Der rätselhafte Protonradius-

Measurement of the proton radius in muonic hydrogen

rp=?

Motivation● Protons are the basic building block of the visible

matter in the universe

● Hydrogen (H) is the most simple bound state

● Proton properties (charge, mass, size) are essential input parameters to theories of proton and hydrogen

● proton -> quantum chromodynamics (QCD)● hydrogen and similar systems

→ bound state quantum electrodynamics (QED)

● comparison of predicted and measured energy levels in hydrogen allow precision tests of theory

● Muonic hydrogen allows more precise measurement

„To understand hydrogen is to understand all of physics“

(Victor Weisskopf, 1908-2002)

● Lepton universality theorem predicts same coupling to all gauge bosons, in particular to photons

Differences between e- and µ-

→ apart from their mass, electrons and muons should behave identical

p

e-

(ep) (µp)

● Muon is much more likely within the proton than the electron → muon „feels“ proton much stronger

µ-

Differences between (ep) and (µp)

.. x200 ..

(CODATA: Committee on Data for Science and Technology)

Outline

● What means rp ?

● Theory of hydrogen and alikes

● Measurement of rp in muonic hydrogen

● Interpretation of the result

Definition of rp

● The geometric shape of a proton is defined by it's formfactor F(q²)

● Differential cross section for elastic e-p scattering with momentum transfer q

→ Not consistent with QED

● In general the proton structure can be seperated into electric (E) and magnetic (M) formfactors (Rosenbluth-formula)

Convention: ,

Scattering angle:

„Sachs“ electric Formfactor:

~ Probability to absorb a photon

Convention:

For point-like particles:

● A series expansion of GE(Q²) leads to

Theory of hydrogen and alikes

● a bound state of two oppositely charged particles,

● solved by quantum mechanics (Schrödinger equation with central potential)

● Bound state characterised by quantum numbers: n=1,2,..; l=0,..,n-1; ml = -l … +l

● Applicable to many two-body systems:hydrogen (pe), positronium (e+e-), muonium (µe),muonic hydrogen (pµ)

(Laguerre-polynoms) (spherical harmonics)

Energy levels and light emission● In a central potential:

Hydrogen spectrum

● Stronger splitting in (µp)

● Reduced mass

Energy corrections - I● Finestructure splitting of the spectrum

● 1. Relativistic corrections (Darwin term)

● 2. L-S coupling between electron-spin (→ magnetic moment) and B-field from e-p rotation (Biot-Savart-law)

● Proton-size has no measurable impact on finestructure (∆E ~ 10 neV)

n=1 → l=0 , s=1/2 → j=1/2

n=2 → l=1 , s=1/2 → j=3/2

→ l=1 , s=1/2 → j=1/2→ l=0 , s=1/2 → j=1/2

(singulett)

(triplett)

Hyperfinestructure and Lamb-shift

● Hyperfinestructure (HFS):

● L-S coupling between Le and Sp

● much smaller effect (1/700) w.r.t Le-Se

● F = Le+ Se + Sp = J + Sp = J ± 1/2

● Lamb-shift:● Explained by quantum electrodynamics (QED)● Exchange of virtual photons between µ and p● Energy splitting:

→ HFS and Lamb-shift are sensitive to finite-size effects of the proton

Hyperfine-structure and Lamb-shift

Energy emissions:

● Decoupling of Lamb-shift and hyperfinestructure

● How does proton radius affect energy levels ?→ Pertubation theory

True Coulomb potential

Potential of a point-like proton

Probability amplitude for absorbing a photon

Using good approximation for low momentum transfer:

~

QED Feynman diagramfor muon-protoninteraction (lowest order)

→

Vacuum polarisation of virtual photon

Modification of the muon mass

Additional corrections

+ many more (~60)

Theoretical prediction of the Lamb-shift

Measurement of rp in muonic hydrogen● Measured at Paul Scherrer Institut (PSI), CH

● In 1999 the first confirmed creation of µp in the 2S state was accomplished, 2009 first results

● Principal workflow – Part I:

H2

muon beam

rate < 1 µ- / msE = 3 – 6 keV

Time-of-flightdetector (ToF)

Identifies muons and provides a start signal for the pulsed laser system (coincidence trigger)

Gas tank

H2 at p= 1 mbar capturesmuons and µp atoms are formed, ~1% of the µp atoms are in longe-lived (1µs) 2S state

t=0

● Principal workflow – Part II:

µp(2S) µp(2S) → µp(2P) → µp(1S) +

Timeline (ns)0 1000

A laser system is triggered.The lasersystem creates a 5-ns laser pulse, tuneablefrom = 5.5 – 6 µm, illuminating the µp from t= 900 … 975 ns

900

975

Laser light excites (or not, in dependence of ) µp to 2P state which immediately (8.5ps) deexcites to 1S state and radiates 2 keV x-ray. X-ray detection must happen in coincidence with illumination.

