1

2 Xiaochao Zheng for the JLab E05-007 Collaboration: Parity Violation in Deep Inelastic Scattering at JLab 6 GeV

EPJ manuscript No.

(will be inserted by the editor)

Parity Violation in Deep Inelastic Scattering at JLab 6 GeV

Xiaochao Zheng

1

for the JLab E05-007 Collaboration

Lab for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Received: date / Revised version: date

Abstract. The parity-violating asymmetry in e−

2

H deep inelastic scattering (DIS) can be used to extract

the weak neutral-current coupling constants C

2q

. A measurement of this asymmetry at two Q

2

values is

planned at Jeﬀerson Lab. Results from this experiment will provide a value of 2C

2u

− C

2d

to a precision of

±0.03, a factor of eight improvement over our current knowledge. If all hadronic eﬀects can be understood,

this result will provide information on possible extensions of the Standard Model, complementary to other

experiments dedicated to new physics searches. Presented here are the physics motivation, experimental

setup, potential hadronic eﬀects and their implications, and t he future of PV DIS at Jeﬀerson Lab.

PACS. 13.60.-r Photon and charged-lepton interactions with hadrons – 12.15.-y Electroweak interactions

– 12.15.Mm Neutral currents – 12.60.-i Models beyond th e standard model

1 Introduction

A measurement of the parity-violating (PV) asymmetry

of e−

2

H deep inelastic scattering (DIS) is planned [1] at

the Thomas Jeﬀerson National Accelerator Facility (JLab)

in Virginia, USA. The measurement will be performed a t

two Q

2

values of 1.1 and 1.9 GeV

2

and a ﬁxed x = 0.3.

The high Q

2

measurement will b e used to extract the ef-

fective weak coupling constants (2C

2u

− C

2d

). The low

Q

2

measurement may provide the ﬁrst observation of the

hadronic higher-twist contribution to the PV DIS asym-

metry, which at JLab energies is the most likely source

of a large deviatio n from the Standard Model prediction.

Using the Sta ndard Model value of 2C

1u

−C

1d

which will

be tested by combining the results from Cs atomic par-

ity violation (APV) and the future Qweak experiment, the

exp ected uncertainty o n (2 C

2u

−C

2d

) is ±0.03. This result

will improve the current knowledge on this quantity by a

factor of eight. It will help to extract the couplings C

3q

from high-energy data, and might reveal possible physics

beyond the Standard Model.

Results from this experiment (E05-007) will provide

an important guidance for the future DIS-parity program,

of which the ultimate goals are two-fold: by choosing a

kinematics where hadronic eﬀects are negligible, we can

extract sin

2

θ

W

and study possible extensions of the Stan-

dard Model to a high precision. By choosing kinematics

where hadronic e ﬀects are e xpected to be large, various in-

teresting phenomena can be studied, such as higher-twist

eﬀects, charge-symmetry violation (CSV), and the parton

distribution function ratio d/u. These results may also

⋆

Present address: Department of Physics, University of Vir-

ginia, Charlottesville, VA 22904, US A

have implications for the interpretation of existing neu-

trino sc attering data.

2 Parity Violation in Deep Inelastic

Scattering oﬀ a Deuterium Target

Historically, PV DIS was one of the ﬁrst tests of the Stan-

dard Model and an early measurement of the PV DIS

asymmetry oﬀ a deuterium target [2,3] ser ved to e stablish

the value of sin

2

θ

W

at sin

2

θ

W

≈ 1/4. Since this ground-

breaking experiment, parity violation has become an im-

portant tool not only for probing the Standard Model [4–6]

but also for probing the structure of the nucleon [7–9].

2.1 PV DIS Asymmetry

In e le c tron scattering, the weak neutral current can be ac -

cessed by measuring a parity-violating asymmetry ca us ed

by the interference term between weak and electromag-

netic scattering amplitudes [10]. The scattering amplitude,

M, for the scattering process is a product of the current

for the electron with the photon or the Z

0

propagator

and the hadron current: M

γ

= j

µ

1/q

2

J

µ

and M

Z

=

j

µ

1/M

2

Z

J

µ

. The cross section for scattering right- and

left-handed electrons oﬀ an unpolarized target is propor-

tional to the square of the total amplitudes: σ

l,r

∝ (M

γ

+

M

l,r

Z

)

2

, where only a longitudinally polarized electron beam

was considered and M

r

Z

and M

l

Z

represent the incident

right- a nd left-handed electrons, respectively. The parity-

violating as ymmetry may be expressed as [10]

