Higher Twist in PVDIS Workshop Conclusions

June 6, 2009 Higher twist summary 1

Higher Twist in PVDIS Workshop Conclusions


Conclusion

• Complications due to higher twist can be handled with the proposed data set, so the proposed SM test is valid.

• We will obtain unique data on 4-quark higher twist operators. This physics should be a bullet in the abstract ov the proposal.


Deep Inelastic Scattering

iii fff

For an isoscalar target like 2H, structure functions largely cancel in the ratio at high x

b(x)

3

10(2C2u C2d )

uv dvu d

a(x) =C1i Qi fi

+(x)i

Qi2 fi

+(x)i

e-

N X

e-

Z* *

y 1 E /E b(x)C2i Qi fi

(x)i

Qi2 fi

(x)i

x xBjorken

a(x)3

10(2C1u C1d ) 1

2s

u d

6.0

APV GFQ2

2a(x)Y (y) b(x)

0

1

at high x

a(x) and b(x) contain quark distribution

functions fi(x)

C2q inaccessible in elastic scatteringSuppressed by a

factor of 7

Hadronic physics in a(x) mustbe controlled to high precision.We can be sloppier with b(x),since it is small.


Phenomenology

21

2

)2

1(2

2 FE

xyMy

yxyF

dxdy

d

EM

}])2

1(2

2{[22

21

2ZZ

A

V

Z

FE

xyMy

yxyFg

G

dxdy

d

])2([22

3

2Z

V

A

Z

FyxgG

dxdy

d

121 )1(

F

FRRFF L

T

L

EM

AZ

VZPV

BA

EM

VZxa

)(

EM

AZxbyf

)()(

There are 5relevant structure

functions

12 2/ FxFFL


Physics of the Dominant Vector- Hadronic Piece: a(x)

xdeDVxVDlVV xiq 4|)0()(|

4

4

|)0()(|

|)0()()0()(|

deDjxjDl

xdeDjxJJxjDlA

xiq

xiq

dduuSdduuV

SSVV

SSCCVVCCA

dudu

31

)(31

)( 1111

xdeddxuxuDlSVSVSSVV xiq 4)0()0()()(|))((

SSVV

SSVV

Bjorken, PRD 18, 3239 (78)

Wolfenstein,NPB146, 477 (78)

Zero in QPM

Pure 4-quark HT operatorNo Quark-gluon HT


4-Quark operators

• APV presents a unique laboratory where 4-quark operators can be isolated form quark-gluon operators.

• If they are large enough for us to observe, they will be very interesting.

• 4-quark matrix elements are easy to compute on the lattice (No disconnected graphs).


Quark-Quark and Quark-Gluon

Parton Modelor

leading twist

Di-quarks

Quark-gluondiagram

What is a truequark-gluonoperator?

u d

Same Flavor


NLO Diagrams

Diagrams (a)-(c) cancel in APV

DGLAP Evolution


Relate HT to Nucleon

• Need anomalous dimensions to evolve HT observations at Q2~10 to low Q2 of models, etc.

• These calculations should be done is a year ( or so).


Heavy Quark Physics Community

• HT is not viewed as important to problems in B meson decays.

• HT is called power corrections by this community.


R for γ vs Z in Neutrino Scattering

From Kulaginand Petti,PRD 76, 094023 (07)


New Insight

• In neutrino scattering, there is an axial-axial piece which is nontrivial.

• For FLγZ, everything is vector. It is

much simpler.


Approximations

• QPM: Cross sections given by PDF’s• DGLAP QPM: Evolve PDF’s• Higher Twist


The RγZ Problem• FL is zero in the QPM but nonzero in

DGLAP QPM.• Source of FL is:

– Gluons– Gluon radiation form quarks

• Both are isoscalar for deuterium, so FL cancels in APV for dueterium.

• Corrections for H can be computed in DGLAP.


Higher Twist Coefficients in parity

conserving (Di) and nonconserving (Ci) Scattering

)/)(1(),(),( 222

22 QxDQxFQxF DGLAP

APV (x,Q2)APV (x)(1C(x) /Q2)

(Does not Evolve)

Evolves accordingTo DGLAP equations

Higher Twist iswhat is left over

Higher Twist is anyQ2-dependent deviationFrom the SM prediction


Going from LO to NNNLO Greatly Reduces Higher Twist

Coefficients

x D(x) D(x) Q2min D/Q2

min(%) D/Q2min(%)

LO NNNLO LO NNNLO

0.1-0.2 -.007 0.01 0.5 -14 2

0.2-0.3 -.11 0.003 1.0 -11 0.0

0.3-0.4 -.06 -0.01 1.7 -3.5 -0.5

0.4-0.5 .22 0.11 2.6 8 4

0.5-0.6 .85 0.39 3.8 22 10

0.6-0.7 2.6 1.4 5.8 45 24

0.7-0.8 7.3 4.4 9.4 78 47

F2(x,Q2)=F2(x)(1+D(x)/Q2) Q2=(W2-M2)/(1/x-1) Q2min=Q2(W=2)

If D(x)~C(x), Parity might show higher twist At high x without needing QCD evolution.

