M = PoS(FPCP2017)027

PoS(FPCP2017)027

NobuhiroShimizufortheBelle ollaboration

∗

† UniversityofTokyo,Aihara/Yokoyamalaboratory,

DepartmentofPhysi s,7-3-1Hongo,Bunkyo-ku,Tokyo113-0033JAPAN E-mail:shimizuhep.phys.s.u-tokyo.a .jp

‡

The Mi hel parameters are fundamental hara teristi s of m and t leptons whi h determine the kinemati distribution of daughterparti les from theirleptoni de ays. The omparison ofexperimentally-measuredvaluesversusthe Standardmodelpredi tionsallowsustotestthe Lorentzstru tureofweakintera tioninmodelindependentway. WereviewthetauMi hel pa-rametermeasurementsperformedbeforeandpresentourre entmeasurementsbyBelle experi-ments.

FlavorPhysi sandCPViolation 5-9June2017

HotelDonGiovanni,Prague,Cze hRepubli

∗

Speaker. †

Belle ollaboration. ‡

PoS(FPCP2017)027

1. Introdu tion

The de ay of tau is known as one of the most important tools to sear h for New Physi s (NP).Thelargemassoft(m

t

=

1776

.

86

±

0

.

12MeV[1 ℄)allowsustoexpe tanenhan ementof thesensitivity totheNP.Forinstan e, theNPmodelssu has2HDM(twoHiggsdoubletmodel) predi t the existen e of harged Higgsand themagnitude of their ouplings are proportional to massofleptons. Therefore, in omparison withmuonde ays,we anexpe tthegainof afa tor

(

m

t

/

m

m

)

2

∼

300inthesimplest ase.

Themassoft makesit possibletode ay intoboth leptonsand hadrons. Theformer one is alled leptoni de ayand a ounts for approximately 35%of all taude ays. Various properties ofthese de ays, des ribed by the ele troweak se tor of the SM, arepre isely al ulated, hen e experimentalresults anbedenitely omparedwiththeoreti alpredi tions.Therestde aysoftau ontainhadrons inthenalstateand alledhadroni de ay. Thesede aysturnouttobebeautiful laboratoryfor studying lowenergy stru ture of thestrongintera tion likethe hiral perturbation theory.

Bothofthesede ay aremediatedbytheweakintera tion. IntheStandard Model(SM),the Lorentzstru tureof orrespondingintermediateparti le,W

±

boson,in ludestheve torand axial-ve tor ontributionsinthesamemagnitudewithopposite signand turnsouttomaximallyviolate thesymmetry ofparity(so alledV

−

A stru ture). Thusthepre ision testofthis stru ture may revealhintsfromthePhysi sBeyondtheStandardModel(BSM)andthemeasurementof Mi hel parametersoftauleptonoffersanideallaboratorytous.

2. Mi helParameters

ThemostgeneralLorentz-invariantderivative-freematrixelement ofleptoni t de ayt

−

_→

ℓ

−

n ¯ n

∗

isrepresentedas[2 ,3℄

M

₌

W t n t n

ℓ

ℓ

=

4G F

√

2 å N

=

S

,

V

,

T i

,

j

=

L

,

R g N ij



u i

(ℓ)

G N v n

(

n

ℓ

) [

u m

(

n t

)

G N u j

(

t

)] ,

whereG F

istheFermi onstant,iand jarethe hiralityindi esforthe hargedleptons,nandmare the hiralityindi esoftheneutrinos,

ℓ

iseorm,G

S

=

1,G V

=

g m andG T

=

i

(

g m g n

−

g n g m

) /

2

√

2 are,respe tively,thes alar,ve torandtensorLorentzstru turesintermsoftheDira matri esg

m , u i andv i

arethefour- omponentspinorsofaparti leandanantiparti le,respe tively, andg N ij

are the orrespondingdimensionless ouplings.IntheSM,t

−

de aysinton t

andW

−

boson,thelatter de ays into

ℓ

−

andright-handed ¯

n

ℓ

, i.e.,the onlynon-zero oupling isg V LL

=

1. Experimentally, onlythesquared matrixelementisobservable andbilinear ombinations oftheg

N ij

area essible. Ofallsu h ombinations,fourMi helparameters, h,r,d andx, anbemeasuredintheleptoni de ayofthetwhenthenal-stateneutrinos arenotobservedorthespinoftheoutgoingleptonis

