(GeV)
γ
M l
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Nev/0.00500
10 20 30 40 50 60 70 80 90
10 3
× τ → e ν ν γ
(a)
(GeV)
γ
M l
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Nev/0.00500
1 2 3 4 5
10 3
× τ → e ν ν γ
(b)enlarged
Figure10.1:Distributionoftheinvariantmassofeletronandphotonm
e
for ! e ¯ andidate:
(a)overallview(b)enlargedview.AsexplainedinChapter4,yellowandgreenhistogramrepresent
theextrabremsstrahlung.
tehniquemaygiveasigniantimprovementinthepurity.EvenatBelle,insomelatterperiod,itis
notimpossibletoaessthehittimeinformationbutwedidnotusethem.
Takingintoaountallfatslistedabove,itisnotfarfromrealistitoexpetanimprovementof
systematiunertaintybythesamegainasstatistial,i.e.,againofthefatorof p
507.
¯
= 1:31:50:8 (10.1)
( )
= 0:80:50:3: (10.2)
Intheeletronmode,isttedbyxing¯ valuetotheStandardModelpreditionof¯ =0andthe
optimalvalueis
( ) e
= 0:40:80:9: (10.3)
The rst errorsare statistialand theseond aresystemati. Thisis therst measurementof both
parametersforthelepton.ThesevaluesareonsistentwiththeSMexpetationwithintheerrors.
Basedonthemeasuredvaluesof¯ and , weobtainedtheupperlimitoftheouplingonstant
ong N
ij
s.Combininglinearombinationofandvaluesweobtain
jg T
RL
j<0:55 (95%C:L): (10.4)
Fromobservedvalue, wealsotriedtoobtainupperlimitofthenormalizedprobabilitythat
leptonoupleswitharight-handeddaughterleptonas
Q
R
< 2:4 (95%C:L): (10.5)
Thisistherstexperimentalonstraintforthetaulepton.
To make the measurement of ¯ and have further signiant impats on the theories BSM,
it is desired to perform more preise measurement using next generation experiments. In the
improvements of the auray of these measurements, it is neessary to redue systemati
uner-tainties,whihisalreadyompetitivetostatistialunertaintiesofBelledatasample.Thekeyofthe
improvementswillbetreatmenthugeamountofdataoftheMCaswellastherealexperimentusing
moderntehnologiesoftheomputing.
Furtheroptimizingtheseletionriteria,wealsomeasuredthebranhingratioofradiativedeays
! ` ¯ . Theresultsare
B(
! e
)¯
E
>10 MeV
=(1:820:020:10)10 2
; (10.6)
B(
!
)¯
E
>10 MeV
=(3:680:020:15)10 3
; (10.7)
wherethersterrorisstatistiandseondissystemati. Thesevaluesareonsistentwiththeresults
byBaBarexperiment.
Toreduevarioussystematieets,inpartiularfrom 0
reonstrutioneÆieny,weobtained
aratioofthebranhingratio
Q=
B( ! e )¯
E
>10MeV
B( ! ¯ )
E
>10MeV
= 4:950:060:20; (10.8)
where thersterror isstatistiand seondissystemati. Themagnitude ofsystematiunertainty
slightlyimprovestogiveQ=Q=4:0%.Thisresultdoesnothangetheonlusiondesribedabove.
Theresultsareonsistentwiththeleadingordertheoretialalulation,whereas,similarlytothe
result ofBaBar experiment, in theeletronmode themeasuredbranhingratio doesnot preferthe
theignoraneofthemultiplephotonemissionsatthestageofeventgenerationandthe
implementa-tionofNLOformalismintheTAUOLAgeneratorisrequiredtodofurtheranalysis.
Basedontheagreementofobservedbranhingratioofradiativedeay,weattempttoonstrain
the oupling onstants of anomalousfour-pointsalar and tensor interations. Integrating the
dif-ferential deaywidthdue tointerferenebetween theanomalousand theSMamplitudes,we
eval-uate the expetedshift of branhing ratioand obtained upper limitsare j S
j < 4:9(68% C:L ) and
j T
j< 1:3(68%C:L ). Thisistherstattempttoonstrainthefour-pointinterations.
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InompletingmyPh.D.thesis,Ihavebeensupportedbyvariouspeopleandawonderfulenvironment
inmanyways. Firstofall,Iwouldliketoextendmygreatestgratitudetothelukydestinythatled
to memeetingmybelovedat. AsFigureAk.1 shows,she happilyhosetobe anewmemberof
my familyratherthanremaininginherlifeasastrayat. Herexistenealwaysmakesusalmand
inspires usto remember theimportaneof our lives. This givesus the patieneand persisteneto
overomevarioushallengesinluding,ofourse,physisresearh.
(a) (b)
FigureAk.1:Mybelovedat:(a)Ahomelessatametoourhouseinthesummerof2011.(b)
Sheisusuallyhappyjustonherownbutbrushingherseemstobeanexeption.
IalsowanttothankallthestaoftheAihara/Yokoyamalaboratorygroupfortheirdailyeduation
andsupport. H.Aiharagavemeapreiousenvironmentforresearhandmuhonstrutiveadvie.
