SLIDE 1 Observables and anomalies in B → K(∗)ℓ+ℓ− decays
Sam Cunliffe on behalf of the LHCb collaboration.
[stc09@ic.ac.uk]
Frontiers in Fundamental Physics, Aix Marseille Universit´ e 18th July 2014
SLIDE 2 Why study rare decays? The LHCb detector b→ sℓℓ Theory The operator-product expansion Observables, observables, observables Isospin asymmetry of B → K(∗)µ+µ− Angular analysis of B0 → K∗0µ+µ− Observables from the angular distribution LHCb measurement Interpretations Global fits Form factor uncertainties Lepton universality in B± → K±ℓ+ℓ− Something strange from charm Conclusions
S.Cunliffe (Imperial) FFP14 2/21
SLIDE 3 Why study rare decays?
◮ ‘Rare’ Flavour-Changing Neutral Current processes
◮ Forbidden at tree level =
⇒ proceed via loops (in SM) s b µ− µ+ W − Z0, γ
◮ Searching for new particles via their indirect influence on rare processes
◮ Access to much higher mass scales (particles are virtual) ◮ Able to be model independent ◮ Search for broad classes of new particles at once
◮ For other flavour observables (and another perspective on b→ sℓℓ), see talk
by F. Mescia, yesterday
S.Cunliffe (Imperial) FFP14 Why study rare decays? 3/21
SLIDE 4 Why study rare decays?
◮ If you want to learn about space... ◮ If you want to find new particles... STS-I Launch - NASA/CC [Source] Very Large Array - Image courtesy of NRAO/AUI [Source]
S.Cunliffe (Imperial) FFP14 Why study rare decays? 4/21
SLIDE 5 Why study rare decays?
◮ If you want to learn about space... ◮ If you want to find new particles... CMS Monojet candidate - [Source]
S.Cunliffe (Imperial) FFP14 Why study rare decays? 4/21
SLIDE 6 Why study rare decays?
◮ If you want to learn about space... ◮ If you want to find new particles...
¯ χ χ q ¯ q
s b µ− µ+ W − Z0, γ ¯ d ¯ d
S.Cunliffe (Imperial) FFP14 Why study rare decays? 4/21
SLIDE 7 Why study rare decays?
◮ If you want to learn about space... ◮ If you want to find new particles...
¯ χ χ q ¯ q
s b µ− µ+ ˜ g ˜ H0 ¯ d ¯ d ˜ d
S.Cunliffe (Imperial) FFP14 Why study rare decays? 4/21
SLIDE 8 Why study rare decays?
◮ If you want to learn about space... ◮ If you want to find new particles...
¯ χ χ q ¯ q
s b µ− µ+ W − Z′ ¯ d ¯ d
S.Cunliffe (Imperial) FFP14 Why study rare decays? 4/21
SLIDE 9 Why study rare decays?
◮ If you want to learn about space... ◮ If you want to find new particles...
¯ χ χ q ¯ q
s b µ− µ+ Z′ ¯ d ¯ d
S.Cunliffe (Imperial) FFP14 Why study rare decays? 4/21
SLIDE 10
Why study rare decays? The LHCb detector b→ sℓℓ Theory The operator-product expansion Observables, observables, observables Isospin asymmetry of B → K(∗)µ+µ− Angular analysis of B0 → K∗0µ+µ− Observables from the angular distribution LHCb measurement Interpretations Global fits Form factor uncertainties Lepton universality in B± → K±ℓ+ℓ− Something strange from charm Conclusions
SLIDE 11 The LHCb detector
Beauty Experiment at Small Theta
◮ Physics reach in other areas than rare b→ sℓℓ
◮ e.g. talks by J. Dalseno on CPV in multibody B
