EIC meeting, April 6,7, MIT

Transcription

1 F L and the Gluon Density EIC meeting, April 6,7, MIT A. Caldwell Rutherford SLAC-MIT, HERA EIC?

2 Motivation At small x, gluons physics dominates In this region, far from initial conditions: universal properties? Fundamental aspect of QCD. F L good probe of this physics.

3 Proton Structure em F 2 -log10 (x) 5 4 HERA F 2 x=6.32e-5 x= x= x= x= x= x= x= x= x= x= ZEUS NLO QCD fit H1 PDF 2000 fit H H1 (prel.) 99/00 ZEUS 96/97 BCDMS E665 NMC Q 2 dependence in agreement with the expectations of perturbative QCD (famous Dokshitzer, Gribov, Lipatov, Altarelli, Parisi evolution equations). DGLAP x= x=0.008 x=0.013 x= x=0.032 x=0.05 x=0.08 x= x=0.18 x=0.25 x=0.4 x= Q 2 (GeV 2 ) F 2 lnq 2 x = S(Q 2 ) 2 1 x 1 x dz z 2 2 e q q x z P x qq z F 2(z,Q 2 ) + dz x z z P x qg z zg(z,q2 )

4 Proton Structure (small selection of data) QCD based fits can follow the data accurately, yield parton densities. DGLAP

5 BUT: many free parameters (18-30) (DGLAP only knows how parton densities evolve in Q 2 ) form of parametrization fixed by hand (not given by theory) Proton Structure Fits don t agree at small-x! In particular, large uncertainty in gluons parametrizations should not be extended beyond measurement range in x (divergence at fixed small-x larger at low Q 2, smaller at high Q 2 )

6 Need better data to test whether our parton densities are reasonable. The structure function F L will provide an important test. F L d 2 (e p) = 2 2 [ Y dxdq 2 xq 4 + F 2 (x,q 2 ) y 2 F L (x,q 2 ) ± Y xf 3 (x,q 2 )] ( ) Y ± = 1 ± (1 y) 2 Need two beam energies to measure F L F 2 r E cm 2 negligible at small Q 2 E cm 1 Q 2 F L = 4 2 L F L = S 4 x 2 1 x F 2 -F L dz 16 z 3 3 F e 2 q (1 x z )zg 0 y 2 /Y + Directly sensitive to xg at small-x 1

7 Measuring F L d 2 dxdq = 2 2 [ Y 2 xq 4 + F 2 (x,q 2 ) y 2 F L (x,q 2 )] Y + = ( 1 + (1 y) 2 ) r = 2 2 Y + xq 4 F 2 r 1 d 2 dxdq = F 2 2 (x,q2 ) y 2 F L (x,q 2 ) Y + Small Q 2, ignore F 3 F L (x,q 2 ) = r (x,q2, y 1 ) r (x,q 2,y 2 ) f (y 2 ) f (y 1 ) F 2 -F L 0 y 2 /Y + 1 f (y) = y 2 Y + For best sensitivity, maximize lever arm (y-range)

8 HERA Kinematics Measuring F L Interesting region Need to go to lowest possible scattered electron energy: lower E P rather than E e trigger efficiency electron finder efficiency electron finder purity (photoproduction background, wrong candidate)

9 HERA Kinematics Measuring F L Low energy run (LER) 140 Low energy run (LER) + High energy run (HER) 17.8 GeV 19.8 GeV GeV 12 GeV y = 1.0 y = BIN SIZE: E p = 460 GeV E e = 4 12 GeV E = 2 GeV e = = 2 E p = 920 GeV E e = GeV E = 2 GeV e = = 1 Bins have square shape in E e and e

10 Low Energy Run The HERA low energy has started and is planned to continue until 2 July, 2007 at 10:00AM. Expect 10 pb -1 of data.

11 F L The F L measurement at HERA will serve primarily as a check of the gluon distributions extracted using the DGLAP fits H1 ZEUS CTEQ5D R=0.25 MRST2002(LO) 0.30 MRST2004(NLO) 0.18 MRST2004(NNLO) 0.18

12 Predictions for F L F L predictions from MRST group at different orders in DGLAP, a fit which resums the leading ln(1/x) and 0 terms, and a dipole type model. Very large differences at small Q 2 where gluon uncertainty large.

13 F L : EIC & other Measurements erhic F L measurement from EIC+HERA EIC standalone DIS F L measurement from EIC+fixed target EIC is in an optimal energy range to extract F L via cross section comparisons to previous experiments.

14 F L from EIC, HERA comparison F L (x,q 2 ) = r(x,q 2,y 1 ) r (x,q 2, y 2 ) f (y 2 ) f (y 1 ) f (y) = y 2 Y + F L [ r (y 1 ) r (y 2 )] F L 1 + R 2 Ry where y 1 is the larger y 1 R = F L F 2 F L Assumptions: E e =20, 10 GeV E p =250,200 GeV 2% cross section measurement precision R=0.2 E =2,3,4,5,6,7.5,9,11

15 F L from EIC, HERA comparison

16 Summary F L is important in really understanding the parton densities at small-x The EIC is in a great kinematic position to give F L measurements over a wide kinematic range Measurements will be possible with EIC alone, and from comparisons of cross sections EIC with existing measurements