Probing Parton Distribution Functions with Neutrinos

Jorge G. Morfín

Fermilab

PDF’s in the 21st Century - Seattle, WA

November, 2004

Outline

Which PDFs need help and where in x?

Quarks at high-x Recent indications of more and less quarks at high-x? d/u

How can Neutrinos help?

What can neutrinos tell us about nuclear PDFs?

An experiment to address these questions.

More Detailed Look at Higher x

CTEQ

Comparison of three modern PDF global fits

Djouadi & Ferrag, hep-ph/0310209

Uncertainty in the Gluon DistributionNormalized to CTEQ6M

Dashed - CTEQ5HJDotted - MRST01Solid - CTEQ5M

CTEQ uncertainties in u and d quark fitsTheory uncertainties NOT included

d Quarks: not bad agreement

Disregard the older results

thanks to Wu-Ki Tung - MSU

u Quarks: even better agreement …but this doesn’t mean we have it right!

thanks to Wu-Ki Tung - MSU

An indication that the valence quarks not quite right at high-x!

E866 Preliminary Results (R. Towell - Hix2004)

• xbeam distribution measures 4u + d as x--> 1.

• Both MRST and CTEQ overestimate valence distributions as x --> 1 by 15-20%.

• Radiative corrections have recently been calculated. (Not yet fully applied)

• Possibly related to d/u ratio as x --> 1.

xtarget xbeam

Latest look at d/u… What’s going on at high-x?

thanks to Wu-Ki Tung - MSU

How do you measure d/u? Can be extracted from electroproduction p and n structure functions

!

Uncertainty from nuclearcorrections to the deuteron

How do you measure F2n?

Just to increase our confusion…. Latest NuTeV Compared to CCFR (currently in PDF fits)at High-x Indicates Effect Opposite to E866-no help for d/u

V. Radescu - DIS04

How do we Resolve the High-x Quark Dilemma?

A clean and straightforward way to studyhigh x quarks, including the d/u ratio, is with

/ - proton scattering

We bring you the axial-vector current….

Neutrino Structure Functions

probe d, s, u, c while probe u, c, d, s

Reverse for

Reverse for

Ability to taste different quarks allows isolation of flavorsNeutrino - Proton Scattering

At high x

F2p - xF3

p = 4xu

No messy nuclear corrections!

F2p + xF3

p = 4xu

Similar Expressions for Neutrino-Nucleus Scattering What Can We Learn With All Six Neutrino Structure Functions?

Combining measured values in a given x-Q2 bin, for example

F 2Ν (x,Q2 ) =x u+ u + d+ d+2 s + 2c[ ]

F 2Ν (x,Q2 ) =x u+ u + d+ d+2s+ 2 c[ ]

xF 3Ν (x,Q2 ) =x u+ d - u - d - 2 s+ 2c[ ]

xF 3Ν (x,Q2 ) =x u+ d - u - d +2s - 2 c[ ]

F2 - xF3

=2 u + d+ 2 c( )=2U + 4 c

F2 - xF3

=2 u + d+ 2 s( )=2U + 4 s

xF3 - xF3

=2 s+ s( ) − c+ c( )[ ] =4 s - 4 c

Using Leading order expressions (for isoscalar target):

Nuclear Effects - modified interaction probabilities

0.7

0.8

0.9

1

1.1

1.2

0.001 0.01 0.1 1

EMCNMCE139E665

shadowing

original

EMC finding

Fermi motion

x sea quark valence quark

EXPECTED to be different for !!

0.7

0.8

0.9

1

1.1

1.2

0.001 0.01 0.1 1

x

Ca

Q2 = 1 GeV2

valence-quark

0.4

0.6

0.8

1

1.2

1.4

0.001 0.01 0.1 1

x

antiquark

S. Kumano

Difference between and nuclear effectsValence and Sea Quark nuclear effects

Sergey Kulagin

How do we measure Neutrino-Nucleus/Proton Scattering? The MINERA Experiment in the NuMI Beam at Fermilab

Approved by PAC in April

C, Fe and PbNuclear targets

Main Physics Topics with Expected Produced Statistics Quasi-elastic 300 K events off 3 tons CH Resonance Production 600 K total, 450 K 1 Coherent Pion Production 25 K CC / 12.5 K NC Nuclear Effects C:0.6M, Fe: 1M and Pb: 1 M Pert/nonPert and Structure Functions 2.8 M total /1.2 M DIS event Strange and Charm Particle Production > 60 K fully reconstructed events Generalized Parton Distributions (few K events?)

