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Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary amplitudes --

Transcript of Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade...

Page 1: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

PionElectroproduc/ons

SatoshiNakamura

UniversidadeCruzeirodoSul(Brazil)

--Analysisofelectrondataandextrac?onofelementaryamplitudes--

Page 2: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

Introduc/on

Howelectronsca5eringisrelevanttoneutrinosca5ering

Page 3: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

Rela/onbetweenneutrinoandelectron(photon)interac/ons

Lcc = GFVud2[Jλ

ccccλ

+ h.c. ]

Charged-current(CC)interac?on(e.g.νµ + n à µ- + p )

Jλcc =Vλ − Aλ cc

λ =ψµγλ (1−γ5 )ψν

Electromagne?cinterac?on(e.g.γ (*) + p à p )

Lem = e JλemAem

λ

Jλem =Vλ +V

ISλ

< p |Vλ | p > = − < n |Vλ | n > < p |V ISλ | p > = < n |V

ISλ | n >

V andVISinJem canbeseparatelydeterminedbyanalyzingphotonforQ2=0

andelectronreac?on(e,e’π), (e,e’X) dataforQ2≠0onbothprotonandneutrontargets, because:

Matrixelementfortheweakvectorcurrentisobtainedfromanalyzingelectromagne?cprocesses

< p |Vλ | n > = 2 < p |Vλ | p >

Page 4: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

Strategytodevelopneutrino-nucleonmodel

•  Vectorcurrent(formfactor)isfixedbyanalyzingelectronscaPeringdata

ßabundantprecisedataareavailable

•  Axialcurrentamplitudecanbedeterminedbyanalyzing:

--Neutrino-nucleon,nucleusdata

--Parity-viola?nginclusiveelectronscaPeringdata

Page 5: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

pionproduc?on

Strategytodevelopneutrino-nucleonmodel

•  Vectorcurrent(formfactor)isfixedbyanalyzingelectronscaPeringdata

ßabundantprecisedataareavailable

•  Axialcurrentamplitudecanbedeterminedbyanalyzing:

--Neutrino-nucleon,nucleusdata

--Parity-viola?nginclusiveelectronscaPeringdata

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pionproduc?on

Strategytodevelopneutrino-nucleonmodel

•  Vectorcurrent(formfactor)isfixedbyanalyzingelectronscaPeringdata

ßabundantprecisedataareavailable

•  Axialcurrentamplitudecanbedeterminedbyanalyzing:

--Neutrino-nucleon,nucleusdata

(neutrino-deuteronpiondataßT.Sato’stalk)

--Parity-viola?nginclusiveelectronscaPeringdata

inthenucleonresonanceregion(laterinthistalk)

pionelectroproduc?ondata

pionproduc?ondata

NàN*

Page 7: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

pionproduc?on

Strategytodevelopneutrino-nucleonmodel

•  Vectorcurrent(formfactor)isfixedbyanalyzingelectronscaPeringdata

ßabundantprecisedataareavailable

•  Axialcurrentamplitudecanbedeterminedbyanalyzing:

--Neutrino-nucleon,nucleusdata

(neutrino-deuteronpiondataßT.Sato’stalk)

--Parity-viola?nginclusiveelectronscaPeringdata

inthenucleonresonanceregion(laterinthistalk)

•  Ouranalysisisdonewithdynamicalcoupled-channels(DCC)model

Inthefollowing:

*DCCmodel*DCCanalysisofpionelectroproduc?ondata*Comparisonwithothermodels*PVelectronscaPering

pionelectroproduc?ondata

pionproduc?ondata

NàN*

Page 8: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

DynamicalCoupled-Channelsmodel

Unifieddescrip?onofpion-,electron-,andneutrino-inducedmesonproduc?ons

Page 9: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

Dynamicalcoupled-channelsmodelformesonproduc?onsinresonanceregion

Δ

2nd 3rdDataforγ p è X

  Severalnucleonresonancesformcharacteris?cpeaks  2π produc?oniscomparableto1πη, Κproduc?ons(mul?-channelcouplingsareimportantphysics)

Needdevelopamodel

todescribethesereac?ons

Page 10: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

Dynamicalcoupled-channelsmodelforresonanceregion

  Channel-couplingsrequiredbyunitarity(πΝ, ηΝ, ΚΛ, ΚΣ stablechannels)

  2π produc?onmechanisms(ρΝ, σΝ , πΔ ßàππΝ channels)

Theore?callysoundmodelshouldalsoaccountfor:

DynamicalCoupled-Channels(DCC)modelaccountsforthesefeatures

developedthroughanalyzingdataforγΝ, πΝ è πΝ, ηΝ, ΚΛ, ΚΣ

∼ 26,000 datapoints

N*iΣ

i+ + + ...

