Rare b-hadron decays - Warwick · 2015. 12. 3. · Rare Decays as probes for New Physics Rare decays: Flavour changing neutral currents (FCNCs) b!qdecays with q= s;dquark In theSM:

Rare b-hadron decays

Christoph Langenbruch1

1University of Warwick

Warwick EPP seminar

December 3rd, 2015

Introduction 2 / 48

Rare Decays as probes for New Physics

� Rare decays: Flavour changing neutral currents (FCNCs)b→ q decays with q = s, d quark

� In the SM: FCNCs forbidden at tree-level, only W± changes flavourbut: higher order penguin processes are possible

b st

W

Z0, γ

SM penguin diagram

b st

H±

Z0, γ

NP penguin diagram

� Loop-suppression → rare processes with B typically 10−5 . . . 10−10� New heavy particles beyond the SM can significantly contribute

� NP does not need to be produced on-shell→ masses up to O(100 TeV) accessible [A. Buras,arXiv:1505.00618]

C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays

http://arxiv.org/abs/1505.00618

Introduction 3 / 48

Effective field theory� FCNCs a multi-scale problem:

ΛNP � mW � mb � ΛQCD? & 1 TeV 80 GeV 5 GeV 0.2 GeV

� In effective field theory: Operator product expansion [A. Burashep-ph/9806471]

Heff = −4GF√

2VtbV

∗tq

∑i

CiOi︸︷︷︸+ C′iO′i︸︷︷︸� Wilson coeff. C(′)i encode short-distance physics, O

(′)i corr. operators

Well known analogon: β decay

d u

e−

ν̄e

W−

d u

e−

ν̄e

GF

Heff = GF√2 cos θC [ūγµ(1− γ5)d× ēγµ(1− γ5)νe]

� Integrate out heavy DoF → Contact interaction with effective coupling GF

Left-handed Right-handed,msmb

suppressed


http://arxiv.org/abs/hep-ph/9806471

Introduction 4 / 48

Operators

b→ sγ B → µµ b→ q``b s

γ

photon penguin

O(′)7 = eg2mb(s̄σµνPR(L)b)Fµν 3 3

b

s

`

`

electroweak penguin

O(′)9 = e2

g2(s̄γµPL(R)b)(µ̄γ

µµ)

O(′)10 = e2


µγ5µ) 33

3

b

s

`

`

(pseudo)scalar penguin

O(′)S = e2

16π2mb(s̄PR(L)b)(µ̄µ)

O(′)P = e2

16π2mb(s̄PR(L)b)(µ̄γ5µ)

3

3


b→ sγ 5 / 48

Operators


γ

photon penguin


b

s

`

`

electroweak penguin

O(′)9 = e2


µµ)

O(′)10 = e2


µγ5µ) 33

3

b

s

`

`


O(′)S = e2


O(′)P = e2


3

3


b→ sγ 6 / 48

Photon polarisation λγ with B+→ K+π−π−γ

u u

b̄ s̄B+ K+π+π−t̄

W

γ

� In SM, photons from b→ sγ decays left-handed (C ′7/C7 ∼ ms/mb)� Can probe λγ with B

+→ K+π+π−γ decays [M. Gronau et al.,PRD 66 (2002) 054008]� Up-down asymmetry Aud =

∫ +10 dcosθ

dΓdcosθ

−∫ 0−1 dcosθ

dΓdcosθ∫ +1

−1 dcosθdΓ

dcosθ

∝ λγ


http://arxiv.org/abs/hep-ph/0205065

b→ sγ 7 / 48

Composition of K+π+π− final state

]2c) [MeV/γππM(K4500 5000 5500 6000 6500

)2 cC

andi

date

s / (

50

MeV

/

0

500

1000

1500

2000

2500

3000

LHCb

]2c) [MeV/ππM(K1200 1400 1600 1800

)2 cC

andi

date

s / (

8 M

eV/

0

50

100

150

200

250

300

350

LHCb

� Signal yield NKππγ = 13 876± 153� Final state consists of several resonances:K1(1270)

+,K1(1400)+,. . .

� Different res. hard to separate, perform analysis in four mKππ bins


b→ sγ 8 / 48

First observation of γ polarisation

θcos-1 -0.5 0 0.5 1

θ d

N/d

cos

×1/

N

0

0.2

0.4

0.6

0.8

1

LHCb

2c[1.1,1.3] GeV/

θcos-1 -0.5 0 0.5 1

θ d

N/d

cos

×1/

N

0

0.2

0.4

0.6

0.8

1

LHCb

2c[1.3,1.4] GeV/

θcos-1 -0.5 0 0.5 1

θ d

N/d

cos

×1/

N

0

0.2

0.4

0.6

0.8

1

LHCb

2c[1.4,1.6] GeV/

θcos-1 -0.5 0 0.5 1

θ d

N/d

cos

×1/

N

0

0.2

0.4

0.6

0.8

1

LHCb

2c[1.6,1.9] GeV/

]2c) [MeV/ππM(K1200 1400 1600 1800

udA

-0.1

-0.05

0

0.05

0.1

LHCb

� Perform angular fit of cos θ distribution to determine Aud� Combination results in first obs. of non-zero photon polarisation at

5.2σ [PRL 112, 161801 (2014)]

� To determine precise value for λγ , resonance structure of final stateneeds to be resolved



B → µµ 9 / 48

Operators


γ

photon penguin


b

s

`

`

electroweak penguin

O(′)9 = e2


µµ)

O(′)10 = e2


µγ5µ) 33

3

b

s

`

`


O(′)S = e2


O(′)P = e2


3

3


B → µµ 10 / 48

The very rare decay B0(s)→ µµ

b̄

s

µ+

µ−

B0s W

t

t

Z0b̄

s

µ+

µ−

B0s t

W

W

νµ

� Loop and additionally helicity suppressed

� Purely leptonic final state: Theoretically and experimentally very clean

� Very sensitive to NP:Possible scalar and pseudoscalar enhanced wrt. SM axialvector

B ∝ |VtbVtq|2[(1− 4m2µ

M2B)|CS − C ′S |2 + |(CP − C ′P ) +

2mµM2B

(C10 − C ′10)|2]� SM prediction (accounting for ∆Γs 6= 0) [C. Bobeth et al.,PRL 112, 101801 (2014)]

B(B0s→ µ+µ−) = (3.66± 0.23)× 10−9

B(B0→ µ+µ−) = (1.06± 0.09)× 10−10



B → µµ 11 / 48

First observation of B0s→ µµ

]2c [MeV/−µ+µm5000 5200 5400 5600 5800

)2 cS

/(S

+B

) w

eigh

ted

cand

. / (

40 M

eV/

0

10

20

30

40

50

60 DataSignal and background

−µ+µ →s0B−µ+µ →0B

Combinatorial bkg.Semileptonic bkg.Peaking bkg.

CMS and LHCb (LHC run I)

� Combined analysis of LHCb and CMS Run 1 data, sharing signal andnuisance parameters [Nature 522 (2015) pp. 68-72]

� First obs. of B0s→ µ+µ− with 6.2σ significance (expected 7.2σ)B(B0s→ µ+µ−) = (2.8+0.7−0.6)× 10−9 compatible with SM at 1.2σ

� First evidence for B0→ µ+µ− with 3.0σ significance (expected 0.8σ)B(B0→ µ+µ−) = (3.9+1.6−1.4)× 10−10 compatible with SM at 2.2σ



B → µµ 12 / 48

The ratio R = B(B0→ µµ)/B(B0s→ µµ)

]9−[10)−µ+µ→0BB(0 0.2 0.4 0.6 0.8

LlnΔ2−

0

2

4

6

8

10SM

]9−[10)−µ+µ→s0BB(

0 2 4 6 8

LlnΔ2−

0

10

20

30

40SM

]9−[10)−µ+µ→s0BB(

0 1 2 3 4 5 6 7 8 9

]9−[1

0)− µ

+ µ→

0B

B(

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

68.27%

95.45%

99.73% 5−10

×6.3

−1

7−10

×5.7

−1

9−10

×2−1

SM


a

b

c

R0 0.1 0.2 0.3 0.4 0.5

Lln∆2−

0

2

4

6

8

10

SM and MFV


� R = B(B0→µµ)B(B0s→µµ) tests MFV hypothesis� RSM = 0.0295+0.0028−0.0025� R = 0.14+0.08−0.06 compatible at 2.3σ


b→ q`` 13 / 48

Operators


γ

photon penguin


b

s

`

`

electroweak penguin

O(′)9 = e2


µµ)

O(′)10 = e2


µγ5µ) 33

3

b

s

`

`


O(′)S = e2


O(′)P = e2


3

3


b→ q`` 14 / 48

b→ s(d)`` decays

b s(d)

αem

`+

`−

W

t

Z0, γ

SM penguin diagram

b s(d)

`+

`−

t

νµ

W

W

SM box diagram

� b→ s(d)`` decays proceed via penguin and box diagrams� B(B0s → µµ)

hel. supp.< B(b→ s``) ∼ 10−6 αem.< B(b→ sγ)

� Plenty of decays due to choice of q = s, d, lepton, hadronic resonance:

b→ sµµ B+→ K+µ+µ− [JHEP 05(2014) 082] [JHEP 09(2014) 177] [JHEP 06(2014) 133] B+→ K∗+µ+µ− [JHEP 06(2014) 133]B+→ K+π+π−µ+µ− [JHEP 10(2014) 064] B0→ K0µ+µ− [JHEP 05(2014) 082] [JHEP 06(2014) 133],B0→ K∗0µ+µ− [LHCb-PAPER-2015-051to be submitted ] B0s→ φµ+µ− [JHEP 09(2015) 179] B0s→ π+π−µ+µ− [PLB 743(2015) 46]Λ0b→ Λµ+µ− [JHEP 06(2015) 115]

b→ dµµ B+→ π+µ+µ− [JHEP 10(2015) 034] B0→ π+π−µ+µ− [PLB 743(2015) 46]b→ see B+→ K+e+e− [PRL 113(2014) 151601] B0→ K∗0e+e− [JHEP 04(2015)064]


http://arxiv.org/abs/1403.8045http://arxiv.org/abs/1408.0978http://arxiv.org/abs/1403.8044http://arxiv.org/abs/1403.8044http://arxiv.org/abs/1408.1137http://arxiv.org/abs/1403.8045http://arxiv.org/abs/1403.8044https://cds.cern.ch/record/2002772http://arxiv.org/abs/1506.08777http://arxiv.org/abs/1412.6433http://arxiv.org/abs/1503.07138http://arxiv.org/abs/1509.00414http://arxiv.org/abs/1412.6433http://arxiv.org/abs/1406.6482http://arxiv.org/abs/1501.03038

b→ q`` 15 / 48

B → V `` differential branching fraction

!"#$%&$%$"'$(

J/ψ(1S)

