steve manly and arie bodek, univ. of rochester 1 electron and neutrino interactions on nucleons and...

Steve Manly and Arie Bodek, Univ. of Rochester

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Electron and Neutrino Interactions on Nucleons

and Nuclei in the Next Decade

A New International Effort led by Rochester1. Bridging Nuclear and High Energy Physics Programs2. Bridging the fields of Electron and Neutrino Interactions3. Bridging QCD and Electroweak Interactions (e.g. Neutrino

Oscillations)4. Investigating Form Factors, Quark-Hadron Duality in Nucleons and

Nuclei with electrons and neutrinos5. Bridging Physics between Jlab, Fermilab and JHF-(JPARC)

Principal Investigators from Rochester• S. Manly -electron scattering Jlab Hall B CLAS data - Final states in

quasielastic, resonance and DIS in nuclei - New Program• A. Bodek, (C. Keppel) - electron scattering Jlab Hall C experiments

(structure functions, form factors, resonances in nuclei, sum rules) - E94-110+ E02-109, E02-103, P03-110 - New Program

• K. McFarland, (C. Keppel, J. Mofin) - Neutrino scattering cross sections FNAL- MINERvA - Near Detector - New Program

• K. McFarland - Neutrino Oscillations (JHF-SuperK, FNAL-off axis) - New Neutrino Oscillations Program -both near and far detectors


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US National Academy of Science

National Research Council Report 2002

In the first decade of the 21st Century,

new discoveries are expected in the fast growing

“areas on the boundaries between the established disciplines”

Examples that come to mind are:

Nuclear and Particle Physics

Physics/Astrophysics Astronomy

Physics and Biology-Genetics-Medical Physics

Physics and Computer Science

Computer Science and Biology-Genetics

And others…


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Within the discipline of Physics, we can make new

Discoveries by drawing the expertise of physicists

Across the various disciplines of Nuclear Physics,

Particle Physics, AstrophysicsIn 2001 The Annual NuInt conferences were started and

focused on

A two overlying unifying goals

“Neutrino Oscillations”

“QCD and Nuclear Structure”

Drawing on contributions from

Nuclear, Particle, and Astrophysics and

To study Neutrino Oscillations Requires Understanding of non-perturbative QCD


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Connection to Physics at Jlab - Electrons as Probes of Hadron/Nuclear Structure QCD.

Connection to Astrophysics -Solar and Atmospheric Neutrinos Also : Is CP Violation (CPV) in the Lepton sector which can lead to

Leptogenesis a possible origin of Matter-Antimatter Asymmetry in the Universe ?


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SuperK Water Cerenkov Detector Atmospheric

neutrinos - up down asymmetry - Discovery of muon neutrino -->

neutrino oscillations. M2 (2->3) with large mixing

Maximal mixing, and

evidence of muon

neutrinos oscillating

To neutrinos

M2 (2->3)


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K2K, First Accelerator Based neutrino oscillations experiment. Dip at the number of expected quasielastic events at 0.7 GeV. - low statistics

Comparison of rate of muon neutrino events to prediction versus energy gives a measurement of M2 (2->3)

"Indications of Neutrino Oscillation in a 250 km Long-baseline Experiment” The K2K collaboration, M.H. Ahn et al, hep-ex/0212007, Phys. Rev. Lett. 90 (2003) 041801. Expected (dashed black line =44 events, observed 29 events). Both normalization and shape indicate oscillations. Precise cross section and flux in the 0.3 to 5 GeV region needed.


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Very low M2 (1->2) With large mixing.


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GOOD NEW FOR FUTURE CPV large mixing (1->2)


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Next generation Neutrino experiments aim at measuring the 3x3 mixing matrix and masses. This is done by looking for transformation of muon neutrinos to electron neutrinos at the 1-3 GeV region. Expect a rate of about 3%.

