Rare b-hadron decays
Christoph Langenbruch1
1 University
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 flavour
but: higher order penguin processes are possible
b
SM penguin diagram
t
s
W
Z 0, γ
b
NP penguin diagram
t
s
H±
Z 0, γ
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
Buras,
→ masses up to O(100 TeV) accessible [A.
arXiv:1505.00618]
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
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 flavour
but: higher order penguin processes are possible
b
SM penguin diagram
t
s
W
Z 0, γ
b
NP penguin diagram
t
s
H±
Z 0, γ
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
Buras,
→ masses up to O(100 TeV) accessible [A.
arXiv:1505.00618]
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Introduction
3 / 48
Effective field theory
FCNCs a multi-scale problem:
ΛNP
mW
mb
ΛQCD
? & 1 TeV
80 GeV
5 GeV
0.2 GeV
Buras
In effective field theory: Operator product expansion [A.
hep-ph/9806471]
X
4GF
Heff = − √ Vtb Vtq∗
Ci Oi + Ci0 Oi0
|{z} |{z}
2
i
m
Left-handed Right-handed, msb suppressed
(0)
(0)
Wilson coeff. Ci encode short-distance physics, Oi corr. operators
Well known analogon: β decay
u
d
W−
GF
e−
ν̄e
Heff =
u
d
G
√F
2
e−
ν̄e
cos θC [ūγµ (1 − γ5 )d × ēγ µ (1 − γ5 )νe ]
Integrate out heavy DoF → Contact interaction with effective coupling GF
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Introduction
3 / 48
Effective field theory
FCNCs a multi-scale problem:
ΛNP
mW
mb
ΛQCD
? & 1 TeV
80 GeV
5 GeV
0.2 GeV
Buras
In effective field theory: Operator product expansion [A.
hep-ph/9806471]
X
4GF
Heff = − √ Vtb Vtq∗
Ci Oi + Ci0 Oi0
|{z} |{z}
2
i
m
Left-handed Right-handed, msb suppressed
(0)
(0)
Wilson coeff. Ci encode short-distance physics, Oi corr. operators
Well known analogon: β decay
u
d
W−
GF
e−
ν̄e
Heff =
u
d
G
√F
2
e−
ν̄e
cos θC [ūγµ (1 − γ5 )d × ēγ µ (1 − γ5 )νe ]
Integrate out heavy DoF → Contact interaction with effective coupling GF
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Introduction
4 / 48
Operators
b
b → sγ
s
γ
photon penguin
(0)
O7 = ge2 mb (s̄σµν PR(L) b)F µν
b
`
s
(0)
` O10
b
`
s
B → µµ
3
electroweak penguin
2
(0)
O9 = ge2 (s̄γµ PL(R) b)(µ̄γ µ µ)
3
e2
(s̄γµ PL(R) b)(µ̄γ µ γ5 µ)
g2
3
(pseudo)scalar penguin
(0)
e2
OS = 16π
2 mb (s̄PR(L) b)(µ̄µ)
(0)
e2
` OP = 16π 2 mb (s̄PR(L) b)(µ̄γ5 µ)
3
3
=
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
b → q``
3
3
b → sγ
5 / 48
Operators
b
b → sγ
s
γ
photon penguin
(0)
O7 = ge2 mb (s̄σµν PR(L) b)F µν
b
`
s
(0)
` O10
b
`
s
B → µµ
3
electroweak penguin
2
(0)
O9 = ge2 (s̄γµ PL(R) b)(µ̄γ µ µ)
3
e2
(s̄γµ PL(R) b)(µ̄γ µ γ5 µ)
g2
3
(pseudo)scalar penguin
(0)
e2
OS = 16π
2 mb (s̄PR(L) b)(µ̄µ)
(0)
e2
` OP = 16π 2 mb (s̄PR(L) b)(µ̄γ5 µ)
3
3
=
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
b → q``
3
3
b → sγ
6 / 48
+
+ − −
Photon polarisation λγ with B → K π π γ
u
B+
b̄
u
K +π+π−
t̄
s̄
W
γ
In SM, photons from b → sγ decays left-handed (C70 /C7 ∼ ms /mb )
Gronau et al.,
Can probe λγ with B + → K + π + π − γ decays [M.
PRD 66 (2002) 054008]
R +1
Up-down asymmetry Aud =
C. Langenbruch (Warwick), Warwick EPP 2015
0
R0
dΓ
dΓ
− −1
dcosθ dcosθ
dcosθ dcosθ
R +1
dΓ
−1 dcosθ dcosθ
Rare b-hadron decays
∝ λγ
b → sγ
7 / 48
+ + −
Candidates / ( 8 MeV/c2 )
Candidates / ( 50 MeV/c2 )
Composition of K π π final state
3000
LHCb
2500
2000
1500
1000
500
0
4500
5000
5500
6000
350
300
200
150
100
50
0
6500
M(Kππγ ) [MeV/c ]
LHCb
250
1200
1400
2
1600
1800
M(Kππ) [MeV/ c2]
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
1
LHCb
0.8
0.6
0.4
1
LHCb
0.8
0.2
[1.1,1.3] GeV/c2
-0.5
0
0.5
1
LHCb
0.8
0
-1
1
cosθ
1/N × dN/dcosθ
0
-1
0.6
0.2
[1.4,1.6] GeV/c2
0
0.5
1
cosθ
0
0.5
1
cosθ
0
-1
0
-0.05
LHCb
0.8
0.4
-0.5
-0.5
0.6
0.2
LHCb
0.05
[1.3,1.4] GeV/c2
1
0.4
0
-1
0.1
0.6
0.4
0.2
1/N × dN/dcosθ
Aud
1/N × dN/dcosθ
1/N × dN/dcosθ
First observation of γ polarisation
-0.1
1200
[1.6,1.9] GeV/c2
-0.5
0
0.5
1400
1
cosθ
1600
1800
M(Kππ) [MeV/ c2]
Perform angular fit of cos θ distribution to determine Aud
Combination results in first obs. of non-zero photon polarisation at
5.2 σ [PRL 112, 161801 (2014)]
To determine precise value for λγ , resonance structure of final state
needs to be resolved
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
B → µµ
9 / 48
Operators
b
b → sγ
s
γ
photon penguin
(0)
O7 = ge2 mb (s̄σµν PR(L) b)F µν
b
`
s
(0)
` O10
b
`
s
B → µµ
3
electroweak penguin
2
(0)
O9 = ge2 (s̄γµ PL(R) b)(µ̄γ µ µ)
3
e2
(s̄γµ PL(R) b)(µ̄γ µ γ5 µ)
g2
3
(pseudo)scalar penguin
(0)
e2
OS = 16π
2 mb (s̄PR(L) b)(µ̄µ)
(0)
e2
` OP = 16π 2 mb (s̄PR(L) b)(µ̄γ5 µ)
3
3
=
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
b → q``
3
3
B → µµ
10 / 48
The very rare decay
b̄
Bs0
s
t
W
0
B(s)
→
µ+
Z0
µµ
b̄
Bs0
t
µ−
µ+
W
νµ
t
s
W
µ−
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
4m2
2m
0 )|2 ]
B ∝ |Vtb Vtq |2 [(1 − M 2µ )|CS − CS0 |2 + |(CP − CP0 ) + M 2µ (C10 − C10
B
B
Bobeth et al.,
SM prediction (accounting for ∆Γs 6= 0) [C.
PRL 112, 101801 (2014)]
B(Bs0 → µ+ µ− ) = (3.66 ± 0.23) × 10−9
B(B 0 → µ+ µ− ) = (1.06 ± 0.09) × 10−10
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
B → µµ
11 / 48
First observation of
Bs0 →
µµ
S/(S+B) weighted cand. / (40 MeV/c2)
CMS and LHCb (LHC run I)
60
Data
Signal and background
Bs0→ µ+µ−
B0→ µ+µ−
Combinatorial bkg.
Semileptonic bkg.
Peaking bkg.