decays and B. Couturier on LHCb outreach/education
◮ 2 < η < 5 ◮ Tracking:
0.4 < δp/p < 0.6%
◮ Vertexing:
σIP = 20 µm
◮ Kaon ID = 95%
(5% mis-ID)
◮ Muon ID = 98%
(1% mis-ID)
/4 π /2 π /4 π 3 π /4 π /2 π /4 π 3 π
[rad]
1
θ [rad]
2
θ
1
θ
2
θ b b
z
LHCb MC = 8 TeV s
S.Cunliffe (Imperial) FFP14 The LHCb detector 5/21
SLIDE 12
Why study rare decays? The LHCb detector b→ sℓℓ Theory The operator-product expansion Observables, observables, observables Isospin asymmetry of B → K(∗)µ+µ− Angular analysis of B0 → K∗0µ+µ− Observables from the angular distribution LHCb measurement Interpretations Global fits Form factor uncertainties Lepton universality in B± → K±ℓ+ℓ− Something strange from charm Conclusions
SLIDE 13 The operator-product expansion
Or: how to be model independent
s b µ− µ+ W − Z0, γ ¯ d ¯ d s b µ− µ+ W − W + νµ ¯ d ¯ d
S.Cunliffe (Imperial) FFP14 b → sℓℓ Theory 6/21
SLIDE 14 The operator-product expansion
Or: how to be model independent
s b γ
“O7” “C7”
s b ℓ+ ℓ−
“O9”, “O10” “C9”, “C10”
◮ “Effective operators” Oi ◮ “Wilson Coefficients” Ci
◮ c.f. GF from 4 point β decay model ◮ Can predict Ci’s for SM and NP scenarios
◮ Have an effective Hamiltonian =
⇒ can calculate things Heff = −4GF √ 2 e2 16π2 VtbV ∗
ts
iO′ i
S.Cunliffe (Imperial) FFP14 b → sℓℓ Theory 7/21
SLIDE 15 The operator-product expansion
Or: how to be model independent
s b γ
“O7” “C7”
s b ℓ+ ℓ−
“O9”, “O10” “C9”, “C10”
◮ “Effective operators” Oi ◮ “Wilson Coefficients” Ci
◮ c.f. GF from 4 point β decay model ◮ Can predict Ci’s for SM and NP scenarios
◮ Have an effective Hamiltonian =
⇒ can calculate things Heff = −4GF √ 2 e2 16π2 VtbV ∗
ts
iO′ i
S.Cunliffe (Imperial) FFP14 b → sℓℓ Theory 7/21
SLIDE 16 The operator-product expansion
Or: how to be model independent
s b γ
“O7” “C7”
s b ℓ+ ℓ−
“O9”, “O10” “C9”, “C10”
◮ “Effective operators” Oi ◮ “Wilson Coefficients” Ci
◮ c.f. GF from 4 point β decay model ◮ Can predict Ci’s for SM and NP scenarios
◮ Have an effective Hamiltonian =
⇒ can calculate things Heff = −4GF √ 2 e2 16π2 VtbV ∗
ts
iO′ i
S.Cunliffe (Imperial) FFP14 b → sℓℓ Theory 7/21
SLIDE 17 The operator-product expansion
Or: how to be model independent
s b γ
“O7” “C7”
s b ℓ+ ℓ−
“O9”, “O10” “C9”, “C10”
◮ “Effective operators” Oi ◮ “Wilson Coefficients” Ci
◮ c.f. GF from 4 point β decay model ◮ Can predict Ci’s for SM and NP scenarios
◮ Have an effective Hamiltonian =
⇒ can calculate things Heff = −4GF √ 2 e2 16π2 VtbV ∗
ts
iO′ i
S.Cunliffe (Imperial) FFP14 b → sℓℓ Theory 7/21
SLIDE 18 A word on QCD
Enter form factor uncertainty
◮ Observables also contain contributions Hadronic Form Factors. ◮ Different theorists use different versions/approximations.
ˆ O = f (Ci, {form factors})
s b µ− µ+ W − Z0, γ ¯ d ¯ d
S.Cunliffe (Imperial) FFP14 b → sℓℓ Theory 8/21
SLIDE 19 A word on QCD
Enter form factor uncertainty
◮ Observables also contain contributions Hadronic Form Factors. ◮ Different theorists use different versions/approximations.
