Standard Model and ion traps: symmetries galore. Jason Clark Exotic Beam Summer School July 28 August 1, 2014

Transcription

1 Standard Model and ion traps: symmetries galore Jason Clark Exotic Beam Summer School July 8 August 1, 014

2 Lecture outline Overview of the Standard Model (SM) Nature of the weak interaction and β decay Tests of the SM description of the weak interaction β-ν correlations unitarity of CKM matrix constancy of Ft values searches for neutrinoless double β decay Methods used to test SM description of weak interaction Paul trap Penning trap

3 Standard Model Extremely successful at describing the world around us in terms of basic constituents and their interactions. Still some open questions: what is dark energy? how did the matter/antimatter asymmetry come to be? Is there something beyond the Standard Model?

4 Tests of the Standard Model: Superallowed Fermi β decay The nucleus is a complex quantum system not generally amenable to an exact description. However, by a proper choice of nuclear system, specific physical processes can be isolated and determined to high precision. (Ex: Superallowed Fermi β decay) Relationship between partial halflife, matrix element, and phase space: A Z 0 +# Q β" t 1/" BR " Ft ft A Z-1 t 1/ And including a bunch of small-ish corrections: = BR G ( V M F f Z, Q β ) 0 +# ( ' + δ )( 1+ δ δ ) K Rearranging gives ft value : ft = 1 R NS C = GV ~1.5% % K G V K ( 1+ Δ V ) R.4% M F = For decays

5 Many things we can investigate after studying several different nuclei Ft constant for decays? Conserved vector current in weak interaction d! u! ν! β# symmetry between EM and weak interaction conservation of vector part of weak interaction (like conservation of charge) V ud from u d transformation! V Value of Ft? Test unitarity of CKM matrix Determine G V and compare to purely leptonic µ decay (G µ ) to extract V ud matrix element = ud G V G µ V ud + Vus + Vub = 1?

6 Penning traps improve precision of previouslystudied isotopes and provide access to new ones Ft value depends strongly on Q b f ( ) Z, Q ~ Q 5 β β Penning trap measurement of 46 V uncovered systematic shift in previous data from ( 3 He,t) measurements Difference between earlier ( 3 He,t) measurements of Q value and modern data Penning traps allow measurement of isotopes where both parent and daughter are radioactive G. Savard et al., PRL 95, (005) Figure from J.C. Hardy

7 Results and impact on weak interaction physics Constancy of ft values: Values constant to ±0.4% for all nuclei conservation of the weak C V current (like EM current) Determine V ud matrix element: V ud = ± And when combined with V us + V ub, gives the unitarity test: V ud + V us + V ub = ± J.C. Hardy and I.S. Towner, PRC 79, (009). Towner & Hardy, Rep. Prog. Phys. 73, (010).

8 Are neutrinos their own antiparticle? What is the neutrino mass scale and hierarchy? Only known way to determine this is neutrinoless double beta decay (0νββ decay). In principle, this is a clear signature but extremely sensitive techniques are required ordinary νββ decay! Equal numbers of! matter ( β ) and antimatter ( ν ) emitted! 0νββ decay! Only matter ( β ) emitted! Broad β energy spectrum (neutrinos escape detection)! Observed:! T 1/ ~10 1 years! Signal at total decay energy! (all energy detected)! Recognized in 1930s! but never been observed:! T 1/ >10 5 years! A mechanism for matter/antimatter asymmetry!

9 Penning traps precisely determine where to search for very tiny signal Penning traps have pinned down Q values for the isotopes to <1 kev νdbd electrons carry away all the decay energy 0νDBD 76 Ge B.J. Mount et al., PRC 81, (010) S. Rahaman et al., PLB 66, 111 (008) G. Douysset et al., PRL 86, 459 (001) 130 Te S. Rahaman et al., PLB 703, 41 (011) N.D. Scielzo et al., PRC 80, (009) M. Redshaw et al., PRL 10, 150 (009) D.A. Nesterenko et al., PRC 86, (01) 8 Se D.L. Lincoln et al., PRL 110, (013) 150 Nd V.S. Kolhinen et al., PRC 8, 0501 (010) 48 Ca M. Redshaw et al., PRC 86, (01) + others

10 Confining ions with both electric and magnetic fields the Penning trap F.M. Penning H. G. Dehmelt

11 The not so easy way to confine ions in 3D z y x V z y x λ λ λ + + = z y x λ λ λ 1 = = Taking the general form of 1D confinement and extending it to 3D: Result it that: ) ( z y x V + = λ ) ( z r V = λ Or in cylindrical coordinates:

12 The not so easy way to confine ions in 3D If we define: then: V ϕ o = at (r,z) = (±r o,0) λ = ϕ o r o r r r r Result is equipotential surfaces: z o r o z o r o = 1 = 1 with with V ϕ o = V ϕo = Dimensional constraint: & $ % r z o o #! " =

13 Ions within a magnetic field B constant axial magnetic field particle orbits in horizontal plane with cyclotron frequency: ω c = qb m free to escape axially

14 Confine ions by adding an electric field Add a harmonic potential (along magnetic field axis) to confine particles. B + Confining potential: Vo V = ( z d & $ z % r Characteristic trap dimension: d = 1 r o o + ) #! " +

15 Motion of ions in a Penning trap B + Equations of motion: F = q( E + v B) + Along magnetic field axis: qv m z = d z Ions undergo oscillations with frequency: ω z = ev md

16 Motion of ions in a Penning trap F = q( E + v B) Effect of the electric field is to split the radial motion into two components: ω c Radial equations of motion: ω z x = x + ω y y ω z = c y ω x c ω+ ω ω + : reduced cyclotron motion ω - : magnetron motion ω ± ωc = ± ωc 4 ω z

17 Putting it all together the frequency hierarchy picture from Frequency relations: ω = ω + ω + ω c + z ω = ω + ω Frequency hierarchy: c + ω << ω << ω ~ z + ω c Frequency values for singly charged ions in a Penning trap with parameters r 0 =14.4 mm, z 0 =8.9 mm, U 0 =10 V, and B=5.9 T, as functions of mass number A.

18 Determining mass of ions in a Penning trap ω Since: c = ω + + ω = ω c depends only on: qb m So if we can find a stable, uniform magnetic field, we can use ω c to make accurate and precise mass measurements. The solution: use a superconducting magnet the mass the magnetic field not on the electric fields

19 The Canadian Penning trap Hockey puck Cigarette

20 Detection of the energy gained from frequency conversion MCP F = F z TOF Detection After excitation, ions are ejected from the trap and guided toward a microchannel plate ion detector Magnetic field gradient outside the Penning trap converts any radial energy into axial energy Higher energy ions arrive with shorter time-of-flight B 0 Magnetic field lines outside the Penning trap B = 0 Linear Energy Orbital Energy Ions from the Penning trap

21 Determining the cyclotron frequency MCP B 0 Magnetic field lines outside the Penning trap B = 0 F = F z TOF Detection Linear Energy Orbital Energy TOF ( µ s) Perform frequency scan where each new bunch of trapped ions is subjected to a different frequency Repeat frequency scan many times to get statistics Sample TOF spectrum: Applied Frequency Hz Ions from the Penning trap ω c = qcb m c c

22 Sample time-of-flight (TOF) spectrum 60 ω c = qcb m c c (TOF in microseconds) / FWHM ~ 5 Hz Unknown: ω? = q? B m? c Applied frequency Hz Unknown Calibration => m? = q q? c ωc m ω? c Well-known mass is a requirement for accurate measurements. 48$

23 What to use as a calibrant? Want to use a well-known mass. Most precise masses: 1 C: Δm = 0 4 He: Δm = 0.06 ev 1 H: Δm = 0.09 ev 16 O: Δm = 0.15 ev Generally, we use compounds of 1 H and 1 C: masses are known precisely and hydrocarbons cover essentially all masses.

24 Energy and mass and precision E = mc Proton: E = ( kg)( m/s) = J = GeV me: E = (7.5 kg)( m/s) = 40 EEeV For A=100, mass precision obtained ~ 300 ev => 3x10-9 precision That s like measuring my mass to kg!

25 Sample TOF spectra 60 Calibration: C 5 H 8 Resolution = Δω FWHM ω (TOF in microseconds) / FWHM ~ 5 Hz Δω FWHM ~ 0.9 T conv Applied frequency Hz Precision, Δm m T conv m qb N

26 Increasing mass precision Precision, Δm m T conv m qb N Limited by half-life of nuclide Higher charge states Stronger fields Statistics For measurements on shortlived isotopes the limiting factors are T CONV and N.! Uncertainty in kev s excitation 1 s excitation 0.5 s excitation 0.1 s excitation 0.05 s excitation 1.E+0 1.E+04 1.E+06 1.E+08 Number of ions

27 Summary! Standard Model is a robust model that describes basic constituents of nature and the interactions between them yet still unresolved issues (matter-antimatter asymmetry, dark energy, )! Low energy tests of SM description of weak interaction (β decay) have been quite fruitful β-ν correlations unitarity of CKM matrix constancy of Ft values searches for neutrinoless double β decay! Ion traps becoming one of the most used tools for precision tests of SM model: Paul trap Penning trap! Potentially many new discoveries/advances early in your career!

28 Questions?