Proposal for high precision measuremens of the e-p differential cross section at small t-values with the recoiled proton detector Rp = 0.877 fm or Rp =0.841 fm ??? A.Vorobyev Petersburg Nuclear Physics Institute Mainz April 6, 2016 Meeting at Mainz April 6, 2016

Proposal for high precision measuremens of the e-p differential cross section at small t-values with the recoiled proton detector Rp = 0.877 fm or Rp =0.841 fm ??? To buy or not to buy ? A.Vorobyev Petersburg Nuclear Physics Institute Mainz April 6, 2016 Meeting at Mainz April 6, 2016

The main goal of the proposed experiment To measure absolute dσ/dt in the t-range 0.002 – 0.04 Gev2 with ≤ 0.2% point -to-point precision ≤ 0.2 % absolute precision This could distingwish the two options (0.887 fm and 0.844 fm) on the 7σ confidence level ~1/t2 0.001 0.04 -t,GeV2 0.02 -t = 2MTR

The proposed experiment is based on the recoiled proton detection method which was used in WA9 and NA8 experiments at CERN to measure small angle pp- and πp- scattering. RecoiIed proton detector ICAR at CERN

Detector ICAR in WA9/NA8 experiments at CERN Time-projection hydrogen ionization chamber Active target +10 kV 0kV -15 kV H2 10 bar Drift velocity: (1±0.003) mm / 200 ns σ(z) : ± 300 µm Gas target thickness: ± 0.4% -t = (Pπ θS )2 E π θS π 106 /sec p TR- proton energy σ(TR) = 70 keV σ(θR) = 2 mrad (≥4MeV) -t = 2MpTR 100,0±0.1 mm

Advantages and problems of the recoil method -t = (Pπ θS )2 π π No wall effects Well defined gas target thickness 100% angular acceptence Absolute measurement of dσ/dt -t = 2MpTR High resolution in TR (>100 resolved points in 0.001 to 0.04 GeV2) t - value does not depend on the scattering particle’s energy TR – θS correlation (BG rejection) θR –measurement (additional constraint) However, TR scale needs to be precisely calibrated !!!

0.4% TR-scale calibration 1% absolute precision in dσ/dt An example from cross sections of πp- and pp- scattering measured with ICAR Nuclear Physics B217 (1983) 285-335 ρ= ReA(0)/ImA(0) b = dσ/dt(t=0) 0.4% TR-scale calibration 1% absolute precision in dσ/dt

Measurements of ReA(0)/ImA(0) in π-p scattering confirmed the validity of the forward dispertion relations and allowed to predict the rise of the πp total cross sections at least up to energy of 2000 GeV. Nuclear Physics B217 (1983) 285-335 ρ= ReA(0)/ImA(0) in π-p scattering π±p total cross sections

Measurements of dσ/dt(t=0) in πp- and pp-scattering discovered Universal shrinkage of the hadronic diffraction cone at high energies with α’P=0.14 GeV-2 Nuclear Physics B217 (1983) 285-335

Study of elastic scattering of exotic nulei on proton Nuclear Physics A766 (2006)1-24 11Li 11Li p 4He, 6He, 8He 6Li, 8Li, 9Li, 11Li 7Be, 9Be, 10Be,11Be, 12Be, 14Be 8B 13C,14C,15C,17C. ICAR in GSI 10

Extraction of proton radius from differential e-p cross section 0.002 0.04 -t,GeV2 0.02 -t = 2MTR

Difference between cross sections corresponding to Rp=0.84 fm and Rp=0.88 fm RpE =RpM=0 Electrons 500 MeV RpE =RpM=0.84 fm RpE =RpM=0.88 fm Main t-range:1MeV ≤ TR ≤ 10MeV Measurements up to TR =20 MeV help to see non-liniarity effects ∆ Rp = 1.2% at TR =10 MeV 0.2% precision in dσ/dt is needed to distingwish reliably the two options

Problems of large scattering angles Pe = 500 MeV/c eS e θS -t=2MTR θR p Sin(θR) = (εe+М)ТR /(РeРR)

Combined recoiled proton @ scattering electron detector H2 20 bar Film separating volumes Ar+CH4 20 bar e-detection coordinates σX = σY = 30µm 0.5 mm Be window σ(θS) ≤ 5 ·10-4 -15 kV -90kV -15kV Scattering point coordinates σX = σY = 30µm ( determined by beam telescope) σZ = 150 µm (determined by TPC)

Why 20 bar ? To stop 10 MeV protons inside the sensitive volume. Also, to increase counting rate. P=20 bar 10 MeV TR MeV R mm 1 4,7 2 16 3 33 4 55.5 5 83.5 6 116 7 154 8 196 9 244 10 296 20MeV 1MeV 5 MeV Diam 700 mm

Lower pressure can be used for measurements at the lowest t-values with better TR resolution 4 MeV P=4 bar TR MeV R mm 1 23.5 2 80 3 165 4 277 3 MeV 2 MeV 1 MeV Diam 700 mm

