Radiative and EW-penguin decays and LFU tests

Radiative and EW-penguin decays and LFU tests

Konstantinos A. Petridison behalf of the LHCb collaboration

University of Bristol

October 12, 2016

K.A. Petridis (UoB) Radiative, EWP, LFU tests Implications 2016 1 / 21

Electroweak penguin processes� b → s`+`− are FCNC transitions and are suppressed in SM→ Only occur via loop or box processes

The operator-product expansionOr: how to be model independent

sb

µ−

µ+

W−

Z0, γ

d d

sb

µ−

µ+

W−

W+

νµ

dd

S.Cunliffe (Imperial) FFP14 b! s`` Theory 6/21

� New physics contributions at the same level as SM→ Highly sensitive to effects of new physics

� New physics enters as virtual particles in loops→ Access energy scales above available collision energy


Introduction

� Run 1 of the LHC provided us with a rich set of results→ Rise of the precision era for rare decays

� Selective set of results with Run 1 and plans with Run 2 data andbeyond in light of current anomalies


LHCb signal yieldschannel Run 1 Run 2 Run 3,4 (50fb−1)B0 → K∗0(K +π−)µ+µ− 2,400 9,000 80,000B0 → K∗+(K 0

Sπ+)µ+µ− 160 600 5,500

B0 → K 0Sµ

+µ− 180 650 5,500B+ → K +µ+µ− 4,700 17,500 150,000Λb → Λµ+µ− 370 1500 10,000B+ → π+µ+µ− 93 350 3,000B0

s → µ+µ− 15 60 500B0 → K∗0e+e− (low q2) 150 550 5,000Bs → φγ 4,000 15,000 150,000

Naively scaling with luminosity and linear scaling of σbb with√

s. Extrapolated yields rounded to the nearest 50/500

� Our measurements of dB/dq2 obtained by normalising rare yield to that ofnormalisation channel B → J/ψK∗

� For higher statistics decays, dominant uncertainty of integrated BF is theknowledge of B(B → J/ψK∗)→ More b → s`` decays in Run 1 than B → J/ψK∗ of B-factories!

� Dominant systematic uncertainty on BFs: Knowledge equivalent J/ψ BF→ Belle2 could help here also resolving isospin asymmetries at Υ(4S) M.Jung[1510.03423]

� With the LHCb upgrade even “tough” modes will be sufficiently populated


An intriguing set of results

1. Measurements of differential branching fractions of B → K (∗)µ+µ−,Λb → Λµ+µ−, Bs → φµ+µ−

� 1σ to 3σ depending on final state

2. Tests of lepton universality between B+ → K +µ+µ− and B+ → K +e+e−

� 2.6σ

3. Angular analyses of B → K (∗0)µ+µ−, Bs → φµ+µ−, Λb → Λµ+µ−

� ∼ 3σMeasurements form a consistent picture.


Interpretations� Several attempts to interpret b → sµ+µ− and b → sγ data

-3 -2 -1 0 1 2

-2

-1

0

1

2

Re(C9NP)

Re(C10NP)

-3 -2 -1 0 1 2-2

-1

0

1

2

3

Re(C9NP)Re(C9� )

Figure 1 – Allowed regions in the Re(CNP9 )-Re(CNP

10 ) plane (left) and the Re(CNP9 )-Re(C0

9) plane (right). The bluecontours correspond to the 1 and 2� best fit regions from the global fit. The green and red contours correspondto the 1 and 2� regions if only branching ratio data or only data on B ! K⇤µ+µ� angular observables is takeninto account.

(including braching ratios and non-LHCb measurements) into sets with data below 2.3 GeV2,between 2 and 4.3 GeV2, between 4 and 6 GeV2, and above 15 GeV2 (the slight overlap of thebins, caused by changing binning conventions over time, is of no concern as correlations aretreated consistently). The resulting 1� regions are shown in fig. 2 (the fit for the region between6 and 8 GeV2 is shown for completeness as well but only as a dashed box because we assumenon-perturbative charm e↵ects to be out of control in this region and thus do not include thisdata in our global fit). We make some qualitative observations, noting that these will have tobe made more robust by a dedicated numerical analysis.

• The NP hypothesis requires a q2 independent shift in C9. At roughly 1�, this hypothesisseems to be consistent with the data.

• If the tensions with the data were due to errors in the form factor determinations, naivelyone should expect the deviations to dominate at one end of the kinematical range whereone method of form factor calculation (lattice at high q2 and LCSR at low q2) dominates.Instead, if at all, the tensions seem to be more prominent at intermediate q2 values whereboth complementary methods are near their domain of validity and in fact give consistentpredictions15.

• There does seem to be a systematic increase of the preferred range for C9 at q2 belowthe J/ resonance, increasing as this resonance is approached. Qualitatively, this is thebehaviour expected from non-factorizable charm loop contributions. However, the centralvalue of this e↵ect would have to be significantly larger than expected on the basis ofexisting estimates 20,21,22,23,24, as conjectured earlier 23.

Concerning the last point, it is important to note that a charm loop e↵ect does not have tomodify the H� and H0 helicity amplitudese in the same way (as a shift in C9 induced by NPwould). Repeating the above exercise and allowing a q2-dependent shift of C9 only in one ofthese amplitudes, one finds that the resulting corrections would have to be huge and of the samesign. It thus seems that, if the tensions are due to a charm loop e↵ect, this must contribute toboth the H� and H0 helicity amplitude with the same sign as a negative NP contribution to C9.

eThe modification of the H+ amplitude is expected to be suppressed 22,24.

Altmannshofer,Straub[1503.06199]

� Modified vector coupling C NP9 6= 0

at ∼ 4σ→ New vector Z ′, leptoquarks,vector-like confinement...Buttazzo et al [1604.03940], Bauer et al[PRL116,141802(2016)], Crivellin et al[PRL114,151801(2015)], Altmannshofer et al[PRD89(2014)095033]...

Could the SM errors be wrong?

•  Largest individual uncertainty on P5’ from cc-loop effects

•  But in reality:

49

Breakdown of factorization

�

µ+

µ�

J/�, J/�0, ...

b s

g

J/�, J/�0, ...

� �e� e�

e+ e+

• Factorizable effects can be related to (full non-perturbative) charm vacuum polarization via a standard dispersion relation & extracted from BESII data on e+e! ! hadrons

u, d

B12/B58


�

µ+

µ�

J/�, J/�0, ...

b sg

• Unfortunately, there are other contributions which cannot be related to vacuum polarization. Such effects break factorization

�

µ+

µ�

J/�, J/�0, ...

b s

g

J/�, J/�0, ...

� �e� e�

e+ e+

u, d

u, d

B13/B58


�

µ+

µ�

J/�, J/�0, ...

b sg

• Unfortunately, there are other contributions which cannot be related to vacuum polarization. Such effects break factorization

�

µ+

µ�

J/�, J/�0, ...

b s

g

J/�, J/�0, ...

