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Precision Measurement of FPrecision Measurement of FLL with the EIC with the EIC

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d2 empNC

dxdQ22em

2 YxQ4

(F2 y2

YFL Y

YxF3)

FFL L ~ ~ ssG(x,QG(x,Q22): the most “direct” way to G(x,Q): the most “direct” way to G(x,Q22))

FFLL needs various needs various √s√s longer programlonger program

In order to extract FIn order to extract FLL one needs one needsat least two measurements at least two measurements of theof theinclusive cross section with a inclusive cross section with a ““wide” span in inelasticity wide” span in inelasticity parameter parameter yy (Q (Q22=sxy)=sxy)

Coverage in x & QCoverage in x & Q2 2 for inclusivefor inclusivecross section measurements cross section measurements

Plots for 4 GeV electrons on Plots for 4 GeV electrons on 50 – 250 GeV protons50 – 250 GeV protons

Measuring FMeasuring FLL with the EIC with the EIC

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Conclusion from this studyConclusion from this study Dominated by sys. uncertaintiesDominated by sys. uncertainties gives max. luminositygives max. luminosity here: 4fbhere: 4fb-1-1 / A / A Depending on x & QDepending on x & Q22 might be might be able to take a hit in luminosityable to take a hit in luminosity need to include need to include detector effectsdetector effects

Lets get a feeling for systematic uncertaintiesLets get a feeling for systematic uncertainties1% energy-to-energy normalization1% energy-to-energy normalization

FFLL for fixed electron energy (4GeV) for fixed electron energy (4GeV)and proton energies:and proton energies:50, 70, 100, 250 GeV50, 70, 100, 250 GeVLuminosity: 4fbLuminosity: 4fb-1 -1 each settingeach setting

Measure gMeasure gAA(x) impact parameter (x) impact parameter dependent dependent

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Stringent requirements on:Stringent requirements on: Momentum resolution Momentum resolution t resolution and ranget resolution and range

EIC INT Program, Seattle 2010 - Week 5EIC INT Program, Seattle 2010 - Week 5

A. Caldwell, H. Kowalski Phys.Rev.C81:025203,2010A. Caldwell, H. Kowalski Phys.Rev.C81:025203,2010

Radiative Correction will impact themRadiative Correction will impact them

Some Info on RadCorsSome Info on RadCors

Inclusive cross sectionInclusive cross section tottot = = elaela + + qelaqela + + inel + inel + vv

for all parts photons can be radiated from the incoming and outgoing for all parts photons can be radiated from the incoming and outgoing lepton, high Z-material Compton peak.lepton, high Z-material Compton peak.

radiation is proportional to Zradiation is proportional to Z22 of target, like bremsstrahlung of target, like bremsstrahlung

radiation is proportional to 1/mradiation is proportional to 1/m2 2 of radiating particle of radiating particle

elastic:elastic:

quasi-elastic: scattering on proton of nuclei quasi-elastic: scattering on proton of nuclei proton stays intactproton stays intact

nuclei breaks upnuclei breaks up two photon exchange? Interference terms? two photon exchange? Interference terms?

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initialinitial finalfinal vacuum loopsvacuum loops

Why are RadCor important?Why are RadCor important?

Modify kinematics Modify kinematics Q Q22:: initial state: E’initial state: E’beambeam = E = Ebeambeam – E – E

photon goes along the beam linephoton goes along the beam line

final state: E’final state: E’outout = E = Eoutout – E – E

photon goes somewhere in Calophoton goes somewhere in Calo

RadCor and detector smearing don’t factorizeRadCor and detector smearing don’t factorize need to have RadCor implemented in MC to unfold effects on need to have RadCor implemented in MC to unfold effects on

kinematicskinematics unfolding in binsunfolding in bins

NNtruetrue=N=Nmeasmeas-N-Nbckgbckg

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eventseventssmeared intosmeared intoacceptanceacceptance

RadCor and smearing unfolding in MCRadCor and smearing unfolding in MC

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generate observed kinematicsgenerate observed kinematicsxxmeasmeas, Q, Q22

measmeas

Radiative Correction CodeRadiative Correction Code

photon radiatedphoton radiated no photon radiatedno photon radiated

xxtruetrue=x=xmeasmeas, , QQ22

truetrue=Q=Q22measmeas

calculatecalculatexxtruetrue, Q, Q22

truetrue

hand kinematics tohand kinematics togenerator (lepto, pythia, ..)generator (lepto, pythia, ..)