Both HEP and NP collaborators

D. Drakoulakos, P. Stamoulis, G. Tzanakos, M. ZoisUniversity of Athens, Athens, Greece

D. CasperUniversity of California, Irvine, California

E. PaschosUniversity of Dortmund, Dortmund, Germany

D. Boehnlein, D. A. Harris, M. Kostin, J.G. Morfin, P. Shanahan, P. Spentzouris

Fermi National Accelerator Laboratory, Batavia, Illinois

M.E. Christy, W. Hinton, C.E .KeppelHampton University, Hampton, Virginia

R. Burnstein, A. Chakravorty, O. Kamaev, N. SolomeyIllinois Institute of Technology, Chicago, Illinois

S.KulaginInstitute for Nuclear Research, Moscow, Russia

I. Niculescu. G. .NiculescuJames Madison University, Harrisonburg, Virginia

G. Blazey, M.A.C. Cummings, V. RykalinNorthern Illinois University, DeKalb, Illinois

W.K. Brooks, A. Bruell, R. Ent, D. Gaskell,,W. Melnitchouk, S. Wood

Jefferson Lab, Newport News, Virginia

S. Boyd, D. Naples, V. PaoloneUniversity of Pittsburgh, Pittsburgh, Pennsylvania

A. Bodek, H. Budd, J. Chvojka, P. de Babaro, S. Manly, K. McFarland, I.C. Park, W. Sakumoto, R. TengUniversity of Rochester, Rochester, New York

R. Gilman, C. Glasshausser, X. Jiang, G. Kumbartzki,K. McCormick, R. Ransome

Rutgers University, New Brunswick, New Jersey

H. Gallagher, T. Kafka, W.A. Mann, W. OliverTufts University, Medford, Massachusetts

J. NelsonWilliam and Mary College, Williamsburg, Virginia

Red = HEP, Blue = NP, Green = Theorist

After initial (parasitic to MINOS) run -would add a Liquid H2/D2(/O/Ar) Target

NOT YET APPROVED FOR THIS

H_2/D_2

MINOS Near

Fid. vol: r = 80 cm. l = 150 cm.

350 K CC events in LH2 800 K CC events in LD2

2.5x1020 POT/yr he- beam.

Technically easy/inexpensive to build and operate. Meeting safety specifications the major effort.

Planes of C, Fe, PbFor part of run

≈ Statistical Errors for .7 / 2 year of he- xBj CH LH2 LD2

.6 - .65 0.6% 2.2% 1.5%

.65 - .7 0.7 2.6 1.7

.7 - .75 1.0 3.7 2.5

.75 - .8 1.3 5 3

.8 - .85 2 7 5

.85 - .9 3 11 7

.9 - 1.0 4 14 10

Measuring Six Structure Functions for Maximal Information on PDF’s

d A

dxdQ2 = GF2

2x12

F 2A (x,Q2 ) + xF3

A (x,Q2 )( ) +1 −y( )2

2F 2

A (x, Q2 ) −xF 3A (x, Q2 )( )

⎡

⎣⎢⎤

⎦⎥

d A

dxdQ2 = GF2

2x12

F 2A (x,Q2 ) −xF 3

A (x,Q2 )( ) +1−y( )2

2F 2

A (x, Q2 ) + xF3A (x,Q2 )( )

⎡

⎣⎢⎤

⎦⎥

,x Q2 , (1− )y 2( )G2 2x

X = 0.1 - 0.125Q2 = 2 - 4 GeV2

Kinematic cuts in (1-y)not shown

+ y2 FL

(1-y)2

R = Rwhitlow

Neutrino1 year he-beam

Anti-Neutrino2 years he-beam

Summary

Aside from low x gluon, PDFs fairly well established for x < 0.3-0.4. For x > 0.3, uncertainty of the gluon grows dramatically. The current fits for the valence u-quark is reasonable out to x = 0.5,

while the d-quark uncertainty blows up around x = 0.3. Both E866 and the latest NuTeV results indicate a possible

surprise for high-x u & d quarks…however in opposing directions! d/u at high-x still uncertain due to spread in deuteron correction. A CLEAN WAY TO MEASURE d/u: + p SCATTERING! The MINERA Experiment at Fermilab, an NP + HEP collaboration,

could make a high-statistics measurement of + p scattering. MINERA will also provide the first detailed study of nuclear

effects with ‘s including quark flavor-dependent nuclear effects.