� �e� e�

e+ e+

u, d

u, d

B13/B58

q2

d�/d

q2

In an ideal world …

4m2c

b s

c

�

µ+

µ�

B8/B58

… in reality

J/�J/��

low-q2 high-q2

q2

d�/dq2

4m2c

B9/B58

Note however that can’t just effect P5’- would see correlated effect in other observables

� Potential problem with ourunderstanding of the contributionfrom B → Xcc (→ µµ)K Lyon,Zwicky[1406.0566], Altmannshofer,Straub[1503.06199],Ciuchini et al [1512.07157]...

→ Mimics vector-like new physicseffects (corrections to C9)


Impact on C eff9

� Dependence of observables on vector couplings enters throughC eff

9 = C9 + Y (q2)

→ Y (q2) summarises contributions from bsqq operators

P. Owen

Effects of • At low q2, main contribution is from the J/ψ.

• Using simple B-W model, get large contributions all the way down to q2=0.

• At high q2 get large (positive) contribution from heavy resonances.

5

of the resonances that are subsequently anal-ysed, resolution e↵ects are neglected. Whilethe (2S) state is narrow, the large branchingfraction means that its non-Gaussian tail issignificant and hard to model. The (2S) con-tamination is reduced to a negligible level byrequiring mµ+µ� > 3770 MeV/c2. This dimuonmass range is defined as the low recoil regionused in this analysis.

In order to estimate the amount of back-ground present in the mµ+µ� spectrum, an un-binned extended maximum likelihood fit is per-formed to the K+µ+µ� mass distribution with-out the B+ mass constraint. The signal shapeis taken from a mass fit to the B+! (2S)K+

mode in data with the shape parameterisedas the sum of two Crystal Ball functions [17],with common tail parameters, but di↵erentwidths. The Gaussian width of the two compo-nents is increased by 5 % for the fit to the lowrecoil region as determined from simulation.The low recoil region contains 1830 candidatesin the signal mass window, with a signal tobackground ratio of 7.8.

The dimuon mass distribution in the lowrecoil region is shown in Fig. 1. Two peaksare visible, one at the low edge correspondingto the expected decay (3770) ! µ+µ� anda wide peak at a higher mass. In all fits, avector resonance component corresponding tothis decay is included. Several fits are made tothe distribution. The first introduces a vectorresonance with unknown parameters. Subse-quent fits look at the compatibility of the datawith the hypothesis that the peaking structureis due to known resonances.

The non-resonant part of the mass fits con-tains a vector and axial vector component. Ofthese, only the vector component will inter-fere with the resonance. The probability den-sity function (PDF) of the signal component

]2c [MeV/−µ+µm3800 4000 4200 4400 4600

)2 cC

andi

date

s / (2

5 M

eV/

0

50

100

150datatotalnonresonantinterferenceresonancesbackground

LHCb

Figure 1: Dimuon mass distribution of data withfit results overlaid for the fit that includes con-tributions from the non-resonant vector and ax-ial vector components, and the (3770), (4040),and (4160) resonances. Interference terms areincluded and the relative strong phases are leftfree in the fit.

is given as

Psig / P (mµ+µ�) |A|2 f 2(m2µ+µ�) , (1)

|A|2 = |AVnr +

X

k

ei�kAkr |2 + |AAV

nr |2 , (2)

where AVnr and AAV

nr are the vector and axialvector amplitudes of the non-resonant decay.The shape of the non-resonant signal in mµ+µ�

is driven by phase space, P (mµ+µ�), and theform factor, f(m2

µ+µ�). The parametrisation ofRef. [18] is used to describe the dimuon massdependence of the form factor. This form fac-tor parametrisation is consistent with recentlattice calculations [19]. In the SM at low re-coil, the ratio of the vector and axial vectorcontributions to the non-resonant component isexpected to have negligible dependence on thedimuon mass. The vector component accountsfor (45± 6) % of the di↵erential branching frac-tion in the SM (see, for example, Ref. [20]).This estimate of the vector component is as-sumed in the fit.

The total vector amplitude is formed by sum-

3

]4/c2 [GeV2q5 10 15 20

) 9(C

∆

4−

2−

0

2

4

6

8

10

phase = 0

/2πphase =

πphase =

Phys. Rev. Lett. 111, 112003 (2013)

cc

cc

Phase = phase at pole + π/2(Same convention as this ref)

� At low q2 main culprit is the J/ψ

→ Corrections to C eff9 (∆C9) all

the way down to q2 = 0→ Effect strongly dependent onrelative phase with penguin

� More data will help resolveapparent q2 dependence of C9


Measuring phase differences� Measure relative phase between narrow resonances and penguin amplitudes→ Model resonances as relativistic BWs multiplied by relative scale andphase Lyon et al. [1406.0566], Hiller et al. [1606.00775]

→ Use this model to replace Y (q2) in C eff9 = Y (q2) + C9

→ B → K form factors constrained to LCSR+Lattice predictions→ Fit for phases and C9 and C10

� Fit dimuon spectrum inB+ → K +µ+µ−

→ Expect precision of phase∼ 0.1 rad (ambiguities over sign ofphase)[Owen Barcelona workshop 2016]

� In final stages of review


https://indico.cern.ch/event/466933/contributions/1974105/attachments/1259183/1860140/powen_barcelona.pdf

Axial vector constraints

� What about if new physics manifests itself also in C10

� Do not suffer from these charm effects

B Æ Kmm

B Æ K*mmBs Æ fmm

All

-3 -2 -1 0 1 2 3-3

-2

-1

0

1

2

3

C9NP

C9'N

P

B Æ Kmm

B Æ K*mmBs Æ fmm

All

-3 -2 -1 0 1 2 3-3

-2

-1

0

1

2

3

C9NP

C10N

P

B Æ Kmm

B Æ K*mmBs Æ fmm

All

-3 -2 -1 0 1 2 3-3

-2

-1

0

1

2

3

C9NP = -C9'

NP

C10N

P=

C10

'N

P

B Æ Kmm

B Æ K*mmBs Æ fmm

All

-3 -2 -1 0 1 2 3-3

-2

-1

0

1

2

3

C9NP = -C9'

NP

C10N

P=-

C10

'N

P

Figure 8: For 4 favoured scenarios, we show the 3 � regions allowed by B ! Kµµ

observables only (dashed green), by B ! K⇤µµ observables only (long-dashed blue), by

Bs ! �µµ observables only (dot-dashed purple) and by considering all data (red, with

1,2,3 � contours). Same conventions for the constraints as in Fig. 7.

• (CNP9 = CNP

10 , CNP90 = CNP

100 ), disfavoured by the data on Bs ! µµ, which prefer a SM

value for C10, leading to a tension with the value of CNP9 needed for B ! K⇤µµ

• (CNP9 = �CNP

10 , CNP90 = �CNP

100 ) and (CNP9 = CNP

90 , CNP10 = CNP

100 ) which could be interesting

candidates but get lower pulls (2.0 and 3.9 � respectively).

We see therefore that Z 0 scenarios could alleviate part of the discrepancies observed in

b ! sµµ data, but with only one or two Wilson coe�cients receiving NP contributions,

31

� b → sµ+µ− gives 25% precision inC10 [DHMV 1510.04329], [Quim priv. comm.]

→ Most power from B → K∗µ+µ−

� With Run 2 and beyond start toprobe the 10% level.→ Exact level depends on howtheory precision evolves. What areprospects here?