A

LR

≡

σ

r

− σ

l

σ

r

+ σ

l

≈

M

r

Z

− M

l

Z

M

γ

. (1)

Xiaochao Zheng for the JLab E05-007 Collaboration: Parity Violation in Deep Inelastic Scattering at JLab 6 GeV 3

Thus, measuring the parity-violating asymmetry gives ac-

cess to the weak neutr al current in a ratio of amplitudes

rather than the square of this ratio, grea tly enhancing its

relative contribution. The size of the asymmetry can be

estimated based on the ratio of the propagato rs:

A

LR

≈

Q

2

M

2

Z

≈ 120 ppm at hQ

2

i = 1 GeV

2

(2)

with M

Z

= 91.2 GeV [11].

Following this formalism, the parity-violating asymme-

try for scattering longitudinally p olarized electrons from

an unpolarized isoscalar target such as deuterium, assum-

ing isospin symmetry, is given by [10,12]

A

d

=

σ

L

− σ

R

σ

L

+ σ

R

= −

3G

F

Q

2

πα2

√

2

×

(2C

1u

− C

1d

) [1 + R

s

] + Y (2C

2u

− C

2d

)R

v

5 + R

s

. (3)

Here, the kinematic variable Y is deﬁned as

Y =

1 − (1 −y)

2

1 + (1 − y)

2

+ f(y, R

LT

)

(4)

with y = ν/E and ν = E − E

′

is the energy lost by

an incident electron of ener gy E scattering to an elec -

tron of energy E

′

. The ratio R

LT

(x, Q

2

) = σ

L

/σ

T

≈ 0.2

measures the vir tua l photon-absorption cross- section ratio

from long itudinally and transversely polarized photons,

and f (y, R

LT

) is a function describing the eﬀect of lon-

gitudinally polarized photons to the asymmetry and van-

ishes when R

LT

= 0. In a work by Blumlein et al. [13]

it was derived that f (y, R

LT

) = −y

2

R

LT

/(1 + R

LT

) when

ν

2

≪ Q

2

. At JLab energ ie s both Eq s. (3) and (4) need

to be modiﬁed to take into account terms proportional

to ν

2

/Q

2

. The ratios R

s

and R

v

depend on the parton

distribution functions:

R

s

(x) =

s(x) + ¯s(x)

u(x) + ¯u(x) + d(x) +

¯

d(x)

and (5)

R

v

(x) =

u

v

(x) + d

v

(x)

u(x) + ¯u(x) + d(x) +

¯

d(x)

, (6)

where we have neglected co ntributions from the charm

quark. The weak couplings C

1q

and C

2q

with q ∈ u, d are

deﬁned as:

C

1u

= g

e

A

g

u

V

= −

1

2

+

4

3

sin

2

(θ

W

), (7)

C

1d

= g

e

A

g

d

V

=

1

2

−

2

3

sin

2

(θ

W

), (8)

C

2u

= g

e

V

g

u

A

= −

1

2

+ 2 sin

2

(θ

W

), (9)

C

2d

= g

e

V

g

d

A

=

1

2

− 2 s in

2

(θ

W

), (10)

where the second equality is valid at the tree-level of the

Standard Model. T hese coupling constants, along with the

Weinberg angle θ

W

itself, are fundamental parameters of

the Standard Model.

In an approximation of moderately large x where sea

quark contributions vanish, R

v

≈ 1 and R

s

≈ 0. The

uncertainty in 2C

2u

−C

2d

extracted from measured asym-

metry is then approximately:

δ(2C

2u

− C

2d

)

2C

2u

− C

2d

≈

δA

d

A

d

1 −

1

Y

2C

1u

− C

1d

2C

2u

− C

2d

(11)

2.2 Exploring New Physics Beyond the Standard

Model from PV DIS

Although ther e exists a large amount of data conﬁrm-

ing the elec troweak sector of the Standard Model at the

level of a few parts per thousand, there also exist strong

conceptual reasons (e.g., the so -called high-energy desert

from M

weak

≈ 250 GeV up to the Planck scale M

P

≈

2.4 × 10

18

GeV) to believe that the Standard Model is

only a piece of some large r framework [14]. This frame-

work should provide answers to the conceptual puzzles of

the Standard Model; but must a lso leave the SU(3)

C

×

SU(2)

L

× U(1)

Y

symmetry of the Standard Model intact

at M

weak

≈ 25 0 GeV. Hence, there e xists intense interest

in the search for physics beyond the Standard Model.