ψ(2S)C(′)7

C(′)7 C(′)9

C(′)9 C

(′)10

4 [m(µ)]2 q2

dΓdq2

)"*(

+,"-(*!.#)"'$(

',"#%!/01,".(&%,2(

)/,3$(,4$"('5)%2(

#5%$.5,6*((

cc̄

� q2 = m2(`+`−) provides separation power between Ci → bin in q2� Regions where J/ψ and ψ(2S) dominate are vetoed → control decays

typically 8 < q2 < 11 GeV2/c4 and 12.5 < q2 < 15 GeV2/c4


b→ q`` 16 / 48

Complication in theory: QCD effects

d̄ d̄

b s

`+

`−

W

t

Z0, γ

d̄ d̄

b s

`+

`−

W

t

Z0, γ

� Hadronic meson in initial and final state→ Predictions require non-perturbative calculation of form factors

� Predictions of B and angular obs. affected by form factor uncertainty� Ideally measure clean observables where form factors (largely) cancel

� ACP =Γ(B−→K−µ+µ−)−Γ(B+→K+µ+µ−)Γ(B−→K−µ+µ−)+Γ(B+→K+µ+µ−)

� Lepton universality, RK =B+→K+µ+µ−B+→K+e+e−

� AI =Γ(B0→K0µ+µ−)−Γ(B+→K+µ+µ−)Γ(B0→K0µ+µ−)+Γ(B+→K+µ+µ−)

� Ratios of angular obs., P(′)i basis

� Recent improvements from lattice (high q2) and LCSR (low q2)[Bharucha et al.,arXiv:1503.05534]

[Horgan et al.,PRD 89 (2014) 094501

] [Horgan et al.,PoS (Lattice2014) 372

][Du et al.,arXiv:1510.02349]


http://arxiv.org/abs/1503.05534http://arxiv.org/abs/1310.3722http://arxiv.org/abs/1501.00367http://arxiv.org/abs/1510.02349

b→ q`` | B0→ K∗0µ+µ− 17 / 48

Golden mode B0 → K∗0[→ K+π−]µ+µ−d

b̄

d

s̄B0 K∗0

µ−

µ+

t̄

W+

Z0, γ

B

K* K*

z

K

++

Figure 1. Kinematic variables of

B̄0d → K̄∗0(→ K−π+) + ¯̀̀ decays:i) the (¯̀̀ )-invariant mass squared q2,

ii) the angle θ` between ` = `− and B̄

in the (¯̀̀ ) center of mass (c.m.), iii)

the angle θK∗ between K− and B̄ in

the (K−π+) c.m. and iv) the angle φbetween the two decay planes spanned

by the 3-momenta of the (Kπ)- and

(¯̀̀ )-systems, respectively.

V is assumed to be on-shell in the narrow-resonance approximation which restricts the number

of kinematic variables to four4. Using B̄0d → K̄∗0(→ K−π+) + ¯̀̀ for illustration, they might bechosen as depicted in figure 1.

The differential decay rate, after summing over lepton spins, factorises into

8π

3

d4Γ

dq2 d cos θ` d cos θK∗ dφ= Js1 sin

2 θK∗ + Jc1 cos

2 θK∗ + (Js2 sin

2 θK∗ + Jc2 cos

2 θK∗) cos 2θ`

+J3 sin2 θK∗ sin

2 θ` cos 2φ+ J4 sin 2θK∗ sin 2θ` cosφ+ J5 sin 2θK∗ sin θ` cosφ

+(Js6 sin2 θK∗ + J

c6 cos

2 θK∗) cos θ` + J7 sin 2θK∗ sin θ` sinφ

+J8 sin 2θK∗ sin 2θ` sinφ+ J9 sin2 θK∗ sin

2 θ` sin 2φ, (1)

that is, into q2-dependent observables5 J ji (q2) and the dependence on the angles θ`, θK∗ and

φ. No additional angular dependencies can be induced by any extension of the SM operator

basis [11] as found by [12, 13]. The following simplifications arise in the limit m` → 0: Js1 = 3Js2 ,Jc1 = −Jc2 and Jc6 = 0.

The differential decay rate d4Γ̄ of the CP-conjugated decay B0d → K0∗(→ K+π−) + ¯̀̀ isobtained through the following replacements

J j1,2,3,4,7 → J̄ j1,2,3,4,7[δW → −δW ], J j5,6,8,9 → − J̄ j5,6,8,9[δW → −δW ], (2)

due to `↔ ¯̀⇒ θ` → θ` − π and φ→ −φ. The CP-violating (weak) phases δW are conjugated.The angular distribution provides twice as many observables (J ji and J̄

ji ) when the decay

and its CP-conjugate decay are measured separately. This doubles again if the ` = e and µ

lepton flavours are not averaged. Notably, CP-asymmetries can be measured in an untagged

sample of B-mesons due to the presence of CP-odd observables (i = 5, 6, 8, 9) [7]. Moreover,

T-odd observables ∼ cos δs sin δW (i = 7, 8, 9) are especially sensitive to weak BSM phases δW[10, 14] contrary to T-even ones ∼ sin δs sin δW (i = 1, . . . , 6), since the CP-conserved (strong)phase δs is often predicted to be small. Note, that in the SM CP-violating effects in b → s aredoubly-suppressed by the Cabibbo angle as Im[VubV

∗us/(VtbV

∗ts)] ≈ η̄λ ∼ 10−2.

4 The off-resonance case has been studied in [9].5 Possibilities to extract q2-integrated Jji from single-differential distributions in θ`, θK∗ or φ can be found in [10].

� Fully described by three helicity angles ~Ω = (θ`, θK , φ) and q2 = m2µµ

� Differential decay rate given by

d4Γ(B0→ K∗0µ+µ−)d~Ω dq2

=9

32π

∑i

Ii(q2)fi(~Ω)

d4Γ̄(B0→ K∗0µ+µ−)d~Ω dq2

=9

32π

∑i

Īi(q2)fi(~Ω)

� Ii(q2) and Īi(q

2) combinations of K∗0 spin amplitudesdepending on Wilson coefficients C

(′)7 , C

(′)9 , C

(′)10 and form factors


b→ q`` | B0→ K∗0µ+µ− 18 / 48

Angular observables in B0 → K∗0µ+µ−� Access to CP -averages Si and CP -asymmetries Ai

[W. Altmannshofer et al.,JHEP 01 (2009) 019

]Si =

(Ii + Īi

)/

(dΓ

dq2+

dΓ̄

dq2

)Ai =

(Ii − Īi

)/

(dΓ

dq2+

dΓ̄

dq2

)� CP -averaged angular distribution in bins of q2

1

d(Γ + Γ̄)/dq2d3(Γ + Γ̄)

d~Ω=

9

32π

[34 (1− FL) sin2 θK + FL cos2 θK

+ 14 (1− FL) sin2 θK cos 2θ` − FL cos2 θK cos 2θ`+ S3 sin

2 θK sin2 θ` cos 2φ+ S4 sin 2θK sin 2θ` cosφ

+ S5 sin 2θK sin θ` cosφ+43AFB sin

2 θK cos θ`

+ S7 sin 2θK sin θ` sinφ+ S8 sin 2θK sin 2θ` sinφ

+ S9 sin2 θK sin

2 θ` sin 2φ]

� Longitudinal polarisation fraction FL, Forward-backward asymmetry AFB

� Perform ratios of angular obs. where form factors cancel at leading orderExample: P ′5 =

S5√FL(1−FL)

[S. Descotes-Genon et al.,JHEP, 05 (2013) 137

]C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays

http://arxiv.org/abs/0811.1214http://arxiv.org/abs/1303.5794

b→ q`` | B0→ K∗0µ+µ− 19 / 48

B0→ K∗0µ+µ− selection

]2c) [GeV/µ+µ-+K(m5.2 5.3 5.4 5.5 5.6 5.7

]4 c/2[G

eV2 q

02

4

6

8

1012

14

1618

20

� -

preliminary

[LHCb-PAPER-2015-051]

� BDT to suppress combinatorial backgroundInput variables: PID, kinematic and geometric quantities, isolation variables

� Veto of B0 → J/ψK∗0 and B0 → ψ(2S)K∗0 (important control decays)and peaking backgrounds using kinematic variables and PID

� Signal clearly visible as vertical band after the full selectionC. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays

b→ q`` | B0→ K∗0µ+µ− 20 / 48

Mass model and B0→ K∗0µ+µ− signal yield

]2c) [MeV/−µ+µ−π+K(m5200 5400 5600

2 cE

vent

s / 5

.3 M

eV/

210

310

410preliminaryLHCb

B0→ J/ψK∗0control decay

]2c) [MeV/−µ+µ−π+K(m5200 5400 5600

2 cE

vent

s / 5

.3 M

eV/

0

50

100

preliminaryLHCb


B0→ K∗0µµ signal1.1 < q2 < 6.0 GeV2/c4

� Signal mass model from high statistics B0 → J/ψK∗0Correction factor from simulation to account for q2 dep. resolution

