Università degli Studi di Ferrara Dottorato in Fisica - XXVI ciclo Ferrara, 13 Dicembre 2013 Spin-tracking studies for EDM search in storage rings Tutor: Prof. Paolo Lenisa External Tutor: PD Dr. Andreas Lehrach Student: Andrea Pesce
Motivation Measure of the permanent separation of positive and negative electrical charges inside the particle itself It has the same direction of the spin vector EDM violates parity P and time reversal symmetry T Assuming the CPT theorem to be valid, the combined CP symmetry is violated
Why it is important to study EDM A strong CP-violation source is required to solve the mistery of baryonantibaryon asymmetry of our universe The Standard Model predicts non-vanishing but unobservally small EDMs: d e SM <10 38 e cm d N SM <10 32 e cm Strong CP problem d n = d p = ( 4.5 10 15 e cm)θ QCD d D = 0 Experimental limits set θ QCD <10 11 Discovery of a non-zero EDM would signal new physics CP violation Models beyond the SM predict EDM values that are detectable for current and future experiments
Searching EDM 1951: Purcell and Ramsey searched for nedm to investigated P violation in the nuclear force First upper limit d n < 3x10-18 e cm dneutral SYSTEMS!! Particle/Atom Current EDM limit Future Goal Neutron <2.9x10-26 ~10-28 199 Hg <3.1x10-29 ~10-29 205 Tl <9x10-25 ~10-28 - 10-31 Proton <7.9x10-25 ~10-29 Deuteron ~10-29
How to measure EDM for charged particles Impossible to trap charged particles in E-field Injection in a Storage Ring with spin aligned to the velocity (Longitudinal Polarization) Freeze the horizontal spin precession and watch for the development of a vertical component External E-field produces a torque on the EDM: Spin precession in the vertical plane EDM SIGNAL τ = d E = d S dt
Storage ring projects BNL all electric ring for protons EDM with E and B-fields at COSY R. Talman A. Lehrach
The frozen spin method Transverse electric and magnetic fields in a ring cause a spin precession in the plane of the trajectory defined by: ω G = ω s ω c = q / 1 m G B ( " 0 + * G $ m 21 )* # p % ' & 2 + β 3 E 1-4,- c 51 BMT Equation " G = g 2 % $ ' # 2 & ω s ω c anomalous magnetic moment spin precession frequency in the horizontal plane particle revolution frequency The aim is to cancel this anomalous spin precession: ω G = 0
Solutions for protons and deuterons Magic condition spin along the momentum vector ω G = q / 1 m G B ( " + G $ m % 0 * ' 21 )* # p & 2 + - β 3 E 1 4 = 0,- c 51 Protons G =1.79 > 0 magic momentum: B = 0 " G m % $ ' # p & 2 = 0 p = m G pure electric ring! = 0.7 GeV c ω ds dt G = 0 = d E Deuterons G = 0.14 < 0 no magic momentum: magnetic field with a radial outward electric field E = GBcβγ 2 1 Gβ 2 γ 2
EDM search and spin dynamics in storage rings Ø The minimal detectable precession angle is d 10 29 e cm Ø If we assume: E =17 MV m T 10 6 s Ø We need the spin to be coherent at least for 10 3 s to detect the EDM signal θ EDM 10 6 rad θ EDM ( t) 10 15 rad turn Spin Coherence Time (SCT) ˆn S ˆn Loss of longitudinal polarization. We have a limited observation time called SCT. At injection spin vectors aligned After some time the spin vectors are all out of phase in the horizontal plane
Spin tracking code Such a precision experiment demands perfect determination of the space dynamics and the spin motion of the stored beam A powerful code to track both the position and the spin of the circulating particles in the ring is requested To this scope, the Juelich collaboration adopted the COSY Infinity code (developed by Prof. Martin Berz at the Michigan State University USA) My task has been to benchmark the code by supporting the spin coherence time tests performed at the COSY ring Only after successful benchmarking, the code can be used for designing an innovative dedicated ring for EDM measurements
COSY-Infinity: Transfer Map Method COSY-Infinity allows to compute the one-turn transfer map for a single optical element in the beam line Using Differential Algebra (DA) techniques to optimize the Taylor expansion cofficients, it calculates the transfer map that relates the initial and the final particle state: z f = Μ z i, δ ( ) z i z f δ where and are the initial and the final condition, is the vector of the system parameters. For a repetitive system, only a one cell map has to be computed: this makes it much faster than ray tracing codes that trace each individual particle through the system.
