[fg]yes IAS Program on High Energy Physics Polarization ...

IAS Program on High Energy Physics

Polarization Free Methods for BeamEnergy Calibration

Nickolai Muchnoi

Budker INP, Novosibirsk

January 20, 2016

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 1 / 20

TALK OUTLINE

1 Introduction

2 Extending beam energy range?

3 Conclusion

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 2 / 20

Introduction

FCC-ee/CEPC aims to improve on electroweak precisionmeasurements, with goals of 100 keV on the Z mass, and afraction of MeV on the W mass.

The resonant depolarization technique is the only knownapproach that showed the accuracy at the level of∆E/E ' 10−6.

My personal experience is based on beam energy measurementsystems for VEPP-4M, BEPC-II and VEPP-2000 colliders. I willtry to extend this approach for higher energies.

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 3 / 20

Inverse Compton Scattering

θεelectron: ε

photo

n: ω

photon: ω0electron: ε0, γ=ε0/m

θω

Scattering parameters, u and κ:

u =ω

ε=θεθω

=ω

ε0 − ω; u ∈ [0, κ] ; κ =

4ω0ε0m2

.

Scattering angles: θω =1

γ

√κ

u− 1; θε =

4ω0

m

√u

κ

(1− u

κ

).

Maximum energy of scattered photon (θω = θε = 0): ωmax =ε0κ

1 + κ.

ε0 =ωmax

2

(1 +

√1 +m2/ω0ωmax

)' m

2

√ωmaxω0

.

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 4 / 20

Laser backscattering for beam energy calibrationHISTORY: Taiwan Light Source1996, BESSY-I,II1998,2002, VEPP-3,4M,20002008,2005,2012, BEPC-II2010, ANKA2015

e. g. BEPC-II HPGe spectrum

, keVγE1980 2000 2020 2040 2060 2080

100

200

300

400

500

600

700

800

900

/NDF = 294.5/2962

χ 0.12: ± = 1.31 0

K

0.20 keV± 0.12 ± = 2025.42 max

ω

mτ =1776.91±0.12+0.10−0.13MeV

Phys. Rev. D90 (2014) 012001

e. g. VEPP-2000 HPGe spectrum

, keVγE1650 1700 1750 1800 1850 1900 1950

co

un

ts

500

1000

1500

2000

2500

3000

3500 2012.04.20 (16:21:34 - 18:53:59) 2012.04.20

Backscattering occurs inside the magnet: evident interference

Phys.Rev.Lett. 110(2013) 140402�� ��Achieved accuracy is ∆E/E ' 3× 10−5 for E < 2 GeV

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 5 / 20

Accurate energy scale transfer: eV→ MeV→ GeV

IR optics, 10P20 CO2 laser line: ω0 = 0.117065228 eV

γ-lines from excited nuclei as a good reference for ωmax:

137Cs τ1/2 ' 30.07 y Eγ = 0661.657± 0.003 keV60Co τ1/2 ' 5.27 y Eγ = 1173.228± 0.003 keV

Eγ = 1332.422± 0.004 keV208Tl τ1/2 ' 3 m Eγ = 2614.511± 0.013 keV16O∗ Eγ = 6129.266± 0.054 keV

High energy physics scale1:

J/ψ 3096.900± 0.002± 0.006 MeVψ(2S) 3686.099± 0.004± 0.009 MeV

1Final analysis of KEDR data, Physics Letters B 749 (2015) 50-56Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 6 / 20

1 Introduction

2 Extending beam energy range?

3 Conclusion

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 7 / 20

Spectrometer with laser calibration

Xedge

Xbeam

BPM

X0

BPM

Compton photonsDIPOLE MAGNET

LASER BEA

M

Compton electrons with min. energy

electron beam

Δθ

θBPM

Here tiny fraction of the beam electrons

are scattered on the laser wave

L

BPMBPM

BPM

Access to the beam energy: E0 =∆θ

θ× m2

4ω0

∆θ

θ= κ =

4ω0E0

m2

E0 =100 GeV, ω0 =1 eV:

∆θ

θ' 1.53

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 8 / 20

Spectrometer with laser calibration

Xedge

Xbeam

BPM

X0

BPM

Compton photonsDIPOLE MAGNET

LASER BEA

M

Compton electrons with min. energy

electron beam

Δθ

θBPM

Here tiny fraction of the beam electrons

are scattered on the laser wave

L

BPMBPM

BPM

Access to the beam energy: E0 =∆θ

θ× m2

4ω0

∆θ

θ= κ =

4ω0E0

m2

E0 =100 GeV, ω0 =1 eV:

∆θ

θ' 1.53

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 8 / 20

Spectrometer with laser calibration

Xedge

Xbeam

BPM

X0

BPM

Compton photonsDIPOLE MAGNET

LASER BEA

M

Compton electrons with min. energy

electron beam

Δθ

θBPM

Here tiny fraction of the beam electrons

are scattered on the laser wave

L

BPMBPM

BPM

Access to the beam energy: E0 =∆θ

θ× m2

4ω0

∆θ

θ= κ =

4ω0E0

m2

E0 =100 GeV, ω0 =1 eV:

∆θ

θ' 1.53

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 8 / 20

Spectrometer with laser calibration

Xedge

Xbeam

BPM

X0

BPM

Compton photonsDIPOLE MAGNET

LASER BEA

M

Compton electrons with min. energy

electron beam

Δθ

θBPM

Here tiny fraction of the beam electrons

are scattered on the laser wave

L

BPMBPM

BPM

Access to the beam energy: E0 =∆θ

θ× m2

4ω0

∆θ

θ= κ =

4ω0E0

m2

E0 =100 GeV, ω0 =1 eV:

∆θ

θ' 1.53

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 8 / 20

What do one has from ∆θ measurement?

��

� ∆θ

m2

4ω0

=1

c

∫Bdl

∆θ is a measure of a B-field integral along the trajectory whichis very close to the beam orbit (see next slides).

∆θ is independent of beam energy: fast energy changes may bedetected by BPMs. I. e. increase of ∆θ measurement time doesnot influence the beam energy measurement accuracy.

Measurement of θ is outside of this talk. One can have a look atthe experience of LEP spectrometer as well as ILC beam energyspectrometer studies.

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 9 / 20

Two arcs in a dipole of length L

Re

L

ΔX

R 0

θ

Δθ Note that�� ��Re = R0/(1 + κ).

S0, R0 – black arc length & radius,Se, Re – red arc length & radius. So

S0 = 2R0arcsin

[L

2R0

]and

Se = 2Rearcsin

[√L2 + ∆X2

2Re

],

where ∆X =

√R2e −

[LRe

2R0

]2−

√R2e −

[L− LRe

2R0

]2.

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 10 / 20

Apparatus: general consideration

L20 m 20 m

ΔX

θ

D

Δθ

Let κ = 1.53 (E = 100 GeV, ω0 = 1 eV):

θ ∆θ L ∆X ∆S/S Dmrad mrad m mm mm1 1.53 10 3.83 2.59 · 10−7 462 3.06 10 7.65 1.04 · 10−6 921 1.53 5 1.91 2.59 · 10−7 462 3.06 5 3.83 1.04 · 10−6 92

∆S/S ∝ κθ a)

∆X ∝ κθ·Ldipole b)

D ∝ κθ·Larm c)

An ideal case: a) small angle; b) short dipole; c) long arm.

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 11 / 20

2D detector for scattered electrons?

A Transverse Polarimeter for a Linear Collider of 250 GeV e Beam EnergyItai Ben Mordechai and Gideon Alexander (LC-M-2012-001)

“... For the detection of the scattered electrons we consider only a position measurement usinga Silicon pixel detector placed at a distance of 37.95 m from the Compton IP. The activedimension of the detector is 2×200 mm2. The size of the pixels cell taken is 50×400 µm2

similar to the one used in the ATLAS detector [9]. This scheme yields an approximate twodimensional resolution of 14.4×115.5 µm2 [10] with a data read-out rate of ...”

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 12 / 20

Scattering cross sections & e-beam polarisation.

Unpolarised

-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1-1

-0.8-0.6

-0.4-0.2

0 0.2

0.4 0.6

0.8 1

0

2

4

6

8

10

12

14

16

18

x

y

Longitudinal

-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1-1

-0.8-0.6

-0.4-0.2

0 0.2

0.4 0.6

0.8 1

-2.5-2

-1.5-1

-0.5 0

0.5 1

1.5 2

2.5 3

x

y

Transverse

-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1-1

-0.8-0.6

-0.4-0.2

0 0.2

0.4 0.6

0.8 1

-1.5

-1

-0.5

0

0.5

1

1.5

x

y

In the plane of electron angles θx, θy(after scattering and bending in a dipole)cross section lies within the elliptical kinematic-bounded area.

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 13 / 20

200×100 pixels “detector”. ξ�ζ‖ = −0.5

Xϑ

0 200 400 600 8001000120014001600

Yϑ2−

1.5−1−

0.5−0

0.51

1.52

0

5000

10000

15000

20000

25000

30000

35000

40000

HDEntries 1e+07

/ ndf 2χ 2662 / 2709 1X 0.1649±0.1313 − 2X 0.06344± 1630 Xσ 0.05565± 21.62 1Y 0.0001923±1.63 − 2Y 0.0001942± 1.63 Yσ 0.0001082± 0.1045 P 0.00103±0.5 −

P 0.002095± 0.0005721 norm 772.3± 1.735e+06

HDEntries 1e+07

/ ndf 2χ 2662 / 2709 1X 0.1649±0.1313 − 2X 0.06344± 1630 Xσ 0.05565± 21.62 1Y 0.0001923±1.63 − 2Y 0.0001942± 1.63 Yσ 0.0001082± 0.1045 P 0.00103±0.5 −