� Finer q2 binning to allow more flexible use in theory� Significant signal yield in all bins, q2 integrated Nsig = 2398± 57


b→ q`` | B0→ K∗0µ+µ− 20 / 48

Mass model and B0→ K∗0µ+µ− signal yield

]2c) [MeV/−µ+µ−π+K(m5200 5400 5600

2 cE

vent

s / 5

.3 M

eV/

0

20

40

preliminaryLHCb

]2c) [MeV/−µ+µ−π+K(m5200 5400 5600

2 cE

vent

s / 5

.3 M

eV/

0

10

20

30

40

preliminaryLHCb

]2c) [MeV/−µ+µ−π+K(m5200 5400 5600

2 cE

vent

s / 5

.3 M

eV/

0

10

20

30

preliminaryLHCb

]2c) [MeV/−µ+µ−π+K(m5200 5400 5600

2 cE

vent

s / 5

.3 M

eV/

0

20

40preliminaryLHCb

]2c) [MeV/−µ+µ−π+K(m5200 5400 5600

2 cE

vent

s / 5

.3 M

eV/

0

20

40

60preliminaryLHCb

]2c) [MeV/−µ+µ−π+K(m5200 5400 5600

2 cE

vent

s / 5

.3 M

eV/

0

20

40

preliminaryLHCb

]2c) [MeV/−µ+µ−π+K(m5200 5400 5600

2 cE

vent

s / 5

.3 M

eV/

0

20

40

60preliminaryLHCb

]2c) [MeV/−µ+µ−π+K(m5200 5400 5600

2 cE

vent

s / 5

.3 M

eV/

0

20

40preliminaryLHCb


[0.1, 0.98] GeV2/c4 [1.1, 2.5] GeV2/c4 [2.5, 4.0] GeV2/c4 [4.0, 6.0] GeV2/c4

[6.0, 8.0] GeV2/c4 [11.0, 12.5] GeV2/c4 [15.0, 17.0] GeV2/c4 [17.0, 19.0] GeV2/c4

� Signal mass model from high statistics B0 → J/ψK∗0Correction factor from simulation to account for q2 dep. resolution

� Finer q2 binning to allow more flexible use in theory� Significant signal yield in all bins, q2 integrated Nsig = 2398± 57


b→ q`` | B0→ K∗0µ+µ− 21 / 48

Acceptance effect

lθcos -1 -0.5 0 0.5 1

Eff

icie

ncy

0

0.5

1

simulationLHCb

Kθcos -1 -0.5 0 0.5 1

Eff

icie

ncy

0

0.5

1

simulationLHCb

φ-2 0 2

Eff

icie

ncy

0

0.5

1

simulationLHCb

[0.1, 1.0] GeV2/c4

[18.0, 19.0] GeV2/c4


� Trigger, reconstruction and selection distorts decay angles and q2 distribution

� Parametrize 4D efficiency using Legendre polynomials Pk

ε(cos θ`, cos θK , φ, q2) =

∑klmn

cklmnPk(cos θ`)Pl(cos θK)Pm(φ)Pn(q2)

� cklmn from moments analysis of B0 → K∗0µ+µ− phase-space MC

� Crosscheck acceptance using B0→ J/ψK∗0 control decay


b→ q`` | B0→ K∗0µ+µ− 22 / 48

Control decay B0→ J/ψK∗0

]2c) [MeV/−µ+µ−π+K(m5200 5400 5600

2 cE

vent

s / 5

.3 M

eV/

0

50

100310×

preliminaryLHCb

lθcos -1 -0.5 0 0.5 1

Eve

nts

/ 0.0

2

0

2000

4000

preliminaryLHCb

Kθcos -1 -0.5 0 0.5 1

Eve

nts

/ 0.0

2

0

2000

4000

6000

8000 preliminaryLHCb

[rad]φ-2 0 2

rad

πE

vent

s / 0

.02

0

2000

4000preliminaryLHCb


� black line: full fit, blue: signal component, red: bkg. part� Angular observables successfully reproduced [PRD 88, 052002 (2013)]



b→ q`` | B0→ K∗0µ+µ− 23 / 48

S-wave pollution

� S-wave: K+π− not from K∗0(892) but in spin 0 configuration� Introduces two add. decay amplitudes resulting in six add. observables

1

d(Γ + Γ̄)/dq2d3(Γ + Γ̄)

d~Ω

∣∣∣∣S+P

=(1− FS)1

d(Γ + Γ̄)/dq2d3(Γ + Γ̄)

d~Ω

∣∣∣∣P

+3

16πFS sin

2 θ` + S-P interference

� FS scales P-wave observables, needs to be determined precisely

� Perform simultaneous mKπfit to constrain FS

� P-wave described by rel. Breit-Wigner

� S-wave described by LASS modelcrosschecked using Isobar param.

]2c) [GeV/−π+K(m0.8 0.85 0.9 0.95

2 cE

vent

s / 1

0 M

eV/

0

20000

40000

60000preliminaryLHCb



b→ q`` | B0→ K∗0µ+µ− 24 / 48

B0→ K∗0µ+µ− Likelihood fit� Full 3 fb−1 allows first simultaneous determination of all eight

CP-averaged observables in a single fit� Allows to quote correlation matrix to include in global fit� Perform maximum likelihood fit to the decay angles and mKπµµ in q

2

bins, simultaneously fitting mKπ to constrain FS

logL =∑i

log[�(~Ω, q2)fsigPsig(~Ω)Psig(mKπµµ)

+ (1− fsig)Pbkg(~Ω)Pbkg(mKπµµ)]

+∑i

log[fsigPsig(mKπ) + (1− fsig)Pbkg(mKπ)

]� Psig(Ω) given by 1d(Γ+Γ̄)/dq2

d3(Γ+Γ̄)

d~Ω

∣∣∣S+P

� Pbkg(Ω) modelled with 2nd order Chebychev polynomials.� Feldman-Cousins method [G. Feldman et al., PRD 57 3873-3889]

to ensure correct coverage at low statistics


http://arxiv.org/abs/physics/9711021

b→ q`` | B0→ K∗0µ+µ− 25 / 48

B0→ K∗0µ+µ− likelihood projections [1.1, 6.0] GeV2/c4

lθcos -1 -0.5 0 0.5 1

Eve

nts

/ 0.1

0

20

40

60preliminaryLHCb

Kθcos -1 -0.5 0 0.5 1

Eve

nts

/ 0.1

0

50

100 preliminaryLHCb

[rad]φ-2 0 2

πE

vent

s / 0

.1

0

20

40

60preliminaryLHCb

]2c) [MeV/−µ+µ−π+K(m5200 5400 5600

2 cE

vent

s / 5

.3 M

eV/

0

50

100

preliminaryLHCb

]2c) [GeV/−π+K(m0.8 0.85 0.9 0.95

2 cE

vent

s / 1

0 M

eV/

0

50

100

preliminaryLHCb

[LH

Cb

-PA

PE

R-2

01

5-0

51

]

� Efficiency corrected distributions show good agreementwith overlaid projections of the probability density function


b→ q`` | B0→ K∗0µ+µ− 26 / 48

B0→ K∗0µ+µ− systematic uncertainties

Source FL S3–S9 A3–A9 P1–P′8

Acceptance stat. uncertainty < 0.01 < 0.01 < 0.01 < 0.01Acceptance polynomial order < 0.01 < 0.02 < 0.02 < 0.04

Data-simulation differences 0.01–0.02 < 0.01 < 0.01 < 0.01Acceptance variation with q2 < 0.01 < 0.01 < 0.01 < 0.01

m(K+π−) model < 0.01 < 0.01 < 0.01 < 0.03Background model < 0.01 < 0.01 < 0.01 < 0.02

Peaking backgrounds < 0.01 < 0.01 < 0.01 < 0.01m(K+π−µ+µ−) model < 0.01 < 0.01 < 0.01 < 0.02

Det. and prod. asymmetries – – < 0.01 < 0.02

� Systematic uncertainties determined using high statistics toys

� Measurement is statistically dominated (and will still be in Run 2)


b→ q`` | B0→ K∗0µ+µ− 27 / 48

B0→ K∗0µ+µ− Results: FL, S3, S4, S5

]4c/2 [GeV2q0 5 10 15

LF

0

0.2

0.4

0.6

0.8

1

LHCb

SM from ABSZ

]4c/2 [GeV2q0 5 10 15

3S

-0.5

0

0.5LHCb

SM from ABSZ

]4c/2 [GeV2q0 5 10 15

4S

-0.5

0

0.5LHCb

SM from ABSZ

]4c/2 [GeV2q0 5 10 15

5S

-0.5

0

0.5LHCb

SM from ABSZ

[LH

Cb

-PA

PE

R-2

01

5-0

51

]

prelim.prelim.

prelim.prelim.

[1503.05534][1411.3161][1503.05534][1411.3161]

[1503.05534][1411.3161][1503.05534][1411.3161]


http://arxiv.org/abs/1503.05534http://arxiv.org/abs/1411.3161http://arxiv.org/abs/1503.05534http://arxiv.org/abs/1411.3161http://arxiv.org/abs/1503.05534http://arxiv.org/abs/1411.3161http://arxiv.org/abs/1503.05534http://arxiv.org/abs/1411.3161

b→ q`` | B0→ K∗0µ+µ− 28 / 48

B0→ K∗0µ+µ− Results: AFB, S7, S8, S9

]4c/2 [GeV2q0 5 10 15

FBA

-0.5

0

0.5

LHCb

SM from ABSZ

]4c/2 [GeV2q0 5 10 15

7S

-0.5

0

0.5LHCb

]4c/2 [GeV2q0 5 10 15

8S

-0.5

0

0.5LHCb

]4c/2 [GeV2q0 5 10 15

9S

-0.5

0

0.5LHCb

prelim.

prelim.

prelim.prelim.

[LH

Cb

-PA

PE

R-2

01

5-0

51

]

[1503.05534][1411.3161]



b→ q`` | B0→ K∗0µ+µ− 29 / 48

B0→ K∗0µ+µ− CP asymmetries: A3, A4, A5, A6s

]4c/2 [GeV2q0 5 10 15

3A

-0.5

0

0.5LHCb

]4c/2 [GeV2q0 5 10 15

4A

-0.5

0

0.5LHCb

]4c/2 [GeV2q0 5 10 15

5A

-0.5

0

0.5LHCb

]4c/2 [GeV2q0 5 10 15

6sA

-0.5

0

0.5LHCb

[LH

Cb

-PA

PE

R-2

01

5-0

51

]

prelim.prelim.

prelim.prelim.


b→ q`` | B0→ K∗0µ+µ− 30 / 48

B0→ K∗0µ+µ− CP asymmetries: A7, A8, A9

]4c/2 [GeV2q0 5 10 15

7A

-0.5

0

0.5LHCb

]4c/2 [GeV2q0 5 10 15

8A

-0.5

0

0.5LHCb

]4c/2 [GeV2q0 5 10 15

9A

-0.5

0

0.5LHCb

[LH

Cb

-PA

PE

R-2

01

5-0

51

]

prelim.prelim.

prelim.


b→ q`` | B0→ K∗0µ+µ− 31 / 48

P ′5

]4c/2 [GeV2q0 5 10 15

5'P

-1

-0.5

0

0.5

1

LHCb

SM from DHMV

prelim.