Target laser cavity

LAAPD – Large area avalanche photo diodes

← Front view: - The LAAPD detect the X-rays - Plastic scintillators (red) detect electrons from µ decay

Top view → The laser cavitiymakes the laser illuminate thetarget volumehomogenously

The measurement● In dependence of the laser wavelength the rate of

2keV X-rays is measured → on-resonance

● The background rate is measured without laserilluminating the target volume → off-resonance

● Up to 13 hours of data taking per laser wavelength

● Background reduction by requiring

● X-ray photon has E ~ 2keV ● Delayed electron detected from µ- decay

after x-ray detection● No 2nd muon is detected in coincidence

(The proton radius determined from other experiments was translated into resonance frequencies)

Interpretation of the result● The discrepancy is about 75GHz, about 4 times the

natural line width of 18.6GHz

● 1. Main Systematic errors that are considered

● calibration of the laser frequency (300MHz)● Zeeman shift in 5T field (< 60MHz)● Doppler shift (<1MHz)

● → many possible effects are smaller in µp due to the smaller size and the heavy muon

(Zeeman effect)(Bohr magneton)

● 2. Theory of hydrogen is well known,uncertainties of theory are comparable toexperimental ones

● 3. „New physics“Discrepancy could be explained by breaking lepton-universality, i.e. muons and electrons behave differently→ New interactions that distinguishbetween electrons and muons

Leptoquarks● Leptoquarks are bosons (Spin=0,1) that carry

electric charge and colour charge and allow interactions between quarks (q) and leptons (l)

● Basic Feynman diagrams

Coupling constantdiffers for e and µ:

New Proton-muon interaction

Proton = uud

Proton = uud

Problems with new theories

● New interactions will also be visiblein other experiments, e.g.

● Inelastic muon-proton scattering

Proton = uud

Neutron = ddu

Result from 2013

[….]

Summary

● The theoretical and experimental aspectsof the proton radius measurementin muonic hydrogen were presented

● The experimental results differ significantly from other results and leave room to „New physics“

● Until today there is no consistentexplanation of the „proton-radius puzzle“

Backup

Probability density distribution

1s

2s 2p

Bohr radius:

Vacuum polarisation of virtual photon

Uehling potential:

Radius-independent contributionsto Lamb-shift

Radius-dependent contributionsto Lamb-shift in µp

All contributions to 2S-HFS in µp

Scheme of the experiment

Bohrsches Atommodel mit e

Weblinks

● http://www.mpg.de/849869/forschungsSchwerpunkt?c=166500

● https://www.mppmu.mpg.de/~rwagner/skript/Quarkverteilungen_Nukleon.html

● http://www.semibyte.de/wp/physics/atomphysics-qm/grundlagen-quantenmechanik-und-statistik/

● http://www.tphys.physik.uni-tuebingen.de/muether/faessler/nuclear.html

●

AbstractDie Vermessung des Protonradius ist eines der grundlegendsten Experimente der Physik und kombiniert Aspekte der Atomphysik, Quantenoptik und Quantenfeldtheorie. Neue experimentelle Techniken ermöglichen die indirekte Bestimmung des Protonradius durch die Messung der Lamb-Verschiebung in myonischem Wasserstoff. Dabei handelt es sich um einen kurzlebigen, gebundenen Zustand aus einem Proton und einem Myon. Aufgrund ihrer etwa 200 mal größeren Masse sind Myonen viel näher am Proton und die Aufspaltung der Energieniveaus stark sensitiv auf die Größe des Protons.Vor kurzem durchgeführte Experimente mit myonischen Wasserstoff zeigen dabei eine Abweichung des so bestimmten Protonradius von 7 Standardabweichungen im Vergleich zu normalen Wasserstoff. Dies könnte ein Hinweis sein auf neue Wechselwirkungen jenseitsder bekannten Physik.In meinem Vortrag werde ich auf die theoretischen und experimentellen Aspekte des Versuches eingehen und möglicheSchlussfolgerungen vorstellen.