x>1: Short Range Correlations and “Superfast” Quarks Jlab Experiment 02-019 Nadia Fomin University of Tennessee User Group Meeting Jefferson Lab June 9th, 2010

E02-019 Overview Inclusive Scattering only the scattered electron is detected, cannot directly disentangle the contributions of different reaction mechanisms. Inclusive Quasielastic and Inelastic Data allows the study of a wide variety of physics topics Duality Scaling (x, y, ξ, ψ) Short Range Correlations – NN force Momentum Distributions Q2 –dependence of the F2 structure function

A long, long time ago….in Hall C at JLab E02-019 ran in Fall 2004 Cryogenic Targets: H, 2H, 3He, 4He Solid Targets: Be, C, Cu, Au. Spectrometers: HMS and SOS (mostly HMS) Concurrent data taking with E03-103 (EMC Effect – Jason Seely & Aji Daniel)

The inclusive reaction MA M*A-1 e- MA M*A-1 Same initial state Different Q2 behavior DIS QES W2=Mn2 W2≥(Mn+Mπ)2 Spectral function 3He

Inclusive Electron Scattering (x>1) x=1 (x<1) The quasi-elastic contribution dominates the cross section at low energy loss, where the shape is mainly a result of the momentum distributions of the nucleons As ν and Q2 increase, the inelastic contribution grows A useful kinematic variable: JLab, Hall C, 1998 Fraction of the momentum carried by the struck parton A free nucleon has a maximum xbj of 1, but in a nucleus, momentum is shared by the nucleons, so 0 < x < A

Deuterium Usually, we look at x>1 results in terms of scattering from the nucleon in a nucleus and they are described very well in terms of y-scaling (scattering from a nucleon of some momentum) Quasielastic scattering is believed to be the dominant process

Usually, we look at x>1 results in terms of scattering from the nucleon in a nucleus and they are described very well in terms of y-scaling (scattering from a nucleon of some momentum) Quasielastic scattering is believed to be the dominant process Deuterium

Short Range Correlations => nucleons with high momentum Independent Particle Shell Model : For nuclei, Sα should be equal to 2j+1 => number of protons in a given orbital However, it as found to be only ~2/3 of the expected value The bulk of the missing strength it is thought to come from short range correlations NN interaction generates high momenta (k>kfermi) momentum of fast nucleons is balanced by the correlated nucleon(s), not the rest of the nucleus

Short Range Correlations 2N SRC 3N SRC Deuteron Carbon NM

Short Range Correlations To experimentally probe SRCs, must be in the high-momentum region (x>1) To measure the probability of finding a correlation, ratios of heavy to light nuclei are taken In the high momentum region, FSIs are thought to be confined to the SRCs and therefore, cancel in the cross section ratios P_min (GeV/c) x

Short Range Correlations – Results from CLAS Egiyan et al, Phys.Rev.C68, 2003 No observation of scaling for Q2<1.4 GeV2 Egiyan et al, PRL 96, 2006

E02-019: 2N correlations in ratios to Deuterium 18° data Q2=2.5GeV2

E02-019: 2N correlations in ratios to Deuterium 18° data Q2=2.5GeV2 R(A, D) 3He 2.08±0.01 4He 3.44±0.02 Be 3.99±0.04 C 4.89±0.05 Cu 5.40±0.05 Au 5.37±0.06

A/D Ratios: Previous Results 18° data Q2=2.5GeV2 4He R E02-019 NE3 3He 2.08±0.01 4He 3.44±0.02 Be 3.99±0.04 C 4.89±0.05 Cu 5.40±0.05 Au 5.37±0.06 3.87±0.12 56Fe 5.38±0.17

E02-019 2N Ratios 3He 3He 12C 12C

2N correlations in ratios to 3He Can extract value of plateau – abundance of correlations compared to 2N correlations in 3He

2N correlations in ratios to 3He A measure of probability of finding a 2N correlation: Recently learned that this correction is probably not necessary (pn >>pp) In the example of 3He: Hall B results (2003) E02-019 statistical errors only

E02-019 Ratios Q2 (GeV2) CLAS: 1.4-2.6 E02-019: 2.5-3 Excellent agreement for x≤2 Very different approaches to 3N plateau, later onset of scaling for E02-019 Very similar behavior for heavier targets

E02-019 Ratios Q2 (GeV2) CLAS: 1.4-2.6 E02-019: 2.5-3 For better statistics, take shifts on E08-014 Excellent agreement for x≤2 Very different approaches to 3N plateau, later onset of scaling for E02-019 Very similar behavior for heavier targets

E02-019 Kinematic coverage E02-019 ran in Fall 2004 Cryogenic Targets: H, 2H, 3He, 4He Solid Targets: Be, C, Cu, Au. Spectrometers: HMS and SOS (mostly HMS) Concurrent data taking with E03-103 (EMC Effect – Jason Seely & Aji Daniel)

