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1
Higher Twist in Parity- Violating Deep Inelastic
ScatteringChien
Yeah Seng
Amherst Center for Fundamental InteractionsUniversity of Massachussetts
Amherst
August 2 2016
ECT* Workshop: Physics beyond the standard model and precision nucleon structure measurements with parity-
violating electron scattering
2
Outline
1.
e-D PVDIS, asymmetry and HT2.
Nucleon spin puzzle 101 and parton
OAM3.
Twist-4 matrix element and its significance in the study of OAM
4.
Summary
3
e-D PVDIS and left-right asymmetry
LR
LRRL dd
ddA
Polarized e, unpolarized
D
03.020.0sin :(1978)ion collaborat SLAC-Yale 2 WC. Prescott et al, PLB77, 347 (1978); 85, 524 (1979)
Left-Right Asymmetry:
Image:A.Deshpande,NNPSS2016
4
e-D PVDIS and left-right asymmetry
ZWLd
~
ɣ-Z interference term:
)'()()()()'(~ '5' kuggkukukuL seA
eVsss
Z
D
D
Z
D
ZZ
FqPMqPi
qPMFq
qqPPq
qqPP
MF
qqq
gW
3
222
12
2
))(()(
EEEy '
(fractional energy lost)
qPQxB
2
2
(Bjorken-x)
Image:A.Deshpande,NNPSS2016
5
e-D PVDIS and left-right asymmetry
The Cahn-Gilman formula:
)}sin623(
)1(1)1(1)sin
310
23{(
53
222
2
22
2
WWF
LR
LRRL
yyQG
ddddA
Assumptions: Single boson exchange Naïve parton
model
Ignore sea quarks Good isospin (Implicit) zero target mass & quark mass
PDF-dependence in the numerator and denominator cancel out(deutron
is isosinglet)
R. N. Cahn and F. J. Gilman, Phys. Rev. D17, (1978) 1313
6
e-D PVDIS as probe of new physics
][2 52
,51 iii
duiiii
FPV qqeeCqqeeCG
General PV electron-quark interaction Lagrangian:
})1(1)1(1~~{
53
22 2
2
21
2
yyaaQGA F
RL
Map to a general Left-Right Asymmetry:
With all the assumptions before, we have:
)2(~idiui CCa
,sin623~ ,sin
310
23~ 2
202
10 WW aa SM tree level:
7
e-D PVDIS as probe of new physics
SUSY. and ' cleptophobiassuch scenarios BSM toprobes sensitive provides
ZARL
M. Gonzalez-Alonso and M. J. Ramsey-Musolf, PRD, 87 (2013) 055013A. Kurylov, M. J. Ramsey-Musolf and S. Su, PLB 582, (2004) 222
Leptophobic
Z’
correction to C2q
8
e-D PVDIS as probe of new physics
• High-precision measurement of ARL is made possible by the 12 GeV
SoLIDexperiment at JLab
11-GeV beam
6.6-GeV beam
Image:SoLIDWhite-Paper 2014
(see Seamus’s talk)
9
e-D PVDIS: Higher-Twist Corrections
)1(~~0 iii Raa
Ri
includes the contribution from SM
and BSM
physics.
We have to make sure we understand all SM correctionsto desired level of precision!
Radiative
Correction
Charge Symmetry Violation (CSV)
Target Mass Correction (TMC)
Sea Quark Effect
Higher Twist (HT)
10
e-D PVDIS: Higher-Twist Corrections
Higher Twist correction: Corrections to naïve partonpicture which scale as: 2/)2(2 )( Qdue to interactions between partons.
Structure of full hadronic
tensor:
Twist"" :
2
11
e-D PVDIS: Higher-Twist Corrections
Higher Twist correction: Corrections to naïve partonpicture which scale as: 2/)2(2 )( Qdue to interactions between partons.
