Heavy Quark Masses. Matthias Steinhauser TTP, University of Karlsruhe. May 2008, CAQCD08, University of Minnesota
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1 Heavy Quark Masses Matthias Steihauser TTP, Uiversity of Karlsruhe May 2008, CAQCD08, Uiversity of Miesota i collaboratio with Kostja Chetyrki, Has Küh, Christia Sturm ad (i part with) the HPQCD Collaboratio: I. Alliso, C.T.H. Davies, E. Follaa, E. Dalgic,. R.R. Horha, K. Horbostel, G.P. Lepage, J. Shigemitsu, H. Trottier, R.M. Woloshy Matthias Steihauser p.1
2 Outlie Motivatio Charm quark I: pqcd ad R exp Bottom quark Charm quark II: pqcd meets LQCD Summary Matthias Steihauser p.2
3 Quark masses Fudametal parameters of the Stadard Model B decays: Γ m 5 b..., B X s γ Spectroscopy Higgs decay ILC Γ(H b b) = G FM H 4 2π m2 b (1 + O(α s) +...) Yukawa uificatio eeded: δm t = 1 GeV δm b = 25 MeV δm t m t δm b m b Matthias Steihauser p.3
4 Quark mass defiitios L QCD = 1 4 G2 µν + q ψ q (D/ m q )ψ q pole mass MS mass kietic mass 1S mass PS mass RS mass... [Bigi,Shifma,Uraltsev,Vaishtei 97] [Hoag,Smith,Stelzer,Willebrock 99] [Beeke 98] [Pieda 01] Choose quark mass defiitio i theory calculatios this mass is extracted whe compariso with experimet is doe Matthias Steihauser p.4
5 Light quark masses PDG: m u m d m = m u + m d 2 m s = MeV = MeV = MeV = 95 ± 25 MeV less accurately kow tha heavy quark masses Recet results for m s (2005/2006): [Chetyrki,Khodjamiria 06; Jami et al ; Nariso 05; Gamiz 05; MILC/HPQCD 06;JP-PACS/JLQCD 06] m s (2 GeV) = 94 ± 10 MeV Matthias Steihauser p.5
6 Top quark masses Tevatro p + p t t Wb + Wb 4 jets + µ + ν recostruct top quark m t = ± 0.8 ± 1.1 GeV [CDF+D0] Which mass? Pole mass? LHC δm t 1 GeV p p t t t b b } } jets jets Iteratioal Liear Collider (ILC) Well-defied c.m. eergy Clea iitial state Threshold sca Simple coutig of t t δm t < 100 MeV e+ e- cross sectio eergy Q _ Q Matthias Steihauser p.6
7 Charm/Bottom Cosider σ(e + e hadros) Cross sectio Eergy m c,m b sum rules, ( SVZ sum rules) [Novikov,Oku,Shifma,Vaishtei,Voloshi,Zakharov 78] Matthias Steihauser p.7
8 R exp [Davier,Eidelma,Höcker,Zhag 02] Matthias Steihauser p.8
9 Charm quark Matthias Steihauser p.9
10 Sum rules R Q = σ(e+ e Q Q +...) σ(e + e µ + µ ) ds s +1R Q(s) (momets) M R Q = 12πIm [ Π Q (q 2 = s + iε) ] M = 12π2! ( d dq 2 ) Π Q (q ) 2 q2 =0 (dispersio relatio) Matthias Steihauser p.10
11 Sum rules (2) M ds s +1R Q(s) large ( ): Υ sum rules threshold regio importat NRQCD,... [Pei,Pivovarov 98; Melikov,Yelkhovsky 98;Beeke,Siger 99;Hoag 00] here: small ( 4) fixed-order perturbatio theory sufficiet Matthias Steihauser p.11
12 M = 12π2! M th ( d dq 2 ) Π Q (q ) 2 q2 =0 compute Taylor expasio Π Q (q 2 ) = Q 2 Q 3 16π 2 0 ( ) q 2 4m 2 Q M th = 9 4 Q2 Q ( 1 4m 2 Q ) δm Q m Q = 1 2 δm M Matthias Steihauser p.12
