 NùğĄĉįĻĹŠĻĠT¶4ĠM"
FDEK;E;FH.&"$" -(FDEK<E<FH

"

EQ"ĞĒFÊěýEĈĠÙĜ |ĲÈďįNùĲÅĘĚāįĠąŬŬ?HĨĭİĕĠąŬ@" ,FDEK<E<FH"F

Q"Ŧ
<ġFi,šš" ,¯JÉ  " ,ąĝĂąĠÒ o²

 ŌŅļŀ¯JÚğÚêĲăį¯JěýŏĸŜŔ
ĹŞĜĠT¶4MrġÚêğ 9ĠĬĂğìĲ¦ÓŠū<ĠNÒ ìĠĐİġŠūsĕĞĠÒl <ě ěßÿÉ2ÀĞ¶4
 ĮĻĹŠĻĜ-ĻĹŠĻ"

FDEK<E<FHG.'EěĠ¶~ ,,("-)+(.-"('´gĠÄòŝŐňŞrěńŗŞŉŜĲ'ĉį
<ŒŁŞĜĠîiå©ěēİĔİE<D9FŝŐňŞńŗŞŉŜĆĀį

E=%)-('!'%D=%)-('!'%ν#-ü F
FDEK<E<FHνF=%)-('!'%lνll%)-('?96@#-ü F"%)-('?96@ü F
#-ü FHÌ}jö
3Ġ´gĲM»?ŒŁŞîi@lνÄòŝŐňŞrĪĿĸŅňrýG ä.ê? @ýőĻłŠŒŁŞĠ ä.ê?)@ýŏŝŊŠ5MĞĝ
ğĬĮ3 ØĲèkŢ"' %%-+('-+" +Ħĕġ -+" +9ĿĸŅň SF(+G9ŝŐňŞ SE9ŒňŕĻĹŠĻĿĸŅň SF9 @¿wØĠÌEBêÌ}? @ĲāĚ3Ĝ¿w

ØĠ'ðĲxç/ďįSZìr?%"$%"!((@ĲM»čý"--"' ĲÅā," '""'ĲÎ®ďįFDEK<E<FH"I- (&)+",('FDEK<E<FHFDEK<E<FH""JEBêÌ}","('+BrğĬį'ðĬĮĩy)ěĀįťŤ©ĠBrĲĘĚÌ}ďį
ëĆxçĞ'ðĲÅĂċĜġ8ñ

2.5

3Signal (test sample)¿w Ø
Background (test sample)

((,-","('+?@Signal (training sample)
Background (training sample)

Kolmogorov-Smirnov test: signal (background) probability = 0.265 (0.052)

2

 0(+$"')+( +,,U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN / dxľŔŘŝŠľřŞŇŠłĲāĕĠ
L¼¶~Ĝņŀň¶~
TMVA overtraining check for classifier: BDT

1.5

1

0.5

0<0.8<0.6<0.4
FDEK<E<FH<0.2

00.2

0.4

0.6

BDT responseè(ĜL¼ãZĠŊŚŞŀĆĬāxç/ġğ¾ıĮČđį&+¶~ġ3Ĝ¿w

ØĲ'ðČđįK"3K;¦ĠÝ(.-).- 'V
(+$"')+( +,,ĦĐōŞXĠxç/ĲÅĂdČİį3K;¦?," '""'@ĲÎ®ďį

Z exp = ∑i

⎛ Si ⎞2 ( Si + Bi ) ln ⎜1+ ⎟ − 2Si⎝ Bi ⎠Si Ū ōŞĠ3rbi Ū ōŞĠ¿w ØrċĠ3K;¦ĲÝčğďįBrĠöĉĲÅĂ

FDEK<E<FH"LBrèk¶~èĢİĕBr ?èĢİĕöğÏá@&99 -()9  9!"9 9)E?9& 9) G@

G/+,H/+,I/+,J/+,K/+,-(),%-!")ExFd3K;¦: D;JE7

(/+"%,,%-L/+,(/+"%,,%-," '""' 0(+$"')+( +,,ŧ¢ĠBrěxĩĬā¶~ĜĞĘĕĠġ -()ýğ-()Ĳ-ăŨ¢ĠBrěxĩĬā¶~ĜĞĘĕĠ
ġŭ ?G#-Ĝ4ıđĚ@þũĠBrĲèĳĖvěēİ," '""'ĆĆĭĞĈĞįþĝĠBrĲĂąĠMĲÅĂ

AG;FE>?FDEIY@ěĠ·ÎÔUĠħĲ½hčĕ?ċĠvěLPĥĝĠ6Ćaĭİĕ@FDEK<E<FHM

"" '%,-+' -!'+'$"'(+$"')+( +,,FDEK<E<FH

"

