ρ ω The R-ratio: comparison to data - becher.itp.unibe.ch · R √ s [GeV] Andrea Banfi Lecture...
Transcript of ρ ω The R-ratio: comparison to data - becher.itp.unibe.ch · R √ s [GeV] Andrea Banfi Lecture...
6 40. Plots of cross sections and related quantities
! and R in e+e! Collisions
10-8
10-7
10-6
10-5
10-4
10-3
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1 10 102
![m
b]
!
"
#
"!
J/$
$(2S)!
Z
10-1
1
10
10 2
10 3
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R !
"
#
"!
J/$ $(2S)
!
Z
!
s [GeV]Figure 40.6: World data on the total cross section of e+e! ! hadrons and the ratio R(s) = !(e+e! ! hadrons, s)/!(e+e! ! µ+µ!, s).!(e+e! ! hadrons, s) is the experimental cross section corrected for initial state radiation and electron-positron vertex loops, !(e+e! !µ+µ!, s) = 4"#2(s)/3s. Data errors are total below 2 GeV and statistical above 2 GeV. The curves are an educative guide: the broken one(green) is a naive quark-parton model prediction, and the solid one (red) is 3-loop pQCD prediction (see “Quantum Chromodynamics” sectionof this Review, Eq. (9.12) or, for more details, K. G. Chetyrkin et al., Nucl. Phys. B586, 56 (2000) (Erratum ibid. B634, 413 (2002)).Breit-Wigner parameterizations of J/$, $(2S), and % (nS), n = 1, 2, 3, 4 are also shown. The full list of references to the original data and thedetails of the R ratio extraction from them can be found in [arXiv:hep-ph/0312114]. Corresponding computer-readable data files are availableat http://pdg.lbl.gov/current/xsect/. (Courtesy of the COMPAS (Protvino) and HEPDATA (Durham) Groups, August 2007. Correctionsby P. Janot (CERN) and M. Schmitt (Northwestern U.)) See full-color version on color pages at end of book.
The R-ratio: comparison to data
QCD Hadron Collider Summer School ’08 G.Zanderighi
Renormalisation group
QCD beta function
Short-distance observables
Comparison of R̂ to experimental data
10-1
1
10
10 2
0.5 1 1.5 2 2.5 3
Sum of exclusivemeasurements
Inclusivemeasurements
3 loop pQCD
Naive quark model
u, d, s
!
"
#
!!
2
3
4
5
6
7
3 3.5 4 4.5 5
Mark-I
Mark-I + LGW
Mark-II
PLUTO
DASP
Crystal Ball
BES
J/$ $(2S)
$3770
$4040
$4160
$4415
c
2
3
4
5
6
7
8
9.5 10 10.5 11
MD-1ARGUS CLEO CUSB DHHM
Crystal Ball CLEO II DASP LENA
!(1S)!(2S)
!(3S)
!(4S)
b
R
!
s [GeV]
Andrea Banfi Lecture 2
The R-ratio: comparison to data
QCD Hadron Collider Summer School ’08 G.Zanderighi
Renormalisation group
QCD beta function
Short-distance observables
Comparison of R̂ to experimental data
10-1
1
10
10 2
0.5 1 1.5 2 2.5 3
Sum of exclusivemeasurements
Inclusivemeasurements
3 loop pQCD
Naive quark model
u, d, s
!
"
#
!!
2
3
4
5
6
7
3 3.5 4 4.5 5
Mark-I
Mark-I + LGW
Mark-II
PLUTO
DASP
Crystal Ball
BES
J/$ $(2S)
$3770
$4040
$4160
$4415
c
2
3
4
5
6
7
8
9.5 10 10.5 11
MD-1ARGUS CLEO CUSB DHHM
Crystal Ball CLEO II DASP LENA
!(1S)!(2S)
!(3S)
!(4S)
b
R
!
s [GeV]
Andrea Banfi Lecture 2
e+e− to hadrons: cross section (PDG)
6 40. Plots of cross sections and related quantities
! and R in e+e! Collisions
10-8
10-7
10-6
10-5
10-4
10-3
10-2
1 10 102
![m
b]
!
