Inclusive Scattering from Nuclei at x>1 and High Q 2 with a 5.75 GeV Beam Nadia Fomin University of Virginia

 Momentum distributions of nucleons inside nuclei  Short range correlations (the NN force)  2-Nucleon and 3-Nucleon correlations  Comparison of heavy nuclei to 2 H and 3 He  Scaling (x, y) at large Q 2  Structure Function Q 2 dependence  Constraints on the high momentum tail of the nuclear wave function Physics topics we can study at x>1

Quasielastic scattering: an example (Deuterium)  At low ν (energy transfer), the cross-section is dominated by quasi-elastic scattering  As the energy transfer increases, the inelastic contribution begins to dominate

Electron scattering and x ranges  Scattering from a free nucleon: 0<x<1 :  x=1 (elastic)  x<1 (inelastic)  x > 1:  momentum is shared between nucleons, so 0<x<A  probing the effect of nuclear medium on quark distributions  kinematics determine whether the electron scatters from quarks or hadrons  Regions being probed:  Low Q 2 – entire nucleus (elastic)  Intermediate Q 2 – single nucleon (Quasielastic Scattering – QES)  Higher Q 2 – DIS (“superfast” quarks at x>1)  x>1 probes the QES and DIS regions

Inelastic Cross Section and x-scaling  The struck nucleon can be excited into a resonance state or be broken up  Inclusive Scattering -> only the electron is detected, so the final hadronic state is unknown  For unpolarized electron scattering from a charged particle with internal structure, the cross-section can be written as:  For the case of inelastic electron-proton scattering, W 1 and W 2 are the proton structure functions  If the reaction time is much less that the hadronization time, the reaction should look like scattering from a quasi-free quark (x.1)

x-scaling (continued)  The cross section for elastic scattering from a free, spin ½ fermion with no internal structure is (x.2)  In the DIS limit, the structure functions from Eq.x.1 simplify and we are able to extract the following expressions:  So, in this limit, the structure functions simplify to functions of, instead of functions of Q 2 and ν independently.

x-scaling (continued again)  For confined quarks, the δ-function is replaced by the momentum distribution of the quarks.  The structure functions are usually expressed in terms of the Bjorken x variable, defined as:, where M is the nucleon mass.  In the limit of ν,Q 2, x is the fraction of the nucleon momentum carried by the struck quark, and the structure function in the scaling limit represents the momentum distribution of quarks inside the nucleon. ∞

More scaling: ξ-scaling  Another variable, in addition to x, is often used to examine scaling behavior in inelastic e-p scattering is the Nachtmann variable ξ. As Q 2  ∞, 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 Q 2 will be different.  It’s been observed that in electron scattering from nuclei, the structure function νW 2, scales at the largest measured values of Q 2 for all values of ξ, including low ξ (DIS) and high ξ (QES).

ξ-scaling (continued) Scaling is observed only at low values of x (x<0.4) Onset of scaling occurs at higher Q 2 for increasing values of ξ, but the structure function appears to approach a universal curve  Iron data from the NE3 experiment at SLAC

ξ-scaling : Competing Explanations  One explanation for ξ-scaling is that it’s a consequence of the Bloom-Gilman duality in e-p scattering  An alternative explanation proposed by Benhar and Liuti explains the observed scaling at high ξ-values in terms of y- scaling of the quasi-elastic cross-section.  A third explanation proposed by Sick and Day explains the apparent scaling by the approximate compensation between the contribution from the QE cross-section and the failure of the resonance and DIS contributions at large ξ and Q 2. Proton Resonance structure functions vs. the deep inelastic limit. Data is from SLAC experiment E133 and the scaling limit is from L.W. Whitlow Bloom and Gilman examined the structure function in the resonance region as a function of ω’=1/x+M 2 /Q 2 and Q 2 They observed that the resonance form factors have the same Q2 behavior as the structure functions The scaling limit of the inelastic structure functions can be generated by averaging over the resonance peaks seen at low Q 2 If the same is true of a nucleon inside a nucleus, then the momentum distribution of the nucleons may cause this averaging of the resonances and the elastic peak. The idea is that the Q 2 -dependence arises from looking at ξ, rather than y, is cancelled by the Q 2 -dependence of the final state interactions

y-scaling: From cross sections to momentum distributions  Inclusive electron scattering by nuclei at high Q 2 is analyzed in the impulse approximation with fully relativistic kinematics. The nucleon cross-section is an incoherent sum over the individual nucleons  k and p=k+q are the initial and final momenta of the struck nucleon  P i (k,E) is the spectral function  M A is the nucleon mass  E=M * A-1 +M-M A is the separation energy  M * A-1 is the mass of the residual nucleon system  σ ei is the fully relativistic off-shell cross section for electron scattering from a nucleon of momentum k. (1)

 Using the delta function to do the angular integral and the constraints of energy and momentum conservation as well as requiring the final state particles to be on mass-shell, we arrive at (2),where φ is the polar angle of k with respect to q.  Next, we introduce a function F: And y is defined using the delta function from eq.1 (3) (4),where

 F is a function of q and y only and at large q for a fixed value of y, F has an asymptotic value -> it scales in y.  As q->∞, the dependence on q is weak, so F=F(y) at large momentum transfer and can be expressed as  n(k) is the nucleon momentum distribution, obtained by integrating the spectral function over energy. Summary:  Scaling : the dependence of the reaction on a single new variable (y), rather than momentum transfer and energy  F(y) is defined as ratio of the measured cross-section to the off-shell electron- nucleon cross-section times a kinematic factor  y is the momentum of the struck nucleon parallel to the momentum transfer. (5) y-scaling: A more detailed example

Y-Scaling (Example: 3 He) y is the momentum of the struck nucleon parallel to the momentum transfer. 0.1<Q 2 <3.9 (GeV 2 )

 Slide provided by John Arrington with plots from Donal Day

New Frontiers Existing data Existing He data

Improved 3 He coverage: another perspective

E Details  E running is completed  E is an extension of E89-008, but with higher E (5.75 GeV) and Q 2.  Cryogenic Targets: H, 2 H, 3 He, 4 He  Solid Targets: Be, C, Cu, Au.  Spectrometers: HMS and SOS (mostly HMS)

Experimental Setup in Hall C SOS HMS Scattering Chamber Beam Line

High Momentum Spectrometer  Superconducting magnets in a QQQD configuration  Maximum central momentum of 6.0 GeV/c with 0.1% resolution and a momentum bite of ±10%  Solid angle of 6.7 msr  Detectors  2 sets of Drift chambers  2 sets of x-y hodoscopes  Gas Čerenkov detector  Lead glass shower counter  Pion Rejection of ~75,000 using the Čerenkov and the Lead Glass Shower Counter

High Momentum Spectrometer

Short Orbit Spectrometer  For E02-019, the SOS is primarily used to estimate the charge symmetric background.  Has a solid angle of 7 msr and a large momentum bite (±20%)  Maximum central momentum of 1.75 GeV/c  QDD magnet configuration (non-superconducting):  Pion Rejection of ~10,000 using the Čerenkov and the Lead Glass Shower Counter  Detector Package is very similar to that of HMS

Newer Data is better Data X bj Cross-section (cm 2 /MeV·sr) y(x=0.94) = -.01GeV

3 He online spectrum  E=5.75 GeV  P hms =5.1 GeV/c  θ hms =18°  All events past x bj =3 y(x=2.32) = -0.58GeV

3 He and Au coverage at 40°  Overlap regions look good

Status  All the data have been taken  This experiment will provide data over an extended kinematic range and significantly improve the 3 He and 4 He data sets  The positron background has been measured and is small for E  Detector calibrations are currently being performed

Summary  The hard work is now beginning  Immediate goals:  Extraction of cross-sections, including acceptance, bin-centering, and radiating corrections  Extraction of scaling and structure functions, and comparison with theory

E Collaboration J. Arrington (spokesperson), L. El Fassi, K. Hafidi, R. Holt, D.H. Potterveld, P.E. Reimer, E. Schulte, X. Zheng Argonne National Laboratory, Argonne, IL B. Boillat, J. Jourdan, M. Kotulla, T. Mertens, D. Rohe, G. Testa, R. Trojer Basel University, Basel, Switzerland B. Filippone (spokesperson) California Institute of Technology, Pasadena, CA C. Perdrisat College of William and Mary, Williamsburg, VA D. Dutta, H. Gao, X. Qian Duke University, Durham, NC W. Boeglin Florida International University, Miami, FL M.E. Christy, C.E. Keppel, S. Malace, E. Segbefia, L. Tang, V. Tvaskis, L. Yuan Hampton University, Hampton, VA G. Niculescu, I. Niculescu James Madison University, Harrisonburg, VA P. Bosted, A. Bruell, V. Dharmawardane, R. Ent, H. Fenker, D. Gaskell, M.K. Jones, A.F. Lung (spokesperson), D.G. Meekins, J. Roche, G. Smith, W.F. Vulcan, S.A. Wood Jefferson Laboratory, Newport News, VA B. Clasie, J. Seely Massachusetts Institute of Technology, Cambridge, MA J. Dunne Mississippi State University, Jackson, MS V. Punjabi Norfolk State University, Norfolk, VA A.K. Opper Ohio University, Athens, OH F. Benmokhtar Rutgers University, Piscataway, NJ H. Nomura Tohoku University, Sendai, Japan M. Bukhari, A. Daniel, N. Kalantarians, Y. Okayasu, V. Rodriguez University of Houston, Houston, TX T. Horn, Fatiha Benmokhtar University of Maryland, College Park, MD D. Day (spokesperson), N. Fomin, C. Hill, R. Lindgren, P. McKee, O. Rondon, K. Slifer, S. Tajima, F. Wesselmann, J. Wright University of Virginia, Charlottesville, VA R. Asaturyan, H. Mkrtchyan, T. Navasardyan, V. Tadevosyan Yerevan Physics Institute, Armenia S. Connell, M. Dalton, C. Gray University of the Witwatersrand, Johannesburg, South Africa