Investigating B τν τ New Statistical Techniques. Matthew Barrett Dept of Electronic and Computer Engineering Brunel University

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1 Investigating B τν τ at Ba Ba r with New Statistical Techniques Matthew Barrett Dept of Electronic and Computer Engineering Brunel University

2 Outline of Talk "#$%&%&'$()*#'+,#-./ 0τν 1$2"3$+4$+.$+-.#'#4.+-56$ 789$.8$4.:;3$0τν. <:''#-.$=#&4:'#,#-.4$>'8,$%&%&'$&-;$ 4.&.+4.+B&?$.#B"-+C:#4/ "#$>:.:'#$>8'$%&%&'$&-;$D#38-;/// "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#,

3 The Experiment "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, 9

4 The <"#'#-G8A$'&;+&.+8- J?:)$I#.:'- EF$ $E+?+B8-$ F#'.#)$'&BG#' H<7$1$H'+>.$<7&,D#' <#-.'#$8>$=&44$ (-#'53$R$ KQ/LSO#F/ =&44$8>$TUVEW/ # M $ N/KO#F # $ P/Q$O#F K/L$,&5-#. (=<$1$ (?#B.'8,&5-#.+B$ <&?8'+,#.#' X:4.$&D8A#$."'#4"8?;$>8'$%%$ *'8;:B.+8-/ %$,#48-4$&?,84.$ &.$'#4./ βγ$r$q/ly "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, :

5 The Experiment %&%&'$4.&'.#; ;&.&$.&G+-5Z$KPPP/ 2+??$>+-+4"$8- [*'+?$\$]QQS/ [>.#'$':--+-5$8-$ TUNEW$&-;$TU]EW/ ^>>$_#&GZ$VQ$=#F$ D#?89$TUVEW/ `8$%$,#48-4$ *'8;:B#;/ =&44$8>$TUNEW$R KQ/NLLO#FaB ] / "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, ;

6 Why Study"" τν? _"34+B4$,8.+A&.#;$D3$8-#$#C:&.+8-Z _&'&,#.#'4$8>$`8.#Z # $1$$$,#48-$;#B&3$B8-4.&-./$ <&-$8-?3$&BB#44$A+&$*:'#?3$?#*.8-+B$$;#B&34/ <:''#-.$A&?:#$>'8,$b&..+B#$c<HZ$ f % $R$UKSP$±$]\W$=#F "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, <

7 Why Study"" τν? _"34+B4$,8.+A&.#;$D3$8-#$#C:&.+8-Z _&'&,#.#'4$8>$`8.#Z =&44$8>$;&:5".#'$?#*.8-$$ l / b#&;4$.8$"#?+b+.3$4:**'#44+8-z$ $$$$$$$$$$$$$$$$$$$$τ : µ :$$% $$$$$$$$$$$$$$$$$$$$K$Z$L KQ dn $ Z$KQ d\ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, =

8 Why Study"" τν? _"34+B4$,8.+A&.#;$D3$8-#$#C:&.+8-Z _&'&,#.#'4$8>$`8.#Z & '( $1$<e=$,&.'+)$#?#,#-./$ <:''#-.$_HO$A&?:#Z$ f& :D f$r$uv/nk$±$q/nqw$ $KQ 1N / Β,#48-$84B+??&.+8-$>'#C:#-B3Z$, ; $$ $> %] $ff.; f ]. BU%$ τνwa$, ;$ $ $ f& :D f] af&.; f ] "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#,.

9 And Beyond the Standard Model? [;;+.+8-&?$J#3-,&-$;+&5'&,$>'8,$7+554$D848-Z M "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, "

10 And Beyond the Standard Model? [;;+.+8-&?$J#3-,&-$;+&5'&,$>'8,$7+554$D848-Z M 98$7+554$H8:D?#.$=8;#?$U]7H=W$&-;$=+-+,&?$ E:*#'43,,#.'3$U=EE=W$?#&;$.8$,8;+>+#;$%'&-B"+-5$ >'&B.+8-Z$$ 2/E/78:$_IH$VS$]NV]$UKPPNW.&-$β$1$'&.+8$8>$A&B::,$#)*#B.&.+8-$A&?:#4/ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, >-

11 How to look for B τν ()*#'+,#-.&??3$B"&??#-5+-5Z 98$8'$"'##$-#:.'+-84$+-$>+-&?$4.&.#/ ^-?3$'#B8-4.':B.$τ$;&:5".#'4/ b&bg$8>$g+-#,&.+b$b8-4.'&+-.4/ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, >>