PoS(FPCP2017)027

notmeasured[4 ℄: r

=

3 4

−

3 4







g V LR





2

+





g V RL





2

+

2





g T LR





2

+

2





g T RL





2

+

 g S LR g T

∗

LR

+

g S RL g T

∗

RL



,

(2.1) h

=

1 2 Â 6g V RL g T

∗

LR

+

6g V LR g T

∗

RL

+

g S RR g V

∗

LL

+

g S RL g V

∗

LR

+

g S LR g V

∗

RL

+

g S LL g V

∗

RR

,

(2.2) x

=

4Â g S LR g T

∗

LR

−

g S RL g T

∗

RL

+





g V LL





2

+

3





g V LR





2

−

3





g V RL





2

−





g V RR





2

+

5





g T LR





2

−

5





g T RL





2

+

1 4







g S LL





2

−





g S LR





2

+





g S RL





2

−





g S RR





2



,

(2.3) xd

=

3 16







g S LL





2

−





g S LR





2

+





g S RL





2

−





g S RR





2



−

3 4







g T LR





2

−





g T RL





2

−





g V LL





2

+





g V RR





2

−

 g S LR g T

∗

LR

+

g S RL g T

∗

RL



.

(2.4) W t n t g

ℓ

n

ℓ

W t n t g

ℓ

n

ℓ

W W t n t g

ℓ

n

ℓ

Figure1:ThreeFeynmandiagramsofthetauradiativeleptoni de ay

TheFeynmandiagramsdes ribingtheradiativeleptoni de ayofthetarepresentedinFig.1. The last amplitude isignored be ause this ontribution turned outto be suppressed by the very smallfa tor

(

m

t

/

m

W

)

2

[5 ℄. AsshowninRefs.[6 ,7℄,throughthepresen eofaradiativephotonin thenalstate,thepolarization oftheoutgoingleptonisindire tlyexposed,a ordinglytwomore Mi helparameters

¯

h andxkbe omeexperimentallya essible:

¯ h

=





g V RL





2

+





g V LR





2

+

1 8







g S RL

+

2g T RL





2

+





g S LR

+

2g T LR





2



+

2







g T RL





2

+





g T LR





2



,

(2.5) xk

=





g V RL





2

−





g V LR





2

+

1 8







g S RL

+

2g T RL





2

−





g S LR

+

2g T LR





2



+

2







g T RL





2

−





g T LR





2



.

(2.6)

•

handr

Twohandr arespin-independentMi helparameters, i.e.,theireffe tsareirrelevanttothe polarization oftaulepton. Figure 2shows anenergy distribution ofmuonint

−

_→

m

−

n ¯ n de ayfor varioush and r values. r parameter mainly affe tsthe highenergy part inthe spe trumwhilehisnot;thush issometimes alledlow-energyparameter.

Important hara teristi sofhisthatitistherstorderintermsofNewPhysi s,unlikeother Mi helparameters. A ordingtoEq.(2.2)andnotingg

V LL

∼

1,h

∼

0

.