ˆ O = f (Ci, {form factors})
s b µ− µ+ W − Z0, γ ¯ d ¯ d
s b µ− µ+ ¯ d ¯ d
S.Cunliffe (Imperial) FFP14 b → sℓℓ Theory 8/21
SLIDE 20 O7
b → sℓℓ
cos θK q2 V (q2) T3(q2)
AL
⊥
A2(q2)
ξ⊥
C9
S6
P ′
5
C7
CNP
9
AFB
|AR
|2
P ′
4
b → sγ
Jc
1
ξ
¯ Js
2
Nomenclature
SLIDE 21 O7
b → sℓℓ
cos θK q2 V (q2) T3(q2)
AL
⊥
A2(q2)
ξ⊥
C9
S6
P ′
5
C7
CNP
9
AFB
|AR
|2
P ′
4
b → sγ
Jc
1
ξ
¯ Js
2
Nomenclature
q2 = m2
ℓℓ
Squared dilepton invariant mass
SLIDE 22 Observables, observables, observables
◮ Need to find measurable quantities that...
◮ ...are sensitive to the Wilson Coefficients ◮ ...cancel the QCD uncertainty (hadronic form factors) wherever possible
Lepton-universality RK = B
B
- B± → K±e+e−
- Isospin asymmetry (spectator-model-asymmetry)
AI = B
−
τB0 τB+ B
B
τB0 τB+ B
- B± → K(∗)±µ+µ−
- S.Cunliffe (Imperial)
FFP14 b → sℓℓ Theory 10/21
SLIDE 23
Why study rare decays? The LHCb detector b→ sℓℓ Theory The operator-product expansion Observables, observables, observables Isospin asymmetry of B → K(∗)µ+µ− Angular analysis of B0 → K∗0µ+µ− Observables from the angular distribution LHCb measurement Interpretations Global fits Form factor uncertainties Lepton universality in B± → K±ℓ+ℓ− Something strange from charm Conclusions
SLIDE 24 Isospin asymmetry of B → K(∗)µ+µ−
[J. High Energy Phys. 06 (2014) 133]
◮ Measure asymmetry in rate
between neutral and charged modes
◮ B0 → K∗0(→ K±π∓)µ+µ− ◮ B± → K∗±(→ K0 Sπ±)µ+µ− ◮ B0 → K0 Sµ+µ− ◮ B± → K±µ+µ−
◮ Asymmetry v.close to zero in SM ◮ Experimental challenge:
◮ K0
S → π+π− reconstruction ◮ Normalise to
B → J/ψ (→ µ+µ−)K(∗)
◮ 3 fb−1 2011+2012 data
]
2
c ) [MeV/
−
µ
+
µ
−
π
+
K ( m
5200 5400 5600
)
2
c Candidates / ( 10 MeV/
200 400
LHCb
−
µ
+
µ
*0
K → B
]
2
c ) [MeV/
−
µ
+
µ
+
π
S
K ( m
5200 5400 5600
)
2
c Candidates / ( 10 MeV/
20 40 60
LHCb
−
µ
+
µ
*+
K →
+
B
S.Cunliffe (Imperial) FFP14 Isospin asymmetry of B → K(∗)µ+µ− 11/21
SLIDE 25 Isospin asymmetry of B → K(∗)µ+µ−
AI = B
−
τB0 τB+ B
B
τB0 τB+ B
4
c /
2
[GeV
2
q
5 10 15 20 I
A
0.5 1
LHCb
−
µ
+
µ K → B
*
]
4
c /
2
[GeV
2
q
5 10 15 20 I
A
0.5 1
LHCb
−
µ
+
µ K → B
◮
Consistent with SM. (AI ≈ 0)
S.Cunliffe (Imperial) FFP14 Isospin asymmetry of B → K(∗)µ+µ− 12/21
SLIDE 26
Why study rare decays? The LHCb detector b→ sℓℓ Theory The operator-product expansion Observables, observables, observables Isospin asymmetry of B → K(∗)µ+µ− Angular analysis of B0 → K∗0µ+µ− Observables from the angular distribution LHCb measurement Interpretations Global fits Form factor uncertainties Lepton universality in B± → K±ℓ+ℓ− Something strange from charm Conclusions
SLIDE 27 Observables from the angular distribtion
For B0 → K∗(892)0(→ K±π∓)µ+µ− decays...
