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Nov 8 2008 INT Electroweak
Deep Inelastic Scattering
iii fff ±≡±
fi(x) are quark distribution functions
For an isoscalar target like 2H, structure functions largely cancel in the ratio:
a(x) =310(2C1u − C1d ) 1+
2s+
u+ + d+
b(x) =
310(2C2u − C2d )
uv + dvu+ + d+
+L
APV =GFQ2
2παa(x) + Y (y)b(x)[ ]
a(x) =C1i Qi fi
+(x)i
∑Qi
2 fi+(x)
i∑
e-
N X
e-
Z* γ* y ≡1− ′ E /E
b(x) =C2i Qi fi
− (x)i
∑Qi2 fi
+ (x)i
∑
x ≡ xBjorken
Especially for x>0.5 or so
At high x, APV becomes independent of x, W, with well
defined SM prediction for Q2 and y
Axial quark coupling C2qSensitive to new physics at the TeV scale
Nov 8 2008 INT Electroweak
PVDIS and SUSY
20 15 10 5 0 5 10 2
1.5
1
0.5
0
0.5
1
(QWe )
SUSY/(Q
We )
SM (%)
(A
d) SU
SY/ (
Ad) S
M
(%
)
(a)
15 10 5 0 5 10 15 2
1.5
1
0.5
0
0.5
1
(QWp )
SUSY/(Q
Wp )
SM (%)
(A
d) SU
SY/ (
Ad) S
M
(%
)
(b)
PVDIS requires <1% precisionIn δA/A to be competitive with Qweak, Møller
No (1-4sin2θW) suppression of APV
RPV Susy is typical of most models
Nov 8 2008 INT Electroweak
Lessons from INT
• Leptoquark phenomenology is complex.• Calculation of limits has not been done for
DIS.• There seems to be no reason to think that
some new physics would affect the C2’s and not the C1’s.
• Can anything useful be said about extra dimensions or compositeness?
Nov 8 2008 INT Electroweak
Design I for PVDIS Physics
• 20o - 35o, E’~ 1.5 - 5 GeV• δp/p ~ 2% some regions 10’s of kHz/mm2
• Pion rejection with Cerenkov + segmented calorimeter.• Asymmetric yoke, detectors in magnetic field
Nov 8 2008 INT Electroweak
Double Toroidal Spectrometer
ČE-cal
Tracking Chambers
Design II (very preliminary)
CustomToroids
Features:1.SimplerDetectors2. Betteracceptance
Nov 8 2008 INT Electroweak
Broad Kinematic AcceptanceQQ22 QQ22
xx xx
11 GeV11 GeV 8.8 GeV8.8 GeV
JLabJLab 11GeV can provide new probe of nucleon structure and unique mea11GeV can provide new probe of nucleon structure and unique measure sure of Weak axialof Weak axial--vector quark couplingsvector quark couplings
xx
QQ22 • 11 GeV Solenoid• 8.8 GeV Solenoid• 11 GeV HMS / SHMSIs this data good
enough to measureApv
Bj to 0.5%?
Nov 8 2008 INT Electroweak
Hadronic Structure for PVDIS
APV =GFQ2
2παa(x) + f (y)b(x)[ ]
∑∑
+
+
=
iii
iiii
xfQ
xfQCxa
)(
)()( 2
1
e-
N X
e-
Z* γ*
∑∑
+
−
=
iii
iiii
xfQ
xfQCxb
)(
)()( 2
2
x ≡ xBjorken
y ≡1− ′ E /E
iii fff ±≡±
fi(x) are quark distribution functionsFor an isoscalar target like 2H, structure functions largely cancel in the ratio:
[ ]
+
+−= ++
+
dusCCxa du21)2(
103)( 11 L+
+
+−= ++
−−
dudu
CCxb du )2(103)( 22
(2C2u-C2d)/(2C1u-C1d)=0.136Especially for x>0.5 or so
APV becomes independent of x, Q2, W, and depends only on y
Nov 8 2008 INT Electroweak
Search for CSV in PV DISδu(x) = up (x) − dn (x)δd(x) = d p (x) − un (x)
•u-d mass difference•electromagnetic effects
up (x) = dn (x)?d p (x) = un (x)?
•Direct observation of parton-level CSV would be very exciting!•Important implications for high energy collider pdfs•Could explain significant portion of the NuTeV anomaly
dudu
AA
PV
PV
+−
=δδδ 28.0For APV in electron-2H DIS:
Sensitivity will be further enhanced if u+d falls off more rapidly than δu-δd as x → 1
•measure or constrain higher twist effects at x ~ 0.5-0.6•precision measurement of APV at x → 0.8 to search for CSV
Strategy:
Nov 8 2008 INT Electroweak
CSV and PV-DISRCSV =
δ APV x( )APV x( )
= 0.28δu x( )− δd x( )
u x( )+ d x( )For PV-DIS from 2H:
Sensitivity will be enhanced if u+d falls off more rapidly than δu - δd as x → 1
%
δAD
AD
from Londergan, using MRST fit
Effects at high-x are predicted to be very large
Nov 8 2008 INT Electroweak
Problem:
• x-independent CSV is indistinguishable from Standard Model violation.
