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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

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


Minimal ward takahashi vertices and light cone pion distribution amplitudes from

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?


Minimal ward takahashi vertices and light cone pion distribution amplitudes from

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?


Minimal ward takahashi vertices and light cone pion distribution amplitudes from

√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


Minimal ward takahashi vertices and light cone pion distribution amplitudes from

GND quark model

Σ(0)

drop some Ω terms


Minimal ward takahashi vertices and light cone pion distribution amplitudes from

Minimal WT Vertices


Minimal ward takahashi vertices and light cone pion distribution amplitudes from

Light cone PDAs


Minimal ward takahashi vertices and light cone pion distribution amplitudes from

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


Minimal ward takahashi vertices and light cone pion distribution amplitudes from

唯像拟合

B=0.60

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

PRD 88,034013(2013)

B=0.30

B=0.00


Minimal ward takahashi vertices and light cone pion distribution amplitudes from

模型计算


Minimal ward takahashi vertices and light cone pion distribution amplitudes from

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 ?


Minimal ward takahashi vertices and light cone pion distribution amplitudes from

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


Minimal ward takahashi vertices and light cone pion distribution amplitudes from

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


Minimal ward takahashi vertices and light cone pion distribution amplitudes from

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 !


Minimal ward takahashi vertices and light cone pion distribution amplitudes from

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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