Strong Coupling Continuum QCD Valencia Strong Coupling Continuum

Strong Coupling Continuum QCD Valencia

Strong Coupling Continuum QCD q Valencia

QCD = q(i QCD q=u, d, s, c, b 1971 D - mq ) q 1 -4 G G

QCD asymptotic freedom confinement strong coupling 0. 5 p. QCD strong QCD 0 0 r (m) 10 -15

confinement perturbative QCD non-perturbative QCD

Masses from Nothing perturbative mass m 0

Schwinger-Dyson Equations

Schwinger-Dyson Equations QED 2 equations 12 equations

Fermion mass generation -1 -1 - wavefunction renormalisation mass function

Fermion mass generation -1 -1 -

Fermion mass generation -1 -1 quenched rainbow -1 -1 - +. . . + +

Fermion mass generation -1 -1 quenched rainbow = cutoff

Fermion mass generation -1 -1 quenched rainbow Landau gauge: = 0

Fermion mass generation -1 -1 quenched rainbow m 0 = 0 M(p) = 0 Landau gauge: = 0

Fermion mass generation -1 -1 quenched rainbow m 0 = 0 M(p) = 0 Landau gauge: = 0

Fermion mass generation -1 -1 quenched rainbow Landau gauge: = 0

Fermion mass generation -1 -1 Landau gauge: = 0 m / m/ quenched rainbow

BUT in other gauges

BUT in other gauges mass = cutoff gauge dependent

Ward – Green –Takahashi q k p q k p = -1 k -1 p

Gauge Invariance and Multiplicative Renormalizibility CP vertex mass = cutoff almost gauge independent

Schwinger-Dyson Equations Ward-Green-Takahashi: q q QED -1 k p k Gauge Invariance & Multiplicative Renormalizibility -1 p

Schwinger-Dyson Equations Slavnov-Taylor Identity axial gauges BBZ QCD covariant gauges

Studies in covariant gauges ghost functions = 1 QCD

Studies in covariant gauges ghost functions = 1 forget ghosts QCD

Studies in covariant gauges first just gluons STI Pagels, Mandelstam, Bar-Gadda

Studies in Landau gauge Brown & P 1988

Studies in Landau gauge s = 0. 25 Nf = 2 Brown & P 1988

QCD running coupling (Q 2) > 1 for Q 2 < Q 02 2 Williams, Fischer, P SB

QCD running coupling (Q 2) > 1 for Q 2 < Q 02 2 Williams, Fischer, P chiral m= 0 SB

QCD vacuum SB +1 < qq >0 ~ - (240 Me. V)3 chiral Maris & Roberts m= 0

Mass generation DIRAC experiment Mass 300 Me. V 0 10 -17 10 -14 r (m) Batley et al Ke 4 results < qq >0 ~ - (240 Me. V)3

Lattice QCD model QCD a 0 V m mq

Lattice QCD a 0 V

Lattice QCD a 0 V

Lattice QCD a 0 V

Lattice and SDE results Bowman et al Roberts et al

Hadrons & quark confinement q q

Hadrons & quark confinement q q q Q Wilson area law

interquark potential + gluon propagator +… M

interquark potential + gluon propagator +… M

interquark potential gluon propagator rp ~ 1 Coulomb : OBE r << 1, p >> 1 r >> 1, p << 1

interquark potential Richardson Potential rp ~ 1 Coulomb : OBE r << 1, p >> 1 r >> 1, p << 1

Charmonium • Positronium Mass [Me. V] Binding energy [me. V] 0 4100 Ionisation energy 3 1 S 0 -1000 2 S 0 1 positronium of QCD 3 3 S 1 2 S 1 3 3 1 D 2 23 P 1 23 P 0 2 P 1 1 33 D 2 33 D 1 33 D 2 ~ 600 me. V P 2(~ 3940) 3 3900 1 S 0 -7000 1 3 S 1 D 2 1 y ¢ (3686) 3700 D 2 3 Threshold h¢ c(3590) 3500 1 P 0(~ 3800) 3 D 1 3 h c(3525) -5000 D 3 (~ 3800) 3 P 1(~ 3880) 3 y ¢¢ (3770) 10 -4 e. V -3000 y ¢¢¢(4040) c 2(3556) c 1(3510) c 0(3415) 3300 8· 10 -4 e. V e+ 0. 1 nm e- 3100 2900 y (3097) hc(2980) C 1 fm C

Tübingen studies in covariant gauges QCD von Smekal, Alkofer et al

Tübingen, Graz, Darmstadt Ghost Fischer Deep Infrared Gluon 20 2 0. 2 distance (fm) 0. 02

Tübingen, Graz, Darmstadt Ghost Fischer Deep Infrared Gluon 20 2 0. 2 distance (fm) 0. 02

Confinement potential QCD von Smekal, Alkofer et al

interquark potential Richardson Potential rp ~ 1 (p) 0, p 0 how does confinement happen?

Alkofer, Fischer, Llanes-Estrada & Schwenzer + + + …

scalar component in vertex V(r) ~ r

Tübingen, Graz, Darmstadt b c mass (Ge. V) Fischer et al s u/d

Tübingen, Graz, Darmstadt Ghost Fischer Gluon 20 2 0. 2 distance (fm) 0. 02

Tübingen, Graz, Darmstadt ? b c mass (Ge. V) Fischer et al s u/d

P S Axial Ward Identity QCD

P S is massless as m q 0

, r calculating hadron masses BSE M ~ 140 P V Scalar/vector mesons q is massless q as m q 0 q q M ~ 770

SDE/BSE – ANL/Kent v MV (Ge. V) pion/vector mesons q q CP-PACS MP 2 (Ge. V 2) P V

SDE/BSE – Tübingen

SDE/BSE – Tübingen v MV (Ge. V) MP (Ge. V) P V Benhaddou, Watson & P

Baryon properties 3 3 3 qq Roberts et al

Baryon properties 3 3 3 N + Roberts et al

Nucleon electromagnetic formfactors * Q q N qq N

Nucleon electromagnetic formfactors * Lomon Iachello, Bij. Q VMD q N qq SDE/BSE Cloet et al N

Nucleon electromagnetic formfactors Lomon Iachello, Bij. VMD SDE/BSE Cloet et al

Nucleon electromagnetic formfactors * Gep 3 Q VMD q N qq SDE/BSE Cloet et al N

Nucleon electromagnetic formfactors * Gep 3 Gep 4, 5 Q VMD q N qq SDE/BSE Cloet et al N

Building bridges SDE/BSE in the continuum

Building bridges SDE/BSE in the continuum connects the lattice to the continuum

Building bridges SDE/BSE in the continuum connects the unphysical to physics

Building bridges SDE/BSE in the continuum connects theory to experiment