50
40
30
20
10
0
5000
5200
5400
5600
5800
mµ+µ− [MeV/ c2]
Combined analysis of LHCb and CMS Run 1 data, sharing signal and
nuisance parameters [Nature 522 (2015) pp. 68-72]
First obs. of Bs0 → µ+ µ− with 6.2 σ significance (expected 7.2 σ)
−9
B(Bs0 → µ+ µ− ) = (2.8+0.7
compatible with SM at 1.2 σ
−0.6 ) × 10
0
+
−
First evidence for B → µ µ with 3.0 σ significance (expected 0.8 σ)
−10
B(B 0 → µ+ µ− ) = (3.9+1.6
compatible with SM at 2.2 σ
−1.4 ) × 10
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
12 / 48
0
µµ)/B(Bs0 →
CMS and LHCb (LHC run I)
40
1−
1−
−5
1
2
3
4
2
4
6
8
B(B 0s → µ + µ −) [10−9]
−2ΔlnL
10
a
0
b
0
0
SM
0.1
0
20
10
0.3
0.2
SM
30
−7
×10
6.3
3%
5%
7%
0.4
99.7
0.6
×10
5.7
0.7
−9
1−
0
2×1
0.8
0.5
µµ)
−2ΔlnL
0.9
95.4
B(B0 → µ + µ −) [10−9]
The ratio R = B(B →
68.2
−2∆ lnL
B → µµ
5
6
7
8
9
B(B0s → µ + µ −) [10−9]
SM
8
6
4
c
2
0
0
0.2
0.4
0.6
0.8
B(B 0 → µ + µ −) [10−9]
CMS and LHCb (LHC run I)
10
SM and MFV
8
6
4
2
0
0
0.1
0.2
0.3
0.4
R=
B(B 0→µµ)
B(Bs0→µµ)
tests MFV hypothesis
RSM = 0.0295+0.0028
−0.0025
R = 0.14+0.08
−0.06 compatible at 2.3 σ
0.5
R
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
b → q``
13 / 48
Operators
b
b → sγ
s
γ
photon penguin
(0)
O7 = ge2 mb (s̄σµν PR(L) b)F µν
b
`
s
(0)
` O10
b
`
s
B → µµ
3
electroweak penguin
2
(0)
O9 = ge2 (s̄γµ PL(R) b)(µ̄γ µ µ)
3
e2
(s̄γµ PL(R) b)(µ̄γ µ γ5 µ)
g2
3
(pseudo)scalar penguin
(0)
e2
OS = 16π
2 mb (s̄PR(L) b)(µ̄µ)
(0)
e2
` OP = 16π 2 mb (s̄PR(L) b)(µ̄γ5 µ)
3
3
=
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
b → q``
3
3
b → q``
14 / 48
b → s(d)`` decays
SM penguin diagram
W
b
s(d) b
Z 0, γ
s(d)
W
t
SM box diagram
t
`+
αem
W
νµ
`−
`+
`−
b → s(d)`` decays proceed via penguin and box diagrams
B(Bs0 → 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 → dµµ
b → see
05
JHEP 09
JHEP 06
+
∗+ µ+ µ− [JHEP 06 ]
B + → K + µ+ µ− [JHEP
(2014) 082] [(2014) 177] [(2014) 133] B → K
(2014) 133
10
0
0 + − [JHEP 05 ] [JHEP 06 ],
B + → K + π + π − µ+ µ− [JHEP
(2014) 064] B → K µ µ
(2014) 082
(2014) 133
09
0
+ − + − [PLB 743 ]
B 0 → K ∗0 µ+ µ− [LHCb-PAPER-2015-051
] Bs0 → φµ+ µ− [JHEP
(2015) 179] Bs → π π µ µ
(2015) 46
to be submitted
06
Λ0b → Λµ+ µ− [JHEP
]
(2015) 115
10
0
+ − + − [PLB 743 ]
B + → π + µ+ µ− [JHEP
(2015) 034] B → π π µ µ
(2015) 46
113
0 → K ∗0 e+ e− [JHEP 04 ]
B + → K + e+ e− [PRL
]
B
(2014) 151601
(2015)064
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
b → q``
15 / 48
B → V `` differential branching fraction
J/ψ(1S)
ψ(2S)
(!)
dΓ
dq 2
C7
(!)
(!)
C7 C9
!"#$%&$%$"'$(
(!)
C9
+,"-(*!.#)"'$(
',"#%!/01,".(&%,2(cc̄
)/,3$(,4$"('5)%2(
#5%$.5,6*((
4 [m(µ)]2
(!)
)"*( C 10
q2
q 2 = m2 (`+ `− ) provides separation power between Ci → bin in q 2
Regions where J/ψ and ψ(2S) dominate are vetoed → control decays
typically 8 < q 2 < 11 GeV2/c4 and 12.5 < q 2 < 15 GeV2/c4
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
b → q``
16 / 48
Complication in theory: QCD effects
d¯
W
b
t
d¯
d¯
s
b
d¯
W
t
`+
Z 0, γ
s
`+
Z 0, 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
Γ(B −→K − µ+ µ− )−Γ(B +→K + µ+ µ− )
Γ(B −→K − µ+ µ− )+Γ(B +→K + µ+ µ− )
ACP =
Lepton universality, RK =
B +→K + µ+ µ−
B +→K + e+ e−
AI =
Ratios of angular obs., Pi
PRD 89 (2014) 094501
C. Langenbruch (Warwick), Warwick EPP 2015
(0)
q2)
basis
LCSR (low q 2 )
and
Du et al.,
[arXiv:1510.02349]
PoS (Lattice2014) 372
Recent improvements
Horgan et al., fromlattice
Horgan et(high
al.,
Bharucha et al.,
[arXiv:1503.05534]
Γ(B 0→K 0 µ+ µ− )−Γ(B +→K + µ+ µ− )
Γ(B 0→K 0 µ+ µ− )+Γ(B +→K + µ+ µ− )
Rare b-hadron decays
b → q`` | B 0 → K ∗0 µ+ µ−
17 / 48
0
∗0
+ −
+ −
Golden mode B → K [→ K π ]µ µ
d
d
B0
K ∗0
t̄
b̄
K
s̄
K*
W+
Z 0, γ
K*
z
B
µ−
+
+
µ+
Figu
B̄d0 →
i) th
ii) t
in th
the
the
betw
by t
¯
(``)-
V is assumed to be on-shell in the narrow-resonance app
0
∗0 (→ K −
to four4 . Using
K̄ 2
~of kinematic
Fully described by three helicity angles Ω
= (θ` ,variables
θK ,inφ)
and q 2 B̄=d →m
µµ
chosen as depicted
figure 1.
The differential decay rate, after summing over lepto
Differential decay rate given by
4
d4 Γ(B 0 → K ∗0 µ+ µ− )
9 X 8π2 2 ~ d Γ
= J s sin2 θK + J1c cos2 θK
=
Ii (q3 dq
)fid(cos
Ω)θ` d cos θK dφ 1
2
~ dq
32π
dΩ
+J3 sin2 θK sin2 θ` cos 2φ + J4 sin 2θK
∗
∗
i
d4 Γ̄(B 0 → K ∗0 µ+ µ− )
9 X¯ 2
~
=
Ii (q )fi (Ω)
2
~
32π
dΩ dq
i
∗
∗
+
∗
s
+(J6s sin2 θK ∗ + J6c cos2
+J8 sin 2θK ∗ sin
that is,amplitudes
into q 2 -dependent observables5 Jij (q 2 ) and the
Ii
and I¯i (q 2 ) combinations of K ∗0 spin
(0) φ.(0)No additional
(0) angular dependencies can be induced
depending on Wilson coefficients C7 , Cbasis
and
form
factors
by [12,
13]. The
following simplificatio
9 ,[11]Cas10found
(q 2 )
C. Langenbruch (Warwick), Warwick EPP 2015
J1c = −J2c and J6c = 0.
The differential
decay rate d4 Γ̄ of the CP-conjugate
Rare b-hadron
decays
b → q`` | B 0 → K ∗0 µ+ µ−
18 / 48
0
∗0 + −
Angular observables in B → K µ µ
Access to CP -averages Si and CP -asymmetries Ai
W. Altmannshofer et al.,
JHEP 01 (2009) 019
dΓ
dΓ̄
+
Si = Ii + I¯i /
2
dq 2 dq
dΓ
dΓ̄
Ai = Ii − I¯i /
+ 2
dq 2
dq
CP -averaged angular distribution in bins of q 2
1
d3 (Γ + Γ̄)
9 3
2
2
=
4 (1 − FL ) sin θK + FL cos θK
~
32π
d(Γ + Γ̄)/dq 2
dΩ
+ 14 (1 − FL ) sin2 θK cos 2θ` − FL cos2 θK cos 2θ`
+ S3 sin2 θK sin2 θ` cos 2φ + S4 sin 2θK sin 2θ` cos φ
+ S5 sin 2θK sin θ` cos φ + 34 AFB sin2 θK cos θ`
+ S7 sin 2θK sin θ` sin φ + S8 sin 2θK sin 2θ` sin φ
+ S9 sin2 θK sin2 θ` sin 2φ
Longitudinal polarisation fraction FL , Forward-backward asymmetry AFB
Perform ratios of angular obs.
