[PPT] - FROM ( e + e had ) JK, Steinhauser, Sturm NPB JK, Steinhauser, PowerPoint Presentation

SLIDE 1

QUARK MASSES AND αs FROM σ(e+e− → had)

JK, Steinhauser, Sturm NPB JK, Steinhauser, Teubner PRD

Universit¨ at Karlsruhe (TH)

Forschungsuniversit¨ at • gegr¨ undet 1825

C

m

p u t a t i

n

a l T h e

r

e t i c a l P a r t i c l e P h y s i c s

SFB TR9

B KA AC

’ ’

SLIDE 2

Main Idea (SVZ)

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SLIDE 3

Data

▲ BES (2001) ❍ MD-1 ▼ CLEO ■ BES (2006) pQCD

√ s (GeV) R(s)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2 3 4 5 6 7 8 9 10

√ s (GeV) R(s)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 3.8 4 4.2 4.4 4.6 4.8

√ s (GeV) R(s)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 3.65 3.675 3.7 3.725 3.75 3.775 3.8 3.825 3.85 3.875 3.9

pQCD and data agree well in the regions 2 – 3.73 GeV and 5 – 10.52 GeV

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experiment energy [GeV] date systematic error BES 2 — 5 2001 4 % MD-1 7.2 — 10.34 1996 4 % CLEO 10.52 1998 2 % PDG J/ψ (7 %) 2.5 % PDG ψ′ (9 %) 2.4 % PDG ψ′′ (15 %) BES ψ′′ region 2006 4 % Future improvements: charm region (CLEO) 3% bottom region ?? (CLEO)

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SLIDE 5

mQfrom

SVZ Sum Rules, Moments and Tadpoles Some definitions: R(s) = 12π Im

Π(q2 = s + iǫ)
−q2gµν + qµ qν
Π(q2)

≡ i

dx eiqxTjµ(x)jν(0)

with the electromagnetic current jµ Taylor expansion: ΠQ(q2) = Q2

Q

3 16π2

n≥0

¯ Cn zn with z = q2/(4m2

Q) and mQ = mQ(µ) the MS mass. 5

SLIDE 6

Coefficients ¯ Cn up to n = 8 known analytically in order α2

s

[Chetyrkin, JK, Steinhauser, 1996] up to high n(∼ 30); VV, AA, PP, SS correlators [Czakon et al., 2006], [Maierh¨

fer, Maier, Marquard, 2007]

➪ reduction to master integrals through Laporta algorithm [Chetyrkin, JK, Sturm]; confirmed by [Boughezal, Czakon, Schutzmeier] evaluation of master integrals numerically through difference equations (30 digits) or Pad´ e method or analytically in terms of transcendentals [Schr¨

der + Vuorinen, Chetyrkin et al., Schr¨
der + Steinhauser,

Laporta, Broadhurst, Kniehl et al.] ¯ C2 would be desirable!

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SLIDE 7

Define the moments Mth

n ≡ 12π2

n!

d

dq2

n

Πc(q2)

q2=0

= 9 4Q2

c

1

4m2

c

n

¯ Cn Mexp

n

=

ds

sn+1Rc(s) constraint: Mexp

n

= Mth

n

➪ mc

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SLIDE 8

update compared to NPB619 (2001) experiment:

αs = 0.1187 ± 0.0020
Γe(J/ψ, ψ′) from BES & CLEO & Babar
ψ(3770) from BES

theory:

N3LO for n=1
N3LO - estimate for n =2,3,4
include condensates

δMnp

n

= 12π2Q2

c

(4m2

c )(n+2)

αs

π G2

an
1 + αs

π ¯ bn

estimate of non-perturbative terms

(oscillations, based on Shifman)

careful extrapolation of Ruds
careful definition of Rc

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SLIDE 9

▲ BES (2001) ❍ MD-1 ▼ CLEO ■ BES (2006) pQCD

√ s (GeV) R(s)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 2 3 4 5 6 7 8 9 10