◮ P → V V ′ (pseudoscalar to vector-vector) ◮ Vector K∗(892) =
⇒ angular distribution, as well as rate, is interesting
B0 K* 0 K+
π - μ - μ+
θK θℓ φ
◮ 3 angles, and q2
◮ Angular distribution −
→ Sets of observables:
T, S9
4, P ′ 5, P ′ 6, P ′ 8} ◮ ...Clever ratios of angular terms
S.Cunliffe (Imperial) FFP14 Angular analysis of B0 → K∗0µ+µ− 13/21
SLIDE 28 Observables from the angular distribtion
For B0 → K∗(892)0(→ K±π∓)µ+µ− decays...
◮ P → V V ′ (pseudoscalar to vector-vector) ◮ Vector K∗(892) =
⇒ angular distribution, as well as rate, is interesting
B0 K* 0 K+
π - μ - μ+
θK θℓ φ
◮ 3 angles, and q2
◮ Angular distribution −
→ Sets of observables:
T, S9
4, P ′ 5, P ′ 6, P ′ 8} ◮ ...Clever ratios of angular terms
S.Cunliffe (Imperial) FFP14 Angular analysis of B0 → K∗0µ+µ− 13/21
SLIDE 29 Angular analysis of B0 → K∗0µ+µ−
[Phys. Rev. Lett. 111 (2013) 191801]
◮ Fit a reduced angular distribution ◮ 3D fit, binned in q2
4, P ′ 5, P ′ 6, P ′ 8
- ◮ Correct for detector acceptance
◮ Observe local 3.7σ deviation
from SM [JHEP 1305 (2013) 137]
◮ Prob. for 24 independent
- bservations (4P’s × 6q2 bins) is
0.5%
◮ 1 fb−1 2011 data ]
4
c /
2
[GeV
2
q
5 10 15 20
'
4
P
0.2 0.4 0.6 0.8 1
SM Predictions Data
LHCb
]
4
c /
2
[GeV
2
q
5 10 15 20
'
5
P
0.2 0.4 0.6 0.8 1
SM Predictions Data
LHCb
S.Cunliffe (Imperial) FFP14 Angular analysis of B0 → K∗0µ+µ− 14/21
SLIDE 30
Why study rare decays? The LHCb detector b→ sℓℓ Theory The operator-product expansion Observables, observables, observables Isospin asymmetry of B → K(∗)µ+µ− Angular analysis of B0 → K∗0µ+µ− Observables from the angular distribution LHCb measurement Interpretations Global fits Form factor uncertainties Lepton universality in B± → K±ℓ+ℓ− Something strange from charm Conclusions
SLIDE 31 Global fits
P ′
5 ⇒ tension in C9
Descotes-Genon, Matias & Virto
[Phys. Rev. D 88, 074002 (2013)] ◮ Global fit including {P ′ 4, P ′ 5, P ′ 6, P ′ 8} ◮ Fit includes b→ sℓℓ and b→ sγ inputs ◮ 4.5σ discrepancy from SM point ◮ Favours CNP 9
≈ −1.5
68.3 C.L 95.5 C.L 99.7 C.L Includes Low Recoil data Only 1,6 bins SM
0.15 0.10 0.05 0.00 0.05 0.10 0.15 4 2 2 4 C7
NP
C9
NP
Altmannshofer & Straub
[Eur. Phys. J. C (2013) 73: 2646] ◮ 3σ discrepancy ◮ Differences:
◮ Definitions of observables ◮ Different q2 ranges ◮ Theory assumptions
◮ Best fit is modified C9 ◮ Data described by additional Z′ at ∼ 7TeV ◮ Hard to reconcile with MSSM
3 2 1 1 2 3 3 2 1 1 2 3
ReC9
NP
ReC9
'
FL S4 S5 AFB BK ΜΜ
S.Cunliffe (Imperial) FFP14 Interpretations 15/21
SLIDE 32 A hint of new physics?
Contributions from new Z′ vector?
Descotes-Genon, et al.
[JHEP 1305 (2013) 137)] ◮ Originally motivated {Pi}
◮ Simplification (assumption) in
choice of form factors
]
4
c /
2
[GeV
2
q
5 10 15 20
'
5
P
0.2 0.4 0.6 0.8 1
SM Predictions Data
LHCb
3.7σ J¨ ager & Camlich
[JHEP 1305 (2013) 043] ◮ Uncertainty due to simplified
choice of form factors (factorisable corrections are underestimated)
S.Cunliffe (Imperial) FFP14 Interpretations 16/21
SLIDE 33 A hint of new physics?
...or underestimated errors
Descotes-Genon, et al.
[JHEP 1305 (2013) 137)] ◮ Originally motivated {Pi}
◮ Simplification (assumption) in
choice of form factors
]
4
c /
2
[GeV
2
q
5 10 15 20
'
5
P
0.2 0.4 0.6 0.8 1
SM Predictions Data
LHCb
3.7σ J¨ ager & Camlich
[JHEP 1305 (2013) 043] ◮ Uncertainty due to simplified
choice of form factors (factorisable corrections are underestimated)
]
4
c /
2
[GeV
2
q
5 10 15 20
'
5
P
1
SM arXiv:1303.5794 SM arXiv:1212.2263
LHCb 1fb
ΑΒ;696∀;4∀&3.<∀Χ8D7.∀Ε;∗.∀?∀//<∀−0∃−−!∀Φ!−,#Γ<∀Η9∋Ι&6∀
S.Cunliffe (Imperial) FFP14 Interpretations 16/21
SLIDE 34
Why study rare decays? The LHCb detector b→ sℓℓ Theory The operator-product expansion Observables, observables, observables Isospin asymmetry of B → K(∗)µ+µ− Angular analysis of B0 → K∗0µ+µ− Observables from the angular distribution LHCb measurement Interpretations Global fits Form factor uncertainties Lepton universality in B± → K±ℓ+ℓ− Something strange from charm Conclusions
SLIDE 35 Lepton universality in B± → K±ℓ+ℓ−
[arXiv:1406.6482] submitted: Phys.Rev.Lett RK = B
B[B± → K±e+e−]
◮ If a Z′ is responsible for P ′ 5 does it
couple equally to lepton flavours?
◮ Altmannshofer et al.
[Phys. Rev. D89 (2014) 095033]
◮ Kr¨
uger & Hiller
[Phys.Rev. D69 (2004) 074020] ◮ Experimental challenge:
◮ Selection of B± → K±e+e− ◮ Bremsstrahlung → q2 movement
◮ Correct for bremsstrahlung with
calorimeter photons
◮ Migration in q2 corrected with
simulation
◮ 3 fb−1 2011+2012 data
]
2
c ) [MeV/
−
e
+
e
+
K ( m
5000 5200 5400 5600
)
2
c Candidates / ( 40 MeV/
5 10
3
10 × LHCb (a)
B± → J/ ψ K±
]
2
c ) [MeV/
−
e
+
e
+
K ( m
5000 5200 5400 5600
)
2
c Candidates / ( 40 MeV/
10 20 30 40 LHCb (d)
B± → K±e+e− S.Cunliffe (Imperial) FFP14 Lepton universality in B± → K±ℓ+ℓ− 17/21
SLIDE 36 Lepton universality in B± → K±ℓ+ℓ−
◮ Experimentally, use double ratio with B± → J/ψ K± decays
◮ Cancels systematic biases
RK = NK±µ+µ− NJ/ψ (µ+µ−)K± NJ/ψ (e+e−)K± NK±e+e− × ǫJ/ψ (µ+µ−)K± ǫK±µ+µ− ǫK±e+e− ǫJ/ψ (e+e−)K±
where Nf is the observed yield for B± → f and ǫf is the corresponding efficiency
◮ RK = 1.000 in SM (argue about
the 4th s.f.)
