PV DIS: SUSY and Higher Twist

M.J. Ramsey-MusolfCaltechWisconsin-Madison

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

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 sin2θW

SUSY Radiative Corrections

Propagator

Box

Vertex & External leg

˜ e −

˜ e + +L+

e− f

Z0 γ˜ χ −

˜ χ +

e−

e−

e−f

f

fγZ0

˜ χ 0

˜ e −

˜ χ −

˜ χ −+ +L

e−

e−

e−

e−

f

f

f

fZ0

Z0˜ e −

˜ ν e

˜ ν e +L

e−

e−

f

f

˜ f

˜ χ

˜ χ

SUSY RPV Effects

e−

d e−

d

˜ q Lj

λ/1j1 λ/

1j1 Δ 1 j 1/ =

λ iji/ 2

4 2G F M ˜ q Lj

2

Comparing AdDIS and Qw

p,e

e

p

RPV

Loops

Probing SUSY with PV eN Interactions

λ111/ ~ 0.06 for mSUSY ~ 1 TeV

0νββ sensitivity

λk31 ~ 0.15 for mSUSY ~ 1 TeV

μ!eγLFV Probes of RPV:

λk31 ~ 0.03 for mSUSY ~ 1 TeV

μ!eLFV Probes of RPV:

λ12k ~ 0.3 for mSUSY ~ 1 TeV & δQWe / QW

e ~ 5%

Lepton Flavor & Number Violation

0.1

1

10

100

1000

Effe

ctiv

e ββ

Mas

s (m

eV)

12 3 4 5 6 7

102 3 4 5 6 7

1002 3 4 5 6 7

1000Minimum Neutrino Mass (meV)

Ue1 = 0.866 δm2sol = 70 meV 2

Ue2 = 0.5 δm2atm = 2000 meV 2

Ue3 = 0

Inverted

Normal

Degenerate0νββ signal equivalent to degenerate hierarchy

Loop contribution to mν of inverted hierarchy scale

λ111/ ~ 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 & JPbut smaller than early theoretical expectations

First look beyond the quark model

Not surprising: ms / Λχ ~ 0.15

Great success for the JLab mission

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

0

0.2

0.4 ΔS11F15

Q2 = 0.7 (GeV/c)2

Q2 = 1.5 (GeV/c)2

2xF

1Q2 = 2.5 (GeV/c)2

Q2 = 3.5 (GeV/c)2

X

0

0.25

0.5

0.75

1

0

0.1

0.2

0.3

0

0.1

0.2

0.3

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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 Cornwalln = 2 Cornwall--Norton MomentsNorton 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 & anomdim 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)

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

+ …

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture

+ …

+ …

+ …

+ …

Flavor: isosingletmixing

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

0

0.2

0.4 ΔS11F15

Q2 = 0.7 (GeV/c)2

Q2 = 1.5 (GeV/c)2

2xF

1Q2 = 2.5 (GeV/c)2

Q2 = 3.5 (GeV/c)2

X

0

0.25

0.5

0.75

1

0

0.1

0.2

0.3

0

0.1

0.2

0.3

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

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 Cornwalln = 2 Cornwall--Norton MomentsNorton 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 GeVθ=12.50

Different PDF fits

Theoretical Challenges

pQCD evolution of twistfour moments

Lattice QCD for τ =4 matrix elements

Organizing the program:what kinematics, complementaritywith PC F1,2 , …

Early days of PVES to probe strangeness:

Extensive theoretical work to ensure results would be intepretableand 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