ItwashismanygiftsthatenabledmetoompletemyPh.D.work. Theenormouseduationaleort
of my supervisorM.Yokoyamaalso helpedme to grow upfrom anegg ofa physiist. In writing
thisthesis,hekindlyhekedmydraftandgavememanyusefulsuggestionsandommentsinspite
of the heavy burden of his oÆework as well ashis researh (this analysis is notdiretly related
to hismain researhsubjet). Ihosethis laboratorymainlybeauseI wasfondof hispersonality
and now I deeplyrealize that thiswas not the wrongdeision. It is an honor for meto be one of
therstPh.D.studentstograduatefromhislaboratory.Y.Onukialsohelpedandsustainedmefora
longtime.Inpartiular,toreeivemymasterdiploma,hiseduationaladvieaboutthedevelopment
of thesilion vertexdetetor forBelleII wereessential. Istrongly believethat itwouldhavebeen
impossible to understand the basis of mehanis(whih are neessary for detetor onstrution)
withouthissupport.
I would like to show my speial and deepest thanks to D. Epifanov, who was a former sta
member of the Aihara group before moving to BINP (Budker Instituteof Nulear Physis) in the
Autumnof2015.Althoughhewasalsoverybusywithhisownresearh(themeasurementofMihel
parameters,,andÆ),hekindlysparedhispreioustimeandallowedmetoshareinhisenormous
in the Belle group. All oftheir hard work helped realizesuh a preiousanalysis. Inpartiular, I
wouldliketoexpressmyrespettoS. I.Eidelman, T.Browder,K.Hayasaka, Y.Kwon,M.Nakao,
S.Nishida,L.Piilonen,Y.SakaiandS.Uehara.Theygavemenumerousadvieandsuggestionsfor
mystudy.
Ialsowouldliketoappreiatemyolleaguesofourlaboratory,IPMUandsoon:M.Alejandro,
J.Changwoo,N. Chikuma,T.Higuhi, F.Hosomi,T.Horiguh, Y.Jin,Y.Kakihi,R. Kameswara,
T.Koga,K.Kono,T.Lou, H.Madokoro,S.Mineo,H.Miyatake,S.Mohida,T.Morii,H. Niikura,
T. Ose, J.Sasaki, N. Sato, Y. Seino, Y. Suda, R. Tamura, T. Yoshinobu, H. Wakana, K. Wan and
I. Watson. Allof themenouragedmeateverymomentinavarietyofways, fromseriousphysis
disussions to a daily hat. The step-by-steppiling up of these experienesand their ooperation
ertainlystrengthenedme. Inpartiular,disussionswithN. Chikuma,T.KogaandJ.Sasakiwere
sometimesreallyexitingandfruitfulformygrowth. Moreover,I. Watsonkindlyhelpedmerevise
English phrasesfor severalpubliations, whihturnedout tobe valuablehanefor meto reeive
orretionsfromanativespeaker.
IoweanimportantdebttotheresearhfellowsoftheJapanSoietyforthePromotionofSiene,
whih kindly supported my life as a dotoral student and funded me for the advanement of our
researh. Thankstothevaluablenanialsupport,Iwasabletoonentrateonextendingthewisdom
ofhumanbeings. Iamproudtobeafellowofthisinstitution.
In the diplomadefense, the ommittee memberskindly heked my thesisand gaveme many
essentialsuggestionsandomments. IwouldliketoexpressmygreatestappreiationforY.Hayato
(hair),K.Hamaguhi,T.Mori,H.SakuraiandJ.Tanaka.
Finally, I want to express my gratitude to Canon and Sigma orporations for their exellent
ameras and lenses. The Canon EOS 6D, whih is the heapest and lightest full-frame format
single-lens reex amera at the time of writing, delivered a huge number of wonderful pitures
with a lot of memories of my dotoral ourse. Sigma has been produing numerous remarkable
lenseswithamazingostperformanelike,the50mmF1.4DGHSMandthe24mmF1.4DGHSM,
whih areveryhelpful forstudentswho arenoteonomiallyprivileged. Thesegadgetsindiretly
supportedmyresearhbyinspiringmyuriosityandpassion.
Now, it's over. Thank you all!
x
x
IborrowedthisphrasefromRef.[92℄
Measurement of the branhing ratio
B( ! ` )¯ (validation)
As one of a validation of our proedures, we measure the branhing ratio of ! ` ¯ deay
for ` = e or . The agreement of the branhing ratio with previous measurements tells us the
additionalonsistenyfortheestimationofRaswellasanevaluationofbakgroundsontamination
for !` ¯ deays.
A.1 Method and evaluation ofsystemati unertainties
Taking into aountthe onrmation purposeof this measurement, we must useompletely same
seletionriteriaasthatofthemeasurementofMihelparameters. Themethodofthemeasurement
of the branhing ratio and its systematiunertainty are same as presented in Chapter9. Sine it
is diÆultto denethesideband region,we usesame value asadierene of bakgroundamount
desribed inChapter9. Takinginto aountafrationofbakgrounds, estimatedsystematieet
on the purity f
bg
is 2.9% and 2.1% for eletron and muon modes, respetively. In Table A.1, we
summarizetheontributionsofthesystematiunertaintiesforeahitem.