1. J.Feltesse1 Measurement of F L the longitudinal structure function at HERA Low x meeting, Lisbon, Portugal 28 June 2006

2. 2 Outlook Motivation Direct measurement of F L (x,Q 2 ) F L D (x,Q 2,x Pom ) Conclusion

3. 3 Physics motivations F L simply related to σ L, the inclusive cross section of longitudinally polarised photons : At low x, the gluon density dominates. F L is a clean probe of the gluon distribution at HERA. In QPM : In LO : QCD radiation generates quark P T Helicity conservation

4. 4 At fixed beam energy high y (i.e. small x at fixed Q 2 ) data are sensitive to F L. Q 2 =s xy s=(cm energy) 2

5. 5 MRST, CTEQ have trouble fitting the H1 low Q2 data consistently at NLO H1 96-97 MRST Fits similar problems ZEUS 96-97 data show the same effects Ex: CTEQ6.1M (Tung, DIS 2006) Lines: fits Red points: raw data points; Green points: data points shifted by optimal correlated Sys Err.

6. 6 F L and gluon density at low x are poorly constrained by present data.

7. 7 Direct measurement of F L (Q 2,x) At fixed (Q 2,x), measure cross sections at several beam energies (minimum 2), i.e. at different y. Perform straight line fit of σ r to extract F 2 and F L F L is very sensitive to small relative shifts on cross sections F 2 -F L F2F2 Reduced cross section

8. 8 Direct measurement of F L (Q 2,x) ZEUS and H1 have investigated the optimum beam energy for the low energy run. Requirements : A large y difference to maximize lever arm ~ 1/E p Enough luminosity. Lumi scales as E p 2 → Reduce proton beam energy to lowest energy considered reasonable by HERA. E p 920 GeV 460 GeV Lumi 30 pb -1 10 pb -1 Estimated time : 3 months. The highest possible y at low beam energies (error on F L ~ 1/y 2 → Go to lowest possible scattered electron energy

9. 9 Measurement with ZEUS Daniel Kollar DIS2006

10. 10 Measurement with ZEUS

11. 11 Measurement with H1

12. 12 Measurement of electron scattered energy demonstrated down to 3 GeV. Measurement of the charge provides statistical substraction of background Measurement with H1

13. 13 Caldwell, DIS 2006

14. 14 30 pb -1, E p =920 GeV 10 pb -1, E p =460 GeV Measurement with H1- Fast simulation

15. 15 Measurement with ZEUS – detailed simulation Daniel Kollar, DIS2006

16. 16 Attempt to put information in one number (ZEUS) Daniel Kollar, DIS 2006

17. P.Newman17 →vary y at fixed Q 2, β, x by changing s (i.e. proton beam energy) x P =Q 2 /(sy β)

18. 18 Encouraging result ! F L D extracted to 3 – 4 σ in 3 bins At = 12 GeV 2 and = 0.23 H1 simulation

19. 19 F L D has never been measured F L D predicted from QCD fits to be large at low β! Inclusive diffraction cannot be fully understood without separating out F L D contribution.

20. 20 Conclusion A direct measurement of F L at x from 10 -4 to 10 -3 is difficult but feasible by running HERA for a few weeks at low proton beam energy. Agreed by both H1 and ZEUS and supported by the PRC. The measurement of F L provides a very attractive added value to the legacy of HERA. It could also provide the first measurement of F L D at the 3-4 sigmas level. Let’s do it.

21. 21 EXTRAS

22. 22

23. 23 Motivations The structure function F L is a basic Structure Function. Q 2 = s xy s = (center of mass energy) 2 Small Q 2, xF 3 terms neglected

24. 24 Why not using the radiative events? e + p → e + γ + X We get radiative events fo free ! Need a huge statistics (~200 pb -1 ) [Krasny, Placzek, Spiesberger,1991] However : –For a fixed (Q 2,x) bin, at different y, the overlap in the same part of the detector is quite small –No access to very high y (E’ e > 3 GeV) –Severe pile up of Bethe-Heitler events (e p→e p γ) in the gamma detector [Favart, Maracek, 1996] ▬► huge errors on F L ~ 50-100 %!

25. 25 E p = 920 GeV E p = 460 GeV

26. 26

27. 27 10 pb -1 at E p =460GeV 5 pb -1 at E p = 460 GeV and 3.5 pb -1 at E p = 575 GeV

28. 28