� Bs → µ+µ− will help here as well.


Imaginary contributions to C9 and C10� We have measured complete set of CP asymmetric observables LHCb

[JHEP02(2016)104]

→ Sensitive to imaginary NP contributions

Altmannshofer et al [EPJC(2013)73], LHCb [JHEP02(2016)104]

5 10 15-0.2

-0.1

0.0

0.1

0.2

q 2 @GeV2D

A 7

C7NP=-0.1+0.1‰C7'=-0.1-0.1‰

C9NP=-1.2+1.0‰C9'=1.0+1.0‰

C9NP=-1.2-1.0‰

C9'=1.0-1.0‰

5 10 15-0.2

-0.1

0.0

0.1

0.2

q 2 @GeV2D

A 7

C9NP=-2+2‰

C10' =-0.5+1‰

C9NP=-2+2‰

C10' =-0.5-1‰

C9NP=-2-2‰

C10' =-0.5+1‰

5 10 15-0.2

-0.1

0.0

0.1

0.2

q 2 @GeV2DA 8

C7NP=-0.1+0.1‰C7'=-0.1-0.1‰

C9NP=-1.2+1.0‰C9'=1.0+1.0‰

C9NP=-1.2-1.0‰

C9'=1.0-1.0‰

5 10 15-0.2

-0.1

0.0

0.1

0.2

q 2 @GeV2D

A 8

C9NP=-2+2‰

C10' =-0.5+1‰

C9NP=-2+2‰

C10' =-0.5-1‰

C9NP=-2-2‰

C10' =-0.5+1‰

‡

‡‡

5 10 15-0.2

-0.1

0.0

0.1

0.2

q 2 @GeV2D

A 9

C7NP=-0.1+0.1‰C7'=-0.1-0.1‰

C9NP=-1.2+1.0‰C9'=1.0+1.0‰

C9NP=-1.2-1.0‰

C9'=1.0-1.0‰

‡

‡‡

5 10 15-0.2

-0.1

0.0

0.1

0.2

q 2 @GeV2DA 9

C9NP=-2+2‰

C10' =-0.5+1‰

C9NP=-2+2‰

C10' =-0.5-1‰

C9NP=-2-2‰

C10' =-0.5+1‰

Figure 9: Predictions for the CP asymmetries A7, A8 and A9 as function of the di-muon invari-ant mass squared q2 in various scenarios that address the observed discrepancies inB ! K⇤µ+µ�. The values for the Wilson coe�cients corresponding to each scenarioare indicated explicitly in the plots. SM predictions for the CP asymmetries arenegligibly small throughout the whole q2 range.

22

]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

]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

Figure 10: The CP -asymmetric observables in bins of q2, determined from a moment analysis ofthe data.

27

� With 300fb−1 collected by Run 5, LHCb could have ∼500,000B0 → K∗0µ+µ−

� More than entire Run 1 B0 → J/ψK∗0 sample!� Uncertainties in plots shrink by ∼ ×10 assumptions about systs

→ Sensitive to NP contributions of order shown


Scalar and tensor couplings

� Angular analysis ofB+ → K +µ+µ− sensitive to scalarand tensor contributions→ Re(CT ) ∈ [−0.32, 0.16] @ 68%FH only, for SM like C9 Beaujean et al[EPJC(2015)75]

Beaujean et al [EPJC(2015)75]

3

�0.6 �0.4 �0.2 0.0 0.2 0.4 0.6CT

0.00

0.05

0.10

0.15

0.20

0.25

0.30

hFHi [1

.1,6

]

LHCbC NP

9 = 0

C NP9 = �1.1

�0.6 �0.4 �0.2 0.0 0.2 0.4 0.6CT

0.00

0.05

0.10

0.15

0.20

0.25

0.30

hFHi [1

5,22

]

LHCbC NP

9 = 0

C NP9 = �1.1

�0.6 �0.4 �0.2 0.0 0.2 0.4 0.6CT

0.5

1.0

1.5

2.0

2.5

hB(K

)i[1

.1,6

]

⇥10�7

LHCbC NP

9 = 0

C NP9 = �1.1

�0.6 �0.4 �0.2 0.0 0.2 0.4 0.6CT

0.5

1.0

1.5

2.0

2.5

hB(K

)i[1

5,22

]

⇥10�7

LHCbC NP

9 = 0

C NP9 = �1.1

�0.6 �0.4 �0.2 0.0 0.2 0.4 0.6CT

0.51.01.52.02.53.03.54.04.5

hB(K

⇤ )i [1

,6]

⇥10�7

LHCbC NP

9 = 0

C NP9 = �1.1

�0.6 �0.4 �0.2 0.0 0.2 0.4 0.6CT

0.51.01.52.02.53.03.54.04.5

hB(K

⇤ )i [1

6,19

]

⇥10�7

LHCbC NP

9 = 0

C NP9 = �1.1

�0.6 �0.4 �0.2 0.0 0.2 0.4 0.6CT

0.0

0.5

1.0

1.5

2.0

2.5

t B⇥

hJ1c

+J 2

ci[1

.1,6

]

⇥10�8

C NP9 = 0

C NP9 = �1.1

�0.6 �0.4 �0.2 0.0 0.2 0.4 0.6CT

0.0

0.5

1.0

1.5

2.0

2.5t B

⇥hJ

1c+

J 2ci

[15,

19]

⇥10�8

C NP9 = 0

C NP9 = �1.1

�0.6 �0.4 �0.2 0.0 0.2 0.4 0.6CT

0.0

0.2

0.4

0.6

0.8

1.0

1.2

t B⇥

hJ1s

�3J

2si [1

.1,6

]

⇥10�7

C NP9 = 0

C NP9 = �1.1

�0.6 �0.4 �0.2 0.0 0.2 0.4 0.6CT

0.0

0.2

0.4

0.6

0.8

1.0

1.2

t B⇥

hJ1s

�3J

2si [1

5,19

]

⇥10�7

C NP9 = 0

C NP9 = �1.1

Fig. 1 The sensitivity to the tensor coupling Re(CT ) of FµH and Bµ in B+ ! K+µµ as well as Bµ , (J1c + J2c), and (J1s �3J2s) in B0 ! K⇤0µµ .

Angular observables are rescaled by the lifetime of the B meson, tB. The bands represent the theory uncertainties at 68% and 95% probability ofthe prior predictive. Two sets of bands are shown for C NP

9 = 0 (blue) and C NP9 = �1.1 (red). If available, the gray band indicates the latest 68%

confidence interval reported by LHCb. All observables are integrated over q2 2 [q21, q2

2] bins denoted as h. . .i[q21,q2

2] to match LHCb.

� Measurements of most B0 → K∗0µ+µ− angular observables ignore leptonmasses and scalar/tensor couplings→ With larger datasets lift assumptions

� Have measured S6c using a moment analysis of decay

LHCb [JHEP02(2016)104]

This observable is consistent with zero, as expected in the SM. As a cross-check, the observ-593

ables have also been determined by a moment analysis in the approximately 2 GeV2/c4 q2594

bins used in the likelihood fit of the angular observables. The di↵erences between the cen-595

tral values of the two methods are compatible with those expected from pseudoexperiments.596

The correlation matrices for all of the q2 bins are available in Appendices F–H.597

]4c/2 [GeV2q0 5 10 15

6cS

-1

-0.5

0

0.5

1

LHCb

Figure 12: The observable S6c in bins of q2, as determined from a moment analysis of the data.