form factors
cancel at leading order
S. where
Descotes-Genon et al.,
Example: P50 = √ S5
JHEP, 05 (2013) 137
FL (1−FL )
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
b → q`` | B 0 → K ∗0 µ+ µ−
0
19 / 48
∗0 + −
q2 [GeV2/c4]
B → K µ µ selection
[LHCb-PAPER-2015-051]
20
18
preliminary
16
14
12
10
8
6
4
2
0
5.2
5.3
5.4
5.5
5.6
5.7
m(K +� -µ +µ-) [GeV/c2]
BDT to suppress combinatorial background
Input variables: PID, kinematic and geometric quantities, isolation variables
Veto of B 0 → J/ψ K ∗0 and B 0 → ψ(2S)K ∗0 (important control decays)
and peaking backgrounds using kinematic variables and PID
Signal clearly visible as vertical band after the full selection
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
b → q`` | B 0 → K ∗0 µ+ µ−
20 / 48
0
∗0 + −
Mass model and B → K µ µ signal yield
LHCb
preliminary
100
B 0 → K ∗0 µµ signal
1.1 < q 2 < 6.0 GeV2/c4
50
Events / 5.3 MeV/c2
Events / 5.3 MeV/c2
[LHCb-PAPER-2015-051]
LHCb
preliminary
104
B 0 → J/ψ K ∗0
control decay
103
102
0
5200
5400
5600
m(K +π −µ +µ −) [MeV/c2]
5200
5400
5600
m(K +π −µ +µ −) [MeV/c2]
Signal mass model from high statistics B 0 → J/ψ K ∗0
Correction factor from simulation to account for q 2 dep. resolution
Finer q 2 binning to allow more flexible use in theory
Significant signal yield in all bins, q 2 integrated Nsig = 2398 ± 57
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
b → q`` | B 0 → K ∗0 µ+ µ−
20 / 48
∗0 + −
0
20
40
LHCb
preliminary
30
20
30
[LHCb-PAPER-2015-051]
[2.5, 4.0] GeV2/c4
[4.0, 6.0] GeV2/c4
Events / 5.3 MeV/c2
LHCb
preliminary
40
[1.1, 2.5] GeV2/c4
Events / 5.3 MeV/c2
[0.1, 0.98] GeV2/c4
Events / 5.3 MeV/c2
Events / 5.3 MeV/c2
Mass model and B → K µ µ signal yield
LHCb
preliminary
20
10
LHCb
preliminary
40
20
10
2
Events / 5.3 MeV/c2
0
5600
m(K +π −µ +µ −) [MeV/c2]
[6.0, 8.0] GeV /c
4
LHCb
preliminary
60
40
20
0
5200
5400
0
5600
m(K +π −µ +µ −) [MeV/c2]
2
[11.0, 12.5] GeV /c
4
LHCb
preliminary
40
20
5200
5400
0
5600
m(K +π −µ +µ −) [MeV/c2]
2
[15.0, 17.0] GeV /c
4
LHCb
preliminary
60
40
5200
5400
5600
m(K +π −µ +µ −) [MeV/c2]
[17.0, 19.0] GeV2/c4
Events / 5.3 MeV/c2
5400
Events / 5.3 MeV/c2
5200
Events / 5.3 MeV/c2
0
LHCb
preliminary
40
20
20
5200
5400
5600
m(K +π −µ +µ −) [MeV/c2]
0
5200
5400
5600
m(K +π −µ +µ −) [MeV/c2]
0
5200
5400
5600
m(K +π −µ +µ −) [MeV/c2]
0
5200
5400
5600
m(K +π −µ +µ −) [MeV/c2]
Signal mass model from high statistics B 0 → J/ψ K ∗0
Correction factor from simulation to account for q 2 dep. resolution
Finer q 2 binning to allow more flexible use in theory
Significant signal yield in all bins, q 2 integrated Nsig = 2398 ± 57
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
b → q`` | B 0 → K ∗0 µ+ µ−
21 / 48
Acceptance effect
1
0.5
[0.1, 1.0] GeV2/c4
[18.0, 19.0] GeV2/c4
1
0.5
LHCb
simulation
0
-1
-0.5
Efficiency
Efficiency
Efficiency
[LHCb-PAPER-2015-051]
1
0.5
LHCb
simulation
0
0.5
1
cos θ l
0
-1
-0.5
LHCb
simulation
0
0.5
1
cos θ K
0
-2
0
2
φ
Trigger, reconstruction and selection distorts decay angles and q 2 distribution
Parametrize 4D efficiency using Legendre polynomials Pk
X
cklmn Pk (cos θ` )Pl (cos θK )Pm (φ)Pn (q 2 )
ε(cos θ` , cos θK , φ, q 2 ) =
klmn
cklmn from moments analysis of B 0 → K ∗0 µ+ µ− phase-space MC
Crosscheck acceptance using B 0 → J/ψ K ∗0 control decay
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
b → q`` | B 0 → K ∗0 µ+ µ−
22 / 48
0
LHCb
preliminary
LHCb
preliminary
4000
50
5200
5400
0
5600
-1
m(K +π −µ +µ −) [MeV/c2]
LHCb
preliminary
8000
6000
4000
-0.5
0
0.5
1
cos θ l
LHCb
preliminary
4000
2000
2000
0
-1
-0.5
0
0.5
1
cos θ K
0
-2
0
2
[LHCb-PAPER-2015-051]
2000
0
Events / 0.02
×103
Events / 0.02
100
Events / 0.02 π rad
Events / 5.3 MeV/c2
Control decay B → J/ψ K
∗0
φ [rad]
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
b → q`` | B 0 → K ∗0 µ+ 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
1
d3 (Γ + Γ̄) d3 (Γ + Γ̄) =(1
−
F
)
S
~
~
d(Γ + Γ̄)/dq 2
d(Γ + Γ̄)/dq 2
dΩ
dΩ
S+P
P
3
2
+
FS sin θ` + S-P interference
16π
FS scales P-wave observables, needs to be determined precisely
Perform simultaneous mKπ
fit to constrain FS
P-wave described by rel. Breit-Wigner
S-wave described by LASS model
crosschecked using Isobar param.
Events / 10 MeV/c2
[LHCb-PAPER-2015-051]
40000
20000
0
0.8
C. Langenbruch (Warwick), Warwick EPP 2015
LHCb
preliminary
60000
Rare b-hadron decays
0.85
0.9
0.95
m(K +π −) [GeV/c2]
b → q`` | B 0 → K ∗0 µ+ µ−
0
24 / 48
∗0 + −
B → K µ 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
h
X
~ q 2 )fsig Psig (Ω)P
~ sig (mKπµµ )
log L =
log (Ω,
i
i
~ bkg (mKπµµ )
+ (1 − fsig )Pbkg (Ω)P
h
i
X
+
log fsig Psig (mKπ ) + (1 − fsig )Pbkg (mKπ )
i
Psig (Ω) given by
d3 (Γ+Γ̄) 1
~
d(Γ+Γ̄)/dq 2
dΩ
S+P
nd
Pbkg (Ω) modelled with 2
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
b → q`` | B 0 → K ∗0 µ+ µ−
25 / 48
∗0 + −
LHCb
preliminary
60
Events / 0.1 π
Events / 0.1
B → K µ µ likelihood projections [1.1, 6.0] GeV2/c4
Events / 0.1
0
LHCb
preliminary
100
40
LHCb
preliminary
60
40
50
20
0.5
-0.5
LHCb
preliminary
100
50
0
0
-1
1
cos θ l
5200
5400
5600
m(K +π −µ +µ −) [MeV/c2]
0
0.5
0
1
cos θ K
-2
LHCb
preliminary
100
50
0
0.8
0.85
0.9
0.95
m(K +π −) [GeV/c2]
0
[LHCb-PAPER-2015-051]
0
Events / 10 MeV/c2
-0.5
Events / 5.3 MeV/c2
0
-1
20
Efficiency corrected distributions show good agreement
with overlaid projections of the probability density function
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
2
φ [rad]
b → q`` | B 0 → K ∗0 µ+ µ−
0
26 / 48
∗0 + −
B → K µ µ systematic uncertainties
Source
Acceptance stat. uncertainty
Acceptance polynomial order
Data-simulation differences
Acceptance variation with q 2
m(K + π − ) model
Background model
Peaking backgrounds
m(K + π − µ+ µ− ) model
Det. and prod. asymmetries
FL
< 0.01
< 0.01
0.01–0.02
< 0.01
< 0.01
< 0.01
< 0.01
< 0.01
–
S3 –S9
< 0.01
< 0.02
< 0.01
< 0.01
< 0.01
< 0.01
< 0.01
< 0.01
–
A3 –A9
< 0.01
< 0.02
< 0.01
< 0.01
< 0.01
< 0.01
< 0.01
< 0.01
< 0.01
P1 –P80
< 0.01
< 0.04
< 0.01
< 0.01
< 0.03
< 0.02
< 0.01
< 0.02
< 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`` | B 0 → K ∗0 µ+ µ−
27 / 48
∗0 + −
0
1
S3
FL
B → K µ µ Results: FL , S3 , S4 , S5
0.5
LHCb prelim.
0.8
0.6
LHCb prelim.
SM from ABSZ
SM from ABSZ
[1503.05534][1411.3161]
[1503.05534][1411.3161]
0
0.4
0.2
-0.5
5
10
15
0
5
10
0.5
0.5
LHCb prelim.
LHCb prelim.
SM from ABSZ
SM from ABSZ
[1503.05534][1411.3161]
[1503.05534][1411.3161]
0
0
-0.5
0
15
q2 [GeV2/ c4]
S5
S4
q2 [GeV2/ c4]
-0.5
5
10
15
0
5
q2 [GeV2/ c4]
C. Langenbruch (Warwick), Warwick EPP 2015
10
15
q2 [GeV2/ c4]
Rare b-hadron decays
[LHCb-PAPER-2015-051]
0
0
b → q`` | B 0 → K ∗0 µ+ µ−
28 / 48
∗0 + −
0
S7
A FB
B → K µ µ Results: AFB , S7 , S8 , S9
0.5
0.5
LHCb prelim.
0
0
LHCb prelim.
SM from ABSZ
0
-0.5
[1503.05534][1411.3161]
5
10
15
0
5
10
0.5
0.5
LHCb prelim.
0
LHCb prelim.
0
-0.5
0
15
q2 [GeV2/ c4]
S9
S8
q2 [GeV2/ c4]
-0.5
5
10
15
0
5
q2 [GeV2/ c4]
C. Langenbruch (Warwick), Warwick EPP 2015
10
15
q2 [GeV2/ c4]
Rare b-hadron decays
[LHCb-PAPER-2015-051]
-0.5
b → q`` | B 0 → K ∗0 µ+ µ−
29 / 48
∗0 + −
0
A4
0.5
0.5
LHCb prelim.
LHCb prelim.
0
0
-0.5
0
-0.5
5
10
15
0
5
10
0.5
0.5
LHCb prelim.
0
LHCb prelim.
0
-0.5
0
15
q2 [GeV2/ c4]
A 6s
A5
q2 [GeV2/ c4]
-0.5
5
10
15
0
5
q2 [GeV2/ c4]
C. Langenbruch (Warwick), Warwick EPP 2015
10
15
q2 [GeV2/ c4]
Rare b-hadron decays
[LHCb-PAPER-2015-051]
A3
B → K µ µ CP asymmetries: A3 , A4 , A5 , A6s
b → q`` | B 0 → K ∗0 µ+ µ−
30 / 48
∗0 + −
0
0.5
0.5
LHCb prelim.
0
0
-0.5
0
LHCb prelim.
-0.5
5
10
15
0
5
A9
q2 [GeV2/ c4]
LHCb prelim.
0
-0.5
5
10
15
q2 [GeV2/ c4]
C. Langenbruch (Warwick), Warwick EPP 2015
15
q2 [GeV2/ c4]
0.5
0
10
Rare b-hadron decays
[LHCb-PAPER-2015-051]
A8
A7
B → K µ µ CP asymmetries: A7 , A8 , A9
b → q`` | B 0 → K ∗0 µ+ µ−
31 / 48
P50
5
P'
[LHCb-PAPER-2015-051]
1
LHCb
prelim.
0.5
SM from DHMV
[1407.8526]
0
-0.5
-1
0
5
10
15
q2 [GeV2/ c4]
Tension seen in P50 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
b → q`` | B 0 → K ∗0 µ+ µ−
31 / 48
P50
5
P'
[LHCb-PAPER-2015-051]
1
LHCb
prelim.
0.5
SM from DHMV
[1407.8526]
0
-0.5
-1
0
5
10
15
q2 [GeV2/ c4]
Tension seen in P50 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
b → q`` | B 0 → K ∗0 µ+ µ−
32 / 48
15
10
5
LHCb
prelim.