5Â

{

g S RR

}

. Indeed,h

PoS(FPCP2017)027

*

max

/E

*

l

E

0

0.2

0.4

0.6

0.8

1

Arbitrary units

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

= 0.00

η

= 0.25

η

= 0.50

η

= 0.75

η

= 1.00

η

)

ν

ν

µ

→

τ

spectrum (

*

l

E

(a)

*

max

/E

*

l

E

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Arbitrary units

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

= 0.00

ρ

= 0.25

ρ

= 0.50

ρ

= 0.75

ρ

= 1.00

ρ

)

ν

ν

µ

→

τ

spectrum (

*

l

E

(b)

Figure2:Dependen eoftheenergyofdaughtermuoninthetaurestframeon(a)hand(b)r(t

−

_→

m

−

n ¯

n de ay).HorizontalaxisisnormalizedintermsofmaximumenergyE max

= (

m 2 t

+

m 2

ℓ

)/

2m t .

parameterisrelatedtoNewPhysi svariablesofthe2HDM[8 ℄:

h

= −

m t m

ℓ

2



tanb m H

±



2

,

(2.7) wherem t ,m

ℓ

and m H

±

aremassesoftau,daughterlepton and hargedHiggs, respe tively, b isaratioofva uum expe tationvaluebetweenup-typeanddown-type quarks. Unfortu-nately,theeffe tsfromhissuppressedbythesmallmassofdaughterlepton.Moreexpli itly, thegeneralizedbran hingratio anbewrittenby

B

₍

t

−

_{→ ℓ}

−

n ¯ n

)

B

S M

(

t

−

→ ℓ

−

nn¯

)

=

1

+

h m

ℓ

m t

,

(2.8)

thusitisdif ulttomeasureh parameterfromtheele tronmodet

−

_→

e

−

n ¯ n.

rparameterisusedto onstrainmagnitudeofea h oupling oef ient.1

−

r anbewritten by 1

−

r

=

1 16





g S LL





2

+

1 16





g S RR





2

+

1 4





g V LL





2

+

1 4





g V RR





2

+





g V LR





2

+





g V RL





2

+

1 16





g S LR

+

6g T LR





2

+

1 16





g S RL

+

6g T RL





2 (2.9)

and therighthandside ofEq. (2.9) isnon-negative. Itisthus, the experimentalvalue an giveupperlimit.

•

x andxd

PoS(FPCP2017)027

parametersarein luded inthedifferential de aywidthtogether withthespin ve torof tau lepton. Themeasurementrequires,therefore,theextra tionoftau-spininformation. Exper-imentally,thespin-spin orrelation oftauleptonsintheannihilationpro esse

+

e

−

_→

t

+

t

−

isutilized[9 ℄. Polarization ofbothtausareanti- orrelatedea hother and onsequently an observation ofspe tra ofde ay produ tsfrombothtaus makesitpossible toextra tx and xd parameters.

Ofparti ularinterestofthesetwoparametersisthefa tthatthenormalizedprobabilitythat right-handedtaulepton oupleswithW

−

boson,Q t

R

, anbe al ulatedby ombiningx and xd parameters: Q t R

=

1 2



1

+

1 3 x

−

16 9 xd



.

(2.10)

Thisisforbidden intheSMandtheexperimentalvalueofQ t

R

=

0

.

00

±

0

.

02 †

is onsistent withtheSMpredi tion.

•

¯

handxk

¯

handxk areadditionalparameterswhi h anbemeasuredonlythroughtheobservationof theradiative leptoni de ays t

−

_{→ ℓ}

−

n ¯

ng. The angular distribution of photon versus the spe trumofdaughterleptonexposesthepolarizationofdaughterleptonandthisisree ted ontheappearan eofnewparameters.

¯

happearsinspin-independenttermsofthedifferentialde aywidthoft

−

_{→ ℓ}

−

n ¯

ng. Sin e alltermsinEq.(2.5)arestri tlynon-negative,similarlyto1

−

r situation,theupperlimiton

¯

hprovidesa onstraintonea h oupling onstantaswell.

On the other hand, xk is a spin-dependent parameter and this measurement requires the tauspin information. A ordingto Ref.[10 ℄, xk isrelated tothe normalized probability that the t

−

de ays into the right-handed harged daughter lepton Q

ℓ

R

= (

1

+

x

+

4xk

−

8xd

/

3

)/

2[11 ℄.