• What error should we add? 2%?
Nov 8 2008 INT Electroweak
Higher Twist Coefficients in parity conserving (Di) and nonconserving
(Ci) Scattering
)/)(1(),(),( 222
22 QxDQxFQxF DGLAP +=
Evolves accordingTo DGLAP equations
Higher Twist iswhat is left over
APV (x,Q2) = APV (x)(1+ C(x) /Q2)
Higher Twist is anyQ2-dependent deviationFrom the SM prediction
(Does not Evolve)
Nov 8 2008 INT Electroweak
Ptroblem:
• Can we assume that HT is larger at higher x?
• If so, we can really neglect HT at x-values that are best for the Standard Model test.
• At INT, the answer seems to be a resounding NO!
Nov 8 2008 INT Electroweak
Interpretation of Higher Twist
≠
• APV sensitive to diquarks: ratio of weak to electromagnetic charge depends on amount of coherence
• Do diquarks have twice the x of single quarks?• If Spin 0 diquarks dominate, likely only 1/Q4 effects• On the other hand, some higher twist effects may cancel in ratio, so APV may have
little dependence on Q2.
Observing a clean higher twist operatorhas recently become very interesting.
Nov 8 2008 INT Electroweak
What is going on at high x?
• Real higher twist• Slow convergence of NnLO analysis• Limited Q2 range
Consensus: real higher twist(DIS008)
Nov 8 2008 INT Electroweak
Complete PV DIS Program (Including 12 GeV)
• Hydrogen and Deuterium targets• Better than 2% errors for each point
– It is unlikely that any effects are larger than 5-10%• x-range 0.25-0.75• W2 well over 4 GeV2
• Q2 range a factor of 2 for each x point– (Except x~0.75)
• Moderate running times
•With HMS/SHMS: integrates all of this physics •With larger solid angle apparatus: higher twist, CSV, d/u…
Nov 8 2008 INT Electroweak
Scorecard
XNoYesNoNew Physics
XNoNoYesd/u
XNoNoYes?Isospin
XYesNoYesHigher twist
dpQ2yx
Problem: Cannot change Q2 and y independently
Nov 8 2008 INT Electroweak
Theory Error Budget to Interpret ±1% Data
b(x)/a(x)~13%0.3<f(y)<0.8
a(x)Theory dirt must be <0.5%
Observe hadronic physics effects>3%Background for electroweak studies
`Theory dirt’includes unknownand uninteresting
effects
b(x)Theory dirt must be <3%
Set new limits on the small C2’s
Nov 8 2008 INT Electroweak
Phenomenology and R
T
LRRFFσσγγ =→+= )1(21
γγσ21
2
)2
1(22 FE
xyMyy
xyFdxdyd
EM
−−+∝
])2
1(22[22 21
2ZZ
A
V
Z
FE
xyMyy
xyFgGdxdyd γγ
γ πασ
−−+−∝
])2([22 3
2Z
V
A
Z
FyxgGdxdyd γ
γ πασ
−−∝
EM
AZxbyf
σσγ=)()(
EM
VZxa
σσγ=)(
EM
AZ
VZPV
BAσ
σσ γγ +=
Nov 8 2008 INT Electroweak
Most QCD cancels in a(x)
ασσγ Gxa
EM
VZ ≈=)(
Assumptions:1: CVC (Charge Symmetry)2: Quarks contribute incoherently (Higher Twist)Goal of program is to test these assumptions.
R=σL/σT cancels (in DIS limit)
Charge Symmetry1: Strange quarks (absent at large x)2: up≠dn (Our main interest)
Nov 8 2008 INT Electroweak
Higher Twist without the QPMBjorken,
PRD 18, 3239 (78)
∫∫
⋅
⋅+∝
4
4
|)0()(|
|)0()()0()(|
deDjxjDl
xdeDjxJJxjDlA
xiq
xiq
νµµν
νµνµµν
Wolfenstein,NPB146, 477 (78)
( ) ( )dduuSdduuV µµµµµµ γγγγ +=⇔−= xdeDVxVDlVV xiq 4|)0()(|∫ ⋅= νµµν
SSVV
SSCCVVCCA
dudu
31
)(31)( 1111
+
++−= Zero in QPM
xdeddxuxuDlSVSVSSVV xiq 4)0()0()()(|))(( ⋅∫∝+−=− νµµν γγ
δ3.01−∝ASSVVSSVV
+−
=δ
Nov 8 2008 INT Electroweak
Problem
• RγZ introduces new parameters.• RγZ introduces new higher twist terms.• We can only vary Q2 in a way correlated
with Y• Can HT of RγZ be related to F1 HT?• Can RγZ be computed perturbatively?
