31
Dark Matter at the LHC Martino Borsato Universida de Santiago de Compostela on behalf of ATLAS, CMS, LHCb (SM) (mediator) (DM)

(DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

  • Upload
    others

  • View
    14

  • Download
    0

Embed Size (px)

Citation preview

Page 1: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Dark Matter at

the LHC

Martino Borsato†

†Universida de Santiago de Compostela

on behalf of ATLAS, CMS, LHCb

(SM)(mediator)

(DM)

Page 2: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

What to look for

๏ Experimental constraints:

• Relic density observed

• (Thermal) DM mass > keV

• Effectively EM neutral

• Cosmologically stable

• No or small self-interaction

!2

Planck, AA 594(2016)A13

e.g. Lovell et al. MNRAS 439(2014)300-317

Stable charged particle and direct detection

"Bullet cluster" AJ 648(2006)L109-L113

or more Slatyer and Wu. PRD95(2017)2,023010

0

1000

2000

3000

4000

5000

6000

DTT

![µK

2]

30 500 1000 1500 2000 2500

!

-60

-30

0

30

60

∆D

TT

!

2 10

-600

-300

0

300

600

Planck 2015

Bullet cluster→ Compelling WIMP scenario

Page 3: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

DM signals

!3

SM

DM

SM

DM

Direct detection

Detect interactions of the DM wind

XENON, Panda, Lux, DarkSide, …

Collider search

• Mediator → DM

(holistic search)

• Mediator → SM

(peak search)

Indirect detection

Signals from DM annihilation

FERMI, PAMELA, AMS, HESS, IceCube, CTA, …

Page 4: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Mediator → DM

!4

Page 5: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

Mono-X searches at the LHC

๏ Exploit initial state radiation

• Missing energy + large-pT

‣ X = jet, photon, W, Z

๏ Main challenge: measure precisely SM backgrounds

• e.g. Z(νν)+X is irreducible

!5

SM DM

SM DM

X MET

χ

q

χ

q

q

Z′

χ χZ'

ν

q

χ

q

q

Z′

χ νZ

Page 6: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

Mono-jet backgrounds

๏ Vector+jet backgrounds

• 50-80% is Z(νν)+jet (irreducible)

๏ Estimate using control regions:

• Z()+jet, removing from event

• W(ν)+jet, removing from event

• γ+jet, removing γ from event

!6

Events

/ G

eV

2−10

1−10

1

10

210

310

410

510

610

(13 TeV)-1

35.9 fb

CMS

monojet

Data

inv.→H(125)

= 2.0 TeVmed

Axial-vector, m

)+jetsννZ(

)+jetsνW(l

WW/WZ/ZZ

Top quark

+jetsγ(ll), γZ/

QCD

Data

/ P

red.

0.8

0.9

1

1.1

1.2

[GeV]miss

Tp

400 600 800 1000 1200 1400

Unc.

(Data

-Pre

d.)

2−

0

2

μuon (2)

μuon (1)Jet

nsMET

Remove µµ

arXiv:1712.02345

Page 7: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

+je

tsγ

Z(ll)+

jets

/

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22+jets DataγZ(ll)+jets /

+jets MC γZ(ll)+jets /

(13 TeV)-1

35.9 fb

CMS

monojet

[GeV]T

Hadronic recoil p

400 600 800 1000 1200 1400

Data

/ P

red.

0.5

1

1.5

Mono-jet backgrounds

๏ Ratio dσ(Z+jet)/dσ(W+jet)

and dσ(Z+jet)/dσ(γ+jet)

to simplify modelling

• Control-region to signal-region transfer factors from theory

๏ Progress in theory

• pT dependent NLO QCD+EW corrections of LO MC

• Including pT dependent correlations for corrections

• Ratios stable at few %

๏ Validation test on data

• Jet uncertainties cancel out

๏ Simultaneous fits of control

and signal regions

!7

LONLO QCDNNLO QCD

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

pp →Z(`+`−)+ jet / pp →W(`ν)+ jet @ 13 TeV

Z(`

+`−)+

jet

/W(`

ν)+

jet

100 200 500 1000 30000.9

0.95

1.0

1.05

pT,V [GeV]

R/

RN

LO

QC

D

3000

LONLO QCDNNLO QCD

0.01

0.02

0.03

0.04

0.05

0.06

pp →Z(`+`−)+ jet / pp →γ+ jet @ 13 TeV

Z(`

+`−)+

jet

/γ+

jet

100 200 500 1000 30000.9

0.95

1.0

1.05

pT,V [GeV]

R/

RN

LO

QC

D

)+je

tsν

Z(ll)+

jets

/ W

(l

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22)+jets DataνZ(ll)+jets / W(l

)+jets MCνZ(ll)+jets / W(l

(13 TeV)-1

35.9 fb

CMS

monojet

[GeV]T

Hadronic recoil p

400 600 800 1000 1200 1400

Data

/ P

red.

0.5

1

1.5

arXiv:1712.02345 arXiv:1712.02345

Lindert et al arXiv:1705.04664 Lindert et al arXiv:1705.04664

Page 8: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

Mono-jet results

๏ Results on simplified DM models

• Vector, axial-vector, scalar, pseudo-

scalar mediator (s-channel)

• 4 parameters: mDM, mmed, gSM, gDM

๏ Reach for gDM=1, mmed = 3 mDM:

• Up to ~1.6-1.8 TeV for mmed (vector)

• Below gSM ~ 0.1 for low mmed < 1TeV

!8

[GeV]VZm

0 1000 2000

[G

eV

m

0

500

1000exp

σ 2 ±Expected limit

)exp

σ 1 ±Expected limit (

)PDF, scale

theoryσ 1 ±Observed limit (

Relic Density (MadDM)

ATLAS-1

= 13 TeV, 36.1 fbs

Vector Mediator

Dirac Fermion DM

= 1.0χ

= 0.25, gq

g

95% CL limits

χ

= 2

mVZm

SM DM

SM DMmed

arXiv:1712.02345

arXiv:1711.03301

Page 9: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

Mono-X results

๏ Searched in mono-jet, but also

mono-γ and mono-V

๏ No excess in ATLAS+CMS

(36/fb from 2015+2016)

• Best sensitivity to date

• In the era of precision searches

๏ 40/fb on tape from 2017 and

2018 run happening now

๏ Challenging analysis in future

high-luminosity upgrade

!9

Signature ATLAS CMS

Mono-jet 36/fb 1711.03301 36/fb 1712.02345

Mono-γ 36/fb 1704.03848 13/fb 1706.03794

Mono-V(had) 3.2/fb 1608.02372 36/fb 1712.02345

Mono-Z(lep) 36/fb 1708.09624 36/fb 1711.00431

Mono-H(γγ,ττb,b)36.1/fb 1706.03948,

1707.0130236/fb EXO-16-055

[GeV] medMediator mass M0 500 1000 1500 2000 2500

[G

eV

] D

MD

ark

matter

mass m

0

100

200

300

400

500

600

700

800

900

1000

LHCP 2017 PreliminaryCMS

Axial-vector mediator

Dirac DM = 1.0

DMg

= 0.25q

g

= 0l

gExclusion at 95% CL

Observed

Expected

[EXO-16-048]

)-1 (35.9 fbDM + j/V(qq)

[EXO-16-039]

)-1 (12.9 fbγDM +

[EXO-16-052]

)-1 (35.9 fbDM + Z(ll)

DM = 2 x m

MedM

0.12≥ 2 hcΩ

LHCP 2017 PreliminaryCMS

Axial-vector mediator

Dirac DM = 1.0

DMg

= 0.25q

g

= 0l

g

Page 10: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

SUSY searches

๏ SUSY provides a candidate for DM

• χ0 down to 100 GeV still allowed

• Many different searches constraining DM candidate

• Interplay with direct searches investigated with global fits

!10

pMSSM11 EPJC78(2018)3-256

E.Bagnaschi, K.Sakurai, MB, et al

100 101 102 103

mχ0

1[GeV]

10−50

10−48

10−46

10−44

10−42

10−40

10−38

σSI

p[c

m2]

PANDAX-II

XENO

N1T

LUX

XENONnT

XENON1T

LZ

CRESST-II

CDMSlite

CDEX-1

pMSSM11 w/ LHC13 : best fit, 1σ, 2σ, 3σpMSSM11 w/o LHC13 : best fit, 1σ, 2σ, 3σ

µ > 0, Ωχ0

1

= ΩCDM

mAMSB EPJC77(2017)4-268

E.Bagnaschi, MB, K.Sakurai, et al

Page 11: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

DM from Higgs decays

๏ Powerful search channel if mDM < mH/2

• H(125) only scalar we know, a portal to DM?

๏ Gluon fusion and VH

• Tag with ISR jet or a boson V(hh) or Z()

• Same final state as monoX searches

๏ Vector-boson fusion (VBF)

• Tag using forward jets (large ∆η)

• Low backgrounds (S/B ~ 0.5)

• Most sensitive signature

‣ 13TeV result from CMS BR < 28%(21% exp)

• Z(νν), W(ν) bkgs from control regions

• Shape fit to maximise sensitivity

‣ 8TeV result from ATLAS BR < 28%(31% exp)

• Still competitive, update soon!

!11Combined VBF-tag Z(ll)H-tag V(qq')H-tag ggH-tag

SM

σ inv.)

/→

x B

(H

σ95%

CL u

pper

limit o

n

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Observed

Median expected

68% expected

95% expected

(13 TeV)-1

35.9 fb

CMS Preliminary

Combined limit: 0.24 (0.18)

H(125)

χ

χ

H(125) χ

χ

W/Z∗

H

χ

χ

W/ZggF

VBF

VH

CMS PAS-HIG-17-023ATLAS 1508.07869

CMS PAS-HIG-17-023

Page 12: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Mediator → SM

!12

Page 13: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

0 500 1000 1500 2000 2500

0.0

0.5

1.0

1.5

2.0

2.5

MZ'B(GeV)

gB

UA2

CDF Run I

CDF 1.1 fb!1

CMS

0.13 fb!1

ATLAS 1 fb!1

CMS

4 fb!1

CMS 5 fb!1

CMS 20 fb!1

ATLAS

13 fb!1

L ∝gB

6Z 0

Bµqγµq

arXiv:1306.2629

Mediator searches

๏ New mediator can decay back to SM

๏ If mmed accessible at LHC could be

key to establish characteristics of

DM interaction

๏ Low sensitivity for light mmed due

to trigger pT thresholds

‣ Recently progress on this front:

1. Boosted dijets (ISR jet tag)

2. Data scouting (trigger-level jets)

!13

SM DM

SM DMmed

SM SM

SM SMmed

Page 14: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USCZ' mass (GeV)

50 100 200 300 1000

q'

couplin

g, g

0.02

0.03

0.04

0.1

0.2

0.3

0.4

1CMS

(13 TeV)-135.9 fb

95% CL upper limits

UA2 [13]

CDF Run 1 [18]

CDF Run 2 [19]

[24]-1ATLAS 8 TeV, 20.3 fb

[34]-1CMS 8 TeV, 18.8 fb

[35]-1CMS 13 TeV, 12.9 fb

Z Width (indirect) [71]

ObservedExpected 1 std. deviation±

2 std. deviation±

Mediator searches

Boosted dijets

๏ Require an ISR jet or γ to satisfy trigger threshold

๏ Boosted collimated dijet reconstructed as large-R jet

• Use jet substructure to separate

from single-jet background

๏ Example: CMS JHEP 01(2018)097

• Narrow ISR jet pT > 500 GeV

• Probing m(Z’) down to 50 GeV

• Background from single-jet control regions

(substructure variable uncorrelated from mass)

๏ Example: ATLAS arXiv:1801.08769

• Extending down to m(Z’) = 100 GeV

!14

Events

/ 5

GeV

0

5000

10000

15000

20000

25000Data 3)×W(qq)+jets (

Total SM pred. 3)×Z(qq)+jets (

Multijet pred. 3)×(qq)+jets (tt/t

=135 GeVZ'

=0.17, mq'

Z'(qq), g

(13 TeV)-1

35.9 fb

CMS

: 500-600 GeVT

p

(GeV)SDm50 100 150

Data

/Pre

dic

tion

0.9

1

1.1

JHEP 01(2018)097

JHEP 01(2018)097

Page 15: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

Mediator searches

Data scouting

๏ Reduce trigger rates at “low" mass

• Online jet reconstruction

• Compact event format

๏ Example: ATLAS arXiv:1804.03496

• Construct jets in HLT from Calorimeter

• Only jets pi and quality to disk (0.5%)

• ET > 100 GeV (29/fb), ET > 75 GeV (3.6/fb)

• Searching down to m(Z’) = 450 GeV

๏ Example: CMS PAS-EXO-16-056

• Calorimeter scouting m > 0.5 TeV:

• Particle-Flow scouting m > 1.25 TeV:

!15 [GeV]Z’

m

400 600 800 1000 1200 1400 1600 1800 2000

qg

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

|y*| < 0.3 |y*| < 0.6

1− 3.6 fb 1− 29.3 fb

ATLAS

= 13 TeVs

95% CL upper limits

TLA Observed

)σ 1-2±TLA Expected (

Dijet Observed

Eve

nts

/ B

in

410

510

610

710

810

2−

02

[GeV]jjm500 600 700 800 9001000 2000

2−

02

Sig

nific

an

ce

ATLAS

, |y*| < 0.3-1Data, 3.6 fbBackground fitBumpHunter interval

x 500σZ’, = 0.1

q = 550 GeV, gZ’m

, |y*| < 0.6-1Data, 29.3 fbBackground fitBumpHunter interval

x 500σZ’, = 0.1

q = 750 GeV, gZ’m

-value = 0.6pBH

-value = 0.42p 2χ

-value = 0.44pBH

-value = 0.13p 2χ

arXiv:1804.03496

arXiv:1804.03496

Page 16: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC.....

.....

.....

......

.....

.....

.....

......

.....

.....

.....

......

.....

.....

.....

......

.....

......

.....

.....

.