0
3
3.5
4
[LHCb-PAPER-2015-051]
SM
∆χ 2
Compatibility with the SM
4.5
Re (C9)
Perform χ2 fit of measured Si observables using [EOS] software
Beaujean et al.,
Varying Re(C9 ) and incl. nuisances according [F.EPJC
74 (2014) 2897]
∆Re(C9 ) = −1.04 ± 0.25 with global significance of 3.4 σ
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
b̄
−
+ −
→ φ[→ K K ]µ µ
s
Bs0
+
s
φ
t̄
s̄
W+
Z 0, γ
µ−
µ+
18
16
14
12
10
8
6
4
2
0
103
102
10
LHCb
5.3
5.4
5.5
[JHEP 09 (2015) 179]
The rare decay
33 / 48
Bs0
q2 [GeV2/ c4]
0
b → q`` | Bs
→ φµ+ µ−
1
−
m(K +K µ +µ −) [GeV/c2]
Dominant b → sµ+ µ− decay for Bs0 , analogous to B 0 → K ∗0 µ+ 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
Clean selection due to narrow φ resonance, S-wave negligible
fs
fd
C. Langenbruch (Warwick), Warwick EPP 2015
∼ 41 ,
B(φ→K + K − )
B(K ∗0→K + π − )
=
Rare b-hadron decays
3
4
0
b → q`` | Bs
→ φµ+ µ−
Bs0 →
34 / 48
+ −
φµ µ mass model
LHCb
B0s→ φ µ +µ −
100
50
5300
5400 −
5500
Events / 10 MeV/c2
Events / 10 MeV/c2
[JHEP 09 (2015) 179]
LHCb
15000
B0s→ J / ψ φ
10000
5000
5300
m(K +K µ +µ −) [MeV/c2]
5400 −
5500
m(K +K µ +µ −) [MeV/c2]
Signal mass model (double CB) taken from Bs0 → J/ψ φ
q 2 dep. resolution accounted for with scale factor from simulation
Background described using Exponential
Signal yield Nφµµ = 432 ± 24 (q 2 -integrated)
Bs0 → J/ψ φ yield NJ/ψ φ = 62 033 ± 260
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
0
b → q`` | Bs
→ φµ+ µ−
Bs0 →
35 / 48
+ −
φµ µ differential branching fraction
2 < q2 < 5 GeV2/ c4
15
10
5
Events / 10 MeV/c2
m(K
+
5500
[MeV/c2]
LHCb
20
15 < q2 < 17 GeV2/ c4
10
5300
5400
5300
−
K µ +µ −)
5500
[MeV/c2]
−
m(K +K µ +µ −)
5400
m(K
+
17 < q2 < 19 GeV2/ c4
10
5
5300
5400
5 < q2 < 8 GeV2/ c4
20
10
5500
[MeV/c2]
LHCb
15
30
5300
−
K µ +µ −)
5400
m(K
Events / 10 MeV/c2
5400
Events / 10 MeV/c2
5300
LHCb
5500
[MeV/c2]
−
m(K +K µ +µ −)
+
1 < q2 < 6 GeV2/ c4
10
5400
5500
−
m(K +K µ +µ −) [MeV/c2]
LHCb
11 < q2 < 12.5 GeV2/ c4
15
10
5
5500
[MeV/c2]
20
5300
20
5300
−
K µ +µ −)
LHCb
30
Events / 10 MeV/c2
10
LHCb
Events / 10 MeV/c2
0.1 < q2 < 2 GeV2/ c4
25
20
Events / 10 MeV/c2
20
Events / 10 MeV/c2
Events / 10 MeV/c2
[JHEP 09 (2015) 179]
LHCb
5400
40
5500
−
m(K +K µ +µ −) [MeV/c2]
LHCb
15 < q2 < 19 GeV2/ c4
30
20
10
5300
5400
5500
−
m(K +K µ +µ −) [MeV/c2]
Bs0 → J/ψ φ used for normalisation
Differential branching fraction:
φµµ
Nφµµ
dB(Bs0 → φµ+ µ− )
1
= 2
×
×
× B(Bs0 → J/ψ φ) × B(J/ψ → µ+ µ− )
2
dq 2
NJ/ψ φ J/ψ φ
qmax. − qmin.
φµµ from (corrected) simulation, many effects cancel in ratio
J/ψ φ
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
0
b → q`` | Bs
→ φµ+ µ−
36 / 48
+ −
9
LHCb
8
7
6
5
4
3
SM pred.
SM (wide)
SM LQCD
Data
Data (wide)
2
1
0
5
10
[JHEP 09 (2015) 179]
φµ µ differential branching fraction
dB(B0s → φ µ µ )/dq2 [10-8GeV-2c4]
Bs0 →
15
q2 [GeV2/ c4]
In 1 < q 2 < 6 GeV2/c4 diff. B more than 3 σ 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(Bs0 → φµ+ µ− )
−4
= (7.41+0.42
−0.40 ± 0.20 ± 0.21) × 10 ,
B(Bs0 → J/ψ φ)
−7
B(Bs0 → φµ+ µ− ) = (7.97+0.45
−0.43 ± 0.22 ± 0.23 ± 0.60) × 10 ,
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
0
b → q`` | Bs
→ φµ+ µ−
Bs0 →
37 / 48
+ −
φµ µ angular analysis
Non-flavour specific final state → reduced number of accessible
observables 4 CP averages, 4 CP asymmetries
9 3
1
d3 (Γ + Γ̄)
2
2
2
1
=
4 (1 − FL ) sin θK + FL cos θK + 4 (1 − FL ) sin θK cos 2θ`
~
32π
d(Γ + Γ̄)/dq 2
dΩ
− FL cos2 θK cos 2θ` + S3 sin2 θK sin2 θ` cos 2φ
+ S4 sin 2θK sin 2θ` cos φ + A5 sin 2θK sin θ` cos φ
+ A6 sin2 θK cos θ` + S7 sin 2θK sin θ` sin φ
+ A8 sin 2θK sin 2θ` sin φ + A9 sin2 θK sin2 θ` sin 2φ
ub. ML fit in m(K + K − µ+ µ− ) and {cos θ` , cos θK , φ} in bins of q 2
Angular background modelled with 2nd order Chebyshev polynomials
Same acceptance method used as for B 0 → J/ψ K ∗0
cross-checked using Bs0 → J/ψ φ
Feldman-Cousins method due to very limited statistics
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
0
b → q`` | Bs
→ φµ+ µ−
38 / 48
+ −
1.5
LHCb
0.5
0.5
0.0
0.0
-0.5
5
10
q2
1.0
15
[GeV2/ c4]
LHCb
-1.0
0.5
0.0
0
-0.5
-0.5
5
10
q2
15
[GeV2/ c4]
LHCb
SM pred.
SM (wide)
Data
Data (wide)
5
-1
15
q2 [GeV2/ c4]
LHCb
5
Good agreement of angular obs. with SM predictions
C. Langenbruch (Warwick), Warwick EPP 2015
10
1
0.5
-1.0
[JHEP 09 (2015) 179]
1.0
1.0
-0.5
S4
S3
φµ µ angular analysis
S7
FL
Bs0 →
Rare b-hadron decays
10
15
q2 [GeV2/ c4]
0
b → q`` | Bs
→ φµ+ µ−
39 / 48
+ −
φµ µ angular analysis
A5
1
LHCb
A6
Bs0 →
0.5
0.5
0
0
-0.5
-0.5
5
10
q2
A8
1
-1
15
[GeV2/ c4]
LHCb
A9
-1
0.5
0
0
-0.5
-0.5
5
10
q2
15
[GeV2/ c4]
LHCb
5
-1
15
q2 [GeV2/ c4]
LHCb
5
Good agreement of angular obs. with SM predictions
C. Langenbruch (Warwick), Warwick EPP 2015
10
1
0.5
-1
[JHEP 09 (2015) 179]
1
Rare b-hadron decays
10
15
q2 [GeV2/ c4]
b → q`` | b → sµ+ µ− branching fractions
40 / 48
(∗) + −
Number of signal events in full 3 fb−1 data sample
Nsig
B + → K ∗+ µ+ µ−
162 ± 16
Normalise with respect to B 0 → J/ψ KS0 (K ∗0 ) and B + → J/ψ K + (K ∗+ )
Differential branching fractions
dB/dq2 [10-8 × c4/GeV2]
LCSR
Lattice
Data
+ + −
B →K µ µ
LHCb
5
+
4
3
2
1
0
0
5
10
15
20
q2 [GeV2/c4]
B 0 → K ∗0 µ+ µ−
2361 ± 56
LCSR
Lattice
Data
B → K 0µ +µ −
LHCb
5
0
4
3
2
1
0
0
5
10
15
Compatible with but lower than SM predictions
h
ih
i
A. Khodjamirian et al.,
Ball et al.,
Light cone sum rules (LCSR): P.
PRD 71 (2005) 014029
JHEP 09 (2010) 089
h
ih
i
Horgan et al.,
C. Bouchard et al.,
Lattice: R.
PRD 88 (2013) 054509
PRD 89 (2014) 094501
dB(B 0 → K ∗0 µ+ µ− )/dq 2 with 3 fb−1 in preparation
C. Langenbruch (Warwick), Warwick EPP 2015
20
q2 [GeV2/c4]
Rare b-hadron decays
[JHEP 06 (2014) 133]
B + → K + µ+ µ
4746 ± 81
dB/dq2 [10-8 × c4/GeV2]
B 0 → KS0 µ+ µ−
176 ± 17
[JHEP 06 (2014) 133]
B → K µ µ branching fraction measurements
b → q`` | b → sµ+ µ− branching fractions
40 / 48
(∗) + −
Number of signal events in full 3 fb−1 data sample
Nsig
B + → K ∗+ µ+ µ−
162 ± 16
LCSR
20
Lattice
Data
*+ + −
B →K µ µ
LHCb
+
15
10
5
0
0
5
10
15
20
1.5
Theory
LHCb
Binned
LHCb
B 0 → K ∗0 µ+ µ−
1
0.5
0
0
5
10
Compatible with but lower than SM predictions
h
ih
i
A. Khodjamirian et al.,
Ball et al.,
Light cone sum rules (LCSR): P.
