1. Physics Potential of an ep Collider at the VLHC  Why ep? When?  Physics Results from the first ep Collider – HERA  Future ep Physics Priorities  Perturbative QCD Dynamics  Proton Structure  Beyond the Standard Model  Detectors for Future ep Options  Conclusions Stephen R. Magill Argonne National Laboratory

2. Why ep?  Electron/positron/muon is an ideal probe for understanding hadron structure  Large known range in hard scattering scale is accessible and tunable  Relatively background-free studies of QCD parameters and properties  Unique couplings to exotica, i.e., leptoquarks All of the above are necessary for understanding of new physics from future hadron colliders

3. A Multi-TeV ep Collider - When?  ep “Livingston Plot” HERA –  s ~ 300 GeV Resolution ~.001 fm THERA –  s ~ 1 TeV Resolution ~.0003 fm epVLHC –  s ~ 5 TeV Resolution ~.00006 fm 300 GeV e X 20 TeV p First event – January 3, 2025

4. Physics Results from the first ep Collider - HERA  Discovery of steep rise in the proton structure function F2 at low x -> related to large gluon density  Discovery of hard diffractive scattering in DIS  Confirmation of the pointlike nature of partons  Investigations of QCD dynamics through transitions from small to large distances, low to high parton densities

5. Proton Structure Functions Inclusive F 2 F 2 charm CC Events Fixed Target DIS

6. QCD Parameters and Dynamics

7. Future ep Physics Priorities 1) Perturbative QCD Dynamics at Low x – understanding of high energy, high density parton interactions Linear parton evolution : DGLAP (ln Q 2 ) -> DLLA (ln Q 2 ln 1/x) -> BFKL (ln 1/x) High/medium x -> low x -> small x limit Fixed target DIS -> HERA/THERA -> ep @ VLHC Non-linear evolution : High Density QCD Saturation effects Forward Jet Production : All of the above as local effects? 2) Proton Structure – understanding of backgrounds in new physics searches at hadron colliders Inclusive F 2 Flavor Decomposition -> heavy q pdfs 3) Beyond the Standard Model – as  s increases, explore unique couplings to new physics processes Leptoquarks

8. Perturbative QCD Dynamics : Linear Parton Evolution DGLAP – fixed x, Q 2 evolution (ln Q 2 >> ln 1/x) HERA inclusive (F 2 ) DLLA – x, Q 2 variable, ln Q 2 ~ ln 1/x HERA exclusive (HFS) BFKL – fixed Q 2, x evolution (ln 1/x >> ln Q 2 ) HERA forward jets

9. Linear Evolution at a Future ep Collider Tests of BFKL/DLLA/DGLAP evolution : At HERA, can reach x = 10 -4 if Q 2 = 10 GeV 2 ln 1/x = 9.2, ln Q 2 = 2.3 At epVLHC (250 GeV e X 20 TeV p, x reach is 5 X 10 -7 at Q 2 = 10 GeV 2 ln 1/x = 14.5, ln Q 2 = 2.3 -> Much larger region at epVLHC with ln 1/x > ln Q 2 -> QCD fit (of F 2 ) with DGLAP evolution only should be much harder, even at Q 2 = 10 GeV 2 – a difference in required input parameters between HERA and epVLHC would be a clear sign of the failure of DGLAP at very low x.

10. Perturbative QCD Dynamics : Non-linear Effects.. Evolution in Bjorken or Infinite Momentum frame 1. Number of partons increases with time (emission  density) Note that in this illustration, transverse size (  1/Q) of the partons is constant (BFKL case) 2. The number of partons increases until they cover the surface of the (flat) proton 3. Overlapping (low x) partons can recombine into a high x parton (  density 2 ) 4. Tradeoff between emission and recombination produces saturation in the number of partons

11. Approaching the Unitarity Boundary Where is the boundary at which saturation sets in (unitarity boundary)? Note that at Q 2 ~ 10 GeV 2, need to go to x ~ 10 -6 to reach the unitarity boundary – need epVLHC Inclusive measurement of slope of F 2 vs Q 2

12. Unitarity Boundary – Gluon Distribution Unitarity boundary defined by : xg ~ Q 2 /  s At Q 2 = 5 GeV 2, the unitarity boundary is reached when xg ~ 30 x is in the 10 -5 – 10 -6 range At Q 2 = 20 GeV 2, xg ~ 130 at boundary!

13. Beyond the Boundary – High Density QCD Effective Theory – no observation yet! – reached at epVLHC? In this region, perturbation theory breaks down, even if the coupling constant is small - non-linear effects are large. The physical picture of saturation region is called a Color Glass Condensate – which comes from the effective theory and its associated properties used to describe this region (conventional QCD input, not, eg Pomeron-based). Color Glass Condensate – matter made of gluons in high density regime.

14. Perturbative QCD Dynamics : Forward Jet Production Why Forward Jets? 1) Investigate parton evolution. 2) Investigate local density fluctuations in the small region of the proton where the jet originates. It may be that the approach to saturation begins in small, local regions – “hot spots”, which exhibit the high density, non-linear effects sooner than could be seen in the whole proton by an inclusive measurement.

15. Proton Structure : pdf Determination Inclusive measurement – extension of Q 2, x region from HERA to epVLHC Flavor decomposition of pdfs – MC studies of heavy quark distributions to optimize beam choices and detector type

16. Beyond the Standard Model : Leptoquarks Also, Contact interactions, Extra dimensions, SUSY Leptoquark processes by Fermion number (F = 0,2) compared to SM process At epVLHC, can study Leptoquark properties including M LQ up to ~ 4.5 TeV. Also, spins, fermion numbers, and branching fractions can be measured.

17. Detectors for Future ep Options Future Configurations : Most likely – E P >> E e (E P /E e ~ 80 for 250 GeVe X 20 TeV p) Detector – Asymmetric like HERA detectors (only more so) For heavy quark pdfs, need tagging in (far) forward direction Probably large backgrounds in (forward) detector THERA detector – low x configuration Extended configuration when lumi is low Least likely – E e ~ E P Detector – Symmetric like Tevatron detectors Easier tagging requirements Less background

18. Conclusions  An ep Collider is a QCD “Factory”, ideally suited to study all aspects of QCD including parton evolution and the transition to and properties of the high density regime.  An ep Collider at the VLHC can be used to measure proton structure functions and pdfs, extending the present kinematic region by several orders of magnitude.  New non-Standard Model physics can be investi- gated at multi-TeV scales.