[1407.8526]

� Tension seen in P ′5 in [PRL 111, 191801 (2013)] confirmed� [4.0, 6.0] and [6.0, 8.0] GeV2/c4 local deviations of 2.8σ and 3.0σ

� Compatible with 1 fb−1 measurement



b→ q`` | B0→ K∗0µ+µ− 32 / 48

Compatibility with the SM

)9C(Re3 3.5 4 4.5

2 χ∆

0

5

10

15

LHCb

SM

prelim. [LH

Cb

-PA

PE

R-2

015-

051]

� Perform χ2 fit of measured Si observables using [EOS] software

� Varying Re(C9) and incl. nuisances according [F. Beaujean et al.,EPJC 74 (2014) 2897]� ∆Re(C9) = −1.04± 0.25 with global significance of 3.4σ


http://project.het.physik.tu-dortmund.de/eos/http://arxiv.org/abs/1310.2478

b→ q`` | B0s→ φµ+µ− 33 / 48

The rare decay B0s → φ[→ K+K−]µ+µ−

s

b̄

s

s̄

B0s φ

µ−

µ+

t̄

W+

Z0, γ

1

10

210

310

]2c) [GeV/−µ+µ−

K+K(m 5.3 5.4 5.5

]4

c/2

[G

eV

2q

0

2

4

6

8

10

12

14

16

18

LHCb [JH

EP

09(2

015)

179]

� Dominant b→ sµ+µ− decay for B0s , analogous to B0→ K∗0µ+µ−� K+K−µ+µ− final state not self-tagging→ reduced number of angular observables: FL, S3,4,7, A5,6,8,9

� Signal yield lower due to fsfd ∼14 ,

B(φ→K+K−)B(K∗0→K+π−) =

34

� Clean selection due to narrow φ resonance, S-wave negligible



b→ q`` | B0s→ φµ+µ− 34 / 48

B0s→ φµ+µ− mass model

]2c [MeV/)−µ+µ−K+m(K5300 5400 5500

2 cE

vent

s / 1

0 M

eV/

50

100LHCb

−µ+µφ→0sB

]2c [MeV/)−µ+µ−K+m(K5300 5400 5500

2 cE

vent

s / 1

0 M

eV/

5000

10000

15000 LHCbφψ/J →0sB

[JHEP 09 (2015) 179]

� Signal mass model (double CB) taken from B0s→ J/ψφq2 dep. resolution accounted for with scale factor from simulation

� Background described using Exponential

� Signal yield Nφµµ = 432± 24 (q2-integrated)� B0s→ J/ψφ yield NJ/ψφ = 62 033± 260



b→ q`` | B0s→ φµ+µ− 35 / 48

B0s→ φµ+µ− differential branching fraction

]2c [MeV/)−µ+µ−K+m(K5300 5400 5500

2 cE

vent

s / 1

0 M

eV/

10

20LHCb

4c/2 < 2 GeV2q0.1 <

]2c [MeV/)−µ+µ−K+m(K5300 5400 5500

2 cE

vent

s / 1

0 M

eV/

5

10

15

20

25

LHCb4c/2 < 5 GeV2q2 <

]2c [MeV/)−µ+µ−K+m(K5300 5400 5500

2 cE

vent

s / 1

0 M

eV/

10

20

30LHCb

4c/2 < 8 GeV2q5 <

]2c [MeV/)−µ+µ−K+m(K5300 5400 5500

2 cE

vent

s / 1

0 M

eV/

5

10

15

20 LHCb4c/2 < 12.5 GeV2q11 <

]2c [MeV/)−µ+µ−K+m(K5300 5400 5500

2 cE

vent

s / 1

0 M

eV/

10

20LHCb

4c/2 < 17 GeV2q15 <

]2c [MeV/)−µ+µ−K+m(K5300 5400 5500

2 cE

vent

s / 1

0 M

eV/

5

10

15 LHCb4c/2 < 19 GeV2q17 <

]2c [MeV/)−µ+µ−K+m(K5300 5400 5500

2 cE

vent

s / 1

0 M

eV/

10

20

30 LHCb4c/2 < 6 GeV2q1 <

]2c [MeV/)−µ+µ−K+m(K5300 5400 5500

2 cE

vent

s / 1

0 M

eV/

10

20

30

40 LHCb4c/2 < 19 GeV2q15 <

[JHEP 09 (2015) 179]

� B0s→ J/ψφ used for normalisation� Differential branching fraction:

dB(B0s→ φµ+µ−)dq2

=1

q2max. − q2min.× NφµµNJ/ψφ

× �φµµ�J/ψφ

× B(B0s→ J/ψφ)× B(J/ψ→ µ+µ−)

��φµµ�J/ψφ

from (corrected) simulation, many effects cancel in ratio



b→ q`` | B0s→ φµ+µ− 36 / 48

B0s→ φµ+µ− differential branching fraction

]4c/2 [GeV2q5 10 15

]4

c-2

GeV

-8 [

10

2q

)/d

µµ

φ→

s0B

dB

( 0

1

2

3

4

5

6

7

8

9

SM pred.SM (wide)SM LQCDDataData (wide)

LHCb

[JH

EP

09(2

015)

179]

� In 1 < q2 < 6 GeV2/c4 diff. B more than 3σ below SM prediction� Confirming deviation seen in 1 fb−1 analysis [JHEP 07 (2013) 084]� Most precise measurement of relative and total branching fraction

B(B0s→ φµ+µ−)B(B0s→ J/ψφ)

= (7.41+0.42−0.40 ± 0.20± 0.21)× 10−4,

B(B0s→ φµ+µ−) = (7.97+0.45−0.43 ± 0.22± 0.23± 0.60)× 10−7,



b→ q`` | B0s→ φµ+µ− 37 / 48

B0s→ φµ+µ− angular analysis

� Non-flavour specific final state → reduced number of accessibleobservables 4 CP averages, 4 CP asymmetries

1

d(Γ + Γ̄)/dq2d3(Γ + Γ̄)

d~Ω=

9

32π

[34(1− FL) sin2 θK + FL cos2 θK + 14(1− FL) sin2 θK cos 2θ`

− FL cos2 θK cos 2θ` + S3 sin2 θK sin2 θ` cos 2φ+ S4 sin 2θK sin 2θ` cosφ+A5 sin 2θK sin θ` cosφ

+A6 sin2 θK cos θ` + S7 sin 2θK sin θ` sinφ

+A8 sin 2θK sin 2θ` sinφ+A9 sin2 θK sin

2 θ` sin 2φ]

� ub. ML fit in m(K+K−µ+µ−) and {cos θ`, cos θK , φ} in bins of q2� Angular background modelled with 2nd order Chebyshev polynomials

� Same acceptance method used as for B0→ J/ψK∗0cross-checked using B0s→ J/ψφ

� Feldman-Cousins method due to very limited statistics


b→ q`` | B0s→ φµ+µ− 38 / 48


]4c/2 [GeV2q5 10 15

LF

-0.5

0.0

0.5

1.0

1.5LHCb

]4c/2 [GeV2q5 10 15

3S

-1.0

-0.5

0.0

0.5

1.0LHCb

SM pred.SM (wide)DataData (wide)

]4c/2 [GeV2q5 10 15

4S

-1.0

-0.5

0.0

0.5

1.0LHCb

]4c/2 [GeV2q5 10 15

7S

-1

-0.5

0

0.5

1LHCb

[JHEP 09 (2015) 179]

� Good agreement of angular obs. with SM predictions



b→ q`` | B0s→ φµ+µ− 39 / 48


]4c/2 [GeV2q5 10 15

5A

-1

-0.5

0

0.5

1LHCb

]4c/2 [GeV2q5 10 15

6A

-1

-0.5

0

0.5

1LHCb

]4c/2 [GeV2q5 10 15

8A

-1

-0.5

0

0.5

1LHCb

]4c/2 [GeV2q5 10 15

9A

-1

-0.5

0

0.5

1LHCb

[JHEP 09 (2015) 179]

� Good agreement of angular obs. with SM predictions



b→ q`` | b→ sµ+µ− branching fractions 40 / 48

B → K(∗)µ+µ− branching fraction measurements� Number of signal events in full 3 fb−1 data sample

B0 → K0Sµ+µ− B+ → K+µ+µ B0 → K∗0µ+µ− B+ → K∗+µ+µ−Nsig 176± 17 4746± 81 2361± 56 162± 16

� Normalise with respect to B0 → J/ψK0S(K∗0) and B+ → J/ψK+(K∗+)� Differential branching fractions

]4c/2 [GeV2q0 5 10 15 20

]2/G

eV4 c ×

-8 [

102 q

/dBd 0

1

2

3

4

5

LCSR Lattice Data

LHCb

−µ+µ+ K→+B

]4c/2 [GeV2q0 5 10 15 20

]2/G

eV4 c ×

-8 [

102 q

/dBd 0

1

2

3

4

5

LCSR Lattice Data

−µ+µ0 K→0BLHCb

[JH

EP

06(2

014)

133]

[JH

EP

06(2

014)

133]

� Compatible with but lower than SM predictions

Light cone sum rules (LCSR):[

P. Ball et al.,PRD 71 (2005) 014029

] [A. Khodjamirian et al.,JHEP 09 (2010) 089

]Lattice:

[R. Horgan et al.,PRD 89 (2014) 094501

] [C. Bouchard et al.,PRD 88 (2013) 054509

]� dB(B0 → K∗0µ+µ−)/dq2 with 3 fb−1 in preparation


http://arxiv.org/abs/1403.8044http://arxiv.org/abs/1403.8044http://arxiv.org/abs/hep-ph/0412079http://arxiv.org/abs/1006.4945http://arxiv.org/abs/1310.3722http://arxiv.org/abs/1306.2384

b→ q`` | b→ sµ+µ− branching fractions 40 / 48

B → K(∗)µ+µ− branching fraction measurements� Number of signal events in full 3 fb−1 data sample

B0 → K0Sµ+µ− B+ → K+µ+µ B0 → K∗0µ+µ− B+ → K∗+µ+µ−Nsig 176± 17 4746± 81 2361± 56 162± 16

� Normalise with respect to B0 → J/ψK0S(K∗0) and B+ → J/ψK+(K∗+)� Differential branching fractions