PRD 71 (2005) 014029
JHEP 09 (2010) 089
h
ih
i
Horgan et al.,
C. Bouchard et al.,
Lattice: R.
PRD 88 (2013) 054509
PRD 89 (2014) 094501
dB(B 0 → K ∗0 µ+ µ− )/dq 2 with 3 fb−1 in preparation
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
15
20
q 2 [GeV2/ c 4]
[JHEP 08 (2013) 131]
Differential branching fractions
q2 [GeV2/c4]
B 0 → K ∗0 µ+ µ−
2361 ± 56
Normalise with respect to B 0 → J/ψ KS0 (K ∗0 ) and B + → J/ψ K + (K ∗+ )
dB/dq2 [10-8 × c4/GeV2]
B + → K + µ+ µ
4746 ± 81
dB /dq 2 [10-7 × c 4 GeV-2]
B 0 → KS0 µ+ µ−
176 ± 17
[JHEP 06 (2014) 133]
B → K µ µ branching fraction measurements
Global b → s fits
41 / 48
Global fits to b → s data
h
W. Altmannshofer et al.,
EPJC 75 (2015) 382
i
S. Descotes-Genon et al.,
arXiv:1510.04239
Angular observables
Branching fractions
Combined
Combine exp. information from rare b → s processes in global fit of Ci
b → sγ,
B-fact.
B(Bs0 → µ+ µ− ),
LHCb+CMS
Ang.(B 0 → K ∗0 µ+ µ− ),
LHCb 3 fb−1
Ang.+B(Bs0 → φµ+ µ− ),
LHCb 1 fb−1 (3 fb−1 )
B(B 0,+ → K 0,+(∗) µ+ µ− ),
LHCb 3 fb−1 (1 fb−1 )
Tension can be reduced with ∆Re(C9 ) ∼ −1, significances around 4 σ
Consistency between angular observables and branching fractions
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Global b → s fits
42 / 48
NP or hadronic effect?
cc̄ loop
Possible NP
γ
s
b
c
Z0
µ−
µ+
q2
`+
b
s
d¯
d¯
Possible explanations for shift in C9
c̄
`−
et al.] [Buras et al.]
NP e.g. Z 0 [Gauld
Leptoquarks
[Altmannshofer et al.] [Crivellin et al.]
hadronic charm loop contributions
[Hiller et al.] [Biswas et al.]
[Buras et al.] [Gripaios et al.]
dependence: cc̄ loops rise towards J/ψ, NP q 2 -independent
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Global b → s fits
42 / 48
NP or hadronic effect?
W. Altmannshofer et al.,
arXiv:1503.06199
S. Descotes-Genon et al.,
Possible explanations for shift in C9
q2
arXiv:1510.04239
et al.] [Buras et al.]
NP e.g. Z 0 [Gauld
Leptoquarks
[Altmannshofer et al.] [Crivellin et al.]
hadronic charm loop contributions
[Hiller et al.] [Biswas et al.]
[Buras et al.] [Gripaios et al.]
dependence: cc̄ loops rise towards J/ψ, NP q 2 -independent
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
B + → π + µ+ µ−
43 / 48
+ −
+ + −
+
The b → dµ µ decay B → π µ µ
u
B+
b̄
u
t̄
W+
Z 0, γ
π+
¯
d
µ−
µ+
Candidates / ( 30 MeV/ c2 )
[JHEP 10 (2015) 034]
70
LHCb
60
B+→π+µ+µB+→K +µ+µ0
B+→D µ+ν
B0,+→ρ0,+µ+µB0s →f 0µ+µCombinatorial
50
40
30
20
10
0
5200
5400
5600
5800
2
b → dµ+ µ− transition in SM sup. by VVtd
∼
ts
Measure diff. branching fraction and ACP (O(−0.1) in the SM)
1
25
6000
m(π+µ+µ-) (MeV/c2)
wrt. b → sµ+ µ−
Assuming SM, measure |Vtd /Vts |, |Vtd |, |Vts | using B + → K + µ+ µ−
+
+ µ+ µ− )
+
+ µ+ µ− )
|Vtd |2 = B(B R→π
and |Vts |2 = B(B R→K
Fπ dq 2
F dq 2
K
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
B + → π + µ+ µ−
43 / 48
+ −
+ + −
+
The b → dµ µ decay B → π µ µ
u
B+
b̄
u
t̄
W+
Z 0, γ
π+
¯
d
µ−
µ+
Candidates / ( 10 MeV/ c2 )
[JHEP 10 (2015) 034]
600
LHCb
500
B+→K +µ+µB+→K +µ+µ-X
Combinatorial
400
300
200
100
0
5200
5400
5600
5800
2
b → dµ+ µ− transition in SM sup. by VVtd
∼
ts
Measure diff. branching fraction and ACP (O(−0.1) in the SM)
1
25
6000
m(K +µ+µ-) (MeV/c2)
wrt. b → sµ+ µ−
Assuming SM, measure |Vtd /Vts |, |Vtd |, |Vts | using B + → K + µ+ µ−
+
+ µ+ µ− )
+
+ µ+ µ− )
|Vtd |2 = B(B R→π
and |Vts |2 = B(B R→K
Fπ dq 2
F dq 2
K
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
B + → π + µ+ µ−
+
44 / 48
+ + −
2.5
LHCb
APR13
HKR15
FNAL/MILC15
LHCb
2
1.5
1
0.5
0
0
10
20
q2
(GeV
[JHEP 10 (2015) 034]
Candidates / ( 0.05 GeV2/ c4 )
dB/dq2 (10-9 GeV-2c4)
B → π µ µ diff. B, ACP and CKM matrix elements
10
LHCb
8
6
4
2
0
0.2
0.4
0.6
0.8
1
q2 (GeV2/ c4)
2
/ c 4)
Good agreement with but slightly lower than SM predictions
APR13 [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
+0.9
−3 and |V | = 3.2+0.4 × 10−2
| VVtd
| = 0.24+0.05
ts
−0.04 , |Vtd | = 7.2−0.8 × 10
−0.4
ts
Du et al.,
New lattice predictions from MILC collaboration [D.
arXiv:1510.02349]
→ CKM elements from RDs competitive with B(s) oscillation meas.
→ Combined 2 σ tension of B(B + → K + (π + )µ+ µ− ) with SM prediction
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
B + → π + µ+ µ−
Test of lepton universality in B → K ` `
B(B + →K + µ+ µ− )
B(B + →K + e+ e− )
= 1 ± O(10−3 ) in the SM, not affected by cc̄ loops
B + → K + µ+ µ−
25
LHCb (a)
4
10
20
3
10
ψ(2S)K +
15
J/ψK +
B + → K + e+ e−
25
103
LHCb (b)
20
ψ(2S)K +
15
102
J/ψK +
10
102
10
5
10
5
1
0
10
radiative tails
0
4800
5000
radiative tails
5200
5400
5600
m(K +µ +µ −) [MeV/c2]
4800
5000
5200
5400
Experimental challenges for B + → K + e+ e− mode
1. Trigger 2. Bremsstrahlung
Use double
N ratio to cancel
N systematic
uncertainties
K + e+ e−
J/ψ (e+ e− )K +
J/ψ (µ+ µ− )K +
K + µ+ µ−
RK = N + + −
N
+ + −
+ −
+
+ −
+
K
+
e
J/ψ (µ
e
Use B → J/ψ K
+
µ
)K
K
µ
µ
J/ψ (e
as cross-check
C. Langenbruch (Warwick), Warwick EPP 2015
5600
m(K +e+e−) [MeV/c2]
Rare b-hadron decays
e
)K
1
[PRL 113, 151601 (2014)]
RK =
q2 [GeV2/ c4]
q2 [GeV2/ c4]
45 / 48
+ + −
+
B + → π + µ+ µ−
46 / 48
+ + −
+
B + → J/ψ (→ e+ e− )K +
LHCb
10
(a)
triggered on e
5
0
5000
RK
LHCb
5200
BaBar
5400
5600
m(K +e+e−) [MeV/c2]
LHCb
1.5
1
0.5
10
LHCb
30
(d)
triggered on e
20
10
0
5000
5200
5400
5600
m(K +e+e−) [MeV/c2]
15
20
q2 [GeV2/ c4]
C. Langenbruch (Warwick), Warwick EPP 2015
Use theoretically and experimentally
favoured q 2 region ∈ [1, 6] GeV2
+0.090
RK = 0.745−0.074
(stat.) ± 0.036(syst.),
compatible with SM at 2.6σ
Bq2 ∈[1,6] GeV2 (B + → K + e+ e− ) =
+0.19 +0.06
−7
(1.56−0.15
−0.04 ) × 10
SM
5
40
Belle
2
0
0
B + → K + e+ e−
[arxiv:1406.6482]
×103
Candidates / ( 40 MeV/ c2 )
Candidates / ( 40 MeV/ c2 )
Test of lepton universality in B → K ` `
Rare b-hadron decays
Lepton universality
47 / 48
Lepton universality and lepton flavour violation
Due
to the cleanness
SM prediction,
a lot of attention
K received
Glashow
Hillerofet the
Crivellin etR
et al.
al.
al.
Including RK in global fits increases tension with SM hypothesis
PRL 114 (2015) 091801
PRD 90 (2014) 054014
PRL 114 (2015) 151801
B(B 0→K ∗0 µ+ µ− )
B(B 0→K ∗0 e+ e− )
B(B 0→φµ+ µ− )
Naturally motivates RK ∗ =
B(B → K (∗) µ± e∓ ) [B(B → K (∗) µ± τ ∓ )] could be O(10−8 ) [O(10−6 )]
Other anomalies
and Rφ = B(Bs0→φe+ e− )
s
et al.
