd→K∗γfew × 0.01 0.01 −0.16± 0.22 0.03 Super-B

SBs→φγ few × 0.01 0.01 — 0.05 LHCb

AdSL −5× 10−4 10−4 −(5.8± 3.4)× 10−3 10−3 LHCb

AsSL 2× 10−5 < 10−5 (1.6± 8.5)× 10−3 10−3 LHCb

ACP (b→ sγ) < 0.01 < 0.01 −0.012± 0.028 0.005 Super-B

B(B → τν) 1× 10−4 20%→ 5%Latt (1.73± 0.35)× 10−4 5% Super-B

B(B → µν) 4× 10−7 20%→ 5%Latt < 1.3× 10−6 6% Super-B

B(Bs → µ+µ−) 3× 10−9 20%→ 5%Latt < 5× 10−8 10% LHCb

B(Bd → µ+µ−) 1× 10−10 20%→ 5%Latt < 1.5× 10−8 [?] LHCb

AFB(B → K∗µ+µ−)q20

0 0.05 (0.2± 0.2) 0.05 LHCb

B → Kνν 4× 10−6 20%→ 10%Latt < 1.4× 10−5 20% Super-B

1G. Isidori, Y. Nir and G. Perez, “Flavor Physics Constraints for Physics Beyond theStandard Model,” arXiv:1002.0900 [hep-ph]

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 7 / 32

Page 9: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

NP in B Decays

Can be model dependent or model independent..Use an Effective Field Theory

Leff = LSM +∑ c

(d)i

Λ(d−4)NP

O(d)i (SM fields)

Flavour Changing Neutral Currents

Suppressed at tree level by Vij and MW

Big effects if ΛNP provides similar suppression

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 8 / 32

Page 10: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Model Independent

MFV

Strictest bounds from B → Xsγ ⇒ Assume Flavour Violating StructureBeyond the SM linked to known SM Yukawas

FCNC’s suppressed even for Λ ∼ few TeV

Naturally implementable in Leff

Not a theory of flavour

Difficult to prove but might be easy to disprove : B → Xsl+l− /

B → l+l−?

EXTENSIONS:

MFV with additional Higgs doublet/ large tanβMFV with additional flavour diagonal phases

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 9 / 32

Page 11: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Model Dependent

SUSY

Provides a well motivated model for various MFV scenarios

Flavour Structure determind by SUSY breaking soft mass termsand Trilinear couplings

Flavour Blind MSSM (FBMSSM): MFVMSSM modified by someflavour conserving but CP-violating phases in the soft SUSY breakingtrilinear couplings

General MSSM (GMSSM): No MFV, and generic flavour- andCP-violating soft SUSY-breaking terms allowed

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 10 / 32

Page 12: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Looking for NP in B → K∗µ+µ−

No. of events seen at Belle is 230⇒ B → K∗µ+µ− is one of the rarest B decays ever observed

LHCb predicts 7200 signal events with 2fb−1 ⇔ 1 year’s data.

FCNC, but bounds much weaker than for B → Xsγ

SM CP violation is doubly Cabibbo suppressed, NP CPV morevisible

4 body decays, many angular observables, sensitive to NP

Experiment BaBar Belle CDFB(B → K∗µ+µ−)× 107 11.1± 1.9± 0.7 10.8+1.0

−1.0 ± 0.9 8.1± 3.0± 1.0# of BB events 384× 106 657× 106 −

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 11 / 32

Page 13: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

A B Physicists Tool Box

Effective Field Theories

L =∑i

CiOi

Contain short distance effectsand possibly NP

Hard Spectator Effects

For B → K∗µ+µ− QCDfactorization/ SCET/ HQET...

Hadronic Matrix Elements

e.g. 〈B|J |K∗〉

Described by Form Factors

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 12 / 32

Page 14: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Relating Observables to NP: EFTs

For B → K∗ decays, important Operators are..

Electromagnetic Dipole O7 Vector/Axial Current O9(10)

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 13 / 32

Page 15: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Relating Observables to NP: EFTs

For B → K∗(→ K−π+)µ+µ−, important NP O’s are..

