KIT – Universität des Landes Baden-Württemberg und
nationales Forschungszentrum in der Helmholtz-Gemeinschaft
Institut für Experimentelle Kernphysik
www.kit.edu
W. de Boer, KIT, Karlsruhe
Measurements of the strong coupling constant:
History and Perspectives for Grand Unified Theories
Outline
Measurements of s
Perspectives for GUTs
2 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Incomplete History of the SM (1972-2012)
pp
QCD at TeV scale
Higgs at 126 GeV
LHC
ep
HERA
e+e-
(+fixed target) c,b,tau,gluon
3 neutrinos
SUSY unification
PEP, PETRA,
TRISTAN
SLC, LEP
THE
PARTICLE
PHYSICS
TRIUMF
pp
top quark
W,Z bosons
Tevatron
SPS
-
Lattice
non-pert.
QCD
Electro-
Weak
Unification
Higgs
Mechanism
.
QCD
Asymptotic
Freedom
3 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
History of s measurements
From PDG 1992
0.113 0.003
(170+45 ) -30
Factor 4 improvement in s error in last 20 yrs?
(NLO)
(NNLO)
(NNNLO)
(NNNLO)
(NNLO)
Phys. Rev. D86, 010001 (2012)
From PDG 2012
ap
ple
s a
nd
ora
ng
es?
(=Lattice)
4 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
D'Agostini, WdB ,Grindhammer,
PLB 1989
Early s data
EW fit values from e+e-
MZ=89.41.3 GeV,
sin2W=0.2200.0023
s (MZ)=0.1250.015
e+e- pbarp
UA2 UA2 at SPS:
mW=80.84±0.22±0.17±0.81GeV/c2
mZ=91.74±0.28±0.12±0.92GeV/c2
ΓW=2.10±0.14±0.08GeV/c2
sin2θW=0.2234±0.0072
αs(MW)=0.123±0.018±0.017
mt=160 ± 60GeV/c2 (for mH=100GeV/c2).
10-20% measurements of s
6 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
s from DIS
DIS
Fractional energy of parton in proton
can be determined from electron energy:
Cross section only dependent on x in parton model,
if parton probability distribution (PDF) independent
of Q2 (Bjorken scaling).
However, at larger Q2 more gluons resolved,
thus enhancing x-section at small x and decreasing
it at large x (scaling violation). Scaling violation
dependent on s, but strongly correlated with
gluon PDF
DIS with measurement of only
lepton is inclusive measurement.
since integrated over all jet
multiplicities. Exclusive
measurement of jet multiplicities
also dependent on s. Combining
incl. and excl. meas. decorrelate
gluon PDF and s (ZEUS).
7 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Legacy measurements from HERA
Larger x-range, equal Q2
Non-pert propt 2/Q2
Calc. In NLO only
T. Schorner-Sadenius, arXiv1111.7290,
for HERA combination group
Scale dependence (4%)
dominant in NLO
αS (MZ) = 0.1202 ± 0.0013(exp) ±
0.0007(mod) ± 0.0012(had)+0.004(scale).
8 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Effect of adding excl. DIS
incl. DIS only
10 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
s from scaling violation in e+e- annihilation
DIS e+e-
Pro: no PDF of proton involved
same range of Q2 (LEP=104 GeV2)
Con: much smaller range of x (Feynman long.
scaling of quark fragmentation function) (CM=LAB, so low energy particles inside beam pipe)
b,c-quark prod. higher at Z0)
(have to parametrize heavy quark fragm., light quark
fragm. and gluon fragm.)
Results: using lund string fragm. fct. as
parametrization of fragm. fcts and
integrating O(s2) ME:
s(MZ)=0.118 0.005 (DELPHI,1993)
polynomial param. of fragm. fct. and
DGLAP eqns:
s(MZ)=0.126 0.009 (ALEPH,1994)
s(MZ)=0.124 0.0060.009 (DELPHI,1997) (error dominated by scale dep. in NLO, as in DIS)
crossing
12 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
PRD, arXiv:1006.3080, World data on
Thrust reanalysed in NNLO.
Systematics? QCD at parton level is
NOT experiment at hadron level!
Event shapes in e+e- annihilation (PDG 2012)
14 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
LHC electroweak production x-sections in NNLO QCD
excl. n-jets
15 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
.– Inclusive jet cross sections test pQCD over 9 orders of magnitude up to 7 TeV
– Primary and powerful source of PDF constraint!
– LHC experiments are covering larger phase space in jet pT and |y| than Tevatron
(probe down to x0.5x10-3, well studied earlier by DIS)
QCD at Hadron Colliders
16 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
s measurements at hadron colliders:
D0 from pT dependence of inclusive jet cross section :
αs(MZ) = 0.1161+0.0041−0.0048 (NLO) arXiv:0911.2710
CMS from ttbar x-section (NLO):
s(mZ) = 0.1178+0.0048-0.0042, CMS PAS TOP-12-022
Problem:
4-5% uncertainty largely due to higher order uncertainties in NLO
Will need to use NNLO calculations and fit simultaneously PDF‘s
and s , since both are correlated. Hard to use NLO PDF*s from
HERA for NNLO physics at LHC.
