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Nuclear Physics B (Proc. Suppl.) 156 (2006) 203–206 0920-5632/$ – see front matter © 2006 Elsevier B.V. All rights reserved. www.elsevierphysics.com doi:10.1016/j.nuclphysbps.2006.02.129

Strategies for combating systematics at LHCb

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Page 1: Strategies for combating systematics at LHCb

� � � � � � � � � � � � � � � � � � � " � � � � � � � � � ) + - �/ 0 2 4 5 7 9 5 : ; = : ?

@ = A B C D F G H J H = 7 7 M J = A M B 5 = :? R : 5 S D A ; 5 B 2 = X Y [ X = A ^ ` a D : 2 ; 4 5 7 9 5 : ; = : c 0 5 7 ^ 5 : d ` e D J 7 D g = M ^ ` Y [ X = A ^ ` Y i j k g G ` R : 5 B D ^ e 5 : d ^ = m

n p q r s t u s v p s w p y z p | } ~ � � q � � � z � s � z � � � s z r � � s � s � p r � � ~ � � q � � z p q � � � � r s � � z � � s r � q p y s t v s � � s � p r p z p q r p q v z �u � s v q r q � � � � � � w v � � p � � � � � r � r p s � z p q v s � s v p r q r p y s � s � � � s s r r s � p q z � � n p q r w q r v � r r s w y � � p y q r v y z � � s � � s � q � � � s � s p �� � u y z r q r q r � q � s � p � p y s u � � � � s � � � � s z r � � q � � p y s � z � � � � p z � � q � � u s � � � � � z � v s � � r � � � z � � q r z � r � u � s r s � p s w � �

p y s � � p u � p r p � s z � r � y q v y � q � � � s � r s w p � v z � q � � z p s p y s u � � u s � p q � s � s r � � � p q � � z � w u z � p q v � s q w s � p q   v z p q � � �¡ ¢ £ ¤ ¥ ¦ ¨ © ª ¬ ¥ £ ¨ ¤

F G H J ® 5 7 7 M ¯ ¯ 0 m 0 7 M B D S D A 2 C 5 d C ; B M B 5 ; B 5 ¯ ; 5 :M ® 5 ^ D A M : d D = X ¯ C M : : D 7 ; ; D : ; 5 B 5 S D B = H ² S 5 = 7 M ´

B 5 = : ¶ @ = A D [ M m · 7 D ` = S D A ¸ ¹ ¹ 9 B A 5 d d D A D ^ M : ^ A D ´¯ = : ; B A 0 ¯ B D ^ D S D : B ; ® 5 7 7 J D M ¯ ¯ 0 m 0 7 M B D ^ 5 : = : D: = m 5 : M 7 2 D M A = X = · D A M B 5 = : 5 : B C D ¯ C M : : D 7 ½ ¾ ¿

À Á Â Ã Ä Ä Å Æ ¾Ç È j É ¶ Ê : = A ^ D A : = B B = ¯ = m · A = m 5 ; D B C 5 ;; B M B 5 ; B 5 ¯ M 7 · A D ¯ 5 ; 5 = : ` D [ ¯ D 7 7 D : B ; 2 ; B D m M B 5 ¯ ¯ = : B A = 7

5 ; A D Ë 0 5 A D ^ ¶Ì 2 ; B D m M B 5 ¯ ¯ C M 7 7 D : d D ; m 0 ; B J D = S D A ¯ = m D 5 :

m M : 2 M A D M ; ¶ G D A D · A D 7 5 m 5 : M A 2 ; B 0 ^ 5 D ; M A D · A D ´; D : B D ^ ® C 5 ¯ C M ^ ^ A D ; ; B C D · A = J 7 D m = X m D M ; 0 A 5 : d