12 How to look for B τν I#B8+?$[-&?34+4$.#B"-+C:#Z J:??3$I#B8-4.':B.$."#$8."#'$%$1$% '#B8 / "+4$B8-4.'&+-4$."#$4+5-&?$%$1$% '#B8+? / 98$;+>>#'#-.$.3*#4Z 7&;'8-+B$.&5Z )*$U*$R$7&;'8-4$ 1$π ± g$π Q g$+ ± g$+ E W$ E#,+b#*.8-+B$.&5hZ )lν*"u*$r$γg$π Q g$8'$-8."+-5w h>:??3$'#b8-4.':b.$#)b#*.$."#$-#:.'+-8/ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, >

13 How to look for B τν I#B8+?$[-&?34+4$.#B"-+C:#Z J:??3$I#B8-4.':B.$."#$8."#'$%$1$% '#B8 / "+4$B8-4.'&+-4$."#$4+5-&?$%$1$% '#B8+? / 98$;+>>#'#-.$.3*#4Z 7&;'8-+B$.&5Z )*$U*$R$7&;'8-4$ 1$π ± g$π Q g$+ ± g$+ E W$ E#,+b#*.8-+B$.&5hZ )lν*"u*$r$γg$π Q g$8'$-8."+-5w h>:??3$'#b8-4.':b.$#)b#*.$."#$-#:.'+-8/ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, >9

14 How to look for B τν τ$+4$'#b8-4.':b.#;$+-$>+a#$,8;#4z τ e ν e ν τ $ τ µ ν µ ν τ τ π ν τ $ τ ρ (π π 0 )ν τ (τ a 1 (π + π π )ν τ ) " #$%#&'()#*%+,#$'#-&%.#/+0+'.#'()%$%1 "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, >:

15 The E Extra Variable =84.$;+4B'+,+-&.+-5$A&'+&D?#$&A&+?&D?#/ E:,$8>$(-#'53$;#*84+.#;$+-$<&?8'+,#.#'g$."&.$+4$-8.$&..'+D:.#;$.8$&-3$'#B8-4.':B.#;$*&'.+B?#/ E"8:?;$D#$UB?84#$.8W$i#'8$>8'$.':#$4+5-&?$#A#-.4/ %&BG5'8:-;$.3*+B&??3$,:B"$"+5"#'/ j4#;$.8$;#>+-#$4+5-&?$d8)/ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, >;

16 Current Results "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, ><

17 Semileptonic Tags $_"34/$I#A/$H$\Yg$QL]QQ]$U]QQ\W j4#;$nsn$)$kq Y $%%$*&+'4/ <&''3$8:.$b+G#?+"88;$>+.$.8$3+#?;$ +-$>8:'$.&:$B"&--#?4/ $BU τνwr$uq/p$±$q/yu4.&.w$±$ Q/KU434.WW$)$KQ V / PQk$<b$jbZ$BU τνwl$k/\$)$kq V /$ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, >=

18 Hadronic Tags [?48$:4#4$NSN$)$KQ Y $%%$*&+'4/ =#&4:'#;$%'&-B"+-5$>'&B.+8-Z PQk$<b$j**#'$b+,+.Z BU τνw$l$n/v$ $KQ V /$ B &?48$B&?B:?&.#;$>'8,$?+G#?+"88;$'&.+8$>+.$.8$."#$ +-;+A+;:&?$.&:$B"&--#?$3+#?;4/ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, >.

19 &'m+azq\qy/]qnq Combined Result <8,D+-#$4#,+?#*.8-+B$&-;$ "&;'8-+B$'#4:?.4/ E.&.+4.+B&??3$+-;#*#-;#-./ ().#-;$?+G#?+"88;$'&.+8$.#B"-+C:#$:4#;$+-$D8."$.8$ ;#.#',+-#$B8,D+-#;$'#4:?./ <#-.'&?$A&?:#Z ]/Yσ$4+5-+>+B&-B#$+-B?:;+-5$:-B#'.&+-.3$8-$D&BG5'8:-;/ UN/]σ$+>$."+4$+4$8,+..#;/W %#??#$'#4:?.Z$$$$ _Ib$P\g$]LKSQ]$U]QQYW E=$*'#;+B.+8-Z$K/Y$ $KQ V "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, >"