]4c/2 [GeV2q0 5 10 15 20

]2/G

eV4 c ×

-8 [

102 q

/dBd 0

5

10

15

20LCSR Lattice Data

LHCb

−µ+µ*+ K→+B

]4c/2 [GeV2q0 5 10 15 20

]-2

GeV

4 c × -7

[10

2q

/dBd

0

0.5

1

1.5

LHCb

Theory BinnedLHCb

[JH

EP

06(2

014)

133]

[JH

EP

08(2

013)

131]

B0→ K∗0µ+µ−

� Compatible with but lower than SM predictions

Light cone sum rules (LCSR):[

P. Ball et al.,PRD 71 (2005) 014029

] [A. Khodjamirian et al.,JHEP 09 (2010) 089

]Lattice:

[R. Horgan et al.,PRD 89 (2014) 094501

] [C. Bouchard et al.,PRD 88 (2013) 054509

]� dB(B0 → K∗0µ+µ−)/dq2 with 3 fb−1 in preparation


http://arxiv.org/abs/1403.8044http://arxiv.org/abs/1304.6325http://arxiv.org/abs/hep-ph/0412079http://arxiv.org/abs/1006.4945http://arxiv.org/abs/1310.3722http://arxiv.org/abs/1306.2384

Global b→ s fits 41 / 48

Global fits to b→ s data[W. Altmannshofer et al.,EPJC 75 (2015) 382

] [S. Descotes-Genon et al.,arXiv:1510.04239

]

Angular observablesBranching fractionsCombined

� Combine exp. information from rare b→ s processes in global fit of Cib→ sγ, B(B0s→ µ+µ−), Ang.(B0→ K∗0µ+µ−), Ang.+B(B0s→ φµ+µ−), B(B0,+ → K0,+(∗)µ+µ−), . . .B-fact. LHCb+CMS LHCb 3 fb−1 LHCb 1 fb−1 (3 fb−1) LHCb 3 fb−1 (1 fb−1)

� Tension can be reduced with ∆Re(C9) ∼ −1, significances around 4σ� Consistency between angular observables and branching fractions


http://arxiv.org/abs/1411.3161http://arxiv.org/abs/1510.04239http://arxiv.org/abs/1411.4413https://cds.cern.ch/record/2002772http://arxiv.org/abs/1305.2168http://arxiv.org/abs/1506.08777http://arxiv.org/abs/1403.8044http://arxiv.org/abs/1304.6325


NP or hadronic effect?

b s

µ−

µ+

Z ′

Possible NP

b s

d̄ d̄

c̄c

γ

`+

`−cc̄ loop

� Possible explanations for shift in C9� NP e.g. Z ′ [Gauld et al.] [Buras et al.][Altmannshofer et al.] [Crivellin et al.] Leptoquarks

[Hiller et al.] [Biswas et al.][Buras et al.] [Gripaios et al.]

� hadronic charm loop contributions

� q2 dependence: cc̄ loops rise towards J/ψ, NP q2-independent


http://arxiv.org/abs/1308.1959http://arxiv.org/abs/1309.2466http://arxiv.org/abs/1308.1501http://arxiv.org/abs/1501.00993http://arxiv.org/abs/1408.1627http://arxiv.org/abs/1409.0882http://arxiv.org/abs/1409.4557http://arxiv.org/abs/1412.1791


NP or hadronic effect?

[W. Altmannshofer et al.,arXiv:1503.06199

] [S. Descotes-Genon et al.,arXiv:1510.04239

]

� Possible explanations for shift in C9� NP e.g. Z ′ [Gauld et al.] [Buras et al.][Altmannshofer et al.] [Crivellin et al.] Leptoquarks

[Hiller et al.] [Biswas et al.][Buras et al.] [Gripaios et al.]

� hadronic charm loop contributions

� q2 dependence: cc̄ loops rise towards J/ψ, NP q2-independent


http://arxiv.org/abs/1503.06199http://arxiv.org/abs/1510.04239http://arxiv.org/abs/1308.1959http://arxiv.org/abs/1309.2466http://arxiv.org/abs/1308.1501http://arxiv.org/abs/1501.00993http://arxiv.org/abs/1408.1627http://arxiv.org/abs/1409.0882http://arxiv.org/abs/1409.4557http://arxiv.org/abs/1412.1791

B+→ π+µ+µ− 43 / 48

The b→ dµ+µ− decay B+→ π+µ+µ−

u

b̄

u

d̄

B+ π+

µ−

µ+

t̄

W+

Z0, γ

)2) (MeV/c-µ+µ+π(m5200 5400 5600 5800 6000

)2 cC

andi

date

s / (

30

MeV

/

0

10

20

30

40

50

60

70

LHCb-µ+µ+π→+B-µ+µ+K→+B

ν+µ0

D→+B-µ+µ0,+ρ→0,+B

-µ+µ0f→s0B

Combinatorial

[JHEP 10 (2015) 034]

� b→ dµ+µ− transition in SM sup. by∣∣∣VtdVts ∣∣∣2 ∼ 125 wrt. b→ sµ+µ−

� Measure diff. branching fraction and ACP (O(−0.1) in the SM)� Assuming SM, measure |Vtd/Vts|, |Vtd|, |Vts| using B+→ K+µ+µ−|Vtd|2 = B(B

+→π+µ+µ−)∫Fπdq2

and |Vts|2 = B(B+→K+µ+µ−)∫FKdq2



B+→ π+µ+µ− 43 / 48

The b→ dµ+µ− decay B+→ π+µ+µ−

u

b̄

u

d̄

B+ π+

µ−

µ+

t̄

W+

Z0, γ

)2) (MeV/c-µ+µ+K(m5200 5400 5600 5800 6000

)2 cC

andi

date

s / (

10

MeV

/

0

100

200

300

400

500

600

LHCb-µ+µ+K→+BX-µ+µ+K→+B

Combinatorial

[JHEP 10 (2015) 034]

� b→ dµ+µ− transition in SM sup. by∣∣∣VtdVts ∣∣∣2 ∼ 125 wrt. b→ sµ+µ−

� Measure diff. branching fraction and ACP (O(−0.1) in the SM)� Assuming SM, measure |Vtd/Vts|, |Vtd|, |Vts| using B+→ K+µ+µ−|Vtd|2 = B(B

+→π+µ+µ−)∫Fπdq2

and |Vts|2 = B(B+→K+µ+µ−)∫FKdq2



B+→ π+µ+µ− 44 / 48

B+→ π+µ+µ− diff. B, ACP and CKM matrix elements

)4c/2 (GeV2q0 10 20

)4 c-2

GeV

-9 (

102 q

dB/d

0

0.5

1

1.5

2

2.5LHCb APR13 HKR15 FNAL/MILC15

LHCb

)4c/2 (GeV2q0.2 0.4 0.6 0.8 1

)4 c/2C

andi

date

s / (

0.0

5 G

eV

0

2

4

6

8

10

LHCb

[JHEP 10 (2015) 034]

� Good agreement with but slightly lower than SM predictionsAPR13 [PRD 89 (2014) 094021] HKR15 [PRD 92 (2015) 074020] FNAL/MILC15 [PRL 115 (2015) 152002]

� B = (1.83± 0.24± 0.05)× 10−8 and ACP = −0.11± 0.12± 0.01� |VtdVts | = 0.24

+0.05−0.04, |Vtd| = 7.2+0.9−0.8 × 10−3 and |Vts| = 3.2+0.4−0.4 × 10−2

� New lattice predictions from MILC collaboration [D. Du et al.,arXiv:1510.02349]→ CKM elements from RDs competitive with B(s) oscillation meas.→ Combined 2σ tension of B(B+→ K+(π+)µ+µ−) with SM prediction


http://arxiv.org/abs/1509.00414http://arxiv.org/abs/1312.2523http://arxiv.org/abs/1506.07760http://arxiv.org/abs/1507.01618http://arxiv.org/abs/1510.02349

B+→ π+µ+µ− 45 / 48

Test of lepton universality in B+ → K+`+`−� RK = B(B

+→K+µ+µ−)B(B+→K+e+e−) = 1±O(10−3) in the SM, not affected by cc̄ loops

1

10

210

310

410

]2c) [MeV/−µ+µ+K(m4800 5000 5200 5400 5600

]4 c/2 [

GeV

2 q

0

5

10

15

20

25

LHCb (a)

1

10

210

310

]2c) [MeV/−e+e+K(m4800 5000 5200 5400 5600

]4 c/2 [

GeV

2 q

0

5

10

15

20

25

LHCb (b)

[PR

L11

3,15

1601

(201

4)]B+ → K+µ+µ− B+ → K+e+e−

ψ(2S)K+

J/ψK+

ψ(2S)K+

J/ψK+

radiative tails radiative tails

� Experimental challenges for B+ → K+e+e− mode1. Trigger 2. Bremsstrahlung

� Use double ratio to cancel systematic uncertainties

RK =(NK+µ+µ−NK+e+e−

)(NJ/ψ (e+e−)K+NJ/ψ (µ+µ−)K+

)(�K+e+e−�K+µ+µ−

)(�J/ψ (µ+µ−)K+�J/ψ (e+e−)K+

)� Use B+→ J/ψK+ as cross-check



B+→ π+µ+µ− 46 / 48

Test of lepton universality in B+ → K+`+`−

]2c) [MeV/−e+e+K(m5000 5200 5400 5600

)2 cC

andi

date

s / (

40

MeV

/

0

5

10

310×

LHCb

(a)

]2c) [MeV/−e+e+K(m5000 5200 5400 5600

)2 cC

andi

date

s / (

40

MeV

/

0

10

20

30

40 LHCb

(d)

]4c/2 [GeV2q0 5 10 15 20

KR

0

0.5

1

1.5

2

SM

LHCbLHCb

LHCb BaBar Belle

B+ → J/ψ (→ e+e−)K+ B+ → K+e+e−

triggered on e triggered on e

[arx

iv:1

406.