◮ SM Higgs v.suppressed
◮ LHCb measures
RK = 0.745+0.090
−0.074 ± 0.036
◮ In range q2 ∈ [1, 6] GeV2/c4 ◮ Only agrees with SM within 2.6σ
]
4
c /
2
[GeV
2
q
5 10 15 20
K
R
0.5 1 1.5 2 SM
LHCb LHCb
LHCb BaBar Belle
BaBar:
[Phys. Rev. D86 (2012) 032012]
Belle:
[Phys.Rev.Lett. 103 (2009) 171801]
S.Cunliffe (Imperial) FFP14 Lepton universality in B± → K±ℓ+ℓ− 18/21
SLIDE 37
Why study rare decays? The LHCb detector b→ sℓℓ Theory The operator-product expansion Observables, observables, observables Isospin asymmetry of B → K(∗)µ+µ− Angular analysis of B0 → K∗0µ+µ− Observables from the angular distribution LHCb measurement Interpretations Global fits Form factor uncertainties Lepton universality in B± → K±ℓ+ℓ− Something strange from charm Conclusions
SLIDE 38 Something strange from charm
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
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) χ
2/d.o.f=1.05
BESII e+e− → hadrons/e+e− → µ+µ−
0.5 1 1.5 2 2.5 3 3.5 3.6 3.8 4 4.2 4.4 4.6
dBr d√ q2 [B+ → K+µµ]/10−7GeV−1
Ψ(3770) Ψ(4040) Ψ(4160) Ψ(4400) a) afac b) ηcafac c) ρr ∈ R d) ρr ∈ C LHCb Ψ(4415) Ψ(2S)
LHCb data: B± → K±µ+µ−, L&Z fits
Lyon & Zwicky
[arXiv:1406.0566] ◮ Fit BESII and LHCb data ◮ Necessary to add in large corrections (fudge factors) to get good fit ◮ Are we underestimating the non-factorisable effects in Ceff 9 ?
◮ Could explain P ′
5 effect
◮ And/or motivate new physics studies in b→ ccs operators S.Cunliffe (Imperial) FFP14 Something strange from charm 19/21
SLIDE 39 Something strange from charm (loops)
ℓ ¯ cc O1,2 ℓ ℓ γ(q) b s (a) (b) ℓ O1,2 ℓ ℓ γ(q) b s ℓ
J/Ψ, Ψ′..
O1,2 ℓ ℓ γ(q) b s ℓ O1,2 ℓ ℓ γ(q) b s ℓ O1,2 b s ¯ cc O1,2 b s OG b s g ℓ ℓ γ(q) ℓ ℓ (c)
◮ Massively underestimated terms like (a) at low q2 ◮ The green gluons can’t account for this
S.Cunliffe (Imperial) FFP14 Something strange from charm 20/21
SLIDE 40
Why study rare decays? The LHCb detector b→ sℓℓ Theory The operator-product expansion Observables, observables, observables Isospin asymmetry of B → K(∗)µ+µ− Angular analysis of B0 → K∗0µ+µ− Observables from the angular distribution LHCb measurement Interpretations Global fits Form factor uncertainties Lepton universality in B± → K±ℓ+ℓ− Something strange from charm Conclusions
SLIDE 41 Conclusions
◮ FCNC processes probe higher mass scales for NP
◮ Formalism gives model-independence ◮ Observables!
◮ Interesting results in b→ sℓℓ processes
◮ Isospin asymmetry in B → K(∗)µ+µ− ◮ Angular analyses of B0 → K∗0µ+µ− ◮ Lepton universality in B± → K±ℓ+ℓ−
◮ Interest from our theory/phenomenology friends ◮ LHCb data-taking in 2015... ◮ Belle-II physics runs late 2016...
S.Cunliffe (Imperial) FFP14 Conclusions 21/21
SLIDE 42
[Backup Slides]
SLIDE 43 The actual definitions of the Wilson Operators
Heff = −4GF √ 2 e2 16π2 VtbV ∗
ts
iO′ i
O7 = e g2 ¯ mb(¯ sσµνPRb)F µν, O′
7 = e
g2 ¯ mb(¯ sσµνPLb)F µν, O9 = e2 g2 (¯ sγµPLb)(¯ ℓγµℓ), O′
9 = e2
g2 (¯ sγµPRb)(¯ ℓγµℓ), O10 = e2 g2 (¯ sγµPLb)(¯ ℓγµγ5ℓ), O′
10 = e2
g2 (¯ sγµPRb)(¯ ℓγµγ5ℓ),
S.Cunliffe (Imperial) FFP14 Backup 23/21
SLIDE 44 The actual definitions of the Wilson Operators
Ci = CSM
i
+ CNP
i
, C′
i = C′ SM i
+ C′ NP
i
.