What subprocess isWhat subprocess isgenerated is regulatedgenerated is regulated

by phase spaceby phase space

Hand particlesHand particlesto GEANTto GEANT

What do we know?What do we know?

A lot of radiative correction codes for protonA lot of radiative correction codes for proton much less existing for eAmuch less existing for eA

all experiments apart from HERMES had all experiments apart from HERMES had -beams-beamssuppressed radiationsuppressed radiation

HERMES uses modified version of RADGEN HERMES uses modified version of RADGEN (hep-ph/9906408v1)(hep-ph/9906408v1)

Radiative corrections to deep inelastic scattering on heavy Radiative corrections to deep inelastic scattering on heavy nuclei at HERAnuclei at HERA

I. Akushevich and H. SpiesbergerI. Akushevich and H. Spiesberger

http://www.desy.de/~heraws96/proceedings/nuclei/Akushehttp://www.desy.de/~heraws96/proceedings/nuclei/Akushevich.ps.gzvich.ps.gz

QED radiative processes in electron-heavy ion collisions at QED radiative processes in electron-heavy ion collisions at HERAHERA

K. KurekK. Kurek

http://www.desy.de/~heraws96/proceedings/nuclei/Kurek.phttp://www.desy.de/~heraws96/proceedings/nuclei/Kurek.ps.gzs.gz

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What do we know?What do we know?

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RC(A)d A / dyd B

A / dy 1 RC(A)

1RC(A)1RC(D)

1

1010-4-4 < x < 10 < x < 10-3 -3 and 27.5 GeV x 410 GeVand 27.5 GeV x 410 GeV

solid: inelastic rad. correctionssolid: inelastic rad. corrections dashed: inelastic, quasi-elastic and elastic rad. corrections dashed: inelastic, quasi-elastic and elastic rad. corrections

Huge effects at high yHuge effects at high y

PbPbSSCC

HeHeDD

What do we know?What do we know?

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Compton peak relevant if momentumCompton peak relevant if momentumtransfer to nucleus very smalltransfer to nucleus very small

(1 y)sine'ysin

effect of nuclear form factor includedeffect of nuclear form factor included

What do we know?What do we know?

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Two photon exchangeTwo photon exchange

two photon exchange only important for very heavy nucleitwo photon exchange only important for very heavy nuclei

Can we suppress things?Can we suppress things?

elastic/quasi-elastic part: require some hadrons in elastic/quasi-elastic part: require some hadrons in detectordetector

solid line: inelastic contributionsolid line: inelastic contribution dashed line: after cuts Edashed line: after cuts E > 10 GeV > 10 GeV E-p E-pz z from hadronic from hadronic

state is smallerstate is smaller

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Need a code, which puts all together to make full calculationsNeed a code, which puts all together to make full calculationsneed to test analysis strategies to suppress rad. corrections need to test analysis strategies to suppress rad. corrections

SSCC

HeHeDD

DjangohDjangoh http://wwwthep.physik.uni-mainz.de/~hspiesb/djangoh

/djangoh.html is compiled at BNL and running is compiled at BNL and running

eA part is included need to do more studieseA part is included need to do more studies HERACLES can be interfaced with other MC codesHERACLES can be interfaced with other MC codes

HERMES code (RADGEN + eA version of lepto) is HERMES code (RADGEN + eA version of lepto) is installed at BNL and close to run. No nuclear effects installed at BNL and close to run. No nuclear effects are included.are included.

can compare results between eA-RADGEN with can compare results between eA-RADGEN with HERACLESHERACLES can nPDFs be included?can nPDFs be included?

Hubert Spiesberger is coming to INT next week, juhuHubert Spiesberger is coming to INT next week, juhuE.C. E.C.

AschenauerAschenauerEIC INT Program, Seattle 2010 - Week 5EIC INT Program, Seattle 2010 - Week 5 1313

and Summaryand Summary

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