PV DIS: SUSY and Higher Twist

M.J. Ramsey-Musolf

CaltechWisconsin-Madison

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S. Mantry, K. Lee, G. Sacco Caltech

Outline

I. PV DIS & new physicsModel independent

analysis SUSY effects

II. PV DIS & Higher twist Puzzles from JLab data

The twist expansion What does

QCD predict? Q2-dependence, operator

matrix elements

III. General remarks

I. PV DIS & New physics

Model Independent Constraints

Low energy effective PV eq interaction

PV DIS eD asymmetry: leading twist

Model Independent Constraints

P. Reimer, X. Zheng

QW and SUSY Radiative Corrections

Tree Level

Radiative CorrectionsFlavor-dependent

Flavor-independent

Normalization Scale-dependent effective weak mixing

Constrained by Z-pole precision observables

Like QWp,e ~ 1 - 4 sin2W

SUSY Radiative Corrections

Propagator

Box

Vertex & External leg

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˜ e −

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Z 0

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˜ ν e

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˜ ν e

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SUSY RPV Effects

e−

d e−

d

˜ q Lj

1j1

1j1Δ1j1

/ =λiji

/ 2

4 2GFM˜ q Lj

2

Comparing AdDIS and Qw

p,e

e

p

RPV

Loops

Probing SUSY with PV eN Interactions

111/ ~ 0.06 for mSUSY ~ 1 TeV

sensitivity

k31 ~ 0.15 for mSUSY ~ 1 TeV

!eγ LFV Probes of RPV:

k31 ~ 0.03 for mSUSY ~ 1 TeV

!e LFV Probes of RPV:

12k ~ 0.3 for mSUSY ~ 1 TeV & QWe / QW

e ~ 5%

Lepton Flavor & Number Violation

0.1

1

10

100

1000

Effective

( )Mass meV

12 3 4 5 6 7

12 3 4 5 6 7

12 3 4 5 6 7

1 ( )Minimum Neutrino Mass meV

U1e = .866 m2

sol = 7 meV

2

U2e = .5 m2

atm = 2 meV

2

U 3e =

Inverted

Normal

Degenerate signal equivalent to degenerate hierarchy

Loop contribution to m of inverted hierarchy scale

111/ ~ 0.06 for mSUSY ~ 1 TeV

II. PV DIS & Higher Twist

Preliminary

Probing the strange sea with PV

World Data 4/24/06

GMs = 0.28 +/- 0.20

GEs = -0.006 +/- 0.016

~3% +/- 2.3% of proton magnetic moment

~20% +/- 15% of isoscalar magnetic moment

~0.2 +/- 0.5% of Electric distribution

Courtesy of Kent Pashke (U Mass)

Consistent with s-quark contributions to mP & JP but smaller than early theoretical expectations

First look beyond the quark model

Not surprising: ms / ~ 0.15

Great success for the JLab mission

Probing Higher Twist: Beyond Probing Higher Twist: Beyond the Parton Modelthe Parton Model

Alekhin NNLOMRST NNLOMRST NNLO withBarbieri Target Mass Corrections

• Smooth transition from DIS (solid squares) to resonance region • Resonances oscillate about perturbative curves (quark-hadron duality in transverse channel) - all Q2

•Target mass corrections large and important

2xF2xF1 1 Experimental StatusExperimental Status

Data from JLab E94-110 (nucl-ex/0410027, submitted to PRL) Courtesy C Keppel

~ 50% fluctuations about leading twist

n = 2 Cornwall-Norton Momentsn = 2 Cornwall-Norton Moments

FFLL

2xF2xF11

F2, F1 in excellent agreement with NNLO + TM above Q2 = 2 GeV2

No (or canceling) higher twists

Yet, dominated by large x and resonance region

Remove known HT (a bit novel), the elastic, and there is no more down to Q2 = 0.5 GeV2

The case looks different for FL (data or curve?)

FF22

Where are the qq and qqg correlations ?

Twist Expansion

twist 2

twist 4

Light cone expansion: x2 ~ 0

Momentum sum rules

Twist = d(n) - j

Power corr:

Jaffe ‘97

Twist Expansion

twist 2

twist 4

Light cone expansion: x2 ~ 0

Momentum sum rules

Twist = d(n) - j

Power corr:

Twist Expansion: Q2 Evolution

Twist two

Singlet moments: 2 x 2 mixing only

Non singlet

Singlet

Singlet

Twist four: correlations

Operator mixing: basis size grows with n (for nth moment)

Twist Expansion : Q2 Evolution

Equivalence to parton model: twist two

Anomalous dimension

DGLAP splitting function

No known analog for twist four

Need RGE & anom dim computation

Twist Expansion : Q2 Evolution

Twist two

Singlet moments: 2 x 2 mixing only

Non singlet

Singlet

Singlet

Twist four: correlations

Operator mixing: basis size grows with n (for nth moment)

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+ …

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+ …

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Flavor: isosinglet mixing

Probing Higher Twist: Beyond Probing Higher Twist: Beyond the Parton Modelthe Parton Model

Alekhin NNLOMRST NNLOMRST NNLO withBarbieri Target Mass Corrections

• Smooth transition from DIS (solid squares) to resonance region • Resonances oscillate about perturbative curves (quark-hadron duality in transverse channel) - all Q2

•Target mass corrections large and important

2xF2xF1 1 Experimental StatusExperimental Status

Data from JLab E94-110 (nucl-ex/0410027, submitted to PRL) Courtesy C Keppel

~ 50% fluctuations about leading twist

n = 2 Cornwall-Norton Momentsn = 2 Cornwall-Norton Moments

FFLL

2xF2xF11

F2, F1 in excellent agreement with NNLO + TM above Q2 = 2 GeV2

No (or canceling) higher twists

Yet, dominated by large x and resonance region

Remove known HT (a bit novel), the elastic, and there is no more down to Q2 = 0.5 GeV2

The case looks different for FL (data or curve?)

FF22

Where are the qq and qqg correlations ?

>> 10 % ??

•Are twist 4 matrix elements suppressed or canceling?

•Need C(Q2) to unpack matrix elements from data

• Complementary probes (PV DIS) could provide new insight

Probing Higher Twist with PV

Sacco, R-M preliminary

€

APV Q2

€

y

Looking beyond the parton descriptionPV Deep Ineslastic eD (J Lab 12 GeV)

~0.4%

E=11 GeV =12.50

Different PDF fits

Theoretical Challenges

pQCD evolution of twistfour moments

Lattice QCD for =4 matrix elements

Organizing the program:what kinematics, complementarity with PC F1,2 , …

Early days of PVES to probe strangeness:

Extensive theoretical work to ensure results would be intepretable and meaningful (many thanks to T.W. Donnelly)

We can do the same for PV DIS

III. General remarks

• PV DIS provides a comprehensive probe of QCD beyond the parton model & possible deviations from the SM EW sector

• Looking beyond the parton model is a natural continuation of the JLab strange quark searches

• Rich set of challenges for theory & experiment: higher twist, CSB in pdfs, d/u…

• Important complement to 12 GeV Moller that would be a focused and powerful probe of EW SM & possible new physics