Figure 13 shows the observables S4, S5 and AFB resulting from the fit to the q2-598

dependent decay amplitudes. The results are in agreement with those obtained from599

the likelihood fit of the angular observables and the moments analysis. For AFB, the600

best-fit to the data (the line in the figure) has two zero-crossing points in the range601

1.1 < q2 < 6.0 GeV2/c4 with di↵erent slopes. As discussed in Sec. 7.3, only the solution602

consistent with the data in the range q2 > 6.0 GeV2/c4 is cited, i.e. the solution with the603

positive slope (see Figs. 6 and 9). The zero-crossing points determined from the amplitude604

fit are605

q20(S5) 2 [2.49, 3.95] GeV2/c4 at 68% confidence level (C.L.) ,

q20(AFB) 2 [3.40, 4.87] GeV2/c4 at 68% C.L. .

It is not possible to determine if S4 has a zero-crossing point at 68% confidence level. If606

there is a zero-crossing then607

q20(S4) < 2.65 GeV2/c4 at 95% C.L. .

The correlations between the measured values are less than 10%. The measured zero-608

crossing points are all consistent with their respective SM expectations. Standard Model609

predictions for q20(AFB) are typically in the range 3.9 � 4.4 GeV2/c4 [68–70] and have610

relative uncertainties below the 10% level, for example, q20(AFB) = 4.36 +0.33

�0.31 GeV2/c4 [69].611

29

� By Run 5, expect sensitivity toτB J6c O(10−9) assumptions about systs

→ Probing interesting allowedregion of scalar NP couplingsBeaujean et al [EPJC(2015)75]

→ Bs → µ+µ− will be moreconstraining but final states withelectrons should win (LNU)


Other mKπ regions

� Measure S-wave fraction in 644 < mKπ < 1200 MeV/c2 LHCb [1606.04731]

→ Enables first determination of P-wave only B0 → K∗0(892)µ+µ−

differential branching fraction

B Likelihood fit projections

Figures 6–9 show the projections of the fitted probability density function on mK⇡µµ,mK⇡ and cos ✓K . Figure 6 shows the wider q2 bins of 1.1 < q2 < 6.0 GeV2/c4 and 15.0 <q2 < 19.0 GeV2/c4, Figs. 7–9 show the mK⇡µµ, mK⇡ and cos ✓K projections respectively forthe finer q2 bins. In all figures, the solid line denotes the total fitted distribution. Theindividual components, signal (blue shaded area) and background (red hatched area), arealso shown.

]2c [MeV/µµπKm5200 5400 5600

2 cC

andi

date

s / 1

5 M

eV/

0

100

200

300LHCb

4c/2 < 6.0 GeV2q1.1 <

]2c [MeV/µµπKm5200 5400 5600

2 cC

andi

date

s / 1

5 M

eV/

0

100

200

300LHCb

4c/2 < 19.0 GeV2q15.0 <

]2c [MeV/πKm 800 1000 1200

2 cC

andi

date

s / 2

8 M

eV/

0

100

200

300LHCb

4c/2 < 6.0 GeV2q1.1 <

]2c [MeV/πKm 800 1000 1200

2 cC

andi

date

s / 2

8 M

eV/

0

100

200

300

400LHCb

4c/2 < 19.0 GeV2q15.0 <

Kθcos1− 0.5− 0 0.5 1

Can

dida

tes /

0.1

0

50

100

150 LHCb4c/2 < 6.0 GeV2q1.1 <

Kθcos1− 0.5− 0 0.5 1

Can

dida

tes /

0.1

0

20

40

60

80 LHCb4c/2 < 19.0 GeV2q15.0 <

Figure 6: Angular and mass distributions for the q2 bins 1.1 < q2 < 6.0GeV2/c4 (left) and15.0 < q2 < 19.0 GeV2/c4 (right). The distributions of cos ✓K and mK⇡ are shown for candidatesin the signal mK⇡µµ window of ±50 MeV/c2 around the known B0 mass.

19

]4c/2 [GeV2q0 5 10 15

120

0 6

44 | SF

0

0.1

0.2

0.3

0.4LHCb

]4c/2 [GeV2q0 5 10 15

996

796

| SF

0

0.05

0.1

0.15

0.2LHCb

Figure 4: Results for the S-wave fraction (FS) in bins of q2 in the range (left) 644 < mK⇡ <1200MeV/c2 and (right) 796 < mK⇡ < 996MeV/c2. The uncertainties shown are the quadraticsum of the statistical and systematic uncertainties. The shape of FS is found to be compatiblewith the smoothly varying distribution of FL, as measured in Ref. [27].

Table 1: S-wave fraction (FS) in bins of q2 for two mK⇡ regions. The first uncertainty is statisticaland the second systematic.

q2 bin (GeV2/c4) FS|996796 FS|1200

644

0.10 < q2 < 0.98 0.021+0.015�0.011 ± 0.009 0.052+0.035

�0.027 ± 0.013

1.1 < q2 < 2.5 0.144+0.035�0.030 ± 0.010 0.304+0.058

�0.053 ± 0.013

2.5 < q2 < 4.0 0.029+0.031�0.020 ± 0.010 0.071+0.069

�0.049 ± 0.015

4.0 < q2 < 6.0 0.117+0.027�0.023 ± 0.008 0.254+0.048

�0.044 ± 0.012

6.0 < q2 < 8.0 0.033+0.022�0.019 ± 0.009 0.082+0.049

�0.045 ± 0.016

11.0 < q2 < 12.5 0.021+0.021�0.016 ± 0.007 0.049+0.048

�0.039 ± 0.014

15.0 < q2 < 17.0 �0.008+0.033�0.014 ± 0.006 �0.016+0.069

�0.030 ± 0.012

17.0 < q2 < 19.0 0.018+0.013�0.017 ± 0.009 0.034+0.024

�0.032 ± 0.019

1.1 < q2 < 6.0 0.101+0.017�0.017 ± 0.009 0.224+0.032

�0.033 ± 0.013

15.0 < q2 < 19.0 0.010+0.017�0.014 ± 0.007 0.019+0.030

�0.025 ± 0.015

10

NOT FOR DISTRIBUTION JHEP_164P_0616 v1

]4c/2 [GeV2q0 5 10 15

]2/G

eV4 c [2 q

/dB d

0

0.05

0.1

0.156−10×

LHCb

Figure 5: Di↵erential branching fraction of B0! K⇤(892)0µ+µ� decays as a function of q2. Thedata are overlaid with the SM prediction from Refs. [47,48]. No SM prediction is included in theregion close to the narrow cc resonances. The result in the wider q2 bin 15.0 < q2 < 19.0 GeV2/c4

is also presented. The uncertainties shown are the quadratic sum of the statistical and systematicuncertainties.