ED

¶~3]ZġdĬĮĩĖāģĈ&Ěāįþ %"-"('ğ5ĎÌ}jěŃĶŒŁŞĠ3]ZĩË<:D;MEûD;EK
" '""':G;D
FDEK<E<FH

EE"`ĜĦĜĨŇŠłĠ·Îê¡?GK=E@ğġYĠuĠ¶~ě.'FĠħěG7ğ*æ?1)-@Ġ·ÎêĲ@ĪďċĜěĠÌ}ąĭED P©ZĠfZ6ĆÉÞĦİįŢĦĕÿĞqÂĲÅĘĚāįţĦĜĨNùĠFćĞ¢ĠęěĀĘĕ " ,¯JĆÉęąĘĕ;ýēĠcÚĲÕĤįċĜ
ġéÈĞņŠœěĀį
" ,¯JĜ=*.+$ĜĠT¶4ĠMġēĠěĩéÈĞņŠœĠęxsĠ$[¶~ěġ3]Zġ ĜÝčąĞĮnİčĚāįuĠ¶~ğz_š
FDEK<E<FH

"

EF

ŊŅĻĴŅŐEG"

FDEK<E<FHĞ¿w
3?ŒŁŞîi@lØ?E%)-('@ňŅŐĻĹŠĻPiŝŐňŞĪ ýŒňŕĻ
ĹŠĻĿĸŅň SFĲÈčĚĩĘĚćĚčĦĂþνľŞļŜňŅŐŒŁŞ QĿĸŅňĲčĚÉ¬ĩįÿĞĿĸŉŝŠłĲāĚÔUĲÉ¬ĩį
FDEK<E<FH"

EHĠÉ¬ĩĮĠÉ¬ĩĮğġ$-(+&-!(Ĳ"#-Ĳe$-(+Ĳ)-9 -? @"'ğ&ď,!)ĲÉ¬ĩį

FDEK<E<FH

EI"ĝĠĬĂğBrĲèkďįą

1
0.8
0.6
0.4
0.2
0

1

2

3

4

5

0.1
0.08
0.06
0.04
0.02
0

6

20

40

60

80

100

120

140

×10160mbb [MeV]dRBBĞ¿w ØěĀį--+ġŭĆFćĈĞį6ĆĀĮýQ#-ġRČĈĞį 6ĆĀį 0(+$"')+( +,,×100.12
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

1.2

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN / 0.147

1.4Signal
Background

Input variable:mbb−3(1/N) dN / 3.65e+03 MeV

 0(+$"')+( +,,Input variable: dRBB ŌŅļŀ¯JěĀİĢýEFIßğŎŠĻĆĀį

1BrğĄāĚxĩ3Ĝ¿w ØĠ'ðÀ+Ġúāý&9ĜāĂ ęĠBrĲĦĐèkďįēĠ`ęĐęēĠĠÆĜĞįBrĲ4ıđĚEBêÌ}ĲÅāýxĩĬā¶~ĜĞĘĕBrĲŧ¢ĠBrĜďį
5ĎċĜĲŨ¢íĠBrğPčĚĩÅāýd3K;¦Ć6čĞĈĞįĦě¹ĮàďþFDEK<E<FH"EJEBêÌ}ğāįBrÆďįBrĠÆ10 0(+$"')+( +,,U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.1)%

108642010010200300

400 500600 0(+$"')+( +,,Input variable: dYWH

700 800

1U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%12(1/N) dN / 0.136

Input variable:
Mtop<6(1/N) dN / 1.95e+04 MeV&99 9-()9)9!" &"'9
!"9)E9)F9!" 9) 9&99
?('%2 (+G#-,@?& @?) G@BrĠÆġ.'EĲÜÇ Ĝ -()ġsčĈÛčĕÆBr0.80.6
0.40.20012345dYWH

Mtop [MeV] ŒŁŞĜŌŅļŀŒŁŞĠŚŎŇņĵŠU-()ŒŁŞĜĿĸŅňęĜĠBÚê
EK"FDEK<E<FHBrèk¶~Ŧ ěāĕBrºCĠ:ï×?  @ğďį
BrĲĨįvěġ ·ÎĆ0'ěġĞĈý  ĠvěġŇŠł
êĆ@ăýČĭğ-+.-! - "' ĜāĂjĲQ"ďįċĜěý·ÎĩČĭğ«ĊįĕĨýĬĮEĈĠBrĆèĢİįtĆy)ğĞįþ

 ěġ.'EěčĕBrºğý-()Ĝŭ Ĳâ-ďįċĜĜĞįþ

FDEK<E<FH

"

EL

+,.%-,

EM"
"

FDEK<E<FH
FDEK
K<E
E<FH

"$%"!(("--"' ìrn#NŇŠłĶőŞňrμ3]ZōŞĠd3ĶőŞňrōŞĠd¿w ØĶőŞňrSd3ĶőŞňrBd¿w ØĶőŞňrġ'.",')+&-+,?@Ġìr

