Electron sca,ering data and its use in constraning neutrino models Jarek Nowak NuSTEC Neutrino Generator School Outline •  Neutrino physics due to low amount of data need and should use electron sca,ering data to constrain our models of neutrino interac>ons. –  Nucleon structure –  Nuclear Structure –  In medium modifica>ons (PDFs, hadroniza>on and FSI) Jarek Nowak, Lancaster University 2 Nuclear cross sec>ons and IA •  To boost sta>s>cs, neutrino experiments use nuclear targets, typically H2O Fe + CH Ar • 
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Neutrino-­‐nucleus cross sec>ons are typically computed using the Impulse Approxima/on IA: Nuclear cross sec/ons (vA) described by incoherent sca<ering off quasi-­‐free nucleons Descrip>ons of free nucleon cross sec>on important! → Nucleon structure Jarek Nowak, Lancaster University 3 Nucleon structure measurements •  Elas>c nucleon form factors measurements ( → neutrino QE ) •  Structure func>on measurements ( → neutrino DIS ) •  Study of resonance excita>on ( → transi>on from QE to DIS ) Jarek Nowak, Lancaster University 4 Two types of interac>ons •  Neutrino interact only via exchange of W and Z bosons Charge Current Neutral Current Jarek Nowak, Lancaster University 5 Electron sca,ering data •  Electron sca,ering data provides informa>on about the vector part of the interac>on. •  All weak processes can be parametrized in term of vector and axial structure func>ons. •  They describe all kinema>cs distribu>ons of the final state lepton, and are applicable at all energies for electron sca,ering as well as neutrino and an>neutrinos Jarek Nowak, Lancaster University 6 Electron sca,ering data •  Theore>cal models must describe the vector parts of both longitudinal and transverse structure func>on of electron sca,ering measurements for the appropriate reac>ons at the level of a few percent. •  Neutrino sca,ering data need to be used to constrain the axial structure func>ons Jarek Nowak, Lancaster University 7 Neutrino cross sec>ons •  All neutrino oscilla>on experiments require good knowledge of energy dependence of neutrino cross sec>ons and kinema>c distribu>ons of the final state for the reac>on: ν + nucleon → µ + X
•  We need to know neutrino cross sec>on at low energies and on nuclear targets. W2 = (p+q)2 = M2+ 2Mν–Q2 ν = energy transfer to target y = ν/E=inelas>city Q2=square of the four momentum transfer x=Q2/2Mν=frac>on of momentum carried by quark) x=1 for quasielas>c sca,ering Jarek Nowak, Lancaster University 8 Neutrino cross sec>on •  In electron and neutrino sca,ering we categorize cross sec>on by the mass of the final state hadronic state: W –  W= 0.983 GeV: (quasi-­‐)elas>c sca,ering –  1.1 < W < 1.9 GeV: inelas>c sca,ering in the resonance region –  W > 1.9 GeV: Inelas>c sca,ering in the con>nuum Jarek Nowak, Lancaster University 9 Neutrino cross sec>on Neutrino An>neutrino •  All data points are for the νµ
Jarek Nowak, Lancaster University 10 Electron sca,ering •  The term quasielas>c sca,ering means different things to the electron sca,ering community and to the neutrino sca,ering community. • 
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Electron sca2ering at x=1. W=M On Free nucleons => elas=c sca2ering = Delta Func=on On nucleons bound in Nuclei -­‐> Quasielas=c sca2ering (quasi free) • 
Δ resonance (1234) • 
In neutrino physics QE sca2ering means – 
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Neutrino charged current at X=1, W=M On free nucleons à Quasielas=c ( neutrino à muon) – 
On nucleons bound in nuclei à quasielas=c sca2ering (quasi free, same as for electron) Electron sca2ering on Carbon Jarek Nowak, Lancaster University 11 Quasi-­‐elas>c reac>on and axial mass 2
2
F
(
Q
)
F
(
Q
)
2
ν
2
2
P
Γµ = γ µ F1 (Q ) + iσ µν q
+ γ µ γ 5 FA (Q ) + γ 5 qµ
2M
M
V CVC – for F1 and F2 we can use electromagne>c data -­‐A PCAC – FA and FP are not independent 2 M 2 FA (Q 2 )
FP (Q ) =
2
mπ + Q 2
2
We need the axial form-­‐factor; the standard dipole form 2
FA (Q ) =
gA
⎛
Q 2 ⎞
⎜1 +
⎟
⎜ M 2 ⎟
A ⎠
⎝
2
gA =1.267 from β decay; MA a free parameter (the only one) The value of axial mass is obtained from experimental data. Jarek Nowak, Lancaster University 12 Quasi-­‐elas>c reac>on (-­‐) for neutrinos (+) for an=neutrinos Elas>c proton and neutron form factors Determined from eN (CVC) Jarek Nowak, Lancaster University 13 • 