20 Constraint on Unitarity Triangle <8,D+-#$% τν$9+."$, ; $,#&4:'#,#-.4$.8$B8-4.'&+-$ <e=$'&.+8$ff :D faff.; f/ # "B&-B#?4$1$?#&4.$9#??$G-89-$ A&?:#/ E"89-$&4$&$5'&*"+B&?$B8-4.'&+-.$ 8-$j-+.&'+.3$'+&-5?#/ <8-4+4.#-.$9+."$E=/ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, -

21 Implications for New Physics ()B?:4+8-4$+-$, 7$.&-$β$*?&-#/, 7 $1$<"&'5#;$7+554$,&44/ τν.&-$β$1$'&.+8$8>$a/#/a/$8>$ ]7H/$ _?8.4$4"89-$>8'$'#5+8-$&D8A#$ ;+'#B.$4#&'B"$?+,+.$>'8,$b(_/ <&-$D#$B8,D+-#;$9+."$,#&4:'#,#-.$8>$D,γ/ τν$m$d,γ τν,8'#$:4#>:?$&.$"+5"#'$ A&?:#4$8>$.&-$β/ _?8.4$>'8,$E/$E#G:?& "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, >

22 Multivariate Analysis "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#,

23 Multivariate Analysis j4#$&$b8,d+-&.+8-$8>$,&-3$a&'+&d?#4$.8$4#?#b.$#a#-.4/ =&G#$:4#$8>$B8''#?&.+8-4$D#.9##-$A&'+&D?#4/ j4#$b8,d+-&.+8-$8>$9#&g?3$b?&44+>3+-5$a&'+&d?#4$."&.$ B8:?;$-8.$D#$B:.$8-/ ()&,*?#4$8>$=:?.+A&'+&.#$<?&44+>+#'4$+-B?:;#Z J+4"#'$H+4B'+,+-&-.g$`#:'&?$`#. "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, 9

24 Multivariate Analysis Packages 98$*&BG&5#4$B8,,8-?3$:4#;$+-$_&'.+B?#$_"34+B4/ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$88?G+.$>8'$=:?.+F&'+&.#$[-&?34+4Z "..*Zaa.,A&/48:'B#>8'5#/-#.a E.&._&..#'-I#B Z "..*4Zaa48:'B#>8'5#/-#.a*'8n#B.4a4.&.*&.'#B J:??3$B8,*&.+D?#$9+."$I^^/ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, :

25 General Strategy for MVA "#$B"84#-$B?&44+>+#'$,:4.$D#$.'&+-#;/ "'##$4.#*4$1$;+A+;#$&A&+?&D?#$;&.&$U.3*+B&??3$=8-.#d <&'?8W$+-.8$."'##$;&.&4#.4/ '&+-+-5 F&?+;&.+8-$1$B"#BGg$&-;$8*.+,+4#$.'&+-+-5$*&'&,#.#'4/ #4.+-5$1$'#&?+4.+B$#A&?:&.+8-$8>$*#'>8',&-B#/ ()&,*?#$;+A+4+8-$8>$;&.&Z$$LQkZ]LkZ]Lk/ E#*&'&.#$4&,*?#4$'#;:B#4$;&-5#'$8>$8A#'d.'&+-+-5/ #4.+-5$4&,*?#$:4#;$>8'$&??$*#'>8',&-B#$*?8.4$4"89-/ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, ;

26 Decision Tree "#$%$&'()*""(+"*,&*-%(-.'/( #0)%(&'($'+0)(1.*$.23"%4 5"+.*.)"("1"')%($')&(6'&7"%89(((( %$:'.3;3$<"(&*( 2.#<:*&0'7;3$<"4 =""+(%+3$))$':>(0')$3('&( '"?('&7"%(#.'(2" #.33"7(63".1"%84 EZ$KL$%ZQ] E+5-&? A".,(%$B"($%(-&%)($-+&*).')( )*.$'$':(1.*$.23"4 EZ$V\$%Z]K 3$l$SY/] EZ$QP$%ZKL %&BG5'8:-; EZ$LQ$%Z$LQ )$o$]/n EZ$N]$%ZKP i$l$1k/] EZ$QN$%Z]P %&BG5'8:-; EZ$]N$%ZQV E+5-&? "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, <

