Workshop on Progress on J-PARC Hadron Physics in 2014
Measurement of the proton Zemach
radius from the ground-state hyperfine
splitting energy in muonic hydrogen
RIKEN
Masaharu Sato
1/Dec/2014
Outline

Introduction and physics motivation

Experimental principle

Feasibility in J-PARC MLF

Summary
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Introduction
proton : a building block of the Universe
 structure of the proton is one of the most fundamental observables in the
atomic and nuclear physics
electric/magnetic form factor, proton radius etc
Muonic hydrogen atom
exotic atom composed with m- and p
mμ/me ~ 200, R ~ aB/200
μp
probability in the proton :
(rp/aB)3 = (ammp rp )3 ~ 8 x 106
bound m feels the effect of the proton structure
Muonic hydrogen atom is good tool to study the internal structure of proton
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Lamb shift in muonic hydrogen
r.m.s. charge radius RE : measured many times by e-p scattering and H spectroscopy
PSI group:
CODATA 2006 RE = 0.8768(69) fm
Laser spectroscopy of 2SF=11/2 2PF=23/2 (Lamb shift) of muonic hydrogen (μ-p)
μ-p
Measured value : 206.2949(32) meV R. Pohl et al., Nature 466 (2010)
DELamb = : 209.8778(49)-5.2262 RE2 + 0.0347 RE3 meV
RE = 0.84184(67) fm
X10 better precision
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Proton radius puzzle
 “electronic” (hydrogen spectroscopy / e-p scattering )
 “muonic” (muonic hydrogen Lamb shift )
e-p & H
μ-p
7s
~4%
“Proton radius puzzle”
Still unsettled question:
errors in the measurements?
structure-dependent corrections are wrong?
QED needs modification (in m- p interaction)?
new physics beyond the Standard Model?
What about magnetic distribution?
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Motivation
proton Zemach radius Rz
(convolution of charge (rE ) and magnetic moment (rM ) distributions)
proton electronic & magnetic structure
Hyperfine splitting
determined from hyperfine splitting energy of H-like atom
𝑡ℎ
D𝐸𝐻𝐹𝑆
= 𝐸𝐹 1 + 𝑄𝐸𝐷 + 𝑠𝑡𝑟
 EF :Fermi energy
13S1 (F=1)
1S
DEHFS
 QED :higher order QED correction
11S0 (F=0)
 str :proton structure correction
str = 𝑍𝑒𝑚𝑎𝑐ℎ + 𝑟𝑒𝑐𝑜𝑖𝑙 + 𝑝𝑜𝑙 + ℎ𝑉𝑃
𝑍𝑒𝑚𝑎𝑐ℎ = −2a𝑚m𝑝 𝑅𝑍 + 𝑂 𝛼 2
F : total angular momentum
directly connected to Rz
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Past measurements on Zmeach radius
hydrogen spectroscopy
Rz =1.037(16) fm Dupays et al., PRA(2003)
=1.047(19) fm Volotka et al., EPJ(2005)
e-p scattering
Rz =1.086(12) fm Friar & Sick, PLB(2004)
=1.045(4) fm Distler et al., PLB(2011)
muonic hydrogen 2S HFS
Rz = 1.082(37) fm
 Latest values of e-p and H spectroscopy are consistent within
their errors.
 m-p value differs? But accuracy is insufficient to verify.
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Our strategy : measurement of μp 1S DEHFS
muonic hydrogen 1S HFS energy  not measured before
laser spectroscopy : 0.183 eV = ~6.78 mm (= ~44.2 THz)
Goals
:
mid-infrared laser is needed
determine 1S DEHFS with an accuracy of ~ 100 MHz (~ 2 ppm)
due to accuracy of frequency
the 1st precise measurement of g.s. DEHFS of μ-p
fundamental quantity of μ-p system
(can determine proton structure correction (str) with ~ppm accuracy)
derive the proton Zemach radius from DEHFS
𝑅𝑍 =
𝐸𝐹 (1 + 𝑄𝐸𝐷 + 𝑟𝑒𝑐𝑜𝑖𝑙 + 𝑝𝑜𝑙 +
𝑒𝑥𝑝
ℎ𝑣𝑝 − D𝐸𝐻𝐹𝑆
/2a𝑚m𝑝
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Expected precision
𝑅𝑍 =
𝑒𝑥𝑝
𝐸𝐹 (1 + 𝑄𝐸𝐷 + 𝑟𝑒𝑐𝑜𝑖𝑙 + 𝑝𝑜𝑙 + ℎ𝑣𝑝 − D𝐸𝐻𝐹𝑆 /1.281(8?)
1130(1) ppm 1700(1) ppm
460(80) ppm
20(2) ppm
(2) ppm
Dupays et al., PRA 2003
RZ = 1.0??(12) fm
Improved factor ~3 from PSI results
Proton polarizability term 𝑝𝑜𝑙
dominates in error.
pol = 460(80) ppm
Cherednikova et al., NPA 2002
We need help from theorists for further improvement of precision.
improvement of proton polarizability correction (pol) drastically reduces uncertainty of Rz
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Experimental principle
