Measurements of the strong coupling constant: History and

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

PDF

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


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)


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



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).


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).


Effect of adding excl. DIS

incl. DIS only



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



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 electroweak production x-sections in NNLO QCD

excl. n-jets


.– 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


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.



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


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




s values from lattice QCD (PDG 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)


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


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!)



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.


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



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


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)


Ward et al., PLB, hep-ph/9811245

Jadach, hep-ph/0306083: lumi error 3.10-4

Uncertainties in LEP luminosity (BHLUMI, Jadach, Ward)



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!)



Unification with SUSY possible

Amaldi, WdB, Furstenau, PL B260(1991)

Unification possible with

SUSY scale around 1 TeV


SUSY scale sensitive to s

WdB, Sander, PL B 2003, 0307049)


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


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


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




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!)



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

http://arxiv.org/abs/hep-ph/0106311v2


















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


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


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


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.




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

Documents

Measurements of the strong coupling constant: History and