The value of sin

2

θ

W

at the Z-pole (Q

2

= M

2

Z

) is mea-

sured to remarkable precision, sin

2

θ

W

[M

Z

]

MS

= 0.23120±

0.00015 [11]; however, a careful c omparison of measure-

ments involving pure ly leptonic and semi-leptonic elec-

troweak currents shows a la rge inconsistency. This strongly

suggests additional physics not included in the Standard

Model or that one or more of the e xperiments has sig-

niﬁcantly understated its uncertainties [15,16]. Below the

Z- pole , there are only three precise measurements: Atomic

parity violation (APV) in Cs atoms [5] yields a result

which, while in agree ment with Standard Model predic-

tions, has somewhat large uncertainties, and a diﬃcult

theoretical calculation is neces sary to extract sin

2

θ

W

from

the meas ured asymmetry. The NuTeV experiment at Fer -

milab measured sin

2

θ

W

through a careful comparison of

neutrino a nd anti-neutrino deep inelastic scattering (DIS).

Their result is approximately three standard deviations

from Standard Model predictions [18]; however, the NuTeV

result is not without considerable controversy. Most re-

cently, the SLAC E-158 [4] experiment used the asymme-

try in Møller scattering to determine a precis e value of

sin

2

θ

W

that is consistent with the Standard Model pre-

diction. A fourth measurement, the Qweak experiment [6],

is planned at JLab, and will determine sin

2

θ

W

to 0.3% by

measuring the weak charge of the proton.

Among various experimental eﬀorts to search for new

physics, PV DIS involves the exchange of a Z

0

between

electrons and quarks a nd thus is sensitive to physical pro-

cesses that might not be seen in purely leptonic observ-

ables, such as the precision A

LR

at SLC and A

l

F B

at LEP.

The recent NuTeV [18] result o n sin

2

θ

W

at low Q

2

in-

volves a particular set of semi-leptonic charged and neutral

current reactions and disagrees with the Standard Model

prediction by three standard deviations. A precision mea-

surement of DIS-Parity will provide a clea n semi-leptonic

observable to the world data below the Z-pole and will

4 Xiaochao Zheng for the JLab E05-007 Collaboration: Parity Violation in Deep Inelastic Scattering at JLab 6 GeV

Right HRS

Left HRS

LD Target

Polarimeter

Compton

Moller

Polarimeter

Raster

BCM BPM

ARC eP

2

Luminosity

Monitor

Fig. 1. Hall A ﬂoor plan for the p roposed measurement.

provide essential clues as to the source of these discrepan-

cies.

The values of C

1q

have been determined to a reason-

able prec ision [17]. However, our present knowledge of C

2q

is poo r: δ(2C

2u

− C

2d

) = ±0.24. This also aﬀect the ex-

traction of C

3q

≡ g

e

A

g

q

A

from neutrino scattering data. A

precision measurement of C

2q

is highly desirable to explore

possible extensions of the Standard Model. PV DIS is a

semi-leptonic process and is sensitive to the C

2q

’s, there-

fore it is complementary to other Standard Model test ex -

periments including the Qweak exper iment – which stud-

ies semi-leptonic processes but is only sensitive to C

1q

’s.

For example, a la rge axial quark coupling could cause the

NuTeV eﬀect, but canno t be seen in C

1q

. Quark and lepton

compositeness is accessible only through C

2q

but no t C

1q

if a particular symmetry, SU(12), is respected. A preci-

sion PV DIS measurement will signiﬁcantly strengthen the

constraints o n these possible extensions to the Standard

Model. Possible new physics that PV DIS may be sensi-

tive to are Z

′

Searches, quark and lepton compositeness,

lepto quarks a nd supersymmetry. We are currently work-

ing with theorists on an updated list of new physics limits

achievable from the measurement described here [19,20].

The “mass s c ale” for which PV DIS is sensitive to physics

beyond the Standard Model would be [20]

Λ

g

=

1

q

2

√

2G

F

δ(2C

2u

− C

2d

)

≈ 1.0 TeV. (12)

3 Experimental Se tup

3.1 Ov erview

The ﬂoor plan for our experimental setup is shown in

Fig. 1. We will us e an 85 µA polarized beam and a 25 cm

long liquid deuterium target. The scattered elec trons will

be detected by the two standard Hall A High Resolution

Spectr ometers (HRS). In the following we will describe

some details of the ex perimental setup, focusing on two

major upgrades required by the measurement.

