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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

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？

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？

√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

GND quark model

Σ(0)

drop some Ω terms

Minimal WT Vertices

Light cone PDAs

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

唯像拟合

B=0.60

T.Huang,T.Zhong,X.G.Wu

PRD 88,034013(2013)

B=0.30

B=0.00

模型计算

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 ?

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

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 !