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Minimal Ward-Takahashi vertices and light cone pion distribution amplitudes from

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. Motivation 1 strong interaction. At level of quark & gluon, dominant non-pert SI effect ：. DCSB & confinement ×.

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Minimal Ward-Takahashi vertices and light cone pion distribution amplitudes from

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  1. Minimal Ward-Takahashi vertices and light cone pion distribution amplitudes from Gauge invariant Nonlocal Dynamical quark model 清华大学物理系 王 青 Nov 27, 2013

  2. Motivation 1 strong interaction At level of quark & gluon, dominant non-pert SI effect： DCSB & confinement × Typical signature of DCSB is nonzero chiral limit √ 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? Pagels & Stokar SDE & BS approach momentum behavior？

  3. Motivation 2 Field theory & New physics M=0 ? Q: Difference between nonlocal interaction and local interaction： NP at LE region usually is described by local operators！ Nonlocal or local？QCD orQFDSearch for UV completion ！ Strongly coupled and composite or weakly interacting and fundamental？

  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 ♣Minimal WT vertices ♣light cone PDAs

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

  6. Minimal WT Vertices

  7. Light cone PDAs

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

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

  10. 模型计算

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

  12. asymptotic flat H.N.Li,Y.L.Shen,Y.M.Wang,ArXiv:1310.3672[hep-ph] Non-asymptotic a2=0.05 NLO JR LO JR NLO NLO CR LO LO CR

  13. 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 someend point delta function terms

  14. 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 !

  15. 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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