3.2 Beam Line and the Compton Polarimetry Upgrade

We plan to use a 6.0 GeV 85 µA beam with an 85% polar-

ization. To reduce the heat impact o n the targe t, the beam

will be circularly rastered such that the beam spot size at

the target is ∼ 4mm in diameter. The b e am energy can

be meas ured to ∆E/E = 2 × 10

−4

using either the ARC

or eP devices [21]. The helicity-dependent asymmetry of

the electro n b e am will be controlled by a DAQ specially

developed in Hall A for parity-violation experiments [7]. A

luminosity monitor will be used downstream of the target

to monitor helicity-dependent target-density ﬂuctuations

and other possible false asymmetries.

We need 1% precision in the beam polarization mea-

surement in order to achieve an acceptable systematic un-

certainty on the ﬁnal results. T he current Compton po-

larimetry in Hall A measures the asymmetry of Compton

scattering between the electro n beam and a high-power

IR laser (1 kW, 1064 nm) achieved by a Fabry- Perot cav-

ity. The current systematic uncertainty of the Compton

polarimeter is about 1.9% for a 6 GeV beam. In order

to achieve a 6 1% precision, we will upgrade the current

IR laser to a green laser (532 nm), and replace the c ur-

rent 600 µm micro-strips used in the electron detector by

300 µm strips. With these upgrades the total systema tic

uncertainty is expected to be reduced to 6 0.9%. These

upgrades are presently being carried out at JLab and we

exp ect to install and commissio n the new Compton po-

larimeter by late 2007.

3.3 Spectrometers and the DAQ Upgrade

We will use the standard Hall A HRSs [21] to detect

the scattered electrons. For each HRS the eﬀective solid-

angle acceptance for an extended target is 5.4 msr and

the momentum acceptance is ±4.5%. The HRS central

momentum can be c alculated from the dipole ﬁeld mag-

nitude to 5 × 10

−4

and the central angle can be deter-

mined to ±0.2 mrad, giving an uncertainty of ±0.004/Q

2

on 2C

2u

−C

2d

where Q

2

is in GeV

2

. Particle identiﬁcation

(PID) in each HRS will be done with a CO

2

˘

Cerenkov de-

tector and a double-layered lead-glass shower detector. We

exp ect to achieve a pion rejection factor of ≥ 10

4

at an

electron eﬃciency of ≥ 99%.

Because of the need to separate the pion background

we must use a counting method instead of an integrating

DAQ. The detecto r signals we will use include those fr om

the two PID detectors and scintillators (for crude dir e c -

tional information). To process this information we are

considering a Flash ADC (FADC) -based DAQ presently

being designed by the Fast Electronics Group at JLab.

This design will allow for the possibility of counting ex-

periments at approximately 1 MHz with a low and pre-

cisely measurable dead time, e.g. a 1% dead time mea-

sured w ith a 0.3% absolute accuracy. The FADC ﬁlls an

on-board memory at 250 MHz with ∼ 4 µs latency (buﬀer

size). An on-board processor (FPGA) will analyze the dig-

itized data and perform the PID. The DAQ will be ﬂexible

enough to accommodate a variety of experiments. A ﬁrst

version of the FADC is expected to be ready by 2007.

As an alternative, a scaler-based DAQ using fast NIM

electronics is also being considere d. We plan to build both

Xiaochao Zheng for the JLab E05-007 Collaboration: Parity Violation in Deep Inelastic Scattering at JLab 6 GeV 5

APV−Ti

APV−Cs

Bates

Qweak

PDG/SLAC

SAMPLE

JLab E05−007 (Expected)

Fig. 2. The eﬀective couplings C

1q

(left) and C

2q

(right) . The

future Qweak experiment combined with the APV-Cs result

will provide the most precise data and the best Standard Model

test on C

1q

. For C

2q

, the SAMPLE result for C

2u

− C

2d

at

Q

2

= 0.1 GeV

2

[22] and the current PDG value for 2C

2u

− C

2d

are shown. Assuming the SM prediction of 2C

1u

− C

1d

, the

value of 2C

2u

− C

2d

can be determined from this experiment

to ∆(2C

2u

− C

2d

) = ±0.03.

systems such that the FADC-based DAQ can be cross-

checked with the regular HRS counting DAQ at a low

rate (<4 kHz) and with the scaler-based DAQ at a high

rate (up to 1 MHz).

