Precision Møller Scattering at Low Energies...M˝ller Scattering at Low Energy Baseline process for nuclear physics experiments, e.g.: OLYMPUS1: measure two-photon exchange in lepton-proton

Precision Møller Scattering

at Low Energies

Charles Epstein

Intense Electron Beams Workshop, Cornell University

June 18, 2015

Outline

1 Applications at Low Energies2 Radiative Corrections at Low Energy3 Upcoming Measurements

Outline


Møller Scattering at Low Energy

This talk will cover the process

e− + e− → e− + e− + (γ)

• Precision calculations including radiative corrections• Unpolarized, QED only

• Relevance to future experiments

• Upcoming new measurements

Charles Epstein (MIT) Low-Energy Møller Scattering June 18, 2015 1 / 25


• Baseline process for nuclear physics experiments, e.g.:• OLYMPUS1: measure two-photon exchange in lepton-proton

scattering via e+p/e−p cross-section ratio @ 2 GeV

• Separate e+/e− beams: normalize to Møller/Bhabha

• PRad2: measure proton form factor at low Q2: charge radius• Normalize ep to Møller at forward angles

• High-rate noise background: e.g. DarkLight @ 100 MeV

• Potential searches for new physics via vacuum polarizationdiagrams

1R. Milner, D. K. Hasell, et al., Nucl. Instrum. Methods Phys. Res. A 741, 1 (2014).2M. Meziane and P. Collaboration, AIP Conference Pro- ceedings 1563, 183 (2013).





























DarkLight

Measure e−p → e−pe+e− at 100 MeV, L = 6× 1035 cm−2s−1

Solenoid

Tracker

BeamMøller Cone

H2 Target

e-

e-

e+

p

• Sweep Møller e− with solenoid: still significant backscattering

• Møller photons produce high rate of secondaries


Outline


Theoretical Goals

+

Desired andProduced:

• Unpolarized Møller (and Bhabha) scattering

• Full calculation including NLO radiativecorrections (QED only)

• No peaking, ultra-relativistic (etc)approximations

• Full treatment of bremsstrahlung

• C++ event generator → drive simulations


Approach to the radiative corrections

Separate “elastic” from radiative events by an Eγ cutoff: ∆E

Treat types of events separately

• Eγ > ∆E : Hard-photon bremsstrahlung• Exact e e → e e γ cross-section

• Eγ < ∆E : “Close enough” to elastic kinematics• Apply soft-photon radiative corrections


Soft Radiative Corrections: Eγ < ∆E

• Integrate soft photon over all Ω and up to Eγ = ∆E

• Soft-photon + loop-level IR divergences cancel

dσ

dΩ= (1 + δ)

dσ

dΩ

∣∣∣∣Born

δ = δ(∆E, s, t, u)

Expect that as ∆E gets smaller, δ gets smaller

• Many formulations use ultra-relativistic approximations: me → 0

• Recently worked out beyond URA for Møller3, Møller/Bhabha4

3I. Akishevich, H. Gao, A. Ilyichev, and M. Meziane, Euro Phys Journal A 51 (2015).4N. Kaiser, J. Phys. G: Nucl. Part. Phys. 37 (2010).


Soft Radiative Corrections: Eγ < ∆E

• Integrate soft photon over all Ω and up to Eγ = ∆E

• Soft-photon + loop-level IR divergences cancel

dσ

dΩ= (1 + δ)

dσ

dΩ

∣∣∣∣Born

δ = δ(∆E, s, t, u)

Expect that as ∆E gets smaller, δ gets smaller

• Many formulations use ultra-relativistic approximations: me → 0

• Recently worked out beyond URA for Møller3, Møller/Bhabha4

3I. Akishevich, H. Gao, A. Ilyichev, and M. Meziane, Euro Phys Journal A 51 (2015).4N. Kaiser, J. Phys. G: Nucl. Part. Phys. 37 (2010).


Ultra-relativistic Approximations

• Higher-order me terms often neglected• For high beam energies, typically a good approximation

• Effects visible at low energy:at angles where m2

e/t or m2e/u no longer 1

δ grows as ∆E gets smaller

• Unphysical → implies higher rate at smaller energy windows


Lab-frame angles at which m2e/t = 0.1

0.1

1

10

100 150 200 250 300 350 400 450 500

Acc

epta

ble

Ang

ular

Ran

ge[

]

Beam Energy [MeV]


Improper behavior of δ:√s = 10.16 MeV (DL)

0

2

4

Delta E @MeVD

020

4060

80 Theta CM @ºD

-0.05

0.00

0.05

δ(∆E , θ)

(Tsai, 1960)