Resonanceexcita?on+non-resonantmeson-exchangemechanisms

γ π, η, Κ

Page 11: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

,

Coupled-channelsandhadronrescaPeringrequiredbyunitarityisfullytakenintoaccount

Kamanoetal.,PRC88,035209(2013)

Inaddi?on,γΝ channelisincludedperturba?vely

Coupled-channelLippmann-Schwingerequa?onformeson-baryonscaPering

Page 12: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

,

Coupled-channelsandhadronrescaPeringrequiredbyunitarityisfullytakenintoaccount

Kamanoetal.,PRC88,035209(2013)

Inaddi?on,γΝ channelisincludedperturba?vely

Coupled-channelLippmann-Schwingerequa?onformeson-baryonscaPering

Page 13: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

,

Coupled-channelsandhadronrescaPeringrequiredbyunitarityisfullytakenintoaccount

Kamanoetal.,PRC88,035209(2013)

Inaddi?on,γΝ channelisincludedperturba?vely

Coupled-channelLippmann-Schwingerequa?onformeson-baryonscaPering

Page 14: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

,

Coupled-channelsandhadronrescaPeringrequiredbyunitarityisfullytakenintoaccount

Kamanoetal.,PRC88,035209(2013)

Inaddi?on,γΝ channelisincludedperturba?vely

Coupled-channelLippmann-Schwingerequa?onformeson-baryonscaPering

π

Δ

Page 15: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

BysolvingtheLSequa?on,coupled-channelunitarityisfullytakenintoaccount

,

Kamanoetal.,PRC88,035209(2013)

Coupled-channelLippmann-Schwingerequa?onformeson-baryonscaPering

TV V V

Inaddi?on,γΝ channelisincludedperturba?vely

T

Page 16: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

Kamano,Nakamura,Lee,Sato,2012 Kamano,Nakamura,Lee,Sato,PRC88(2013)

γpàπ0p dσ/dΩforW<2.1GeV ComparisonofDCCmodelwithdata

Reasonablefittodata

inthewholeresonanceregion

Vectorcurrent(Q2=0)for1π

Produc?oniswell-testedbydata

Page 17: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

Par/alwaveamplitudesofπNsca5ering

Kamano, Nakamura, Lee, Sato, PRC88(2013)

Previous model (fitted to πN à πN data only) [PRC76 065201 (2007)]

Real part

Imaginary partData:SAIDπΝamplitude

Page 18: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

Par/alwaveamplitudesofπNsca5ering

Kamano, Nakamura, Lee, Sato, PRC88(2013)

Previous model (fitted to πN à πN data only) [PRC76 065201 (2007)]

Real part

Imaginary partData:SAIDπΝamplitude

ConstraintonaxialcurrentthroughPCAC

Page 19: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

Analysisofpionelectroproduc/ondata

withdynamicalcoupled-channelsmodel

SXN,H.Kamano,andT.Sato,Phys.Rev.D92,074024(2015)

Page 20: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

γ * (q)e - (k)

e - (k’)

π

Crosssec?onforsinglepionelectroproduc?on

x*:variablesinCMofthefinalπΝ system

σX ( X = T, L, LT, LT ’, TT ) :structurefunc?onsh :electronhelicity

Only σT + ε σL contributestotheintegratedcrosssec?on

àMostimportantstructurefunc?ons

Page 21: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

•  p(e,e’π0)p•  p(e,e’π+)n•  both

Analysisofelectron-protonscaPeringdata

Purpose:DetermineQ2–dependenceofvectorcouplingofp-N*:VpN*(Q2)

Data:*1π electroproduc?on

0

1

2

3

1.2 1.4 1.6 1.8 2

Q2 (G

eV/c

)2

W (GeV)

Database

Page 22: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

•  p(e,e’π0)p•  p(e,e’π+)n•  both

Analysisofelectron-protonscaPeringdata

Purpose:DetermineQ2–dependenceofvectorcouplingofp-N*:VpN*(Q2)

Data:*1π electroproduc?on

0

1

2

3

1.2 1.4 1.6 1.8 2

Q2 (G

eV/c

)2

W (GeV)