6482

]

� Use theoretically and experimentallyfavoured q2 region ∈ [1, 6] GeV2

� RK = 0.745+0.090−0.074(stat.)± 0.036(syst.),compatible with SM at 2.6σ

� Bq2∈[1,6] GeV2(B+ → K+e+e−) =(1.56+0.19−0.15

+0.06−0.04)× 10−7



Lepton universality 47 / 48

Lepton universality and lepton flavour violation� Due to the cleanness of the SM prediction, RK received a lot of attention[

Glashow et al.PRL 114 (2015) 091801

] [Hiller et al.PRD 90 (2014) 054014

] [Crivellin et al.PRL 114 (2015) 151801

]� Including RK in global fits increases tension with SM hypothesis

� Naturally motivates RK∗ =B(B0→K∗0µ+µ−)B(B0→K∗0e+e−) and Rφ =

B(B0s→φµ+µ−)B(B0s→φe+e−)

� Also motivates searches for lepton flavour violation[

Glashow et al.PRL 114 (2015) 091801

]“Lepton non-universality generally implies lepton flavour violation”

� B(B→ K(∗)µ±e∓) [B(B→ K(∗)µ±τ∓)] could be O(10−8) [O(10−6)]� Other anomalies

[One Leptoquark to Rule Them All: A Minimal Explanationfor RD∗, RK and (g − 2)µ,M. Bauer et al., arXiv:1511.01900

]Explain RK and h→ µτ [

A.

Crivellin

etal.

PR

L1

14

(20

15

)1

51

80

1 ]

[ R.

Alo

nso

etal.

arXiv:1

50

5.0

51

64 ]

RK , RD∗ and B−→ τ−ν̄


http://arxiv.org/abs/1411.0565http://arxiv.org/abs/1408.1627http://arxiv.org/abs/1501.00993http://arxiv.org/abs/1411.0565http://arxiv.org/abs/1511.01900http://arxiv.org/abs/1501.00993http://arxiv.org/abs/1505.05164

Conclusions 48 / 48

Conclusions

� Rare B decays are an excellent laboratory to search for BSM effects

� LHCb an ideal environment to study these decays

� Most measurements in good agreement with SM predictions,setting strong constraints on NP

� However, several interesting tensions in rare b→ s`` decays:P ′5 in B

0→ K∗0µ+µ−, B(B0s→ φµ+µ−), RK� Consistent NP explanations exist

� But unexpectedly large hadronic effectscan not yet be excluded

� Looking forward to the additionaldata from Run 2

� 5-6 fb−1 at√s = 13 TeV expected


Backup 49 / 48

Complementarity of flavour and direct searches

Figure by D. Straub


Backup 50 / 48

The LHC as heavy flavour factory

bb̄ polar angles

� bb̄ produced correlated predominantly in forward (backward) direction→ single arm forward spectrometer (2 < η < 5)

� Large bb̄ production cross sectionσbb̄ = (75.3± 14.1)µb [Phys.Lett. B694 (2010)] in acceptance

� ∼ 1× 1011 produced bb̄ pairs in 2011, excellent environment to studyB0 → K∗0µ+µ− and other rare decays



Backup 51 / 48

The LHCb detector: Tracking

Tracking system

Vertexdetector

Interactionpoint

PV

SVL ∼ 7 mmB0

IP

µ+

µ−π−

K+

p p

B0 → K∗0µ+µ− signature

� Excellent Impact Parameter (IP) resolution (20µm)→ Identify secondary vertices from heavy flavour decays

� Proper time resolution ∼ 45 fs→ Good separation of primary and secondary vertices

� Excellent momentum (δp/p ∼ 0.5− 1.0%) and inv. mass resolution→ Low combinatorial background


Backup 52 / 48

The LHCb detector: Particle identification and Trigger

Muon system

RICH1

RICH2 K/π separation [arxiv:1211.6759]

� Excellent Muon identification �µ→µ ∼ 97% �π→µ ∼ 1-3%� Good Kπ separation via RICH detectors �K→K ∼ 95% �π→K ∼ 5%→ Reject peaking backgrounds

� High trigger efficiencies, low momentum thresholdsMuons: pT > 1.76 GeV at L0, pT > 1.0 GeV at HLT1B → µµX: �Trigger ∼ 90%



Backup 53 / 48

Data taken by LHCb


Backup 54 / 48

Moments analysis

]4c/2 [GeV2q0 5 10 15

FBA

-0.5

0

0.5

LHCb

SM from ABSZLikelihood fitMethod of moments

]4c/2 [GeV2q0 5 10 15

5'P

-2

-1

0

1

2

LHCb

SM from DHMVLikelihood fitMethod of moments

prelim.

prelim.


� Angular terms fi(~Ω) are orthogonal→ can determine obs. via their moments M̂i = 1∑

e we

∑ewefi(

~Ωe)

� 10-30% less sensitive than Maximum Likelihood fit [F. Beaujean et al.,PRD 91 (2015) 114012]but allows narrow 1 GeV2/c4 wide q2 bins

� Consistency of the results checked using toys



Backup 55 / 48

Amplitude fit and Zero-crossing points

]4c/2 [GeV2q2 3 4 5 6

FBA

-0.5

0

0.5LHCb

Likelihood fitMethod of moments

Amplitude fit

]4c/2 [GeV2q2 3 4 5 6

5S

-0.5

0

0.5LHCb

Likelihood fitMethod of moments

Amplitude fit

prelim.prelim.


� Zero-crossing points sensitive tests of SM, form factor uncertainties cancel

� Perform q2 dependent amplitude fit with AnsatzAL,R0,‖,⊥ = α+ βq2 + γ 1q2 in the region 1.1 < q2 < 6 GeV2/c4

� Resulting zero crossing points in good agreement with SM predictionsq20(AFB) ∈ [3.40, 4.87] GeV2/c4 @ 68% CL,q20(S4) < 2.65 GeV

2/c4 @ 95% CL,

q20(S5) ∈ [2.49, 3.95] GeV2/c4 @ 68% CL


Backup 56 / 48

Search for hidden sector boson in B0→ K∗0µ+µ−

b

d

Vtb Vtss

d

µ−

µ+

t

W+

χ

B0 K∗0

) [MeV]−µ+µ(m1000 2000 3000 4000

Can

dida

tes

/ 10

MeV

5

10

15

20Prompt

DisplacedLHCb

ω φ ψJ/ (3770)ψ(2S)+ψ

200

[PRL 115 (2015) 161802]

� Search for hidden sector boson in B0→ K∗0χ with χ→ µ+µ−

� Scan m(µ+µ−) distribution for an excess of χ signal candidates

� Search for prompt and displaced (τ(µ+µ−) > 3στ(µ+µ−)) χ vertices

� Narrow resonances (ω, φ, J/ψ, ψ(2S), ψ(3770)) are vetoed

� Normalisation to B0→ K∗0µ+µ− in 1.1 < q2 < 6.0 GeV2/c4

� No excess → Upper limits on B(B0→ K∗0χ(→ µ+µ−)) set at 95% CL



Backup 56 / 48

Search for hidden sector boson in B0→ K∗0µ+µ−

b

d

Vtb Vtss

d

µ−

µ+

t

W+

χ

B0 K∗0

) [MeV]−µ+µ(m1000 2000 3000 4000

-210

-110

1LHCb

=1000psτ

=100psτ

=10psτ

))−µ

+µ(

χ*0

K →0

B(B

2)[

1.1,

6.0]

GeV

−µ

+µ

*0K

→0B(

B

))−

µ +µ(

χ*0

K → 0

B(B

-910

-810

-710

[PRL 115 (2015) 161802]

� Search for hidden sector boson in B0→ K∗0χ with χ→ µ+µ−

� Scan m(µ+µ−) distribution for an excess of χ signal candidates

� Search for prompt and displaced (τ(µ+µ−) > 3στ(µ+µ−)) χ vertices

� Narrow resonances (ω, φ, J/ψ, ψ(2S), ψ(3770)) are vetoed

� Normalisation to B0→ K∗0µ+µ− in 1.1 < q2 < 6.0 GeV2/c4

� No excess → Upper limits on B(B0→ K∗0χ(→ µ+µ−)) set at 95% CL



Backup 57 / 48

Exclusion limits for specific models

) [MeV]−µ+µ(m400 600 800 1000

2 θ

-810

-710

-610

-510

-410

LHCb

Theory

Theory

CH

AR

M

) [MeV]−µ+µ(m1000 2000 3000 4000

0.5

1

1

2

)=10 T

eVh(

m [PeV

], β 2

)tanχ(

f

)=1

TeV

h(m

[Pe

V],

β2

)tan

χ(f

hadrons) = 0→χ(B hadrons) = 0.99→χ(B

LHCb

[PRL 115 (2015) 161802]

Resulting 95% CL exclusion limits for specific models

� Axion model [M. Freytsis et al., PRD 81 (2010) 034001]Exclusion regions for large tanβ, large m(h)

� Inflaton model [F. Bezrukov et al., PLB 736 (2014) 494]Constraints on mixing angle θ between Higgs and inflaton fields


http://arxiv.org/abs/1508.04094http://arxiv.org/abs/0911.5355http://arxiv.org/abs/1403.4638

Backup 58 / 48

B → K(∗)µ+µ− isospin

� Isospin asymmetry AI =B(B0→K(∗)0µ+µ−)− τ0

τ+B(B+→K(∗)+µ+µ−)

B(B0→K(∗)0µ+µ−)+ τ0τ+B(B+→K(∗)+µ+µ−)

� SM prediction for AI is O(1%)

]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 *

[JH

EP

06(2

014)

133]

� Results with 3 fb−1 consistent with SM� p-value for deviation of AI(B → Kµµ) from 0 is 11% (1.5σ)



Backup 59 / 48

Reminder: B0 → K∗0µ+µ− angular observables (1 fb−1)

]4c/2 [GeV2q0 5 10 15 20

LF

0

0.2

0.4

0.6

0.8

1

Theory BinnedLHCb

LHCb

]4c/2 [GeV2q0 5 10 15 20

FB

A

-1

-0.5

0

0.5

1

LHCb

Theory BinnedLHCb

[JHEP 08 (2013) 131]

� Angular observables in good agreement withSM prediction [C. Bobeth et al. JHEP 07 (2011) 067]

� Zero crossing point of AFB free from FF uncertainties

� Result q20 = 4.9± 0.9 GeV2 consistent with SM predictionq20,SM = 4.36

+0.33−0.31 GeV

2 [EPJ C41 (2005) 173-188]


http://arxiv.org/abs/1304.6325http://arxiv.org/abs/1105.0376http://arxiv.org/abs/hep-ph/0412400

Backup 60 / 48

Less form factor dependent observables P ′i (1 fb−1)

� Less FF dependent observables P ′i introduced in [JHEP 05 (2013) 137]