50 100 200 300 1000 2000

[GeV]Z'M

1−10

1

qg

'

5% = Z'M / Z'Γ

10% = Z'M / Z'Γ

30% = Z'M / Z'Γ

50% = Z'M / Z'Γ

100% = Z'M / Z'Γ

qq→Z'

95% CL exclusions

~100% < Z'M / Z'Γ[ATLAS-EXOT-2017-01]

ATLAS Boosted Dijet, 13 TeV

[EXO-16-046]

, 13 TeVχCMS Dijet

[ATLAS-EXOT-2016-21]

ATLAS Dijet, 13 TeV

~10% < Z'M / Z'Γ[ATLAS-CONF-2016-030]

ATLAS TLA, 13 TeV

[EXO-16-056]

CMS Dijet, 13 TeV

[ATLAS-CONF-2016-070]

, 13 TeVγATLAS Dijet+ISR

[EXO-14-005]

CMS Dijet, 8 TeV

[ATLAS-CONF-2016-070]

ATLAS Dijet+ISR j, 13 TeV

[EXO-16-057]

CMS Dijet b tagged, 8 TeV[Nucl. Phys. B 400, 3 (1993)]UA2

[EXO-17-001]

CMS Boosted Dijet, 13 TeV[Phys. Rev. D 55, 5263 (1997)]CDF Run1

[Phys. Rev. D 79, 112002 (2009)]CDF Run2

[arXiv:1404.3947]

)Z'

/MZ'

ΓZ width (all

CMS Preliminary

Limits on the universal coupling between a leptophobic boson and quarks [EXO- 6- ] from various dijet analyses from CMS,ATLAS, CDF, and UA . The limits are shown in solid lines, with the excluded area above the lines. The grey dashed lines show thevalues at fixed values of . Most of the analyses, with the exception of Dijet , assume that the intrinsic width is negligiblecompared to the experimental resolution and hence are valid for . The Dijet analysis is valid for

. Also shown is an indirect constraint on from the boson width, which is valid for all values of .

|

boosted dijet

b-tagged

8 TeV

Dijet X

Dijet

Dijet ATLAS

Dijet 8 TeV

boosted dijet

(ATLAS)

UA2

Summary of dijet searches

•Searched also Z’→

‣CMS PAS-EXO-16-031

‣ATLAS arXiv:1707.02424

!16

[PRL 117,031802(2016)]

[JHEP 1801(2018)097]

[arXiv:1802.06149]

[arXiv:1803.08030]

CMS TLA jets

ATLAS

ATLAS TLA, 13 TeV

[arXiv:1804.03496]

Page 17: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

Mediator Mass [TeV]

0 0.5 1 1.5 2 2.5 3

DM

Mass [T

eV

]

0.2

0.4

0.6

0.8

1

1.2DM Simplified Model Exclusions Preliminary July 2017ATLAS

= 1DM

= 0, gl

= 0.25, gq

gAxial-vector mediator, Dirac DM

All limits at 95% CL

Pert

urb

ativ

e U

nita

rity

Dije

t

arXiv:1703.09127 [hep-ex]

-1 = 13 TeV, 37.0 fbs

Dijet

Dije

t 8 T

eV

Phys. Rev. D. 91 052007 (2015)

-1 = 8 TeV, 20.3 fbs

Dijet 8 TeVD

ijet T

LA

ATLAS-CONF-2016-030

-1 = 13 TeV, 3.4 fbs

Dijet TLA

Dije

t +

IS

R

ATLAS-CONF-2016-070

-1 = 13 TeV, 15.5 fbs

Dijet + ISR

γ+missTE

Eur. Phys. J. C 77 (2017) 393

-1 = 13 TeV, 36.1 fbs

γ+missTE

+jetmissTE

ATLAS-CONF-2017-060

-1 = 13 TeV, 36.1 fbs

+jetmissTE

+ZmissTE

ATLAS-CONF-2017-040

-1 = 13 TeV, 36.1 fbs

+ZmissTE

DM

Mas

s =

Med

iato

r Mas

s

×2

= 0

.12

2hcΩ

Therm

al R

elic

Mono-X vs mediator searches

!17

gq = 0.25, g = 0 arXiv:1708.09674

Page 18: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

Mono-X vs mediator searches

!18

gq = 0.1, g = 0.01

Francesco Lo Sterzo Mediator Mass [TeV]

0 0.5 1 1.5 2 2.5 3

DM

Ma

ss [

Te

V]

0.2

0.4

0.6

0.8

1

1.2DM Simplified Model Exclusions Preliminary July 2017ATLAS

= 1DM

= 0.01, gl

= 0.1, gq

gVector mediator, Dirac DM

All limits at 95% CL

Dije

tDijet

Phys. Rev. D. 91 052007 (2015)

-1 = 8 TeV, 20.3 fbsDijet 8 TeV

arXiv:1703.09127 [hep-ex]

-1 = 13 TeV, 37.0 fbsDijet

ATLAS-CONF-2016-030

-1 = 13 TeV, 3.4 fbsDijet TLA

ATLAS-CONF-2016-070

-1 = 13 TeV, 15.5 fbsDijet + ISR

+XmissTE

+XmissTE

Eur. Phys. J. C 77 (2017) 393

-1 = 13 TeV, 36.1 fbs γ+

miss

TE

ATLAS-CONF-2017-060

-1 = 13 TeV, 36.1 fbs+jet

miss

TE

Dile

pto

n

CERN-EP-2017-119

-1 = 13 TeV, 36.1 fbs

Dilepton

DM

Mas

s =

Med

iato

r Mas

s

×2

= 0

.12

2hcΩ

Therm

al R

elic

arXiv:1708.09674

Page 19: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Lighter mediators → SM

!19

Page 20: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

a

γ

γ

Dark Sectors at the LHC

๏ Address SM problems with light very-

weakly interacting states → Dark Sectors

‣ Can get also DM candidate (e.g. freeze-in)

๏ Dark sector portals:

• Scalar portal (φ)

• Vector portal (A’)

• Neutrino portal (N)

• Axion portal (a)

๏ Search at (low-energy) intensity frontier

• LHC can exploit huge cross-sections

• Main challenge: triggering

!20

portals

Recent review: 1608.08632

φ

h f

f

f

fA0

γ/Z

N ναsin θαN ν

Page 21: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

The LHCb potential

๏ Designed to exploit the LHC

intensity frontier to do B physics

๏ Only LHC detector fully

instrumented in forward region

๏ ~10x lower luminosity (low pile-up)

๏ Excellent vertex and mass resolution

๏ Capable of very soft triggers:

• At hardware level (L0):

‣Muons with pT > 1.8 GeV

‣Calo deposits with ET > 3 GeV

• At Software level (HLT):

‣Triggers on detached vertices

!21

Int.J.Mod.Phys. A 30, 1530022 (2015)

LHCb

MS

Cherenkov

drift tube

pixel silicon strip ECAL

HCAL muon

CMS

LHCb 2<η<5

๏ “Trigger-less” upgrade (2021)• Read-out detector in real time• Can trigger on detached vertices,

precise particle ID and more

TDR: [LHCB-TDR-016]

Page 22: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

๏ Look for new hidden-sector bosons

in b→s penguin transitions

๏ World record samples of B→K(*)µµ

• search for narrow µµ peak

๏ Allow detached µµ (within VELO)

• small SM mixing can give lifetime

๏ Constrain on light scalars

• mixing with SM Higgs

• world-best limits below 2mτ

• Complementary to Ship

!22

Dark Bosons from b→sPhys Rev Lett 115 161802 (2015)

Phys Rev D 95, 071101(R) (2017)

b

d

Vtb Vts

s

d

µ−

µ+

t

W+

χ

0 K

d/u d/u

B0(+)

<latexit sha1_base64="ObjqLKJgn/bRMAdpbge2oPrjOcU=">AAAB7nicbZDLSgMxFIbP1Futt6pLN8EiVIQyUwR1ZdGNywqOLbRjyaSZNjSTGZOMUIa+hBspKrr0FXwNd76N6WWhrT8EPv7/HHLO8WPOlLbtbyuzsLi0vJJdza2tb2xu5bd3blWUSEJdEvFI1n2sKGeCupppTuuxpDj0Oa35vctRXnugUrFI3Oh+TL0QdwQLGMHaWPWLu9QuHh0OWvmCXbLHQvPgTKFw/jkcvgNAtZX/arYjkoRUaMKxUg3HjrWXYqkZ4XSQayaKxpj0cIc2DAocUuWl43kH6MA4bRRE0jyh0dj93ZHiUKl+6JvKEOuums1G5n9ZI9HBqZcyESeaCjL5KEg40hEaLY/aTFKied8AJpKZWRHpYomJNifKmSM4syvPg1sunZWca7tQOYaJsrAH+1AEB06gAldQBRcIcHiEZ3ix7q0n69V6m5RmrGnPLvyR9fED0w2Rmg==</latexit><latexit sha1_base64="y6bscvGIwBEFJETQrCex8ZNBxw8=">AAAB7nicbZDLSsNAFIZP6q3WW9Wlm8EiVISSiKCuLLpxWcHYQhvLZDpph04mcWYilNCXcCPecOsr+BrufBsnbRfa+sPAx/+fw5xz/JgzpW3728rNzS8sLuWXCyura+sbxc2tGxUlklCXRDySDR8rypmgrmaa00YsKQ59Tut+/yLL6/dUKhaJaz2IqRfirmABI1gbq3F+m9rlg/1hu1iyK/ZIaBacCZTOPp8yPdfaxa9WJyJJSIUmHCvVdOxYeymWmhFOh4VWomiMSR93adOgwCFVXjqad4j2jNNBQSTNExqN3N8dKQ6VGoS+qQyx7qnpLDP/y5qJDk68lIk40VSQ8UdBwpGOULY86jBJieYDA5hIZmZFpIclJtqcqGCO4EyvPAvuYeW04lzZpeoRjJWHHdiFMjhwDFW4hBq4QIDDA7zAq3VnPVpv1vu4NGdNerbhj6yPHy6Uk18=</latexit><latexit sha1_base64="y6bscvGIwBEFJETQrCex8ZNBxw8=">AAAB7nicbZDLSsNAFIZP6q3WW9Wlm8EiVISSiKCuLLpxWcHYQhvLZDpph04mcWYilNCXcCPecOsr+BrufBsnbRfa+sPAx/+fw5xz/JgzpW3728rNzS8sLuWXCyura+sbxc2tGxUlklCXRDySDR8rypmgrmaa00YsKQ59Tut+/yLL6/dUKhaJaz2IqRfirmABI1gbq3F+m9rlg/1hu1iyK/ZIaBacCZTOPp8yPdfaxa9WJyJJSIUmHCvVdOxYeymWmhFOh4VWomiMSR93adOgwCFVXjqad4j2jNNBQSTNExqN3N8dKQ6VGoS+qQyx7qnpLDP/y5qJDk68lIk40VSQ8UdBwpGOULY86jBJieYDA5hIZmZFpIclJtqcqGCO4EyvPAvuYeW04lzZpeoRjJWHHdiFMjhwDFW4hBq4QIDDA7zAq3VnPVpv1vu4NGdNerbhj6yPHy6Uk18=</latexit><latexit sha1_base64="/85fCUsuSZREU9miVEBUIEYVVYk=">AAAB7nicbVBNSwMxEJ2tX7V+VT16CRahIpRdEdRb0YvHCq4ttGvJptk2NJusSVYoS/+EFw8qXv093vw3pu0etPXBwOO9GWbmhQln2rjut1NYWl5ZXSuulzY2t7Z3yrt791qmilCfSC5VK8Saciaob5jhtJUoiuOQ02Y4vJ74zSeqNJPizowSGsS4L1jECDZWal09ZG715HjcLVfcmjsFWiReTiqQo9Etf3V6kqQxFYZwrHXbcxMTZFgZRjgdlzqppgkmQ9ynbUsFjqkOsum9Y3RklR6KpLIlDJqqvycyHGs9ikPbGWMz0PPeRPzPa6cmuggyJpLUUEFmi6KUIyPR5HnUY4oSw0eWYKKYvRWRAVaYGBtRyYbgzb+8SPzT2mXNu3Ur9bM8jSIcwCFUwYNzqMMNNMAHAhye4RXenEfnxXl3PmatBSef2Yc/cD5/ABFIjtA=</latexit>

K∗(+)

<latexit sha1_base64="MKdkWGTkK1kC+oeEee1cXeXP934=">AAAB8XicbZDLSsNAFIZP6q3WW9Wlm2ARKkJJRFBXFtwIbioYW0hjmUwn7dDJhZkToYQ+hou60OLWJ/A13Pk2Ti8Lbf1h4OP/z2HOOX4iuELL+jZyS8srq2v59cLG5tb2TnF370HFqaTMobGIZcMnigkeMQc5CtZIJCOhL1jd712P8/oTk4rH0T32E+aFpBPxgFOC2nJvH7MmUVg+OR60iiWrYk1kLoI9g9LV53A4AoBaq/jVbMc0DVmEVBClXNtK0MuIRE4FGxSaqWIJoT3SYa7GiIRMedlk5IF5pJ22GcRSvwjNifu7IyOhUv3Q15Uhwa6az8bmf5mbYnDhZTxKUmQRnX4UpMLE2Bzvb7a5ZBRFXwOhkutZTdolklDUVyroI9jzKy+Cc1q5rNh3Vql6BlPl4QAOoQw2nEMVbqAGDlCI4Rle4c1A48UYGe/T0pwx69mHPzI+fgCNzpM1</latexit><latexit sha1_base64="W9PAAnX3ohJW/9H3t8deChSzF78=">AAAB8XicbZDNSsNAFIUn/tb6V3XpZrAIFaEkIqgrC24ENxWMLaSxTKaTduhkEmZuhBL6GC7sQsWtT+BruPNtnLRdaOuBgY9z7mXuvUEiuAbb/rYWFpeWV1YLa8X1jc2t7dLO7r2OU0WZS2MRq2ZANBNcMhc4CNZMFCNRIFgj6F/leeORKc1jeQeDhPkR6UoeckrAWN7NQ9YiGirHR8N2qWxX7bHwPDhTKF9+Puca1dulr1YnpmnEJFBBtPYcOwE/Iwo4FWxYbKWaJYT2SZd5BiWJmPaz8chDfGicDg5jZZ4EPHZ/d2Qk0noQBaYyItDTs1lu/pd5KYTnfsZlkgKTdPJRmAoMMc73xx2uGAUxMECo4mZWTHtEEQrmSkVzBGd25XlwT6oXVefWLtdO0UQFtI8OUAU56AzV0DWqIxdRFKMn9IJeLbBG1pv1PildsKY9e+iPrI8f6UaU+g==</latexit><latexit sha1_base64="W9PAAnX3ohJW/9H3t8deChSzF78=">AAAB8XicbZDNSsNAFIUn/tb6V3XpZrAIFaEkIqgrC24ENxWMLaSxTKaTduhkEmZuhBL6GC7sQsWtT+BruPNtnLRdaOuBgY9z7mXuvUEiuAbb/rYWFpeWV1YLa8X1jc2t7dLO7r2OU0WZS2MRq2ZANBNcMhc4CNZMFCNRIFgj6F/leeORKc1jeQeDhPkR6UoeckrAWN7NQ9YiGirHR8N2qWxX7bHwPDhTKF9+Puca1dulr1YnpmnEJFBBtPYcOwE/Iwo4FWxYbKWaJYT2SZd5BiWJmPaz8chDfGicDg5jZZ4EPHZ/d2Qk0noQBaYyItDTs1lu/pd5KYTnfsZlkgKTdPJRmAoMMc73xx2uGAUxMECo4mZWTHtEEQrmSkVzBGd25XlwT6oXVefWLtdO0UQFtI8OUAU56AzV0DWqIxdRFKMn9IJeLbBG1pv1PildsKY9e+iPrI8f6UaU+g==</latexit><latexit sha1_base64="ezGy9HAVxpiq5MtlN30VZ5WNhic=">AAAB8XicbVBNS8NAEN34WetX1aOXxSJUhJKIoN4KXgQvFYwtpLFstpt26WY37E6EEvozvHhQ8eq/8ea/cdvmoK0PBh7vzTAzL0oFN+C6387S8srq2nppo7y5tb2zW9nbfzAq05T5VAml2xExTHDJfOAgWDvVjCSRYK1oeD3xW09MG67kPYxSFiakL3nMKQErBbePeYcYqJ2ejLuVqlt3p8CLxCtIFRVoditfnZ6iWcIkUEGMCTw3hTAnGjgVbFzuZIalhA5JnwWWSpIwE+bTk8f42Co9HCttSwKeqr8ncpIYM0oi25kQGJh5byL+5wUZxJdhzmWaAZN0tijOBAaFJ//jHteMghhZQqjm9lZMB0QTCjalsg3Bm395kfhn9au6d+dWG+dFGiV0iI5QDXnoAjXQDWoiH1Gk0DN6RW8OOC/Ou/Mxa11yipkD9AfO5w/L+pBr</latexit>

