Proton Radius Measurement with AMBER An approach complementary to PRES - Jan Friedrich Technische Universität München 30 March 2021 PRES ...

Proton Radius Measurement
 with AMBER
 An approach complementary to PRES

 Jan Friedrich
 Technische Universität München

 30 March 2021
 PRES Collaboration Meeting

30.3.2021 Jan Friedrich 1

Planned, ongoing, recent scattering experiments to
 measure the proton form factor at low Q2
The discrepancy between the results – the proton radius puzzle - triggered
many new proposals and experiments:

• ! scattering radiative: ISR electron scattering
• ! scattering at medium E with active-target TPC at MAMI (PRES)
• ! scattering at higher E: PRad at Jefferson Lab

• "/! , "/! scattering at low energy: MUSE / PSI

• "/! at high E at CERN (AMBER)
 different systematics

30.3.2021 Jan Friedrich 2

MUSE – kinematics of low-energy
 elastic muon scattering

 our calculation (muon mass)

30.3.2021 Jan Friedrich 3

Kinematic ranges

30.3.2021 Jan Friedrich 4

Kinematic ranges

30.3.2021 Jan Friedrich 5

Comparison of kinematics

 • at low Q2 the cross section is dominated by GE

 • The cross section is practically independent on the lepton
 energy (above 500 MeV)

30.3.2021 Jan Friedrich 6

AMBER Proton Radius Measurement

• Measurement of low-Q2 elastic-scattering
• Detection of low-energetic recoil-protons and
 scattered muons with small scattering-angle.
• Silicon trackers along large lever arm to

 022; SPSC-P-360
 CERN-SPSC-2019-
 measure small scattering-angles
• Fiber tracker timing (and trigger)
• TPC as an active target with the ability to
 measure the low-energetic recoil-proton
• New continuously-running DAQ
 3. 2. 3.
 0 5 0
 m m m

 30.3.2021 Jan Friedrich 7

Mainz vs JLab data

 1.015
 PRad data Mainz fit Alarcon 19, rp = 0.841 fm
 PRad fit Mainz fit, forced rp = 0.841 fm This proposal, projected stat. errors
 Mainz data Arrington 07
 1.01

 1.005

 1
 GE /Gstd. dipole

 0.995

 0.99

 0.985

 0.98

 0.975

 0.97
 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
 Q2 [(GeV/c)2 ]

 uncertainties for the COMPASS++/AMBER proposal
 • program for 200 days of beam
 • precision on the proton radius < 0.01 fm

30.3.2021 Jan Friedrich 8

Layout of the AMBER PRM

 • Advantages of using the COMPASS spectrometer
 • Measurement of muon momentum and understanding of background.

30.3.2021 Jan Friedrich 9

Layout of the AMBER PRM
 • Advantages of using the COMPASS spectrometer
 CERN-SPSC-2019-022;
 SPSC-P-360

 • COMPASS spectrometer
 → Momentum measurement of scattered muon
 → Radiative background using electromagnetic calorimeter
 → Muon identification with muon filter and hodoscope

30.3.2021 Jan Friedrich 10

TPC for the pilot run

• IKAR TPC was transported from GSI to
 CERN on 22 November 2020
• Refurbishing of the inner part is ongoing
• Pressure and valve tests foreseen in April
• New readout plane has been produced,
 ready to be installed

opened TPC with old electrode structure new segmented readout plane
 Jan Friedrich 11

AMBER and PRES TPCs

 • many similar parameters for the two setups
 • Similar geometry allows for using
 calibrations (e.g. the drift velocity)
 • similar technology for gas system
 (purification, temperature and pressure
 control)
30.3.2021 Jan Friedrich 12

Unified Tracker Station

New design of the detector holding structure to
• accommodate a small distance between the Silicon-pixel detectors
 (SPD) and the Scintillating-Fibre Hodoscope (SFH) (for hit-timing
 association)
• Allow for independent access and cooling infrastructure
• Compatible to connect to beam line elements for the He volume

 Jan Friedrich 13

Charge radius: definition and model dependence

30.3.2021 Jan Friedrich 14

Accelerated charge radiates:
 correction to elastic lepton-nucleon scattering

 figs. from:
 Gramolin et al.,
 arXiv:1401.2959

 !"# = $%&' 1 + 

 includes:

 real virtual
 from: Pieroth et al., NIM B36 (1989)
 internal corrections external bremsstrahlung
30.3.2021 Jan Friedrich 15

1st order internal corrections

 ! ≫ !

