w . de boer

KIT – Universität des Landes Baden-Württemberg undnationales Forschungszentrum in der Helmholtz-Gemeinschaft

Institut für Experimentelle Kernphysik

www.kit.edu

W. de Boer

Measurements of the strong coupling constant:History and Prospects for Grand Unified Theories

Outline

Measurements of s

Prospects for GUTs

2Wim de Boer, Quantum Chromodynamics: History and Prospects, Oberwölz, Sep. 3-8., 2012

Incomplete History of the SM (1972-2012)

pp

QCD at TeV scaleHiggs at 126 GeV

LHC

ep

PDF

HERA

e+e-(+fixed target)

c,b,tau,gluon3 neutrinos

SUSY unification

PEP, PETRA, TRISTANSLC, LEP

THEPARTICLEPHYSICSTRIUMF

pp

top quarkW,Z bosons

TevatronSPS

-

Lattice non-pert.

QCD

Electro-Weak

Unification

HiggsMechanism

.QCD

AsymptoticFreedom


History of s measurements

From PDB 1992 From PDB 2012

0.113 0.003

(170+45 ) -30

Factor 4 improvement in s error in last 20 yrs

Phys. Rev. D86, 010001 (2012)


HERA


Alpha_s from DIS

DIS

Fractional energy of parton in protoncan be determined from electron energy:

Cross section only dependent on x in parton model,if parton probability distribution (PDF) independentof Q2 (Bjorken scaling).However, at larger Q2 more gluons resolved,thus enhancing x-section at small x and decreasingit at large x (scaling violation). Scaling violationdependent on alpha-s, but strongly correlated withgluon PDF

DIS with measurement of onlylepton is inclusive measurement.since integrated over all jetmultiplicities. Exclusive measurement of jet multiplicities also depende on alpha-s. Combining incl. and excl. meas. decorrelate gluon PDF and alpha_s (ZEUS).


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


e+e-fragmentation


Alpha_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 (CM=LAB, so low energy particles inside beam pipe) b-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(s

2) 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


e+e-event shapes


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)


LHC


LHC electroweak production x-sections in NNLO QCD

excl. n-jets


LHC electroweak production x-sections in NLO QCD


Inclusive is one of the most elementary measurements at hadron colliders.– Inclusive jet cross sections at Tevatron/LHC test pQCD over 8-9 orders of magnitude up to 2 TeV– Primary and powerful source of PDF constraint!– LHC experiments are covering larger phase space in jet pT and |y| than Tevatron (probedown to x 0.5x10-3, well studied earlier by DIS) but still have less sensitivity at high x.m

QCD at Hadron Colliders


With ~5/fb per experiment of 2011 data, jet physics extended to the TeV rangeDijet mass leads the way in highest energy reach, with highest masses 4 TeVExcellent confirmation of perturbative QCD up to the very highest scales!

CMS: CMS PAS QCD-11-004 Atlas: arXiv:1112.6297

Di-jet masses at 7 TeV

CMS: CMS PAS QCD-11-004 Atlas: arXiv:1112.6297


Correlated uncertainties look better: typical veto, NNLO ~ 15%.Stewart, Tackmann

Errors at LHC dominated by higher orders

Alphas measurements at hadron colliders:D0 from pT dependence of inclusive jet cross section :αs(M2Z) = 0.1161+0.0041−0.0048 (NLO) arXiv:0911.2710CMS from ttbar x-section (NLO): aS(mZ) = 0.1178+0.0048-0.0042,


LATTICEQCD


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.QCD Scale fixed by masses and mass splittings

n

axd 44


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

http://arxiv.org/abs/hep-lat/9807028


From Kronberg in Alphas Workshop, arXiv:1110.0016v3

Alphas values from lattice QCD

Variation: 0.117-0.121s(MZ)=0.1190.002?


Tau decays and e+e- hadronic

x-sections


Baikov, Chetyrkin, Kühn, 0801.1821

5-loop calculations in QCD (20.000 diagrams)

C

Theor. errors from non-pert. contr. at M dominate. O(s5)=0.005 at Mtau.Errors reduced by evolution.

Errors dominated by experiment.. O(s4) term =+0.005 at MZ.Errors reduced by evolution


Calculation up to NNNLO

Non-perturbative regime(Q2=M=1.7 GeV)

Different approaches fortreatment of the perturbative expansion (fixed-order or “contour-improved”)

SM review rescales errorsto get 2/dof=1

Extrapolation to MZ reducesrelative error:

s(MZ)=0.1200.002

Alpha_s from tau decays

PDG 2012


e+e-hadronic x-sections


G.~D'Agostini, W.~de Boer and G.~Grindhammer, %``Determination Of Alpha-s And The Z0 Mass From Measurements Of The Total Hadronic Cross-section In E+ E- Annihilation,'' Phys.\ Lett.\ B {\bf 229} (1989) 160.

R ratio in e+e-

Simultaneous fit of s, MZ and sin2W: MZ=89.41.3 GeV, s=0.


Electroweak fits from different programs

ZFITTER, Bardin et al. , used by electroweak working group

GAPS, J. Erler, , used in PDB

GFITTER, . 0811.0009, used by GFITTER Group:

All consistent with:

Why experimental error so large? Very simple exp.: number counting withhigh statistics in 4 independent LEP experiments!

Answer: 2 hardly compatible alphas measurements at LEP!!! alphas from hadronic x-section: alphas=error dominated byluminosity errr


Global electroweak fits and gauge coupling unification. Wim de Boer, Christian Sander Phys.Lett. B585 (2004) 276-286 hep-ph/0307049


Jadach, hep-ph/0306083

Theoretical uncertainties in LEP luminosity (BHLUMI)


Summary of alphas at Mz

NNNLO, theor. error dominates

NNLO, theor. error?

NNNLO, theor. error negligible

Average completely dominatedby lattice gauge theory, if onebelieves error and NNNLO negl.

My estimate: 0.1200.001


s=0.118

s=0.116

Heavy Higgs masses near GUT scale strong function of s

.Minimal Supersymmetric SU(5) and Gauge Coupling Unification at Three Loops, W. Martens, L. Mihaila, J. Salomon, M. Steinhauser. Phys.Rev. D82 (2010) 095013 , arXiv:1008.3070 [


Prospects from GigaZ linear collider

Gfitter Group, 0811.0009

Hope to have enough statistics to measure alphas from Rl INDEPENDENT of Lumiand settle hadronic vacuum polarization at 10-4 level! (Input for lattice QCD, g-2 and gauge coupling unification !)

w . de boer

Documents

quantum chromodynamics

history of s measurements

boer measurements

incomplete history

e efragmentationnr

e e annihilationdise

e eevent shapesnr

s error