Test of lepton flavour universality in b s + - decays at...

Test of lepton flavour universalityin b → s`+`− decays at LHCb

Razvan-Daniel (Dan) Moise,

on behalf of the LHCb collaboration

Moriond EW 2021

Dan Moise (Imperial College London) Test of LFU at LHCb 23rd March 2021 1 / 12

Lepton Flavour Universality (LFU) & rare decays

Standard Model (SM) couplings of leptons to vectorbosons are flavour-independent.

any sign of lepton flavour non-universalitywould indicate new physics (NP)

Decays of b-quarks are sensitive to LFU.

example: the rare process b → s`+`−— flavour-changing neutral current (FCNC)

SM only allows FCNCs through loop, but NP can enter at tree level or contribute to theloop (even at high mass scales) ⇒ potential LFU violation


Anomalous flavour observablesA pattern of interlinked anomalies has emerged in studies of b → s`+`− processes.

branching fractions of e.g.I Bs → µ+µ− (see Flavio’s talk)

I B → K (∗)µ+µ− [JHEP 06 (2014) 133]

angular observables in e.g. B0 → K ∗0µ+µ− [PRL 125 (2020) 011802]

ratios of branching fractions, such as RK∗0 [JHEP 08 (2017) 055]

]4c/2 [GeV2q0 5 10 15 20

]2/G

eV4 c ×

-8 [

102 q

/dBd 0

1

2

3

4

5

LCSR Lattice Data

LHCb

−µ+µ+ K→+B

[JHEP 06 (2014) 133]

0 5 10 15]4c/2 [GeV2q

1−

0.5−

0

0.5

1

5'P

(1S)

ψ/J

(2S)

ψ

LHCb Run 1 + 2016SM from DHMV

[PRL 125 (2020) 011802]

0 1 2 3 4 5 6

q2 [GeV2/c4]

0.0

0.2

0.4

0.6

0.8

1.0

RK∗0

LHCb

LHCb

BIP

CDHMV

EOS

flav.io

JC

[JHEP 08 (2017) 055]


https://link.springer.com/article/10.1007/JHEP06(2014)133

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.011802

https://doi.org/10.1007/JHEP08(2017)055




The observable RK

One of the anomalous LFU observables is:

RK =

∫ 6.0 GeV2

1.1 GeV2

dB(B+ → K+µ+µ−

)dq2 dq2

∫ 6.0 GeV2

1.1 GeV2

dB(B+ → K+e+e−

)dq2 dq2

SM= 1±O(10−2) EM correction1

Previous LHCb measurement is in tension with SMprediction at level of 2.5 σ [PRL 122 (2019) 191801].

obtained using data collected up until 2016

subject of this talk: update of the previousmeasurement, with full Run 1 and Run 2 data

I adding 2017 & 2018 data effectively doubles the dataset

I following essentially identical procedure

q2 def= dilepton invariant mass squared

[PRL 122 (2019) 191801]

1 [JHEP 06 (2016) 092] [JHEP 07 (2007) 040] [EPJC 76 (2016) 440] [PRD 69 (2004) 074020] [PRD 68 (2003) 094016] [EOS] [flavio]





https://doi.org/10.1088/1126-6708/2007/12/040

https://doi.org/10.1140/epjc/s10052-016-4274-7

https://doi.org/10.1103/PhysRevD.69.074020


https://eos.github.io/

http://arxiv.org/abs/1810.08132

Challenge: muons vs. electrons at LHCb

Bulk of the analysis is dedicated to getting differencesbetween electron and muon detection under control.

different trigger and particle identification strategies

electrons lose significant portions of energy tobremsstrahlung radiation

7 worse mass resolution and reconstruction efficiencycf. muons

3 mitigated by e.g. recovery algorithm (look forphoton clusters in calorimeter that are compatiblewith electron trajectory)


Measuring RK

Control electron-muon differences through double ratio between rare B+ → K+`+`− modesand control B+ → K+J/ψ(`+`−) channels:

RK =

(Nµµ

rare

εµµrare/Nee

rare

εeerare

)