Nov 8 2008 INT Electroweak
Axial hadronic current2 Methods:
1: Use data only:a: σγZ
A≈F3ν and use neutrino data
b: σγ from electromagnetic data2: Use QPM and make corrections:
a: Sea quarks are absent at high xb: R from electromagnetic datac: Ignore higher twist
EM
AZxbyf
σσγ=)()(
Should be goodto ~3%, which
is ample
Is higher twista big problemat the highest
a values?)1(22)1(1)(
2)()(
2
2
22 Ryyyyf
CCxbyf
du ++−−−
≡≈−
Nov 8 2008 INT Electroweak
Conclusions
• APV to ~0.5% is useful.• CSV is potential source of unertainty.• Issues with RγZ are another important
source.• By the way: aren’t these issues also
serious for some other JLab experiments in DIS?
Nov 8 2008 INT Electroweak
Compare ν F3 to global parton fitson a linear scale
15%
40%
Note verticalscale
0.45 0.55
0.65 0.75
3
3
QPMxFxFδ
Useful at x~0.5Problems at x~0.7
Nov 8 2008 INT Electroweak
Parton Distribution FunctionsSea quarks that contributeto a(x) and s quarks thatcontribute to a(x) vanish
rapidly for x>0.5
CAUTION:PDF’s use as input
40 years of precise dataplus ‘reasonable’ guesses.One must distinguish whichfeatures are data and which
features are guesses.
Nov 8 2008 INT Electroweak
How do we know that antiquarksare negligible at large x?
spx L
F2
≡ 21 xxxF −=
sxxM 212 =µµ
Drell-Yan production of muon pairs
p p
µ+
µ-
θσ 2cos1+∝Ωd
d
When xF=0, x1=x2=x, and M=x2s.Hence x for both the quark and
anti-quark are known.The cross section drops rapidly with x
The small quantityis directly observed.No subtractions are
needed, as is thecase for F3 data.
Clean data exist with x~0.6 and Mµµ2>10 Smith et al.,
PRL 46, 1607(81)
Nov 8 2008 INT Electroweak
Electron-Quark Phenomenology
C2i ≡ 2gVe gA
i
V
AC1i ≡ 2gA
e gVi
A
V
C1u and C1d will be determined to high precision by Qweak, Cs
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
Nov 8 2008 INT Electroweak
PV AsymmetriesWeak Neutral Current (WNC) Interactions at Q2 << MZ
2
Longitudinally Polarized Electron Scattering off Unpolarized Fixed Targets
(gAegV
T +β gVegA
T)
•The couplings gT depend on electroweak physics as well as on the weak vector and axial-vector hadronic current •For PVDIS, both new physics at high energy scales as well as interesting features of hadronic structure come into play•A program with a broad kinematic range can untangle the physics
Nov 8 2008 INT Electroweak
Electron-Quark Phenomenology
C2i ≡ 2gVe gA
i
V
AC1i ≡ 2gA
e gVi
A
V
C1u and C1d will be determined to high precision by Qweak, Cs
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
Nov 8 2008 INT Electroweak
Phenomenological Parton CSV PDFs
Best fit: κ = -0.2, large uncertainty ! Best fit remarkably similar to model CSV predictions
MRST ADEL
Bag model
MRST Phenomenological PDFs include CSV for 1st time:Martin, Roberts, Stirling, Thorne (03):
Choose restricted form for parton CSV: 90% conf limit (κ)
[f(x): 0 integral; matches to valence at small, large x]
Nov 8 2008 INT Electroweak
APV in DIS on 1HAPV =
GFQ2
2παa(x) + f (y)b(x)[ ]
b(x) =322C2uuv (x) − C2d dv (x)4u(x) + d(x) + s(x)
a(x) =322C1uu(x) − C1d (d(x) + s(x))
4u(x) + d(x) + s(x)
a(x) =u(x) + 0.91d(x)u(x) + 0.25d(x)
+ small corrections
•Allows d/u measurement on a single proton!•Vector quark current! (electron is axial-vector)
•Determine that higher twist is under control•Determine standard model agreement at low x•Obtain high precision at high x
Nov 8 2008 INT Electroweak
Uncertainty in d/u at High x; and Needed Errors in PV Measurement
Must simultaneously constrain higher twist effects
The challenge is to get statistical and systematic errors ~ 2%
Deuteron analysis has nuclearcorrections
APV for theproton has no such
corrections. (BONUSuses proton tagging.)