In muon de ay, through the dire t measurement of ele tron polarization in m

+

_→

e

+

n ¯ n, equivalentparametersx

′

andx

′′

₌

16r

/

3

−

4 ¯

h

−

3(seeTable1)havebeenalreadymeasured, whereas

¯

handxk ofthet leptonhavenotbeenmeasuredyet. Therefore,themeasurement ofbothparametersprovidesafurther onstraintontheLorentzstru tureoftheweak urrent.

•

Summaryofsixparameters

Table1summarizestheinformationofdes ribedMi hel parameters. Inadditiontothe ex-plainedparameters,wealsoin ludedh

′′

,x

′

andx

′′

.Figure3showsillustrativesummaryof variousparametersbyseveralexperiments. The ombinedaverages byParti leDataGroup (PDG)are onsistent withtheSMpredi tionwithintheirun ertainties, wherethese un er-taintiesvary1%to3%. Allofthesemeasurements were arriedoutapproximatelytwenty yearsagoandtheupdateisdesiredusingmodernBfa tories.

†

PoS(FPCP2017)027

Table1:Mi helparametersofthetlepton†

Name SM Spin Experimental CommentsandRef. value orrelation result[1 ℄

h 0 no 0

.

013

±

0

.

020 (ALEPH)[12 ℄

r 3

/

4 no 0

.

745

±

0

.

008 (CLEO)[13 ℄ xd 3

/

4 yes 0

.

746

±

0

.

021 (CLEO)[13 ℄

x 1 yes 1

.

007

±

0

.

040 measuredinleptoni de ays(CLEO)[13 ℄ x

h

1 yes 0

.

995

±

0

.

007 measuredinhadroni de ays(CLEO)[13 ℄ h 0 no notmeasured fromradiativede ay(RD)

xk 0 yes notmeasured fromRD

h

′′

0 no notmeasured fromRD,suppressedbym 2 l

/

m 2 t x

′

1 yes - x

′

= −

x

−

4xk

+

8xd

/

3. x

′′

1 no - x

′′

₌

16r

/

3

−

4 ¯ h

−

3. †

ExperimentalresultsrepresentaveragevaluesobtainedbyPDG[1℄.

3. MeasurementsofMi helparametersbyBelleexperiments

Utilizingthelarge number ofstatisti s of tauleptonby Bfa toryas well asthepre ise de-s riptionofprobabilitydensityfun tion,Belle ollaboration measuresh,r,x andxd parameters fromt

−

_{→ ℓ}

−

n ¯

n de ay toa hieve pre ision better than 1%. Whereas fromthe radiative de ay t

−

_{→ ℓ}

−

n ¯ ng, the ¯

h and xk are measured. The latter represents therst measurement ofthese parametersforthetaulepton.Bothoftwoanalysesuset

→

r

(→

pp

0

)

n de ayinthepartnerside oftauandthespin-spin orrelationoftt pairtoextra ttheinformationofsignaltlepton.

3.1 Belleexperiment

TheBelleexperimentatKEK(Tsukuba,Japan) olle ted1040fb

−

1

ofdatasampleusinge

+

e

−

energy-asymmetri olliderKEKBandBelledete tor.ItranfromJune1999toJune2010and on-tributedtotheprogressofhighenergyphysi s. TheBelledete torisdesignedtobemulti-purpose so thatvertexing, momentum tra king, energy measurementof photon andparti leidenti ation areintera tivelyperformedbyseveralsub-dete tors.

TheseBfa toryexperiments areusefullaboratoryalso forthestudyofthet leptons. Atthe resonan eenergyof¡

(

4S

) ∼

10.58GeV,the rossse tionoftaupairprodu tionis ompatiblewith that ofbb pair(s ee

→

tt

=

0

.

9nb

−

1 and s ee

→

bb

=

1

.

1nb

−

1

). Indeed, spending approximately ten years,KEKBa eleratorandBelledete tor olle tedO

(

10

9

)

ofttpairdata.