/(Nµµ

control

εµµcontrol

/Nee

control

εeecontrol

)︸︷︷︸

rJ/ψ

=

(Nµµ

rare

Nµµcontrol

/εµµrare

εµµcontrol

)/(Nee

rare

Neecontrol

/εeerare

εeecontrol

)

Five main steps:

1 obtain electron and muon data through tailored selection

2 calibration of simulation → efficiency calculation

3 estimation of systematic uncertainties

4 conduct cross-checks, such as rJ/ψ (known LFU)

5 fit rare data → extraction of RKRare and control selections identical up tocut on q2


Measuring RK

Control electron-muon differences through double ratio between rare B+ → K+`+`− modesand control B+ → K+J/ψ(`+`−) channels:

RK =

(Nµµ

rare

εµµrare/Nee

rare

εeerare

)/(Nµµ

control

εµµcontrol

/Nee

control

εeecontrol

)︸︷︷︸

rJ/ψ

=

(Nµµ

rare

Nµµcontrol

/εµµrare

εµµcontrol

)/(Nee

rare

Neecontrol

/εeerare

εeecontrol

)

Five main steps:

1 obtain electron and muon data through tailored selection

2 calibration of simulation → efficiency calculation

3 estimation of systematic uncertainties

4 conduct cross-checks, such as rJ/ψ (known LFU)

5 fit rare data → extraction of RKRare and control selections identical up tocut on q2


Efficiency calculation and corrections to simulation

Efficiencies estimated from simulated samples, which are calibrated using control data.Calibration procedure is the same as in [PRL 122 (2019) 191801], and it covers:

trigger performance;

particle identification efficiency;

I method described in [EPJ T&I (2019) 6:1)]

B+ kinematics;

resolutions of q2 and m(K+e+e−). ) [MeV]e(TE0 2000 4000 6000 8000 10000

(L0E

lect

ron)

[%

]ε

0

1020

304050

6070

80

90100

LHCb [PRL 122 (2019) 191801]

Example measurement of electron trigger

performance

This leads to %-level control of efficiency ratios.

verified through a host of cross-checks



https://epjtechniquesandinstrumentation.springeropen.com/articles/10.1140/epjti/s40485-019-0050-z


Cross-check example: the single ratio rJ/ψ

rJ/ψ =B(B+ → K+J/ψ(µ+µ−))

B(B+ → K+J/ψ(e+e−))=

Nµµcontrol

εµµcontrol

/Nee

control

εeecontrol

Single ratio requires control of electrons with respect to muons.

stringent cross-check of efficiencies & yields

Result: rJ/ψ = 0.981± 0.020 (stat. & syst.)

Also compute rJ/ψ in bins of variables relevant to detector response(1D rJ/ψ)

if deviations from flatness are genuine, impact on RK is withinestimated systematic uncertainty

]c) [MeV/+B(T

p0 5000 10000 15000

⟩ ψ

J/ r⟨

/ ψ

J/r

0.9

0.95

1

1.05

1.1

LHCb[LHCb-PAPER-2021-004]

1D rJ/ψ , binned in B+pT


Cross-check: the double ratio Rψ(2S)

Select data at ψ(2S) resonance and evaluate:

Rψ(2S) =B(B+ → K+ψ(2S)(µ+µ−))

B(B+ → K+ψ(2S)(e+e−))

/B(B+ → K+J/ψ(µ+µ−))

B(B+ → K+J/ψ(e+e−))

expected close to unity

test efficiency corrections at q2 away from J/ψ

independent validation of double ratio

Result: Rψ(2S) = 0.997± 0.011 (stat. & syst.)

]2c [MeV/)−µ+µ+(K(2S)ψm5200 5300 5400 5500 5600

)2 cC

andi

date

s / (

4 M

eV/

5000

10000

15000

20000

25000

-1Data 4 fb

Total fit

+)K−µ+µ(2S)(ψ →+B

Combinatorial

LHCb

Fit to 2017 & 2018 B+ → K+ψ(2S)(µ+µ−) data

]2c [MeV/)−e+e+(K(2S)ψm5200 5400 5600

)2 cC

andi

date

s / (

12 M

eV/

2000

4000

6000

8000

10000-1Data 4 fb

Total fit+)K−e+(2S)(eψ →+B*0)K−e+(2S)(eψ →0B

+)K−e+(eψ J/→+B+K−e+ e→+B

+ X) Kψ(2S) (J/ψ →+B(K X)

s X) Hψ (J/c X→B

Combinatorial

LHCb

Fit to 2017 & 2018 B+ → K+ψ(2S)(e+e−) data

Dilepton mass constrained to mass of ψ(2S)


Fits to B+ → K+`+`− dataRK is extracted as a parameter of a simultaneous fit to all B+ → K+`+`− data.