Table 2: Di↵erential branching fraction of B0! K⇤(892)0µ+µ� decays in bins of q2. The firstuncertainty is statistical, the second systematic and the third due to the uncertainty on theB0! J/ K⇤0 and J/ ! µ+µ� branching fractions.

q2 bin (GeV2/c4) dB/dq2 ⇥ 10�7 (c4/ GeV2)

0.10 < q2 < 0.98 1.163+0.076�0.084 ± 0.033 ± 0.079

1.1 < q2 < 2.5 0.373+0.036�0.035 ± 0.011 ± 0.025

2.5 < q2 < 4.0 0.383+0.035�0.038 ± 0.010 ± 0.026

4.0 < q2 < 6.0 0.410+0.031�0.030 ± 0.011 ± 0.028

6.0 < q2 < 8.0 0.496+0.032�0.032 ± 0.012 ± 0.034

11.0 < q2 < 12.5 0.558+0.036�0.036 ± 0.014 ± 0.038

15.0 < q2 < 17.0 0.611+0.031�0.042 ± 0.023 ± 0.042

17.0 < q2 < 19.0 0.385+0.029�0.024 ± 0.018 ± 0.026

1.1 < q2 < 6.0 0.392+0.020�0.019 ± 0.010 ± 0.027

15.0 < q2 < 19.0 0.488+0.021�0.022 ± 0.008 ± 0.033

12

� Additional data should provide sensitivity to potential non-resonant P-wavecontributions→ Orthogonal constraints provided theory uncertainties under contro Das et al

[1406.6681] What are prospects here? Our measurements could help


Other mKπ regions cont’d� Angular moment and differential branching fraction analysis in

1330 < mKπ < 1530 MeV/c2 LHCb [1609.04736]

→ Measure 40 normalised angular moments sensitive to interferencebetween S-, P- and D-wave→ No significant D-wave component observed in contrast toB0 → J/ψK +π−

]2c) [MeV/−π+K(m800 1000 1200 1400 1600

)2 cD

ecay

s / (5

0 M

eV/

0

100

200

300 LHCb4c/2 < 6.0 GeV2q1.1 <

Figure 1: Background-subtracted m(K+⇡�) distribution for B0! K+⇡�µ+µ� decays in therange 1.1 < q2 < 6.0 GeV2/c4. The region 1330 < m(K+⇡�) < 1530 MeV/c2 is indicated by theblue, hatched area.

θl

θK

φ

+ y

+ xl

+ zl + zh

+ xh

[K π]B0

K–

μ–

[μμ]

(a)

θl

θK

φ

+ y

+ xl

+ zl + zh

+ xh

[K π]B0

K+

μ+

[μμ]

(b)

Figure 2: Angle conventions for (a) B0 ! K�⇡+µ�µ+ and (b) B0 ! K+⇡�µ+µ�, as describedin Ref. [12]. The leptonic and hadronic frames are back-to-back with a common y axis. For thedihedral angle � between the leptonic and hadronic decay planes, there is an additional sign flip�! �� compared to previous LHCb analyses [1–4].

and 8.0 GeV2/c4, and in the range 1.1 < q2 < 6.0 GeV2/c4 for which the angular momentsare also measured. The measurements are based on samples of pp collisions collected bythe LHCb experiment in Run 1, corresponding to integrated luminosities of 1.0 fb�1 at acentre-of-mass energy of 7 TeV and 2.0 fb�1 at 8 TeV.

2 Angular distribution

The final state of the decay B0! K+⇡�µ+µ� is fully described by five kinematic variables:three decay angles (✓`, ✓K , �), m(K+⇡�), and q2. Figure 2a shows the angle conventionsfor the B0 decay (containing a b quark): the back-to-back leptonic and hadronic systemsshare a common y axis and have opposite x and z axes. The negatively charged lepton isused to define the leptonic helicity angle ✓` for the B0. The quadrant of the dihedral angle� between the dimuon and the K⇤0 ! K�⇡+ decay planes is determined by requiring the

2

]4c/2 [GeV2q0 2 4 6 8

]2/G

eV4 c [

-8 1

0× 2 q

/dBd

0

0.5

1

1.5

2LHCb

Figure 5: Di↵erential branching fraction of B0 ! K+⇡�µ+µ� in bins of q2 for the range1330 < m(K+⇡�) < 1530MeV/c2. The error bars indicate the sums in quadrature of thestatistical and systematic uncertainties.

Table 2: Di↵erential branching fraction of B0 ! K+⇡�µ+µ� in bins of q2 for the range1330 < m(K+⇡�) < 1530MeV/c2. The first uncertainty is statistical, the second systematicand the third due to the uncertainty on the B0 ! J/ K⇤(892)0 and J/ ! µ+µ� branchingfractions.

q2 [ GeV2/c4] dB/dq2 ⇥ 10�8 [c4/ GeV2][0.10, 0.98] 1.60 ± 0.28 ± 0.04 ± 0.11[1.10, 2.50] 1.14 ± 0.19 ± 0.03 ± 0.08[2.50, 4.00] 0.91 ± 0.16 ± 0.03 ± 0.06[4.00, 6.00] 0.56 ± 0.12 ± 0.02 ± 0.04[6.00, 8.00] 0.49 ± 0.11 ± 0.01 ± 0.03[1.10, 6.00] 0.82 ± 0.09 ± 0.02 ± 0.06

The 41 background-subtracted and acceptance-corrected moments are estimated as

�i =

nsigX

k=1

wkfi(⌦k) � x

nbkgX

k=1

wkfi(⌦k) (5)

and the corresponding covariance matrix is estimated as

Cij =

nsigX

k=1

w2kfi(⌦k)fj(⌦k) + x2

nbkgX

k=1

w2kfi(⌦k)fj(⌦k). (6)

Here nsig and nbkg correspond to the candidates in the signal and background regions,respectively. The signal region is defined within ±50 MeV/c2 of the mean B0 mass, andthe background region in the range 5350 < m(K+⇡�µ+µ�) < 5700 MeV/c2. The scalefactor x is the ratio of the estimated number of background candidates in the signal regionover the number of candidates in the background region and is used to normalise thebackground subtraction. It has been checked in data that the angular distribution of the

8

i2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

iΓ

1−

0.5−

0

0.5

1

LHCb

i22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

iΓ

1−

0.5−

0

0.5

1

LHCb

Figure 6: Measurement of the normalised moments, �i, of the decay B0! K+⇡�µ+µ� in therange 1.1 < q2 < 6.0 GeV2/c4 and 1330 < m(K+⇡�) < 1530 MeV/c2. The error bars indicate thesums in quadrature of the statistical and systematic uncertainties.

background is independent of m(K+⇡�µ+µ�) within the precision of this measurement,and that the uncertainty on x has negligible impact on the results. The weights, wk, arethe reciprocals of the candidates’ e�ciencies and account for the acceptance, described inSec. 5.

The covariance matrix describing the statistical uncertainties on the 40 normalisedmoments is computed as

C ij =

Cij +

�i�j

�21

C11 ��iC1j + �jC1i

�1

�1

�21

, i, j 2 {2, ..., 41}. (7)

The results for the normalised moments, �i, are given in Fig. 6. The uncertaintiesshown are the sums in quadrature of the statistical and systematic uncertainties. Theresults are also presented in Table 3. The various sources of the systematic uncertaintiesare described in Sec. 9.

