Light Hadrons In Chiral Perturbation Theory Elisabetta Pallante
Light Hadrons In Chiral Perturbation Theory Elisabetta Pallante HADRON 07 e. pallante@rug. nl Rijksuniversiteit Groningen
The Many Uses of Chiral Effective Theories
History Theory Its descendants Hot phenomenology Its future
History The formalism of Callan Coleman Wess Zumino (CCWZ) for spontaneously broken global symmetries (1969) Phys. Rev. 177, 2239; 2247 The birth of Chiral Perturbation Theory (Ch. PT) in 1984 Gasser, Leutwyler Ann. Phys. 158, 142 (1984) Nucl. Phys. B 250, 465 (1985) Merging with Heavy Quark Effective Theory (HQET) Eichten, Hill, Phys. Lett. B 234, 511 (1990) Merging with Lattice QCD Bernard, Golterman, EP, Sharpe
Finite T, and density n ts ac tio t ef ola ar rap t ce t ti l ex La ira Ch HBCh. PT HLCh. PT CRMT PQCh. PT LQ CD ET Q H He av yq ua rk s History Ch. PT
The theory External fields Goldstone bosons Pattern of symmetry breaking SU(N)L x SU(N)R SU(N)V N=2, 3
The effective description of a strongly coupled theory Ch. PT Low-energy QCD Expansion in small momenta and light quark masses Its predictive power is entangled to Lc ~ 4 pfp ~ 1 Ge. V
Flavour physics SU(2) mu, md SU(3) mu, md << ms MK << Lc Pion physics Isospin breaking Kaon physics QCD corrections to weak decays Final State Interactions in K pp are pure SU(2) effects
Weak and Strong Decoupling Non decoupling Perturbative matching Non perturbative matching MW OPE mb mc Lc MK Mp Nf=5 Nf=4 Nf=3
Its descendants
Heavy Baryon Ch. PT Heavy-Light Ch. PT Hadrons with anumber heavy quark: strongwe interactions B*, When baryon is conserved can factorofout. B, the D, D* pions baryonwith mass and expand in 1/m. B Double Expansion in 1/m. B and in 1/Lc Heavy quark spin symmetry + Chiral symmetry
Ch. PT and lattice QCD
Typically Goals EFT
QQCD and PQQCD (N=2) QCD QQCD PQQCD ghost+sea
Mass x Volume p-regime mp. L, mp. L 4 >> 1 2 p/L <<Lc << a-1 p/Lc small e’-regime Very asymmetric volumes Approach the chiral limit mp. L ~ e’ << 1 mp. L 4~e’ 2 -a >>1 e-regime mp. L, mp. L 4 ~ e << 1 Zero modes pert. but enhanced ~ Zero-modes resummed
An example: Twisted Mass Ch. PT twisted mass Spurions Power counting c A 2 B 0 (m+imt 3) 2 W 0 a m ~ p 2 ~ a LQCD 2 discretization errors ~ mass effects
Hot phenomenology K decays Rare K decays CKM unitarity Charm physics
Rare K decays ∩ CKM unitarity Kl 3 precise determination of : lepton universality SU(2) breaking/mass ratios SU(3) breaking/ Vus from Kl 3 charm mass is crucial! probes Ch. PT and long distance dynamics
Charm physics Crucial merging of EFT and lattice QCD Charm is not heavy enough Mc >>Lc More relativistic Charm is not light enough Mc >~ Lc smaller discretization errors What needed? Accurate determination of mc Determination of strong interaction phases in D decays probes of CP and indirect probes for physics BSM
Its future In the last two decades we have reshaped our view of quantum field theories. EFT are at the foundations of modern quantum field theory. Effective field theories of low energy QCD significantly contributed to our modern view Where is the future of EFT? High precision very low energy physics e. g. EDM New formalisms? Charm decays Intermediate T, m Bridging (SU)GRA theories and 4 -dimensional universe
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