13 C to 4 loops : 3 loops: <= 8: [Chetyrki,Küh,MS ] 30,..., 40 [Boughezal,Czako,Schutzmeier 06; Maier,Maierhofer,Marquark 07] 4 loops: = 1: [Chetyrki,Küh,Sturm 06; Boughezal,Czako,Schutzmeier 06] = 2: [Maier,Maierhofer,Marquark,Smirov 08] NEW, PRELIMINARY Matthias Steihauser p.13
14 C to 4 loops = + + (0) + α s(µ) π ( ) 2 ( αs (µ) (20) π ( αs (µ) π ( (10) + (11) l mc ) + (21) l mc + (22) ) 3 ( (30) + (31) l mc + l 2 m c ) (32) l 2 m c + (33) l 3 m c ) l mc = l(m 2 c/µ 2 ) (0) (10) (11) (20) (21) (22) (30) (31) (32) (33) Matthias Steihauser p.14
15 C to 4 loops = + + (0) + α s(µ) π ( ) 2 ( αs (µ) (20) π ( αs (µ) π ( (10) + (11) l mc ) + (21) l mc + (22) ) 3 ( (30) + (31) l mc + l 2 m c ) (32) l 2 m c + (33) l 3 m c ) l mc = l(m 2 c/µ 2 ) (0) (10) (11) (20) (21) (22) (30) (31) (32) (33) 6.0 (30) 2 7.0, 6.0 (30) 3 5.2, 6.0 (30) Matthias Steihauser p.14
16 C to 4 loops = + + (0) + α s(µ) π ( ) 2 ( αs (µ) (20) π ( αs (µ) π ( (10) + (11) l mc ) + (21) l mc + (22) ) 3 ( (30) + (31) l mc + l 2 m c ) (32) l 2 m c + (33) l 3 m c ) l mc = l(m 2 c/µ 2 ) (0) (10) (11) (20) (21) loop, = 2 [Maier,Maierhofer,Marquark,Smirov 08] NEW, PRELIMINARY 6.0 (30) 2 7.0, 6.0 (22) (30) (30) 3 5.2, 6.0 (31) (32) (30) (33) Matthias Steihauser p.14
17 M exp = M res + M thresh + M cot M res : R res (s) = 9πM RΓ ee α 2 ( α α(s)) 2 δ(s M 2 R ) J/Ψ Ψ(2S) M Ψ (GeV) (11) (34) Γ ee (kev) 5.55(14) 2.48(6) (α/α(m Ψ )) Matthias Steihauser p.15
18 M exp = M res + M thresh + M cot M res : M thresh : R res (s) = 9πM RΓ ee α 2 ( α α(s)) 2 δ(s M 2 R ) R(s) pqcd BES (2001) J/ψ ψ, MD-1 CLEO BES (2006) s (GeV) Matthias Steihauser p.15
19 M exp = M res + M thresh + M cot M res : R res (s) = 9πM RΓ ee α 2 ( α α(s)) 2 δ(s M 2 R ) M thresh : M cot : 3.73 GeV s 4.8 GeV, BES01,06 s 4.8 GeV o data R theory full mass depedece up to O(α 2 s) rhad: [Harlader,MS 02] Matthias Steihauser p.15
20 M thresh subtract R uds R from data below 3.73 GeV s-depedece from theory u,d,s c cosider deviatios from pqcd: oszillatios of R(s) aroud perturbative result from low-lyig resoaces [Shifma 03] 2 models: R(s) = R pqcd (s)f i f 1 = s 3/2 si (2ρ s δ) ( ) (ρ = 3 GeV 1, δ = 1.32) f 2 = exp 2πsB σ 2 N c si ( 2πs σ 3.08 ) 2 (σ 2 = 2 GeV 2, B = 0.5, N c = 3) f 1 : δm c (3 GeV) 1 MeV f 2 : smaller cotributio Matthias Steihauser p.16
21 M exp M res M thresh M cot M exp M p 10 ( 1) 10 ( 1) 10 ( 1) 10 ( 1) 10 ( 1) (25) (15) (11) (31) (2) (25) (8) (3) (27) (0) (26) (5) (1) (27) (14) (27) (3) (0) (27) (54) Matthias Steihauser p.17
22 m c M th + M p! = M exp ( (µ/m c (µ)) ) 1/(2) m c (µ) = 1 2 M exp M p 1. set µ = 3 GeV m c (3 GeV) 2. RGE m c (m c ) Ucertaities δm exp α s (M Z ) = ± [Bethke 06]; δα s 2 µ = (3 ± 1) GeV δm p Matthias Steihauser p.18
23 m c M th + M p! = M exp ( (µ/m c (µ)) ) 1/(2) m c (µ) = 1 2 M exp M p m c (3 GeV) exp α s µ p total δ (30) m c (m c ) m c (3 GeV) = 0.986(13) GeV [Küh,MS,Sturm 07] Matthias Steihauser p.18
24 m c M th + M p! = M exp ( (µ/m c (µ)) ) 1/(2) m c (µ) = 1 2 M exp M p m c (3 GeV) exp α s µ p total δ (30) m c (m c ) m c (3 GeV) = 0.986(13) GeV Matthias Steihauser p.18