The distributions of each of the decay angles within the signal region are shown in

9

� In Run 1: 230 candidates, by Run 4 7500 candidates (×3 as manycandidates as current B0 → K∗0(892)µ+µ− yield)→ Estimates of B → K∗J=0,2 form-factors exist Lu et al [PRD85(2012)] but moreinput from theory required to constrain Wilson coefficients from thesemeasurements. What are prospects here?


What about baryonic decays

� For example: Run 1: 370 Λb → Λ(→ pπ)µ+µ− events

LHCb [JHEP06(2015)115]

the predictions in the low-q2 region.

Table 4: Measured di↵erential branching fraction of ⇤0b ! ⇤µ+µ�, where the uncertainties

are statistical, systematic and due to the uncertainty on the normalisation mode, ⇤0b ! J/ ⇤,

respectively.

q2 interval [ GeV2/c4 ] dB(⇤0b ! ⇤µ+µ�)/dq2 · 10�7[( GeV2/c4)�1]

0.1 – 2.0 0.36 + 0.12� 0.11

+ 0.02� 0.02 ± 0.07

2.0 – 4.0 0.11 + 0.12� 0.09

+ 0.01� 0.01 ± 0.02

4.0 – 6.0 0.02 + 0.09� 0.00

+ 0.01� 0.01 ± 0.01

6.0 – 8.0 0.25 + 0.12� 0.11

+ 0.01� 0.01 ± 0.05

11.0 – 12.5 0.75 + 0.15� 0.14

+ 0.03� 0.05 ± 0.15

15.0 – 16.0 1.12 + 0.19� 0.18

+ 0.05� 0.05 ± 0.23

16.0 – 18.0 1.22 + 0.14� 0.14

+ 0.03� 0.06 ± 0.25

18.0 – 20.0 1.24 + 0.14� 0.14

+ 0.06� 0.05 ± 0.26

1.1 – 6.0 0.09 + 0.06� 0.05

+ 0.01� 0.01 ± 0.02

15.0 – 20.0 1.20 + 0.09� 0.09

+ 0.02� 0.04 ± 0.25

]4c/2 [GeV2q0 5 10 15 20

]-1 )4 c/2

(GeV

-7 [1

02 q

) / d

µ µ

Λ → b

Λ(Bd 0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

LHCb

SM prediction

Data

Figure 5: Measured ⇤0b ! ⇤µ+µ� branching fraction as a function of q2 with the predictions of

the SM [15] superimposed. The inner error bars on data points represent the total uncertaintyon the relative branching fraction (statistical and systematic); the outer error bar also includesthe uncertainties from the branching fraction of the normalisation mode.

13

]4c/2 [GeV2q0 5 10 15 20

l FBA

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

LHCb SM prediction

Data

]4c/2 [GeV2q0 5 10 15 20

h FBA

-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

LHCb SM prediction

Data

Figure 8: Measured values of (left) the leptonic and (right) the hadronic forward-backwardasymmetries in bins of q2. Data points are only shown for q2 intervals where a statisticallysignificant signal yield is found, see text for details. The (red) triangle represents the values forthe 15 < q2 < 20 GeV2/c4 interval. Standard Model predictions are obtained from Ref. [17].

lFBA

-0.5 0 0.5

Lf

0

0.2

0.4

0.6

0.8

1LHCb 4c/2[15.0,20.0] GeV

Figure 9: Two-dimensional 68% CL region (black) as a function of A`FB and fL. The shaded

area represents the region where the PDF is positive over the complete cos ✓` range. The best fitpoint is given by the (blue) star.

interval 15 < q2 < 20 GeV2/c4) as a two-dimensional 68 % confidence level (CL) region,where the likelihood-ratio ordering method is applied by varying both observables andtherefore taking correlations into account. Confidence regions for the other q2 intervalsare shown in Fig. 10, see Appendix.

18

]4c/2 [GeV2q0 5 10 15 20

l FBA

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

LHCb SM prediction

Data

]4c/2 [GeV2q0 5 10 15 20

h FBA

-0.5-0.4-0.3-0.2-0.1

00.10.20.30.40.5

LHCb SM prediction

Data

Figure 8: Measured values of (left) the leptonic and (right) the hadronic forward-backwardasymmetries in bins of q2. Data points are only shown for q2 intervals where a statisticallysignificant signal yield is found, see text for details. The (red) triangle represents the values forthe 15 < q2 < 20 GeV2/c4 interval. Standard Model predictions are obtained from Ref. [17].

lFBA

-0.5 0 0.5

Lf

0

0.2

0.4

0.6

0.8

1LHCb 4c/2[15.0,20.0] GeV

Figure 9: Two-dimensional 68% CL region (black) as a function of A`FB and fL. The shaded

area represents the region where the PDF is positive over the complete cos ✓` range. The best fitpoint is given by the (blue) star.

interval 15 < q2 < 20 GeV2/c4) as a two-dimensional 68 % confidence level (CL) region,where the likelihood-ratio ordering method is applied by varying both observables andtherefore taking correlations into account. Confidence regions for the other q2 intervalsare shown in Fig. 10, see Appendix.

18

� Additional observables eg ApFB giving access to different combinations of

Wilson coefficients


What about baryonic decays cont’d

vDyk, Meinel [1603.02974],[LHCb implications 2015](toy model low recoil)

Physik Institut

New Types of Constraintsmoch fit of C9(90) given hypothetical measurements, while keeping

C10(100) = C10(100) ' (�4, 0) fixed

-4 -2 0 2 4

-4

-2

0

2

4

C9

C9'

black square: SM point

– existing constraints⇢±

1 blue banded constraints⇢2 golden banded constraint

– new constraints⇢�3 green banded constraints⇢4 red hyperbolic constraint

04.11.2015 ⇤b

! ⇤(! p⇡�)`+`� Page 8

FL (common with B → Kµ+µ−)A`FB (common with B → Kµ+µ−)

A`pFB (unique to Λb → Λµ+µ− [notmeasured yet])Ap

FB (unique to Λb → Λµ+µ−)

� Ongoing work on Λb → Λ∗(→ pK )µ+µ− BF measurement, CP asymmetrymeasurements etc

� With 10,000 candidates by Run 4 and 60,000 by Run 5, LHCb will uniquelycontribute to these new observables


https://indico.cern.ch/event/395704/contributions/1834098/attachments/1181454/1710686/talk-lambdab.pdf

Photon polarisation through Bs → φγ� Untagged measurement of the time dependent decay rate in Bs → φγ LHCb

[1609.02032]

Γ(Bs + Bs)(t) ∝ e−Γs t

[cosh

(∆Γs

2t

)− A∆Γ sinh

(∆Γs

2t

)]

A∆Γ ∼ |A(Bs→φγL)||A(Bs→φγR )|cosφs

→ Sensitive to combinations of C7/C′7

A∆Γ(SM) = 0.047+0.029−0.025 Muheim et al. [PLB664(08)174]

LHCb [1609.02032]

Can

dida

tes /

ps

210

310

410 LHCb

γ0*K→0B

[ps]t0 2 4 6 8 105−

05

Can

dida

tes /

ps

10

210

310 LHCb

γφ→0sB

[ps]t0 2 4 6 8 105−

05

Figure 2: Background-subtracted decay-time distributions for B0! K⇤0� (top) and B0s ! ��

(bottom) decays with the fit projections overlaid and normalized residuals shown below. Fordisplay purposes, the PDF is shown as a histogram, integrated across each decay-time interval.