0.5 1.0 2.0 4.0

mϕ (GeV)

10−12

10−10

10−8

10−6

sin2θ

CODEX-bSHiP

MATHUSLA

CHARM

LHCb, 3 fb−1

LHCb, 300 fb−1

Plot from arXiv:1708.09395

B.Batell, M.Pospelov, A.Ritz, PRD 83, 054005 (2011)F.Bezrukov, D.Gorbunov, JHEP05(2010)010, JHEP07(2013)140

as τ ∝ 1=θ2.from Ref. [2].

as BðBþ→ K

þχÞ ∝ θ2,

fraction into muons is directly

Page 23: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

310

410

510

210

310

410

510

610

710

m(µµ) [MeV ]

Can

didates/σ[m

(µµ)]/2

LHCb√

s = 13TeVµ+µ−

µ±µ±

prompt-like sample

pT(µ) > 1GeV, p(µ) > 20GeV

Dark Photons at LHCb

!23

๏ Can search for Dark Photons (A') in µµ

‣ Can be very light, produced as γ*

‣ Large fraction in forward region, very soft pT

๏ Data scouting technique in LHCb Run 2:

‣ Online reconstruction and tight µ-ID

‣ Only interesting part of the event to disk → no pre-scale down to threshold 2 mµ

γ*/A'

γ*/A'

PRL 120 (2018) no.6, 061801

Prompt-like dimuon

sample with no pre-scale

down to threshold!

Page 24: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC !24

2−10

1−10 1 10

12−10

11−10

10−10

9−10

8−10

7−10

6−10

5−10

4−10

m(A0) [ GeV ]

ε2

LHCb

LHCb

Previous Experiments

90% CL exclusion regions on [m(A0), ε2]

PRL 120 (2018) no.6, 061801

Dark Photons at LHCb

Already competitive below 1 GeV

LHCb

Previous Experiments

First limits above 10 GeV

Page 25: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

Dark Photons at LHCb

๏ Proof of concept for soft µ searches at LHCb

• Multiple dimuons from dark cascade

• Heavy neutral leptons in displaced πµ

!25

2−10

1−10 1 10

12−10

11−10

10−10

9−10

8−10

7−10

6−10

5−10

4−10

m(A0) [ GeV ]

ε2

LHCb

LHCb

Previous Experiments

90% CL exclusion regions on [m(A0), ε2]

First limits above 10 GeV

PRL 120 (2018) no.6, 061801

Already competitive below 1 GeV

First non-beam-dump long lived A’ sensitivity LHCb

Previous Experiments

Other analysis filled the gap

A.Pierce et al. arXiv:1708.05389

Can recast to light scalar searches

Haisch et al. 1802.021566 8 10 12 14

m(φ) [GeV]

0

5

10

15

20

σ(gg→

φ)×B(

φ→

µµ)[pb]

Υ(1S)

Υ(2S)

Υ(3S)

LHCb√s = 8TeV

95% CL upper limits

Median expected

68% expected

95% expected

Observed

CMS expected

CMS observed

Today on the arXiv! 1805.09820

Page 26: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

LHCb Upgrade Dark Photon Reach

!26

-

/ /

/

-

-

/ /

-

-

-

-

-

-

-

-

[ ]

α

w-mass BSM searches, including dark photons (predictions assume 15/fb).

Inclusive A’ →μμ @ LHCb

Ilten, Soreq, Thaler, MW, Xue

[1603.08926]

Radiative Charm Decays @ LHCb

Ilten, Thaler, MW, Xue

[1509.06765]

See talk by W.Xue

on Tu evening

Inclusive A’→µµ at LHCbIlten, Soreq, Thaler, Williams, Xue [1603.08926]

Radiative D Decays at LHCbIlten, Thaler, Williams, Xue [1509.06765]

10

10

ε2

10

m(A0) [ GeV ]

Run 3 reach for dark photons

๏Using D*0 → D0A’(ee)

๏With upgraded trigger

expect 300⨉109 D*0 → D0γ

per fb-1 (15/fb in Run 3)

Page 27: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

Conclusions

๏ Investigating the origin of Dark Matter is one of the main goals of the LHC program

๏ Different and often complementary searches:

• Mediator → DM (holistic)

‣ Mono-X searches

‣ Higgs to invisible searches

• Mediator → SM (peak search)

‣ Searching structure in dijet (dilepton) spectrum

‣ Data scouting and boosted jets to reach lower masses

• Lighter mediators → SM (dark sectors)

‣ LHCb recently demonstrated to be very sensitive

!27

Page 28: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

BACKUP

!28

Page 29: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

Theory uncertainties for mono-X

!29

Uncertainty source Process (magnitude) Correlation

Fact. & renorm. scales (QCD)Z → νν/W → `ν (0.1 – 0.5%)Z → νν/γ+jets (0.2 – 0.5%)

Correlated between processes;and in pT

pT shape dependence (QCD)Z → νν/W → `ν (0.4 – 0.1%)Z → νν/γ+jets (0.1 – 0.2%)

Correlated between processes;and in pT

Process dependence (QCD)Z → νν/W → `ν (0.4 – 1.5%)Z → νν/γ+jets (1.5 – 3.0%)

Correlated between processes;and in pT

Effects of unknown Sudakov logs (EW)Z → νν/W → `ν (0 – 0.5%)Z → νν/γ+jets (0.1 – 1.5%)

Correlated between processes;and in pT

Missing NNLO effects (EW)Z → νν (0.2 – 3.0%)W → `ν (0.4 – 4.5%)γ+jets (0.1 – 1.0%)

Uncorrelated between processes;correlated in pT

Effects of NLL Sudakov approx. (EW)Z → νν (0.2 – 4.0%)W → `ν (0 – 1.0%)γ+jets (0.1 – 3.0%)

Uncorrelated between processes;correlated in pT

Unfactorized mixed QCD-EW correctionsZ → νν/W → `ν (0.15 – 0.3%)Z → νν/γ+jets (<0.1%)

Correlated between processes;and in pT

PDFZ → νν/W → `ν (0 – 0.3%)Z → νν/γ+jets (0 – 0.6%)

Correlated between processes;and in pT

CMS mono-X arXiv:1712.02345

Page 30: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

HNL in B→π+µ−µ−

๏ Lepton number violating B−→π+µ−µ− can

proceed via on-shell Majorana neutrinos

๏ Look for B mass peak, then extract limit

as a function of mN

๏ Limit set on N(πµ) lifetimes up to 1000 ps

๏ Constraints on mixing angle Vµ4

• Recently revisited

๏ Also searched in charm D+→π−µ+µ+

!30

Neutrino mass [MeV]

1000 2000 3000 4000 5000

Upper

lim

it

-910

-810

-710

-610 1 ps

10 ps

100 ps

200 ps

500 ps

1000 ps

LHCb

W

+

+

u N

W

b

B

Can be displaced

Phys Rev Lett 112 131802 (2014)

B Shuve, ME Peskin, PRD94 (2016) no.11, 113007

PLB 724 (2013) 203-212B → ×

B(D+→ π−µ+µ+) < 2.2 (2.5)× 10−8,

B(D+s→ π−µ+µ+) < 1.2 (1.4)× 10−7.

Page 31: (DM) (SM) (mediator)...Martino Borsato - USC DM signals!3 SM DM SM DM Direct detection Detect interactions of the DM wind XENON, Panda, Lux, DarkSide, … Collider search • Mediator

Martino Borsato - USC

Future HNL at LHCb

๏ Inclusive search

๏ Can also search higher masses using

on-shell W−→jet µ−µ−

!31

c/u<latexit sha1_base64="74+gvOBNZY+T/A4RJFsbaUsh+FI=">AAAB6XicdVBNS8NAEJ34WetX1aOXpUUQhJikhdZb0YvHisYW2lA22027dPPB7kYooT/BiwcVT4L/yJv/xm1TQUUfDDzem2Fmnp9wJpVlfRhLyyura+uFjeLm1vbObmlv/1bGqSDUJTGPRcfHknIWUVcxxWknERSHPqdtf3wx89t3VEgWRzdqklAvxMOIBYxgpaVrcpr2SxXLdGpOo1pDOXHqC1K1kW1ac1Sa5d7JKwC0+qX33iAmaUgjRTiWsmtbifIyLBQjnE6LvVTSBJMxHtKuphEOqfSy+alTdKSVAQpioStSaK5+n8hwKOUk9HVniNVI/vZm4l9eN1VBw8tYlKSKRiRfFKQcqRjN/kYDJihRfKIJJoLpWxEZYYGJ0ukUdQhfn6L/ieuYZ6Z9pcM4hxwFOIQyHIMNdWjCJbTABQJDuIdHeDK48WA8Gy9565KxmDmAHzDePgHpfY88</latexit><latexit sha1_base64="UmCQHWR8Z1L0YMnsYGxLmxMZlCo=">AAAB6XicdVBNS8NAEN3Ur1q/qh69LC2CIMQkLbTeil48VjS20Iay2W7apZtN2N0IIfQneBFR8eo/8tZ/47apoKIPBh7vzTAzz48ZlcqyZkZhZXVtfaO4Wdra3tndK+8f3MkoEZi4OGKR6PpIEkY5cRVVjHRjQVDoM9LxJ5dzv3NPhKQRv1VpTLwQjTgNKEZKSzf4LBmUq5bp1J1mrQ5z4jSWpGZD27QWqLYq/dOnWSttD8of/WGEk5BwhRmSsmdbsfIyJBTFjExL/USSGOEJGpGephyFRHrZ4tQpPNbKEAaR0MUVXKjfJzIUSpmGvu4MkRrL395c/MvrJSpoehnlcaIIx/miIGFQRXD+NxxSQbBiqSYIC6pvhXiMBMJKp1PSIXx9Cv8nrmOem/a1DuMC5CiCI1ABJ8AGDdACV6ANXIDBCDyAZ/BiMOPReDXe8taCsZw5BD9gvH8C8WGQwg==</latexit><latexit sha1_base64="UmCQHWR8Z1L0YMnsYGxLmxMZlCo=">AAAB6XicdVBNS8NAEN3Ur1q/qh69LC2CIMQkLbTeil48VjS20Iay2W7apZtN2N0IIfQneBFR8eo/8tZ/47apoKIPBh7vzTAzz48ZlcqyZkZhZXVtfaO4Wdra3tndK+8f3MkoEZi4OGKR6PpIEkY5cRVVjHRjQVDoM9LxJ5dzv3NPhKQRv1VpTLwQjTgNKEZKSzf4LBmUq5bp1J1mrQ5z4jSWpGZD27QWqLYq/dOnWSttD8of/WGEk5BwhRmSsmdbsfIyJBTFjExL/USSGOEJGpGephyFRHrZ4tQpPNbKEAaR0MUVXKjfJzIUSpmGvu4MkRrL395c/MvrJSpoehnlcaIIx/miIGFQRXD+NxxSQbBiqSYIC6pvhXiMBMJKp1PSIXx9Cv8nrmOem/a1DuMC5CiCI1ABJ8AGDdACV6ANXIDBCDyAZ/BiMOPReDXe8taCsZw5BD9gvH8C8WGQwg==</latexit><latexit sha1_base64="FES1SF9sUkMcGtPGBklCv7Z5x3g=">AAAB6XicdVBNS8NAEJ3Ur1q/qh69LBbBU0zSQuut6MVjRWMLbSib7aZdutmE3Y1QSn+CFw8qXv1H3vw3btsIKvpg4PHeDDPzwpQzpR3nwyqsrK6tbxQ3S1vbO7t75f2DO5VkklCfJDyRnRArypmgvmaa004qKY5DTtvh+HLut++pVCwRt3qS0iDGQ8EiRrA20g05y/rlimN7Na9RraEl8eo5qbrItZ0FKpCj1S+/9wYJyWIqNOFYqa7rpDqYYqkZ4XRW6mWKppiM8ZB2DRU4piqYLk6doROjDFCUSFNCo4X6fWKKY6UmcWg6Y6xH6rc3F//yupmOGsGUiTTTVJDloijjSCdo/jcaMEmJ5hNDMJHM3IrICEtMtEmnZEL4+hT9T3zPPrfda6fSvMjTKMIRHMMpuFCHJlxBC3wgMIQHeIJni1uP1ov1umwtWPnMIfyA9fYJ2IeNsw==</latexit>

