Phenomenology of Multi-Loops Johann H. K uhn Encyclopaedia - PowerPoint PPT Presentation

Phenomenology of Multi-Loops Johann H. K¨ uhn

Encyclopaedia Britannica: phenomenology a philosophical movement originating in the 20th century, the primary objective of which is the direct investiga- tion and description of phenomena as consciously experienced, without theories about their causal explanation and as free as possible from unexamined preconceptions and presuppositions . The word itself is much older, however, going back at least to the 18th century, when the Swiss-German mathematician and philosopher Johann Heinrich Lambert applied it to that part of his theory of knowledge that distinguishes truth from illusion and error . Multi-Loops how to attack them what are they good for 2

Lots of technicalities: 3

have to have a goal 4

need some inspiration 5

don’t stumble across your feet 6

• Selected Results • (no technicalities) • α s • ρ -parameter: m t ⇐ ⇒ M W ⇐ ⇒ M H • m c und m b 7

α s from σ ( e + e − ⇒ had) and τ -decays 8

� � Q 2 �� R ( s ) = 1 parton model f α s 1955 + QED K¨ allen, Sabry; π Schwinger QCD, � 2 Chetyrkin, Kataev, Tkachov; � α s 1979 + # π Dine, Sapirstein; gives meaning to α s Celmaster, Gonsalves Gorishny, Kataev, Larin; � 3 � α s 1988/1991 + # required for precision Surguladze, Samuel; π general gauge: Chetyrkin (1996) remove theory error � 4 � α s 2008 + # slight shift in α s Baikov, Chetyrkin, JK π by 0 . 0005 9

 α s (from Z) = 0 . 1190 ± 0 . 0026 N 3 LO   → α s = 0 . 1198(15) − − − − α s (from τ ) = 0 . 1202 ± 0 . 0019   10

ρ - parameter m t ⇐ ⇒ M W ⇐ ⇒ M H 11

relative shift of M Z and M W t ), ( b ¯ b ) and ( t ¯ from ( t ¯ b ) fluctuations     t t b  vs W W Z Z + Z Z    ¯ ¯ b t b √ 2 G F M 2 leading term: ∆ ρ = 3 t (Veltman) 16 π 2 = ⇒ early limit on M t ( � 200 GeV) 12

Large difference between MS and OS mass M t − m t (m t ) ≈ 10 GeV ⇒ importance of higher orders for ∆ ρ = 1 Loop G F m 2 Veltman t 1977 2 Loop α s G F m 2 Djouadi, Verzegnassi; t 1987 Kniehl, JK, Stuart 3 Loop α 2 s G F m 2 Chetyrkin, JK, Steinhauser; t 1995 Fleischer,Tarasov,Jegerlehner � 2 � G F m 2 α s 3 Loop t � 3 . . . Chetyrkin, . . . � 2001-2003 G F m 2 t α 3 s G F m 2 Chetyrkin + Karlsruhe; 4 Loop t Czakon + . . . 13

Result: δM W in MeV α 0 α 1 α 2 α 3 α s α weak s s s s m 2 611 . 9 − 61 . 3 − 10 . 9 − 2 . 1 2 . 5 t log + const 136 . 6 − 6 . 0 − 2 . 6 − − − − 1 − 9 . 0 − 1 . 0 − 0 . 2 − − − − m 2 t Σ 739 . 5 − 68 . 3 − 13 . 7 − 2 . 1 2 . 5 α 2 s -term: 13 . 7 MeV ˆ = δm t = 2 GeV (TEVATRON) α 3 s -term: 2 . 1 MeV ˆ = δm t = 0 . 3 GeV (ILC) Conversely: M Pole fixed δα s = 2 · 10 − 3 = δM W = 1 . 7 MeV ⇒ 14

m c und m b from ITEP sum rules to precise quark masses 15

The concept d s � M exp s n +1 R Q ( s ) ≡ n � 12 π 2 � n � n � � d = 9 1 � M th Π Q ( q 2 ) 4 Q 2 � ≡ C n � n Q 4 m 2 d q 2 n ! � Q � q 2 =0 1   2 n m Q = 1  9 C n 4 Q 2 M exp = M th = ⇒ n n Q  M exp 2 n C n can be evaluated pertubatively q 2 = 0 ⇒ tadpoles 16

C (0) C n ( s ) = n 2 Loop π C (1) α s + short distance mass ITEP n 1977/1978 3 Loop � 2 C (2) � α s + precise m Q n Chetyrkin, JK, Steinhauser π 1996/2001 4 Loop reduction of theor. error, � 3 C (2) � α s + n Chetyrkin + KA , Czakon + π 2006/2008 application to lattice 17

Bodenstein et. al 10 finite energy sum rule, NNNLO HPQCD 10 lattice + pQCD HPQCD + Karlsruhe 08 lattice + pQCD Kuehn, Steinhauser, Sturm 07 low-moment sum rules, NNNLO Buchmueller, Flaecher 05 B decays α s2 β 0 Hoang, Manohar 05 B decays α s2 β 0 Hoang, Jamin 04 NNLO moments deDivitiis et al. 03 lattice quenched Rolf, Sint 02 lattice (ALPHA) quenched Becirevic, Lubicz, Martinelli 02 lattice quenched Kuehn, Steinhauser 01 low-moment sum rules, NNLO QWG 2004 PDG 2010 0.8 0.9 1 1.1 1.2 1.3 1.4 m c (3 GeV) (GeV) 18

HPQCD 10 Karlsruhe 09 low-moment sum rules, NNNLO, new Babar Kuehn, Steinhauser, Sturm 07 low-moment sum rules, NNNLO Pineda, Signer 06 Υ sum rules, NNLL (not complete) Della Morte et al. 06 lattice (ALPHA) quenched Buchmueller, Flaecher 05 B decays α s2 β 0 Mc Neile, Michael, Thompson 04 lattice (UKQCD) deDivitiis et al. 03 lattice quenched Penin, Steinhauser 02 Υ (1S), NNNLO Pineda 01 Υ (1S), NNLO Kuehn, Steinhauser 01 low-moment sum rules, NNLO Hoang 00 Υ sum rules, NNLO QWG 2004 PDG 2010 4.1 4.2 4.3 4.4 4.5 4.6 4.7 m b (m b ) (GeV) 19

Moving on: the artistic aspect 20

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