H2 20 bar Ar+CH4 20 bar Mylar foil TPC Electron detector CSC

CSC TPC

Gas pressure up to 20 bar Pressure control 10-4 Temperature control 0.1 deg H2 purity 10 -7 Diameter 1 meter Length 2 meters

Comparison of the TPC parameters in the WA9/NA8 experiments with those in the proposed experiment H2 pressure 10 bar 20 bar, 4 bar Drift distance, mm 100,0 ± 0.1 300,0 ± 0.1 Drift velocity,mm/200ns 1,000 ± 0,003 1,000 ± 0,001 σ(z-coordinate) ±300µm ±150µm σ (target thickness) 0.4% 0.1% σ (TR) 60 KeV 40 KeV TR-scale calibration 0.5%

TR –scale calibration - t = 2MTR To determine t with 0.1 % precision from the scattering angle one should provide better than 0.05% absolute precision both in θs and in Ee . !!! Request to the accellerator Absolute value of Ee better than 5·10-4

Measurement of absolute value of beam momentum NIM 177(1980)353-359 Gas filling He(90%) + H2 (10%) (P*θ)2 = 2MTR 234 U Eα 4 774,6 кэВ (71,38 % Absolute precision σP= 0.05%

Possible TPC calibration in hadronic beams For example, in a proton beam at Gatchina synchrocyclotron. ep- scattering 500 MeV Advantages: \ Flat dσ/dt. Higher rates Higher precision. Goal : Calibration of TR –scale to 0.1% precision pp-scattering 250 GeV -t=2MTR

Statistics and beam time Target thickness = 5.2·1022 p/cm2 P =20bar L =50cm Beam intensity 2·106 sec-1 Running time 18 days (1.5 ·106 sec) N events norm t-scale σ(Rp) 1.5 ·107 fixed to 1 fixed ± 0.002 fm free ± 0.003 fm Goal: σ(Rp) ≤ ± 0.005 fm

Radiative corrections

Radiative corrections Two advantages Wide kinematic range, experimental cuts can be varied offline • Control of radiative corrections at the smalles t –values by absolute measurement of dσ/dt.

Conclusions The proposed experiment could provide measurements of the ep- elastic cross sections in the t-range from 0.002 to 0.04 GeV2 with 0.2% point-to-point and 0.2% asolute precisions. This would allow to extract the proton radius with 0.5% precision This experimental method could be applied also to study the small angle scattering on deuterium and 4He. Also, there is a possibility to extend the t-range up to 0.08 GeV2 by filling the TPC with CH4.

Back up slides

Vacuum polarization correction Q2 GeV2 e-loop µ-loop 0.002 1.13% 0.02 1.49% 0.048% 0.04 1.59% e,µ,τ

Electron vertex correction Q2 Gev2 δvertex 0.0001 -2.12% 0.002 -6.26% 0.02 -10.85% 0.04 -12.46%

Real photon emission by electrons ln Sp(0)=0 Sp(1)= π2/6

Partial mutual cancellation of δV and δR δV +δR = δV +δR(1 )+δR(2) = = α/π {3/2 ln(Q2/m2) -2} + α/π {ln(∆E2/EE`) ln(Q2/m2) } Q2 Gev2 δV +δR(1 ) δR(2) ∆E/E=0.1 0.0001 1.6% -6.3% 0.002 2.65% -9.58% 0.02 3.43% -12% 0.04 3.69% - 12.76 Note that δR(2) depends on the experimental conditions (cuts). Hope in our experiment it will be much less and controlable ( the cuts mostly off-line )

Two Photon Exchange correction example: Pe =500 Mev, Q2 = 0.02, θ = 16 deg, ε = 0.98, a and b were free parameters in the fits and were obtained to be a ≈ 0.1 and b ≈ 0.4 GeV-2 Therefore δTPE ≈ 10-5 at Q2 =0.02 GeV2

Corrections with proton contributions Relatively small corrections But to be understood

∆Es cuts in A1 855 MeV

e-p - Scattering Layout Block Diagram RPD ESD HV1 RPD_FE ESD_FE RPD_LOG BD BD_FE BK X Y ESD_LOG BK_LOG CRB Ethernet Beam RST TR ESD (RQ; DT; CL) RPD (RQ; DT; CL) BD_FE - Beam Detector Front-End RPD_LOG – RPD Logic RPD_FE – Recoiled Proton Detector Front-End ESD_LOG = TSD Logic ESD_FE – Electron Scattering Detector Front-End BK_LOG – Beam Killer Logic CRB – Control Readout Box TR – Trigger, RQ – Request, DT – Data, CL – Clock, RST - Reset e-p - Scattering Layout Block Diagram

Fig.2 e-p - Scattering Trigger, Control & Readout Timing Diagram DATA ENCODING & READOUT REQUEST 100 ns ESD: RQ ~ 70 mks RPD: CL ~ 10 mks TRIGGER TR = BD·BK ESD: DT RPD: RQ RPD: DT ESD: CL RST READOUT TR Reset if no ESD_DT Fig.2 e-p - Scattering Trigger, Control & Readout Timing Diagram