# Presentation: 728158

## Measurement of FLthe longitudinal structure function at HERA

- Low x meeting, Lisbon, Portugal
- 28 June 2006

- J.Feltesse

## Outlook

- Motivation
- Direct measurement of FL(x,Q2)
- FLD(x,Q2,xPom)
- Conclusion

## Physics motivations               

-    FL simply related to σL , the inclusive cross section of longitudinally polarised photons :

-   At  low x,  the gluon density dominates.
-  FL is a clean probe of the gluon distribution at HERA.

- In QPM :

- In LO :

- QCD radiation generates quark PT

- Helicity conservation

## At fixed  beam energy high y (i.e. small x at fixed Q2) data are sensitive to FL.

- Q2=s xy
- s=(cm energy)2

## 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.

## FL  and gluon density at low x  are

- FL  and gluon density at low x  are
-   poorly constrained by present data.

## Direct measurement of FL(Q2,x)               

- At fixed (Q2,x),  measure cross  sections  at  several beam energies (minimum 2), i.e. at different y.
-  Perform straight line fit of σr to extract F2 and FL
- FL  is very sensitive to small relative shifts on cross sections

**F****2****-F****L**

- F2

- Reduced cross section

## Direct measurement of FL(Q2,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/Ep
- Enough luminosity. Lumi scales as Ep2
- → Reduce proton beam energy to lowest energy considered reasonable by HERA.
-                    Ep               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 FL ~ 1/y2
- → Go to lowest possible scattered electron energy

## Measurement with ZEUS

- Daniel Kollar DIS2006

## Measurement with ZEUS

## Measurement with H1

## Measurement with H1

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

## Caldwell, DIS 2006

## Measurement with H1- Fast simulation

- 10 pb-1, Ep=460 GeV

## Measurement with ZEUS – detailed simulation

- Daniel Kollar, DIS2006

## Attempt to put information in one number (ZEUS)

- Daniel Kollar, DIS 2006

## →vary y at fixed Q2, β, x by changing s (i.e. proton beam energy)

- →vary y at fixed Q2, β, x by changing s (i.e. proton beam energy)

- xP=Q2/(sy β)

- P.Newman

## H1 simulation

- Encouraging result !
- FLD extracted to 3 – 4 σ in 3 bins
- At  <Q2 > = 12 GeV2    and  <β> = 0.23

## FLD has never been measured

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

## Conclusion

-   A direct measurement of FL 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 FL provides a very attractive added value to the legacy of HERA.
-    It could also provide the first measurement of FLD at the 3-4 sigmas level.
-     Let’s do it.

## EXTRAS

## Slide 22

## Motivations                       

- The structure function FL is a basic Structure Function.

- Q2 = s xy                                  s = (center of mass energy)2

- Small Q2, xF3 terms neglected

## 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 (Q2,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 FL ~ 50-100 %!

## Ep = 920 GeV

- Ep = 920 GeV

- Ep= 460 GeV

## Slide 26

## 10 pb-1 at Ep=460GeV

- 10 pb-1 at Ep=460GeV

- 5 pb-1 at Ep = 460 GeV and
- 3.5 pb-1 at Ep = 575 GeV

## Slide 28