b<latexit sha1_base64="QSyx+HS8ENDAsXLg8oIOGTA1Eko=">AAAB53icdZBLSwMxFIXv1FcdX1WXboJFcDXMTAutC7HoxmUL1hbaoWTSTBubeZBkhDIU3LtxoeLWX+Penf/G9CGo6IHAxzn3knuvn3AmlW1/GLml5ZXVtfy6ubG5tb1T2N27lnEqCG2SmMei7WNJOYtoUzHFaTsRFIc+py1/dDHNW7dUSBZHV2qcUC/Eg4gFjGClrYbfKxRtyy271VIZzcGtLKDkIMeyZyqevZmndwBQ7xXeu/2YpCGNFOFYyo5jJ8rLsFCMcDoxu6mkCSYjPKAdjREOqfSy2aATdKSdPgpioV+k0Mz93pHhUMpx6OvKEKuh/J1Nzb+yTqqCqpexKEkVjcj8oyDlSMVoujXqM0GJ4mMNmAimZ0VkiAUmSt/G1Ef42hT9D03XOrGchl2sncNceTiAQzgGBypQg0uoQxMIULiHR3gybowH49l4mZfmjEXPPvyQ8foJAcaOxw==</latexit><latexit sha1_base64="hXIwlQmACxAnj0epNeKDWwUTeB0=">AAAB53icdZDNSsNAFIUn9a/Gv6pLN4NFcBWStNC6EItuXLZgbKENZTKdtGMnkzAzEUroE7hxoeJWfBj3bsS3cdooqOiBgY9z7mXuvUHCqFS2/W4UFhaXlleKq+ba+sbmVml751LGqcDEwzGLRSdAkjDKiaeoYqSTCIKigJF2MD6b5e1rIiSN+YWaJMSP0JDTkGKktNUK+qWybblVt16pwhzc2idUHOhY9lzlkxfzOHl+M5v90mtvEOM0IlxhhqTsOnai/AwJRTEjU7OXSpIgPEZD0tXIUUSkn80HncID7QxgGAv9uIJz93tHhiIpJ1GgKyOkRvJ3NjP/yrqpCut+RnmSKsJx/lGYMqhiONsaDqggWLGJBoQF1bNCPEICYaVvY+ojfG0K/wfPtY4sp2WXG6cgVxHsgX1wCBxQAw1wDprAAxgQcAPuwL1xZdwaD8ZjXlowPnt2wQ8ZTx/x0pA7</latexit><latexit sha1_base64="hXIwlQmACxAnj0epNeKDWwUTeB0=">AAAB53icdZDNSsNAFIUn9a/Gv6pLN4NFcBWStNC6EItuXLZgbKENZTKdtGMnkzAzEUroE7hxoeJWfBj3bsS3cdooqOiBgY9z7mXuvUHCqFS2/W4UFhaXlleKq+ba+sbmVml751LGqcDEwzGLRSdAkjDKiaeoYqSTCIKigJF2MD6b5e1rIiSN+YWaJMSP0JDTkGKktNUK+qWybblVt16pwhzc2idUHOhY9lzlkxfzOHl+M5v90mtvEOM0IlxhhqTsOnai/AwJRTEjU7OXSpIgPEZD0tXIUUSkn80HncID7QxgGAv9uIJz93tHhiIpJ1GgKyOkRvJ3NjP/yrqpCut+RnmSKsJx/lGYMqhiONsaDqggWLGJBoQF1bNCPEICYaVvY+ojfG0K/wfPtY4sp2WXG6cgVxHsgX1wCBxQAw1wDprAAxgQcAPuwL1xZdwaD8ZjXlowPnt2wQ8ZTx/x0pA7</latexit><latexit sha1_base64="Yf/uA7VcYpGSAYFYm1exYqWNcPE=">AAAB53icdVBNS8NAEN3Ur1q/qh69LBbBU0jSQuut6MVjC9YW2lA220m7drMJuxuhhP4CLx5UvPqXvPlv3LYRVPTBwOO9GWbmBQlnSjvOh1VYW9/Y3Cpul3Z29/YPyodHtypOJYUOjXksewFRwJmAjmaaQy+RQKKAQzeYXi387j1IxWJxo2cJ+BEZCxYySrSR2sGwXHFsr+Y1qjW8Il49J1UXu7azRAXlaA3L74NRTNMIhKacKNV3nUT7GZGaUQ7z0iBVkBA6JWPoGypIBMrPlofO8ZlRRjiMpSmh8VL9PpGRSKlZFJjOiOiJ+u0txL+8fqrDhp8xkaQaBF0tClOOdYwXX+MRk0A1nxlCqGTmVkwnRBKqTTYlE8LXp/h/0vHsC9ttO5XmZZ5GEZ2gU3SOXFRHTXSNWqiDKAL0gJ7Qs3VnPVov1uuqtWDlM8foB6y3T5RMjPo=</latexit>

N2<latexit sha1_base64="zFpMC0YgcmGD5gIEbU4ALIW6DqQ=">AAAB6XicdVBNS8NAEJ3Ur1q/qoIXL4tF8BSStNB6K3rxJC1aW2hD3Ww37dLNB7sboYT+BC8eVLz6j7x58be4bSqo6IOBx3szzMzzYs6ksqx3I7e0vLK6ll8vbGxube8Ud/duZJQIQlsk4pHoeFhSzkLaUkxx2okFxYHHadsbn8/89h0VkkXhtZrE1A3wMGQ+I1hp6eqy7/SLJct0Kk6tXEEZcaoLUraRbVpzlOoHzY9bAGj0i2+9QUSSgIaKcCxl17Zi5aZYKEY4nRZ6iaQxJmM8pF1NQxxQ6abzU6foWCsD5EdCV6jQXP0+keJAykng6c4Aq5H87c3Ev7xuovyam7IwThQNSbbITzhSEZr9jQZMUKL4RBNMBNO3IjLCAhOl0ynoEL4+Rf+TlmOemnZTh3EGGfJwCEdwAjZUoQ4X0IAWEBjCPTzCk8GNB+PZeMlac8ZiZh9+wHj9BCjXj3A=</latexit><latexit sha1_base64="5yIK94qaiELvoSmHoC5hazs8Wls=">AAAB6XicdVDLSsNAFJ3UV62vquDGzWARXIUkLbTuSt24khaNLbShTKaTduhkEmYmQgn9BDcuVNy69i/8Andu/BanTQUVPXDhcM693HuPHzMqlWW9G7ml5ZXVtfx6YWNza3unuLt3LaNEYOLiiEWi4yNJGOXEVVQx0okFQaHPSNsfn8389g0Rkkb8Sk1i4oVoyGlAMVJaurzoO/1iyTKdilMrV2BGnOqClG1om9YcpfpB64O+NF6b/eJbbxDhJCRcYYak7NpWrLwUCUUxI9NCL5EkRniMhqSrKUchkV46P3UKj7UygEEkdHEF5+r3iRSFUk5CX3eGSI3kb28m/uV1ExXUvJTyOFGE42xRkDCoIjj7Gw6oIFixiSYIC6pvhXiEBMJKp1PQIXx9Cv8nrmOemnZLh9EAGfLgEByBE2CDKqiDc9AELsBgCG7BPXgwmHFnPBpPWWvOWMzsgx8wnj8BeFyRLA==</latexit><latexit sha1_base64="5yIK94qaiELvoSmHoC5hazs8Wls=">AAAB6XicdVDLSsNAFJ3UV62vquDGzWARXIUkLbTuSt24khaNLbShTKaTduhkEmYmQgn9BDcuVNy69i/8Andu/BanTQUVPXDhcM693HuPHzMqlWW9G7ml5ZXVtfx6YWNza3unuLt3LaNEYOLiiEWi4yNJGOXEVVQx0okFQaHPSNsfn8389g0Rkkb8Sk1i4oVoyGlAMVJaurzoO/1iyTKdilMrV2BGnOqClG1om9YcpfpB64O+NF6b/eJbbxDhJCRcYYak7NpWrLwUCUUxI9NCL5EkRniMhqSrKUchkV46P3UKj7UygEEkdHEF5+r3iRSFUk5CX3eGSI3kb28m/uV1ExXUvJTyOFGE42xRkDCoIjj7Gw6oIFixiSYIC6pvhXiEBMJKp1PQIXx9Cv8nrmOemnZLh9EAGfLgEByBE2CDKqiDc9AELsBgCG7BPXgwmHFnPBpPWWvOWMzsgx8wnj8BeFyRLA==</latexit><latexit sha1_base64="47xBygJwTP031YuHu3KBa/IPs2o=">AAAB6XicdVBNS8NAEJ3Ur1q/qh69LBbBU0jSQuut6MWTVDS20Iay2W7apZtN2N0IpfQnePGg4tV/5M1/47aNoKIPBh7vzTAzL0w5U9pxPqzCyura+kZxs7S1vbO7V94/uFNJJgn1ScIT2QmxopwJ6mumOe2kkuI45LQdji/mfvueSsUScasnKQ1iPBQsYgRrI91c9b1+ueLYXs1rVGtoSbx6Tqoucm1ngQrkaPXL771BQrKYCk04VqrrOqkOplhqRjidlXqZoikmYzykXUMFjqkKpotTZ+jEKAMUJdKU0Gihfp+Y4lipSRyazhjrkfrtzcW/vG6mo0YwZSLNNBVkuSjKONIJmv+NBkxSovnEEEwkM7ciMsISE23SKZkQvj5F/xPfs89s99qpNM/zNIpwBMdwCi7UoQmX0AIfCAzhAZ7g2eLWo/VivS5bC1Y+cwg/YL19ApwVjYs=</latexit>

µ+

<latexit sha1_base64="e4UYffSBDlaINmlONT93YLcqkuY=">AAAB63icdVBNS8NAEJ34WetXtUcvi6UgCCFJC623ghePFYwttLFsttt26WYTdjdCKb159+JBxat/yJs3f4rbpoKKPhh4vDfDzLww4Uxpx3m3VlbX1jc2c1v57Z3dvf3CweG1ilNJqE9iHst2iBXlTFBfM81pO5EURyGnrXB8Pvdbt1QqFosrPUloEOGhYANGsDaS343Sm9NeoeTYXtWrV6ooI15tSSoucm1ngVKjWL77AIBmr/DW7cckjajQhGOlOq6T6GCKpWaE01m+myqaYDLGQ9oxVOCIqmC6OHaGykbpo0EsTQmNFur3iSmOlJpEoemMsB6p395c/MvrpHpQD6ZMJKmmgmSLBilHOkbzz1GfSUo0nxiCiWTmVkRGWGKiTT55E8LXp+h/4nv2me1emjDqkCEHR3AMJ+BCDRpwAU3wgQCDe3iEJ0tYD9az9ZK1rljLmSL8gPX6CcSmkFk=</latexit><latexit sha1_base64="M9qt9YkZazwGO5SXMXFYABHENf0=">AAAB63icdVDLSsNAFJ3UV62vapduBktBEEKSFlp3BTcuKxhbaGOZTCft0MkkzEyEErpz78aFilt/xQ9wpx/gF/gBTpsKKnrgwuGce7n3Hj9mVCrLejVyS8srq2v59cLG5tb2TnF370JGicDExRGLRMdHkjDKiauoYqQTC4JCn5G2Pz6Z+e0rIiSN+LmaxMQL0ZDTgGKktOT2wuTyqF8sW6ZTcxrVGsyIU1+Qqg1t05qj3CxVrj+e399a/eJLbxDhJCRcYYak7NpWrLwUCUUxI9NCL5EkRniMhqSrKUchkV46P3YKK1oZwCASuriCc/X7RIpCKSehrztDpEbytzcT//K6iQoaXkp5nCjCcbYoSBhUEZx9DgdUEKzYRBOEBdW3QjxCAmGl8ynoEL4+hf8T1zGPTftMh9EAGfJgHxyAQ2CDOmiCU9ACLsCAghtwB+4NbtwaD8Zj1pozFjMl8APG0yc8GJLz</latexit><latexit sha1_base64="M9qt9YkZazwGO5SXMXFYABHENf0=">AAAB63icdVDLSsNAFJ3UV62vapduBktBEEKSFlp3BTcuKxhbaGOZTCft0MkkzEyEErpz78aFilt/xQ9wpx/gF/gBTpsKKnrgwuGce7n3Hj9mVCrLejVyS8srq2v59cLG5tb2TnF370JGicDExRGLRMdHkjDKiauoYqQTC4JCn5G2Pz6Z+e0rIiSN+LmaxMQL0ZDTgGKktOT2wuTyqF8sW6ZTcxrVGsyIU1+Qqg1t05qj3CxVrj+e399a/eJLbxDhJCRcYYak7NpWrLwUCUUxI9NCL5EkRniMhqSrKUchkV46P3YKK1oZwCASuriCc/X7RIpCKSehrztDpEbytzcT//K6iQoaXkp5nCjCcbYoSBhUEZx9DgdUEKzYRBOEBdW3QjxCAmGl8ynoEL4+hf8T1zGPTftMh9EAGfJgHxyAQ2CDOmiCU9ACLsCAghtwB+4NbtwaD8Zj1pozFjMl8APG0yc8GJLz</latexit><latexit sha1_base64="qyJgAYJD1pLiUGPLihZx/+flexM=">AAAB63icdVBNS8NAEJ34WetX1aOXxSIIQkjSQuut4MVjBWMLbSyb7aZdutmE3Y1QQn+DFw8qXv1D3vw3btsIKvpg4PHeDDPzwpQzpR3nw1pZXVvf2Cxtlbd3dvf2KweHtyrJJKE+SXgiuyFWlDNBfc00p91UUhyHnHbCyeXc79xTqVgibvQ0pUGMR4JFjGBtJL8fZ3fng0rVsb2616zV0ZJ4jYLUXOTazgJVKNAeVN77w4RkMRWacKxUz3VSHeRYakY4nZX7maIpJhM8oj1DBY6pCvLFsTN0apQhihJpSmi0UL9P5DhWahqHpjPGeqx+e3PxL6+X6agZ5EykmaaCLBdFGUc6QfPP0ZBJSjSfGoKJZOZWRMZYYqJNPmUTwten6H/ie/aF7V471VazSKMEx3ACZ+BCA1pwBW3wgQCDB3iCZ0tYj9aL9bpsXbGKmSP4AevtE0S9jn0=</latexit>

