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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints
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Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 18 / 32
NP in B decays B physics Tool-Box Theory: B → K∗µ+µ− Prospects at LHCb: B → K∗µ+µ− Constraints
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Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 19 / 32
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
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)
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Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 21 / 32
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)
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Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 21 / 32
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
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Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 21 / 32
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
3Π8 Π8
Π4
3Π8
Aoife Bharucha (IPPP) B → K∗µ+µ− February 18, 2010 22 / 32
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
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
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
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
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
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
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
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
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
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
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
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
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
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