The decay-time-dependent e�ciency is parameterized as

✏(t) = e�↵t [a (t � t0)]n

1 + [a (t � t0)]nfor t � t0, (3)

where the parameters a and n describe the curvature of the e�ciency function at lowdecay times, t0 is the decay time below which the e�ciency function is zero, and ↵describes the decrease of the e�ciency at high decay times. Large simulated samples ofB0

s ! �� or B0 ! K⇤0� decays are used to validate this parameterization. The signalPDF is found to describe the reconstructed decay-time distribution of selected simulatedcandidates over the full decay-time range. To assess whether the simulation reproducesthe decay-time-dependent e�ciency, the B0! K⇤0� data sample alone is used to fit ⌧B0 ,fixing the e�ciency parameters to those from the simulation. The fitted value of ⌧B0 is1.524 ± 0.013 ps, where the uncertainty is statistical only, in agreement with the worldaverage value [3]. In the simultaneous fit to the data, a and n are fixed to the values in

4

� Requires good understanding of thedetection efficiency as a functiondecay time → Use B0 → K∗0γdata to constrain the efficiency

� A∆Γ = −0.98+0.46−0.52

+0.23−0.20 within 2σ

from SM


Constraints on C(′)7

� Current angular B0 → K∗0ee measurements provide best constraints to C(′)7

Paul, Straub [1608.02556]

�0.3 �0.2 �0.1 0.0 0.1 0.2 0.3

Re(CNP7 )

�0.3

�0.2

�0.1

0.0

0.1

0.2

0.3

Re(

C�N

P7

)

�0.3 �0.2 �0.1 0.0 0.1 0.2 0.3

Re(C � NP7 )

�0.3

�0.2

�0.1

0.0

0.1

0.2

0.3

Im(C

� 7)

global

branching ratios

A��(Bs ! ��)

hP1i(B0 ! K�0e+e�)

SK��

hAImT i(B0 ! K�0e+e�)

Figure 2: Constraints on NP contributions to the Wilson coe�cients C7 and C 07. For the global

constraints, 1 and 2� contours are shown, while the individual constraints are shownat 1� level.

of NP contributions to Re C7 vs. Re C 07 and Re C 0

7 vs. Im C 07. The contours correspond to

constant values of ��2 with respect to a best fit point, obtained by combining (correlated)experimental and theoretical uncertainties7. In each of the plots, we have assumed NP to onlya↵ect the two quantities plotted (e.g., in the first plot, both coe�cients are assumed to bereal). In addition to the global 1 and 2� constraints, we also show the 1� constraints fromindividual exclusive observables as well as from the combination of all branching ratios. Theseplots highlight the complementarity of the exclusive observables: while the imaginary part ofC 0

7 is constrained by AImT , the real part is constrained by A�� and P1, while SK⇤� leads to a

constraint in the complex C 07 plane that is “rotated” by the B0 mixing phase 2�. The new

measurement of A�� shows a preference for non-zero Re C 07, but given its large uncertainties,

it is not in disagreement with the measurement of P1.Since the experimental central value of A�� is at the border of the physical domain, we

provide best fit values and correlated errors on the real and imaginary parts of C 07 in a fit

without A�� and in a fit including it, obtained by approximating the likelihood in the vicinityof the best fit point as a multivariate Gaussian. We find

✓Re C 0NP

7 (µb)Im C 0

7(µb)

◆=

✓0.019 ± 0.0430.005 ± 0.034

◆, ⇢ = 0.39 (without A��), (41)

✓Re C 0NP

7 (µb)Im C 0

7(µb)

◆=

✓0.052 ± 0.0390.006 ± 0.042

◆, ⇢ = 0.31 (with A��), (42)

where ⇢ are the correlation coe�cients.

4. Conclusions and outlook

The b ! s� transition belongs to the most important probes of NP in the flavour sector.While the most stringent constraint on new contributions with left-handed photon helicity

7See [7] and the documentation of the FastFit class in flavio for details on the procedure.

13

� Large program of radiative decays for Run 2 and beyond including ACP (t)with KSπ

0γ

� Additional B0 → K∗0ee observables become available with Run 2 data andbeyond→ 200 times more data with 300fb−1 assuming trigger and reconstructionefficiencies are maintained


Lepton Non Universality testsLHCb [PRL113(2014)151601]

T. Blake

RK result• In the Run 1 dataset, LHCb

determines:

!

in the range 1 < q2 < 6 GeV2, which is consistent with the SM at 2.6!.

• Take double ratio with B+→J/ѱK+ to cancel possible sources of systematic uncertainty.

• Correct for migration of events in q2 due to Bremsstrahlung using MC (with PHOTOS).

29

]4c/2 [GeV2q0 5 10 15 20

KR

0

0.5

1

1.5

2

SM

LHCb BaBar Belle

LHCb

LHCb [PRL113 (2014) 151601 ]!BaBar [PRD 86 (2012) 032012]!Belle [PRL 103 (2009) 171801]

RK = 0.745+0.090�0.074

+0.036�0.036

NB RK ≃ 0.8 is a prediction of one class of model explaining the B0→K*0"+"− angular observables, see L" - L# models W. Altmannshofer et al. [PRD 89 (2014) 095033]

� Mild tension inRK = B(B+→K +µ+µ−)

B(B+→K +e+e−) consistentwith b → sµ+µ− anomalies if newphysics couples only to muons andnot electrons

� Rich program to measure RK∗ , Rφ,RΛ∗ , “Rangular”

� Note: FSR simulated using PHOTOS. Dominant effect to q2 migrations isdue to Bremsstrahlung in material of the detector.

� In Run 1: measure RK to 10%, RK∗ to 20%, Rφ to 35% (naive scaling)

� With 50fb−1, measurements become systematic limited� With 300fb−1 reach O(1)% precision→ Maintain performance for electrons and work to reduce systematicuncertainties


B+ → π+µ+µ− differential branching fraction

� Very relevant if tensions persist → test MFV nature of new physics� Latest lattice results enable further precision tests of CKM paradigm

Buras,Blanke[1602.04020], FNAL/MILC[1602.03560]

� Current measurement from penguin decays of |Vtd/Vts | = 0.201± 0.020FNAL/MILC[PRD93,034005(2016]

LHCb [JHEP10(2015)034] FNAL/MILC[1602.03560], FNAL/MILC[PRD93,034005(2016)]

)4c/2 (GeV2q0 10 20

)4 c-2

GeV

-9 (1

02 q

dB/d

0

0.5

1

1.5

2

2.5LHCb APR13 HKR15 FNAL/MILC15

LHCb

Figure 4: The di↵erential branching fraction of B+! ⇡+µ+µ� in bins of dilepton invariant masssquared, q2, compared to SM predictions taken from Refs. [1] (APR13), [6] (HKR15) and fromlattice QCD calculations [7] (FNAL/MILC15).

and in the region 15.0 < q2 < 22.0 GeV2/c4 is

B(B+! ⇡+µ+µ�)

B(B+! K+µ+µ�)= 0.037 ± 0.008 (stat) ± 0.001 (syst) .