Present limit is about 10% at

SuperK 3-generation fit not as good as CHOOZ Limit


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Requires good knowledge of cross sections

Plan for next 10 year program at JHF and Fermilab

FNAL

Off axisJHF to

SK


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--------

1 Pion production/

resonances ---- Quasielastic W=Mp

------total includingDIS W>2GeV

1. Bubble Chamber language. - Exclusive final states

2. Resonance language. - Excitation Form Factors of Resonances and decays

3. Deep Inelastic Scattering -PDFs and fragmentation to excl. final states

NEED to Understand Hadron/Nuclear Physics both at Low and High Energies

/E

E(GeV)0.1 1 10

Good News: Solar mixing is LARGE - GOOD FOR CPV Challenge: We Also NEED PRECISION

NEUTRINO and composition of final states


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MIT SLAC DATA 1972 e.g. E0 = 4.5 and 6.5 GeV

e-P scattering A. Bodek PhD thesis 1972

[ PRD 20, 1471(1979) ] Proton Data

Electron Energy = 4.5, 6.5 GeV Data

‘ The electron scattering data in the Resonance Region is the “Frank Hertz Experiment” of the Proton. The Deep Inelastic Region is the “Rutherford Experiment” of the proton’ SAID

V. Weisskopf * (former faculty member at Rochester and at MIT when he showed these data at an MIT Colloquium in 1971 (* died April 2002 at age 93)

What doThe Frank Hertz” and “Rutherford Experiment” of the proton’ have in common?

A: Quarks! And QCD

(e/ /-N cross sections at low energy

Neutrino interactions --Quasi-Elastic / Elastic (W=Mp)

+ n --> - + p (x =1, W=Mp) Described by form factors (And also need to account for Fermi Motion/binding effects in nucleus) e.g. Bodek and Ritchie (Phys. Rev. D23, 1070 (1981)

Resonance (low Q2, W< 2) + p --> - + p + n

Poorly measured , Adding DIS and resonances together without double counting is tricky. 1st resonance and others modeled by Rein and Seghal. Ann Phys 133, 79, (1981)

Deep Inelastic + p --> - + X (high Q2, W> 2)

well measured by high energy experiments and well described by quark-parton model (pQCD with NLO PDFs), but doesn’t work well at low Q2

region.

(e.g. SLAC data at Q2=0.22)Issues at few GeV :Resonance production and low Q2 DIS contribution meet.The challenge is to describe ALL THREE processes at ALL neutrino (and electron) energies

GRV94 LO

1st resonance

X = 1

(quasi)elastic

F2 quasi

integral=0.43

Very large

e-p

Intellectual Reasons:Understand how QCD works in both neutrino and electron scattering at low energies -different spectator quark effects. (There are fascinating issues )How is fragmentation into final state hadrons affected by nuclear effects in electron versus neutrino reactions.Of interest to : Nuclear Physics/Medium Energy, QCD/ Jlab communitiesIF YOU ARE INTERESTED in QCD

Practical Reasons: Determining the neutrino sector mass and mixing matrix precisely requires knowledge of both Neutral Current (NC) and Charged Current(CC) differential Cross Sections and Final States These are needed for the NUCLEAR TARGET from which the Neutrino Detector is constructed (e.g Water, Carbon, Iron)-of interest toParticle Physics/ HEP/ FNAL /KEK/ Neutrino communitiesIF YOU ARE INTERESTED IN NEUTRINO MASS and MIXING.

What do we want to know about low energy electron/ reactions and why

Astrophysics community interested in both

At Rochester we have a long tradition of collaborationBetween Nuclear Physics and Particle Physics, and expertise in

both electron scattering and neutrino physics.• PHOBOS at RHIC (Manly) - Currently Funded by DOE Nuclear

Physics Division (Manly’s PhD Thesis was in neutrino physics).---> Evolving towards Jlab Hall B and Hall C expts.

• SLAC Experiments E139, E140, E140x - EMC Effect, precision nucleon and nuclear structure functions: Bodek (co-spokesperson) Funded by DOE Nuclear Physics Division in 1980’s-1990s (initially started as collaboration between A. Bodek and Tom Cormier). Provided the upgrades needed for the NPAS program at SLAC. Provided world’s standard data sets for F2, R, and EMC effects on nucleons and nuclei ----> Now evolving towards Jlab Hall C experiments.