µ+

<latexit sha1_base64="e4UYffSBDlaINmlONT93YLcqkuY=">AAAB63icdVBNS8NAEJ34WetXtUcvi6UgCCFJC623ghePFYwttLFsttt26WYTdjdCKb159+JBxat/yJs3f4rbpoKKPhh4vDfDzLww4Uxpx3m3VlbX1jc2c1v57Z3dvf3CweG1ilNJqE9iHst2iBXlTFBfM81pO5EURyGnrXB8Pvdbt1QqFosrPUloEOGhYANGsDaS343Sm9NeoeTYXtWrV6ooI15tSSoucm1ngVKjWL77AIBmr/DW7cckjajQhGOlOq6T6GCKpWaE01m+myqaYDLGQ9oxVOCIqmC6OHaGykbpo0EsTQmNFur3iSmOlJpEoemMsB6p395c/MvrpHpQD6ZMJKmmgmSLBilHOkbzz1GfSUo0nxiCiWTmVkRGWGKiTT55E8LXp+h/4nv2me1emjDqkCEHR3AMJ+BCDRpwAU3wgQCDe3iEJ0tYD9az9ZK1rljLmSL8gPX6CcSmkFk=</latexit><latexit sha1_base64="M9qt9YkZazwGO5SXMXFYABHENf0=">AAAB63icdVDLSsNAFJ3UV62vapduBktBEEKSFlp3BTcuKxhbaGOZTCft0MkkzEyEErpz78aFilt/xQ9wpx/gF/gBTpsKKnrgwuGce7n3Hj9mVCrLejVyS8srq2v59cLG5tb2TnF370JGicDExRGLRMdHkjDKiauoYqQTC4JCn5G2Pz6Z+e0rIiSN+LmaxMQL0ZDTgGKktOT2wuTyqF8sW6ZTcxrVGsyIU1+Qqg1t05qj3CxVrj+e399a/eJLbxDhJCRcYYak7NpWrLwUCUUxI9NCL5EkRniMhqSrKUchkV46P3YKK1oZwCASuriCc/X7RIpCKSehrztDpEbytzcT//K6iQoaXkp5nCjCcbYoSBhUEZx9DgdUEKzYRBOEBdW3QjxCAmGl8ynoEL4+hf8T1zGPTftMh9EAGfJgHxyAQ2CDOmiCU9ACLsCAghtwB+4NbtwaD8Zj1pozFjMl8APG0yc8GJLz</latexit><latexit sha1_base64="M9qt9YkZazwGO5SXMXFYABHENf0=">AAAB63icdVDLSsNAFJ3UV62vapduBktBEEKSFlp3BTcuKxhbaGOZTCft0MkkzEyEErpz78aFilt/xQ9wpx/gF/gBTpsKKnrgwuGce7n3Hj9mVCrLejVyS8srq2v59cLG5tb2TnF370JGicDExRGLRMdHkjDKiauoYqQTC4JCn5G2Pz6Z+e0rIiSN+LmaxMQL0ZDTgGKktOT2wuTyqF8sW6ZTcxrVGsyIU1+Qqg1t05qj3CxVrj+e399a/eJLbxDhJCRcYYak7NpWrLwUCUUxI9NCL5EkRniMhqSrKUchkV46P3YKK1oZwCASuriCc/X7RIpCKSehrztDpEbytzcT//K6iQoaXkp5nCjCcbYoSBhUEZx9DgdUEKzYRBOEBdW3QjxCAmGl8ynoEL4+hf8T1zGPTftMh9EAGfJgHxyAQ2CDOmiCU9ACLsCAghtwB+4NbtwaD8Zj1pozFjMl8APG0yc8GJLz</latexit><latexit sha1_base64="qyJgAYJD1pLiUGPLihZx/+flexM=">AAAB63icdVBNS8NAEJ34WetX1aOXxSIIQkjSQuut4MVjBWMLbSyb7aZdutmE3Y1QQn+DFw8qXv1D3vw3btsIKvpg4PHeDDPzwpQzpR3nw1pZXVvf2Cxtlbd3dvf2KweHtyrJJKE+SXgiuyFWlDNBfc00p91UUhyHnHbCyeXc79xTqVgibvQ0pUGMR4JFjGBtJL8fZ3fng0rVsb2616zV0ZJ4jYLUXOTazgJVKNAeVN77w4RkMRWacKxUz3VSHeRYakY4nZX7maIpJhM8oj1DBY6pCvLFsTN0apQhihJpSmi0UL9P5DhWahqHpjPGeqx+e3PxL6+X6agZ5EykmaaCLBdFGUc6QfPP0ZBJSjSfGoKJZOZWRMZYYqJNPmUTwten6H/ie/aF7V471VazSKMEx3ACZ+BCA1pwBW3wgQCDB3iCZ0tYj9aL9bpsXbGKmSP4AevtE0S9jn0=</latexit>

π−

<latexit sha1_base64="z7varlndyPLhA1qQhsQf2JYsGd0=">AAAB63icdZDNSsNAFIVv6l+tf1WXbgaL4MaQtIXWlQU3LqsYW2hjmUwn7dDJJMxMhFL6DG5cqLj1HVz5EO58G6eNgooeGPg4517m3hsknCntOO9WbmFxaXklv1pYW9/Y3Cpu71ypOJWEeiTmsWwHWFHOBPU005y2E0lxFHDaCkans7x1Q6VisbjU44T6ER4IFjKCtbG8bsKuj3rFkmOXq+V6pYoyKNc+oeIi13bmKp28vlyAUbNXfOv2Y5JGVGjCsVId10m0P8FSM8LptNBNFU0wGeEB7RgUOKLKn8yHnaID4/RRGEvzhEZz93vHBEdKjaPAVEZYD9XvbGb+lXVSHdb9CRNJqqkg2UdhypGO0Wxz1GeSEs3HBjCRzMyKyBBLTLS5T8Ec4WtT9D94ZfvYds+dUqMOmfKwB/twCC7UoAFn0AQPCDC4hXt4sIR1Zz1aT1lpzvrs2YUfsp4/APaQkH0=</latexit><latexit sha1_base64="7JMcI4G5Ucara4svYP1IbxxiQbY=">AAAB63icdZDNSsNAFIUn/tb6V3UpyGAR3BiStNC6suDGZQvGFtpYJtNJO3QyCTMToYQuXbtxoeLWd+jKh3DnM/gSTpsKKnpg4OOce5l7rx8zKpVlvRsLi0vLK6u5tfz6xubWdmFn90pGicDExRGLRMtHkjDKiauoYqQVC4JCn5GmPzyf5s0bIiSN+KUaxcQLUZ/TgGKktOV2Ynp90i0ULdMpO9VSGWbgVOZQsqFtWjMVz14njY/bg0m9W3jr9CKchIQrzJCUbduKlZcioShmZJzvJJLECA9Rn7Q1chQS6aWzYcfwSDs9GERCP67gzP3ekaJQylHo68oQqYH8nU3Nv7J2ooKql1IeJ4pwnH0UJAyqCE43hz0qCFZspAFhQfWsEA+QQFjp++T1Eb42hf+D65inpt2wirUqyJQD++AQHAMbVEANXIA6cAEGFNyBB/BocOPeeDKes9IFY96zB37IePkE/kaSwg==</latexit><latexit sha1_base64="7JMcI4G5Ucara4svYP1IbxxiQbY=">AAAB63icdZDNSsNAFIUn/tb6V3UpyGAR3BiStNC6suDGZQvGFtpYJtNJO3QyCTMToYQuXbtxoeLWd+jKh3DnM/gSTpsKKnpg4OOce5l7rx8zKpVlvRsLi0vLK6u5tfz6xubWdmFn90pGicDExRGLRMtHkjDKiauoYqQVC4JCn5GmPzyf5s0bIiSN+KUaxcQLUZ/TgGKktOV2Ynp90i0ULdMpO9VSGWbgVOZQsqFtWjMVz14njY/bg0m9W3jr9CKchIQrzJCUbduKlZcioShmZJzvJJLECA9Rn7Q1chQS6aWzYcfwSDs9GERCP67gzP3ekaJQylHo68oQqYH8nU3Nv7J2ooKql1IeJ4pwnH0UJAyqCE43hz0qCFZspAFhQfWsEA+QQFjp++T1Eb42hf+D65inpt2wirUqyJQD++AQHAMbVEANXIA6cAEGFNyBB/BocOPeeDKes9IFY96zB37IePkE/kaSwg==</latexit><latexit sha1_base64="mCH2ggVHulpHWeE9uzEKbCSK6io=">AAAB63icdVBNS8NAEJ34WetX1aOXxSJ4MSRpofVW8OKxgrGFNpbNdtMu3WzC7kYoob/BiwcVr/4hb/4bt20EFX0w8Hhvhpl5YcqZ0o7zYa2srq1vbJa2yts7u3v7lYPDW5VkklCfJDyR3RArypmgvmaa024qKY5DTjvh5HLud+6pVCwRN3qa0iDGI8EiRrA2kt9P2d35oFJ1bK/uNWt1tCReoyA1F7m2s0AVCrQHlff+MCFZTIUmHCvVc51UBzmWmhFOZ+V+pmiKyQSPaM9QgWOqgnxx7AydGmWIokSaEhot1O8TOY6Vmsah6YyxHqvf3lz8y+tlOmoGORNppqkgy0VRxpFO0PxzNGSSEs2nhmAimbkVkTGWmGiTT9mE8PUp+p/4nn1hu9dOtdUs0ijBMZzAGbjQgBZcQRt8IMDgAZ7g2RLWo/VivS5bV6xi5gh+wHr7BDoZjnY=</latexit>

PV (SV) TV

p<latexit sha1_base64="W/km4v70f5ZOHnM2DbTiziC6ch0=">AAAB53icdVA9SwNBEJ3zM8avaEqbxRCwOu4ugcQuYGOZgGcCyRH2NnvJmr0PdveEcKSzs7FQsfUv2dn5U9zkIqjog4HHezPMzPMTzqSyrHdjbX1jc2u7sFPc3ds/OCwdHV/LOBWEuiTmsej5WFLOIuoqpjjtJYLi0Oe0608vFn73lgrJ4uhKzRLqhXgcsYARrLTUSYalimU6dadZq6OcOI0VqdnINq0lKq1y9e4DANrD0ttgFJM0pJEiHEvZt61EeRkWihFO58VBKmmCyRSPaV/TCIdUetny0DmqamWEgljoihRaqt8nMhxKOQt93RliNZG/vYX4l9dPVdD0MhYlqaIRyRcFKUcqRouv0YgJShSfaYKJYPpWRCZYYKJ0NkUdwten6H/iOua5aXd0GE3IUYATOIUzsKEBLbiENrhAgMI9PMKTcWM8GM/GS966ZqxmyvADxusnJmyO2g==</latexit><latexit sha1_base64="f4iqZQHIoyzijSISsKvotJ5Kzp8=">AAAB53icdVDLSsNAFJ3UV62vapduBkvBVUjSQuuu4MZlC8YW2lAm00k7djIJMxOhhO7cuXGh4taf8QPc6Qf4BX6A06aCih64cDjnXu69x48ZlcqyXo3cyura+kZ+s7C1vbO7V9w/uJBRIjBxccQi0fWRJIxy4iqqGOnGgqDQZ6TjT07nfueKCEkjfq6mMfFCNOI0oBgpLbXjQbFsmU7NaVRrMCNOfUmqNrRNa4Fys1S5/nh+f2sNii/9YYSTkHCFGZKyZ1ux8lIkFMWMzAr9RJIY4QkakZ6mHIVEeuni0BmsaGUIg0jo4gou1O8TKQqlnIa+7gyRGsvf3lz8y+slKmh4KeVxogjH2aIgYVBFcP41HFJBsGJTTRAWVN8K8RgJhJXOpqBD+PoU/k9cxzwx7bYOowEy5MEhOALHwAZ10ARnoAVcgAEBN+AO3BuXxq3xYDxmrTljOVMCP2A8fQKdz5F0</latexit><latexit sha1_base64="f4iqZQHIoyzijSISsKvotJ5Kzp8=">AAAB53icdVDLSsNAFJ3UV62vapduBkvBVUjSQuuu4MZlC8YW2lAm00k7djIJMxOhhO7cuXGh4taf8QPc6Qf4BX6A06aCih64cDjnXu69x48ZlcqyXo3cyura+kZ+s7C1vbO7V9w/uJBRIjBxccQi0fWRJIxy4iqqGOnGgqDQZ6TjT07nfueKCEkjfq6mMfFCNOI0oBgpLbXjQbFsmU7NaVRrMCNOfUmqNrRNa4Fys1S5/nh+f2sNii/9YYSTkHCFGZKyZ1ux8lIkFMWMzAr9RJIY4QkakZ6mHIVEeuni0BmsaGUIg0jo4gou1O8TKQqlnIa+7gyRGsvf3lz8y+slKmh4KeVxogjH2aIgYVBFcP41HFJBsGJTTRAWVN8K8RgJhJXOpqBD+PoU/k9cxzwx7bYOowEy5MEhOALHwAZ10ARnoAVcgAEBN+AO3BuXxq3xYDxmrTljOVMCP2A8fQKdz5F0</latexit><latexit sha1_base64="wS1jWt03+ojTamNFPbJOjzGtn8c=">AAAB53icdVBNS8NAEJ34WetX1aOXxSJ4CklaaL0VvHhswdhCG8pmu2nXbjZhdyOU0F/gxYOKV/+SN/+N2zaCij4YeLw3w8y8MOVMacf5sNbWNza3tks75d29/YPDytHxrUoySahPEp7IXogV5UxQXzPNaS+VFMchp91werXwu/dUKpaIGz1LaRDjsWARI1gbqZMOK1XH9upes1ZHK+I1ClJzkWs7S1ShQHtYeR+MEpLFVGjCsVJ910l1kGOpGeF0Xh5kiqaYTPGY9g0VOKYqyJeHztG5UUYoSqQpodFS/T6R41ipWRyazhjrifrtLcS/vH6mo2aQM5FmmgqyWhRlHOkELb5GIyYp0XxmCCaSmVsRmWCJiTbZlE0IX5+i/4nv2Ze223GqrWaRRglO4QwuwIUGtOAa2uADAQoP8ATP1p31aL1Yr6vWNauYOYEfsN4+AaZ0jP4=</latexit>