Spin Tune and Spin Coherence Time The spin tune ν is the number of revolutions of the spin vector around the spin invariant axis in one turn n i = S i S i+1 n i = Si Si+1 sin(ϑ i ) 0 i 2 10 5 " $ ϑ i = arcsin$ $ # Particle displacements (Δx, Δy, Δp/p) cause a change in the spin tune during the motion Such a change is called spin tune spread and it is related to the spin coherence time in the way: S i ni Si+1 % ' ' ' & τ SC 1/Δν S i+1 ˆn θ i S i ν i = θ i /2π
Spin tracking: Reference Particle Deuterons with p = 970 MeV/c 2x10 5 turns S 0 = (0,0,1) S = (S x,s y,s z ) S x S y S z SPIN TUNE: ν RP = Gϒ = 0.1604981 1 spin rotation every ~6.23 turns Polarization Polarization Polarization 1 0.5 Polarization 1 0.5 0 0-0.5-0.5-1 -1 0 20 40 60 80 100 N 0 1 2 3 4 5 6 N
Spin Tune Spread estimation Effect of Δx, Δy and Δp/p on the spin tune Spin Tune vs. Δp/p - Sext OFF - 3rd order ν 0.16049815 0.1604981 0.16049805 0.160498 0.16049795 0.1604979 0.16049785 0.1604978 0.16049775 ν 0.1604985 0.160498 0.1604975 0.160497 0.1604965 0.160496 0.1604955 0.160495 χ 2 / ndf 9.71e-16 / 6 Prob 1 p0 0.1605 ± 6.429e-09 p1-0.0001023 ± 1.642e-05 p2-2.294 ± 0.07249-3 10-0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 Δp/p Spin Tune vs. Δx - RF ON - V = 0.7 KV χ 2 / ndf 3.43e-16 / 12 Prob 1 p0 0.1605 ± 2.078e-09 p1 5.462e-10 ± 6.39e-11 p2-3.106e-09 ± 3.33e-12 ν 0.160499 0.1604989 0.1604988 0.1604987 0.1604986 0.1604985 0.1604984 0.1604983 Δν = <ν> - <ν RP > Spin Tune vs. Δy - RF ON - V = 0.7 KV χ 2 / ndf 2.365e-19 / 12 Prob 1 p0 0.1605 ± 5.458e-11 p1-2.019e-15 ± 1.678e-12 p2 6.652e-10 ± 8.743e-14 0.1604945 0.1604982 0.160494-40 -30-20 -10 0 10 20 30 40 Δx (mm) 0.1604981-40 -30-20 -10 0 10 20 30 40 Δy (mm)
COSY-Infinity vs. Data ν 0.1604985 Spin Tune vs. Δx - RF ON - V = 0.7 KV 0.160498 0.1604975 0.160497 0.1604965 0.160496 0.1604955 0.160495 χ 2 / ndf 5.728e-16 / 12 Prob 1 p0 0.1605 ± 2.686e-09 p1 5.885e-10 ± 8.258e-11 p2-3.091e-09 ± 4.303e-12 0.1604945 0.160494-40 -30-20 -10 0 10 20 30 40 Δx (mm) x exp = 5 mm τ exp = 11.4 s exp = 11.4 s (Ed Stephenson s note on SCT) Scaling using the beta functions: εβ x = ( Δx) 2 Δx COSY = τ COSY = 11.6 s β x(exp) β x(cosy ) Δx exp = 2.73mm Simulated SCT comparable to the measured one
Sextupole Corrections The aim is to use the sextupoles families in the arcs to cancel the spin tune spread due to x and y offsets We start switching on the sextupoles of MXS and MXL families separately, making a K 2 scan to find the maximum of the SCT In the end we will have to check that the two effects add linearly for both x and y offsets: K 2 (MXL) = C 0 + C 1 *K 2 (MXS) To correctly evaluate the sextupoles effect, the sextupole component of the dipoles was implemented in the code
Using two sextupole families it is possible to correct also the vertical offset s effect: K 2 (MXL) = C 0 + C 1 *K 2 (MXS) MXL - MXS Plane - Correction for Δx = 1 mm MXL - MXS Plane - Correction for Δx = 1 mm and Δy = 1 mm ) -3 MXL (m 1.2 ) -3 MXL (m 1.2 Δx Δy 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-3 MXS (m ) 0-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8-3 MXS (m ) The two straight lines cross each other simultaneous cancellation is possible Due to acceptance problems of the COSY ring, no data for the vertical offset case will be available
Radial offset s effect compensation It is necessary to compensate the spin tune quadratic dependence on a radial offset sextupole fields 1 2 = A θ x τ SC + a θ x 2 We need: a = -A offset s effect sextupoles effect τ SC = p 0 k 2 MXS p 1 Run May 2012 Spin Coherence Time vs. MXS - Δx = 1mm - Dipoles Sext Fit Value ON (s) SC τ 6 10 p0 1.512 ± 0.1302 p1 0.756 ± 1.838e-06 5 10 4 10 3 10 0.7556 0.7557 0.7558 0.7559 0.756 0.7561 0.7562 0.7563 0.7564-3 MXS (m )
Conclusions COSY-Infinity correctly reproduces spin dynamics in storage rings Beam-size and momentum distribution limit the Spin Coherence Time of the beam (also in an ideal lattice) It is possible to compensate for these effects by using sextupole magnets, whose contribution increases the SCT The K 2 values in the simulation are a factor ~7 off the measured one, suggesting the presence of further sextupole components in the ring The next step will be to compensate the momentum spread effect