Database

Page 23: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

•  p(e,e’π0)p•  p(e,e’π+)n•  both

Analysisofelectron-protonscaPeringdata

Purpose:DetermineQ2–dependenceofvectorcouplingofp-N*:VpN*(Q2)

Data:*1π electroproduc?on

0

1

2

3

1.2 1.4 1.6 1.8 2

Q2 (G

eV/c

)2

W (GeV)

Database

*Empiricalinclusiveinelas?cstructurefunc?onsσΤ , σL çChristyetal,PRC81(2010)

regionwhereinclusiveσΤ & σL arefiPed

Page 24: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

AnalysisresultQ2=0.40(GeV/c)2

σΤ + ε σL forW=1.1–1.68GeV

p(e,e’π0)p p(e,e’π+)n

0

10

20

301100 1120 1140 1160 1180

1200

0

10

20

1220 1240

1260 1280 1300 1320

0

4

1340 1360 1380 1400

1420 1440

0

4 1460

1480 1500 1520

1540 1560

0

4

-1 0 1cos θπ*

1580

0 1cos θπ*

1600

0 1cos θπ*

1620

0 1cos θπ*

1640

0 1cos θπ*

1660

0 1cos θπ*

1680

0

10

201110 1130 1150 1170 1190

1210

0

10

1230 1250 1270 1290 1310 1330

0

5

101350 1370 1390 1410 1430

0 1cos θπ*

1450

0

5

10

-1 0 1cos θπ*

1470

0 1cos θπ*

1490

0 1cos θπ*

1510

0 1cos θπ*

1530

0 1cos θπ*

1550

Page 25: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

0

200

400

1200 1400 1600 1800 2000

σT,

L (µ

b)

W (MeV)

AnalysisresultQ2=0.40(GeV/c)2

σΤ & σL (inclusiveinelas?c)

DCC

ChristyetalPRC81σΤ

σL

regionwhereinclusiveσΤ & σL arefiPed

Page 26: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

0

1

2

31150 1170 1190

1210 1230 1250

0

1

21270 1290 1310 1330 1350 1370

0

1

21390 1410 1430 1450

1470 1490

0

1

2

1510 1530

1550 1570 1590 1610

0

1

21620 1630 1650 1660 1670 1700

0

1

2

-1 0 1cos θπ*

1740

0 1cos θπ*

1780

0 1cos θπ*

1830

0 1cos θπ*

1890

0 1cos θπ*

1950

0 1cos θπ*

2010

AnalysisresultQ2=1.76(GeV/c)2

σΤ + ε σL forW=1.1–2.1GeV

p(e,e’π0)p

p(e,e’π+)n

0

1

2

31100 1120 1140 1160 1180

1200

0

1

2

1220 1240

1260 1280 1300 1320

0

1

21340

0 1cos θπ*

1360

0 1cos θπ*

1380

0 1cos θπ*

1400

0 1cos θπ*

1420

0 1cos θπ*

1440

0

1

2

-1 0 1cos θπ*

1460

Page 27: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

0

10

20

30

40

50

1200 1400 1600 1800 2000

σT,

L (µ

b)

W (MeV)

AnalysisresultQ2=1.76(GeV/c)2

σΤ & σL (inclusiveinelas?c)

DCC

ChristyetalPRC81σΤ

σL

regionwhereinclusiveσΤ & σL arefiPed

Page 28: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

AnalysisresultQ2=2.95(GeV/c)2

σΤ + ε σL forW=1.11–1.67GeV

p(e,e’π0)p p(e,e’π+)n

0

0.5

11100 1130 1150 1170 1190

1210

0

0.5

1230

1250 1270

0 1cos θπ*

1290

0 1cos θπ*

1310

0 1cos θπ*

1330

0

0.5

-1 0 1cos θπ*

1350

0 1cos θπ*

1370

0 1cos θπ*

1390

0

0.5

11150 1170 1190

1210 1230 1250

0

0.5

1270 1290 1310 1330 1350 1370

0

0.5

1 1390 1410 1430

1450 1470 1490

0

0.5

1

1510 1530 1550

0 1cos θπ*

1570

0 1cos θπ*

1590

0 1cos θπ*

1610

0

0.5

-1 0 1cos θπ*

1630

0 1cos θπ*

1650

0 1cos θπ*

1670

Page 29: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

10

20

1200 1400 1600 1800 2000

σT,

L (µ

b)

