PV DIS: NP and Higher Twist

M.J. Ramsey-MusolfWisconsin-MadisonQuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

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http://www.physics.wisc.edu/groups/particle-theory/

NPACTheoretical Nuclear, Particle, Astrophysics & Cosmology

PVDIS Workshop, June 2009 S. Mantry & M. Glatzmaier MadisonG. Sacco JPLG. Paz IAS

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, Sacco thesis

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

Ciq and 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

Weak Mixing in the Standard Model

Scale-dependence of Weak Mixing

JLab Future

SLAC Moller

Parity-violating electron scattering

Z0 pole tension

New atomic th’y

Derevianko et al

SUSY Radiative Corrections

Propagator

Box

Vertex & External leg

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˜ e −

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˜ e +

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+L

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e−

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f€

Z 0

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γ

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˜ χ −

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˜ χ +€

e−

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e−

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f

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f

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γ

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Z 0

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˜ χ 0

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˜ e − €

˜ χ −

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˜ χ −

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+

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+L

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e−€

e−

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e−

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e−

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f€

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f€

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Z 0

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Z 0

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˜ e −

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˜ ν e

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˜ ν e

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+L

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e−€

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f€

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WRPV = ijk LiLjEk + ijk LiQjDk +/

i LiHu

+ ijkUiDjDk

L=1

B=1

Li, Qi

Ei, Ui, Di

SU(2)L doublets

SU(2)L singlets

proton decay: Set

ijk =0

R-Parity Violation (RPV)“Superpotential” : a convenient way to derive supersymmetric interactions by taking derivatives w.r.t. scalar fields

RPV: no DM

Four-fermion Operators

μ−

ν e e−

νμ

˜ e Rk

12k 12k

e−

d e−

d

˜ q Lj

1j1

1j1

L=1 L=1

Δ12k =λ12k

2

4 2GF M˜ e Rk

2 Δ1j1/ =

λiji/ 2

4 2GFM˜ q Lj

2

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

II. PV DIS & Higher Twist

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: OPE I

twist 2

twist 4

Light cone expansion: x2 ~ 0

Momentum sum rules

Twist = d(n) - j

Power corr:

Jaffe ‘97

Twist Expansion: OPE II

twist 2

twist 4

Light cone expansion: x2 ~ 0

Momentum sum rules

Twist = d(n) - j

Power corr:

Twist Expansion: EFP I

Ellis, Furmanski, Petronzio Factorization

Hard: S(k)

Soft: (k)

1. Taylor expand S(k) about k = xp

2. Insert 1 =

3. Power count in g: associate deriv in lower-order graph with gluon in next order graph

4. Write in co-ord space using

5. Convert to light cone transformation using

Soft functions:

Twist Expansion: EFP II

6. Apply gauge invariance (Ward identities) to get factorization formula

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4 quark (double hand bag) not included here

OPE & EFP

Expand A etc in powers of p, n

A0() p is LT term; all others are HT

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Expand in powers of n & take moments: recover OPE expressions for moments in terms of forward matrix elements of local operators

Sacco Thesis I

Structure Functions: 2 quark contributions

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Analogous formulae for F EM-NC

Sacco Thesis II

Structure Functions: 4 quark contributions

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Sacco Thesis III

Computation of Tj(x,y) and Uj(x,y,z) in MIT bag model:

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Compute moments & use inverse Mellin Transform

LT: pdf

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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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Flavor: isosinglet mixing

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 , …

Bjorken ‘78

Isospin decomposition:

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V = isovector

S = isoscalar

y-independent term: C1q

Differences in VV and SS:

C1q terms are “contaminated” only by 4q, double handbag = 4 effects

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

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