]2c [MeV/)−µ+µ+m(K5200 5300 5400 5500 5600

)2 cC

andi

date

s / (

7 M

eV/

0

100

200

300

400

500

600-1Data 9 fb

Total fit−µ+µ+ K→+B

Combinatorial

LHCb

[LHCb-PAPER-2021-004]

N(K+µ+µ−) ∼ 3850

]2c [MeV/)−e+e+m(K5000 5500 6000

)2 cC

andi

date

s / (

24 M

eV/

020406080

100120140160180200220240

-1Data 9 fbTotal fit

−e+e+ K→+B+)K−e+(eψ J/→+B

Part. Reco.Combinatorial

LHCb

N(K+e+e−) ∼ 1640

correlations between selection efficiencies taken into account

shape parameters derived from calibrated simulation

systematic effect of chosen signal & background models is ∼ 1%


Fits to B+ → K+`+`− dataRK is extracted as a parameter of a simultaneous fit to all B+ → K+`+`− data.

]2c [MeV/)−µ+µ+m(K5200 5300 5400 5500 5600

)2 cC

andi

date

s / (

7 M

eV/

0

100

200

300

400

500

600-1Data 9 fb

Total fit−µ+µ+ K→+B

Combinatorial

LHCb


N(K+µ+µ−) ∼ 3850

]2c [MeV/)−e+e+m(K5000 5500 6000

)2 cC

andi

date

s / (

24 M

eV/

020406080

100120140160180200220240


−e+e+ K→+B+)K−e+(eψ J/→+B

Part. Reco.Combinatorial

LHCb

N(K+e+e−) ∼ 1640

correlations between selection efficiencies taken into account

shape parameters derived from calibrated simulation

systematic effect of chosen signal & background models is ∼ 1%

And now, the final result


RK with full Run 1 and Run 2 LHCb data

The measured value of RK is:

RK = 0.846 +0.042−0.039 (stat.) +0.013

−0.012 (syst.)

dominant systematic effect: fit modelI effects such as calibration of trigger & kinematics

are at permille-level

p-value under SM hypothesis: 0.0010

significance: 3.1σ (evidence for LFU violation inB+ → K+`+`− decays)

0.5 1 1.5KR

-1LHCb 9 fb4c/2 < 6.0 GeV2q1.1 <

Belle4c/2 < 6.0 GeV2q1.0 <

BaBar4c/2 < 8.12 GeV2q0.1 <

[PRD 86 (2012) 02]

[JHEP 03 (2021) 105]


0.7 0.8 0.9 1 1.1

KR

0

2

4

6

8

10

12

14 )m

inL

/ L

ln(

−Pr

ofile

of

LHCb-19 fb


— 1σ— 3σ— 5σ


Other results

0 5 10 15 20]4c/2 [GeV2q

0

1

2

3

4

5

]2/G

eV4 c ×

-8 [

102 q

/dBd

LHCb SM prediction-1electrons 9fb-1muons 3fb

Combining measured RK value with B(B+ → K+µ+µ−) result from [JHEP 06 (2014) 133] gives:

B(B+ → K+e+e−) = (28.6 +1.5−1.4(stat.) ± 1.3(syst.))× 10−9

in the range q2 ∈ [1.1, 6.0] GeV2/c4.


https://link.springer.com/article/10.1007/JHEP06(2014)133

Summary

performed most precise measurement of the LFU ratio RK using full LHCb Run 1 andRun 2 data

gained factor ∼ 2 statistics cf. previous result [PRL 122 (2019) 191801]

3.1σ tension with SM prediction1

I evidence for violation of LFU in B+ → K+`+`− decays

LHCb will continue to study flavour anomalies, including LFU-sensitive observables

paper submitted to Nature Physics [LHCb-PAPER-2021-004]