3.4 Expected Results

The asymmetry A

d

will be extracted from the measured

raw counting asymmetry as

A

d

=

A

raw

P

beam

+ ∆A

RC

EM

(13)

where P

beam

is the beam polarization. A

RC

EM

is the elec-

tromagnetic radiative co rrection a nd can be calculated to

0.2% (relative to A

d

). Pr ovided that all uncertainties re-

lated to hadronic structure are well under control, one can

then extract 2C

2u

− C

2d

from A

d

using Eq.(3). The ex-

pected total uncertainty in 2C

2u

− C

2d

is shown in Fig. 2

along with existing world data. For illustration, current

knowledge of C

1q

’s and their expected results fr om the

Qweak experiments ar e also shown. We expect to run E0 5-

007 in early 2009 and ﬁrst results may become available

within one year of its completion.

4 Interpretation of the Data and Discussions

on Hadronic Eﬀects

While we can extract 2C

2u

−C

2d

from the measured asym-

metry, there are uncertainties coming from hadronic physics

which may complicate the interpretation of this asymme-

try in terms of Standard Model parameters. This section

will describe some of these interesting issues.

4.1 Uncert ainty from Parton Distributions and R

LT

The uncertainties due to R

s

and R

v

in Eq. (3) can be

estimated using CTEQ [23,24] and MRST [25 ,26] PDF

parameterizations. We ﬁnd that our c urrent knowledge of

PDFs gives an uncertainty at the level of δ(2C

2u

−C

2d

) 6

±0.0025. The ratio R

LT

= σ

L

/σ

T

is taken from a global

ﬁt, R1998 [27]. Propagation of the uncertainty from the

this ﬁt yields an uncertainty of δ(2C

2u

−C

2d

) 6 ±0.0017.

4.2 Higher-Twist Eﬀects

Among all hadronic eﬀects that could c ontribute to PV

electron-scattering observables, higher-twist (HT) eﬀects

are expected to be the most probable for kinematics at

JLab. Here higher-twist eﬀects refer to the fa ct that the

strong interactions between the quarks become observable

at low Q

2

and the process cannot be described by the γ(Z)

exchange between the electron and a single quark (the

leading-twist process). For electromagnetic scattering pro-

cesses, these interactions introduce a scaling violation to

the structure functions for Q

2

< 1 GeV

2

that is stronger

than the ln(Q

2

)-dependence of the DGLAP equations of

perturbative QCD (pQCD). For PV e−

2

H scattering, HT

eﬀects start from twist-four terms which diminish as 1/Q

2

.

Hence, observation of any Q

2

-dependent deviation from

the expected asymmetry would strongly imply a contri-

bution from HT.

The theor y for HT is not well established. In a naive

picture, HT is expected to vanish in the asymmetry A

d

be-

cause the strong coupling between the struck quark and

other spectator quarks (the origin of HT) should not de-

pend on what type of the gauge boson (γ or Z

0

) is probing

the quark, hence the HT contributions cancel in the ratio.

In less hand-waving picture s, most of existing HT mod-

els show that the HT contribution to A

d

is below 1%/Q

2

level (see e.g. Ref. [1]), which is acceptable fo r interpret-

ing our exp ected data in terms of Standard Mo del tests.

However, these models were developed primarily during

and after the previous PV DIS experiment in the 1970’s.

A modern calculation of the HT from Q CD is needed and

we hope such calculation will bec ome available in the nex t

1-2 year(s) [19].

On the other hand, HT provides information on non-

perturbative aspects of the strong interaction, which by

itself has its own value. So fa r ﬁrst-hand information on

HT comes primarily fr om experimental data, e.g. by ob-

serving the non-ln Q

2

dependence of DIS structur e func-

tions. However, such an extraction is complicated by the

determination of the leading-twist term, which ha s a large

uncertainty from the truncation of higher order terms in

α

S

. By contrast, the prospects for observing HT contribu-

tions in PV-DIS ar e relatively uncomplicated because the

QCD higher o rder terms are expected to cancel in the

asymmetry. Thus our PV DIS experiment will provide

valuable insights into the study of the non-perturbative

side of strong interactions.

One interesting remark is that it has been shown that

although the NuTeV measurement was performed at hQ

2

i

=20 GeV

2

, the HT contribution to the typically measured

Paschos-Wolfenstein (P-W) ratio could be of the same

magnitude as that of the PV DIS observable at Q

2

≈

2 GeV

2

[28]. If the NuTeV deviation fr om the Standard