3.2 t spinextra tion

To measurex, xd, xk parameters, thespin of t mustbe measured. Thisisextra ted using thespin-spin orrelationoftauleptonpairs.InthebeamenergyofKEKBa elerator,the hirality oftauleptonsareanti- orrelatedby

∼

95%,thuson ewemeasurethespinoftheothersideoftau lepton,ortagside,we anextra tthespinofsignaltaulepton. Inthetagside,weuset

→

rn

→

PoS(FPCP2017)027

0.3

−

−

0.2

−

0.1

0

0.1

0.2

0.3

ALEPH

0.012

±

0.026

DELPHI

-0.005

±

0.052

OPAL

0.027

±

0.055

L3

0.270

±

0.140

SLD

-0.130

±

0.493

CLEO

-0.015

±

0.087

ARGUS

0.030

±

0.121

parameter

η

(a)

0.65

0.7

0.75

0.8

0.85

0.9

0.95

ALEPH

0.742

±

0.015

DELPHI

0.775

±

0.030

OPAL

0.781

±

0.033

L3

0.762

±

0.035

ARGUS

0.731

±

0.031

SLD

0.720

±

0.095

CLEO

0.747

±

0.012

parameter

ρ

(b)

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

ALEPH

0.992

±

0.011

DELPHI

0.997

±

0.029

OPAL

1.020

±

0.133

L3

1.032

±

0.031

SLD

0.930

±

0.108

CLEO

1.290

±

0.282

ARGUS

1.017

±

0.039

parameter

h

ξ

( )

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

ALEPH

0.776

±

0.051

DELPHI

0.779

±

0.075

OPAL

0.650

±

0.157

L3

0.700

±

0.110

ARGUS

0.630

±

0.090

SLD

0.880

±

0.273

CLEO

0.745

±

0.028

parameter

δ

ξ

(d)

Figure3: SummaryofthemeasuredMi helparameters: (a)h (b)r ( )x h

and(d)xd. Linesand lledregionsarethe ombinedvaluesandtheirun ertaintiessummarizedinTable1.

pp 0

n de aymodeasaspin-analyzer. Indeed, thedifferentialde aywidthoft

→

rn

→

pp 0 n is writtenby dG

(

t

→

rn

→

pp 0 n

)

µA

+ ~

B

·~

S t

,

(3.1)

where A and

~

B are known fun tions of kinemati variables of p and p 0

, and

~

S t

isa spin oft. Equation(3.1)representsthereisasensitivitytothespin. Formoredetails,seeRefs.[15,16 ℄.

3.3 Extra tionofMi helparameters

Combiningthekinemati observablesofbothsignalandtagsides,thephasespa eofanevent formsmulti-dimension variables:

~

x

= {

P

ℓ

,

W

ℓ

,

P

r

,

W r

,

m 2 pp

,

˜ W p

}

PoS(FPCP2017)027

usingt

−

t

+

_{→ (ℓ}

−

n ¯ n

)(

r

+

¯ n

)

and

~

x

= {

P

ℓ

,

W

ℓ

,

P g

,

W g

,

P r

,

W r

,

m 2 pp

,

˜ W p

}

for ¯ handxkmeasurement using t

−

t

+

_{→ (ℓ}

−

n ¯ ng

)(

r

+

¯ n

)

. Here, P i and W i

(i

= ℓ,

g

,

r) arethemomentum and solidangle, respe tively, m pp is an invariant massof pp 0 -system, and ˜ W p

is a solid angle of p in the pp 0

system. Forthe observable

~

x, we al ulate the probability density fun tion (PDF) P

(~

x

)

and the minimizationofnegativelogarithmi likelihoodfun tion(NLL)allowsonetogetthebestestimator ofMi helparametersforagivensetof

~

x

i (i

=

1

, . . . ,

N): NLL

= −

logL

(

Q

) = −

N å i

=

1 logP

(~

x i

),

(3.2) whereQ

= {

h

,

r

,

x

,

xd

}

orQ

= {

¯ h

,

xk

}

.