FDEK<E<FH

"

ġ>{¡ğġÊ'VĠ¦OZìrĲăįFD+,.%-,FE"

FDEK<E<FH+,.%-,(+$"')+( +,,FDEK<E<FH(+$"')+( +,,"FF"' % (+"-!&ōŞĲ³ĈďİĢōŞğÛčĀĊį3fZġúĈĞįĆýÔUĠ^ôĆFćĈĞį ėīĂĝĬāōŞXğÐMďįbÈĆĀį,:3Ġ# ĶőŞňr
 :¿w ØĠ# ĶőŞňr',:3ĠĀįōŞąĭĀįōŞĦěĠ ĶőŞňr' :¿w ØĠĀįōŞąĭĀįōŞĦěĠ ĶőŞňr
,9 :ŏśŠŋŚŖŠł?ED9I Ć 7ĠÐM@ċĠĆťğĞįĬĂğōŞXĲÐMďį

FDEK<E<FHFG

"((,-?)-"/((,-"' @,"' %","('-+',',"-"/-(,--",-"%%.-.-"(',"'-!-+"'"' -;!"((&"'"' &'29(+(+,-(","('-+,0,)+()(,-((/+(&-!",,-"%"-2)+(%&;
!(+" "'%/'-0" !-,+.,(+-!-+"'"' (-!"+,--+0!"%,.,*.'--+,+&.%-")%"2(&&('((,-0" !- "/24SER8 0!+8 ",-!,.&(0" !-,(-!&",%,,""/'-,"/"2-!-(-%,.&(0" !-,;

FDEK<E<FH

"FH

((,-?)-"/((,-"' @1 N
BDTresponse = ∑ ln(α i )⋅ hiN i
N :.& (+,
αi :" !-,hi :!SE?," '%@!S=E? @FDEK<E<FH

"

FI/+-+"'"'',"-"/"-2-(%.-.-"(',"'-!-+"'"' -",$'(0,(/+=-+"'"' ;,"&)%02-(&,.+-!&(.'-((/+=-+"'"' ",-((&)+-!)+(+&'+,.%-,-0'-!"')''-+"'"' '-,,&)%,;FDEK<E<FH"FJ

0123450.04
0.02
406080100 120

0.2
000.5

11.5

22.5

Input variable:
pTB1<6102015
1050200250300

350

1086426080

108642

Input variable:
MET<6(1/N) dN / 0.136(1/N) dN / 8.2e+03 MeV

00050

1234

FDEK<E<FH

100150200250300

103501210108642010010200300

400 500

600700 800

Mtop [MeV]10876543211005 0(+$"')+( +,,U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.24mTW [MeV]

10.4

61020 40 60 80 100 120 140 160 180 200 220

0Input variable: dYWH

0.68Input variable:
Mtop<6pTB2 [MeV]

0.8

10pTB1 [MeV]1210100 120 140 160 180

Br'V32

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

122.2 2.4 2.6 2.8

1010450400

1014(1/N) dN / 5.51e+03 MeV

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN / 4.04e+03 MeV

142dPhiVBB

Input variable:
mTW<61016

1.4 1.6 1.8pTV [MeV]

1840025

3

Input variable:
pTB2<602140 160

Input variable:
pTV<6dPhiLBmin

204(1/N) dN / 7.75e+03 MeV

0.4

6U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.68(1/N) dN / 7.69e+03 MeV

1.2
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN / 0.0805

Input variable: dPhiLBmin

0.810mBB [MeV]dRBB

1121006(1/N) dN / 0.0465

0.06

U/O-flow (S,B): (0.0, 0.5)% / (0.0, 0.0)%

0.2

0.08

14

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

0.40.1

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.1)%

0.6

Br'V
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%

10.8

Input variable: dPhiVBB

100.12(1/N) dN / 1.95e+04 MeV

1.2(1/N) dN / 3.93e+03 MeV

Input variable:mBB<3Signal
Background1.4

U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN / 0.147

Input variable: dRBB

50100

150200250300FK"

MET [MeV]

dYWH

Br5AĠť!£ì
Correlation Matrix (background)

Correlation Matrix (signal)
Linear correlation coefficients in %MET-33dYWH

5103564427-6393100-2-5-6-4-3-911 100

3713385

3100

1139

3100

3-9-640385-32733-44456

Mtop -73

81752-5-5-4-10pTB2 -67

9942473100

pTB1 -33

1517883 100

336 100mTWpTV-63

1122dPhiLBmin -64-1915 100

dPhiVBB -19mBB

834771-636842 -1052-5

31522179-417-29-1911159-5838 -19 -64 -63 -33-67-5-73-1 10038 100dRBB 100-1dRB mB dPh dPh pTV
BiVB iLBmB
BinpTB