p<latexit sha1_base64="W/km4v70f5ZOHnM2DbTiziC6ch0=">AAAB53icdVA9SwNBEJ3zM8avaEqbxRCwOu4ugcQuYGOZgGcCyRH2NnvJmr0PdveEcKSzs7FQsfUv2dn5U9zkIqjog4HHezPMzPMTzqSyrHdjbX1jc2u7sFPc3ds/OCwdHV/LOBWEuiTmsej5WFLOIuoqpjjtJYLi0Oe0608vFn73lgrJ4uhKzRLqhXgcsYARrLTUSYalimU6dadZq6OcOI0VqdnINq0lKq1y9e4DANrD0ttgFJM0pJEiHEvZt61EeRkWihFO58VBKmmCyRSPaV/TCIdUetny0DmqamWEgljoihRaqt8nMhxKOQt93RliNZG/vYX4l9dPVdD0MhYlqaIRyRcFKUcqRouv0YgJShSfaYKJYPpWRCZYYKJ0NkUdwten6H/iOua5aXd0GE3IUYATOIUzsKEBLbiENrhAgMI9PMKTcWM8GM/GS966ZqxmyvADxusnJmyO2g==</latexit><latexit sha1_base64="f4iqZQHIoyzijSISsKvotJ5Kzp8=">AAAB53icdVDLSsNAFJ3UV62vapduBkvBVUjSQuuu4MZlC8YW2lAm00k7djIJMxOhhO7cuXGh4taf8QPc6Qf4BX6A06aCih64cDjnXu69x48ZlcqyXo3cyura+kZ+s7C1vbO7V9w/uJBRIjBxccQi0fWRJIxy4iqqGOnGgqDQZ6TjT07nfueKCEkjfq6mMfFCNOI0oBgpLbXjQbFsmU7NaVRrMCNOfUmqNrRNa4Fys1S5/nh+f2sNii/9YYSTkHCFGZKyZ1ux8lIkFMWMzAr9RJIY4QkakZ6mHIVEeuni0BmsaGUIg0jo4gou1O8TKQqlnIa+7gyRGsvf3lz8y+slKmh4KeVxogjH2aIgYVBFcP41HFJBsGJTTRAWVN8K8RgJhJXOpqBD+PoU/k9cxzwx7bYOowEy5MEhOALHwAZ10ARnoAVcgAEBN+AO3BuXxq3xYDxmrTljOVMCP2A8fQKdz5F0</latexit><latexit sha1_base64="f4iqZQHIoyzijSISsKvotJ5Kzp8=">AAAB53icdVDLSsNAFJ3UV62vapduBkvBVUjSQuuu4MZlC8YW2lAm00k7djIJMxOhhO7cuXGh4taf8QPc6Qf4BX6A06aCih64cDjnXu69x48ZlcqyXo3cyura+kZ+s7C1vbO7V9w/uJBRIjBxccQi0fWRJIxy4iqqGOnGgqDQZ6TjT07nfueKCEkjfq6mMfFCNOI0oBgpLbXjQbFsmU7NaVRrMCNOfUmqNrRNa4Fys1S5/nh+f2sNii/9YYSTkHCFGZKyZ1ux8lIkFMWMzAr9RJIY4QkakZ6mHIVEeuni0BmsaGUIg0jo4gou1O8TKQqlnIa+7gyRGsvf3lz8y+slKmh4KeVxogjH2aIgYVBFcP41HFJBsGJTTRAWVN8K8RgJhJXOpqBD+PoU/k9cxzwx7bYOowEy5MEhOALHwAZ10ARnoAVcgAEBN+AO3BuXxq3xYDxmrTljOVMCP2A8fQKdz5F0</latexit><latexit sha1_base64="wS1jWt03+ojTamNFPbJOjzGtn8c=">AAAB53icdVBNS8NAEJ34WetX1aOXxSJ4CklaaL0VvHhswdhCG8pmu2nXbjZhdyOU0F/gxYOKV/+SN/+N2zaCij4YeLw3w8y8MOVMacf5sNbWNza3tks75d29/YPDytHxrUoySahPEp7IXogV5UxQXzPNaS+VFMchp91werXwu/dUKpaIGz1LaRDjsWARI1gbqZMOK1XH9upes1ZHK+I1ClJzkWs7S1ShQHtYeR+MEpLFVGjCsVJ910l1kGOpGeF0Xh5kiqaYTPGY9g0VOKYqyJeHztG5UUYoSqQpodFS/T6R41ipWRyazhjrifrtLcS/vH6mo2aQM5FmmgqyWhRlHOkELb5GIyYp0XxmCCaSmVsRmWCJiTbZlE0IX5+i/4nv2Ze223GqrWaRRglO4QwuwIUGtOAa2uADAQoP8ATP1p31aL1Yr6vWNauYOYEfsN4+AaZ0jP4=</latexit>

N2<latexit sha1_base64="zFpMC0YgcmGD5gIEbU4ALIW6DqQ=">AAAB6XicdVBNS8NAEJ3Ur1q/qoIXL4tF8BSStNB6K3rxJC1aW2hD3Ww37dLNB7sboYT+BC8eVLz6j7x58be4bSqo6IOBx3szzMzzYs6ksqx3I7e0vLK6ll8vbGxube8Ud/duZJQIQlsk4pHoeFhSzkLaUkxx2okFxYHHadsbn8/89h0VkkXhtZrE1A3wMGQ+I1hp6eqy7/SLJct0Kk6tXEEZcaoLUraRbVpzlOoHzY9bAGj0i2+9QUSSgIaKcCxl17Zi5aZYKEY4nRZ6iaQxJmM8pF1NQxxQ6abzU6foWCsD5EdCV6jQXP0+keJAykng6c4Aq5H87c3Ev7xuovyam7IwThQNSbbITzhSEZr9jQZMUKL4RBNMBNO3IjLCAhOl0ynoEL4+Rf+TlmOemnZTh3EGGfJwCEdwAjZUoQ4X0IAWEBjCPTzCk8GNB+PZeMlac8ZiZh9+wHj9BCjXj3A=</latexit><latexit sha1_base64="5yIK94qaiELvoSmHoC5hazs8Wls=">AAAB6XicdVDLSsNAFJ3UV62vquDGzWARXIUkLbTuSt24khaNLbShTKaTduhkEmYmQgn9BDcuVNy69i/8Andu/BanTQUVPXDhcM693HuPHzMqlWW9G7ml5ZXVtfx6YWNza3unuLt3LaNEYOLiiEWi4yNJGOXEVVQx0okFQaHPSNsfn8389g0Rkkb8Sk1i4oVoyGlAMVJaurzoO/1iyTKdilMrV2BGnOqClG1om9YcpfpB64O+NF6b/eJbbxDhJCRcYYak7NpWrLwUCUUxI9NCL5EkRniMhqSrKUchkV46P3UKj7UygEEkdHEF5+r3iRSFUk5CX3eGSI3kb28m/uV1ExXUvJTyOFGE42xRkDCoIjj7Gw6oIFixiSYIC6pvhXiEBMJKp1PQIXx9Cv8nrmOemnZLh9EAGfLgEByBE2CDKqiDc9AELsBgCG7BPXgwmHFnPBpPWWvOWMzsgx8wnj8BeFyRLA==</latexit><latexit sha1_base64="5yIK94qaiELvoSmHoC5hazs8Wls=">AAAB6XicdVDLSsNAFJ3UV62vquDGzWARXIUkLbTuSt24khaNLbShTKaTduhkEmYmQgn9BDcuVNy69i/8Andu/BanTQUVPXDhcM693HuPHzMqlWW9G7ml5ZXVtfx6YWNza3unuLt3LaNEYOLiiEWi4yNJGOXEVVQx0okFQaHPSNsfn8389g0Rkkb8Sk1i4oVoyGlAMVJaurzoO/1iyTKdilMrV2BGnOqClG1om9YcpfpB64O+NF6b/eJbbxDhJCRcYYak7NpWrLwUCUUxI9NCL5EkRniMhqSrKUchkV46P3UKj7UygEEkdHEF5+r3iRSFUk5CX3eGSI3kb28m/uV1ExXUvJTyOFGE42xRkDCoIjj7Gw6oIFixiSYIC6pvhXiEBMJKp1PQIXx9Cv8nrmOemnZLh9EAGfLgEByBE2CDKqiDc9AELsBgCG7BPXgwmHFnPBpPWWvOWMzsgx8wnj8BeFyRLA==</latexit><latexit sha1_base64="47xBygJwTP031YuHu3KBa/IPs2o=">AAAB6XicdVBNS8NAEJ3Ur1q/qh69LBbBU0jSQuut6MWTVDS20Iay2W7apZtN2N0IpfQnePGg4tV/5M1/47aNoKIPBh7vzTAzL0w5U9pxPqzCyura+kZxs7S1vbO7V94/uFNJJgn1ScIT2QmxopwJ6mumOe2kkuI45LQdji/mfvueSsUScasnKQ1iPBQsYgRrI91c9b1+ueLYXs1rVGtoSbx6Tqoucm1ngQrkaPXL771BQrKYCk04VqrrOqkOplhqRjidlXqZoikmYzykXUMFjqkKpotTZ+jEKAMUJdKU0Gihfp+Y4lipSRyazhjrkfrtzcW/vG6mo0YwZSLNNBVkuSjKONIJmv+NBkxSovnEEEwkM7ciMsISE23SKZkQvj5F/xPfs89s99qpNM/zNIpwBMdwCi7UoQmX0AIfCAzhAZ7g2eLWo/VivS5bC1Y+cwg/YL19ApwVjYs=</latexit>

µ+

<latexit sha1_base64="e4UYffSBDlaINmlONT93YLcqkuY=">AAAB63icdVBNS8NAEJ34WetXtUcvi6UgCCFJC623ghePFYwttLFsttt26WYTdjdCKb159+JBxat/yJs3f4rbpoKKPhh4vDfDzLww4Uxpx3m3VlbX1jc2c1v57Z3dvf3CweG1ilNJqE9iHst2iBXlTFBfM81pO5EURyGnrXB8Pvdbt1QqFosrPUloEOGhYANGsDaS343Sm9NeoeTYXtWrV6ooI15tSSoucm1ngVKjWL77AIBmr/DW7cckjajQhGOlOq6T6GCKpWaE01m+myqaYDLGQ9oxVOCIqmC6OHaGykbpo0EsTQmNFur3iSmOlJpEoemMsB6p395c/MvrpHpQD6ZMJKmmgmSLBilHOkbzz1GfSUo0nxiCiWTmVkRGWGKiTT55E8LXp+h/4nv2me1emjDqkCEHR3AMJ+BCDRpwAU3wgQCDe3iEJ0tYD9az9ZK1rljLmSL8gPX6CcSmkFk=</latexit><latexit sha1_base64="M9qt9YkZazwGO5SXMXFYABHENf0=">AAAB63icdVDLSsNAFJ3UV62vapduBktBEEKSFlp3BTcuKxhbaGOZTCft0MkkzEyEErpz78aFilt/xQ9wpx/gF/gBTpsKKnrgwuGce7n3Hj9mVCrLejVyS8srq2v59cLG5tb2TnF370JGicDExRGLRMdHkjDKiauoYqQTC4JCn5G2Pz6Z+e0rIiSN+LmaxMQL0ZDTgGKktOT2wuTyqF8sW6ZTcxrVGsyIU1+Qqg1t05qj3CxVrj+e399a/eJLbxDhJCRcYYak7NpWrLwUCUUxI9NCL5EkRniMhqSrKUchkV46P3YKK1oZwCASuriCc/X7RIpCKSehrztDpEbytzcT//K6iQoaXkp5nCjCcbYoSBhUEZx9DgdUEKzYRBOEBdW3QjxCAmGl8ynoEL4+hf8T1zGPTftMh9EAGfJgHxyAQ2CDOmiCU9ACLsCAghtwB+4NbtwaD8Zj1pozFjMl8APG0yc8GJLz</latexit><latexit sha1_base64="M9qt9YkZazwGO5SXMXFYABHENf0=">AAAB63icdVDLSsNAFJ3UV62vapduBktBEEKSFlp3BTcuKxhbaGOZTCft0MkkzEyEErpz78aFilt/xQ9wpx/gF/gBTpsKKnrgwuGce7n3Hj9mVCrLejVyS8srq2v59cLG5tb2TnF370JGicDExRGLRMdHkjDKiauoYqQTC4JCn5G2Pz6Z+e0rIiSN+LmaxMQL0ZDTgGKktOT2wuTyqF8sW6ZTcxrVGsyIU1+Qqg1t05qj3CxVrj+e399a/eJLbxDhJCRcYYak7NpWrLwUCUUxI9NCL5EkRniMhqSrKUchkV46P3YKK1oZwCASuriCc/X7RIpCKSehrztDpEbytzcT//K6iQoaXkp5nCjCcbYoSBhUEZx9DgdUEKzYRBOEBdW3QjxCAmGl8ynoEL4+hf8T1zGPTftMh9EAGfJgHxyAQ2CDOmiCU9ACLsCAghtwB+4NbtwaD8Zj1pozFjMl8APG0yc8GJLz</latexit><latexit sha1_base64="qyJgAYJD1pLiUGPLihZx/+flexM=">AAAB63icdVBNS8NAEJ34WetX1aOXxSIIQkjSQuut4MVjBWMLbSyb7aZdutmE3Y1QQn+DFw8qXv1D3vw3btsIKvpg4PHeDDPzwpQzpR3nw1pZXVvf2Cxtlbd3dvf2KweHtyrJJKE+SXgiuyFWlDNBfc00p91UUhyHnHbCyeXc79xTqVgibvQ0pUGMR4JFjGBtJL8fZ3fng0rVsb2616zV0ZJ4jYLUXOTazgJVKNAeVN77w4RkMRWacKxUz3VSHeRYakY4nZX7maIpJhM8oj1DBY6pCvLFsTN0apQhihJpSmi0UL9P5DhWahqHpjPGeqx+e3PxL6+X6agZ5EykmaaCLBdFGUc6QfPP0ZBJSjSfGoKJZOZWRMZYYqJNPmUTwten6H/ie/aF7V471VazSKMEx3ACZ+BCA1pwBW3wgQCDB3iCZ0tYj9aL9bpsXbGKmSP4AevtE0S9jn0=</latexit>

p<latexit sha1_base64="W/km4v70f5ZOHnM2DbTiziC6ch0=">AAAB53icdVA9SwNBEJ3zM8avaEqbxRCwOu4ugcQuYGOZgGcCyRH2NnvJmr0PdveEcKSzs7FQsfUv2dn5U9zkIqjog4HHezPMzPMTzqSyrHdjbX1jc2u7sFPc3ds/OCwdHV/LOBWEuiTmsej5WFLOIuoqpjjtJYLi0Oe0608vFn73lgrJ4uhKzRLqhXgcsYARrLTUSYalimU6dadZq6OcOI0VqdnINq0lKq1y9e4DANrD0ttgFJM0pJEiHEvZt61EeRkWihFO58VBKmmCyRSPaV/TCIdUetny0DmqamWEgljoihRaqt8nMhxKOQt93RliNZG/vYX4l9dPVdD0MhYlqaIRyRcFKUcqRouv0YgJShSfaYKJYPpWRCZYYKJ0NkUdwten6H/iOua5aXd0GE3IUYATOIUzsKEBLbiENrhAgMI9PMKTcWM8GM/GS966ZqxmyvADxusnJmyO2g==</latexit><latexit sha1_base64="f4iqZQHIoyzijSISsKvotJ5Kzp8=">AAAB53icdVDLSsNAFJ3UV62vapduBkvBVUjSQuuu4MZlC8YW2lAm00k7djIJMxOhhO7cuXGh4taf8QPc6Qf4BX6A06aCih64cDjnXu69x48ZlcqyXo3cyura+kZ+s7C1vbO7V9w/uJBRIjBxccQi0fWRJIxy4iqqGOnGgqDQZ6TjT07nfueKCEkjfq6mMfFCNOI0oBgpLbXjQbFsmU7NaVRrMCNOfUmqNrRNa4Fys1S5/nh+f2sNii/9YYSTkHCFGZKyZ1ux8lIkFMWMzAr9RJIY4QkakZ6mHIVEeuni0BmsaGUIg0jo4gou1O8TKQqlnIa+7gyRGsvf3lz8y+slKmh4KeVxogjH2aIgYVBFcP41HFJBsGJTTRAWVN8K8RgJhJXOpqBD+PoU/k9cxzwx7bYOowEy5MEhOALHwAZ10ARnoAVcgAEBN+AO3BuXxq3xYDxmrTljOVMCP2A8fQKdz5F0</latexit><latexit sha1_base64="f4iqZQHIoyzijSISsKvotJ5Kzp8=">AAAB53icdVDLSsNAFJ3UV62vapduBkvBVUjSQuuu4MZlC8YW2lAm00k7djIJMxOhhO7cuXGh4taf8QPc6Qf4BX6A06aCih64cDjnXu69x48ZlcqyXo3cyura+kZ+s7C1vbO7V9w/uJBRIjBxccQi0fWRJIxy4iqqGOnGgqDQZ6TjT07nfueKCEkjfq6mMfFCNOI0oBgpLbXjQbFsmU7NaVRrMCNOfUmqNrRNa4Fys1S5/nh+f2sNii/9YYSTkHCFGZKyZ1ux8lIkFMWMzAr9RJIY4QkakZ6mHIVEeuni0BmsaGUIg0jo4gou1O8TKQqlnIa+7gyRGsvf3lz8y+slKmh4KeVxogjH2aIgYVBFcP41HFJBsGJTTRAWVN8K8RgJhJXOpqBD+PoU/k9cxzwx7bYOowEy5MEhOALHwAZ10ARnoAVcgAEBN+AO3BuXxq3xYDxmrTljOVMCP2A8fQKdz5F0</latexit><latexit sha1_base64="wS1jWt03+ojTamNFPbJOjzGtn8c=">AAAB53icdVBNS8NAEJ34WetX1aOXxSJ4CklaaL0VvHhswdhCG8pmu2nXbjZhdyOU0F/gxYOKV/+SN/+N2zaCij4YeLw3w8y8MOVMacf5sNbWNza3tks75d29/YPDytHxrUoySahPEp7IXogV5UxQXzPNaS+VFMchp91werXwu/dUKpaIGz1LaRDjsWARI1gbqZMOK1XH9upes1ZHK+I1ClJzkWs7S1ShQHtYeR+MEpLFVGjCsVJ910l1kGOpGeF0Xh5kiqaYTPGY9g0VOKYqyJeHztG5UUYoSqQpodFS/T6R41ipWRyazhjrifrtLcS/vH6mo2aQM5FmmgqyWhRlHOkELb5GIyYp0XxmCCaSmVsRmWCJiTbZlE0IX5+i/4nv2Ze223GqrWaRRglO4QwuwIUGtOAa2uADAQoP8ATP1p31aL1Yr6vWNauYOYEfsN4+AaZ0jP4=</latexit>