• the first-order real and virtual corrections need to be merged on cross-section level
• formally: $ = +∞ and % = −∞
• the underlying ”infrared” divergence is not related to the regularization scheme
• under certain kinematic conditions and depending on the choice of the cut-off
 energy Δ , parts of the corrections may cancel (or become even zero) – this does
 not imply that the correction is “really small”
• uncertainty has to be estimated in any case, and can be larger than the correction

 30.3.2021 Jan Friedrich 16

Peak shape with no experimental ( resp. external) smearing

 &'→) ”danger zone”,
• the correction $ + ∞ was exponentiation
 originally introduced as “small (/resolution)

 correction”
• it expresses the probability to emit
 one real photon along the Born
 process
 soft 1/k
• if the emission of a photon with a control region
 certain energy is large, it is hard photon emission,
 plausible that two or more photons kinematic and FF effects
 are emitted: Eg

 E’

 30.3.2021 Jan Friedrich 17

Exponentiation procedure

• if the emission of a photon with a certain energy is large, it is plausible that
 two (and more) photons are emitted

• inspired by the higher-order divergence cancellation proof (Jennie, Frautschi,
 Suura 1961): infinitely soft photon emission / absorption becomes independent
• unclear for finite Δ (no cheap way around calculating the higher orders)

30.3.2021 Jan Friedrich 18

Exponentiation procedure

 + +

 $ Δ 
 1 + Δ → ! "#
 = 1 + Δ + +⋯
 2
 • unclear for finite Δ (no cheap way around the calculation of the
 higher orders)
 • theory homework for 2nd order Feynman diagrams is done, check
 integral (over 4-particle f.s.)

30.3.2021 Jan Friedrich 19

Radiative corrections for electron and muon scattering

30.3.2021 Jan Friedrich 20

Radiative corrections in the interpretation of
 lepton-proton scattering data

 • Measuring the recoil of the proton can save to mix different Q2
 (as happens in case of single-arm measurement without
 constraint to the elastic peak)
 • The interpretation of the Q2 cross-section dependence still
 requires a precise understanding of the influence of radiative
 effects
 0.045 5
 10

 Qp = 2Mp Ekin
 0.04
 4
 2
 0.035 10

 0.03
 3
 10
 0.025

 0.02
 2
 10
 0.015

 0.01
 10

 0.005

 0 1
 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
 Q2µ = (p µ qµ)2

 “Primakoff effect” in forward kinematics (high-energy muon scattering)

30.3.2021 Jan Friedrich 21

External bremsstrahlung

• calculus of the total bremsstrahlung
 probability down to zero scattering angle
 • screening by atomic electrons
 • long-wavelength limit: contribution from
 different scattering centers
 • coherent bremsstrahlung in crystals
• “sublimation” of all effects into Tsai’s
 radiation lengths ) may not be the full
 answer to describe correctly the external
 bremsstrahlung in a given setup
• best way: measure it

 from: J.F. PhD thesis 2000

 30.3.2021 Jan Friedrich 22

Bremsstrahlung: real-photon emission and
 observation along muon-proton scattering
 ~10m
 ECAL2
 SF2 SF3

cuum) scattered muon

 Bremsstrahlung photon
 beam muon

 recoil proton
 SI02 SI03 SI04 COMPASS spectrometer

 • Bremsstrahlung accompanies the elastic process
 • for low-energy photons roughly 1/Eg (‘infrared divergence‘)
 • angular spectrum: peaking in the relativistic case, opening angle 1/g
 [Lorentz factor]
 • 100 GeV beam: Eg between 50 MeV and 5 GeV emission probability at
 qµ =0.3mrad (Q2=0.001): 5 x10-4
 • Bremsstrahlung events for 7e7 elastic events in Q2=0.001…0.04 GeV2/c2
 are about 38000