"
#
"!
J/$
$(2S)!
Z
10-1
1
10
10 2
10 3
1 10 102
R !
"
#
"!
J/$ $(2S)
!
Z
!
s [GeV]Figure 40.6: World data on the total cross section of e+e! ! hadrons and the ratio R(s) = !(e+e! ! hadrons, s)/!(e+e! ! µ+µ!, s).!(e+e! ! hadrons, s) is the experimental cross section corrected for initial state radiation and electron-positron vertex loops, !(e+e! !µ+µ!, s) = 4"#2(s)/3s. Data errors are total below 2 GeV and statistical above 2 GeV. The curves are an educative guide: the broken one(green) is a naive quark-parton model prediction, and the solid one (red) is 3-loop pQCD prediction (see “Quantum Chromodynamics” sectionof this Review, Eq. (9.12) or, for more details, K. G. Chetyrkin et al., Nucl. Phys. B586, 56 (2000) (Erratum ibid. B634, 413 (2002)).Breit-Wigner parameterizations of J/$, $(2S), and % (nS), n = 1, 2, 3, 4 are also shown. The full list of references to the original data and thedetails of the R ratio extraction from them can be found in [arXiv:hep-ph/0312114]. Corresponding computer-readable data files are availableat http://pdg.lbl.gov/current/xsect/. (Courtesy of the COMPAS (Protvino) and HEPDATA (Durham) Groups, August 2007. Correctionsby P. Janot (CERN) and M. Schmitt (Northwestern U.)) See full-color version on color pages at end of book.
e+e− to hadrons: R-ratio (PDG)
First experimental evidence for colour
I. Existance of !++ particle: particle with three up quarks of the same spin and with symmetric spacial wave function. Without an additional quantum number Pauli’s principle would be violated ⇒ color
II.R-ratio: ratio of (e+e- ! hadrons)/(e+e- ! µ+µ-)
U †U = UU † = 1 det(U) = 1
!
i
!!i !i !
!
ijk
U!ij!jUik!k =
!
k
!!k!k
!
ijk
!i!j!k !!
ijki!j!k!U!
ii!Ujj!Ukk!!i!!j!!k! =!
i!j!k!!i!!j!!k!
nq " nq̄ = n · 3 with n integer
R # e+e" ! hadrons
e+e" ! µ+µ" $ Nc
!
f
Q2f
1
Data compatible with Nc=3 (r, g, b). Will come back to R later.
charge 2/3mass=
upfew MeV
charm~1.25 GeV
top~172 GeV
charge -1/3mass =
downfew MeV
strange~100 MeV
bottom~5 GeV
QCD Hadron Collider Summer School ’08 G.Zanderighi
The R-ratio: comparison to data
QCD Hadron Collider Summer School ’08 G.Zanderighi
Renormalisation group
QCD beta function
Short-distance observables
Comparison of R̂ to experimental data
10-1
1
10
10 2
0.5 1 1.5 2 2.5 3
Sum of exclusivemeasurements
Inclusivemeasurements
3 loop pQCD
Naive quark model
u, d, s
!
"
#
!!
2
3
4
5
6
7
3 3.5 4 4.5 5
Mark-I
Mark-I + LGW
Mark-II
PLUTO
DASP
Crystal Ball
BES
J/$ $(2S)
$3770
$4040
$4160
$4415
c
2
3
4
5
6
7
8
9.5 10 10.5 11
MD-1ARGUS CLEO CUSB DHHM
Crystal Ball CLEO II DASP LENA
!(1S)!(2S)
!(3S)
!(4S)
b
R
!
s [GeV]
Andrea Banfi Lecture 2
The R-ratio: comparison to data
QCD Hadron Collider Summer School ’08 G.Zanderighi
Renormalisation group
QCD beta function
Short-distance observables
Comparison of R̂ to experimental data
10-1
1
10
10 2
0.5 1 1.5 2 2.5 3
Sum of exclusivemeasurements
Inclusivemeasurements
3 loop pQCD
Naive quark model
u, d, s
!
"
#
!!