Also motivates searches for lepton flavour violation Glashow
PRL 114 (2015) 091801
“Lepton non-universality generally implies lepton flavour violation”
h
One Leptoquark to Rule Them All: A Minimal Explanation
for RD∗ , RK and (g − 2)µ , M. Bauer et al., arXiv:1511.01900
RK , RD∗ and B − → τ − ν̄
Explain RK and h → µτ
R. Alonso et al.
[arXiv:1505.05164
]
PRL 114 (2015) 151801
A. Crivellin et al.
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
i
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:
P50 in B 0 → K ∗0 µ+ µ− , B(Bs0 → φµ+ µ− ), RK
Consistent NP explanations exist
But unexpectedly large hadronic effects
can not yet be excluded
Looking forward to the additional
data 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 section
σbb̄ = (75.3 ± 14.1) µb [Phys.Lett. B694 (2010)] in acceptance
∼ 1 × 1011 produced bb̄ pairs in 2011, excellent environment to study
B 0 → K ∗0 µ+ µ− and other rare decays
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Backup
51 / 48
The LHCb detector: Tracking
Tracking system
Vertex
detector
B 0 → K ∗0 µ+ µ− signature
L ∼ 7 mm SV
0
PV B
Interaction
point
p
−
µ+ π
µ−
K+
p
IP
Excellent Impact Parameter (IP) resolution (20 µm)
→ 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
RICH2
K/π separation
[arxiv:1211.6759]
RICH1
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 thresholds
Muons: pT > 1.76 GeV at L0, pT > 1.0 GeV at HLT1
B → µµX: Trigger ∼ 90%
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Backup
53 / 48
Data taken by LHCb
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Backup
54 / 48
Moments analysis
5
P'
A FB
[LHCb-PAPER-2015-051]
2
LHCb prelim.
0.5
1
0
SM from DHMV
Likelihood fit
Method of moments
0
LHCb prelim.
SM from ABSZ
Likelihood fit
Method of moments
-0.5
0
5
10
-2
0
15
q2
-1
5
10
15
2
[GeV
q2 [GeV2/ c4]
/ c4]
~ are orthogonal
Angular terms fi (Ω)
→ can determine obs. via their moments M̂i =
P1
e
we
P
~
e we fi (Ωe )
et al.,
10-30% less sensitive than Maximum Likelihood fit [F.PRDBeaujean
91 (2015) 114012]
but allows narrow 1 GeV2/c4 wide q 2 bins
Consistency of the results checked using toys
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Backup
55 / 48
Amplitude fit and Zero-crossing points
S5
A FB
[LHCb-PAPER-2015-051]
0.5
0.5
LHCb prelim.
LHCb prelim.
Amplitude fit
Likelihood fit
Method of moments
Amplitude fit
Likelihood fit
Method of moments
0
0
-0.5
-0.5
2
3
4
5
6
2
3
q2 [GeV2/ c4]
4
5
Zero-crossing points sensitive tests of SM, form factor uncertainties cancel
Perform q 2 dependent amplitude fit with Ansatz
1
2
2 4
2
AL,R
0,k,⊥ = α + βq + γ q 2 in the region 1.1 < q < 6 GeV /c
Resulting zero crossing points in good agreement with SM predictions
q02 (AFB ) ∈ [3.40, 4.87] GeV2/c4 @ 68% CL,
q02 (S4 ) < 2.65 GeV2/c4 @ 95% CL,
q02 (S5 ) ∈ [2.49, 3.95] GeV2/c4 @ 68% CL
C. Langenbruch (Warwick), Warwick EPP 2015
6
q2 [GeV2/ c4]
Rare b-hadron decays
Backup
56 / 48
0
∗0 + −
Search for hidden sector boson in B → K µ µ
µ
χ
µ−
t
Vtb
Vts
b
s
W+
B0
d
K ∗0
d
Candidates / 10 MeV
[PRL 115 (2015) 161802]
+
ω
φ
J/ψ
20
15
ψ (2S)+ψ (3770)
Prompt
Displaced
LHCb
10
5
200
1000
2000
3000
Search for hidden sector boson in B 0 → K ∗0 χ 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 B 0 → K ∗0 µ+ µ− in 1.1 < q 2 < 6.0 GeV2/c4
4000
m(µ +µ −) [MeV]
No excess → Upper limits on B(B 0 → K ∗0 χ(→ µ+ µ− )) set at 95% CL
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Backup
56 / 48
0
∗0 + −
Search for hidden sector boson in B → K µ µ
[PRL 115 (2015) 161802]
Vts
b
s
W+
B0
d
K ∗0
d
LHCb
10-1
10-8
τ =100ps
10-2
τ =10ps
10-9
1000
2000
3000
4000
m(µ +µ −) [MeV]
Search for hidden sector boson in B 0 → K ∗0 χ 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 B 0 → K ∗0 µ+ µ− in 1.1 < q 2 < 6.0 GeV2/c4
10-7
τ =1000ps
No excess → Upper limits on B(B 0 → K ∗0 χ(→ µ+ µ− )) set at 95% CL
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
B(B0→ K *0χ (µ +µ −))
µ−
t
Vtb
B(B0→ K *0χ (µ +µ −))
µ
χ
B(B0→ K *0µ +µ −)[1.1,6.0]GeV2
1
+
Backup
57 / 48
Exclusion limits for specific models
1
2
1000
2000
3000
4000
m(µ +µ −) [MeV]
10
10-6
LHCb
RM
1
Theory
-5
CHA
0.5
10-4
θ2
LHCb
B(χ → hadrons) = 0.99
f (χ)tan2β [PeV], m(h)=10 TeV
f (χ)tan2β [PeV], m(h)=1 TeV
[PRL 115 (2015) 161802]
B(χ → hadrons) = 0
10-7
Theory
10-8
400
600
800
Resulting 95% CL exclusion limits for specific models
Axion model [M. Freytsis et al., PRD 81 (2010) 034001]
Exclusion regions for large tan β, 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
1000
m(µ +µ −) [MeV]
Backup
58 / 48
(∗) + −
B → K µ µ isospin
τ
B(B 0 →K (∗)0 µ+ µ− )− τ 0 B(B + →K (∗)+ µ+ µ− )
SM prediction for AI is O(1%)
1
LHCb
AI
AI
Isospin asymmetry AI =
B → K µ +µ −
1
LHCb
0.5
0.5
0
0
-0.5
-0.5
-1
0
5
10
15
20
-1
0
5
B → K *µ +µ −
10
q2 [GeV2/c4]
15
20
q2 [GeV2/c4]
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
[JHEP 06 (2014) 133]
+
τ
B(B 0 →K (∗)0 µ+ µ− )+ τ 0 B(B + →K (∗)+ µ+ µ− )
+
Backup
59 / 48
Reminder: B → K µ µ angular observables (1 fb−1 )
∗0 + −
1
Theory
LHCb
Binned
AFB
FL
0
LHCb
0.8
1
Theory
LHCb
Binned
LHCb
0.5
0.6
0
0.4
-0.5
0.2
0
0
5
10
15
20
q 2 [GeV2/ c 4]
-1
0
5
10
15
20
q 2 [GeV2/ c 4]
[JHEP 08 (2013) 131]
Angular observables in good agreement with
SM prediction [C. Bobeth et al. JHEP 07 (2011) 067]
Zero crossing point of AFB free from FF uncertainties
Result q02 = 4.9 ± 0.9 GeV2 consistent with SM prediction
2
2
q0,SM
= 4.36+0.33
−0.31 GeV [EPJ C41 (2005) 173-188]
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Backup
60 / 48
Less form factor dependent observables
Pi0
−1
(1 fb )
Less FF dependent observables Pi0 introduced in [JHEP 05 (2013) 137]
p
0
For P4,5
= S4,5 / FL (1 − FL ) leading FF uncertainties cancel for all q 2
3.7σ local deviation from SM prediction [JHEP 05 (2013) 137] in P50
1
0.8
SM Predictions
0.6
0.4
P 5'
P 4'
LHCb
1
0.8
Data
SM Predictions
0.4
0.2
Data
0.2
0
0
-0.2
-0.2
-0.4
-0.4
-0.6
-0.6
-0.8
-0.8
-1
0
LHCb
0.6
5
10
15
20
-1
0
3.7σ
5
q 2 [GeV2/c 4]
10
15
20
q 2 [GeV2/c 4]
[PRL 111, 191801 (2013)]
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Backup
61 / 48
0
B(s)
Study of rare
+ − + −
→ π π µ µ decays I
s
s
Bs0
t̄
b̄
d
f0
s̄
W+
Z 0, γ
d
B0
t̄
b̄
W+
Z 0, γ
µ−
µ+
Bs0 → f0 µ+ µ− : b → s transition similar to B 0 → K ∗0 µ+ µ−
B 0 → ρ0 µ+ µ− : b → d transition, |Vtd /Vts |2 suppressed in SM
SM predictions show large variation
BSM (Bs0 → f0 µ+ µ− ) = 0.6 × 10−9 − 5.2 × 10−7
[PRD 79 014013], [PRD 81 074001], [PRD 80 016009]
BSM (B 0 → ρ0 µ+ µ− ) = (5 − 9) × 10−8
[PRD 56 5452-5465], [Eur.Phys.J.C 41 173-188]
C. Langenbruch (Warwick), Warwick EPP 2015
µ−
µ+
Contributions from
ρ0
¯
d
Rare b-hadron decays
Backup
62 / 48
+ − + −
→ π π µ µ decays II
B0s→ J/ψ π+ πB0→ J/ψ π+ π0
0
B → J/ψ K*(892)
Bs0 → J/ψ φ
0
Bs → J/ψ η’
B+→ J/ψ K+
Combinatorial
+
+
Bc → J/ψ π π-π+
Total fit
103
102
LHCb
Signal decay
Events/(20 MeV/c2)
Events/(20 MeV/c2)
Resonant decay
40
B0s→ π+ π- µ+ µB0→ π+ π- µ+ µ0
0
B → K*(892) µ+ µB0s → η’ µ+ µ-
30
Combinatorial
Total fit
20
LHCb
10
10
5.2
[PLB 743 (2015) 46]
Study of rare
0
B(s)
5.6
5.8
5.2
5.4
5.6
5.8
M(π+π-µ+µ-) [GeV/c2]
M(π+π-µ+µ-) [GeV/c2]
Observation of Bs0 → π + π − µ+ µ− with 7.6σ
0
+ − + −
5.4
Evidence for B → π π µ µ
with 4.8σ
Branching fractions compatible with SM predictions
B(Bs0 → π + π − µ+ µ− ) = (8.6 ± 1.5stat. ± 0.7syst. ± 0.7norm. ) × 10−8
B(B 0 → 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
Backup
63 / 48
∗0 + −
0
The rare decay B → K e e
J/ψ(1S)
d
B0
b̄
d
t̄
W+
Z 0, γ
K ∗0
s̄
ψ(2S)
(!)
dΓ
dq 2
C7
(!)