Inourapproa h,thesignalPDFisdes ribedanalyti ally. AsFig.4shows,assumingthemass ofneutrinos arezero,we an onstrainthe andidateoft dire tionontothear . ThevisiblePDF isthendenedasintegrationoftheinitialdifferential rossse tion:

P vis

.

(

x

) ≡

1 s vis

.

ds vis

.

d

~

x

=

1 s

Z

F 2 F 1 dF ds d

~

xdF

.

(3.3)

Figure4:Whenonet de aysleptoni allyandtheothert de ayshadroni ally,thedire tionoft is onstrainedontothear inthe enter-of-masssystem. Thear isanoverlapoftwo onesthatare denedaroundthedire tionofhadronandleptonmomenta.

Thedifferential rossse tion oft

−

t

+

_{→ (ℓ}

−

n ¯ n

)(

r

+

¯

n

)

de ayisgiven asa linear ombina-tionintermsofMi helparameters: ds

vis

.

/

d

~

xµ

C

0

(~

x

) + C

1

(~

x

)

h

+ C

2

(~

x

)

r

+ C

3

(~

x

)

h

+ C

4

(~

x

)

x

+

C

5

(~

x

)

xd forknownfun tions

C

i

(~

PoS(FPCP2017)027

Table2:Listofsystemati un ertainty ontributions

Item s e ¯ h s e xk s m ¯ h s m xk Relativenormalizations 4

.

2 0

.

94 0.15 0.04 Absolutenormalizations 1

.

0 0

.

01 0

.

03 0

.

001 Des riptionoftheba kgroundPDF 2

.

5 0

.

24 0.67 0.22 Inputofbran hingratio 3

.

8 0

.

05 0

.

25 0

.

01 Effe tof lustermergeinECL 2

.

2 0

.

46 0

.

02 0

.

06

Dete torresolution 0.74 0.20 0.22 0.02

Corre tionfa torR 1

.

9 0

.

14 0

.

04 0

.

04

Beamenergyspread negligible negligible negligible negligible

Total 7.0 1.1 0.76 0.24

sele tionef ien y,thenormalizedPDFisgivenby

1 s vis

.

ds vis

.

d

~

x

=

[C

0

(~

x

) + C

1

(~

x

)

h

+ C

2

(~

x

)

r

+ C

3

(~

x

)

h

+ C

4

(~

x

)

x

+ C

5

(~

x

)

xd

]

e

(~

x

)

Z

d

~

x

[C

0

(~

x

) + C

1

(~

x

)

h

+ C

2

(~

x

)

r

+ C

3

(~

x

)

h

+ C

4

(~

x

)

x

+ C

5

(~

x

)

xd

]

e

(~

x

)

,

(3.4)

where e

(~

x

)

isa sele tion ef ien y. The denominator of Eq. (3.4)is evaluated by Monte Carlo simulationand thedifferen e ofthefa tor of ef ien y between thedata and simulationR

(~

x

) ≡

¯ e data

(~

x

)/

¯ e MC

(~

x

)

isdire tlymeasuredfromrealdata.

WemeasureR

(~

x

)

valuesdue tothe orre tions of

ℓ

−

identi ation, p

+

identi ation, p 0

re- onstru tionandtriggeref ien y.Ofallfa tors,theextra tionofthetriggeref ien y orre tion turns out tohave thelargest impa t. Inthe urrent s heme, theexpe ted systemati un ertainty isapproximately3%and weareinvestigating thepro edurehowtopre iselymeasurethetrigger ef ien y orre tion.Weaimtoa hievethea ura ybetterthan1%,whi hisbetterthanprevious measurements.