2
3
4
5
6
7
3 3.5 4 4.5 5
Mark-I
Mark-I + LGW
Mark-II
PLUTO
DASP
Crystal Ball
BES
J/$ $(2S)
$3770
$4040
$4160
$4415
c
2
3
4
5
6
7
8
9.5 10 10.5 11
MD-1ARGUS CLEO CUSB DHHM
Crystal Ball CLEO II DASP LENA
!(1S)!(2S)
!(3S)
!(4S)
b
R
!
s [GeV]
Andrea Banfi Lecture 2
The R-ratio: comparison to data
QCD Hadron Collider Summer School ’08 G.Zanderighi
Renormalisation group
QCD beta function
Short-distance observables
Comparison of R̂ to experimental data
10-1
1
10
10 2
0.5 1 1.5 2 2.5 3
Sum of exclusivemeasurements
Inclusivemeasurements
3 loop pQCD
Naive quark model
u, d, s
!
"
#
!!
2
3
4
5
6
7
3 3.5 4 4.5 5
Mark-I
Mark-I + LGW
Mark-II
PLUTO
DASP
Crystal Ball
BES
J/$ $(2S)
$3770
$4040
$4160
$4415
c
2
3
4
5
6
7
8
9.5 10 10.5 11
MD-1ARGUS CLEO CUSB DHHM
Crystal Ball CLEO II DASP LENA
!(1S)!(2S)
!(3S)
!(4S)
b
R
!
s [GeV]
Andrea Banfi Lecture 2
The R-ratio: comparison to data
QCD Hadron Collider Summer School ’08 G.Zanderighi
Renormalisation group
QCD beta function
Short-distance observables
Comparison of R̂ to experimental data
10-1
1
10
10 2
0.5 1 1.5 2 2.5 3
Sum of exclusivemeasurements
Inclusivemeasurements
3 loop pQCD
Naive quark model
u, d, s
!
"
#
!!
2
3
4
5
6
7
3 3.5 4 4.5 5
Mark-I
Mark-I + LGW
Mark-II
PLUTO
DASP
Crystal Ball
BES
J/$ $(2S)
$3770
$4040
$4160
$4415
c
2
3
4
5
6
7
8
9.5 10 10.5 11
MD-1ARGUS CLEO CUSB DHHM
Crystal Ball CLEO II DASP LENA
!(1S)!(2S)
!(3S)
!(4S)
b
R
!
s [GeV]
Andrea Banfi Lecture 2
low-energy region
The R-ratio: comparison to data
QCD Hadron Collider Summer School ’08 G.Zanderighi
Renormalisation group
QCD beta function
Short-distance observables
Comparison of R̂ to experimental data
10-1
1
10
10 2
0.5 1 1.5 2 2.5 3
Sum of exclusivemeasurements
Inclusivemeasurements
3 loop pQCD
Naive quark model
u, d, s
!
"
#
!!
2
3
4
5
6
7
3 3.5 4 4.5 5
Mark-I
Mark-I + LGW
Mark-II
PLUTO
DASP
Crystal Ball
BES
J/$ $(2S)
$3770
$4040
$4160
$4415
c
2
3
4
5
6
7
8
9.5 10 10.5 11
MD-1ARGUS CLEO CUSB DHHM
Crystal Ball CLEO II DASP LENA
!(1S)!(2S)
!(3S)
!(4S)
b
R
!
s [GeV]
Andrea Banfi Lecture 2
The R-ratio: comparison to data
QCD Hadron Collider Summer School ’08 G.Zanderighi
Renormalisation group
QCD beta function
Short-distance observables
Comparison of R̂ to experimental data
10-1
1
10
10 2
0.5 1 1.5 2 2.5 3
Sum of exclusivemeasurements
Inclusivemeasurements
3 loop pQCD
Naive quark model
u, d, s
!
"
#
!!