p<latexit sha1_base64="W/km4v70f5ZOHnM2DbTiziC6ch0=">AAAB53icdVA9SwNBEJ3zM8avaEqbxRCwOu4ugcQuYGOZgGcCyRH2NnvJmr0PdveEcKSzs7FQsfUv2dn5U9zkIqjog4HHezPMzPMTzqSyrHdjbX1jc2u7sFPc3ds/OCwdHV/LOBWEuiTmsej5WFLOIuoqpjjtJYLi0Oe0608vFn73lgrJ4uhKzRLqhXgcsYARrLTUSYalimU6dadZq6OcOI0VqdnINq0lKq1y9e4DANrD0ttgFJM0pJEiHEvZt61EeRkWihFO58VBKmmCyRSPaV/TCIdUetny0DmqamWEgljoihRaqt8nMhxKOQt93RliNZG/vYX4l9dPVdD0MhYlqaIRyRcFKUcqRouv0YgJShSfaYKJYPpWRCZYYKJ0NkUdwten6H/iOua5aXd0GE3IUYATOIUzsKEBLbiENrhAgMI9PMKTcWM8GM/GS966ZqxmyvADxusnJmyO2g==</latexit><latexit sha1_base64="f4iqZQHIoyzijSISsKvotJ5Kzp8=">AAAB53icdVDLSsNAFJ3UV62vapduBkvBVUjSQuuu4MZlC8YW2lAm00k7djIJMxOhhO7cuXGh4taf8QPc6Qf4BX6A06aCih64cDjnXu69x48ZlcqyXo3cyura+kZ+s7C1vbO7V9w/uJBRIjBxccQi0fWRJIxy4iqqGOnGgqDQZ6TjT07nfueKCEkjfq6mMfFCNOI0oBgpLbXjQbFsmU7NaVRrMCNOfUmqNrRNa4Fys1S5/nh+f2sNii/9YYSTkHCFGZKyZ1ux8lIkFMWMzAr9RJIY4QkakZ6mHIVEeuni0BmsaGUIg0jo4gou1O8TKQqlnIa+7gyRGsvf3lz8y+slKmh4KeVxogjH2aIgYVBFcP41HFJBsGJTTRAWVN8K8RgJhJXOpqBD+PoU/k9cxzwx7bYOowEy5MEhOALHwAZ10ARnoAVcgAEBN+AO3BuXxq3xYDxmrTljOVMCP2A8fQKdz5F0</latexit><latexit sha1_base64="f4iqZQHIoyzijSISsKvotJ5Kzp8=">AAAB53icdVDLSsNAFJ3UV62vapduBkvBVUjSQuuu4MZlC8YW2lAm00k7djIJMxOhhO7cuXGh4taf8QPc6Qf4BX6A06aCih64cDjnXu69x48ZlcqyXo3cyura+kZ+s7C1vbO7V9w/uJBRIjBxccQi0fWRJIxy4iqqGOnGgqDQZ6TjT07nfueKCEkjfq6mMfFCNOI0oBgpLbXjQbFsmU7NaVRrMCNOfUmqNrRNa4Fys1S5/nh+f2sNii/9YYSTkHCFGZKyZ1ux8lIkFMWMzAr9RJIY4QkakZ6mHIVEeuni0BmsaGUIg0jo4gou1O8TKQqlnIa+7gyRGsvf3lz8y+slKmh4KeVxogjH2aIgYVBFcP41HFJBsGJTTRAWVN8K8RgJhJXOpqBD+PoU/k9cxzwx7bYOowEy5MEhOALHwAZ10ARnoAVcgAEBN+AO3BuXxq3xYDxmrTljOVMCP2A8fQKdz5F0</latexit><latexit sha1_base64="wS1jWt03+ojTamNFPbJOjzGtn8c=">AAAB53icdVBNS8NAEJ34WetX1aOXxSJ4CklaaL0VvHhswdhCG8pmu2nXbjZhdyOU0F/gxYOKV/+SN/+N2zaCij4YeLw3w8y8MOVMacf5sNbWNza3tks75d29/YPDytHxrUoySahPEp7IXogV5UxQXzPNaS+VFMchp91werXwu/dUKpaIGz1LaRDjsWARI1gbqZMOK1XH9upes1ZHK+I1ClJzkWs7S1ShQHtYeR+MEpLFVGjCsVJ910l1kGOpGeF0Xh5kiqaYTPGY9g0VOKYqyJeHztG5UUYoSqQpodFS/T6R41ipWRyazhjrifrtLcS/vH6mo2aQM5FmmgqyWhRlHOkELb5GIyYp0XxmCCaSmVsRmWCJiTbZlE0IX5+i/4nv2Ze223GqrWaRRglO4QwuwIUGtOAa2uADAQoP8ATP1p31aL1Yr6vWNauYOYEfsN4+AaZ0jP4=</latexit>

PV

µ+

<latexit sha1_base64="e4UYffSBDlaINmlONT93YLcqkuY=">AAAB63icdVBNS8NAEJ34WetXtUcvi6UgCCFJC623ghePFYwttLFsttt26WYTdjdCKb159+JBxat/yJs3f4rbpoKKPhh4vDfDzLww4Uxpx3m3VlbX1jc2c1v57Z3dvf3CweG1ilNJqE9iHst2iBXlTFBfM81pO5EURyGnrXB8Pvdbt1QqFosrPUloEOGhYANGsDaS343Sm9NeoeTYXtWrV6ooI15tSSoucm1ngVKjWL77AIBmr/DW7cckjajQhGOlOq6T6GCKpWaE01m+myqaYDLGQ9oxVOCIqmC6OHaGykbpo0EsTQmNFur3iSmOlJpEoemMsB6p395c/MvrpHpQD6ZMJKmmgmSLBilHOkbzz1GfSUo0nxiCiWTmVkRGWGKiTT55E8LXp+h/4nv2me1emjDqkCEHR3AMJ+BCDRpwAU3wgQCDe3iEJ0tYD9az9ZK1rljLmSL8gPX6CcSmkFk=</latexit><latexit sha1_base64="M9qt9YkZazwGO5SXMXFYABHENf0=">AAAB63icdVDLSsNAFJ3UV62vapduBktBEEKSFlp3BTcuKxhbaGOZTCft0MkkzEyEErpz78aFilt/xQ9wpx/gF/gBTpsKKnrgwuGce7n3Hj9mVCrLejVyS8srq2v59cLG5tb2TnF370JGicDExRGLRMdHkjDKiauoYqQTC4JCn5G2Pz6Z+e0rIiSN+LmaxMQL0ZDTgGKktOT2wuTyqF8sW6ZTcxrVGsyIU1+Qqg1t05qj3CxVrj+e399a/eJLbxDhJCRcYYak7NpWrLwUCUUxI9NCL5EkRniMhqSrKUchkV46P3YKK1oZwCASuriCc/X7RIpCKSehrztDpEbytzcT//K6iQoaXkp5nCjCcbYoSBhUEZx9DgdUEKzYRBOEBdW3QjxCAmGl8ynoEL4+hf8T1zGPTftMh9EAGfJgHxyAQ2CDOmiCU9ACLsCAghtwB+4NbtwaD8Zj1pozFjMl8APG0yc8GJLz</latexit><latexit sha1_base64="M9qt9YkZazwGO5SXMXFYABHENf0=">AAAB63icdVDLSsNAFJ3UV62vapduBktBEEKSFlp3BTcuKxhbaGOZTCft0MkkzEyEErpz78aFilt/xQ9wpx/gF/gBTpsKKnrgwuGce7n3Hj9mVCrLejVyS8srq2v59cLG5tb2TnF370JGicDExRGLRMdHkjDKiauoYqQTC4JCn5G2Pz6Z+e0rIiSN+LmaxMQL0ZDTgGKktOT2wuTyqF8sW6ZTcxrVGsyIU1+Qqg1t05qj3CxVrj+e399a/eJLbxDhJCRcYYak7NpWrLwUCUUxI9NCL5EkRniMhqSrKUchkV46P3YKK1oZwCASuriCc/X7RIpCKSehrztDpEbytzcT//K6iQoaXkp5nCjCcbYoSBhUEZx9DgdUEKzYRBOEBdW3QjxCAmGl8ynoEL4+hf8T1zGPTftMh9EAGfJgHxyAQ2CDOmiCU9ACLsCAghtwB+4NbtwaD8Zj1pozFjMl8APG0yc8GJLz</latexit><latexit sha1_base64="qyJgAYJD1pLiUGPLihZx/+flexM=">AAAB63icdVBNS8NAEJ34WetX1aOXxSIIQkjSQuut4MVjBWMLbSyb7aZdutmE3Y1QQn+DFw8qXv1D3vw3btsIKvpg4PHeDDPzwpQzpR3nw1pZXVvf2Cxtlbd3dvf2KweHtyrJJKE+SXgiuyFWlDNBfc00p91UUhyHnHbCyeXc79xTqVgibvQ0pUGMR4JFjGBtJL8fZ3fng0rVsb2616zV0ZJ4jYLUXOTazgJVKNAeVN77w4RkMRWacKxUz3VSHeRYakY4nZX7maIpJhM8oj1DBY6pCvLFsTN0apQhihJpSmi0UL9P5DhWahqHpjPGeqx+e3PxL6+X6agZ5EykmaaCLBdFGUc6QfPP0ZBJSjSfGoKJZOZWRMZYYqJNPmUTwten6H/ie/aF7V471VazSKMEx3ACZ+BCA1pwBW3wgQCDB3iCZ0tYj9aL9bpsXbGKmSP4AevtE0S9jn0=</latexit>

SVjet

<latexit sha1_base64="Dei97lZYwkWVZ0J9IMTgOImrZgk=">AAAB7nicdVBNS8NAEJ34WetXtUcvi6XgKSRpofVW8OKxgrWFNpTNdtOu3Xy4uxFK6M1f4MWDild/jzdv/hQ3TQUVfTDweG+GmXlezJlUlvVurKyurW9sFraK2zu7e/ulg8MrGSWC0A6JeCR6HpaUs5B2FFOc9mJBceBx2vWmZ5nfvaVCsii8VLOYugEeh8xnBCst9QYiQNdUFYelimU6dadZq6OcOI0lqdnINq0FKq1y9e4DANrD0ttgFJEkoKEiHEvZt61YuSkWihFO58VBImmMyRSPaV/TEAdUuuni3jmqamWE/EjoChVaqN8nUhxIOQs83RlgNZG/vUz8y+snym+6KQvjRNGQ5Iv8hCMVoex5NGKCEsVnmmAimL4VkQkWmCgdURbC16fof9JxzFPTvtBhNCFHAY7gGE7Ahga04Bza0AECHO7hEZ6MG+PBeDZe8tYVYzlThh8wXj8BjfyRWA==</latexit><latexit sha1_base64="TsAfS0yt8gvSF5uR1mGbF3jPdC4=">AAAB7nicdVDLSsNAFJ3UV62vapduBkvBVUjSQuuu4MZlBWMLbSiT6aQdO5PEmYlQQnd+gRsXKm79Ej/AnX6AX+AHOG0qqOiBC4dz7uXee/yYUaks69XILS2vrK7l1wsbm1vbO8XdvXMZJQITF0csEh0fScJoSFxFFSOdWBDEfUba/vh45reviJA0Cs/UJCYeR8OQBhQjpaVOT3B4QVShXyxbplNzGtUazIhTX5CqDW3TmqPcLFWuP57f31r94ktvEOGEk1BhhqTs2lasvBQJRTEj00IvkSRGeIyGpKtpiDiRXjq/dworWhnAIBK6QgXn6veJFHEpJ9zXnRypkfztzcS/vG6igoaX0jBOFAlxtihIGFQRnD0PB1QQrNhEE4QF1bdCPEICYaUjmoXw9Sn8n7iOeWTapzqMBsiQB/vgABwCG9RBE5yAFnABBgzcgDtwb1wat8aD8Zi15ozFTAn8gPH0CQVuk/I=</latexit><latexit sha1_base64="TsAfS0yt8gvSF5uR1mGbF3jPdC4=">AAAB7nicdVDLSsNAFJ3UV62vapduBkvBVUjSQuuu4MZlBWMLbSiT6aQdO5PEmYlQQnd+gRsXKm79Ej/AnX6AX+AHOG0qqOiBC4dz7uXee/yYUaks69XILS2vrK7l1wsbm1vbO8XdvXMZJQITF0csEh0fScJoSFxFFSOdWBDEfUba/vh45reviJA0Cs/UJCYeR8OQBhQjpaVOT3B4QVShXyxbplNzGtUazIhTX5CqDW3TmqPcLFWuP57f31r94ktvEOGEk1BhhqTs2lasvBQJRTEj00IvkSRGeIyGpKtpiDiRXjq/dworWhnAIBK6QgXn6veJFHEpJ9zXnRypkfztzcS/vG6igoaX0jBOFAlxtihIGFQRnD0PB1QQrNhEE4QF1bdCPEICYaUjmoXw9Sn8n7iOeWTapzqMBsiQB/vgABwCG9RBE5yAFnABBgzcgDtwb1wat8aD8Zi15ozFTAn8gPH0CQVuk/I=</latexit><latexit sha1_base64="XcUGiKFXg2RI7Dllusu/L6PJJAI=">AAAB7nicdVBNS8NAEJ34WetX1aOXxSJ4CklaaL0VvHisYGyhDWWz3bRrN5u4uxFK6J/w4kHFq7/Hm//GbRtBRR8MPN6bYWZemHKmtON8WCura+sbm6Wt8vbO7t5+5eDwRiWZJNQnCU9kN8SKciaor5nmtJtKiuOQ0044uZj7nXsqFUvEtZ6mNIjxSLCIEayN1O3LGN1SXR5Uqo7t1b1mrY6WxGsUpOYi13YWqEKB9qDy3h8mJIup0IRjpXquk+ogx1Izwums3M8UTTGZ4BHtGSpwTFWQL+6doVOjDFGUSFNCo4X6fSLHsVLTODSdMdZj9dubi395vUxHzSBnIs00FWS5KMo40gmaP4+GTFKi+dQQTCQztyIyxhITbSKah/D1Kfqf+J59brtXTrXVLNIowTGcwBm40IAWXEIbfCDA4QGe4Nm6sx6tF+t12bpiFTNH8APW2ycOE498</latexit>