What δ should look like

0

2

4

Delta E @MeVD

020

4060

80 Theta CM @ºD

-0.05

0.00

δ(∆E , θ)

(Kaiser, 2010)


Hard-photon Bremsstrahlung: Eγ > ∆E

Calculated exactly using FeynArts/FormCalc

e−1 + e−2 → e−3 + e−4 + γ


Bremsstrahlung Cross-Section (CM System)

d5σ

dEγ dΩγ dΩ3=

1

32m3e(2π)5

Eγ2EpRc

∑ν

p23ν〈|M |2〉 [5]

E3 =2E (E − Eγ)(2E − Eγ) ∓ Eγm

2e cosαRc

(2E − Eγ)2 − E 2γ cos2 α

Typically only upper sign is permitted.Above a photon energy Eγ0 , both become allowed

5Haug & Nakel, 2004Charles Epstein (MIT) Low-Energy Møller Scattering June 18, 2015 12 / 25

Bremsstrahlung Cross-Section (CM System)

d5σ

dEγ dΩγ dΩ3=

1

32m3e(2π)5

Eγ2EpRc

∑ν

p23ν〈|M |2〉 [5]

E3 =2E (E − Eγ)(2E − Eγ) ∓ Eγm

2e cosαRc

(2E − Eγ)2 − E 2γ cos2 α

Typically only upper sign is permitted.Above a photon energy Eγ0 , both become allowed

5Haug & Nakel, 2004Charles Epstein (MIT) Low-Energy Møller Scattering June 18, 2015 12 / 25

Lepton Constraints

Two values allowed for:

Eγ0 > 2E (E −me)/(2E −me)

Additional constraint:

cosα < − 1

Eγ

√(2E − Eγ)2 − 4E 2(E − Eγ)2/m2

e

θe

αmin

allowedΩ

γ region


Identical Møller electrons: a complication

Cross-section:

dσ

dΩ3=

(1

2

)Symmetry

×〈|M |2〉×[Phase Space]

• Must integrate over “interest” and“recoil” regions

• Easy with elastic kinematics

• Radiative: “recoil” region isn’t simple

(CM system)

Generator: check each event for double-counting



Cross-section:

dσ

dΩ3=

(1

2

)Symmetry





Region

of Interest

“Recoil”

Region

(CM system)




Cross-section:

dσ

dΩ3=

(1

2

)Symmetry





Region

of Interest

“Recoil”

Region γ

(CM system)




Cross-section:

dσ

dΩ3=

(1

2

)Symmetry





Region

of Interest

“Recoil”

Region γ

(CM system)




Cross-section:

dσ

dΩ3=

(1

2

)Symmetry





Region

of Interest

“Recoil”

Region γ

(CM system)



Bremsstrahlung Comparison

Soft-photon corrections and bremsstrahlungshould agree near Eγ ∼ ∆E

Rearrange:

Soft-Photond3σ

dΩ3 dEγ=

dσ

dΩ3

∣∣∣∣Born

× d

d∆E

δ(Ω3,∆E )

Bremsstrahlung d3σ

dΩ3 dEγ=

∫4π

d5σ

dΩ3 dEγ dΩγ

dΩγ


Electron Cross-Section at fixed angles (2 GeV)

106

107

108

109

1010

1011

5 10 15 20

Møl

ler

Cro

ssSe

ctio

n[p

b/

MeV

/ra

dian

]

CM Photon Energy [MeV]∆E

20CM

40CM

90CM


Ratio of hard/soft cross-sections

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2 4 6 8 10 12 14

Rat

io:

Har

dB

rem

sstr

ahlu

ng/

Soft

Pho

ton


20CM

40CM

90CM


Electron Cross-Section at high photon energies

100

102

104

106

108

1010

1012

22 22.1 22.2 22.3 22.4 22.5 22.6

MøllerCross

Section[pb/MeV

/radian]

CM Photon Energy [MeV]

Eγ0

20CM

40CM

90CM


Outline


Møller Scattering at 100 MeV

Why measure unpolarized low-energy Møller scattering?