W (MeV)

AnalysisresultQ2=2.95(GeV/c)2

σΤ & σL (inclusiveinelas?c)

DCC

ChristyetalPRC81σΤ

σL

regionwhereinclusiveσΤ & σL arefiPed

Page 30: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

Data:JLabE00-002(preliminary)

•  Reasonablefittodataforapplica?ontoneutrinointerac?ons•  Important2π contribu?onsforhighWregion

  

 

Inclusiveelectron-protonsca5ering

0

0.1

0.2

1.2 1.4 1.6 1.8 2

d σ

/d Ω

d E

’ (µ

b/sr

GeV

)

W (GeV)

Ee=5.498 GeVQ2=0.96-1.3 (GeV/c)2

θe’=12.97o

0

1

2

3

1.2 1.4 1.6 1.8 2

d σ

/d Ω

d E

’ (µ

b/sr

GeV

)

W (GeV)

Ee=3.118 GeVθe’=12.45o

Q2=0.21-0.40 (GeV/c)2

Page 31: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

Purpose:Vectorcouplingofneutron-N*anditsQ2–dependence:VnN*(Q2) (I=1/2)

I=3/2 parthasbeenfixedbyprotontargetdata

Analysisofelectron-’neutron’scaPeringdata

Data:*1π photoproduc?on(Q2=0)

*Empiricalinclusiveinelas?cstructurefunc?onsσΤ , σL (Q2≠0) çChristyandBosted,PRC77(2010),81(2010)fiPedtoelectron-deuterondataandelectron-protonstructurefunc?onsaresubtracted

Page 32: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

AnalysisresultQ2=0 dσ / dΩ (γ n è π-p) forW=1.1–2.0GeV

0

20

401130 1143 1148 1155

1163 1171 1179 1187 1195 1200 1206 1212

0

201218 1224 1230

1237 1245 1252 1257 1263 1271 1276 1282 1288

0

101300 1308 1315 1320 1329 1336 1343 1349 1357 1363 1371 1378

0

101391 1398 1405 1411 1418 1425 1431 1438 1444 1449 1457 1463

0

101469 1476 1483 1490 1495 1508 1514 1520 1526 1533 1539 1545

0

51551 1557 1569 1575 1587 1604 1616 1625 1633 1648 1662 1673

0

51690 1704 1718 1728 1734 1739 1745 1758 1771 1785 1798

0 1cos θπ*

1819

0

2

4

-1 0 1cos θπ*

1824

0 1cos θπ*

1844

0 1cos θπ*

1849

0 1cos θπ*

1869

0 1cos θπ*

1875

0 1cos θπ*

1894

0 1cos θπ*

1899

0 1cos θπ*

1924

0 1cos θπ*

1948

0 1cos θπ*

1972

0 1cos θπ*

1996

Page 33: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

AnalysisresultQ2=0

dσ / dΩ (γ n è π0n) forW=1.2–1.9GeV

0

20

40

1206 1230 1252 1257

1276 1282 1308 1320 1336 1349 1357 1363

0

51391

1405 1425 1457 1469 1483 1490 1495

0 1cos θπ*

1514

0 1cos θπ*

1520

0 1cos θπ*

1526

0 1cos θπ*

1539

0

2

4

-1 0 1cos θπ*

1551

0 1cos θπ*

1581

0 1cos θπ*

1604

0 1cos θπ*

1611

0 1cos θπ*

1616

0 1cos θπ*

1764

0 1cos θπ*

1869

0 1cos θπ*

1875

Page 34: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

10

20

30

1200 1400 1600 1800 2000

σT,

L (µ

b)

W (MeV)

50

100

150

1200 1400 1600 1800 2000

σT,

L (µ

b)

W (MeV)

Analysisresult

Q2=1(GeV/c)2

σΤ & σL (inclusiveinelas?ce—-’n’ ) DCC

ChristyandBostedPRC77;81

σΤ

σL

Q2=2(GeV/c)2

σL

σΤ

Q2≠0

Page 35: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

0

0.01

1.2 1.4 1.6 1.8 2

d σ

/d Ω

d E

’ (µ

b/sr

GeV

/A)

W (GeV)

Q2=1.76-2.64 (GeV/c)2θe’=25.00o

1π1π

Data:NPB(Proc.Suppl.)159,163(2006)

