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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 ×. - PowerPoint PPT Presentation
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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
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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
NLOLO
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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