These results are the most precise measurements of these quantities to date.

5.2 CKM matrix elements

The ratio of CKM matrix elements |Vtd/Vts| can be calculated from the ratio of branchingfractions, B(B+ ! ⇡+µ+µ�)/B(B+ ! K+µ+µ�), and is given in terms of measuredquantities

|Vtd/Vts|2 =B(B+! ⇡+µ+µ�)

B(B+! K+µ+µ�)⇥

RFKdq2

RF⇡dq2

(3)

where F⇡(K) is the combination of form factor, Wilson coe�cients and phase space factor forthe B+ ! ⇡(K) decay. The values of

RF⇡,Kdq2 are calculated using the EOS package [29],

with B+ ! ⇡+ form factors taken from Refs. [30,31] and B+ ! K+ form factors taken fromRef. [32]. The EOS package is a framework for calculating observables, with uncertainties,in semileptonic b-quark decays for both SM and new physics parameters. In order totake into account the correlations between the theory inputs for the matrix element ratiocalculation, the EOS package is used to produce a PDF as a function of the B+! ⇡+µ+µ�

9

|Vtd | × 103

|Vts | × 103

7 8 9 35 39 43

∆Mq:

this work

PDG

B→K(π)µ+µ

−

CKM unitarity:

full

tree

|Vtd / Vts |

0.18 0.19 0.20 0.21 0.22 0.23

FIG. 16. (left) Recent determinations |Vtd| and |Vts|, and (right) their ratio. The filled circles

and vertical bands show our new results in Eqs. (9.17)–(9.19), while the open circles show the

previous values from Bq-mixing [102]. The squares show the determinations from semileptonic

B ! ⇡µ+µ� and B ! Kµ+µ� decays [183], while the plus symbols show the values inferred

from CKM unitarity [158]. The error bars on our results do not include the estimated charm-sea

uncertainties, which are too small to be visible.

where the errors are from the lattice mixing matrix elements, the measured �Mq, the re-maining parametric inputs to Eq. (2.9), and the omission of charm sea quarks, respectively.The uncertainty on |Vtd/Vts| is 2–3 times smaller than those on |Vtd| and |Vts| individuallybecause the hadronic uncertainties are suppressed in the ratio. The theoretical uncertaintiesfrom the Bq-mixing matrix elements are still, however, the dominant sources of error in allthree results in Eqs. (9.17)–(9.19).

Figure 16 compares our results for |Vtd|, |Vts|, and their ratio in Eqs. (9.17)–(9.19) withother determinations. Our results are consistent with the values from Bq-meson mixing in thePDG review [102], which are obtained using approximately the same experimental inputs,

and lattice-QCD calculations of the f 2Bq

B(1)Bq

and ⇠ from Refs. [13] and [15], respectively.

Our errors on |Vtd|, |Vts| are about two times smaller, however, and on |Vtd/Vts| they aremore than three times smaller, due to the reduced theoretical errors on the hadronic matrixelements.

The CKM matrix elements |Vtd| and |Vts| can be obtained independently from raresemileptonic B-meson decays because the Standard-Model rates for B(B ! ⇡(K)µ+µ�)are proportional to the same combination |V ⇤

td(s)Vtb|. Until recently, these determinationswere not competitive with those from Bq-meson mixing due to both large experimental andtheoretical uncertainties. In the past year, however, the LHCb collaboration published newmeasurements of B(B ! ⇡µ+µ�) and B(B ! Kµ+µ�) [184, 185], and we calculated thefull set of B ! ⇡ and B ! K form factors in three-flavor lattice QCD [131, 186]. Using

54


b → dµ+µ− the new b → sµ+µ−

� First observation of baryonicb → dµ+µ− transition

� B(Λb → pπµµ) =(6.9± 1.9± 1.1+1.3

−1.0)× 10−8

� Paper expected soon

� These decays will greatly benefit with Run 2 and beyond

� Run 1: 93 B+ → π+µ+µ−, 40 B0 → π+π−µ+µ−

� 300fb−1: 18,000 B+ → π+µ+µ− and 4,000 B+ → π+e+e−(naive scaling)

� 300fb−1: 8,000 B+ → π+π−µ+µ− and 2,000 B+ → π+π−e+e−(naive scaling)

→ Allows for precision MFV and MFV+LNU tests


Summary

� Run 1 of the LHC introduced precision era in rare B-decay measurements� Precision started to reveal tensions. Future work aimed at understanding

these:→ Clarify the impact of cc and other resonances in B → K (∗)µ+µ−

observables→ Fully exploit sensitivity of b → s`` to C

(′)10 , Im(C9,10), CT ,S,P

→ Plethora of observables for K∗J=0,2 states and baryonic decays

→ Photon polarisation measurements to constrain new physics in C(′)7

→ Understand LNU hints in RK both by searching in related modes

� Towards Run 2 and beyond→ Clear physics case for rare decays given theory stat precision (thoughlater stages systs important)→ Big gains in b → d transitions and final states with electron→ Critical to maintain detector performance


Backup


How are we doing?channel Lint (fb−1) PublicationdB/dq2 B → K∗+µ+µ− 3 [JHEP06(2014)133]dB/dq2 B → K 0µ+µ− 3 [JHEP06(2014)133]dB/dq2 B → K +µ+µ− 3 [JHEP06(2014)133]dB/dq2 B0 → K∗0µ+µ− 3 [1606.04731]dB/dq2 and moments B0 → K∗0,2µ

+µ− 3 [1609.04736]dB/dq2 B0

s → φµ+µ− 3 [JHEP09(2015)179]B(B+ → φKµ+µ−) 3 [JHEP10(2014)064]dB/dq2 B+ → K +π−π+µ+µ− 3 [JHEP10(2014)064]dB/dq2 Λb → Λµ+µ− 3 [JHEP06(2015)115]dB/dq2 B+ → π+µ+µ− 3 [JHEP10(2015)034]B(Bs,d → µ+µ−) 3 [Nature522(2015)68]B(B0 → π+π−µ+µ−) 3 [PLB743(2015)]B(B0 → K∗0e+e−) 3 [JHEP05(2013)159]B(B+ → K +e+e−) 3 [PRL113(2014)151601]AI B → K (∗)µ+µ− 3 [JHEP06(2014)133]ACP B+ → K +µ+µ− 3 [JHEP09(2014)177]ACP B0 → K∗0µ+µ− 3 [JHEP09(2014)177]ACP B+ → π+µ+µ− 3 [JHEP10(2015)034]Angular B+ → K +µ+µ− 3 [JHEP05(2014)082]Angular B0 → K 0µ+µ− 3 [JHEP05(2014)082]Angular B0 → K∗0µ+µ− 3 [JHEP02(2016)104]Angular B0

s → φµ+µ− 3 [JHEP09(2015)179]Angular Λb → Λµ+µ− 3 [JHEP06(2015)115]


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Radiative and EW-penguin decays and LFU tests