• CCFR/NuTeV Neutrino Program (Bodek, McFarland)-funded by DOE High Energy Physics from 1977-now --> Evolving towards Neutrino Program at Fermilab (MINERvA and JHF).

• Phenomenological description of low energy electron and neutrino scattering (Bodek - in collaboration HEP experimenters and theorists, and nuclear community e.g. J. Arrington) More Jlab data needed

Proposed Rochester ProgramJlab Hall C experiments (structure functions, form factors,

resonances in nuclei, sum rules) - join 3 Jlab approved experiments on H and D , and propose a 4th on nuclear targets used in neutrino experiments (C, Fe, etc).

E94-110 H2 Resonances F2 ,R- Completed -Join this experiment to participate in data analysis

E02-109 D2 Resonance F2, R- Approved to run in 2004. - Join this experiment to take D2 resonance data. -- Proposed to PAC24 to run P03-110 at same time as E02-109.

P03-110 - Resonance F2, R for Nuclear Targets used in Neutrino Experiments. - Leading this experiment (got favorable response from PAC24 - deferred with regret and will considered again in PAC25 to run at same time as D2 experiment E02-109)

E02-103 H2, D2 High Q2 resonance data (and EMC effect in He3, He4) - approved by PAC24 to run in 2004 (J. Arrington). - Join this experiment to get H2 and D2 high Q2 data.

Also include in overall analysis data from F2, R in nuclei at the DIS region from SLAC E140, E140x- high Q2 (Bodek), and Jlab 99-118 - DIS low Q2 (A. Brull, Keppel)


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Arie Bodek, Univ. of Rochester 1

Measurement of F2 and L/ T -on Nuclear Targets - 03-110in the Nucleon Resonance Region PR

First Stage of a Program to InvestigateQuark HadronDuality in Electron and NeutrinoScattering

on Nucleons and Nuclei• . ( ),A Bodek spokesperson . , . ,S Manly K McFarland( .J Chovjka, . . -G B Yu PhD

),( .students DKoltun, . , . - )- L Orr S Rajeev Collaborating theorists University of, , 14627Rochester Rochester NY

• . . , . ,M E Christy W Hinton . ( ),C Keppel spokesperson .E Segbefia- ,Hampton University,Hampton VA

• .P Bosted, . . - , ,S E Rock University of Massachusetts Amherst MA• .I Niculescu - , ,James Madison University Harrisonburg VA• .R Ent, . , . , . , . - D Gaskell M Jones D Mack S Wood Thomas Jefferson National

, ,Accelerator Facility Newport News VA• . - , ,J Arrington Argonne National Laboratory Argonne IL• . - , ,H Gallagher Tufts University Medford MA• . - , ,J Dunne Mississippi State University Mississippi State MS• .P Markowitz, . J Reinhold Florida InternationalUniv., ,University Park FL• . , ,E Kinney University of Colorado Boulder Colorado• . .H P Blok Vrije Universiteit, ,Amsterdam NetherlandsFocus on the Physics Motivation, see proposal for a Detailed Run Plan


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Importance of Hadronic Final States in Electron And Neutrino Scattering

Hall B Program


20Arie Bodek, Univ. of Rochester 3

Charged Current Process is of Interest

• Neutrino mass ΔM2 and MixingAngle : charged current crosssections and final States areneeded : The level of neutrinocharged current cross sectionsversus energy provide the baseline

against which one measures ΔM2

at the oscillation maximum andmixing angles (aim to study CP viol.)

• Measurement of the neutrinoenergy in a detector depends onthe composition of the finalstates (different response tocharged and neutral pions ,muons and final state protons(e.g. Cerenkov threshold, noncompensating calorimeters etc).

Charged - Current: both differential cross sections and final states

W+

νμ

N

π 0 EM shower

EM response

μ muon response

N nucleon response

π + responsePR 03-110 helps pin down cross sections -aim 2% and Study CP Violation

σT/E ν

Poor neutrinodata

E ν Low energy current flux errors 10% to 20%



Neutral Current Process is of Interest

• SIGNAL νμ−>νe

transition ~ 0.1% oscillationsprobability of νμ−>ν e .

