1. Minimal Ward-Takahashi vertices and light cone pion distribution amplitudes from G auge invariant N onlocal D ynamical quark model 清华大学物理系 王 青 Nov 27, 2013

2. 2 Typical signature of DCSB is nonzero √ Dynamical perturbation ： Phys.Rev.D20,2974(1979) Only include in effects from √ Later various local &nonlocal quark models ： B.Holdom ， Phys.Rev.D45,2534(1992) QCD → GND quark model ： Y.Hua,Q.Wang,Q.Lu,Phys.Lett.B532,240(2002) → LEE→ LECs Go beyond low energy expansion? Go beyond low energy expansion? momentum behavior ？ Pagels & Stokar At level of quark & gluon, dominant non-pert SI effect ： SDE & BS approach chiral limit Motivation 1 strong interaction

3. 3 Motivation 2 Field theory & New physics Q: Difference between nonlocal interaction and local interaction ： Nonlocal or local ？ Search for UV completion ！ Nonlocal or local ？ QCD or QFD Search for UV completion ！ NP at LE region usually is described by local operators ！ Strongly coupled and composite or weakly interacting and fundamental ？

4. 4 √ Light cone PDA taken as an example to search the difference √ Ward-Takahashi identity offers constraints on nonlocal interaction √ WT vertex ： vertex satisfy WT identities GND quark model ♣ GND quark model ♣ Minimal WT vertices light cone PDAs ♣ light cone PDAs

5. 5 GND quark model drop some Ω terms Σ(0)

6. 6 Minimal WT Vertices

7. 7 Light cone PDAs

8. 8 I.C.Cloet,L.Chang,C.D.Roberts,S.M.Schmidt,P.C.Tandy, PRL 111,092001(2013) DSE best truncation DSE rainbow-ladder truncation Asymptotic solution Allowed by α - errors

9. 9 B=0.00 B=0.30 B=0.60 T.Huang,T.Zhong,X.G.Wu PRD 88,034013(2013) 唯像拟合

10. 10 模型计算

11. 11 Latest nonlocal chiral quark model: D.G.Dumm,S.Noguera,N.N.Scoccola,S.Scopette, ArXiv1311.3595 LO of evolution NLO LO NLO Nonlocal quark self energy Flat PDA Why simplest flat PDA offers best fit ? ASY ASY 模型计算

12. 12 asymptotic flat Non-asymptotica 2 =0.05 H.N.Li,Y.L.Shen,Y.M.Wang,ArXiv:1310.3672[hep-ph] NLO JR LO JR NLO CR LO CR NLO LO

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16. 16 Conclusion strong interaction √ Direct apply GND quark model to hadron physics is possible √ Not like most results of other works: Local & nonlocal quark masses produce the same flat PDAs at the chiral limit with minimal WT vertices √ The possible non-flat correction comes from: finite momentum cut-off ； nonzero current quark mass plus some end point delta function terms

17. 17 Conclusion field theory √ GND quark model satisfies WTIs, leads minimal WT vertices √ Conventional Feynman parameter can be interpreted as PDA variable u: light-front fraction of π’s total momentum carried by valence quark or momentum fraction carried by valence quark in infinite-momentum frame √ At least for PDAs, there are no qualitative differences between local and nonlocal four fermion interactions Not reach to original aim !

18. 18 Conclusion new physics √ PDAs are not good quantities to judge the underlying interaction is strongly interacting and composite or weakly interacting and fundamental ? √ Present local operator EFT description of particle physics seems good !

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