(!)
C7 C9
e−
!"#$%&$%$"'$(
(!)
C9
(!)
)"*( C 10
+,"-(*!.#)"'$(
',"#%!/01,".(&%,2(cc̄
)/,3$(,4$"('5)%2(
#5%$.5,6*((
e+
4 [m(µ)]22
4[m(`)]
Analyse B 0 → K ∗0 e+ e− at very low q 2 : [0.0004, 1.0] GeV2/c4 ,
accessible due to tiny e mass
Im
Determine angular observables FL , AT , ARe
T , AT
0
sensitive to C7 and C7
Experimental challenges: Trigger and Bremsstrahlung
(2)
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
q2
Backup
63 / 48
∗0 + −
0
The rare decay B → K e e
d
B0
b̄
d
t̄
W+
Z 0, γ
K ∗0
s̄
e−
e+
Candidates / (30 MeV/c2)
[arxiv:1501.03038]
30
B0 → K*0e+e−
B →(K*0X)e+e−
Combinatorial
Data
Model
25
LHCb
20
15
10
5
0
4800
5000
5200
Analyse B 0 → K ∗0 e+ e− at very low q 2 : [0.0004, 1.0] GeV2/c4 ,
accessible due to tiny e mass
Im
Determine angular observables FL , AT , ARe
T , AT
0
sensitive to C7 and C7
Experimental challenges: Trigger and Bremsstrahlung
(2)
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
5400
m(K+π−e+e−) [MeV/c2]
Backup
64 / 48
∗0 + −
0
40
30
20
Candidates / (0.1π rad)
LHCb
50
Candidates / (0.2)
Candidates / (0.2)
Angular analysis of B → K e e decays
LHCb
40
35
30
25
20
15
10
10
35
25
20
15
10
5
5
0
-0.5
0
0.5
cos θl
0
-1
[arxiv:1501.03038]
obs.
result
FL
+0.16 ± 0.06 ± 0.03
(2)
AT
−0.23 ± 0.23 ± 0.05
ARe
+0.10 ± 0.18 ± 0.05
T
AIm
+0.14 ± 0.22 ± 0.05
T
-0.5
0
0.5
1
cos θK
0
0
1
2
[JHEP 05 (2013) 043]
obs.
SM prediction
FL
(2)
AT
ARe
T
AIm
T
+0.10+0.11
−0.05
+0.03+0.05
−0.04
−0.15+0.04
−0.03
−4
(−0.2+1.2
−1.2 ) × 10
Results are in good agreement with SM predictions
Constraints on C7 competitive with radiative decays
(0)
C. Langenbruch (Warwick), Warwick EPP 2015
LHCb
30
Rare b-hadron decays
3
∼
φ [rad]
Backup
0
65 / 48
∗0 + −
B → K µ µ angular observables
Four-differential decay rate for B 0 → K ∗0 µ+ µ−
d4 Γ(B 0 → K ∗0 µ+ µ− )
9 s 2
=
I sin θK + I1c cos2 θK
dq 2 d cos θ` d cos θK dφ
32π 1
+ (I2s sin2 θK + I2c cos2 θK ) cos 2θ`
+ I3 sin2 θK sin2 θ` cos 2φ + I4 sin 2θK sin 2θ` cos φ
+ I5 sin 2θK sin θ` cos φ
+ (I6s sin2 θK + I6c cos2 θK ) cos θ` + I7 sin 2θK sin θ` sin φ
+ I8 sin 2θK sin 2θ` sin φ + I9 sin2 θK sin2 θ` sin 2φ
(0)
(0)
(0)
Ii (q 2 ) combinations of K ∗0 spin amplitudes sensitive to C7 , C9 , C10
Γ̄)
¯ d(Γ+Γ̄)
CP-averages Si = (Ii + I¯i )/ d(Γ+
dq 2 , CP-asymmetries Ai = (Ii − Ii )/ dq 2
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 ∝ sin φ, cos φ
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
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0
65 / 48
∗0 + −
B → K µ µ angular observables
Four-differential decay rate for B 0 → K ∗0 µ+ µ−
d4 Γ(B 0 → K ∗0 µ+ µ− )
9 s 2
=
I sin θK + I1c cos2 θK
dq 2 d cos θ` d cos θK dφ
32π 1
+ (I2s sin2 θK + I2c cos2 θK ) cos 2θ`
((
((
(2θ
+ I3 sin2 θK sin2 θ` cos 2φ + I4 (
sin(2θ
sin
(K(
` cos φ
(
((
(θ(
+ I5 (
sin 2θ (
sin
` cos φ
( ((K
((
(θ(
(K(
+ (I6s sin2 θK + I6c cos2 θK ) cos θ` + (
I7 (
sin(2θ
sin
` sin φ
(
(
((
2
2
(2θ
+ I8 (
sin 2θ (
sin
` sin φ + I9 sin θK sin θ` sin 2φ
( ((K
(0)
(0)
(0)
Ii (q 2 ) combinations of K ∗0 spin amplitudes sensitive to C7 , C9 , C10
Γ̄)
¯ d(Γ+Γ̄)
CP-averages Si = (Ii + I¯i )/ d(Γ+
dq 2 , CP-asymmetries Ai = (Ii − Ii )/ dq 2
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 ∝ sin φ, cos φ
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Backup
2
Ii (q ) depend on K
∗0
spin amplitudes
4m2µ
(2 + βµ2 ) L 2
L R∗
2
R∗
|A⊥ | + |AL
<(AL
⊥ A⊥ + Ak Ak )
k | + (L → R) +
4
q2
4m2µ 2
R 2
R∗
I1c = |AL
|At |2 + 2<(AL
0 A0
0 | + |A0 | +
q2
βµ2
2
L 2
|AL
I2s =
⊥ | + |Ak | + (L → R)
4
c
2
I2 = −βµ2 |AL
0 | + (L → R)
I1s =
For completeness
AL,R
0 ,
βµ2
2
L 2
|AL
⊥ | − |Ak | + (L → R)
2
βµ2
L∗
= √ <(AL
0 Ak ) + (L → R)
2
√
L∗
= 2βµ <(AL
0 A⊥ ) − (L → R)
L∗
= 2βµ <(AL
k A⊥ ) − (L → R)
√
L∗
= 2βµ =(AL
0 Ak ) − (L → R)
I3 =
I4
I5
I6
I7
βµ2
L∗
I8 = √ =(AL
0 A⊥ ) + (L → R)
2
2
L
I9 = βµ =(AL∗
k A⊥ ) + (L → R)
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
AL,R
k ,
66 / 48
AL,R
⊥
Backup
K
∗0
AL,R
0 ,
spin amplitudes
AL,R
k ,
AL,R
⊥
67 / 48
√
V(q2 )
2mb
0eff
eff
0eff
0eff
2
= N 2λ (Ceff
+ 2 (Ceff
9 + C9 ) ∓ (C10 + C10 )
7 + C7 )T1 (q )
mB + mK ∗
q
√
A1 (q2 )
2mb
L(R)
0eff
eff
0eff
0eff
2
+ 2 (Ceff
Ak
= −N 2(m2B − m2K ∗ ) (Ceff
9 − C9 ) ∓ (C10 − C10 )
7 − C7 )T2 (q )
mB − mK ∗
q
eff
2
A2 (q2 ) N
L(R)
eff
0eff
2
2
p
(C9 − C0eff
)
∓
(C
−
C
)
(m
−
m
−
q
)(m
+ mK ∗ )A1 (q2 ) − λ
A0
=−
∗
B
9
10
10
B
K
2
m
∗
B + mK ∗
2mK q
2
λ
eff
0eff
2
2
2
+ 2mb (C7 − C7 ) (mB + 3mK ∗ − q )T2 (q ) − 2
T3 (q )
mB − m2K ∗
L(R)
For completeness
A⊥
(0)eff
Wilson coefficients C7,9,10
Seven form factors (FF) V (q 2 ), A0,1,2 (q 2 ), T1,2,3 (q 2 )
encode hadronic effects and require non-perturbative calculation
Low q 2 ≤ 6 GeV2
→ ξ⊥,k (soft form factors)
Large q 2 ≥ 14 GeV2
→ f⊥,k,0 (helicity form factors)
Theory uncertainties:
FF from non-perturbative calculations
Λ/mb corrections (“subleading corrections”)
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
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68 / 48
m(µ+µ−) [MeV/c2]
Analysis strategy
LHCb
Resonant decays
4000
103
3000
Signal band
10
1000
5200
5400
1
5600
m(K+π−µ+µ−)
J/ψ , ψ(2S) band
102
2000
0
104
[MeV/c2]
Veto of B 0 → J/ψ K ∗0 and B 0 → 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 q 2 bins
2 Determine angular observables in multidimensional likelihood fit
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
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∗0 + −
0
Signal
Combinatorial bkg
20
Peaking bkg
5200
5400
LHCb
2
2
10.09 < q < 12.86 GeV / c
4
40
20
5200
5400
2 < q2 < 4.3 GeV2/ c 4
40
20
m(K+π−µ+µ−) [MeV/c2]
60
0
LHCb
0
5600
5600
m(K+π−µ+µ−) [MeV/c2]
5200
5400
2
2
14.18 < q < 16 GeV / c
20
20
5200
LHCb
16 < q2 < 19 GeV2/ c 4
20
0
5200
2
Use B 0 → J/ψ K ∗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
5600
m(K+π−µ+µ−) [MeV/c2]
40
5600
