PV DIS: SUSY and Higher Twist
M.J. Ramsey-MusolfCaltechWisconsin-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
Model Independent Constraints
Low energy effective PV eq interaction
PV DIS eD asymmetry: leading twist
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
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
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)
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+ …
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+ …
+ …
+ …
+ …
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
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