27 Boosted Decision Tree C&&%)$':(D( &1"*(.(%+"#$,$"7('0-2"*(&,(#/#3"%9 $'#*".%"((?"$:E)(&,(-$%#3.%%$,$"7("1"')% 7"#*".%"(?"$:E)(&,(#&**"#)3/(#3.%%$,$"7("1"')%4 F'#*".%"%(+*"7$#)$1"(+&?"*4 C&&%)"7(7"#$%$&'()*""(#.'('&( 3&':"*(2"(".%$3/(1$%0.3$%"74 G71.').:"%9( H.'(#&+"(?$)E(1"*/(#&**"3.)"7( 1.*$.23"%(.'7(0%"3"%%($'+0)%4 I&(6H0*%"(&,(7$-"'%$&'.3$)/84 "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, =

28 Bagging and Random Forests %88.4.'&**+-5$1$4&,*?+-5$9+."$'#*?&B#,#-./ '&+-$B?&44+>+#'4$8-$D88.4.'&*$'#*?+B&4$8>$.'&+-+-5$;&.&/ ^A#'&??$'#4*8-4#$+4$&A#'&5#$8>$#&B"$B?&44+>+#'$.'&+-+-5/ %88.4.'&**+-5$."#$+-*:.$;+,#-4+8-4$UA&'+&D?#4W$&4$9#??$ +4$B&??#;$&$I&-;8,$J8'#4./ -:,D#'$8>$+-*:.$;+,#-4+8-4$.8$4&,*?#/$ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#,.

29 Using a Boosted Decision Tree for$0τν j4#$&$%h$.8$b?&44+>3$#a#-.4/ =8-.#d<&'?8$H+4.'+D:.+8-4$ '&+-$>8'$#&B"$τ$,8;#/ j4#$,&-3$9#&g?3$;+4b'+,+-&.+-5 A&'+&D?#4$4:B"$&4Z ρg$& K $B&-;+;&.#$,&44g (A#-.4 "#$%&' (&)*$+,-%. =8,#-.:,$8>$τ$;&:5".#'g B84$θ,+44 ///$ j4#$kkdks$a&'+&d?#4$+-$.'&+-+-5 Uτ$,8;#$;#*#-;#-.W/ %H$8:.*:. - ().'& $+4$-8.$:4#;g$48$+.$B&-$D#$&-&?34#;$4#*&'&.#?3/ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, "

30 Using a Boosted Decision Tree for$0τν I&9$4+5-&?aD&BG5'8:-;$ ;+4.'+D:.+8-$-8.$,84.$:4#>:?/ <&?B:?&.#$E+5-&?$(>>+B+#-B3$&-; %&BG5'8:-;$'#n#B.+8-$>8'$ ;+>>#'#-.$B:.4/$ _?8.$E+5-&?$(>>+B+#-B3$&5&+-4.$ %&BG5'8:-;$'#n#B.+8-/ F#'3$"+5"$D&BG5'8:-;$'#n#B.+8- B&-$D#$8D.&+-#;Z [.$B84.$8>$?89#'$4+5-&?$ #>>+B+#-B3/$ (A#-.4 =8-.#d<&'?8$H+4.'+D:.+8-4$ "#$%&' (&)*$+,-%. %H$8:.*:. "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, 9-

31 Using a Boosted Decision Tree for$0τν E.&-;&';$B:.4$*#'>8',$A#'3$ 9#??$+-$#?#B.'8-$,8;#$1$A#'3$ ;+>>+B:?.$.8$D#&.$9+."$=F[/ =8-.#d<&'?8$H+4.'+D:.+8-4$ "#$8."#'$τ$;#B&3$,8;#4$4"89 48,#$*'8,+4#$8>$+,*'8A#,#-.$ :4+-5$=F[/$ (A#-.4 "#$%&' (&)*$+,-%. %H$8:.*:. "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, 9>

32 Visualisation of Parameters =:?.+d;+,#-4+8-&?$*'8d?#,4$&'#$;+>>+b:?.$.8$a+4:&?+4#/ =8'#$;+,#-4+8-4$0$=8'#$H+>>+B:?.$.8$A+4:&?+4#/ _&'&??#?$<88';+-&.#4$&'#$&$A+4:&?+4&.+8-$,#."8;/ ^-#$U*&'&??#?W$&)+4$>8'$#&B"$A&'+&D?#/ (&B"$#A#-.$+4$'#*'#4#-.#;$D3$&$?+-#/ %&BG5'8:-;$.3*#4$'#*'#4#-.#;$D3$&$;+>>#'#-.$B8?8:'4/ <8?8:'$EB"#,#$:4#;$+-$*?8.4Z $$$$$$$$$$$$$$$$$$$$$$E+5-&?$:;4$BB$% Q % Q $% M % d [A&+?&D?#$+-$I^^$L/K\$U&-;$&D8A#W/ ()&,*?#$+4$4"89-$>8'$A&'+&D?#4$>8'$π$,8;#/ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, 9