5400
60
m(K+π−µ+µ−) [MeV/c2]
Fit of Nsig in q bins
4
40
5400
4.3 < q2 < 8.68 GeV2/ c 4
0
LHCb
5200
LHCb
40
5600
60
0
60
m(K+π−µ+µ−) [MeV/c2]
Candidates / ( 10 MeV/c 2 )
0.1 < q2 < 2 GeV2/ c 4
40
60
Candidates / ( 10 MeV/c 2 )
LHCb
0
Candidates / ( 10 MeV/c 2 )
Candidates / ( 10 MeV/c 2 )
60
Candidates / ( 10 MeV/c 2 )
Candidates / ( 10 MeV/c 2 )
B → K µ µ signal yield (2011)
Rare b-hadron decays
5400
5600
m(K+π−µ+µ−) [MeV/c2]
Backup
69 / 48
∗0 + −
0
Signal
1.5
Combinatorial bkg
Peaking bkg
5200
5400
1
60
LHCb
2
0.5
2
10.09 < q < 12.86 GeV / c
40
0
5600
4
0
0
20
LHCb
20
m(K+π−µ+µ−) [MeV/c2]
Candidates / ( 10 MeV/c 2 )
20
Theory
40
LHCb
LHCb
Binned
2 < q2 < 4.3 GeV2/ c 4
5200
5400
5200
5400
5600
m(K+π−µ+µ−) [MeV/c2]
2
2
14.18 < q < 16 GeV / c
10
15
5200
5400
5200
5400
LHCb
16 < q2 < 19 GeV2/ c 4
40
20
20
5600
0
5200
2
Use B 0 → J/ψ K ∗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
5600
m(K+π−µ+µ−) [MeV/c2]
60
m(K+π−µ+µ−) [MeV/c2]
Fit of Nsig in q bins
20
q 2 [GeV2/ c 4]
4
40
0
4.3 < q2 < 8.68 GeV2/ c 4
0
[JHEP 08 (2013) 131]
0
LHCb
40
5600
LHCb
5
60
m(K+π−µ+µ−) [MeV/c2]
60
20
Candidates / ( 10 MeV/c 2 )
0.1 < q2 < 2 GeV2/ c 4
40
60
Candidates / ( 10 MeV/c 2 )
LHCb
0
Candidates / ( 10 MeV/c 2 )
Candidates / ( 10 MeV/c 2 )
60
dB /dq 2 [10-7 × c 4 GeV-2]
Candidates / ( 10 MeV/c 2 )
B → K µ µ differential decay rate
Rare b-hadron decays
5400
5600
m(K+π−µ+µ−) [MeV/c2]
Backup
70 / 48
∗0 + −
0
1
Theory
LHCb
Binned
AFB
FL
B → K µ µ angular observables I
LHCb
0.8
1
Theory
LHCb
Binned
LHCb
0.5
0.6
0
0.4
-0.5
0.2
0
0
5
15
-1
0
20
q 2 [GeV2/ c 4]
LHCb
10
0.4
0.2
0.2
0
0
-0.2
-0.2
-0.4
-0.4
5
5
15
20
q 2 [GeV2/ c 4]
LHCb
0.4
0
10
Binned
A9
S3
Theory
LHCb
10
15
20
q 2 [GeV2/ c 4]
0
LHCb
5
10
Results [JHEP 08 (2013) 131] in good agreement with
SM prediction [C. Bobeth et al. JHEP 07 (2011) 067]
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
15
20
q 2 [GeV2/ c 4]
Backup
71 / 48
+ + −
+
0 + −
0
u(d)
t̄
b̄
s̄
W+
Z 0, γ
µ−
µ+
B + → K + µ+ µ−
500
(a) 1.1 < q2 < 6.0 GeV2/ c4
400
LHCb
300
200
100
0
5200
5400
Candidates / ( 10 MeV/c2 )
u(d)
Candidates / ( 10 MeV/c2 )
Angular analysis of B → K µ µ and B → KS µ µ
B 0 → KS0 µ+ µ−
25
(c) 1.1 < q2 < 6.0 GeV2/ c4
20
LHCb
15
10
5600
m(K +µ+µ−) [MeV/ c2]
5
0
5200
5400
5600
m(K 0S µ+µ−) [MeV/ c2]
[JHEP 05 (2014) 082]
NB + →K + µ+ µ− = 4746 ± 81 and NB 0 →KS0 µ+ µ− = 176 ± 17 in 3 fb−1
Experimental challenge: KS0 reconstruction
Differential decay rate for B + → K + µ+ µ−
1 dΓ(B + → K + µ+ µ− )
3
1
= (1 − FH )(1 − cos2 θ` ) + FH + AFB cos θ`
Γ
d cos θ`
4
2
1 dΓ(B 0 → KS0 µ+ µ− )
3
2
= (1 − FH )(1 − | cos θ` | ) + FH
Γ
d| cos θ` |
2
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
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72 / 48
+ + −
+
0 + −
0
0.5
A FB
FH
Angular analysis of B → K µ µ and B → KS µ µ
LHCb
0.4
B + → K + µ+ µ−
0.2
LHCb
B + → K + µ+ µ−
0.1
0.3
0
0.2
-0.1
0.1
0
0
5
10
15
20
-0.2
0
5
FH
q2 [GeV2/ c4]
1.5
15
20
q2 [GeV2/ c4]
LHCb
B 0 → KS0 µ+ µ−
1
0.5
0
0
10
5
10
15
2D fit in cos θ` and m(Kµ+ µ− )
[JHEP 05 (2014) 082] in good
agreement with SM prediction
20
q2 [GeV2/ c4]
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Backup
+
73 / 48
+ + − + −
+ + −
+
B → K π π µ µ and B → φK µ µ
Candidates / (10 MeV/c2)
50
1.00 < q2 < 6.00
LHCb
40
30
20
10
0
5200
5300
5400
5500
m(K +π +π -µ +µ -) [MeV/c2]
B + → φK + µ+ µ−
Candidates / (10 MeV/c2)
B + → K + π + π − µ+ µ −
60
16
14
(a)
LHCb
B+→ φ K +µ +µ -
12
10
8
6
4
2
0
5200
5300
5400
5500
5600
m(φ K +µ +µ -) [MeV/ c2]
[JHEP 10 (2014) 064]
First observation of these modes with
+6.0
+
+ + −
Nsig (B + → K + π + π − µ+ µ− ) = 367+24
−23 and Nsig (B → φK µ µ ) = 25.2−5.3
Normalise to B + → ψ(2S)(→ J/ψ π + π − )K + and B + → J/ψ φK +
Determine branching fractions
−7
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
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
Backup
74 / 48
+ + − + −
+
8
LHCb
7
6
5
4
3
2
1
0
0
5
10
15
q2 [GeV2/ c4]
Candidates / (35 MeV/c2)
dB/dq2 (×10-8 GeV-2c4)
B → K π π µ µ cont.
60
(a)
LHCb
B+→ K +π +π -µ +µ -
50
40
30
20
10
0
1000
1500
2000
2500
m(K +π +π -) [MeV/ c2]
[JHEP 10 (2014) 064]
Performed measurement of dB(B + → K + π + π − µ+ µ− )/dq 2
Significant contribution from B + → K1+ (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
Backup
75 / 48
250
(a)
200
150
100
50
0
Events / ( 10.6 MeV/c2 )
LHCb
5200
5400
300Direct
250
200
150
B − → K − µ+ µ− prelim.
250
LHCb
(b)
200
150
100
50
0
5600
mK+µ+µ- (MeV/c2)
5200
5400
5600
mK-µ+µ- (MeV/c2)
[JHEP 09 (2014) 177]
300
CP-Asymmetry LHCb
ACP (c)
LHCb (d)
Γ(B̄ → K̄ (∗) µ+ µ−250
) − Γ(B → K (∗) µ+ µ− )
ACP =
Γ(B̄ → K̄ (∗) µ+ µ−200
) + Γ(B → K (∗) µ+ µ− )
ACP tiny O(10−3 ) in the SM
100
Events / ( 10.6 MeV/c2 )
B + → K + µ+ µ− prelim.
Events / ( 10.6 MeV/c2 )
Events / ( 10.6 MeV/c2 )
CP-asymmetry ACP
150
100
Correct for detection and production asymmetry using B → J/ψ K (∗)
50
(∗)
AK
raw
0
5200
µµ
50
(∗)
= ACP + Adet + κAprod , ACP = AK
raw
5400
5600
C. Langenbruch (Warwick), Warwick EPP 2015
0
2
5200
µµ
Rare b-hadron decays
J/ψ K (∗)
− Araw
5400
5600
2
Backup
76 / 48
0.2
ACP (B + → K + µ+ µ− ) prelim.
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
0
LHCb
5
10
15
20
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
0
ACP
ACP
CP-asymmetry ACP cont.
ACP (B 0 → K ∗0 µ+ µ− ) prelim.
LHCb
5
q2 [GeV2/c4]
10
15
q2 [GeV2/c4]
[JHEP 09 (2014) 177]
Measured ACP in good agreement with SM prediction
ACP (B + → K + µ+ µ− ) = 0.012 ± 0.017(stat.) ± 0.001(syst.)
ACP (B 0 → K ∗0 µ+ µ− ) = −0.035 ± 0.024(stat.) ± 0.003(syst.)
Most precise measurement
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays
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Prospects for rare decays in 2018 and beyond
C. Langenbruch (Warwick), Warwick EPP 2015
Rare b-hadron decays