� For P ′4,5 = S4,5/√FL(1− FL) leading FF uncertainties cancel for all q2

� 3.7σ local deviation from SM prediction [JHEP 05 (2013) 137] in P ′5

]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

3.7σ

[PRL 111, 191801 (2013)]



Backup 61 / 48

Study of rare B0(s) → π+π−µ+µ− decays I

s

b̄

s

s̄

B0s f0

µ−

µ+

t̄

W+

Z0, γ

d

b̄

d

d̄

B0 ρ0

µ−

µ+

t̄

W+

Z0, γ

� Contributions from� B0s → f0µ+µ−: b→ s transition similar to B0 → K∗0µ+µ−� B0 → ρ0µ+µ−: b→ d transition, |Vtd/Vts|2 suppressed in SM

� SM predictions show large variation

� BSM(B0s → f0µ+µ−) = 0.6× 10−9 − 5.2× 10−7[PRD 79 014013], [PRD 81 074001], [PRD 80 016009]

� BSM(B0 → ρ0µ+µ−) = (5− 9)× 10−8[PRD 56 5452-5465], [Eur.Phys.J.C 41 173-188]


http://arxiv.org/abs/0811.2648http://arxiv.org/abs/1002.2880http://journals.aps.org/prd/abstract/10.1103/PhysRevD.80.016009http://arxiv.org/abs/hep-ph/9706247http://arxiv.org/abs/hep-ph/0412400

Backup 62 / 48

Study of rare B0(s) → π+π−µ+µ− decays II

]2) [GeV/c-µ+µ-π+πM(5.2 5.4 5.6 5.8

)2

Eve

nts

/(2

0 M

eV

/c

10

210

310

-π

+π ψ J/→s

0B

-π

+π ψ J/→

0B

0 K*(892)ψ J/→

0B

φ ψ J/→ s0

B

’η ψ J/→ s0

B+

Kψ J/→+

B

Combinatorial+π

-π

+π ψ J/→

+cB

Total fit

LHCb

]2) [GeV/c-µ+µ-π+πM(5.2 5.4 5.6 5.8

)2

Eve

nts

/(2

0 M

eV

/c

10

20

30

40

LHCb

-µ +µ -π +π →s

0B

-µ +µ -π +π →

0B

-µ +µ

0 K*(892)→

0B

-µ +µ’ η → s

0B

Combinatorial

Total fit

Resonant decay Signal decay

[PL

B74

3(2

015)

46]

� Observation of B0s → π+π−µ+µ− with 7.6σ� Evidence for B0 → π+π−µ+µ− with 4.8σ� Branching fractions compatible with SM predictions

B(B0s → π+π−µ+µ−) = (8.6± 1.5stat. ± 0.7syst. ± 0.7norm.)× 10−8

B(B0 → π+π−µ+µ−) = (2.11± 0.51stat. ± 0.15syst. ± 0.16norm.)× 10−8

� Motivated work in theory [Wang et al., arxiv:1502.05104], [arxiv:1502.05483]



Backup 63 / 48

The rare decay B0 → K∗0e+e−

d

b̄

d

s̄B0 K∗0

e−

e+

t̄

W+

Z0, γ!"#$%&$%$"'$(

J/ψ(1S)

ψ(2S)C(′)7

C(′)7 C(′)9

C(′)9 C

(′)10

4 [m(µ)]2 q2

dΓdq2

)"*(

+,"-(*!.#)"'$(

',"#%!/01,".(&%,2(

)/,3$(,4$"('5)%2(

#5%$.5,6*((

cc̄

4[m(`)]2

� Analyse B0→ K∗0e+e− at very low q2: [0.0004, 1.0] GeV2/c4,accessible due to tiny e mass

� Determine angular observables FL, A(2)T , A

ReT , A

ImT

sensitive to C7 and C′7

� Experimental challenges: Trigger and Bremsstrahlung


Backup 63 / 48

The rare decay B0 → K∗0e+e−

d

b̄

d

s̄B0 K∗0

e−

e+

t̄

W+

Z0, γ

]2c/ [MeV)−e+e−π+K(m4800 5000 5200 5400

) 2 cC

an

did

ate

s /

(30

Me

V/

0

5

10

15

20

25

30DataModel

−e+e0*K → 0B−e+e)X0*K(→B

Combinatorial

LHCb

[arxiv:1501.03038]

� Analyse B0→ K∗0e+e− at very low q2: [0.0004, 1.0] GeV2/c4,accessible due to tiny e mass

� Determine angular observables FL, A(2)T , A

ReT , A

ImT

sensitive to C7 and C′7

� Experimental challenges: Trigger and Bremsstrahlung



Backup 64 / 48

Angular analysis of B0 → K∗0e+e− decays

lθ cos-0.5 0 0.5

Can

dida

tes

/ (0.

2)

0

10

20

30

40

50 LHCb

Kθ cos-1 -0.5 0 0.5 1

Can

dida

tes

/ (0.

2)

0

5

10

15

20

25

30

35

40 LHCb

[rad]φ∼0 1 2 3

rad

) π

Can

dida

tes

/ (0.

1

0

5

10

15

20

25

30

35 LHCb

[arxiv:1501.03038]

obs. result

FL +0.16± 0.06± 0.03A

(2)T −0.23± 0.23± 0.05

AReT +0.10± 0.18± 0.05AImT +0.14± 0.22± 0.05

[JHEP 05 (2013) 043]

obs. SM prediction

FL +0.10+0.11−0.05

A(2)T +0.03

+0.05−0.04

AReT −0.15+0.04−0.03AImT (−0.2+1.2−1.2)× 10−4

� Results are in good agreement with SM predictions

� Constraints on C(′)7 competitive with radiative decays



Backup 65 / 48

B0 → K∗0µ+µ− angular observables

� Four-differential decay rate for B0 → K∗0µ+µ−d4Γ(B0 → K∗0µ+µ−)dq2 d cos θ` d cos θK dφ

=9

32π

[Is1 sin

2 θK + Ic1 cos

2 θK

+ (Is2 sin2 θK + I

c2 cos

2 θK) cos 2θ`

+ I3 sin2 θK sin

2 θ` cos 2φ+ I4 sin 2θK sin 2θ` cosφ

+ I5 sin 2θK sin θ` cosφ

+ (Is6 sin2 θK + I

c6 cos

2 θK) cos θ` + I7 sin 2θK sin θ` sinφ

+ I8 sin 2θK sin 2θ` sinφ+ I9 sin2 θK sin

2 θ` sin 2φ]

� Ii(q2) combinations of K∗0 spin amplitudes sensitive to C(′)7 , C

(′)9 , C

(′)10

� CP-averages Si = (Ii + Īi)/d(Γ+Γ̄)

dq2 , CP-asymmetries Ai = (Ii − Īi)/d(Γ+Γ̄)

dq2

� For m` = 0: 8 CP averages Si, 8 CP-asymmetries Ai

� Simultaneous fit of 8 observables not possible with the 2011 data set→ Angular folding φ→ φ+ π for φ < 0 cancels terms ∝ sinφ, cosφ


Backup 65 / 48

B0 → K∗0µ+µ− angular observables

� Four-differential decay rate for B0 → K∗0µ+µ−d4Γ(B0 → K∗0µ+µ−)dq2 d cos θ` d cos θK dφ

=9

32π

[Is1 sin

2 θK + Ic1 cos

2 θK

+ (Is2 sin2 θK + I

c2 cos

2 θK) cos 2θ`

+ I3 sin2 θK sin

2 θ` cos 2φ+(((((((

(((I4 sin 2θK sin 2θ` cosφ

+((((

((((((

I5 sin 2θK sin θ` cosφ

+ (Is6 sin2 θK + I

c6 cos

2 θK) cos θ` +((((((((

(I7 sin 2θK sin θ` sinφ

+((((

((((((

I8 sin 2θK sin 2θ` sinφ+ I9 sin2 θK sin

2 θ` sin 2φ]

� Ii(q2) combinations of K∗0 spin amplitudes sensitive to C(′)7 , C

(′)9 , C

(′)10

� CP-averages Si = (Ii + Īi)/d(Γ+Γ̄)

dq2 , CP-asymmetries Ai = (Ii − Īi)/d(Γ+Γ̄)

dq2

� For m` = 0: 8 CP averages Si, 8 CP-asymmetries Ai

� Simultaneous fit of 8 observables not possible with the 2011 data set→ Angular folding φ→ φ+ π for φ < 0 cancels terms ∝ sinφ, cosφ


Backup 66 / 48

Ii(q2) depend on K∗0 spin amplitudes AL,R0 , A

L,R‖ , A

L,R⊥

Is1 =(2 + β2µ)

4

[|AL⊥|2 + |AL‖ |2 + (L→ R)

]+

4m2µq2

Backup 67 / 48

K∗0 spin amplitudes AL,R0 , AL,R‖ , A

L,R⊥

AL(R)⊥ = N

√2λ

{[(Ceff9 + C

′eff9 )∓ (Ceff10 + C′eff10 )

] V(q2)mB +mK∗

+2mbq2

(Ceff7 + C′eff7 )T1(q

2)

}AL(R)‖ = −N

√2(m2B −m2K∗)

{[(Ceff9 −C′eff9 )∓ (Ceff10 −C′eff10 )

] A1(q2)mB −mK∗

+2mbq2

(Ceff7 −C′eff7 )T2(q2)}

AL(R)0 = −

N

2mK∗√q2

{[(Ceff9 −C′eff9 )∓ (Ceff10 −C′eff10 )

][(m2B −m2K∗ − q2)(mB +mK∗)A1(q2)− λ

A2(q2)

mB +mK∗

]+ 2mb(C

eff7 −C′eff7 )

[(m2B + 3mK∗ − q2)T2(q2)−

λ

m2B −m2K∗T3(q

2)]}

� Wilson coefficients C(′)eff7,9,10

� Seven form factors (FF) V (q2), A0,1,2(q2), T1,2,3(q

2)encode hadronic effects and require non-perturbative calculation

� Low q2 ≤ 6 GeV2→ ξ⊥,‖ (soft form factors)

� Large q2 ≥ 14 GeV2→ f⊥,‖,0 (helicity form factors)

� Theory uncertainties:� FF from non-perturbative calculations� Λ/mb corrections (“subleading corrections”)

For

completeness


Backup 68 / 48

Analysis strategy

]2c) [MeV/−µ+µ−π+(Km5200 5400 5600

]2 c)

