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 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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/hep-ph/9806471
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
g2(s̄γµPL(R)b)(µ̄γ
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
b→ sγ 5 / 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
g2(s̄γµPL(R)b)(µ̄γ
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1402.6852
B → µµ 9 / 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
g2(s̄γµPL(R)b)(µ̄γ
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1311.0903
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1411.4413
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
CMS and LHCb (LHC run I)
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
CMS and LHCb (LHC run I)
� 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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
b→ q`` 13 / 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
g2(s̄γµPL(R)b)(µ̄γ
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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]
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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]
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
[LHCb-PAPER-2015-051]
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
C. 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/
0
20
40
preliminaryLHCb
]2c) [MeV/−µ+µ−π+K(m5200 5400 5600
2 cE
vent
s / 5
.3 M
eV/
0
10
20
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preliminaryLHCb
]2c) [MeV/−µ+µ−π+K(m5200 5400 5600
2 cE
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.3 M
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preliminaryLHCb
]2c) [MeV/−µ+µ−π+K(m5200 5400 5600
2 cE
vent
s / 5
.3 M
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0
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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
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eV/
0
20
40
preliminaryLHCb
]2c) [MeV/−µ+µ−π+K(m5200 5400 5600
2 cE
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eV/
0
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60preliminaryLHCb
]2c) [MeV/−µ+µ−π+K(m5200 5400 5600
2 cE
vent
s / 5
.3 M
eV/
0
20
40preliminaryLHCb
[LHCb-PAPER-2015-051]
[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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
[LHCb-PAPER-2015-051]
� 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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
[LHCb-PAPER-2015-051]
� black line: full fit, blue: signal component, red: bkg. part� Angular observables successfully reproduced [PRD 88, 052002 (2013)]
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1307.2782
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
[LHCb-PAPER-2015-051]
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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)
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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]
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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]
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1503.05534http://arxiv.org/abs/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.
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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.
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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.
[LHCb-PAPER-2015-051]
[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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1407.8526http://arxiv.org/abs/1308.1707
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.
[LHCb-PAPER-2015-051]
[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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1407.8526http://arxiv.org/abs/1308.1707
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1506.08777
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1506.08777
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1506.08777
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,
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1506.08777http://arxiv.org/abs/1305.2168
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
b→ q`` | B0s→ φµ+µ− 38 / 48
B0s→ φµ+µ− angular analysis
]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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1506.08777
b→ q`` | B0s→ φµ+µ− 39 / 48
B0s→ φµ+µ− angular analysis
]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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1506.08777
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
Global b→ s fits 42 / 48
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
Global b→ s fits 42 / 48
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1509.00414
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1509.00414
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1406.6482
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1406.6482
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
Backup 49 / 48
Complementarity of flavour and direct searches
Figure by D. Straub
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1009.2731
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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%
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1211.6759
Backup 53 / 48
Data taken by LHCb
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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.
[LHCb-PAPER-2015-051]
� 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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1503.04100
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.
[LHCb-PAPER-2015-051]
� 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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1508.04094
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1508.04094
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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)
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1403.8044
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]
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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)]
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1303.5794http://arxiv.org/abs/1303.5794http://arxiv.org/abs/1308.1707
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]
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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]
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1412.6433http://arxiv.org/abs/1502.05104http://arxiv.org/abs/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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1501.03038
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1501.03038http://arxiv.org/abs/1212.2263
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron 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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1105.0376
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1304.6325http://arxiv.org/abs/1105.0376
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]
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1304.6325http://arxiv.org/abs/1105.0376
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1403.8045
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−
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1403.8045
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1408.1137
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1408.1137
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1408.0978
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
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
http://arxiv.org/abs/1408.0978
Backup 77 / 48
Prospects for rare decays in 2018 and beyond
C. Langenbruch (Warwick), Warwick EPP 2015 Rare b-hadron decays
IntroductionbsBbqB 0 K *0 + - B 0s + - bs + - branching fractions
Global bs fitsB + + + - Lepton universalityConclusionsBackup
Recommended