Leading twist/twist-2 (naïve parton
model) structure:
Twist"" :
12
e-D PVDIS: Higher-Twist Corrections
Higher Twist correction: Corrections to naïve partonpicture which scale as: 2/)2(2 )( Qdue to interactions between partons.
Examples of higher-twist structures:
Twist"" :
13
e-D PVDIS: Higher-Twist Corrections
Higher Twist correction: Corrections to naïve partonpicture which scale as: 2/)2(2 )( Qdue to interactions between partons.
In e-D PVDIS, the only
twist-4 contribution to R1
is proportional to the following hadronic
matrix element
DduddxuxuD |)0()0()()(|
Twist"" :
J.D Bjorken, PRD 18, 3239 (1978);L. Wolfenstein, Nucl. Phys. B 146 477 (1978)
Assumptions: Isospin symmetry neglect sea quark
S. Mantry et al, PRC 82, 065205 (2010)
14
e-D PVDIS: Higher-Twist Corrections
Previous works on twist-4 contribution to R1
Bag model Isotropic light cone wavefunction
S. Mantry et al, PRC 82, 065205(2010)
A.V. Belitsky et al, PRD 84, 014010(2011)
x 222 GeV12GeV4 Q
15
Nucleon Spin Puzzle 101 and Parton OAM
EMC experiment 1989: DIS between longitudinally polarized muon
and proton.
Hadronic
tensor: )()]0(),0([)(41),( 4 PpJJPpxedqPW xiq
})(
)({ 2221][ gqP
SPqggqP
SqiW
Relation of g1
to quark helicity:
i
ii xqexg )(21)( 2
1
16
Nucleon Spin Puzzle 101 and Parton OAM
Ellis-Jaffe’s Sum Rule:
Assumptions: Flavor SU(3) symmetry No net sea quark helicity
J. Ellis and R.L. Jaffe, Phys. Rev. D9 (1974) 1444.
European Muon Collaboration, J. Ashman, et al., Nucl. Phys. B 328 (1989) 1.
17
Nucleon Spin Puzzle 101 and Parton OAM
Ellis-Jaffe’s Sum Rule:
J. Ellis and R.L. Jaffe, Phys. Rev. D9 (1974) 1444.
GQ LLG 21
21
Image: A. Deshpande, NNPSS 2016
18
Nucleon Spin Puzzle 101 and Parton OAM
Information about parton
OAM is partially encoded in the transverse-momentum-dependent (TMD)
distribution functions
Sivers
function Boer-Mulders
function
Measurable in Semi-InclusiveDeep Inelastic Scattering (SIDIS)with unpolarized/transversely-polarized targets.
Image: JW Qiu, NNPSS 2016
Image: Tao Ye, 2015
19
Study of OAM Effects in Twist-Four Matrix Elements
•
Model: OAM-dependent light-cone wavefunction, truncated at three-valence-quarks level
•
Nucleon wavefunction
decomposed into states of definite Lz
of the valence quarks under light-cone gauge
2,23|1,
23|
1,21|0,
21|,|
zz
zz
lhlh
lhlhP
•
Finite-OAM wavefunction
can be obtained from a constituent quark model
•
From nucleon to deuteron: Incoherent impulse approximation assumed
CYS and Michael J. Ramsey-Musolf, PRC 88, 015202 (2013)
B. Pasquini et al, PRD 78, 034025 (2008)
20
Study of OAM Effects in Twist-Four Matrix Elements
An explicit example:
0|)}3()2()3()2(){1(6
))3,2,1()3,2,1(]([0,21| )2(
21)1(
3
kjkji
ijk
z
udduu
kkiXdlh
Only diagonal
components, i.e. < lz
|…|lz
> (same lz
for initialand final states) will contribute.
21
Study of OAM Effects in Twist-Four Matrix Elements
22
Study of OAM Effects in Twist-Four Matrix Elements
Bag model Isotropic light cone wavefunction
This work
Region ofsignificance:Q2≤3GeV2
at xB
~ 0.5-0.7
23
Study of OAM Effects in Twist-Four Matrix Elements
Only one component
of quark OAM contributes significantlyas the others largely cancel out!