•  Modelàaverageofelectron-protonandelectron-neutrondifferen?alcrosssec?ons

ànucleareffects(Fermimo?on,FSI)areignored

•  SpreadofresonancewidthindataàFermimo?on

  

 

Inclusiveelectron-deuteronsca5ering

0

0.5

1

1.5

1.2 1.4 1.6 1.8 2

d σ

/d Ω

d E

’ (µ

b/sr

GeV

/A)

W (GeV)

Q2=0.44-0.66 (GeV/c)2θe’=10.65o

Page 36: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

0

0.01

1.2 1.4 1.6 1.8 2

d σ

/d Ω

d E

’ (µ

b/sr

GeV

/A)

W (GeV)

Q2=1.76-2.64 (GeV/c)2θe’=25.00o

1π1π

Data:NPB(Proc.Suppl.)159,163(2006)

•  Modelàaverageofelectron-protonandelectron-neutrondifferen?alcrosssec?ons

ànucleareffects(Fermimo?on,FSI)areignored

•  SpreadofresonancewidthindataàFermimo?on

  

 

Inclusiveelectron-deuteronsca5ering

DCCvectorcurrentshasbeentestedbyofe—-p &e—-’n’dataforwholekinema>calregion

relevanttoneutrinointerac>onsofEν ≤ 2GeVàisospinsepara>onàweakvectorcurrent

0

0.5

1

1.5

1.2 1.4 1.6 1.8 2

d σ

/d Ω

d E

’ (µ

b/sr

GeV

/A)

W (GeV)

Q2=0.44-0.66 (GeV/c)2θe’=10.65o

Page 37: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

EMNàN*transi?onformfactors

NàΔ(1232) H.Kamano,NSTAR2017

•  Evaluatedattheresonancepoleposi?onàformfactorsarecomplex

Page 38: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

EMNàN*transi?onformfactors

NàΝ (1440) H.Kamano,NSTAR2017

•  Evaluatedattheresonancepoleposi?onàformfactorsarecomplex

Page 39: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

Comparisonwithothermodels

Hernandez,SXN,Nieves,Sato,Sobczyk,inprepara?on

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TheSLmodel T.SatoandT.S.H.Lee,PRC54,2660(1996)T.SatoandT.S.H.Lee,PRC63,055201(2001)

•  Δ(1232)-excita?onmechanisms

•  Meson-exchangenon-resonantmechanisms

•  π N channelisincluded

•  HadronrescaPeringandπ N unitarity

TheSLmodeldescribesπ Nà π N scaPeringandelectroweakpionproduc?onintheΔ(1232)-regionisreasonablydescribedinaunifiedmanner

Themodeltakesaccountof:

TheDCCmodelcanbeviewedasanextensionoftheSLmodel

byincludingothermeson-baryonandππ N channelsandresonances

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TheHNVmodelHernandez,Nieves,Valverde,PRD76,033005(2007)Alvarez-Rusoetal.,PRD93,014016(2016)HernandezandNievesPRD95,053007(2017)

W W

W W

W

W

+ +

+ +

+

+

+

W

∆N

N

N’N’

N’

N’

N’

π π

π π

π π

ππ

N’

N

NN N’

N

N π

N N

, D13

, D13

•  Resonance-excita?onmechanisms

Δ(1232) andD13(1520)

•  Non-resonantmechanisms

derivedfromchiralLagrangian

•  HadronrescaPeringisnotexplicitly

considered

àphasesaremul?pliedtoP33

amplitudetosa?sfy

theWatsontheorem(unitarity)

•  u-channelΔ propagatorismodified

tofitbePerνµ n à µ- π+ n data

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ComparisonofDCC,SL,andHNVmodelsHernandez,SXN,Nieves,Sato,Sobczyk,inprepara?on

Inclusiveelectron-protonscaPeringData:PRL53,1627(1984)

•  GoodagreementbetweenmodelsanddataattheΔ(1232) peak

•  SL(HNV)modelgivessmallercrosssec?onshigher(lower)energies

Q2=0.04-0.18GeV2

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Comparison(cont’d)Singlepionelectroproduc?on