W+

<latexit sha1_base64="khczDvfVNWcrZYn/Bf6NagnUTCg=">AAAB6XicdZDLSsNAFIZP6q3WW9Wlm8EiCEJI2kLryoIbl/USW2hjmUwn7dDJhZmJUEIfwY0LFbe+hCsfwp1v47SpoKI/DHz8/znMOceLOZPKsj6M3MLi0vJKfrWwtr6xuVXc3rmWUSIIdUjEI9H2sKSchdRRTHHajgXFgcdpyxudTvPWLRWSReGVGsfUDfAgZD4jWGnrsnVz1CuWLLNcLdcrVZRBuTaHio1s05qpdPL2egFazV7xvduPSBLQUBGOpezYVqzcFAvFCKeTQjeRNMZkhAe0ozHEAZVuOht1gg6000d+JPQLFZq53ztSHEg5DjxdGWA1lL+zqflX1kmUX3dTFsaJoiHJPvITjlSEpnujPhOUKD7WgIlgelZEhlhgovR1CvoIX5ui/8Epm8emfW6VGnXIlIc92IdDsKEGDTiDJjhAYAB38ACPBjfujSfjOSvNGfOeXfgh4+UTVy2PiQ==</latexit><latexit sha1_base64="fCUL13KFWtJ44Ve5Lc9se2669nI=">AAAB6XicdZDNSsNAFIUn9a/Wv6pLQQaLIAghSQutKwtuXLZobKGNZTKdtEMnkzAzEUrp0qUbFypufYmufAh3PoMv4bSpoKIHBj7OuZe59/oxo1JZ1ruRWVhcWl7JrubW1jc2t/LbO1cySgQmLo5YJJo+koRRTlxFFSPNWBAU+ow0/MHZNG/cECFpxC/VMCZeiHqcBhQjpa2LxvVxJ1+wTKfkVIolmIJTnkPRhrZpzVQ4fZ3UP273J7VO/q3djXASEq4wQ1K2bCtW3ggJRTEj41w7kSRGeIB6pKWRo5BIbzQbdQwPtdOFQST04wrO3O8dIxRKOQx9XRki1Ze/s6n5V9ZKVFDxRpTHiSIcpx8FCYMqgtO9YZcKghUbakBYUD0rxH0kEFb6Ojl9hK9N4f/gOuaJadetQrUCUmXBHjgAR8AGZVAF56AGXIBBD9yBB/BoMOPeeDKe09KMMe/ZBT9kvHwCXuORzg==</latexit><latexit sha1_base64="fCUL13KFWtJ44Ve5Lc9se2669nI=">AAAB6XicdZDNSsNAFIUn9a/Wv6pLQQaLIAghSQutKwtuXLZobKGNZTKdtEMnkzAzEUrp0qUbFypufYmufAh3PoMv4bSpoKIHBj7OuZe59/oxo1JZ1ruRWVhcWl7JrubW1jc2t/LbO1cySgQmLo5YJJo+koRRTlxFFSPNWBAU+ow0/MHZNG/cECFpxC/VMCZeiHqcBhQjpa2LxvVxJ1+wTKfkVIolmIJTnkPRhrZpzVQ4fZ3UP273J7VO/q3djXASEq4wQ1K2bCtW3ggJRTEj41w7kSRGeIB6pKWRo5BIbzQbdQwPtdOFQST04wrO3O8dIxRKOQx9XRki1Ze/s6n5V9ZKVFDxRpTHiSIcpx8FCYMqgtO9YZcKghUbakBYUD0rxH0kEFb6Ojl9hK9N4f/gOuaJadetQrUCUmXBHjgAR8AGZVAF56AGXIBBD9yBB/BoMOPeeDKe09KMMe/ZBT9kvHwCXuORzg==</latexit><latexit sha1_base64="fpbWSJIMcQ28FtNOPZUs1HQsS+0=">AAAB6XicdVBNS8NAEJ3Ur1q/qh69LBZBEEKSFlpvBS8eKxpbaGPZbDft0s0m7G6EUvoTvHhQ8eo/8ua/cdtGUNEHA4/3ZpiZF6acKe04H1ZhZXVtfaO4Wdra3tndK+8f3Kokk4T6JOGJ7IRYUc4E9TXTnHZSSXEcctoOxxdzv31PpWKJuNGTlAYxHgoWMYK1ka7bd2f9csWxvZrXqNbQknj1nFRd5NrOAhXI0eqX33uDhGQxFZpwrFTXdVIdTLHUjHA6K/UyRVNMxnhIu4YKHFMVTBenztCJUQYoSqQpodFC/T4xxbFSkzg0nTHWI/Xbm4t/ed1MR41gykSaaSrIclGUcaQTNP8bDZikRPOJIZhIZm5FZIQlJtqkUzIhfH2K/ie+Z5/b7pVTaTbyNIpwBMdwCi7UoQmX0AIfCAzhAZ7g2eLWo/VivS5bC1Y+cwg/YL19ApqnjYI=</latexit>

b → Xµ+µ+π−

<latexit sha1_base64="zpCYndi4fHY0hWyfF2YxfbfFz0k=">AAACBnicdVBNS0JBFL3Pvsy+LJdBDIUQRPLeU9B2QpuWBr0U9CnzxlEH530wM68Qceemv9KmRUXbfkO7dv2URp9BRR24l8M59zJzjxdxJpVpvhuppeWV1bX0emZjc2t7J7u7dy3DWBDqkJCHouFhSTkLqKOY4rQRCYp9j9O6Nzyf+fUbKiQLgys1iqjr437AeoxgpaVO9sBrCdYfKCxEeIsaqOXH7ZOkRax92skemQW7ZFeKJZQQu7wgRQtZBXOOo2ouP/0AgFon+9bqhiT2aaAIx1I2LTNS7hgLxQink0wrljTCZIj7tKlpgH0q3fH8jgnKa6WLeqHQFSg0V79vjLEv5cj39KSP1UD+9mbiX14zVr2KO2ZBFCsakOShXsyRCtEsFNRlghLFR5pgIpj+KyIDLDBROrqMDuHrUvQ/cezCWcG61GFUIEEa9uEQjsGCMlThAmrgAIEp3MMjPBl3xoPxbLwkoyljsZODHzBePwFSR5qq</latexit><latexit sha1_base64="2Gxsm41z/ThrywCkJMKUlM60paU=">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</latexit><latexit sha1_base64="2Gxsm41z/ThrywCkJMKUlM60paU=">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</latexit><latexit sha1_base64="xw386N9LGCYzMJwmfsZffstlDtw=">AAACBnicdVDLSsNAFJ34rPUVdSnIYBEEMSRpoXVXcOOygrGFJi2T6aQdOnkwM1FK6M6Nv+LGhYpbv8Gdf+O0iaCiB+7lcM69zNzjJ4wKaZof2sLi0vLKammtvL6xubWt7+xeizjlmDg4ZjHv+EgQRiPiSCoZ6SScoNBnpO2Pz2d++4ZwQePoSk4S4oVoGNGAYiSV1NcPfJfT4UgizuNb2IFumPZO8pbQ3mlfr5iGXbMb1RrMiV0vSNWClmHOUQEFWn393R3EOA1JJDFDQnQtM5FehrikmJFp2U0FSRAeoyHpKhqhkAgvm98xhUdKGcAg5qoiCefq940MhUJMQl9NhkiOxG9vJv7ldVMZNLyMRkkqSYTzh4KUQRnDWShwQDnBkk0UQZhT9VeIR4gjLFV0ZRXC16Xwf+LYxplhXZqVZqNIowT2wSE4Bhaogya4AC3gAAzuwAN4As/avfaovWiv+eiCVuzsgR/Q3j4B0k+Yzg==</latexit>

0.1 1 10 10010-12

10-10

10-8

10-6

10-4

0.01

1

MN HGeVL

VmN

2

BBN Seesaw

KÆmn

E949

NuTeV

DELPHI

L3

CMS

ATLAS

LHC14

SHiPFCC-ee

CHARM

FMMF

EWPD

PS191

BEBC

NA3

KÆmmp

LHCb

Belle

LBNE

arXiv:1502.06541

B(b → Xµ+ν)

B(B+ → µ+ν)> 105

<latexit sha1_base64="Rb70ZSi/oZFwp5rBGIU7z1u0uYM=">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</latexit><latexit sha1_base64="lIczusWrSkgZ1Br0SIfwJEe9Iuk=">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</latexit><latexit sha1_base64="lIczusWrSkgZ1Br0SIfwJEe9Iuk=">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</latexit><latexit sha1_base64="caxWieCNpVlyijLsRcSQEWzuF6Q=">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</latexit>

u/c

W−

N

µ− µ−

π+

W−

W+

<latexit sha1_base64="tSZupQOdSjWlvrWmx0hKgo16iAc=">AAAB6XicbZC7SgNBFIbPeo3xFrW0GQxCQAi7NmplwMYyXtYEkjXMTs4mQ2Znl5lZIYQ8go2Fiq29tc9h59s4uRSa+MPAx/+fw5xzwlRwbVz321lYXFpeWc2t5dc3Nre2Czu7dzrJFEOfJSJR9ZBqFFyib7gRWE8V0jgUWAt7F6O89oBK80Temn6KQUw7kkecUWOtm9r9UatQdMvuWGQevCkUzz8+r8Gq2ip8NdsJy2KUhgmqdcNzUxMMqDKcCRzmm5nGlLIe7WDDoqQx6mAwHnVIDq3TJlGi7JOGjN3fHQMaa92PQ1sZU9PVs9nI/C9rZCY6DQZcpplBySYfRZkgJiGjvUmbK2RG9C1QpridlbAuVZQZe528PYI3u/I8+Mfls7J35RYrJZgoB/twACXw4AQqcAlV8IFBBx7hGV4c4Tw5r87bpHTBmfbswR857z/af48l</latexit><latexit sha1_base64="d+tDvyTuV+KS+1LQNKiwEP7lamY=">AAAB6XicbZC7SgNBFIbPxluMt6ilIINBCAhhN41aGbCxTNA1gWQNs5PZZMjs7DIzK4QlpaWNhYqtvXWew85n8CWcXApN/GHg4//PYc45fsyZ0rb9ZWWWlldW17LruY3Nre2d/O7erYoSSahLIh7Jho8V5UxQVzPNaSOWFIc+p3W/fznO6/dUKhaJGz2IqRfirmABI1gb67p+d9LOF+ySPRFaBGcGhYuPUe374XBUbec/W52IJCEVmnCsVNOxY+2lWGpGOB3mWomiMSZ93KVNgwKHVHnpZNQhOjZOBwWRNE9oNHF/d6Q4VGoQ+qYyxLqn5rOx+V/WTHRw5qVMxImmgkw/ChKOdITGe6MOk5RoPjCAiWRmVkR6WGKizXVy5gjO/MqL4JZL5yWnZhcqRZgqCwdwBEVw4BQqcAVVcIFAFx7hGV4sbj1Zr9bbtDRjzXr24Y+s9x/iNZFq</latexit><latexit sha1_base64="d+tDvyTuV+KS+1LQNKiwEP7lamY=">AAAB6XicbZC7SgNBFIbPxluMt6ilIINBCAhhN41aGbCxTNA1gWQNs5PZZMjs7DIzK4QlpaWNhYqtvXWew85n8CWcXApN/GHg4//PYc45fsyZ0rb9ZWWWlldW17LruY3Nre2d/O7erYoSSahLIh7Jho8V5UxQVzPNaSOWFIc+p3W/fznO6/dUKhaJGz2IqRfirmABI1gb67p+d9LOF+ySPRFaBGcGhYuPUe374XBUbec/W52IJCEVmnCsVNOxY+2lWGpGOB3mWomiMSZ93KVNgwKHVHnpZNQhOjZOBwWRNE9oNHF/d6Q4VGoQ+qYyxLqn5rOx+V/WTHRw5qVMxImmgkw/ChKOdITGe6MOk5RoPjCAiWRmVkR6WGKizXVy5gjO/MqL4JZL5yWnZhcqRZgqCwdwBEVw4BQqcAVVcIFAFx7hGV4sbj1Zr9bbtDRjzXr24Y+s9x/iNZFq</latexit><latexit sha1_base64="qUlsTyrYqhtZcp5P32Ai1IBMip0=">AAAB6XicbVBNS8NAEJ34WetX1aOXxSIUhJJ4UW8FLx4rGltoY9lsN+3SzSbsToQS+hO8eFDx6j/y5r9x2+agrQ8GHu/NMDMvTKUw6Lrfzsrq2vrGZmmrvL2zu7dfOTh8MEmmGfdZIhPdDqnhUijuo0DJ26nmNA4lb4Wj66nfeuLaiETd4zjlQUwHSkSCUbTSXevxrFepunV3BrJMvIJUoUCzV/nq9hOWxVwhk9SYjuemGORUo2CST8rdzPCUshEd8I6lisbcBPns1Ak5tUqfRIm2pZDM1N8TOY2NGceh7YwpDs2iNxX/8zoZRpdBLlSaIVdsvijKJMGETP8mfaE5Qzm2hDIt7K2EDammDG06ZRuCt/jyMvHP61d179atNmpFGiU4hhOogQcX0IAbaIIPDAbwDK/w5kjnxXl3PuatK04xcwR/4Hz+ADOojS4=</latexit>