MRST, PLB582,222 (04)

APV=APV(1+C(x)/Q2)


F2D(x): All x on Same Scale

Are momentsdominated by

large x?

Plot by Mindy

Caution:target mass

not subtracted


D(x) versus x Fractional HT

APV at largex is very sensitive

to HT

Plot by Mindy

Probably quark-gluon(but it could bequark-quark)


x-dependence of Higher Twist

• Relative 4-quark higher twist should increase with x???


Target Mass Corrections

• Talk by Tim.• Various methods. (Subject is

complex)• Lots of cancellation.• Errors negligible if corrections are

done consistently with other corrections.


New Strategy for b(x) HT

• Use data for F2γ

• F3ν HT data provides some

information on F3γZ HT


Measured Higher Twist in F3 and FL

γ

June 6, 2009 Higher twist summary 28PAC34

Statistical Errors (%) vs Kinematics

4 months at 11 GeV

2 months at 6.6 GeV

Error bar σA/A (%)shown at center of binsin Q2, x

Strategy: sub-1% precision over broad kinematic range for sensitive Standard Model test and detailed study of hadronic structure contributions


Coherent Program of PVDIS Study

• Measure AD in NARROW bins of x, Q2 with 0.5% precision• Cover broad Q2 range for x in [0.3,0.6] to constrain HT• Search for CSV with x dependence of AD at high x• Use x>0.4, high Q2, and to measure a combination of the Ciq’s

Strategy: requires precise kinematics and broad range

x y Q2

New Physics no yes no

CSV yes no no

Higher Twist yes no yes

2

23)1(

11 x

QxAA CSVHT Fit data to:

C(x)=βHT/(1-x)3


Sensitivity with PVDIS

RCSV APV x APV x 0.28

u x d x u x d x

Thanks to K. Paschke


Sensitivity: C1 and C2 Plots

Cs

PVDIS

Qweak PVDIS

World’s data

Precision Data

6 GeV


Fits

Plot by Mindy


Other Strategies

• Above analysis assumes SM, HT, and CVS physics are all in play.

• Each of these effects may be small.• As an approximation, we can do

three additional analyses in which either SM, CSV, or HT effects are neglected.


APV in DIS on 1H

APV GFQ2

2a(x) f (y)b(x)

a(x)u(x) 0.91d(x)u(x) 0.25d(x)

•Determine that higher twist is under control•Determine standard model agreement at low x•Obtain high precision at high x

•Allows d/u measurement on a single proton!•Vector quark current! (electron is axial-vector)

a(x)3

2

2C1uu(x) C1d (d(x) s(x))

4u(x) d(x) s(x)

b(x)3

2

2C2uuv (x) C2d dv (x)

4u(x) d(x) s(x)

+ small corrections


PVDIS on the Proton: d/u at High x

Deuteron analysis has largenuclear corrections (Yellow)

APV for the proton has no such corrections(complementary to

BONUS)

The challenge is to get statistical and systematic errors ~ 2%

)(25.0)(

)(91.0)()(

xdxu

xdxuxaP

3-month run


Higher Twist without the QPM

xdeDVxVDlVV xiq 4|)0()(|

4

4

|)0()(|

|)0()()0()(|

deDjxjDl

xdeDjxJJxjDlA

xiq

xiq

dduuSdduuV

SSVV

SSCCVVCCA

dudu

31

)(31

)( 1111

xdeddxuxuDlSVSVSSVV xiq 4)0()0()()(|))((

SSVV

SSVV

3.01A

Bjorken, PRD 18, 3239 (78)

Wolfenstein,NPB146, 477 (78)

Zero in QPM

Higher-Twistquark-quark correlations


Electron-Quark Phenomenology

C2u and C2d are small and poorly known: one combination can be accessed in PV DIS

New physics such as compositeness, leptoquarks:

Deviations to C2u and C2d might be fractionally large

A

V

V

A

C2’s are a factor of 7 smaller than the C1’s

Higher Twist in PVDIS Workshop Conclusions

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