B C D Ñ M S = 0 A B M d d 5 : d · D A X = A m M : ¯ D ` M : D ; ; D : B 5 M 7 5 : ´d A D ^ 5 D : B 5 : B 5 m D ´ ^ D · D : ^ D : B H ² M ; 2 m m D B A 2 m D M ´; 0 A D m D : B ; ¶ Ó J A 5 D X ; 0 m m M A 2 5 ; M 7 ; = d 5 S D : = X B C DC 5 d C ; B M B 5 ; B 5 ¯ ; ¯ = : B A = 7 ¯ C M : : D 7 ; B A D M m ; ® C 5 ¯ C ® 5 7 7J D = 0 B · 0 B J 2 B C D C 5 d C 7 D S D 7 B A 5 d d D A ` 5 : = A ^ D A B =C D 7 · ® 5 B C = B C D A ¯ M 7 5 J A M B 5 = : B M ; 9 ; ¶

Õ ¢ ¬ Ö × £ Ø ¦ Ö ¥ £ ¨ ¤ ¨ Ù ¥ Û Ü Ù × Ö Þ ¨ ª ¦¥ Ö ß ß £ ¤ ß

Õ ¢ ¡ ¢ ¬ à á â ã à ä ¬ å æ á á ç ä èÊ : m D M ; 0 A 5 : d M B 5 m D ´ ^ D · D : ^ D : B H ² M ; 2 m m D B A 2

5 B 5 ; : D ¯ D ; ; M A 2 B = 9 : = ® ® C D B C D A B C D 5 : 5 B 5 M 7 ; B M B D = XB C D m D ; = : = X 5 : B D A D ; B ¯ = : B M 5 : D ^ M é = A M é Ë 0 M A 9 ¶ê C D · A = ¯ D ^ 0 A D J 2 ® C 5 ¯ C B C 5 ; 5 ; ^ = : D 5 ; 9 : = ® : M ;

ë ì í î ï ð ñ ì ò ò ó õ ò ¶ Ê : F G H J Ñ M S = 0 A B M d d 5 : d 5 ; · D A ´X = A m D ^ B C A = 0 d C M ¯ = m J 5 : M B 5 = : = X ; D S D A M 7 m D B C ´= ^ ; ¶ ê C D ; D 5 : ¯ 7 0 ^ D 7 D · B = : ; M : ^ 9 M = : ; X A = m B C D

ö = B C D A ÷ c 5 : B C D D S D : B ` ö ; M m D ; 5 ^ D ÷ · 5 = : ; Ã 9 M = : ; ÅM ; ; = ¯ 5 M B D ^ ® 5 B C B C D X A M d m D : B M B 5 = : · A = ¯ D ; ; ® C 5 ¯ C· A = ^ 0 ¯ D ^ B C D ½ ¾ Ã ½ ¾ù Å = X 5 : B D A D ; B ` M : ^ S D A B D [ M : ^

ú D B ¯ C M A d D B M d ; ¶Ê : · A M ¯ B 5 ¯ D ` Ñ M S = 0 A B M d d 5 : d 5 ; : = B · D A X D ¯ B ` M : ^

m 5 ; B M d ; ® 5 7 7 = ¯ ¯ 0 A ® 5 B C ; = m D · A = J M J 5 7 5 B 2 ` 0 ; 0 M 7 7 2^ D û : D ^ M ; ü ¶ ê C D ¯ = : ; D Ë 0 D : ¯ D = X m 5 ; B M d ; 5 ; B C M B

B C D = J ; D A S D ^ M ; 2 m m D B A 2 5 ; ^ 5 7 0 B D ^ J 2 M X M ¯ B = AÃ j þ ¸ ü Å ® 5 B C A D ; · D ¯ B B = B C D B A 0 D M ; 2 m m D B A 2 ¶ Ê :

= A ^ D A B = D [ B A M ¯ B B C D 0 : ^ D A 7 2 5 : d · C 2 ; 5 ¯ ; 5 B 5 ; B C 0 ;: D ¯ D ; ; M A 2 B = 9 : = ® B C D S M 7 0 D = X ü ¶ / 5 S D : B C D D [ ´· D ¯ B D ^ ; B M B 5 ; B 5 ¯ M 7 · A D ¯ 5 ; 5 = : = : B C D H ² M ; 2 m m D ´

B A 5 D ; X = A B C D m = ; B 5 m · = A B M : B ¯ C M : : D 7 ; ` 5 B ¯ M : J DD ; B 5 m M B D ^ B C M B ü m 0 ; B J D 9 : = ® : ® 5 B C M A D 7 M B 5 S D· A D ¯ 5 ; 5 = : = X J D B B D A B C M : j � 5 : = A ^ D A : = B B = ¯ = : ´B A 5 J 0 B D M ^ = m 5 : M : B D A A = A ¶