1 [JHEP 06 (2016) 092] [JHEP 07 (2007) 040] [EPJC 76 (2016) 440] [PRD 69 (2004) 074020] [PRD 68 (2003) 094016] [EOS] [flavio]




https://doi.org/10.1088/1126-6708/2007/12/040

https://doi.org/10.1140/epjc/s10052-016-4274-7



https://eos.github.io/

http://arxiv.org/abs/1810.08132

BACKUP


K+`+`− final states at LHCb

5.0 5.2 5.4 5.6 5.8 6.0]2c [GeV/)−µ+µ+m(K

0

5

10

15

20

25]4 c/2 [

GeV

2 q

1

10

210

310

410

510LHCb

4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0]2c [GeV/)−e+e+m(K

0

5

10

15

20

25]4 c/2 [

GeV

2 q

1

10

210

310

410

510LHCb

[PRL 122 (2019) 191801]



Semileptonic background vetoes

]2c) [MeV/−e+K(m1000 2000 3000 4000 5000

Nor

mal

ised

dis

trib

utio

n

5−10

4−10

3−10

2−10

1−10

−e+e+ K→+B

eν +) eeν −e+ K→(0

D →+B

]−e →[−π )eν −e+ K→(

0D →+B

eν +) e ]−e →[−π+ K→(

0D →+B

LHCb simulation

]2c) [MeV/]−π →[−e+K(m

1700 1800 1900 2000

Nor

mal

ised

dis

trib

utio

n

0.00

0.01

0.02

0.03

0.04

0.05 LHCbsimulation


Backgrounds coming from b → c`−ν` transitions removed by mass vetoes.


Trigger strategy

Same approach as in the previous analysis:

for µµ channels, trigger on muons: L0Muon

for ee channels, use three exclusive trigger categories: L0Electron,L0Hadron, L0TIS

systematics calculated and cross-checks performed foreach trigger individually


Fits to control data: muons

]2c) [MeV/−µ+µ+K(ψJ/m5200 5300 5400 5500 5600

)2 cC

andi

date

s / (

4 M

eV/

10

210

310

410

510 -1Data 5 fbTotal fit

+)K−µ+µ(ψ J/→+B+π)−µ+µ(ψ J/→+B

Combinatorial

LHCb

Previous data

]2c) [MeV/−µ+µ+K(ψJ/m5200 5300 5400 5500 5600

)2 cC

andi

date

s / (

4 M

eV/

10

210

310

410


+)K−µ+µ(ψ J/→+B+π)−µ+µ(ψ J/→+B

Combinatorial

LHCb

New data



Fits to control data: electrons

]2c) [MeV/−e+e+K(ψJ/m5200 5400 5600

)2 cC

andi

date

s / (

12 M

eV/

210

310

410


+)K−e+(eψ J/→+BPart. Reco.

+π)−e+(eψ J/→+BCombinatorial

LHCb

]2c) [MeV/−e+e+K(ψJ/m5200 5400 5600

)2 cC

andi

date

s / (

12 M

eV/

210

310

410




LHCb

Electron trigger

]2c) [MeV/−e+e+K(ψJ/m5200 5400 5600

)2 cC

andi

date

s / (

12 M

eV/

210

310

410-1Data 5 fb

Total fit+)K−e+(eψ J/→+B

Part. Reco.+π)−e+(eψ J/→+B

Combinatorial

LHCb

]2c) [MeV/−e+e+K(ψJ/m5200 5400 5600

)2 cC

andi

date

s / (

12 M

eV/

210

310

410-1Data 4 fb

Total fit+)K−e+(eψ J/→+B

Part. Reco.+π)−e+(eψ J/→+B

Combinatorial

LHCb

Hadron trigger

]2c) [MeV/−e+e+K(ψJ/m5200 5400 5600

)2 cC

andi

date

s / (

12 M

eV/

210

310




LHCb

]2c) [MeV/−e+e+K(ψJ/m5200 5400 5600

)2 cC

andi

date

s / (

12 M

eV/

210

310




LHCb

Independent trigger



Cross-check: 2D rJ/ψ

The 1D rJ/ψ cross-check is extended to two variables.