√ s (GeV) R(s)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 4 5 9

SLIDE 10

Contributions from

narrow resonances:

R = 9 Π MR Γe

α2(s)

δ(s − M2

R)

threshold region (2 mD – 4.8 GeV)
perturbative continuum (E ≥ 4.8 GeV)

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SLIDE 11

Results (mc) n mc(3 GeV) exp αs µ np total δ ¯ C30

n

mc(mc) 1 0.986 0.009 0.009 0.002 0.001 0.013 — 1.286 2 0.979 0.006 0.014 0.005 0.000 0.016 0.006 1.280 3 0.982 0.005 0.014 0.007 0.002 0.016 0.010 1.282 4 1.012 0.003 0.008 0.030 0.007 0.032 0.016 1.309 n = 1:

mc(3 GeV) = 986 ± 13 MeV
mc(mc) = 1286 ± 13 MeV

Knowledge of C30

n

for n = 2, 3 !?

ther (”experimental”) determinations of Mn ?

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SLIDE 12

n mc(3 GeV) (GeV)

0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3 1 2 3 4 5

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SLIDE 13

Results (mb) n mb(10 GeV) exp αs µ total δ ¯ C30

n

mb(mb) 1 3.593 0.020 0.007 0.002 0.021 — 4.149 2 3.609 0.014 0.012 0.003 0.019 0.006 4.164 3 3.618 0.010 0.014 0.006 0.019 0.008 4.173 4 3.631 0.008 0.015 0.021 0.027 0.012 4.185 n = 2:

mb(mb) = 4164 ± 25 MeV
mb(10GeV) = 3609 ± 25 MeV
mb(mt) = 2703 ± 18 ± 19 MeV
mt/mb = 59.8 ± 1.3

Knowledge of C30

n

for n = 2, 3 to confirm estimate!? data above 11GeV?

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SLIDE 14

n mb(10 GeV) (GeV)

3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 1 2 3 4 5

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SLIDE 15

mc(3 GeV) = 0.986(13) GeV mc(mc) = 1.286(13) GeV mb(10 GeV) = 3.609(25) GeV mb(mb) = 4.164(25) GeV (old result: mc(mc) = 1.304(27)GeV, mb(mb) = 4.191(51)GeV)

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SLIDE 16

Kuehn, Steinhauser, Sturm 07 Buchmueller, Flaecher 05 Hoang, Manohar 05 Hoang, Jamin 04 deDivitiis et al. 03 Rolf, Sint 02 Becirevic, Lubicz, Martinelli 02 Kuehn, Steinhauser 01 PDG 2006

mc(mc)

1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6

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SLIDE 17

Kuehn, Steinhauser, Sturm 07 Pineda, Signer 06 Della Morte et al. 06 Buchmueller, Flaecher 05 Mc Neile, Michael, Thompson 04 deDivitiis et al. 03 Penin, Steinhauser 02 Pineda 01 Kuehn, Steinhauser 01 Hoang 00 PDG 2006

mb(mb)

4.1 4.2 4.3 4.4 4.5 4.6 4.7

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SLIDE 18

R measurement and αs

▼ CLEO (1998) ■ CLEO (2007)

√ s (GeV) R(s)

3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7 3.75 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11

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SLIDE 19

αs and R basic idea: Rexp = Rth(αs, mq) ➪ αs (weak dependence on variation of mq)

rhad: [Harlander,Steinhauser’02]

Rth(s) :

full quark mass dependence up to O(α2

s)

O(α3

s ): (m2 q /s)0, (m2 q /s)1, (m2 q/s)2

. . .
consistent running and decoupling of αs

[v. Ritbergen,Larin,Vermaseren’97,Czakon’05] [Chetyrkin,Kniehl,Steinhauser’97]

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SLIDE 20

αs and R basic idea: Rexp = Rth(αs, mq) ➪ αs (weak dependence on variation of mq)

rhad: [Harlander,Steinhauser’02]