ê C D m 5 ; B M d A M B D ¯ M : J D m D M ; 0 A D ^ ^ 5 A D ¯ B 7 2 X A = m¯ = : B A = 7 ¯ C M : : D 7 ; ® 5 B C M Ñ M S = 0 A ; · D ¯ 5 û ¯ û : M 7 ; B M B D ¶ê C D ; D 5 : ¯ 7 0 ^ D ½ � ¿ À Á Â Æ � ` ½ ¾ ¿ À Á Â Æ � ¾ M : ^½ ¾ù ¿ � �ù � ¶ G = ® D S D A ` 5 : ; 5 m 0 7 M B 5 = : ; B 0 ^ 5 D ; B C D

S M 7 0 D ; = X B C D m 5 ; B M d ; m D M ; 0 A D ^ = : B C D ; D ¯ = : B A = 7¯ C M : : D 7 ; M A D X = 0 : ^ B = ^ 5 D A X A = m D M ¯ C = B C D A ` M : ^

X A = m B C = ; D S M 7 0 D ; m D M ; 0 A D ^ = : ; 5 d : M 7 ¯ C M : : D 7 ; 0 ; ´5 : d B A 0 B C 5 : X = A m M B 5 = : ¶ Ó ; D 7 D ¯ B 5 = : = X B C D ; D m 5 ; B M dA M B D ; 5 ; 7 5 ; B D ^ 5 : ê M J 7 D j ¶ ê C D A D 5 ; M ; 5 d : 5 û ¯ M : BS M A 5 M B 5 = : 5 : · D A X = A m M : ¯ D ® C 5 ¯ C 5 ; 7 M A d D ¯ = m · M A D ^

B = B C D ^ D ; 5 A D ^ · A D ¯ 5 ; 5 = : ¶ ê C 5 ; S M A 5 M B 5 = : 5 ; C = ® ´D S D A D [ · D ¯ B D ^ ` M : ^ M A 5 ; D ; J D ¯ M 0 ; D = X ¯ = A A D 7 M B 5 = : ;J D B ® D D : B C D B A 5 d d D A M : ^ B M d d 5 : d ¶

Õ ¢ Õ ¢ ¬ à ã ã ç ä æ â � à á è � � â å â å ç × Û ¬ � ¥ ã � � � ç ãê C D F G H J B A 5 d d D A ; 2 ; B D m 5 ; ^ D ; ¯ A 5 J D ^ 5 : ^ D ´

B M 5 7 D 7 ; D ® C D A D È ¸ É ¶ G D A D B C D m = ; B D ; ; D : B 5 M 7 ¯ = m ´· = : D : B ; M A D ; 0 m m M A 5 ; D ^ ¶ Ó B B C D D M A 7 5 D ; B 7 D S D 7 = X

B A 5 d d D A 5 : d ` F ¹ ` B C D D S D : B 5 ; M ¯ ¯ D · B D ^ 5 X M ; 5 : d 7 DC 5 d C B A M : ; S D A ; D m = m D : B 0 m à � � Å m 0 = : ` D 7 D ¯ B A = := A C M ^ A = : 5 ; ^ D B D ¯ B D ^ ¶ ê C D : D [ B ; B M d D ` F j ` A D ´

Nuclear Physics B (Proc. Suppl.) 156 (2006) 203–206

0920-5632/$ – see front matter © 2006 Elsevier B.V. All rights reserved.

www.elsevierphysics.com

doi:10.1016/j.nuclphysbps.2006.02.129

Page 2: Strategies for combating systematics at LHCb

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G. Wilkinson / Nuclear Physics B (Proc. Suppl.) 156 (2006) 203–206204

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G. Wilkinson / Nuclear Physics B (Proc. Suppl.) 156 (2006) 203–206 205

Page 4: Strategies for combating systematics at LHCb

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G. Wilkinson / Nuclear Physics B (Proc. Suppl.) 156 (2006) 203–206206