Electron nucleon and muon-­‐nucleon sca,ering –  Structure func>on descrip>on –  Transverse and longitudinal descrip>on • 
Terms of the structure func>ons F 1 = MW1 (x,Q 2 )
F 2 = ν W2 (x,Q 2 )
F 3 = ν W3 (x,Q 2 )
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Rela>on between the two descrip>ons • 
Since R is small what is general used is a mixed descrip>on in terms of F2, R, F3 Jarek Nowak, Lancaster University 14 • 
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Rela>ons between electric and magne>c form factors and structure func>ons for elas>c electron sca,ering • 
For neutrino QE sca,ering: vector form factors are known from electron sca,ering But we also have axial form factors • 
Where • 
and • 
And GMp and GMn contribute to the transverse virtual photon-­‐absorp>on cross sec>on and GEp and GEn contribute to the longitudinal cross sec>on FOR elas>c/QE sca,ering Transverse cross sec=on is on magne=c moment distribu=on FF Longitudinal cross sec=on is on electric charge distribu=on FF Jarek Nowak, Lancaster University 15 Nucleon form factor measurements •  Rosenbluth separa>on σR=ε/τ(GE2+GM2) •  Fix Q2, measure cross sec>on as func>on of polariza>on ε
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Linear fit: Slope and offset give elas>c form factors •  Problems: –  Cross sec>on measurement limited by systema>cs –  Polariza>on-­‐dependent modifica>on due to >1 photon contribu>ons –  GM term dominates at large Q2 (poor determina>on of GE) Jarek Nowak, Lancaster University 16 Rosenbluth separa>on – form factors Jarek Nowak, Lancaster University 17 Nucleon form factor measurements •  Polariza>on measurements –  First proposed by A.I.Akhiezer et al, Sov.Phys.JETP 6, 588 (1958) –  First used at MIT-­‐Bates by Milbrath et al., Phys.Rev.Le,.80, 452 (1998) •  A polarized electron will transfer its polariza>on to the recoil nucleon –  Measuring the recoil nucleon polariza>on Recent experiments at JLAB (Hall A) → Q2 < ~6 GeV2 •M.K.Jones et al., Phys.Rev.Le,.84, 1398 (2000) •O.Gayou et.al., Phys.Rev.Le,.88,092301 (2002) •  Equivalently: measure the polarized electron asymmetry in sca,ering off polarized targets Jarek Nowak, Lancaster University 18 `Rosenbluth' & `Polariza>on' Results: GEp/GMp • 
Polariza>on measurements ( closed markers) • 
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Rosenbluth measurements Include: – 
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Arrington et al re-­‐analysis of SLAC data Phys.Rev.C 68: 034325 (2003) Christy et al re-­‐analysis of JLAB data Phys.Rev.C70:015206 (2004) – 
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Methods self-­‐consistent – 
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Results from a new JLAB experiment @ Hall A Qa,an et al, PRL94:142301(2005) but disagree with each-­‐other Polariza>on results seen more reliable – 
2 photon contribu>ons at Rosenbluth? Form factor scaling ? Hyde-­‐Wright and De Jagger, Ann.Rev.Nucl.Part.Sci 2004 54:217 GEp decreases with Q2 faster than dipole form factors Jarek Nowak, Lancaster University 19 Recent Results: GEn H. Zhu et al., PRL 87 (2001) 081801 R. Madey et al., PRL 91 (2003) 122002 G. Warren et al., PRL 92 (2004) 042301 B. Plaster et al., PRC 73 (2006) 025205 Jarek Nowak, Lancaster University 20 New form factor parametriza>ons Improving accuracy of vN CCQE • BBBA07, Eur.Phys.J.C53:349-­‐354,2008. • BBA05, Nucl.Phys.B. 159 (2006) • J.J.Kelly, PRC 70, 068202 (2004 Re-­‐extrac=on of axial form factor Bodek, Bradford, Budd, Avvakumov, Eur.Phys.J.C53:349-­‐354,2008 Jarek Nowak, Lancaster University 21 Resonant region W<1.9 GeV R+
•  Charge Current •  Neutral Current Jarek Nowak, Lancaster University 22 Cross sec>on •  In the Rarita-­‐Swinger formalism –  Hadronic current –  Hadronic tensor –  –  is a projec>on operator for spin 3/2 Jarek Nowak, Lancaster University 23 Jarek Nowak, Lancaster University 24 Cross sec>on •  Vector form factor Cvi are related to the EM form factors •  Paschos-Lalakulich model tuned to agree with
MAID wrt Δ(1232) helicity amplitudes.