2
3
4
5
6
7
3 3.5 4 4.5 5
Mark-I
Mark-I + LGW
Mark-II
PLUTO
DASP
Crystal Ball
BES
J/$ $(2S)
$3770
$4040
$4160
$4415
c
2
3
4
5
6
7
8
9.5 10 10.5 11
MD-1ARGUS CLEO CUSB DHHM
Crystal Ball CLEO II DASP LENA
!(1S)!(2S)
!(3S)
!(4S)
b
R
!
s [GeV]
Andrea Banfi Lecture 2
charm quark region .√
s � 2mc
40. Plots of cross sections and related quantities 7
R in Light-Flavor, Charm, and Beauty Threshold Regions
10-1
1
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10 2
0.5 1 1.5 2 2.5 3
Sum of exclusivemeasurements
Inclusivemeasurements
3 loop pQCD
Naive quark model
u, d, s
!
"
#
!!
2
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3 3.5 4 4.5 5
Mark-IMark-I + LGWMark-IIPLUTODASPCrystal BallBES
J/$ $(2S)
$3770
$4040
$4160
$4415
c
2
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8
9.5 10 10.5 11
MD-1 ARGUS CLEO CUSB DHHM
Crystal Ball CLEO II DASP LENA
!(1S)!(2S)
!(3S)
!(4S)
b
R
!s [GeV]
Figure 40.7: R in the light-flavor, charm, and beauty threshold regions. Data errors are total below 2 GeV and statistical above 2 GeV.The curves are the same as in Fig. 40.6. Note: CLEO data above ! (4S) were not fully corrected for radiative e!ects, and we retainthem on the plot only for illustrative purposes with a normalization factor of 0.8. The full list of references to the original data andthe details of the R ratio extraction from them can be found in [arXiv:hep-ph/0312114]. The computer-readable data are available athttp://pdg.lbl.gov/current/xsect/. (Courtesy of the COMPAS (Protvino) and HEPDATA (Durham) Groups, August 2007)
The R-ratio: comparison to data
QCD Hadron Collider Summer School ’08 G.Zanderighi
Renormalisation group
QCD beta function
Short-distance observables
Comparison of R̂ to experimental data
10-1
1
10
10 2
0.5 1 1.5 2 2.5 3
Sum of exclusivemeasurements
Inclusivemeasurements
3 loop pQCD
Naive quark model
u, d, s
!
"
#
!!
2
3
4
5
6
7
3 3.5 4 4.5 5
Mark-I
Mark-I + LGW
Mark-II
PLUTO
DASP
Crystal Ball
BES
J/$ $(2S)
$3770
$4040
$4160
$4415
c
2
3
4
5
6
7
8
9.5 10 10.5 11
MD-1ARGUS CLEO CUSB DHHM
Crystal Ball CLEO II DASP LENA
!(1S)!(2S)
!(3S)
!(4S)
b
R
!
s [GeV]
Andrea Banfi Lecture 2
bottom quark region . √
s � 2mb
40. Plots of cross sections and related quantities 7
R in Light-Flavor, Charm, and Beauty Threshold Regions
10-1
1
10
10 2
0.5 1 1.5 2 2.5 3
Sum of exclusivemeasurements
Inclusivemeasurements
3 loop pQCD
Naive quark model
u, d, s
!
"
#
!!