Quantities withfew precision

data

• Distribution of E at fixed θ: radiative tail• Verify bremsstrahlung calculation

• Precise electron-electron cross-section vs θ• Verify soft-photon radiative corrections→ beyond URA

Requirements

• Measure electrons with energy 1-5 MeV/c

• Momentum resolution δp/p ∼ 1%

• Scattering angles 25-45





data



Requirements








data



Requirements





Measurement Summary

The radiative Møller process will be measured in tandem with theDarkLight experiment

• Jefferson Lab LERF/ERL: 100 MeV electrons

• Energy measurement with magnetic spectrometers

• Map out electron energy spectrum at various θ

• ∼100 settings


Møller Measurement Layout

Two-Spectrometer Layout

Dipole

Detector

Top View Beamline View

r = 3

0 cm

fixed Dipole

• Pointlike target: 5µm MicroMatter diamond-like carbon foil

• Measure electron p and θ; normalize to e-C scattering


Møller Measurement Layout

= 25°

= 45°

Bellows

Collimator

Target

• 25 to 45 every 5

• Entirely vacuum until detector: eliminate multiple scattering


Cross-Sections: Inelastic

e−e− → e−e−γ single-e− cross-section: 25± 0.5

103

104

105

106

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Cro

ss-S

ection

[Hz

/M

eV/c

/1

/1

]

Electron Momentum [MeV/c]


Cross-Sections: Inelastic

e−e− → e−e−γ single-e− cross-section: 45± 0.5

104

105

106

107

108

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Cro

ss-S

ection

[Hz

/M

eV/c

/1

/1

]

Electron Momentum [MeV/c]


Detector Concept

2D array of crossed scintillating fibers

1mm

• Two 2-layer arrays at 90

• Detector Size: 15cm × 5cm

• Light collection: SiPM array or multianode PMT

arXiv:1011.0226, https://userweb.jlab.org/~yez/Work/SFT/SFT_Status.pdf


https://userweb.jlab.org/~yez/Work/SFT/SFT_Status.pdf

Summary

Calculated

• Single-photon bremsstrahlung to extend Møller/Bhabhasoft-photon corrections

• Beyond URA → optimal for low beam energies

• Incorporated into a new Monte Carlo event generator

Plan to Measure

• Møller electrons: 25-45

• Map out energy distribution every 5

• Magnetic spectrometers: 30cm, 90 dipole• Potential: 2D scintillating fiber detector


Backup

Target and Beam Parameters

Luminosity ∼ 2× 1034 cm−2s−1

Target 5 µm diamond-like carbonTarget e− thickness ∼ 3× 1020 cm−2 @ 5 µmBeam 100 MeV, 0.01 mABeam power deposition 0.027 Watts / 0.01 mA


Spectrometer Parameters

DetectorsTwo dipole spectrometers+ readout planes

Dipole radius 30 cmDipole angle 90

Momentum acceptance ∆p/p ∼10%Momentum resolution δp/p ∼10−3-10−2

θ acceptance ±0.5

φ acceptance 1

θ pos. resolution < 0.1

Luminosity Angle ∼ 25

Signal Angles 25 to 45 (in 5 steps)Luminosity electron momentum ∼100 MeV/cLuminosity detector field ∼1.2 T: existing magnetSignal electron momentum 1− 5 MeV/cSignal detector field 120− 600 Gauss


Target Parameter Estimates

• ERL transverse emittance ∼ 10 mm-mrad (normalized)• Multiple scattering ∼1 mrad• Beam spot ∼0.1 mm → ∼0.5 mrad angular spread• MS increases emittance ∼2× (OK)

• Power deposition in 5 µm C: ∼ 0.027 Watts at 100 MeV, 0.01mA

• ∆T ∼ P/t4πλ [1 + ln(R/r)] (λ ∼ 70 W/m-K)

• At R = 1 cm, r = 0.1 mm, t = 5 microns, ∆T ∼ 34C• P = εσAT 4: A ∼ 2× π · (1 mm)2, ε = 0.7 → T ∼ 574 K


Positron Cross-Section at fixed angles

105

106

107

108

109

1010

5 10 15 20

Bha

bha

Cro

ssSe

ctio

n[p

b/

MeV

/ra

dian

]


20CM

40CM

90CM


Ratio of hard/soft cross-sections (Bhabha)

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2 4 6 8 10 12 14

Rat

io:

Har

dB

rem

sstr

ahlu

ng/

Soft

Pho

ton


20CM

40CM

90CM


Positron Cross-Section at high photon energies

105

106

107

108

109

22 22.1 22.2 22.3 22.4 22.5 22.6

Bhab

haCross

Section[pb/MeV

/radian]

CM Photon Energy [MeV]

Eγ0

20CM

40CM

90CM


Elastic vs Møller Cross-Sections

100

102

104

106

108

1010

1012

1014

1016

0 20 40 60 80 100 120 140 160 180

Rat

eat

6×

1035

cm−2s−

1[H

z/

1]

Angle []

Rate of 100 MeV Elastic, Moller Scattering in 1 Bins

ElasticMoller


Documents

Precision Møller Scattering at Low Energies...M˝ller Scattering at Low Energy Baseline process for nuclear physics experiments, e.g.: OLYMPUS1: measure two-photon exchange in lepton-proton