33 Example for π Variables "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, 99

34 Signal Only "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, 9:

35 Light Continuum (uds) Only "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, 9;

36 All MC types "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, 9<

37 Prospects %&%&'$"&4$B8??#B.#;$+.4$>:??$;&.&4#.$8>$TUVEW$;#B&34/ "#$-#).$4#.4$8>$&-&?34#4$B&''+#;$8:.$&+,$.8$D#$."#$ ;#>+-+.+A#$%&%&'$&-&?34#4/ 28'G$+4$ $.8$+-B8'*8'&.#$&4$,&-3$+,*'8A#,#-.4$ &4$*844+D?#$;:'+-5$."+4$+-.#-4#$&-&?34+4$*#'+8;/ % τν$9+??$b8-.+-:#$.8$d#$&$4:dn#b.$8>$5'#&.$+-.#'#4.$&.$ *8.#-.+&?$&.$."#$-#).$5#-#'&.+8-$8>$*'8*84#;$ %d>&b.8'+#4z$$e:*#'%$&-;$e:*#'e(e%/ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, 9=

38 Summary "#$;#B&3" τν$b&-$d#$:4#;$.8$,#&4:'#$*&'&,#.#'4$ :-&A&+?&D?#$.8$8."#'$%$;#B&34g$&-;$.8$B8-4.'&+-$."#$ 7+554$4#B.8'/ %&D&'$&-;$%#??#$"&A#$4##-$#A+;#-B#$8>$."+4$;#B&3/ `#9$,#."8;4$B8:?;$"8*#>:??3$,8A#$."+4$$B?84#'$.8$&$ ;+4B8A#'3/ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, 9.

39 Back-Up Slides "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, 9"

40 TU-EW Physics &G#-$NQ>D dk $&.$TUNEW$'#48-&-B#g$rPQ=$TUNEW$#A#-.4/ rkq $."#$*'#A+8:4$?&'5#4.$4&,*?#/$ &G#$]Q>D dk $&.$."#$TU]EW$'#48-&-B#g$rKVQ=$#A#-.4/ E.&-;&';$=8;#?Z E#&'B"$>8'$-#9$4.&.#4s %8..8,8-+:,$E*#B.'84B8*3/ %#38-;$."#$E.&-;&';$=8;#?Z b89$,&44$7+554/ b#*.8-$j?&a8:'$a+8?&.+8-/ b89$,&44$h&'g$=&..#' "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, :-

41 TU-EW Physics - Bottomonium E8?+;$?+-#4Z$$ H+4B8A#'#;/ H&4"#;$?+-#4Z$$ _'#;+B.#;/ =84.$*'#;+B.#;$ 4.&.#4$&BB#44+D?#/ e-89-$4.&.#4$"&a#$ >#9$,#&4:'#;$ D'&-B"+-5$ >'&B.+8-4/$ "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, :>

42 TU-EW Physics Light Higgs I#B#-.$98'G$+-$`=EE=$+-.#'#4.#;$+-$?89$,&44$<_d8;;$ 7+554$U&W/ [A8+;4$;+'#B.$b(_$B8-4.'&+-.4/ π π 28:?;$;#B&3$.8$ττg$?+5". "&;'8-4$8'$B"&',#;$"&;'8-4 ;#*#-;+-5$8-$,&44/ # M # 1 TUNEW 7+??#'g$"#*d*"aQVQV]]Q TUKEW H#',+4#Gg$O:-+8-g$=B(?'&."g$"#*d*"aQYK]QNK γ & "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, :

43 TU-EW Physics - Leptons =#&4:'#$?#*.8-+B$;#B&34$8>$TU-EW/ H+>>#'#-.$'&.#4$>8'$#/5/$BUTU-EWW $τ M τ 1 $&-;$ BUTU-EWW $µ M µ 1 $$98:?;$D#$;#*&'.:'#$>'8,$b#*.8-$ j-+a#'4&?+.3/ <8:?;$D#$B&:4#;$D3$?89$,&44$7+554/ [?48$4#&'B"$>8'$?#*.8-$>?&A8:'$A+8?&.+8-g$#/5/ BUTUNEWW $τ M µ 1 / "#$%&'()*+),%--. /0%1+))'##%2%1)*3'4%5367')86#, :9

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