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

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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? momentum behavior ？

Pagels & Stokar

At level of quark & gluon, dominant non-pert SI effect ：

SDE & BS approach

chiral limit

Motivation 1 strong interaction

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Motivation 2 Field theory & New physics

Q: Difference between nonlocal interaction and local interaction ：

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 ？

M=0 ?

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√ 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

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GND quark model

drop some Ω terms Σ(0)

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Minimal WT Vertices

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Light cone PDAs

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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

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B=0.00

B=0.30

B=0.60

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

PRD 88,034013(2013)

唯像拟合

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模型计算

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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

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asymptotic flat

Non-asymptotic a2=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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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

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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 !

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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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