Chiral Dynamics and Peripheral Transverse Densities

Transcription

1 Chral Dnamcs and erpheral Transverse Denses Chare and Curren Denses Ener omenum Tensor and Oral nular omenum Carlos Granados Chrsan Wess Jefferson La Vrna US

2 m and Cone Spaal represenaon of hadrons as relavsc ssems GDs Transverse Denses Unversal n lare dsance dnamcs: Chral smmer rean effecve feld heor Sud of chral perpher of ransverse nucleon srucure Chare and curren denses E form facors aer dens and anular momenum ener momenum ensor and GDs

3 ehodolo ovaon Reveal spaal srucure of χet: π - vs. shor dsance conruons Eplore dfferen formulaons of oral anular momenum n feld heor appled o a π ssem raccal Calculae model ndependen chral componens of he nucleon srucure Consran form facors perpheral GDs Epermen orm facors measuremens n he low Q reon JLa E--6 Q ~ GeV Connec chral dnamcs wh erpheral rocesses n Hh Ener ep and pp Reacons: EIC LHC

4 ehodolo χet L π Invaran ormulaon Infne omenum rame Specral uncons Im EQUIVLET TRSVERSE DESITIES ρ Lh-Cone W Ψ GDs ρh

5 ourer Transform n Transverse omenum rom Elecromanec E orm acors rom Ener-omenum Tensor ET Transverse Chare and Curren Denses Defnon U U J Δ Δ U U Δ C ~ Δ C Δ B Δ J d T T e d T

6 Transverse Chare and Curren Denses Defnon d T e T T Chare dsruon n ransverse plane: roper denses Relavsc Ssems roper d σ J σ δ δ ρ aron curren pcure G.ller RL997 T T J T T Δ J Δ T T... S T e T ρ σ σ

7 Transverse Chare and Curren Denses Dsperson Represenaon Specral uncons orm acors nalc Connuaon Im p l Or an - channel echane π Branch cu Re Dsperson Relaon : or Re< d Im

8 Transverse Chare and Curren Denses Dsperson Represenaon Specral uncons and nalc Srucure ear Threshold Im d J d Im π d

9 Transverse Chare and Curren Denses Dsperson Represenaon Specral uncons d Im π =.75/ π - e =/ π - =.5/ π - s rows s sampled closer o hreshold hr = π

10 Transverse Chare and Curren Denses Dsperson Represenaon Specral uncons or lare Transverse denses are domnaed near hreshold values of specral funcons Im

11 Transverse Chare and Curren Denses nalc Srucure ear Threshold Im p su π Su-hreshold snular End-pon snular Inermedae nucleon on-shell π θ l Re l Im Lms converence of epanson near hreshold Conrols lare ~ - π ehavor of ransverse denses su l B cos ~ B f cos dcos B cos su su

12 Transverse Chare and Curren Denses aramerc Reons Chral Reon Δ~ ~ /.5fm olecular Reon Δ > 56 9fm

13 erpheral Denses from Invaran χt Chral ET Laranan Relavsc formulaon of pon-nucleon dnamcs a a a ac c L n 5... al Vecor coupln and conac erms E curren. Leadn π conruons o sovecor specral funcons: J Δ U J U Δ

14 erpheral Denses from Invaran χt nd Specral uncons Im nsead Cuos Rules on on mass-shell 8 8 I I I l D D D d I D D d I m m D l D D d I cm cm d I cos 6 Im p p cm

15 Specral uncons Su-hreshold snular a su =± erpheral Denses from Invaran χt arcan Im 6 arcan 8 arcan 8 Im 5 5 su Im Im Srman Wess RC8

16 erpheral Denses from Invaran χt d π Im

17 erpheral Denses from Invaran χt Chral vs. on-chral Chral componen domnan onl a >> fm ρ~e - π π π ρ~e - ρ ρ ller Srman Wess RC8 55

18 erpheral Denses from Invaran χt Heav Baron Epanson ~ O C C C HB f ε f f f Im HB C Im %Dff.

19 erpheral Denses from Invaran χt Heav Baron Epanson

20 erpheral Denses from Invaran χt Conruons from Δ and Lare c Lm Conssenc wh QCD n he Lare c Lm Lare c π ~ c Δ ~ c π ~ c / πδ ~ c / ρ~ c Bu n he Lare c Lm consdern onl nucleonc nermedae sae χt conruons o lead o B c c Conruons from Δ- nermedae saes remed hs dscrepanc B B c B c c Δ

21 erpheral Denses from Invaran χt Conruons from Δ and Lare c Lm π Δ comparale o π a < fm Cancelaon of leadn c componen

22 erpheral Denses n Lh-ron χt Develop a paronc formulaon of chral dnamcs Chare and curren of pons n he chral perpher Oral anular momenum decomposon of chral π- LCW Demonsrae equvalence wh nvaran formalsm Connec o GD formalsm Compue model ndependen χgds

23 orm facors from he nfne momenum frame LCW from π pseudo scalar coupln In mpac parameer space T T L T T d d d d c J J L U U T 5 T T e d T erpheral Denses n Lh-ron χt

24 Transverse denses from form facors Chare and curren denses from pon-nucleon lh-cone wave funcons wh T T e d T C.T. d d R e erpheral Denses n Lh-ron χt

25 d Slower pons a larer mpac parameer = π / d erpheral Denses n Lh-ron χt

26 Ener-omenum Tensor: aer dens and Oral nular omenum Ener-omenum ensor form facors calculale n χt nular momenum of a pon-nucleon ssem Transverse denses ρ ρ B from form facors and B and +B. B d Im B π Calculaed leadn chral conruon o specral funcons Cuos Rules. o conac erm darams! B ~ C C u p u p hr J B [X.JRD97]

27 smpoc ehavor of ρ conroled Im a hreshold and near hreshold arcan Im arcan 8 Im 5 5 B... ~ O... ~ O Ener-omenum Tensor: aer dens and Oral nular omenum

28 Ener-omenum Tensor: aer dens and Oral nular omenum ET form facors n I Correspondn Transverse denses as overlap of LC- wave funcons aer dsruons n mpac parameer space: omens of paron dsruons d d B R B L ρ = ρ / = π /

29 Ener-omenum Tensor: aer dens and Oral nular omenum d d B

30 Summar Eplored ucleonc Srucure n a sen ha uaranees a model ndependen analss of he dnamcs overned χ ET. Derved E and ET ransverse perpheral denses from correspondn rom specral funcons nvaran formalsm Dsnush paramercal reons chral and molecular scales ccurac of he Heav Baron epanson Conssenc wh he QCD Lare c lm add Δ- conruon Lh fron χt I Equvalen o nvaran formalsm Calculaed ransverse denses from LC-Wave uncons Connecon o GD formalsm

31 Ouloo Undersand orn of conac erm hher mass saes nucleon composeness Use he chral pon nucleon ssem as a o model for eplorn he naure of oral anular momenum O and oher operaors n feld heor momens of GDs al form facors Tes use of π-lcw n epermenal sudes a Low and Hh eneres erpheral eclusve processes n e- scaern a EIC [Srman Wess hs.rev. D69 5; EIC Whe aper ]