Spin-Flipped EM Dipole O′7 Scalar/Pseudoscalar OS(P )

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 13 / 32

Page 16: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Brief Interlude-Form Factors

Matrix elements responsible for B → K∗l+l− can be expressed as:

8 Full form factors (FF’s)

〈K∗(p)|sγµγLb|B(pB)〉 = −ie∗µ(mB +m∗K)A1(q2) + i(pB + p)µe∗.q

A2(q2)

mB +m∗K

+ iqµ(e∗.q)2mK∗

q2

`A3(q2)−A0(q2)

´+ εµνρσe

∗νpρB pσ 2V(q2)

mB +m∗K

〈K∗(p)|sσµνqνγLb|B(pB)〉 = iεµνρσe∗νpρBp

σ2T1(q2) + T2(q2)e∗µ(m2B −m2

K∗)

−T2(q2)(e∗.q) (pB + p)µ + T3(q2)(e∗.q)

qµ −

q2

m2B −m2

K∗(pB + p)µ

ff

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 14 / 32

Page 17: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Form Factor Predictions

Theoretical Prections:

Lattice: High q2, Unstable particles eg. K∗ difficult

Light Cone Sum Rules: Low q2

Range of Form Factors:

Kinematic Range: 0 ≤ q2 ≤ 20GeV2

QCDF Range for B → K∗µ+µ−: 1 ≤ q2 ≤ 6GeV2

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 15 / 32

Page 18: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Angular Observables for B → K∗µ+µ−

Choosing a good place to look..

d4Γ

dq2dΩ=

9

32πI(q2, θl, θK , φ)

K

Π

B

Φ

Θl ΘK

Μ+

Μ-

..where I(q2, θl, θK , φ) =∑9

i=1 I(s/c)i (q2)ωi(θl, θK , φ)

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 16 / 32

Page 19: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Emphasize CP conserving and CP violating2 effects

S(a)i =

I(a)i + I

(a)i

d(Γ + Γ)/dq2

A(a)i =

I(a)i − I

(a)i

d(Γ + Γ)/dq2

2Also considered in C. Bobeth, G. Hiller and G. Piranishvili arXiv:0805.2525Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 17 / 32

Page 20: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

1 2 3 4 5 60.00

0.02

0.04

0.06

0.08

q2 HGeV2L

S2s

1 2 3 4 5 6

-0.8

-0.6

-0.4

-0.2

0.0

q2 HGeV2L

S2c

1 2 3 4 5 6

-0.020

-0.015

-0.010

-0.005

0.000

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0.010

q2 HGeV2L

S3

1 2 3 4 5 6-0.10

-0.05

0.00

0.05

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0.20

q2 HGeV2L

S4

1 2 3 4 5 6-0.4

-0.3

-0.2

-0.1

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q2 HGeV2L

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1 2 3 4 5 6

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1 2 3 4 5 60.00

0.01

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q2 HGeV2L

S7

1 2 3 4 5 6-0.025

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q2 HGeV2L

S8

1 2 3 4 5 6

0.0000

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0.0010

0.0015

0.0020

q2 HGeV2L

S9

1 2 3 4 5 60

10

20

30

40

q2 HGeV2L

dHG+GLdq2

H10-21

GeV

-3 L

1 2 3 4 5 60.0

0.2

0.4

0.6

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q2 HGeV2L

ATH3L

1 2 3 4 5 60.0

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ATH4L

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 18 / 32

Page 21: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

1 2 3 4 5 6

-0.0010

-0.0005

0.0000

0.0005

q2 HGeV2L

A2s

1 2 3 4 5 6

-0.007

-0.006

-0.005

-0.004

-0.003

-0.002

-0.001

0.000

q2 HGeV2L

A2c

1 2 3 4 5 6

-0.00020

-0.00015

-0.00010

-0.00005

0.00000

q2 HGeV2L

A3

1 2 3 4 5 6

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

q2 HGeV2L

A4

1 2 3 4 5 6

-0.006

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-0.001

0.000

q2 HGeV2L

A5

1 2 3 4 5 6-0.006

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-0.004

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0.000

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A6s

1 2 3 4 5 60.000

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1 2 3 4 5 6

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1 2 3 4 5 6

0.00000

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1 2 3 4 5 6

0.000

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0.004

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q2 HGeV2L

ACP

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 19 / 32

Page 22: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Model Independent Analysis

Observable Most affected by

Ss1, Sc1, Ss2, Sc2 C7, C ′7, C9, C ′9, C10, C ′10S3 C ′7, C ′9, C ′10 .

S4 C7, C ′7, C10, C ′10S5 C7, C ′7, C9, C ′10Ss6 C7, C9

A7 C7, C ′7, C10, C ′10A8 C7, C ′7, C9, C ′9, C ′10A9 C ′7, C ′9, C ′10Sc6 CS − C ′S

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 20 / 32

Page 23: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Theoretical Predictions: Specific Scenarios

Correlate zeros of S4, S5, Ss6 with B(b→ sγ)

ææ

àà

ìì

1.0 1.5 2.0 2.51.6

1.7

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Xs

ΓL

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s L HGeV2L

"##############################

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Xs

ΓL

´10

2

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 21 / 32

Page 24: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Theoretical Predictions: Specific Scenarios

Correlate zeros of S4, S5, Ss6 with B(b→ sγ)

ææ

òò

1.0 1.5 2.0 2.51.6

1.7

1.8

1.9

2.0

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102

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102

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102

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 21 / 32

Page 25: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Theoretical Predictions: Specific Scenarios

ææ

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ÈdeÈ He cmL

XA7\

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 21 / 32

Page 26: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Correlations at large tanβ

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-6 -4 -2 0 2 4 60

2

4

6

8

103XS6

c\

108

BRHB

s®Μ+Μ-L

Π8

Π4

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Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 22 / 32

Page 27: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

General MSSM: No MFV constraints

1 2 3 4 5 6-0.10

-0.05

0.00

0.05

0.10

0.15

q2 HGeV2L

S3

1 2 3 4 5 6

-0.10

-0.05

0.00

0.05

0.10

0.15

q2 HGeV2L

A9

GMSSMII

GMSSMI

SM

GMSSMII

SM

GMSSMI

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 23 / 32

Page 28: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Current Status/Prospects at LHCb

Belle (2008) - ICHEP200 events

BaBar (2008) 0804.4412100 events

LHCb < 0.1 fb−1 100 events2 fb−1 7200 eventsq2 < m2

J/ψ, 3900 eventsa

aJ. Dickens, V. Gibson, C. Lazzeroni andM. Patel, CERN-LHCB-2007-038

EvtGen Model for B → K∗µ+µ− at NLO

Includes trigger studies, acceptance effects

Finds sets of allowed WCs using current experimental constraints

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 24 / 32

Page 29: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Observables for early measurement

Using S’s and A’s reconstruct standard observables e.g. forward-backwardasymmetry, AFB , longtitudinal polarization fraction, FL :

AFB =38

(2Ss6 + Sc6) and FL = −Sc2.

Extract by counting in angular bins:

AFB =4

3

„Z 1

0−Z 0

−1

«dθl

d2(Γ + Γ)

dq2 dθl

ffid(Γ + Γ)

dq2

FL =1

9

16

Z 1/2

−1/2

d(Γ + Γ)

dq2 d cos θK∗

ffid(Γ + Γ)

dq2− 11

!

S5 =4

3

Z π/2

0+

Z 2π

3π/2−Z 3π/2

π/2

!dφ

„Z 1

0−Z 0

−1

«d cos θK∗

d3(Γ− Γ)

dq2 d cos θK∗ dφ

ffid(Γ + Γ)

dq2

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 25 / 32

Page 30: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Sensitivity to New Physics