18 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
LATTICE QCD (WILSON 1974)
Discretise space time on lattice with V=L3xt
Lattice spacing a small compared with nucleon size
Quarks exist on lattice points,
Gauge fields on links
Path Integrals solved on supercomputers.
momentum scale (1/a) fixed by masses and mass
splittings
n
axd 44
19 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
QUENCHED APPROXIMATION
In the quenched
approximation vacuum
polarization effects of quark
loops are turned off.
Popular approximation in
past (reduces computation
time by about 103-105)
Nowadays 2+1
approximation, i.e. 2 light
quarks + s-quark in loop
What are remaining errors? R. Gupta, “Introduction to Lattice QCD”,
arXiv:hep-lat/9807028
20 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
s values from lattice QCD (PDG 2012)
21 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
CHALLENGE OF LATTICE CALC.
Want to calculate s in perturbative regime (at large scale in MS-
scheme)
Scale 1/a fixed in lattice QCD at masses in non-perturbative regime
WINDOW problem:
QCD << << 1/a NOT TRUE for 200 MeV << 90 GeV << Mquark
Problem circumvented by scaling lattice spacing, but lattice
artifacts hard to circumvent see detailed paper by S. Aoki et al.
0906.3906
They consider all problems of having many different scales (and
volumes) needed and convert to MS-scheme (only NLO possible!)
s(MZ) = 0.12050.0008 (stat) 0.0005 (match) (+0.0−0.0017) (a->0)
22 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
PDG recipe for determining average from lattice QCD
PROBLEM: most conservative error estimates get lowest weight
more determinations reduce error, but errors strongly correlated,
so error should NOT be reduced
23 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
From Kronberg in Alphas Workshop, arXiv:1110.0016v3
Alphas values from lattice QCD
Range: 0.117-0.121 (NOT covered by PDG average)
Better: take average of range and half of
range as error: s(MZ)=0.1190.002
(increase of error by factor 3!)
25 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Baikov, Chetyrkin, Kühn, 0801.1821
5-loop calculations in QCD (20.000 diagrams)
C
Theor. errors from HO contr.
at M dominate (0.015 at M).
Errors reduced by evolution (5->2%)
Errors dominated by experiment.
. O(s4) term =+0.0005 at MZ.
26 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Calculation up to NNNLO
Non-perturbative regime
(Q2=M=1.7 GeV)
Different approaches for
treatment of the perturbative
expansion (fixed-order or
“contour-improved”)
SM review rescales errors
to get 2/dof=1 (all values
within central value + error)
Extrapolation to MZ reduces
relative error:
s(MZ)=0.1200.002
s from tau decays
PDG 2012
0.0022 in ew section of pdg
28 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
LEP electroweak fits from different programs
ZFITTER, Bardin et al. , used by electroweak working group
GAPPS, J. Erler, , used in PDB
GFITTER, 0811.0009, used by GFITTER Group:
All consistent with:
Why error so large? Very simple exp.: number counting with
high statistics in 4 independent LEP experiments, theo error negligible.
Answer: 2 hardly compatible s measurements at LEP!!!
s from hadronic x-section: dominated by luminosity error
(common for all LEP exp.!)
s from Rl = had/lep indep. of lumi, dominated by statistics
29 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
WdB, C. Sander PLB, hep-ph/0307049
Comparison of s fromhad and Rl
Error in had and N dominated by lumi error.
N and s strongly correlated: requiring
N=3 brings s from 0.1154 to 0.1196.
(This implies had measured too high by 3
or 1 ‰ . Since error dominated by lumi,
Lumi too low by 1 ‰)
Difference 0.007 (2-3)
30 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Ward et al., PLB, hep-ph/9811245
Jadach, hep-ph/0306083: lumi error 3.10-4
Uncertainties in LEP luminosity (BHLUMI, Jadach, Ward)
32 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
My estimate of s at MZ
Prefer to quote 2 values:
Theory (Lattice QCD, NNLO): s(MZ) = 0.1190.002
Exp. (NNNLO ): s(MZ) = 0.1210.002
(average of `= 0.1200.0022, Rl=0.12300.0037)
IF YOU WANT TO REDUCE ERROR BY AVERAGING IS A QUESTION OF TASTE,
BUT USING PDG ESTIMATE IS EXTREMELY OPTIMISTIC, SINCE DOMINATED
BY THEIR LATTICE ESTIMATE OF s(MZ) =0.11850.0007 (does not cover
spread in published values!)