•  Goodagreementbetweenmodelsanddata

formostofstructurefunc?ons

•  HNVmodelgivesrathersmallσLT’

forp ( e,e’ π0 ) p ß σLT’isfromnon-zerorela?vephasebetween

differentmechanismsandformfactors

ßDCCandSLmodelsincludemeson-loops

toproduceaddi?onalphases;HNVdoesnot

×

Q2=0.4GeV2,WπN = 1.22GeVp ( e,e’ π0 ) p p ( e,e’ π+ ) n

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Parity-viola/ngelectron-nucleonsca5ering

andaxialformfactors

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Inclusiveelectron-protonscaPering(e- p àe- X )

Differen?alcrosssec?onwithrespecttoleptonkinema?cs

em em

Wiem (W, Q2):structurefunc?ons(allinforma?onofhadrondynamicsencodedin)

W1em =

12

f J emx i2+ f J emy i

2( )f∑

i∑ δ (4)(pi + q− pf )

W2em =

Q2

!q 2W1em +

Q2

!q 2Q2

!qc2 f J em0 i

2

f∑

i∑ δ (4)(pi + q− pf )

γ∗ (q)

p

e -

X

e -

-

-

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Parity-viola?nginclusiveelectron-protonscaPering

Parity-viola?ngasymmetry

γ∗ (q)

p

e -

X

e -

Ζ (q)

p

e -

X

e -

+

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Parity-viola?nginclusiveelectron-protonscaPering

Parity-viola?ngasymmetry

γ∗ (q)

p

e -

X

e -

Ζ (q)

p

e -

X

e -

+

Jncµ = (1− 2sin2θW )Jem

µ − Visoscalarµ − A3

µ

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Parity-viola?nginclusiveelectron-protonscaPering

Parity-viola?ngasymmetry

γ∗ (q)

p

e -

X

e -

Ζ (q)

p

e -

X

e -

+

Jncµ = (1− 2sin2θW )Jem

µ − Visoscalarµ − A3

µ

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Parity-viola?ngasymmetry

γ∗ (q)

p

e -

X

e -

Ζ (q)

p

e -

X

e -

+

A = −Q2 GF

24πα2− 4sin2θW +ΔV +ΔA( )

Parity-viola?nginclusiveelectron-protonscaPering

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Parity-viola?ngasymmetry

γ∗ (q)

p

e -

X

e -

Ζ (q)

p

e -

X

e -

+

A = −Q2 GF

24πα2− 4sin2θW +ΔV +ΔA( )

≈8.99x10-5(GeV-2) ≈1.075(mainterm)

1− 4sin2θW ≈ 0.08

Parity-viola?nginclusiveelectron-protonscaPering

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Parity-viola?ngasymmetry

γ∗ (q)

p

e -

X

e -

Ζ (q)

p

e -

X

e -

+

A = −Q2 GF

24πα2− 4sin2θW +ΔV +ΔA( )

≈8.99x10-5(GeV-2) ≈1.075(mainterm)

2W3em-nc =W3

CC

∝ f Viso-vector i f Aiso-vector i*

à  PVasymmetrydataforbackwardelectronkinema?cscanmeasure W3 forneutrinoCCprocess andaxialmatrixelement(formfactors)

• 

1− 4sin2θW ≈ 0.08•  ΔV ispropor?onaltoisoscalarcurrentàsmallinΔ(1232) region

Parity-viola?nginclusiveelectron-protonscaPering

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A /Q2 = −89.9×10−6 1.075 + ΔV + ΔA( )

ΔV,ΔA contribu?onsfromSLmodel

ΔA gives∼10%correc?ontoA

θe’ = 110°θe’ = 60°

Matsui,Sato,Lee,PRC72,025204(2005)

[1/GeV2]

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-120

-110

-100

-90

-80

0 0.2 0.4 0.6 0.8 1

A/Q

2 (x

10-6

/GeV

2 )

Q2 (GeV2)

MAN∆ = 1.0 GeV

MAN∆ = 1.2 GeV

Sensi?vityofPVasymmetrytoNàΔ(1232)axialformfactor

W = 1232 MeV, θe’ = 110°

•  5%precisionPVasymmetrydatamaydiscriminate0.2GeVdifferenceintheaxialmass

•  Sensi?vitytoNàN*, Δ* (higherresonances)transi?onaxialformfactors

canbestudiedwiththeDCCmodel

NàΔ(1232)dipoleformfactorwithMA

A /Q2 = −89.9 1.075 + ΔV + ΔA( )[10-6/GeV2]

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ComparisonwithPVasymmetrydatafromJLab ThePVDISCollabora?on,PRC91045506(2015)

•  Forwardelectronkinema?csàaxialcurrenthardlycontribute

•  Devia?onfromdatainΔ(1232)maybefromnucleareffects(FSI,Fermimo?on,etc.)

