Size of the proton

Sai Neha Santpur290E

22nd March 2017

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Outline

● The puzzle

● Motivation

● Hydrogen spectroscopy

● ep elastic scattering

● Muonic Hydrogen

● Possible explanations

● Future

● Summary

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The puzzle

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The puzzleEarly electron scattering experiments

Recent electron scattering experiments

>5

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The puzzle (Simplified version)

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Motivation

● Hydrogen – simplest atom and perfect for comparison between theory and experiment

● Looking back..

Balmer series Bohr model and quantum mechanics

Spin-orbit coupling Validated Dirac equation

Lamb shift Quantum Electrodynamics

Proton radius puzzle ???

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Hydrogen spectroscopy

● Lamb shift measurement

Lamb shift

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● Theoretically, simplified result for Lamb shift for S states can be written as

where R is Rydberg constant

and rp is the proton radius

– What does this tell us?

1. Lower n more sensitive to rp

2. Higher n Precise measurement of R

2. You need at least two transitions to comment on rp from Lamb shift measurements

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● Experimentally,

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ep elastic Scattering

where Q2 = Momentum transfer

GE and GM are electronic and magnetic form factors

= Q²/4m²

= lab scattering angle and

Here, proton radius is obtained by finding slope of GE when Q2=0

One photon echange

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Phys. Rev. C 93, 065207

Mainz A1 collaborationr

p = 0.895(20) fm

Modern scattering experiment values are more or less the same.

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Muonic hydrogen

● m ~ 105 MeV and me ~ 0.5 MeV

● Back of the envelope calculation:

– Probability of lepton being inside proton radius =

where mr = reduced lepton mass

– Probability of muon being inside proton radius is 8 million times more than electron!

– Muon must be more sensitive to proton radius.

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● Experimentally challenging!

Dominates

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2010 experiment

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● Using simplified expression for the transition after considering the Lamb shift and hyperfine splitting, the energy expression is

● Result: rp = 0.84184(67) fm

Previously agreed result: 0.8768(69) fm

>5 deviation!! Experimental artifact?

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● Using simplified expression for the transition after considering the Lamb shift and hyperfine splitting, the energy expression is

● Result: rp = 0.84184(67) fm

Previously agreed result: 0.8768(69) fm

>5 deviation!! Experimental artifact?

● Measured same transition in H and found

rp = 0.84087(39) fm

>7 deviation!!

No!2013 experiment

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Possible explanations

● Depends on which theorist you ask!

– Quantum gravity

– Extra dimensions

– New boson?

...

● Experimental error in measuring Rydberg Constant?

– Error of the order 1012 can explain this dicrepancy.

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Future

● PRad (New Proton Radius experiment)

● MUSE (MUon Scattering Experiment)

● Spectroscopy of electronic atoms and ions to determine Rydberg constant to very high precision.

● Muonic deuterium

● Muonic helium vs electronic helium

...

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PRad

● Experiment at Jlab

● ep elastic scattering method

● Data taken: May-June 2016

● Result: Coming soon!

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MUSE

● p elastic scattering

● This is messy– Muon beams have lower flux

– Need higher acceptance spectrometer

– Might decay into electrons

– Higher background due to ,e-

...

● Status: Not operational yet!

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Summary

● Proton radius measurement has significant discrepencies.

● Different experiments are using different techniques to make an independent measurement of the radius.

● Many more results to come in the future..

– which could either resolve the discrepancy or lead to some new physics

● Stay tuned!

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References● Muonic Hydrogen: https://www.jlab.org/indico/event/160/session/0/contribution/97/material/slides/0.pdf

● Nature 466: 213-216, 2010

● Science 339 (6118), 417-420

● http://www.physics.rutgers.edu/~rgilman/elasticmup/

● Annu. Rev. Nucl. Part. Sci. Vol 63 (2013)

● Particlebites.com

● https://www.jlab.org/prad/collaboration.html