34 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Unification with SUSY possible
Amaldi, WdB, Furstenau, PL B260(1991)
Unification possible with
SUSY scale around 1 TeV
35 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
SUSY scale sensitive to s
WdB, Sander, PL B 2003, 0307049)
36 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Uncertainties in couplings
3 discrepancies in sin2W
Higgs mass of 126 suggests
truth closer to sin2W from AFB
For s above 0.12 and SUSY
mass scales around 1 TeV
unification perfect
Wdb., Sander, PLB 2004, hep-ph/0307049
unification
37 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
GUT threshold corrections very sensitive to s
s=0.118
s=0.116
.W. Martens, L. Mihaila, J. Salomon,
M. Steinhauser. PRD, arXiv:1008.3070
s=0.121
For perfect unification Higgs
multiplets at GUT scale can be
at MGUT, as expected.
For non-perfect unification need
to have them several orders
of magnitude below GUT scale
(„threshold corrections“)
Question extremely sensitive
to future value of s
A 90-350 GeV ILC would be the right machine to study s, top and Higgs
38 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Prospects from future colliders
GigaZ collider: sin2W order of magnitude more precise
s factor 3-6 more precise (from Rl, independent of lumi)
Allows to check
Unification
GUT threshold corrections
lattice gauge theories
Gfitter Group, 0811.0009
41 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Higgs mechanism in Supersymmetry
2 Higgs doublets needed in SUSY (instead of 1 in SM).
H2 gives masses to up-type quarks and m2 parameter driven <0 by large
top Yukawa coupling, thus inducing symmetry breaking radiatively.
Works only if top mass large enough:
140 < mt <190 GeV
(heavy top mass predicted by Inoue 1982 (BEFORE top discovery!)
refined later, wdb et al., hep-ph/9805378)
Higgs potential:
Furthermore: couplings of H4 terms MUST be gauge couplings in SUSY
(arbitr. in SM!) can predict lightest Higgs mass to be below 130 GeV.
LHC sees Higgs at 126 GeV. BINGO! (and it seems to be non-SM Higgs!)
43 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Approximate triple Yukawa coupling unification for large tan
Yukawa coupling
Unification
wdb et al, PLB 2001,
arXiv:hep-
ph/0106311
GUT: quarks and leptons in same
multiplet
Quark and lepton masses related
Correct b/ mass ratio
Triple Yukawa coupling
unification for large tan=v2/v1
correct mt, mb, mtau massess
mt=173 GeV
45 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
WIMP miracle
f
f
A
χ
χ
~
~
tan(β)·mfd
mW
8
N1N3(4)
tan(β)·mfd ↔tan(β)
mfu
f
f
A
χ
χ
~
~
tan(β)·mfd
mWmW
88
N1N3(4)
tan(β)·mfd ↔tan(β)
mfu
Annihilation cross
section 1/dark matter
density ()
ann 103 pb
Dark matter scattering
cross section: exp. limit
scat <10-7 pb
10 orders of magnitude difference in cross sections (connected by crossing)
explained, if exchange via Higgs particles:
higgs coupling to proton only to s-quark condensate!
In annihilation phase space allows heavy quarks, so large coupling
WIMP miracle: annihilation
cross section determined
from cosmology coincides
with SUSY neutralino
annihilation x-section
Is weakly interacting massive particle (WIMP)
Scattering amplitude
M Cq <Nmq qqN>
R. Young, Lattice 2012
46 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Effective couplings N scattering
Coupling from lattice QCD gives order of magnitude smaller
effective coupling than deduced from N scattering!
This lower cross section implies that the WIMP mass must be only
above 130 GeV instead of 260 GeV (Beskidt, WdB,.. arXiv:1207.3185,
arXiv:1202.3366) (but still comparable with LHC limit!!!!!)
Large uncertainty from virtual strange quark density
allowed
excluded LHC
WIMP
searches
47 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Prospects for the future at the LHC
Higgs boson couplings will be established with high precision
(and test if it is a SM boson or more complicated Higgs sector (exp. in SUSY)
SUSY might be discovered at the LHC -> this would explain why
Gauge couplings unify, thus paving the way for a Grand Unified Theory
No quadratic divergencies exist, so theory valid up to Planck scale
Relations between quark and lepton masses of 3th generation
Higgs boson is below 130 GeV
more than 80% of matter consists of DM
48 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Talk dedicated to Julius Wess, who was born here and wrote down the Lagrangian
for Supersymmetry in Karlsruhe in 1974 together with Bruno Zumino.
Picture from his public lecture in July 2007 at the SUSY 2007 Conference in Karlsruhe
with the title: From Symmetry to Supersymmetry. He died in August, 2007.
51 Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012
Is discovery at LHC a SM Higgs boson?
CF = scale factor
for coupling
to fermions
95%CL:
0.3 < CF < 1.0
CV = scale factor
For coupling
to vector bosons
95%CL:
0.7 < CV < 1.2
SM: CF = CV = 1
At least coupling to vector bosons SM like