2
3
4
5
6
7
3 3.5 4 4.5 5
Mark-IMark-I + LGWMark-IIPLUTODASPCrystal BallBES
J/$ $(2S)
$3770
$4040
$4160
$4415
c
2
3
4
5
6
7
8
9.5 10 10.5 11
MD-1 ARGUS CLEO CUSB DHHM
Crystal Ball CLEO II DASP LENA
!(1S)!(2S)
!(3S)
!(4S)
b
R
!s [GeV]
Figure 40.7: R in the light-flavor, charm, and beauty threshold regions. Data errors are total below 2 GeV and statistical above 2 GeV.The curves are the same as in Fig. 40.6. Note: CLEO data above ! (4S) were not fully corrected for radiative e!ects, and we retainthem on the plot only for illustrative purposes with a normalization factor of 0.8. The full list of references to the original data andthe details of the R ratio extraction from them can be found in [arXiv:hep-ph/0312114]. The computer-readable data are available athttp://pdg.lbl.gov/current/xsect/. (Courtesy of the COMPAS (Protvino) and HEPDATA (Durham) Groups, August 2007)
R = K Nc
�
q
e2q and K̄ = 1−K
34th International Conference on High Energy Physics, Philadelphia, 2008
HPQCD + Karlsruhe 08
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
QWG 2004
PDG 2006
mc(3 GeV)
lattice + pQCD
low-moment sum rules, NNNLO
B decays !s2"0
B decays !s2"0
NNLO moments
lattice quenched
lattice (ALPHA) quenched
lattice quenched
low-moment sum rules, NNLO
0.8 0.9 1 1.1 1.2 1.3 1.4
Kuehn, Steinhauser, Sturm 07Pineda, Signer 06Della Morte et al. 06Buchmueller, Flaecher 05Mc Neile, Michael, Thompson 04deDivitiis et al. 03Penin, Steinhauser 02Pineda 01Kuehn, Steinhauser 01Hoang 00QWG 2004PDG 2006
mb(mb)
low-moment sum rules, NNNLO
# sum rules, NNLL (not complete)
lattice (ALPHA) quenched
B decays !s2"0
lattice (UKCD)
lattice quenched
#(1S), NNNLO
#(1S), NNLO
low-moment sum rules, NNLO
# sum rules, NNLO
4.1 4.2 4.3 4.4 4.5 4.6 4.7
Figure 1: Comparison of recent determinations of mc(3GeV) and mb(mb).
sensitive to non-perturbative contributions from condensates, to the Coulombic higher order e!ects, the variation of
µ and the parametric !s dependence. For n = 1:
mc(3 GeV) = 0.986(13) GeV . (3)
The moment with n = 2 is less sensitive to data for R(s) from the continuum region above 5 GeV, where experimental
results are scarce and the aforementioned theory uncertainties are still relatively small. The agreement between
n = 1 and n = 2 (mc(3 GeV) = 0.976(16)GeV), together with the nice convergence with increasing order in !s can
be considered as additional confirmation of this approach.
Instead of measuring the moments Mexpn in e+e! annihilation they can also be determined in lattice simulations.
This approach has recently been pioneered in [10] using the Highly Improved Staggered Quarks (HISQ) discretization
of the quark action in combination with four-loop perturbative results [3, 4, 5, 9, 11]. The final result, mc(3 GeV) =
0.986(10) GeV corresponds to a scale-invariant mass mc(mc) = 1.268(9)GeV and is in excellent agreement with the
determinations based on e+e! data.
The approach based on e+e! data is also applicable to the determination of mb. The three results based on n = 1, 2
and 3 are of comparable precision. The relative size of the contributions from the threshold and the continuum region
decreases for the moments n = 2 and 3. On the other hand, the theory uncertainty is still small. Therefore the
result from n = 2 was taken as the final answer [5], despite the fact that C̄2 was not yet known. The result,
mb(10 GeV) = 3.609(25) GeV, corresponds to mb(mb) = 4.164(25) GeV. The recent evaluation [9] of C̄2 has lead to
a decrease of the central value by 2 MeV and a reduction of the error from 25 MeV to 19 MeV. A comparison of a
few selected mb- and mc-determinations is shown in Fig. 1.
2. The strong coupling constant
One of the most precise and theoretically safe determination of !s is based on measurements of the cross section
for electron-positron annihilation into hadrons [12]. These have been performed in the low-energy region between
2 GeV and 10 GeV and, in particular, at and around the Z resonance at 91.2 GeV. Conceptually closely related is
the measurement of the semileptonic decay rate of the " -lepton, leading to a determination of !s at a scale below
2 GeV [13]. The perturbative expansion for the ratio R(s) ! #(e+e! " hadrons)/#(e+e! " µ+µ!) in numerical
form is given by
R = 1 + as + (1.9857 # 0.1152 nf) a2s + (#6.63694# 1.20013nf # 0.00518n2
f) a3s
+ (#156.61 + 18.77 nf # 0.7974 n2f + 0.0215 n3
f) a4s . (4)
Here as ! !s/$ and the normalization scale µ2 = s. The a4s corrections are conveniently classified according to their
power of nf , with nf denoting the number of light quarks. The a4sn
3f term is part of the “renormalon chain”, the
2