3.4 ¯

handxkmeasurementusingt

−

→ ℓ

−

n ¯ ngde ay Themeasurementof ¯ h andxk usingt

−

_{→ ℓ}

−

n ¯

ng is arriedoutinthesimilarwayash

,

r

,

x and xd analysis. Figure 5showsthephotonenergydistribution forthemuon de aymodet

−

_→

ℓ

−

nn¯g. Duetotheba kground ontaminationtothesignalphoton andidates,theeventsele tion suffers fromthein lusion ofba kgrounds thant

−

_{→ ℓ}

−

n ¯

n ase. Thepurityof signaleventsare approximatelysixtyper entforthemuonmode.

InTable2,wesummarizethe ontributionsofvarioussour esofsystemati un ertainties. The dominantsystemati sour efortheele tronmodeisthe al ulation ofthenormalizations. Dueto the pe uliarity of the signal PDF when m

l

→

m

e

, the evaluation of the normalization fa tor is ina urateandresultsinanotableeffe t. Theun ertaintyoftherelativenormalizationisevaluated usingthe entrallimittheorem.

Thelargest systemati un ertainty forthemuon mode isdue tothe limitedpre ision ofthe des ription ofba kgroundPDF.Thesetofminorba kground sour esistreatedasone additional

PoS(FPCP2017)027

(GeV)

γ

E

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-1

Nev/0.01000 GeV

2

4

6

8

10

12

14

16

18

20

22

3

10

×

ν

ν

γ

e

→

τ

Exp.

] (28.9%)

rad

γ

)[

γ

τ

ν

e

ν

-)(e

τ

ν

0

π

+

π

(

→

-τ

+

τ

] (52.8%)

brems.

γ

)[

τ

ν

e

ν

-)(e

τ

ν

0

π

+

π

(

→

-τ

+

τ

] (7.5%)

brems.

γ

)[

γ

τ

ν

e

ν

-)(e

τ

ν

0

π

+

π

(

→

-τ

+

τ

others (10.7%)

(GeV)

γ

E

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-1

Nev/0.01000 GeV

0.5

1

1.5

2

2.5

3

3.5

4

4.5

3

10

×

τ

→

µ

ν

ν

γ

Exp.

] (57.4%)

rad

γ

)[

γ

τ

ν

µ

ν

-µ

)(

τ

ν

0

π

+

π

(

→

-τ

+

τ

] (16.2%)

beam

γ

)[

τ

ν

µ

ν

-µ

)(

τ

ν

0

π

+

π

(

→

-τ

+

τ

] (7.7%)

ISR

γ

)[

τ

ν

µ

ν

-µ

)(

τ

ν

0

π

+

π

(

→

-τ

+

τ

] (5.1%)

rad

γ

)[

γ

τ

ν

µ

ν

-µ

)(

τ

ν

0

π

0

π

+

π

(

→

-τ

+

τ

] (3.8%)

0

π

from

γ

)[

τ

ν

0

π

-π

)(

τ

ν

0

π

+

π

(

→

-τ

+

τ

] (1.2%)

0

π

from

γ

)[

τ

ν

0

π

0

π

-π

)(

τ

ν

0

π

+

π

(

→

-τ

+

τ

others (8.6%)

Figure 5: Distribution of thephoton energy inthemuon de aymodet

−

_→

m

−

n ¯ ng. The empty and oloredhistogramsarethesignalandba kgroundMonteCarlodistributions. Dotswith un er-taintiesaredata.

ategory that is based on MCdistributions. This effe tive des ription dis ards the information about orrelationsinthephasespa eandtherebygivessigni antbias.

Sin ethesensitivity toh¯ issuppressedby thefa tor ofm l

/

m t

,weextra t itfromthemuon modeonly. Using832644and72768sele ted eventsfort

+

t

−

_{→ (}

p

+

p 0 ¯ n

)(

e

−

n ¯ ng

)

andt

+

t

−

_→

(

p

+

p 0 ¯ n

)(

m

−

n ¯

ng

)

andidates,respe tively,weobtainpreliminaryvalues

(

xk

)

(

e

)

= −

0

.

5

±

0

.

8

±

1

.

1

,

(3.5) ¯ h m

= −

2

.

0

±

1

.

5

±

0

.