Rexp(s) ➪ α(4)

s

(s) (nf = 4) √s (GeV) α(4)

s

(s) δαstat

s

δαsys,cor

s

δαsys,uncor

s

α(4)

s

(s)|CLEO 10.538 0.2113 0.0026 0.0618 0.0444 0.232 10.330 0.1280 0.0048 0.0469 0.0445 0.142 9.996 0.1321 0.0032 0.0516 0.0344 0.147 9.432 0.1408 0.0039 0.0526 0.0291 0.159 8.380 0.1868 0.0187 0.0461 0.0195 0.218 7.380 0.1604 0.0131 0.0404 0.0138 0.195 6.964 0.1881 0.0221 0.0386 0.0134 0.237 ⇑ massless approx.!!!

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SLIDE 21

αs and R basic idea: Rexp = Rth(αs, mq) ➪ αs (weak dependence on variation of mq)

rhad: [Harlander,Steinhauser’02]

Rexp(s) ➪ α(4)

s

(s) (nf = 4)

Evolve to common scale and combine

➪ α(4)

s

(9 GeV) = 0.160 ± 0.024 ± 0.024

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SLIDE 22

αs and R basic idea: Rexp = Rth(αs, mq) ➪ αs (weak dependence on variation of mq)

rhad: [Harlander,Steinhauser’02]

Rexp(s) ➪ α(4)

s

(s) (nf = 4)

Evolve to common scale and combine

➪ α(4)

s

(9 GeV) = 0.160 ± 0.024 ± 0.024

α(4)

s

(9 GeV) → α(4)

s

(µdec

b

) → α(5)

s

(µdec

b

) → α(5)

s

(MZ) (practically) independent from µdec

b

(4-loop running and 3-loop decoupling)

RunDec: [Chetyrkin,JK,Steinhauser’00]

➪ α(5)

s

(MZ) = 0.110+0.010

−0.012 +0.010 −0.011 = 0.110+0.014 −0.017 [JK,Steinhauser,Teubner’07]

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SLIDE 23

αs and R basic idea: Rexp = Rth(αs, mq) ➪ αs (weak dependence on variation of mq)

rhad: [Harlander,Steinhauser’02]

Rexp(s) ➪ α(4)

s

(s) (nf = 4)

Evolve to common scale and combine

➪ α(4)

s

(9 GeV) = 0.160 ± 0.024 ± 0.024

α(4)

s

(9 GeV) → α(4)

s

(µdec

b

) → α(5)

s

(µdec

b

) → α(5)

s

(MZ) (practically) independent from µdec

b

(4-loop running and 3-loop decoupling)

RunDec: [Chetyrkin,JK,Steinhauser’00]

➪ α(5)

s

(MZ) = 0.110+0.010

−0.012 +0.010 −0.011 = 0.110+0.014 −0.017 [JK,Steinhauser,Teubner’07]

CLEO analysis: α(5)

s

(M2

Z)|CLEO = 0.126 ± 0.005+0.015 −0.011

massless approximation for R(s), no decoupling of αs

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SLIDE 24

R: experiment + theory

▼ CLEO (1998) ■ CLEO (2007)

√ s (GeV) R(s)

3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7 3.75 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11

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SLIDE 25

R: experiment + theory

▼ CLEO (1998) ■ CLEO (2007)

√ s (GeV) R(s)

3.35 3.4 3.45 3.5 3.55 3.6 3.65 3.7 3.75 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11

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SLIDE 26

αs from R

α(5)

s

(MZ) = 0.110+0.010

−0.012 +0.010 −0.011 = 0.110+0.014 −0.017 [JK,Steinhauser,Teubner’07]

Combine with α(5)

s

(MZ) = 0.124+0.011

−0.014 [JK,Steinhauser’01]

R measurements between 2 and 10.5 GeV from BES’01, MD-1’96, CLEO’97 ➪ α(5)

s

(MZ) = 0.119+0.009

−0.011

Compare: α(5)

s

(MZ) = 0.1189 ± 0.0010

[Bethke’06]

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