1105Linear correlation coefficients in %100

9116-23dYWH-1

48Mtop -34-13

1045mTW

67-320pTB22735-70pTB150

50

13 -5361 100<20pTV

4158-5100<40dPhiLBmin -73-60

15 100-5dPhiVBB -13-5100

1581384 100-5-601584 -13 -73

4MET

8060

<60<80-33pTB mT Mto dYW MEp2
WH TmBB

8dRBB 100

<100100

2911183

3100-4-5-822 100

331-732-3100

223-24-555100-3-81840-272243 100

532-51120

43

5-7-429061

22-53141<20-53-27 -24

45

8-23

<40-7-3104650

35

7-13-11150

276-3441

dRB mB dPh dPh pTV
BiVB iLBm
B
B
inpTB

1

80
60

<60
<808pTB mT Mto dYW ME
p2WH T<100 0(+$"')+( +,,FDEK<E<FH

"FL/+-+"'"' !$2.5

 0(+$"')+( +,,Signal (test sample)

Signal (training sample)

Background (test sample)

Background (training sample)

Kolmogorov-Smirnov test: signal (background) probability = 0.003 (0.171)

2
U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%(1/N) dN / dx

TMVA overtraining check for classifier: BDT

1.5
10.5
0
<1

<0.8

<0.6

<0.4

<0.2

00.2

0.4

0.6

BDT response

FDEK<E<FH

"

FM

(+("% ! ))+-.

FDEK<E<FH

"

GD

''+-+$+--(+,FDEK<E<FH

"

GE

-.%"-2+&0(+$' 9 -*.%"-2",,,,,2!$"' !",-( +&('-'-'(&)+"'  "',-++'!",-( +&,(-! ('%"' '(%"';!+,.%-,(-!!$,9%(' 0"-!"'(+&-"(' +(&-!--(+('-+(%2,-&?/(%- 9 -&)+-.+,9
-;@9+.,-(-+&"' -!,--.,(!--(+FDEK<E<FH

"GFt6ąĭÉİĢ'ð2š

t6ąĭĖĉěġ
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FDEK<E<FH

; -( ?,.$.@"GGÖ" ,FDEK<E<FH;Ġ±¯JLĠµħóWği,čĚāįÖ°þċİġýÁğK;ďįò§£ ş\ā£ş]ā£ şé+£ Ġ HęĠ%é+£ DĠ GęĠ£ ĲóWğÂĈÏáčĚāįþÖĲiďį¯Jġýğ Gªøğ'ĉĭİįþÚĲiďį¯Jý 5£ ĲIďį¯JýĠ±¯JğÚêĲmĕđ
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ŚļŚŞĿĴŞOZĲ
2
1
LQED = Dμφ − Fμν F μν −V (φ )4Dμ = ∂μ + ieAμFμν = ∂μ Aν − ∂ν Aμ9

6ġò§?ý3ġŀĺŚŠ?
?E@ĽŠĿBpğPčĚφ (x) → φ ′(x) = eiα ( x )φ (x)1Aμ (x) → Aμ′ (x) = Aμ (x) − ∂μα (x)eBğčĬĂĜďįĜýÚêõĠQ"ĆÑČİĞāčąčýNïğġ<ġÚêĲmęĞĒąŬŬ"

FDEK<E<FHGIŌŅļŀ?F@Ħě½hčĕŚļŚŞĿĴŞOZ21 α 1g′
L = Dμφ − Aμν− Bμν B μν −V (φ ) 9 Dμ = ∂μ + igAμaτ a − i Bμ244ŌŅļŀ?
ļŀ?
⎞1⎛
0⎟
ϕ (x) = ⎜⎜2 ⎝ υ + h(x) ⎟⎠Dμφ2

⎞′⎞
⎛
1⎛
1100⎟⎟ (∂μ + gAμaτ a + g′Bμ )(∂μ + gAμbμτ b + g′Bμ ) ⎜⎜⎟⎟
= ⎜⎜2 ⎝ υ + h(x) ⎠22⎝ υ + h(x) ⎠1
1= (∂μ h(x))2 + (υ + h(x))2 [g 2 (Aμ1 )2 + g 2 (Aμ2 )2 + (−gAμ3 + g′Bμ )2 ]82ķĵŠĻŒŁŞĠ?Ĳ
1Wμ± =(Aμ1 ∓ Aμ2 )21(gAμ3 + g′Bμ )Z μ (x) =22g + g′Á¡P¨cĠ¥İğĬĘĚ¤­z_ /ĲmėýċİğĬĮĽŠĿB
cĲ¸mčĞĆĭýķĵŠĻŒŁŞğÚ
11L = (∂μ h(x))2 + (1+ h(x) / υ )[mW2 W + μWμ− + mZ2 Z μ Z μ ] êĲmĕđį22

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