◮ ∄ right-handed interactions i = 9, 10 operators in SM
C′ SM
9,10 = 0 ◮ ∃ helicity-suppressed right-handed SM contributions to O′ 7 so
C′
7 = ms
mb (CSM
7
+ CNP
7
) + C′ NP
7
.
S.Cunliffe (Imperial) FFP14 Backup 24/21
SLIDE 45 Angular distribution of B0 → K∗0µ+µ−
The distribution of for vector K∗0(892)
d4Γ d cos θKd cos θldφdq2 = 9 32π
1 sin2 θK + Jc 1 cos2 θK
+ (Js
2 sin2 θK + Jc 2 cos2 θK) cos 2θℓ
+ J3 sin2 θK sin2 θℓ cos 2φ + J4 sin 2θK sin 2θℓ cos φ + J5 sin 2θK sin θℓ cos φ + J6 sin2 θK cos θℓ + J7 sin 2θK sin θℓ sin φ + J8 sin 2θK sin 2θℓ sin φ + J9 sin2 θK sin2 θℓ sin 2φ
FFP14 Backup 25/21
SLIDE 46 Angular distribution of B0 → K∗0µ+µ−
The principle moments
J1s = 3 4
⊥|2 + |AL |2 + |AR ⊥|2 + |AR |2
J1c = |AL
0 |2 + |AR 0 |2
J2s = 1 4
⊥|2 + |AL |2 + |AR ⊥|2 + |AR |2
J2c = −
0 |2 + |AR 0 |2
J3 = 1 2
⊥|2 − |AL |2 + |AR ⊥|2 − |AR |2
J4 = 1 √ 2
0 AL∗
0 AR∗ )
√ 2
0 AL∗ ⊥ − AR 0 AR∗ ⊥ )
AL∗ ⊥ − AR AR∗ ⊥ )
√ 2
0 AL∗
0 AR∗ )
1 √ 2
0 AL∗ ⊥ − AR 0 AR∗ ⊥ )
AL ⊥ + AR∗ AR ⊥).
(1)
S.Cunliffe (Imperial) FFP14 Backup 26/21
SLIDE 47 The Amplitudes
Calculated in the effective field theory
AL,R
⊥
= N √ 2λ1/2 (Ceff
9
+ Ceff′
9
) ∓ (Ceff
10 + Ceff′ 10 )
mB + mK∗ + 2mb q2 (Ceff
7
+ Ceff′
7
)T1(q2)
AL,R
√ 2(m2
B − m2 K∗)
(Ceff
9
− Ceff′
9
) ∓ (Ceff
10 − Ceff′ 10 )
mB − mK∗ + 2mb q2 (Ceff
7
− Ceff′
7
)T2(q2)
AL,R = − N 2mK∗∗
(Ceff
9
− Ceff′
9
) ∓ (Ceff
10 − Ceff′ 10 )
B − m2 K∗∗ − q2)(mB + mK∗∗)A1(q2) − λ
A2(q2) mB + mK∗∗
7
− Ceff′
7
)
B + 3m2 K∗∗ − q2)T2(q2) −
λ m2
B − m2 K∗∗
T3(q2)
S.Cunliffe (Imperial) FFP14 Backup 27/21
SLIDE 48 The Amplitudes
Calculated in the effective field theory
...where N = VtbV ∗
ts
F α2
3 · 210π5m3
B
q2λ1/2βµ 1/2 , with λ = m4
B + m4 K∗ + q4 − 2(m2 Bm2 K∗ + m2 K∗q2 + m2 Bq2) and
βµ =
µ/q2.
S.Cunliffe (Imperial) FFP14 Backup 28/21
SLIDE 49 What are the Pi observables?
P ′
i ≡
Si
= 1 2 1 dΓ/dq2 Ji + ¯ Ji
P ′
5 ≡ 1
2 1 dΓ/dq2 √ 2
0 AL∗ ⊥ − AR 0 AR∗ ⊥ )
◮ The asymmetry of the cross term between the longitudinal and
perpendicularly polarised amplitudes.
S.Cunliffe (Imperial) FFP14 Backup 29/21