How to determine DEHFS
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Experimental principle (1)
Laser spectroscopy : signals of the resonance frequency
 decay asymmetry of polarized muons
1) Produce m-p atom by pulsed muon source
e
muonic hydrogen
atomic capture
shoot m- into hydrogen
 g.s. m--p atom
m
p
lifetime ~ 2.2 us
2) spin polarization by laser
13S1 (F=1 )
1S
DEHFS ~ 0.183 eV
polarization
selective excitation
11S0 (F=0 )
polarization in F=1 state
circularly-polarized laser
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Experimental principle (2)
3) detect decay electrons
μ-  e- + νe + νμ
muon decay asymmetry with polarization (P)
𝑑𝜎
𝑒−
1
𝜃 𝑑Ω  1 − 𝑃 cos 𝜃 𝑑Ω
3
polarized
μ- decay
e－
more decay electrons in
opposite direction of muon spin
Spin polarization (= frequency is on resonanace)
can be detected decay asymmetry of muons
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Conceptual design of experimental setup
1) H2 target
Top view of setup
2) tunable mid-infrared laser
3) decay electron counter(forward and backward)
detect forward/backward
electrons
Asymmetry = NF - NB
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Feasibility
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Feasibility
e-
F=0  F=1 transition probability
𝑃=2 ×
10−5
decay
𝐸
𝑆 𝑇
E/S : laser power density [J/m2], T : temperature [K]
excitation by laser
NIM B281(2012)72 & D. Bakalov, private communication
 laser power
 need high laser power
collisional
quench
F=1  F=0 collisional quench rate
competitive process with muon decay in F=1
mp( ) + p  mp( ) + p
then, polarization is lost
tquench VS tm(= ~2.2 us)
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Laser system
tunable mid-infrared laser
(developed by RIKEN Wada group)
frequency ~6.8 um = ~44 THz
band width ~50 MHz
repetition ~ 25 Hz
seeded OPO with ZnGeP2 non-linear crystal
double pulse 10 mJ x 2 sets = 40 mJ
40 mJ laser power is achievable
multi-pass cavity
mirror
mirror
Hydrogen
laser
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Collisional quench rate
 F=1 F=0 quench by collision with surrounding atoms
mp( ) + p  mp( ) + p
F=1
(polarization is lost)
J. Cohen, PRA43(1991)9
quench
quench rate (lQ)
F=0
proportional to H2 density
Quench rate (lQ) at 20 K
timing gate
t = 50 ps at liq H2  gas H2 is needed
If 0.1% LHD (liquid hydrogen density), then tquench = 50 ns
P = 3.7 % in ~700 ns time gate
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Experiment in J-PARC MLF
a proposal submitted to MLF PAC “S1-type project”
Stage-1 approved
18
J-PARC muon facility
World highest pulsed muon source
protons
from RCS
μ- (decay) intensity
(Kawamura san, private communication)
5x105 [s-1] (at 300 kW)
present RCS
Pμ = 40 MeV/c
D-line exp. area
H2 cryostat
detectors
Laser cabin
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Resonance hunting

scanning scheme
𝑠𝑖𝑔𝑛𝑎𝑙
𝑁𝐹 − 𝑁𝐵
𝑆𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑐𝑒 =
=
𝑓𝑙𝑢𝑐𝑡𝑢𝑎𝑡𝑖𝑜𝑛
𝑁𝐹 + 𝑁𝐵
Interval : 100 MHz
range : ±5.7 GHz
(~ Zemach +  pol )
Parameters for estimation
negative muon
5x105 [s-1] (at 300 kW)
Pμ = 40 MeV/c
dp/p = ±10 %
laser ( ~44 THz)
Power
40 mJ
repetition 25 Hz
bandwidth 50 Hz
mirror R 99.95 %
H2 target
density 0.1 % of LHD
resonance search
:
frequency determination :
~22 days
~5 days
expected
spectrum
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Summary
 New measurement of proton Zeamch radius and ground-state
hyperfine splitting energy in muonic hydrogen by spectroscopy with a
mid-IR laser
 Accuracy of DEHFS : ~ 2 ppm and RZ : ~ 1%
(We need help from theory for further precision)
 Experiment is feasible in J-PARC MLF muon facility
~ 1 month beam time (with present RCS power of 300 kW)
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Collaboration
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