25 m c (3 GeV) m c (3 GeV) (GeV) [Küh,MS 01] Matthias Steihauser p.19
26 m c (3 GeV) m c (3 GeV) (GeV) [Küh,MS,Sturm 07] Matthias Steihauser p.19
27 Charm compariso m c (m c ) Kueh, Steihauser, Sturm 07 low-momet sum rules, NNNLO Buchmueller, Flaecher 05 B decays α s 2β 0 Hoag, Maohar 05 B decays α s 2β 0 Hoag, Jami 04 NNLO momets dedivitiis et al. 03 lattice queched Rolf, Sit 02 lattice (ALPHA) queched Becirevic, Lubicz, Martielli 02 lattice queched Kueh, Steihauser 01 low-momet sum rules, NNLO QWG 2004 PDG Matthias Steihauser p.20
28 Bottom quark Matthias Steihauser p.21
29 M th m b (µ) = 1 2 m b! = M exp 1. set µ = 10 GeV m b (10 GeV) 2. RGE m b (m b ) ( ) 1/(2) M exp Ucertaities δm exp α s (M Z ) = ± [Bethke 06]; δα s 2 µ = (10 ± 5) GeV Matthias Steihauser p.22
30 M th m b (µ) = 1 2 m b! = M exp ( ) 1/(2) M exp m b (10 GeV) exp α s µ total (30) δ m b (m b ) m b (10 GeV) = 3.609(25) GeV [Küh,MS,Sturm 07] Matthias Steihauser p.22
31 m b (10 GeV) m b (10 GeV) (GeV) [Küh,MS 01] Matthias Steihauser p.23
32 m b (10 GeV) m b (10 GeV) (GeV) [Küh,MS,Sturm 07] Matthias Steihauser p.23
33 Bottom compariso m b (m b ) Kueh, Steihauser, Sturm 07 low-momet sum rules, NNNLO Pieda, Siger 06 Υ sum rules, NNLL (ot complete) Della Morte et al. 06 lattice (ALPHA) queched Buchmueller, Flaecher 05 B decays α s 2β 0 Mc Neile, Michael, Thompso 04 lattice (UKCD) dedivitiis et al. 03 lattice queched Pei, Steihauser 02 Υ(1S), NNNLO Pieda 01 Υ(1S), NNLO Kueh, Steihauser 01 low-momet sum rules, NNLO Hoag 00 Υ sum rules, NNLO QWG 2004 PDG Matthias Steihauser p.24
34 Charm quark II Matthias Steihauser p.25
35 Lattice: LQCD ad PQCD [HPQCD Collaboratio: Alliso et al.] Highly Improved Staggered Quark (HISQ) simulatio of relativistic c quarks lattice spacig ad quark masses are tued to reproduce Υ Υ meso mass differece m 2 π, 2m 2 K m2 π, m ηc, m Υ compute momets of the pseudo-scalar curret vector, axial-vector curret check Perturbatio theory: momets of the pseudo-scalar curret 4 loops: = 1 ad = 2 [Sturm, i preparatio] Matthias Steihauser p.26
36 m c (3 GeV) Note: 1 ot sesitive to m c but to α s m c (3 GeV) from = 2, 3, 4 PRELIMINARY m c (3 GeV) total lattice α s h.o. p Matthias Steihauser p.27
37 m c (3 GeV) Note: 1 ot sesitive to m c but to α s m c (3 GeV) from = 2, 3, 4 PRELIMINARY m c (3 GeV) total lattice α s h.o. p m c (3 GeV) = 0.984(16) GeV Matthias Steihauser p.27
38 α s = 1: PRELIMINARY α (4) s (3 GeV) = 0.230(18) α (5) s (M Z ) = 0.113(4) PDG: α (5) s (M Z ) = (20) Matthias Steihauser p.28
39 Coclusios R exp ad PQCD (vector correlator): m c (3 GeV) = 0.986(13) GeV m b (10 GeV) = 3.609(25) GeV NNNLO aalysis MS mass Possible improvemets: experimetal measuremets: R(s), Γ ee LQCD ad PQCD (pseudo-scalar correlator): m c (3 GeV) = 0.984(16) GeV α (5) s (M Z ) = 0.113(4) PRELIMINARY δm s m s 10%; δm c m c 1%; δm b m b 0.6%; δm t m t 1% Matthias Steihauser p.29
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