1 2 3 4 5 6

-0.2

-0.1

0.0

0.1

0.2

q2

Afb

1 2 3 4 5 60.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

q2

FL

At Leading Order:

q20(AFB ) = −2mBmb

Ceff7

Ceff9

q20(S5) =

−mBmb(Ceff7 + C ′eff

7 )Ceff

9 + mb(Ceff7 + C ′eff

7 ) 1 2 3 4 5 6-0.6

-0.4

-0.2

0.0

0.2

q2

S 5

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 26 / 32

Page 31: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

AFB and S5 at LHCb

2 4 6 8-0.5-0.4-0.3-0.2-0.1

0.00.10.2

q2HGeV2

L

AF

B

2 4 6 8

-0.6

-0.4

-0.2

0.0

0.2

0.4

q2HGeV2

LS

5

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 27 / 32

Page 32: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Experimental Sensitivities

Observable 2fb−1 1fb−1 0.5fb−1

〈AFB 〉1−6 GeV 2+0.03−0.04

+0.05−0.03

+0.08−0.06

〈FL 〉1−6 GeV 2+0.02−0.02

+0.04−0.03

+0.04−0.06

〈S5 〉1−6 GeV 2+0.07−0.08

+0.09−0.11

+0.16−0.15

q20(AFB ) +0.56

−0.94+1.27−0.97 –

q20(S5 ) +0.27

−0.25+0.53−0.40 –

〈V 〉1−6 GeV 2 =∫ 6 GeV 2

1 GeV 2

dq2

(V (q2)

d(Γ + Γ)dq2

)/∫ 6 GeV 2

1 GeV 2

dq2 d(Γ + Γ)dq2

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 28 / 32

Page 33: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Existing Constraints for b→ s

Observable Experiment SM Theory

B(Bs → µ+µ−) 3.6 · 10−8 (3.70± 0.31) · 10−9

B(B → Xsl+l−)1−6 GeV2 (1.60± 0.51) · 10−6 (1.97± 0.11) · 10−6

B(B → Xsγ) (3.52± 0.23± 0.09) · 10−9 (3.28± 0.25) · 10−4

S(B → K∗γ) (−1.6± 2.2) · 10−1 (−0.26± 0.05) · 10−1

〈AFB〉1−6 GeV2 −0.26± 0.29 0.04± 0.03〈FL〉1−6 GeV2 0.67± 0.24 0.76± 0.08

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 29 / 32

Page 34: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Constraints on C7 and C ′7

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 30 / 32

Page 35: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Constraints on C7 and C ′7

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 30 / 32

Page 36: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Constraints on C9 and C ′10

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 31 / 32

Page 37: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Constraints on C9 and C ′10

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 31 / 32

Page 38: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Summary

B decays will lead to interesting complementaryinformation about the nature of NP

B→ K∗µ+µ− observables provide insight into flavourstructure of NP: MFV/ MFV+flavour blindphases/MFV+Higgs doublet

New NLO EvtGen model, promising preliminaryresults for zero’s of S5, AFB and integrated S5, AFB

and FLConstraints on Wilson Coefficients will be greatlyaffected by these measurements, especially S5

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 32 / 32

Page 39: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Summary

B decays will lead to interesting complementaryinformation about the nature of NP

B→ K∗µ+µ− observables provide insight into flavourstructure of NP: MFV/ MFV+flavour blindphases/MFV+Higgs doublet

New NLO EvtGen model, promising preliminaryresults for zero’s of S5, AFB and integrated S5, AFB

and FLConstraints on Wilson Coefficients will be greatlyaffected by these measurements, especially S5

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 32 / 32

Page 40: Finding New Physics with B decays: Prospects for B KAoife Bharucha (IPPP) B!K + February 18, 2010 1 / 32 NP in B decaysB physics Tool-BoxTheory: B!K + Prospects at LHCb: B!K + Constraints

NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints

Summary

B decays will lead to interesting complementaryinformation about the nature of NP

B→ K∗µ+µ− observables provide insight into flavourstructure of NP: MFV/ MFV+flavour blindphases/MFV+Higgs doublet

New NLO EvtGen model, promising preliminaryresults for zero’s of S5, AFB and integrated S5, AFB

and FLConstraints on Wilson Coefficients will be greatlyaffected by these measurements, especially S5

Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 32 / 32