deviations from flatness again covered by systematic uncertainty on RK

rJ/ψ tests show efficiencies understood across phase space

) bin number−l, +l(α ×)) −l(p)), +l(pmax(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

⟩ ψ

J/ r⟨

/ ψ

J/r

0.9

1

1.1 LHCb[LHCb-PAPER-2021-004]

2D rJ/ψ , binned in max lepton momentum andangle between leptons

K+`+`− & K+J/ψ distributions


Additional rJ/ψ checks

]c)) [MeV/−l(T

p), +l(T

pmin(1000 2000 3000 4000 5000

Can

dida

tes

(arb

itrar

y un

its)

0

0.2

0.4

0.6

0.8

1

1.2 LHCb simulation

) [rad]−l, +l(α0 0.1 0.2 0.3 0.4 0.5

Can

dida

tes

(arb

itrar

y un

its)

0

0.2

0.4

0.6

0.8

1

1.2 LHCb simulation

]c)) [MeV/−l(T

p), +l(T

pmin(1000 2000 3000 4000 5000

⟩ ψ

J/ r⟨

/ ψ

J/r

0.9

0.95

1

1.05

1.1

LHCb

) [rad]−l, +l(α0 0.1 0.2 0.3 0.4 0.5

⟩ ψ

J/ r⟨

/ ψ

J/r

0.9

0.95

1

1.05

1.1

LHCb

[LHCb-PAPER-2021-004]Dan Moise (Imperial College London) Test of LFU at LHCb 23rd March 2021 12 / 12

Distributions of rare & control samples (I)

) [rad]−l, +l(α0 0.1 0.2 0.3 0.4 0.5

Can

dida

tes

/ (a.

u.)

0.0

0.2

0.4

0.6

0.8

1.0

1.2 LHCb simulation

) [rad]−l, +K(α0 0.1 0.2 0.3 0.4 0.5

Can

dida

tes

/ (a.

u.)

0.0

0.2

0.4

0.6

0.8

1.0

1.2 LHCb simulation

) [rad]+l, +K(α0 0.1 0.2 0.3 0.4 0.5

Can

dida

tes

/ (a.

u.)

0.0

0.2

0.4

0.6

0.8

1.0

1.2 LHCb simulation

]c) [MeV/+K(T

p2000 4000 6000 8000

Can

dida

tes

/ (a.

u.)

0.0

0.2

0.4

0.6

0.8

1.0

1.2 LHCb simulation

]c)) [MeV/−l(T

p), +l(T

pmax(2000 4000 6000 8000 10000

Can

dida

tes

/ (a.

u.)

0.0

0.2

0.4

0.6

0.8

1.0

1.2 LHCb simulation −e+e+ K→+B−µ+µ+ K→+B

+)K−e+(eψ J/→+B+)K−µ+µ(ψ J/→+B

[PRL 122 (2019) 191801]



Distributions of rare & control samples (II)

)+K(η2 3 4 5

Can

dida

tes

/ (a.

u.)

0.0

0.2

0.4

0.6

0.8

1.0

1.2 LHCb simulation

))−l(η), +l(ηmin(2 3 4 5

Can

dida

tes

/ (a.

u.)

0.0

0.2

0.4

0.6

0.8

1.0

1.2 LHCb simulation

))−l(η), +l(ηmax(2 3 4 5

Can

dida

tes

/ (a.

u.)

0.0

0.2

0.4

0.6

0.8

1.0

1.2 LHCb simulation

))+B(IP2χ(

10log

4− 2− 0 2

Can

dida

tes

/ (a.

u.)

0.0

0.2

0.4

0.6

0.8

1.0

1.2 LHCb simulation

))+B(Vtx2χ(

10log

2− 0 2

Can

dida

tes

/ (a.

u.)

0.0

0.2

0.4

0.6

0.8

1.0

1.2 LHCb simulation −e+e+ K→+B−µ+µ+ K→+B

+)K−e+(eψ J/→+B+)K−µ+µ(ψ J/→+B

[PRL 122 (2019) 191801]



Test of lepton flavour universality in b s + - decays at...

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Transcript of Test of lepton flavour universality in b s + - decays at...