•  Devia?onsinhigherWregionàcallingimprovementonthemodel(isospinsepara?on)

Ee = 4.867 GeV, θe’ = 12.9°Q2

≈ 1 GeV2 nearΔ(1232)

W(GeV)

Deuterontargetdataàprotonandneutroncrosssec?onsaresimplysummedincalcula?on

A /Q2 = − 89.9 × 1.075+ΔV +ΔA( )[10-6/GeV2]

30-50%precisiondataforA alreadyexistàEventratemeasuredat0.3%precision

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Conclusion

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Extrac/ngelementaryvectoramplitudes(transi/onformfactors)

withDCCmodelfromelectronsca5eringdatainresonanceregion

StartwithDCCmodeldevelopedthroughanalyzing γΝ, πΝ è πΝ, ππΝ, ηΝ, ΚΛ, ΚΣ

è extensionofvectorcurrenttoQ2≠0region

throughanalysisofe—- p &e—-’n’ dataforW ≤ 2GeV,Q2≤ 3(GeV/c)2

à  isospinseparatonàneutrino-inducedreac?ons

NàN*transi?onformfactorsaredetermined

Detailedcomparisonofstate-of-artelementarypionproduc/onmodels

Structurefunc?onsforpionelectroproduc?onfromDCC,SLandHNVmodelsarecompared

•  Goodagreementbetweenmodelsanddataformostofstructurefunc?ons

•  HNVmodelgivesσLT’forp ( e,e’ π0 ) p significantlysmallerthandata

DCCandSLmodelsreproducethedatabecausemeson-loopscangeneratephase

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Parity-viola/ngelectron-nucleonsca5eringforextrac/ng

elementaryaxialamplitudes(transi/onformfactors)

•  PVasymmetrydataforbackwardelectronkinema?cscanmeasure W3

forneutrinoCCprocess andaxialelementaryamplitude(formfactors)

•  5%precisionPVasymmetrydatamaydiscriminate0.2GeVdifferenceintheaxialmass

•  Currentdataprecisionis30-50%forPVasymmetry(0.3%precisioneventrate)

•  Needes?materadia?vecorrec?ons

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ThankyouverymuchforyouraPen?on

Acknowledgments

•  FinancialsupportforthisworkFAPESP2016/15618-8KAKENHIJP25105010

•  Compu?ngresourceNERSCBEBOP,LCRC,ArgonneNa?onalLab

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BACKUP

Page 60: Pion Electroproduc/ons - int.washington.edu · Pion Electroproduc/ons Satoshi Nakamura Universidade Cruzeiro do Sul (Brazil) -- Analysis of electron data and extrac?on of elementary

Kamano,Nakamura,Lee,Sato,2012

SXN,Kamano,Lee,Sato,arXiv:1804.04757γnàπ0n dσ/dΩforW<2GeV

0

18

dσ/dΩ

(µb/

sr)

0

6

dσ/dΩ

(µb/

sr)

-0.5 0 0.5cosθ

0

2

dσ/dΩ

(µb/

sr)

-0.5 0 0.5cosθ

-0.5 0 0.5cosθ

-0.5 0 0.5cosθ

-0.5 0 0.5cosθ

-0.5 0 0.5cosθ

-0.5 0 0.5cosθ

-0.5 0 0.5cosθ

1202 1230 1254 1282 1310 1335 1346 1360

1371 1388 1413 1420 1454 1480 1489 1514

1540 1563 1600 1660 1720 1780 1840 1900

γnàπ-p

0

15

dσ/dΩ

(µb/

sr)

0

5

dσ/dΩ

(µb/

sr)

-0.5 0 0.5cosθ

-0.5 0 0.5cosθ

-0.5 0 0.5cosθ

-0.5 0 0.5cosθ

-0.5 0 0.5cosθ

0

2

dσ/dΩ

(µb/

sr)

-0.5 0 0.5cosθ

-0.5 0 0.5cosθ

-0.5 0 0.5cosθ

1114 1233 1318 1353 1401 1435 1473 1498

1523 1561 1607 1653 1693 1731 1769 1800

1836 1872 1902 1948

:newfit

:previousfitPRC88(2013)

RecentMAMIdataincludedPRL112,142001(2014)

RecentJLabdataincludedPRC96,035204(2017)