Pion-Pion Scattering and Vector Symmetry

Transcription

1 0 th National Nuclear Physics Suer School Pion-Pion Scattering and Vector Syetry egina Azevedo ongoing work with Pro. Bira van Kolck University o Arizona Supported in part by US DOE

2 Outline Motivation Chiral Perturbation Theory Vector Model Breaking Vector Syetry Pion-Pion Interaction Conclusion and Outlook

3 Experiental data and χpttheory T Scattering aplitudes Exp. bup NO χpt O χpt ail -energies s MeV Donoghue airez Valencia 88 IDEA: Include -eson in EFT with a rational power counting and low-energy degree o reedo Might be iportant or nuclear physics?

4 lobal roups Chiral Perturbation Theory = SU SU H = SU V Weinberg 79 asser eutwyler 84 γ r r 5 iα τ / q = q e Spontaneously broken isospin q = Massless particles Pauli atrices in isospin space r r = σ Field atrix oldstone bosons: pions = e i = 93.MeV decay constant o the pion

5 lobal/ocal roups Vector Syetry H. eorgi 90 P. Cho 90 = SU SU SU SU dynaic groups; only hadronic level Vector Syetry break H = SU SU Massless particles oldstone bosons: Pions pseudoscalars and Scalars? i e e is = i e e is Eaten by Higgs echanis longitudinal

6 Building EFT agrangian Ininite powers o series operators o increasing diension with unspeciied coeicients Each derivative Q M QCD Each ter M QCD Q ~ Each ass Q M QCD = n e VS n n n = = O Q n VS M QCD M QCD n = O NO = Tr VS i i

7 Tr = D i D i ig D = ig D = = M M M i g g [ ] ig ν ν ν ν = Breaking Vector Syetry M M Tr ν ν ν ν Tr ive ass to the eson ive ass to the pions...

8 ˆ g Tr e = Tr Tr Tr ν ν ˆ Tr [ ] Tr... igtr [ ] [ ν g Tr ][ ] ν ν ν ig igtr [ ] Tr [ [ [ ]

9 χpt Q Q ~ ~ O ~ Q Pion-Pion Scattering Q 4 Power Counting Vector ealization NO Close to resonance. Azevedo U. van Kolck Q ~ δq Q Q ~ ~ ~ >> δq enhanceent << 0 T = I= l= = Π ν i iπ ν i Π ν i Π ν =

10 i i s i e it δ Γ Γ = = = Γ e ν Π = ν = I Π Γ Bare ass a paraeter o the agrangian enoralized ass observable

11 Preliinaries resonance Protopopescu et al7 it : exp. : 50 5 = MeV = 770 ± 3MeV Vector eal. O Fit smev it : Γ exp. : Γ OK qualitatively quantitatively: NO = 75.8MeV = 53 ± MeV

12 Next-to-leading order NO T = Γ Π Q Γ = Π = All loops diagras

13 Conclusions and Outlook Vector ealization: a possible way to introduce in the EFT with a rational power counting; scattering: O NO next ; Include -nucleon interactions in the theory----nuclear orces. Γ OK Not OK yet

14 Experiental data and theory χpt Phase Shit l= I= NO χpt O χpt ail asser Meissner 9 higher energies IDEA: Include in EFT Might be iportant or nuclear physics?

15 Motivation eading order O or the inite range o the nucleon-nucleon interaction exchanging one pion = r e S e r r r r V r r OPE σ σ τ τ ˆ ˆ 3 σ σ σ σ = r r S The only other eson with isospin one in the nucleon-nucleon interaction is the -eson Also -ass is large and the -interaction thereore short-ranged.

16 The tensor ters arise ro one-pion-exchange and one-rho-exchange potentials Inclusion o the rho in EFT should reduce the N tensor orce at short distances The idea is sipliying the renoralization o the O nuclear potential by canceling the with the counterters ound in the pionul EFT J. SpethV. Klet J. Wabach.E.Brown Nucl. Phys. A We need power expansions o Suggestion: A new realization o Chiral Syetry The Vector Phenoenology M QCD H. eorgi Nucl. Phys. B ; P. Cho Nucl. Phys. B