Jarek Nowak, Lancaster University 25 Neutrino DIS sca,ering: Formalism F2, xF3 combina>ons of PDFs: in LO: Jarek Nowak, Lancaster University 26 `The triumph of NNLO pQCD' * Next to next to leading order (NNLO) perturba>ve QCD with target-­‐mass correc>ons Shown data from • SLAC • BCDMS • NMC Plot & remark from A.Bodek's Panofsky prize 2004 talk, Nucl.Phys.Proc.Suppl.139:165-­‐192,2005 Jarek Nowak, Lancaster University 27 Effec>ve LO models for Monte Carlos Effec>ve model for Monte Carlos LO pdfs (GRV98LO) New scaling variable absorbs TM, HT, higher order correc>ons “K factors” for valence & sea PDFs Bodek and Yang, Nucl.Phys.Proc.Suppl.139:113-­‐118,2005 Jarek Nowak, Lancaster University 28 New PDFs with Bodek-­‐Yang modifica>ons for structure func>ons Jarek Nowak, Lancaster University 29 Applica>on to MINOS R at low Q^2 ? xF3 → ξω F3 Tuning factor: asympto>c cross sec>on (x~1.032) Jarek Nowak, Lancaster University 30 Experience from MINOS • 
Measured muon angle → • 
Sensi>ve to x, Q^2 distribu>ons • 
Excellent agreement with data Debda,a Bha,acharya (Pi,sburgh U.) FERMILAB-­‐THESIS-­‐2009-­‐11, Mar 2009 Jarek Nowak, Lancaster University 31 QE → DIS Transi>on from QE → DIS has been mapped out in detail using electron sca,ering data Transi=on from vQE → vDIS difficult to model • ~18 baryon resonances up to W = 2 GeV • Non-­‐resonance backgrounds Jarek Nowak, Lancaster University 32 Cross sec>on tuning in the ~GeV range • 
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Duality-­‐inspired Bodek-­‐Yang model: Valid all the way down to photo-­‐produc>on threshold. Includes resonances `on average' No resonance structure but, for nuclear targets, structure largely washed-­‐out due to Fermi mo>on Many poten>al op>ons available for vMC's: numu+Fe56, Ev = 5 GeV •  QE + BodekYang ( W > MNuc) •  QE + Delta + BodekYang (W > MDelta+width) •  QE + Delta + higher RES + non RES bkg + + BodekYang (W > ~2 GeV) Jarek Nowak, Lancaster University 33 From free nucleon to nuclear targets • 
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Sca,ering is smeared by Fermi mo>on (large x) Internal structure of nucleons modified by medium (e.g. EMC effect) Nucleons can shadow each other at low Q2 ( small x) For QE sca,ering at very low Q2 there should be Pauli suppression since final state cannot occupy the same state as the other nucleon(Q2<0.1GeV2) For QE transverse sca,ering (magne>c) there can be sca,ering from addi>onal current in the nucleus (e.g MEC) For QE longitudinal (electric) sca,ering -­‐ since change is conserved the integral over longitudinal sca,ering should be conserved -­‐besides the small distor>on of the internal structure (form factor), and Pauli suppression (Q2<0.1 GeV2) Electron sca2ering data can be used to study all of these nuclear effects Jarek Nowak, Lancaster University 34 Nuclear structure Electron-­‐sca2ering is ideal for studying nuclear structure •  Interac>on well understood (QED) •  Electron is a `weak probe': Virtual photon doesn't disturb the nuclear target (even at large Q2) Phys. Rev. 91, 422 -­‐ 423 (1953) Jarek Nowak, Lancaster University 35 Mapping out the nuclear structure Energy levels Nucleon momentum distribu=ons via “electro-­‐disintegra=on” Charge distribu=ons R.Hofstadter, Rev.Mod.Phys.28, 214 (1956) Jarek Nowak, Lancaster University 36 Electron quasielas>c data → kF, epsilon Just as quasi-­‐elas>c sca,ering on quarks (DIS) tells us about PDFs → Quasi-­‐elas=c sca2ering on nucleons tells us about the nucleon momentum distribu=ons Moniz et al., Phys.Rev.Le,. 26 (1971) Quasi-­‐elas/c electron sca<ering is the source of all these “usual numbers” entering into the FGM models of neutrino MCs. Jarek Nowak, Lancaster University 37 Honorable men>ons
•  Electron sca,ering data is use in modelling other elements of neutrino cross sec>on –  Nuclear effects: Spectral Func>on, Local Density Approxima>on, Op>cal poten>al –  Hadroniza>on: crea>on of final state hadrons form the available hadronic invariant mass –  Final State Interac>ons –  … Jarek Nowak, Lancaster University 38 backup Jarek Nowak, Lancaster University 39 Cross sec>on tuning in the ~GeV range • 
Gallagher, Nucl.Phys.B(Proc.Suppl.) 159 (2006) 229-­‐234 • 
On MINOS (neugen3/GENIE) we exercised the various schemes using electron sca2ering data • 
(then tuned selected scheme to world's total, exclusive 1pi and exclusive 2pi data) Jarek Nowak, Lancaster University 40