• Background: Electrons from misidentified π0 in NC events without a muon from higherenergy neutrinos are a background

Neutral - Current both differential cross sections and final states

e- -> EM

shower

W+

ν μ or ν e

in beam

PN

π +Z

νμ

Nπ 0 EM shower

FAKE electron

νμ

NZ

N

π 0

ντ

NSIGNAL νμ−>ντ

PR 03-110 pins down crosssections -aim 2% -Study CP Violation

ντCanobserveντ eventsbelowτ thresholdVs. sterileν

Poor neutrinodata

E ν Low energy current flux errors 10% to 20%What do muon neutrinos oscillate to?

Backround


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JHF region 0.7 GeV

FNAL region 3 GeV

JHF region 0.7 GeV


23JHF region

0.7 GeV

FNAL region

3 GeV


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Start with: Quasielastic: C.H. Llewellyn Smith (SLAC).Phys.Rept.3:261,1972

Vector form factors

From electron

scattering

Via CVC

Axial form factor fromNeutrino experiments

Neutrino experiments useDipole form factors with Gen=0 -Because this is what was put in the LS paper (not exactly correct)

Vector

VectorAxial

Updated recentlyBy Bodek, Budd andArrington 2003


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What does axial form factor Fa do between 1 and 3 GeV2 ????

Budd, Bodek, Arrington BBA-2003 Form Factor Fits to SLAC/JLAB data. Vector Nucleon form factors display deviations from dipole. Controversy on Gep high Q2


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K2K Near detectordata on Water wasFit with wrong Vector Form factors. NewBBA2003 form factorsand updated M_A have asignificant effect on Neutrino oscillations Results.


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Updating Neutrino Axial Form Factors:-->

Use new BBA-2003 Precise Vector Form Factors as input to neutrino data. With BBA-2003 Form Factors, Axial Vector M_A=1.00. However, no information on Axial form factor for Q2>1 GeV2.

Future: Very High Statistics neutrino data will be available on Carbon. Need precise vector form factors, as modified in Carbon (including effect of experimental cuts)

Can measure F_A(Q2)/ GM_V(Q2) at High Q2 - By combining Jlab and MINERvA data

Quasielastic

Old Bubble Chamber

Data on D2. (Steve Manly was

A member of this collaboration

(as a PhD Thesis student)



Baker 1981 D2

Q2<0.3 Region, Interest

1. Determine Ma=radius of axial proton

2. Compare to Ma from pion electroproduction

3. Determine quaielastic cross section where mostof the events are - for neutrino oscillation in the1 GeV region , e.g. K2K,JHF MiniBoone.

4. Sensitive to both Pauli Exclusion and final stateID if a nuclear target is used, e.g. Carbon, Water.Lose Quasielastic events, or misID resonanceevents. -> - Need to use Jlab Hall B data on D2, Cand Fe - Manly Analysis proposal

5. Low recoil proton momentum P=Sqrt(Q2)

Q2 > 1 GeV2 Region, Interest

1. Determine deviations from Dipoleform factors is it like Gep or Gmp .

2. Not sensitive to Paul Exclusion,but sensitive to final state ID. -> -Need to use Jlab Hall B data on D2,C and Fe - Manly analysisproposal

3. Higher recoil proton momentumP=Sqrt(Q2)

Pauli effect on C12, Q2<0.3 GeV2

Measure F_A(Q2)/GM_V(Q2) by comparing neutrinoAnd electron e-e’-p data on Carbon with 1 Million events


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One Example: Precise measurement of Axial Form factor of the Nucleon can only be done using a combined analysis (with the same cuts) of a sample of e-e’-p data from electron scattering at Jlab (on Carbon) with the Corresponding - ’ p data from neutrino scattering On Carbon and using same cuts (on final state proton etc). (measure F_A at high Q2 for first time).

Since future high statistics neutrino data will only be done with nuclear targets (e.g. scintillator), Nuclear Effects can both be studied, as well as cancelled by performing a combined analysis of these two data sets.

Goal of our program in Hall B: Produce well understood DSTs of e-e’ X on Carbon that can be used in a combined analysis with neutrino data. Start with quasielastic, and continue on to resonances, and DIS. In the process, also do physics such as nuclear transparency, modification of resonance and DIS final states in nuclei, etc.


Motivation of Hall C programCurrently - Low Energy Neutrino Data worse than

where electron scattering was in the 1960’s• In the 1960’s: Electron scattering data was poor. We measured the momentum sum rule,

but we never thought that we will investigate the Q2 dependance of many QCD sum rules(logarithmically varying with Q2). A few examples include.

• (1) The Bjorken Sum rule in Polarized lepton scattering• (2) The Gross-Llewellyn-Smith Sum (GLS) sum rule in neutrino scattering• (3) The Gottfried Sum Rule (proton-neutron) in electron/muon DIS scattering

In 2002: (1) Q2 dependence of Bjorken and GLS rules has been used to extract αs(Q2)(2) Gottfried ( - )Sum is used to extract dbar ubar

, 2%.In a few years next generation neutrino beams will have fluxes known toAim - ( ) .at testing current algebra exact sum rules like the Adler Sum rule ,However

.input from electron scattering experiments is crucial

.Motivation of next generation neutrino experiments is neutrino oscillations

2% Need these cross sections to to get precise neutrino mixing angles


Motivation, the Short Story

ÿ Similar to electron scattering experiments needing good models of the cross sections atall Q2 to do radiative corrections, neutrino experiments need good models of crosssections and final states to extract cross sections

ÿ However, neutrino Monte Carlo models must be based on understanding of the physics,and checked by data

ÿ A collaborative program between the high and medium energy communities to developreliable global models linking electron and neutrino scattering measurements covering awide range of kinematics

ÿÿ Nuclear data necessary for comparison with neutrino measurements for global modeling

effortsÿ No L/T separated structure function measurements exist on nuclei in the resonance

regionÿ In the resonance region, nuclear effects may be large, different from the DIS region, and

Q2 dependent.

ÿ Will reduce large, model-dependent uncertainties in neutrino oscillation measurements -Of interest to the neutrino oscillations community

ÿ Further tests of duality, QCD, and Current Algebra sum rules.ÿ ---> Of interest to the medium energy physics community


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Duality, QCD Sum Rules, and Current Algebra Sum Rules.

Local duality and Global duality appears to work for Q2 > 1.5 GeV2 in electron scattering: This is basically a consequence of the fact that if target mass effects are included, higher twists are small and QCD sum rules are approximately true for Q2 > 1.5 GeV2 .

(e.g. momentum sum rule - quarks carry about 1/2 of the proton momentum) F2

eP, F2eN are related to PDFs

weighted by quark charges).At high Q2, duality also seems to work for nuclear

corrections. All of these break down at low Q2.A complete model which works at all energies must relate electrons to neutrino

structure functions and form factors within a theoretical framework. For DIS it is parton distributions, for quasielastic it is form factors (I=1/2) and for resonances it is excitation form factors for a combination of I=1/2 and I=2/3 states. Needs to work at ALL Q2 (Also, need to add the axial vector form factors, which cannot be determined from electron scattering)

What happens at low Q2 ?


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- = W2 (Anti-neutrino -Proton)

+ = W2 (Neutrino-Proton) q0=

Adler Sum rule EXACT all the way down to Q2=0 includes W2 quasi-elastic

S. Adler, Phys. Rev. 143, 1144 (1966) Exact Sum rules from Current Algebra. Sum Rule for W2 DIS LIMIT is just Uv-Dv =1

[see Bodek and Yang hep-ex/0203009] and references therein

Vector Part of W2, 0 at Q2=0, 1 at high Q2-Inelastic

Adler is a number sum rule at high Q2

DIS LIMIT is just Uv-Dv.

=1 is

€

[F2−(ξ)−F2

+(ξ)]

ξ 0

1

∫dξ=[Uv(ξ)−Dv(ξ)]dξ0

1

∫=2−1

F2-= F2 (Anti-neutrino -Proton) = W2

F2+= F2 (Neutrino-Proton) = W2

we use: dq0) = d ( )d at fixed q2= Q2

Elastic Vector =1 Q2=0

Elastic Vector = 0 high Q2

Elastic gA=(-1.267)2 Q2=0

Elastic gA = 0 high Q2

Axial W2 = non zero at Q2=0

Axial W2 =1 at high Q2, Inelastic

+ Similar sum rules for W1, W3, and strangeness changing structure functions


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Outline of a Program in Investigating Nucleon and Nuclear Structure at all Q2 - Starting with PR 03-110 - Focusing on Resonance Region in Hall C in this talk and backup slides)

• Update Resonance Vector Form Factors and Rvector of the large number of resonances in the Nucleon, e.g. within Rein-Seghal-Feynman Quark Oscillator model (and other resonance models) by fitting all NEW- F2 and R Electron Resonance data E94-110 (H, F2 and R) (just taken in 2003) (+ previous SLAC + photoproduction+ and other data) aim at adding E02-109 (D, F2 and R), E02-103 (H and D F2 at high Q2) and PR03-110 (nuclear targets in summer 04)nuclear targets at the same time as E0109 (D)]

• Improve on Inelastic Continuum modeling of Vector F2 and R (e.g. using a formalism like Bodek/Yang) using Jlab, SLAC, H and D data, photoproduction and HERA data - and Add neutrino data from CHORUS on Pb. (for DIS Axial scattering)

• Within these models, convert EM Vector Form Factor to Weak Vector Form Factors - use the Various isospin rules I=1/2 and I=3/2 of elastic, resonance and inelastic Form Factors fits to H and D data E94-110, E02-109

• Investigate if the Model predictions for Vector Scattering in neutrino reactions satisfy QCD sum rules and duality at high Q2 and Adler Vector Rum rules at ALL Q2.

• Investigate if the Models predictions for Axial scattering in neutrino reactions satisfy QCD sum rules and duality at high Q2 and Adler Axial Rum rules at ALL Q2.


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1. Apply nuclear corrections for DIS and resonance region to predict Neutrino and Antineutrino data on nuclei from PR 03-110 - Requires 5 days of running - Also use E99-118 and SLAC E140 and other for DIS A dependence.

2. Compare predictions to existing low statistics neutrino data and to new precise neutrino data to become available in a couple of years (MINERvA, and JHF- Japan) - Do predictions from models (which satisfy all sum rules and duality) also model the neutrino and antineutrino data well?

3. In parallel - Final states in nuclear targets to be investigated in a collaboration with Hall B experiments in electron experiments and in new neutrino experiments.

•Nucleon +Resonance Vector Form Factors, Vector Continuum F2 at all Q2, Rvectror =L/T in great details.

• Nuclear effects on various targets in res, and quasielastic region as a function of Q2

•Hadronic Final Stares in electron scattering

•Check on Current Algebra sum rules and understanding duality -

•Axial vector contribution to F2 at low Q2

•Different nuclear effects in neutrino scatt.

•Account for Raxial different from Rvector

•Hadronic final states in neutrino scattering

Things can be learned from electron scattering Things that are learned in neutrino scattering

Collaborative approach between High Energy and Nuclear Physics community

High x and low Q2 PDFs for e/neutrino, Resonance form factors, nuclear corrections1.Electron scattering exp.starting with JLAB P03-110 - with investigation of final states2.New Near Detector neutrino exp. at Fermilab-NUMI/JHF - -->Years of data e.g. MINERvA +

JHF


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We will be submitting a proposal to DOE Nuclear Physics Division to fund a Rochester group at Jlab (building on the Rochester SLAC E140 nuclear physics group group and the Rochester PHOBOS nuclear physics group).

Rochester will be a Liaison between Electron Scattering and Neutrino Scattering communities, and lead several effort

(a) A combined analysis of electron and neutrino data (in collaboration with other high energy and nuclear experimentalists and theorists).

(b) A program of measurement and analysis of cross sections, form factors and structure functions on nuclear targets in Hall C. Hall C experimenters are enthusiastic about this collaboration - Bodek is leading this effort by joining E02-

(c) A program of measurement and analysis of hadronic final states in Hall B - CLAS collaboration is enthusiastic about this participation - Here the CLAS collaboration (and not the PAC) approves the program. Professor Manly will be leading this effort.

Participants• A. Bodek , S. Manly , K. McFarland - Experimental faculty• Also (D. Koltun, L. Orr, S. Rajeev - Collaborating theory faculty) • 2 students, J. Chovjka, G.B. Yu- Experimental PhD students) - to be

stationed at Jlab • 2 postdocs to be stationed at Jlab (1 for Hall C and one for Hall B)


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Some relevant results from previous DOE-

Nuclear Funded Program at Rochester

(SLAC E139, E140, E140x)


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Correct for Nuclear Effects measured in e/ expt. In DIS and resonance region Fe/D data

Comparison of Fe/D F2 data

In resonance region (JLAB)

Versus DIS SLAC data

In TM (C. Keppel 2002).

DIS Region

TM

Red Jlab Resonance

Green DIS Data E87, E139, E140

MUST USE TM

These results are from Rochester

Results of SLAC E87, E139, E140



F2, R comparison with NNLO QCD+TM black

=> NLO HT are missing NNLO terms (Q2>1)Size of the higher twist effect with NNLO analysis is really small (but not 0) a2= -0.009 (in NNLO) versus –0.1( in NLO) - > factor of 10 smaller, a4 nonzero



Compare to what one has done for Hydrogen in E94-110 F2, FL, F1?Compare to what one has done for Hydrogen in E94-110 F2, FL, F1?

(All data for Q2 < 9(GeV/c)2)

Now able to extract F2, F1,FL and study duality!withhigh precision .

R = L/T <

=R L/T • Now able to study the Q2

dependence of individual 2, ,resonance regions for F FL

• 1!F

• Clear resonant behaviourcan !be observed

Initial quark mass m I and final mass ,mF=m * bound in a proton of mass M -- Summary: INCLUDE quark initial Pt) Get scaling (not x=Q2/2M )

for a general parton Model

Is the correct variable which is Invariant in any frame : q3 and P in opposite directions.

P= P0 + P3,M

PF= PI0,PI

3,mI

€

ξ=PI

0 +PI3

PP0 +PP

3

PI ,P0

quark ⏐ → ⏐ ⏐ ⏐ ⏐

q3,q0

photon← ⏐ ⏐ ⏐ ⏐ ⏐

€

q+PI( )2=PF

2 → q2 +2PI ⋅q+PI2 =mF

2

ξW =Q2 +mF

2 +A

{Mν[1+ (1+Q2 /ν2)]+B}formI

2,Pt=0

PF= PF0,PF

3,mF=m*

q=q3,q0

Most General Case: (Derivation in Appendix) ‘w= [Q’2 +B] / [ M (1+(1+Q2/2) ) 1/2 +A] (with A=0, B=0)<<<<<<<<where2Q’2 = [Q2+ m F 2 - m I

2 ] + { ( Q2+m F 2 - m I 2 ) 2 + 4Q2 (m I

2 +P2t) }1/2

Bodek-Yang 2002-2003: Add B and A to account for effects of additional m2

from NLO and NNLO (up to infinite order) QCD effects.

Special cases:(1) Bjorken x, xBJ=Q2/2M, -> x

For m F 2 = m I 2 =0 and High 2,

(2) Numerator m F 2 : Slow Rescaling as in charm production (3) Denominator: Target mass term =Nachtman Variable =Light Cone Variable =Georgi Politzer Target Mass var. (all the same )

Please derive this on the plane


42

2 = 1268 / 1200 DOF

Dashed=GRV98LO QCD F2 =F2QCD (x,Q2)

Solid=modified GRV98LO QCD

F2 = K(Q2) * F2QCD( w, Q2)

Bodek/YangModified GRV98 PDFsTo DIS DataFit to electronAnd muonScatteringDIS data.Predict reson.Photo andNeutrino data


43Predict Resonance, Neutrino

And photoproduction data

How well does it work?


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steve manly and arie bodek, univ. of rochester 1 electron and neutrino interactions on nucleons and...

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