 30.3.2021 Jan Friedrich 23

Peaking and forward effect for small ,

• Bremsstrahlung of ultra-relativistic
 moving charges is peaked with
 opening angle 1/ 
• emission probability in exact forward
 direction practically vanishes
• if the lepton scattering angle is in the
 order of the radiation opening angle
 ( * ≈ * ), interference becomes
 important

 30.3.2021 Jan Friedrich 24

Bremsstrahlung emission angle, E=100GeV

 XYspec XYspec
 5.5
 0.002
 Ebeam=100GeV, Egam=1GeV, thmu=14mrad> 3
 0.005
 0.001 th_mu=4.5mrad< 5

 0
 0 2.5 4.5
 -0.001

 -0.005 -0.002 4
 2
 -0.003
 3.5
 -0.01
 -0.004
 1.5
 -0.005 3
 -0.015
 -0.006
 1 2.5
 -0.02
 -0.01 -0.005 0 0.005 0.01 -0.003 -0.002 -0.001 0 0.001 0.002 0.003 0.004 0.005

 • forward cancellation in case of 100 GeV muon scattering at
 * < * ≈ 0.01 GeV * ( + ≈ 1mrad)
 • similar effect discussed in Fadin & Gerasimov, PLB 795 (2019)
 (however “neglect * compared with * and * ”)

30.3.2021 Jan Friedrich 25

Generators

 • for a concise description of the experimental conditions, the simulation
 must include all effects from
 • atomic collision energy loss (Landau straggling)
 • external bremsstrahlung
 • internal radiative corrections

 • for the internal 1st order corrections, the ESEPP generator became
 available (arXiv-1401.2959)
 • implementation of full corrections including the real-photon
 distributions
 • usage of the TFoam (CERN/root) library for importance sampling

from arXiv-1401.2959 about higher orders:

 do the calculation with Δ = 0.01 GeV and get
 the uncertainty orders of magnitude higher.
 30.3.2021 Jan Friedrich 26

two-photon exchange

 • Effect of positive vs. negative
 muons presumably too small
 (unless two full experiments are
 made)

30.3.2021 Jan Friedrich 27

Summary

 • AMBER is approved at CERN for various measurements of
 QCD, including the proton charge radius
 • with a 100 GeV muon beam
 • about 150 days of beam time

 • The AMBER measurement has many similarities with PRES
 • a similar active-target TPC is employed
 • four 400 mm drift cells instead of two
 • Similar geometry allows for synergy effects in the
 construction, operation and calibration procedures

30.3.2021 Jan Friedrich 28

30.3.2021 Jan Friedrich 29

Real-photon energy spectrum

 MC simulation of 500k events in qµ =0.3 … 2 mrad, Eg > 1 MeV

 800
 ISR effect

 700
 104
 600
 srad µ 1/Ekin
 500

 3
 10 400

 300 0.05 < Eg /GeV < 5

 102 200

 100

 0
 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -3 -2 -1 0 1 2
 Eg [GeV] log10( Eg /GeV )

 ISR effect: if incoming muon loses much of its energy, the scattering off the
 proton under a specific scattering angle happens at lower average Q2 and
 accordingly a larger cross section
30.3.2021 Jan Friedrich 30

Impact on Q2 reconstruction

 0.045 5
 Q2p = 2Mp Ekin 10

 0.04
 4
 0.035 10

 0.03
 3
 10
 0.025

 0.02
 2
 10
 0.015

 0.01
 10

 0.005

 0 1
 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
 Q2µ = (p µ qµ)2

 real-photon emission distorts the kinematics, correlation of reconstruction
 from muon and recoil proton becomes blurred

30.3.2021 Jan Friedrich 31

PRad

 from: H. Gao, ICSAC2019,
 Losinj, Croatia
30.3.2021 Jan Friedrich 32

General cross-section behavior

 • steep increase towards smaller Q2 with 1/Q4
 • forever rising? µ
 • not for scattering off atoms / molecules:
 p

 that’s what
 mainly
 happens

 that’s what
 atomic scale we are
 a-2 ~ 10-11 GeV2 interested in

30.3.2021 Jan Friedrich 33