P 0.002095± 0.0005721 norm 772.3± 1.735e+06

= 500, P = [ 0.0, 0.0, -0.5, 0.0 ]0

ϑ = 3.26, κ

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 14 / 20

Fit results. ξ�ζ‖ = −0.5

X fit range is [200 : 1650]200 horizontal bins means resolution σX/X ' 0.005/

√12 = 0.14%

FCN=2662.5 FROM MIGRAD STATUS=CONVERGED 257 CALLS 258 TOTAL

EDM=3.9346e-08 STRATEGY=1 ERROR MATRIX UNCERTAINTY 0.8 per cent

NO. NAME VALUE ERROR Remark

1 X1 -1.3130e-01 1.64882e-01 ∆X1/X2 ' 1.0 · 10−4

2 X2 1.62998e+03 6.34381e-02 ∆X2/X2 ' 3.9 · 10−5

3 σX 2.16201e+01 5.56481e-02 horizontal beam size4 Y1 -1.6298e+00 1.92272e-04 vertical axis5 Y2 1.62973e+00 1.94174e-04 vertical axis6 σY 1.04485e-01 1.08179e-04 vertical spread7 P‖ -5.0003e-01 1.02951e-03 P‖ = −0.500± 0.001

8 P⊥ 5.72060e-04 2.09542e-03 P⊥ = 0.000± 0.0029 norm 1.73486e+06 7.72345e+02

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 15 / 20

200×100 pixels “detector”. ξ�ζ⊥ = 0.5

Xϑ

0 2004006008001000120014001600 Yϑ2− 1.5− 1− 0.5− 0 0.5 1 1.5 2

0

5000

10000

15000

20000

25000

30000

35000

40000

HDEntries 1e+07

/ ndf 2χ 2652 / 2711 1X 0.1596± 0.1629 2X 0.07658± 1630 Xσ 0.06821± 21.62 1Y 0.0001934±1.63 − 2Y 0.0002122± 1.63 Yσ 0.0001094± 0.1046 P 0.0009531± 0.0003713

P 0.002411± 0.5007 norm 777.3± 1.707e+06

HDEntries 1e+07

/ ndf 2χ 2652 / 2711 1X 0.1596± 0.1629 2X 0.07658± 1630 Xσ 0.06821± 21.62 1Y 0.0001934±1.63 − 2Y 0.0002122± 1.63 Yσ 0.0001094± 0.1046 P 0.0009531± 0.0003713

P 0.002411± 0.5007 norm 777.3± 1.707e+06

= 500, P = [ 0.0, 0.0, 0.0, 0.5 ]0

ϑ = 3.26, κ

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 16 / 20

Fit results. ξ�ζ⊥ = 0.5

X fit range is [200 : 1650]200 horizontal bins means σX/X ' 0.005/

√12 = 0.14%

FCN=2651.75 FROM MIGRAD STATUS=CONVERGED 258 CALLS 259 TOTAL

EDM=4.0963e-07 STRATEGY=1 ERROR MATRIX UNCERTAINTY 0.4 per cent

NO. NAME VALUE ERROR Remark

1 X1 1.62941e-01 1.59586e-01 ∆X1/X2 ' 1.0 · 10−4

2 X2 1.63002e+03 7.65815e-02 ∆X2/X2 ' 4.7 · 10−5

3 σX 2.16220e+01 6.82096e-02 horizontal beam size4 Y1 -1.6298e+00 1.93423e-04 vertical axis5 Y2 1.63003e+00 2.12161e-04 vertical axis6 σY 1.04595e-01 1.09394e-04 vertical spread7 P‖ 3.71312e-04 9.53123e-04 P‖ = 0.000± 0.001

8 P⊥ 5.00724e-01 2.41133e-03 P⊥ = 0.501± 0.0029 norm 1.70728e+06 7.77293e+02

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 17 / 20

1 Introduction

2 Extending beam energy range?

3 Conclusion

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 18 / 20

Conclusion

1 High energy lepton colliders require beam polarisation at leastfor use of resonant depolarisation approach at “low” energies.

2 With a 2D detector for scattered electrons both spin polarisationdegree and direction could be measured with high accuracy.

3 Beam energy spectrometer was used at LEP and a lot of studieswere made for ILC. No doubt it should be implemented on HF.

A novel way for B-field integral measurements along the beamorbit is suggested with accuracy in the range of 1 – 100 ppm.

With no additional equipment (except required for items 1,2,3)the accuracy of beam energy determination is limited by theaccuracy of bending angle measurement (10 – 100 ppm) .

Further studies require detailed simulations with realisticmachine and scattered electrons detector parameters.

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 19 / 20

The end

THANK YOU!

Special thanks to the conference organizers for theinvitation and warm welcome!

Nickolai Muchnoi IAS Program on High Energy Physics January 20, 2016 20 / 20