[MeV

/− µ+ µ(

m

0

1000

2000

3000

4000

1

10

210

310

410

LHCb

Signal band

J/ψ , ψ(2S) band

Resonant decays

� Veto of B0 → J/ψK∗0 and B0 → ψ(2S)K∗0 (valuable control channels!)� Suppression of peaking backgrounds with PID

Rejection of combinatorial background with BDT

1 Determine the differential branching fraction in q2 bins

2 Determine angular observables in multidimensional likelihood fit


Backup 69 / 48

B0 → K∗0µ+µ− signal yield (2011)

]2c) [MeV/−µ+µ−π+(Km5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

20

40

60

4c/2 < 2 GeV20.1 < q

LHCb

Signal

Combinatorial bkg

Peaking bkg

]2c) [MeV/−µ+µ−π+(Km5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

20

40

60

4c/2 < 4.3 GeV22 < q

LHCb

]2c) [MeV/−µ+µ−π+(Km5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

20

40

60

4c/2 < 8.68 GeV24.3 < q

LHCb

]2c) [MeV/−µ+µ−π+(Km5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

20

40

60

4c/2 < 12.86 GeV210.09 < q

LHCb

]2c) [MeV/−µ+µ−π+(Km5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

20

40

60

4c/2 < 16 GeV214.18 < q

LHCb

]2c) [MeV/−µ+µ−π+(Km5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

20

40

60

4c/2 < 19 GeV216 < q

LHCb

� Fit of Nsig in q2 bins

� Use B0 → J/ψK∗0 as normalisation channel� SM prediction [C. Bobeth et al. JHEP 07 (2011) 067]

� Data somewhat low but large theory uncertainties due to FF



Backup 69 / 48

B0 → K∗0µ+µ− differential decay rate

]2c) [MeV/−µ+µ−π+(Km5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

20

40

60

4c/2 < 2 GeV20.1 < q

LHCb

Signal

Combinatorial bkg

Peaking bkg

]2c) [MeV/−µ+µ−π+(Km5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

20

40

60

4c/2 < 4.3 GeV22 < q

LHCb

]2c) [MeV/−µ+µ−π+(Km5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

20

40

60

4c/2 < 8.68 GeV24.3 < q

LHCb

]2c) [MeV/−µ+µ−π+(Km5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

20

40

60

4c/2 < 12.86 GeV210.09 < q

LHCb

]2c) [MeV/−µ+µ−π+(Km5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

20

40

60

4c/2 < 16 GeV214.18 < q

LHCb

]2c) [MeV/−µ+µ−π+(Km5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

20

40

60

4c/2 < 19 GeV216 < q

LHCb

]4c/2 [GeV2q0 5 10 15 20

]-2

GeV

4 c × -7

[10

2q

/dBd

0

0.5

1

1.5

LHCb

Theory BinnedLHCb

[JHEP 08 (2013) 131]

� Fit of Nsig in q2 bins

� Use B0 → J/ψK∗0 as normalisation channel� SM prediction [C. Bobeth et al. JHEP 07 (2011) 067]

� Data somewhat low but large theory uncertainties due to FF



Backup 70 / 48

B0 → K∗0µ+µ− angular observables I

]4c/2 [GeV2q0 5 10 15 20

LF

0

0.2

0.4

0.6

0.8

1

Theory BinnedLHCb

LHCb

]4c/2 [GeV2q0 5 10 15 20

FB

A

-1

-0.5

0

0.5

1

LHCb

Theory BinnedLHCb

]4c/2 [GeV2q0 5 10 15 20

3S

-0.4

-0.2

0

0.2

0.4 LHCb

Theory BinnedLHCb

]4c/2 [GeV2q0 5 10 15 20

9A

-0.4

-0.2

0

0.2

0.4

LHCb

LHCb

� Results [JHEP 08 (2013) 131] in good agreement withSM prediction [C. Bobeth et al. JHEP 07 (2011) 067]



Backup 71 / 48

Angular analysis of B+ → K+µ+µ− and B0 → K0Sµ+µ−

u(d)

b̄

u(d)

s̄

µ−

µ+

t̄

W+

Z0, γ

]2c) [MeV/−µ+µ+K(m5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

100

200

300

400

500

LHCb4c/2 < 6.0 GeV2q(a) 1.1 <

B+ → K+µ+µ−

]2c) [MeV/−µ+µ S0K(m

5200 5400 5600

)2 cC

andi

date

s / (

10

MeV

/

0

5

10

15

20

25

LHCb4c/2 < 6.0 GeV2q(c) 1.1 <

B0 → K0Sµ+µ−

[JHEP 05 (2014) 082]

� NB+→K+µ+µ− = 4746± 81 and NB0→K0Sµ+µ− = 176± 17 in 3 fb−1

� Experimental challenge: K0S reconstruction

� Differential decay rate for B+ → K+µ+µ−1

Γ

dΓ(B+ → K+µ+µ−)d cos θ`

=3

4(1− FH)(1− cos2 θ`) +

1

2FH +AFB cos θ`

1

Γ

dΓ(B0 → K0Sµ+µ−)d| cos θ`|

=3

2(1− FH)(1− | cos θ`|2) + FH

� Flat parameter FH sensitive to (Pseudo)scalar contributions, small in SM

� Forward backward asymmetry AFB zero in SM



Backup 72 / 48

Angular analysis of B+ → K+µ+µ− and B0 → K0Sµ+µ−

]4c/2 [GeV2q0 5 10 15 20

HF

0

0.1

0.2

0.3

0.4

0.5

LHCb

]4c/2 [GeV2q0 5 10 15 20

FBA

-0.2

-0.1

0

0.1

0.2

LHCb

]4c/2 [GeV2q0 5 10 15 20

HF

0

0.5

1

1.5LHCb

� 2D fit in cos θ` and m(Kµ+µ−)

� [JHEP 05 (2014) 082] in goodagreement with SM prediction

B+ → K+µ+µ− B+ → K+µ+µ−

B0 → K0Sµ+µ−



Backup 73 / 48

B+ → K+π+π−µ+µ− and B+ → φK+µ+µ−

]2c) [MeV/-µ+µ-π+π+Km(5200 5300 5400 5500

)2 cC

andi

date

s / (

10 M

eV/

0

10

20

30

40

50

60

LHCb < 6.002q1.00 <

]2c) [MeV/-µ+µ+Kφm(5200 5300 5400 5500 5600

)2 cC

andi

date

s / (

10 M

eV/

0

2

4

6

8

10

12

14

16LHCb

-µ+µ+Kφ →+B(a)

[JHEP 10 (2014) 064]

B+ → K+π+π−µ+µ− B+ → φK+µ+µ−

� First observation of these modes withNsig(B

+→ K+π+π−µ+µ−) = 367+24−23 and Nsig(B+→ φK+µ+µ−) = 25.2+6.0−5.3

� Normalise to B+ → ψ(2S)(→ J/ψπ+π−)K+ and B+ → J/ψφK+� Determine branching fractions

B(B+ → K+π+π−µ+µ−) =(4.36 +0.29−0.27 (stat)± 0.20 (syst)± 0.18 (norm)

)× 10−7

B(B+ → φK+µ+µ−) =(0.82 +0.19−0.17 (stat)± 0.04 (syst)± 0.27 (norm)

)× 10−7



Backup 74 / 48

B+ → K+π+π−µ+µ− cont.

]4c/2 [GeV2q0 5 10 15

)4 c-2

GeV

-810×

(2 q/d

Bd

0

1

2

3

4

5

6

7

8 LHCb

]2c) [MeV/-π+π+Km(1000 1500 2000 2500

)2 cC

andi

date

s / (

35 M

eV/

0

10

20

30

40

50

60 LHCb-µ+µ-π+π+ K→+B

(a)

[JHEP 10 (2014) 064]

� Performed measurement of dB(B+ → K+π+π−µ+µ−)/dq2

� Significant contribution from B+ → K+1 (1270)µ+µ− expected� Low statistics → no attempt to resolve contributions to K+π+π− final state



Backup 75 / 48

CP-asymmetry ACP

)2 (MeV/c-µ+µ+Km5200 5400 5600

)2E

vent

s / (

10.

6 M

eV/c

0

50

100

150

200

250 LHCb (a)

)2 (MeV/c-µ+µ-Km5200 5400 5600

)2E

vent

s / (

10.

6 M

eV/c

0

50

100

150

200

250 LHCb (b)

)2 (MeV/c-µ+µ+Km5200 5400 5600

)2E

vent

s / (

10.

6 M

eV/c

0

50

100

150

200

250

300LHCb (c)

)2 (MeV/c-µ+µ-Km5200 5400 5600

)2E

vent

s / (

10.

6 M

eV/c

0

50

100

150

200

250

300LHCb (d)

[JHEP 09 (2014) 177]

B+ → K+µ+µ− prelim. B− → K−µ+µ− prelim.

� Direct CP-Asymmetry ACP

ACP =Γ(B̄ → K̄(∗)µ+µ−)− Γ(B → K(∗)µ+µ−)Γ(B̄ → K̄(∗)µ+µ−) + Γ(B → K(∗)µ+µ−)

� ACP tiny O(10−3) in the SM� Correct for detection and production asymmetry using B → J/ψK(∗)AK(∗)µµraw = ACP +Adet + κAprod, ACP = AK

(∗)µµraw −AJ/ψK

(∗)raw



Backup 76 / 48

CP-asymmetry ACP cont.

]4/c2 [GeV2q0 5 10 15 20

CP

A

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

LHCb

]4/c2 [GeV2q0 5 10 15

CP

A

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

LHCb

[JHEP 09 (2014) 177]

ACP (B+ → K+µ+µ−) prelim. ACP (B0 → K∗0µ+µ−) prelim.

� Measured ACP in good agreement with SM predictionACP (B+ → K+µ+µ−) = 0.012± 0.017(stat.)± 0.001(syst.)

ACP (B0 → K∗0µ+µ−) = −0.035± 0.024(stat.)± 0.003(syst.)

� Most precise measurement



Backup 77 / 48

Prospects for rare decays in 2018 and beyond


IntroductionbsBbqB 0 K *0 + - B 0s + - bs + - branching fractions

Global bs fitsB + + + - Lepton universalityConclusionsBackup

Documents

Rare b-hadron decays - Warwick · 2015. 12. 3. · Rare Decays as probes for New Physics Rare decays: Flavour changing neutral currents (FCNCs) b!qdecays with q= s;dquark In theSM: