SaturationattheLHeC

JeffForshawUniversityofManchester

IncollaborationwithMaxKlein,PaulNewman&EmmanuellePerez

LHeC

70GeVelectronsintheLHCtunnel

7TeVprotons

1033cm‐2s‐1luminosity

AfantasticopportunitytoexploreverylowxdynamicsatmoderateQ2

ThreefitstoHERAdata,extrapolatedtoLHeC.

Firstglancelooksverypromising….

Systematics1‐3%

1fb‐1ofdata~1year

WhatcanbedonewithF2?

Dipolemodel

1 -z

z

b

r

!L,T!!p =

!dz d2r |"L,T (z, r)|2!(s∗, r)

σ(s∗, r) ∼ αsπ2r2

3xg(x,A2/r2)

• F2(andcharm,beauty)• FL• DiffractiveDIS(highmass?)• DVCS• Exclusivevectormesons(mesonwavefunction?)

Universaldipolecross‐section:

Reggeinspireddipole:FS04nosat

JF&Shaw:JHEP0412:052(2004).

Onlydipoleswithr<rsscatterwitha~x‐0.3cross‐section.Largerdipolesscatterwithaweaker~x‐0.06cross‐section. Saturation:rsdecreaseswithdecreasingx.

SaturationdipoleI:FS04sat

Onlydipoleswithr<r0scatterwitha~x‐0.3cross‐section.Largerdipolesscatterwithaweaker~x‐0.07cross‐section. Nosaturation:r0isconstant.

SaturationdipoleII:CGC

Dipoleswithr<rsscatterwitha~BFKLcross‐section.Largerdipolesscatterwithaconstantcross‐section. Saturation:rsdecreaseswithdecreasingx

Iancu,Itakura,Munier:Phys.Lett.B590:199(2004);Kowalski,Motyka,Watt:Phys.Rev.D74:074016(2006).

HERAdata•  SometentativeevidenceforsaturationbutitreliesonF2dataatQ2below2GeV2.

• AllotherdatacanbefittedusingtheReggemodeloreitherofthesaturationmodels.

Nosaturation Saturation

SeealsoKowalski,Motyka,Watt.

DVCS

100 1000W [GeV]

10

20

30

! [n

b]

FS04 satFS04 no satCGC

ZEUS (e+p)

ZEUS (e-p)

Q2 = 9.6 GeV

2

B = 4.0 GeV-2

100 1000

100

200

300

400

500

! [

nb

]

ZEUS

H1

FS04 no sat, Gaussian

FS04 sat, Gaussian

CGC, Gaussian

100 10000

100

200

300

400

100 1000

W [GeV]

100

200

300

! [

nb

]

100 1000

W [GeV]

0

50

100

150

Q2=0

Q2 = 3.1 (ZEUS); 3.2 (H1)

Q2 = 0.4

Q2=6.8 (ZEUS); 7.0 (H1)

0 10 20 30 40 50 60

Q2 [GeV

2]

0.1

1

10

! [

nb

]

H1FS04 no satFS04 satCGC

W = 82 GeV

B = 6.02 GeV-2

J/Psi

0 5 10 15 20 25 30

Q2 [GeV

2]

0

0.5

1

1.5

2

2.5

3

R

H1ZEUSFS04 sat, Gaussian

FS04 no sat, Gaussian

CGC, Gaussian

Also F c2

JF,Sandapen&Shaw:JHEP0611:025(2006)

DiffractiveDIS

Note1:lowbetaregionistheoreticallyuncertainNote2:theorydoesnotincludesecondaryexchangesrelevantforxpom>0.01

F2atLHeC

Curves:CTEQ6.1(extrapolated)

Points:FakeLHeCdatausingCGC&FS04(1fb‐1)

CanweseeDGLAPfailatQ2>fewGeV2?

CanDGLAPbemadetofitdatawhichincludesaturation?

Butweshouldre‐fitDGLAPbeforedrawingconclusions:

=Fit6parameters:Aq, Bq, Ag, Bg, x0, ! and Cg

=UseH1pdf2kforvalencequarksandCq

=NLOevolution()

=Fixedflavournumberscheme

= and

MS

!s(Mz) = 0.1185

Mc = 1.4 GeV and Mb = 4.5 GeV

Q20 = 1.9 GeV2

xq̄(x,Q0) = AqxBq (1! x)Cq

xg(x,Q0) = Ag(1! exp[!Bg log2((x0/x)!)])(1! x)Cg

FitistodatawithQ2≤20GeV2(χ2=92for92datapoints)

⇒ ConsistentwithwhatwesawextrapolatingCTEQ

⇒ Onlythe4pointsathighestQ2andlowestxcauseproblems

FittingtheFS04LHeC“data”+ZEUSdatausingDGLAP

Q2evolutionofFS04andCGCisanextrapolationofthefittoHERAdata.

Q2 = 2 GeV2 Q2 = 5 GeV2

Q2 = 10 GeV2 Q2 = 20 GeV2

Q2 = 50 GeV2

FS04

FittingtheCGCLHeC“data”+ZEUSdatausingDGLAP

FitistodatawithQ2≤3GeV2(χ2=10.5for14datapoints)

⇒ ConsistentwithwhatwesawextrapolatingCTEQ

⇒ Cannotfitevolveddata

Q2 = 2 GeV2 Q2 = 5 GeV2

Q2 = 10 GeV2 Q2 = 20 GeV2

Q2 = 50 GeV2

CGC

FLatLHeC

FS04fittedtoQ2≤20GeV2:F2andFL CGCfittedtoQ2≤3GeV2:F2andFL

Varyingprotonbeamenergyfrom7TeVdownto450GeV(or1TeV)

FS04 CGC

Q2 = 13.5 GeV2 Q2 = 30 GeV2

Q2 = 2 GeV2 Q2 = 5 GeV2

Q2 = 13.5 GeV2 Q2 = 30 GeV2

Q2 = 2 GeV2 Q2 = 5 GeV2

Curvesarethe“predictions”afterextrapolatingCTEQ

Q2 = 13.5 GeV2 Q2 = 30 GeV2

Q2 = 2 GeV2 Q2 = 5 GeV2

Q2 = 13.5 GeV2 Q2 = 30 GeV2

Q2 = 2 GeV2 Q2 = 5 GeV2

FS04 CGC

• SaturationeffectsmaywellbepresentinHERAdatabutthereisnoevidencewithintheperturbativedomain.

• SaturationmodelswhichfittheHERAdataleadtopredictionsforLHeCwhichcannotbe“faked”byDGLAPevolution.

• Itwouldbeveryimportanttomeasurethelongitudinalstructurefunction.

• Otherobservableswouldalsoprovideahandle:heavyquarkstructurefunctions,DVCS,exclusivevectormesons,diffractivedeepinelasticscattering.

Conclusions