24
Study of OAM Effects in Twist-Four Matrix Elements
1zL 1zL
True physics or model artifact?
25
Study of OAM Effects in Twist-Four Matrix Elements
•
Twist-4 correction to e-D PVDIS provides a clean probe to the Lz
= 0 piece of quark OAM!
Twist-4 PDF (arbitrary normalization)
Uniqueness of the cancelation: Contrast with PDF
26
Study of OAM Effects in Twist-Four Matrix Elements
•
Twist-4 correction to eD-PVDIS is essentially transparent to the parton AM dynamics that generates Sivers
and Boer-Mulders
function in SIDIS.
•
Detailed study of different DIS observables helps disentangling
effects of different parton
AM components.
aLbLba zz || .... ||:
27
Summary
1.
e-D PVDIS serves as a sensitive probe of both BSM physics and hadron/nuclear structure.
2.
Effect of twist-4 matrix element on R1
is expected to comes in when Q2≤3GeV2
in region xB
~ 0.5-0.7. Far outside this region, the SM corrections that enter JLab
e-D PVDIS result are unlikely to include twist-4
3.
The study of higher twist comes with a bonus of helping us to understand the role of parton
angular
momentum
in nucleon structure.
Thank You!
28
Backup Slides
29
Bjorken-Wolfenstein’s argument
• The operator of our interest is a product between EM- current and weak neutral current
• The deuteron is an isosinglet• We can decompose both currents into isovector (V)
and isoscalar (S).• Since deuteron is isosinglet, so <SV>=<VS>=0. • For leading twist, <SS>=<VV>. The difference <SS>-
<VV> is just the twist-four matrix element we showed before.
• Assumptions we made here: isospin symmetry, and that the contributions from sea quarks are negligible.
J.D Bjorken, PRD 18, 3239 (1978);L. Wolfenstein, Nucl. Phys. B 146 477 (1978)
30
Brief discussions of other SM effects
)()()()(~
)()()()()()(
1 xdxuxdxuR
xuxdxdxdxuxu
CSV
np
np
A leading-twist effect
Effect estimated using phenomenological parametrizations ornon-perturbative calculations
• Target Mass Correction (TMC): Correction due to non-zero target mass M (the normal identification that x=momentum fracton only holds in the M0 limit (or equivalently Q^2infinity limit). Also scales as 1/Q2. Should be distinguishable from HT bylooking at the x-dependence.
• Sea quark effect: Large only at small x (say x<1/3), so should be distinguishable from HT-effect that peaked at 0.5<x<0.7.
• Charge symmetry violation (CSV):
31
T. Hobbs and W. Melnitchouk, Phys. Rev. D77, 114023 (2008)
32
Spin-dependent structure function g1 and the Ellis- Jaffe Sum rule:
)](272)(
361)(
61[)(
41)( 5
058
531 ypSypSypSeypdxg yixpp
Relevant matrix elements:
...)(2
)()()0,0()( 55 PpQQPpPpSPp aa
• a=3,8: Evaluated based on flavor SU(3) symmetry. Expressed in terms of baryon-meson coupling strengths D and F.
• a=0: ???
33
Spin-dependent structure function g1 and the Ellis- Jaffe Sum rule:
)](272)(
361)(
61[)(
41)( 5
058
531 ypSypSypSeypdxg yixpp
Relevant matrix elements:
...)(2
)()()0,0()( 55 PpQQPpPpSPp aa
• Ellis-Jaffe’s assumption: the net helicity of sea quarks is zero.• With this,
)()0,0()(2)()0,0()( 50
50 PpSPpPpSPp
34
Experimental result:
J. Ellis and R.L. Jaffe, Phys. Rev. D9 (1974) 1444.
Ellis-Jaffe sum rule: