1. F2/FL with HERA III/eRHIC A. Caldwell, Max-Planck-Institut f. Physik
New Detector for HERA/eRHIC
Physics - QCD in the high energy limit
March 16, 2004
A. Caldwell, MPI fuer Physik

2. A. Caldwell, MPI fuer Physik
Kinematics
Ee= GeV
EP= GeV r *
s=(k+P)2 = ( GeV)2 CM energy squared
Q2=-(k-k`)2 virtualiy
W2=(q+P)2 *P CM energy squared
Transverse distance scale probed: r  hc/Q
McAllister, Hofstadter Ee=188 MeV rmin=0.4 fm
Bloom et al GeV fm
CERN, FNAL fixed target GeV fm
EIC TeV fm
HERA TeV fm /
March 16, 2004
A. Caldwell, MPI fuer Physik

3. A. Caldwell, MPI fuer Physik
Proton  momentum frame
Proton rest frame
Rutherford
d2/dW dQ2 =  (T +  L)
is flux of photons
T,L are cross sections for transversely,
longitudinally polarized photons to
scatter from proton
 is the relative flux
d2/dxdQ2=22/xQ4[(1+(1-y)2)F2 - y2FL]
F2 = f e2f x {q(x,Q2) + q(x,Q2) }
ef is quark charge
q(x,Q2) is quark density
FL = 0 in LO (QPM), non-zero after gluon
radiation. Key test of our understanding
F2 = Q2/42 (T +  L)
March 16, 2004
A. Caldwell, MPI fuer Physik

4. A. Caldwell, MPI fuer Physik
Track
Cal
Structure function measurements – measure distribution of quarks at the end of the radiation chain. Try to understand result with various QCD based evolution approaches.
March 16, 2004
A. Caldwell, MPI fuer Physik

5. A. Caldwell, MPI fuer Physik
Physics Picture in Proton Rest Frame r * b
r ~ 0.2 fm/Q (0.02 – 2 fm for 100>Q2>0.01 GeV2) transverse size of probe
ct ~ 0.2 fm (W2/2MPQ2 ) (<1 fm to 1000‘s fm) – scale over which photon fluctuations survive
And, in exclusive processes, can vary the impact parameter
b ~ 0.2 fm/sqrt(t) t=(p-p‘)2
Can control these parameters experimentally !
March 16, 2004
A. Caldwell, MPI fuer Physik

6. A. Caldwell, MPI fuer Physik
Cross sections as a function of Q2
The rise of F2 with decreasing x observed at HERA is strongly dependent on Q2
Equivalently, strongly rising *P cross section with W at high Q2
March 16, 2004
A. Caldwell, MPI fuer Physik

7. The behavior of the rise with Q2
Below Q2 0.5 GeV2, see same energy dependence as observed in hadron-hadron interactions. Observe transition from partons to hadrons (constituent quarks) in data. Distance scale  0.3 fm ??
What physics causes this transition ?
Hadron-hadron scattering energy dependence (Donnachie-Landshoff)
March 16, 2004
A. Caldwell, MPI fuer Physik

8. A. Caldwell, MPI fuer Physik
In general, NLO pQCD (DGLAP) fits do a good job of reproducing the data over the full measurement range.
March 16, 2004
A. Caldwell, MPI fuer Physik

9. A. Caldwell, MPI fuer Physik
Analysis of F2 in terms of parton densities (quarks and gluons)
NLO DGLAP fits can follow the data accurately, yield parton densities. BUT:
many free parameters (18-30)
form of parametrization fixed (not given by theory)
Constraints, e.g., dsea=usea put in by hand. Is this correct ? Need more constraints to untangle parton densities (deuterons, FL).
March 16, 2004
A. Caldwell, MPI fuer Physik

10. See breakdown of NLO DGLAP approach ...
Gluon density known with good precision at larger Q2. For Q2=1, gluons go negative. NLO, so not impossible, BUT – cross sections such as L also negative !
March 16, 2004
A. Caldwell, MPI fuer Physik

11. A. Caldwell, MPI fuer Physik
FL shows tremendous variations when attempt to calculate at different orders. But FL is an observable – unique result.
FL is hard to measure but a very sensitive test. Should be measured.
March 16, 2004
A. Caldwell, MPI fuer Physik

12. A. Caldwell, MPI fuer Physik
Large-x
Motivation:
No data on parton densities for x>0.75 in DIS regime.
Phenomenology uses standard parametrizations for large x, q(x)  (1-x)b , but not well motivated. Could have surprises at large-x. At very high-x, novel QCD effects expected (ends in ‘on’).
Parton densities need to be well understood for searches for new physics.
Requirements:
Max possible luminosity
e+, e- for valence quark flavor separation
low EP running for added sensitivity to large-x
March 16, 2004
A. Caldwell, MPI fuer Physik

13. A. Caldwell, MPI fuer Physik
Large-x
Uncertainties in parton densities from ZEUS NLO fit: includes available fixed target data. Parametrization uncertainty not included.
Fractional error
March 16, 2004
A. Caldwell, MPI fuer Physik

14. A. Caldwell, MPI fuer Physik
Statistics at large-x (HERA II):
From 1 fb-1 with Ep=920 GeV. 15% measurement at x> Will be a first measurement of this quantity.
March 16, 2004
A. Caldwell, MPI fuer Physik

15. Precision eA measurements
Enhancement of possible nonlinear effects (saturation) r b
At small x, the scattering is coherent over nucleus, so the diquark sees much larger # of partons: xg(xeff,Q2)  A1/3 xg(x,Q2)
This should enhance the chances to see saturated gluon state (CGC) in nuclei. Need quantitative predictions for behavior of structure functions with x in heavy nuclei.
March 16, 2004
A. Caldwell, MPI fuer Physik

16. A. Caldwell, MPI fuer Physik
HERA-III Initiative
Two letters of intent were submitted to the DESY PRC (May 7,8 2002)
H1 Collaboration
Focus initially on eD: isospin symmetry of sea at small-x
uv/dv at large-x
diffraction on n, D
Discuss also interest in: eA, F2,FL at small Q2, forward jets,
spin structure
New Collaboration
Optimized detector for precision structure function measurements, forward jets and particle production over a
large rapidity interval (eP, eD, eA)
March 16, 2004
A. Caldwell, MPI fuer Physik

17. A. Caldwell, MPI fuer Physik
Possible upgrades of H1 detector
Upgrade in electron direction for low Q2 F2 and FL measurements
+ very forward proton, neutron detectors
Upgrade in proton direction for forward particle, jets measurements
March 16, 2004
A. Caldwell, MPI fuer Physik

18. Precision eD measurements
Universality of PDF‘s at small-x, isospin symmetry
Can measure F2p-F2n w/o nuclear corrections if can tag scattered nucleon
March 16, 2004
A. Caldwell, MPI fuer Physik

19. A. Caldwell, MPI fuer Physik
Simulation with H1 based on 50 pb-1
Flavor dependence at high-x
Behavior of F2p/F2n as x  1
SU(6) symmetry F2p/F2n = 2/3
Dominant scalar diquark F2p/F2n = 1/4
Can measure this ratio w/o need to correct for nuclear effects if can tag scattered nucleon.
March 16, 2004
A. Caldwell, MPI fuer Physik

20. A new detector to study strong interaction physics
Si tracking stations
EM Calorimeter
Hadronic
Calorimeter
Compact – fits in dipole magnet with inner radius of 80 cm.
Long - |z|5 m e
March 16, 2004
A. Caldwell, MPI fuer Physik

21. A. Caldwell, MPI fuer Physik
FL Measurement Range
d2/dxdQ2=22/xQ4[ (1+(1-y)2)F2(x,Q2) - y2FL(x,Q2) ]
Fix x, Q2. Use different beam energies to vary y.
Critical issue: e/ separation
FL can be measured precisely in the region of maximum interest. This will be a strong test of our understanding of QCD radiation.
March 16, 2004
A. Caldwell, MPI fuer Physik

22. A. Caldwell, MPI fuer Physik
EIC kinematics
March 16, 2004
A. Caldwell, MPI fuer Physik

23. A. Caldwell, MPI fuer Physik
Summary
Existing data (F2 fits, forward jets,+…) show limitations of pQCD calculations. Transition region observed.
Exciting theoretical developments over the past few years. We are approaching a much deeper understanding of the high energy limit of QCD.
Measure with more precision, over wider kinematical range, to see where/how breakdown takes place (high rapidities, high-t exclusive processes, expanded W, MX range for diffraction, full coverage of transition region)
Precision FL measurement: key observable for pinning down pQCD. Large differences in predictions at LO, NLO, NNLO, dipole model.
eD, eA measurements to probe high density gluon state, parton densities for nuclei.
Additional benefits: parton densities for particle, astroparticle and nuclear high energy physics experiments. Crucial for cross section calculations.
March 16, 2004
A. Caldwell, MPI fuer Physik