8

,

(3.6)

(

xk

)

(

m

)

=

0

.

8

±

0

.

5

±

0

.

2

,

(3.7) wherethersterrorisstatisti al andthese ondissystemati . Theresultsofxkare ombinedto give

xk

=

0

.

6

±

0

.

4

±

0

.

2

.

(3.8) Figure 6 shows the ontour thelikelihood for t

→

mn

¯

ng events. As the shape suggests, a orrelationbetween

¯

handxkissmall. Themagnitudeofthe orrelation oef ientdeterminedby theerrormatrixisapproximately7%. Thisistherstexperimentaltrialtomeasurethe

¯

handxk parameters.

PoS(FPCP2017)027

η

6

−

−

5

−

4

−

3

−

2

−

1

0

1

2

κξ

2

−

1.5

−

1

−

0.5

−

0

0.5

1

1.5

2

Contour of likelihood

Contour of likelihood

Figure6:Contourofthelikelihoodfort

→

mn ¯

ngevents.The ir lesindi ate1s,2sand3s statisti aldeviationsfrominnertooutersides,respe tively. The rossistheSMpredi tion.

4. Con lusion

Pre ision studies of leptoni de ays of tau lepton isone ofthe most usefulways tosear h for the effe ts from New Physi s. Of all strategies, measurement of Mi hel parameters allows us toverifythe Lorentzstru tureofweak intera tion inmodelindependent way. Observing the ordinaryleptoni de ay,t

−

→ ℓ

−

nn¯,fourMi helparametersh,r,x andxdaremeasuredwhereas theradiative leptoni de ayt

−

_{→ ℓ}

−

n ¯

ng tells us information ofspinof daughterlepton, whi h a ordinglygivesmoretwoparameters

¯

h andxk.

Usingele tron-positron olliders,variousexperimentshadmeasured thefour Mi hel param-eterswithinapre isionofafewper ent. Itisdesiredtoupdatethesemeasurementusingmodern B-fa toryapparatuses.Ontheotherhand,thetwoparameters

¯

handxkhavenotbeenmeasured. Utilizingmu h abundant statisti s of B-fa tory, Belle experiment triesto measure these six Mi hel parameters. In these measurements, it is important to extra t the ef ien y orre tions pre isely. Of all orre tions, the fa tor oftrigger ef ien yturns outtohavethe largest system-ati ontribution. For h,r,x and xd measurement, we areinvestigating thes heme toa hieve pre isionbetterthan1%.

Onthe ontrary,theun ertaintyofh¯ andxk measurementsaredominatedbystatisti al u -tuation. Basedon832644and72768sele tedeventsfort

+

t

−

_{→ (}

p

+

p 0 ¯ n

)(

e

−

n ¯ ng

)

andt

+

t

−

_→

(

p

+

p 0 ¯ n

)(

m

−

n ¯

ng

)

andidates,respe tively,weobtainedpreliminaryresulttobe

(

xk

)

(

e

)

= −

0

.

5

±

0

.

8

±

1

.

1, ¯ h m

= −

2

.

0

±

1

.

5

±

0

.

8and

(

xk

)

(

m

)

=

0

.

8

±

0

.

5

±

0

.

2. Theseresultsare onsistentwith theSMpredi tionwithintheirun ertainties. Thisisthersttrialtomeasure

¯

handxkparameters.

Referen es

PoS(FPCP2017)027

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[4℄ W.Fets herandH.J.Gerber,Adv.Ser.Dire t.HighEnergyPhys.14,657(1995).

[5℄ M.Fael,L.Mer olliandM.Passera,Phys.Rev.D88,no.9,093011(2013).

[6℄ C.FronsdalandH.Uberall,Phys.Rev.113,654(1939).

[7℄ A.B.ArbuzovandT.V.Kopylova,JHEP.1609,109(2016).

[8℄ A himStahl,Phys.Lett.B,324,121(1994).

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[14℄ A.Abashianetal.,Nu l.Instrum.Meth.A479117(2002)

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