Higher Twist in Parity- Violating Deep Inelastic Scattering Yeah Seng... · Higher Twist in Parity-Violating Deep Inelastic Scattering Chien ... leptophobic ' and SUSY. ... The study

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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


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


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:

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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

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• 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)

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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)

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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



Leading twist/twist-2 (naïve parton

model) structure:

Twist"" :

12



Examples of higher-twist structures:

Twist"" :

13



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)

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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

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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

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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.

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Ellis-Jaffe’s Sum Rule:


GQ LLG 21

21

Image: A. Deshpande, NNPSS 2016

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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

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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)

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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.

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22


Bag model Isotropic light cone wavefunction

This work

Region ofsignificance:Q2≤3GeV2

at xB

~ 0.5-0.7

23


Only one component

of quark OAM contributes significantlyas the others largely cancel out!

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1zL 1zL

True physics or model artifact?

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•

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

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•

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 || .... ||:

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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!

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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)

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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):

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T. Hobbs and W. Melnitchouk, Phys. Rev. D77, 114023 (2008)

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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: ???

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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

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Experimental result:


Ellis-Jaffe sum rule:

Documents

Higher Twist in Parity- Violating Deep Inelastic Scattering Yeah Seng... · Higher Twist in Parity-Violating Deep Inelastic Scattering Chien ... leptophobic ' and SUSY. ... The study