On the higher Q2 side of things Au Jlab, Hall C, 2004 F2A x ξ In the limit of high (ν, Q2), the structure functions simplify to functions of x, becoming independent of ν, Q2. As Q2 ∞, ξ x, so the scaling of structure functions should also be seen in ξ, if we look in the deep inelastic region. However, the approach at finite Q2 will be different. It’s been observed that in electron scattering from nuclei, the structure function F2, scales at the largest measured values of Q2 for all values of ξ

SLAC, NE3 Jlab, E89-008 Q2 -> 0.44 - 2.29 (GeV/c2)

ξ-scaling: is it a coincidence or is there meaning behind it? Interested in ξ-scaling since we want to make a connection to quark distributions at x>1 Improved scaling with x->ξ, but the implementation of target mass corrections (TMCs) leads to worse scaling by reintroducing the Q2 dependence

ξ-scaling: is it a coincidence or is there meaning behind it? Interested in ξ-scaling since we want to make a connection to quark distributions at x>1 Improved scaling with x->ξ, but the implementation of target mass corrections (TMCs) leads to worse scaling by reintroducing the Q2 dependence TMCs – accounting for subleading 1/Q2 corrections to leading twist structure function Following analysis discussion focuses on carbon data

From structure functions to quark distributions 2 results for high x SFQ distributions (CCFR & BCDMS) both fit F2 to e-sx, where s is the “slope” related to the SFQ distribution fall off. CCFR: s=8.3±0.7 (Q2=125 GeV/c2) BCMDS: s=16.5±0.5 (Q2: 52-200 GeV/c2) We can contribute something to the conversation if we can show that we’re truly in the scaling regime Can’t have large higher twist contributions Show that the Q2 dependence we see can be accounted for by TMCs and QCD evolution

CCFR BCDMS

How do we get to SFQ distributions We want F2(0), the massless limit structure function as well as its Q2 dependence Schienbein et al, J.Phys, 2008

Iterative Approach Step 1 – obtain F2(0)(x,Q2) Choose a data set that maximizes x-coverage as well as Q2 Fit an F2(0), neglecting g2 and h2 for the first pass Use F2(0)-fit to go back, calculate and subtract g2,h2, refit F2(0), repeat until good agreement is achieved. Step 2 – figure out QCD evolution of F2(0) Fit the evolution of the existing data for fixed values of ξ (no good code exists for nuclear structure evolution, it seems)

Cannot use the traditional W2>4GeV/c2 cut to define the DIS region Q2(x=1) θHMS Cannot use the traditional W2>4GeV/c2 cut to define the DIS region Don’t expect scaling around the quasielastic peak (on either side of x=1)

Fit log(F20) vs log(Q2) for fixed values of ξ to p2,p3 fixed p1 governs the “slope”, or the QCD evolution. fit p1 vs ξ ξ=0.5 ξ=0.75 Q2 Use the QCD evolution to redo the F20 fit at fixed Q2 and to add more data (specifically SLAC)

P1 parameter vs ξ, i.e. the QCD evolution F20 fit with a subset of E02-019 and SLAC data Final fit at Q2=7 GeV2

Putting it all Together With all the tools in hand, we apply target mass corrections to the available data sets With the exception of low Q2 quasielastic data – E02-019 data can be used for SFQ distributions E02-019 carbon SLAC deuterium BCDMS carbon

Putting it all Together With all the tools in hand, we apply target mass corrections to the available data sets With the exception of low Q2 quasielastic data – E02-019 data can be used for SFQ distributions E02-019 carbon SLAC deuterium BCDMS carbon | CCFR projection (ξ=0.75,0.85,0.95,1.05)

Final step: fit exp(-sξ) to F20 and compare to BCDMS and CCFR CCFR – (Q2=125GeV2) s=8.3±0.7 BCDMS – (Q2: 52-200 GeV2) s=16.5±0.5 s=15.05±0.5

Analysis repeated for other targets All data sets scaled to a common Q2 (at ξ=1.1)

Summary Short Range Correlations ratios to deuterium for many targets with good statistics all the way up to x=2 different approach to scaling at x>2 in ratios to 3He than what is seen from CLAS Future: better/more data with 3He at x>2 in Hall A (E08-014) “Superfast” Quarks Once we account for TMCs and extract F20 – we find our data is in the scaling regime and can be compared to high Q2 results of previous experiments appears to support BCDMS results TO DO: check our Q2 dependence against pQCD evolution Follow-up experiment approved with higher energy (E12-06-105)

Greater disagreement in ratios of heavier targets to 3He Show?

F2A for all settings and most nuclei for E02-019