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
light cone pion distribution amplitudes
Gauge invariant Nonlocal Dynamical 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 ×
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?
Pagels & Stokar
SDE & BS approach
Motivation 2 Field theory & New physics
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？
√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
drop some Ω terms
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
Nonlocal quark self energy
Why simplest flat PDA offers best fit ?
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
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 !
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 !