Physics Letters B 736 (2014) 344–349
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Improved estimates of the nuclear structure corrections in μD
O.J. Hernandez
a,b
, C. Ji
a,∗
, S. Bacca
a,b
, N. Nevo Dinur
c
, N. Barnea
c
a
TRIUMF, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada
b
Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2, Canada
c
Racah Institute of Physics, The Hebrew University, Jerusalem 9190401, Israel
a r t i c l e i n f o a b s t r a c t
Article history:
Received
20 June 2014
Received
in revised form 21 July 2014
Accepted
21 July 2014
Available
online 25 July 2014
Editor:
W. Haxton
Keywords:
Muonic
atoms
Nuclear
polarizability
Chiral
potential
We calculate the nuclear structure corrections to the Lamb shift in muonic deuterium by using
state-of-the-art nucleon–nucleon potentials derived from chiral effective field theory. Our calculations
complement previous theoretical work obtained from phenomenological potentials and the zero range
approximation. The study of the chiral convergence order-by-order and the dependence on cutoff
variations allows us to improve the estimates on the nuclear structure corrections and the theoretical
uncertainty coming from nuclear potentials. This will enter the determination of the nuclear radius from
ongoing muonic deuterium experiments at PSI.
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP
3
.
1. Introduction
The root-mean-square charge radius of the proton was recently
determined by spectroscopic measurements of the 2S–2P atomic
shift, i.e., the Lamb shift (LS) [1], in muonic hydrogen [2,3], where
the proton is orbited by a muon instead of an electron as in ordi-
nary
hydrogen. With respect to the CODATA-2010 compilation [4],
which is based on the combined electron proton scattering data
and the spectroscopic measurements in the ordinary hydrogen
atom, the accuracy was improved ten-fold and a proton radius
value smaller by 7 standard deviations was observed. This large
deviation between the muonic and the electronic measurements
constitutes the so-called “proton radius puzzle”. It has attracted
a lot of attention since 2010, from both theoretical and exper-
imental
viewpoints. Several beyond-the-standard-model theories,
including lepton universality violations, have attempted to solve
this puzzle (see e.g. [5] for a review). For example, the authors
of Refs. [6–8] investigated the possibility of the existence of new
interaction mediators that can explain not only the proton radius
puzzle, but also the (g − 2) muon anomaly. As yet, none of these
theories have been either verified or ruled out by experiments. Al-
ternative
explanations are being sought after either through novel
aspects of hadronic structure [9–11], or from renewed analyses of
the electron scattering data, e.g., Refs. [12,13]. To date, no com-
*
Corresponding author.
E-mail
addresses: javierh@triumf.ca (O.J. Hernandez), jichen@triumf.ca (C. Ji),
bacca@triumf.ca (S. Bacca), nir.nevo@mail.huji.ac.il (N. Nevo Dinur),
nir@phys.huji.ac.il (N. Barnea).
monly accepted explanation of the puzzle has been found. Various
new dedicated experiments have been planned to measure elec-
tron [14,15] and
muon [16] scattering on the proton. In addition,
experimental reexamination of ordinary hydrogen spectroscopy is
under way, e.g., Ref. [17]. A complementary experimental program
based on high-precision spectroscopic measurements on various
muonic atoms aims to study the systematics of the discrepancy
with ordinary atoms as a function of the atomic mass A and charge
number Z. In particular, the CREMA collaboration [18] plans to
measure the Lamb shift and isotope shifts in several light muonic
atoms. The deuteron is the lightest compound nucleus, made up
of one proton and one neutron, and it plays an important role in
few-body nuclear physics. The Lamb shift of its muonic atom, μD,
is currently being measured at PSI. This measurement will pro-
vide
a solid and independent test of the systematic uncertainties
in the μH experiment. Furthermore, assuming a new interaction
mediator that violates lepton universality, the μD experiment may
help to constrain the possible couplings of this new interaction to
the proton and the neutron. Therefore, it is important to compare
the deuteron charge radius r
2
ch
1/2
d
extracted from the μD Lamb
shift with the values determined from previous and ongoing ex-
periments
on eD scattering [19,20], as well as from the precision
measurements on the H/D isotope shift [21,22].
The
extraction of the nuclear charge radius from LS measure-
ments
relies heavily on theoretical input. For the deuteron, the
2S–2P energy transition is related to r
2
ch
1/2
d
by [23]
E = δ
QED
+δ
pol
+δ
Zem
+
m
3
r
α
4
12
r
2
ch
d
, (1)
http://dx.doi.org/10.1016/j.physletb.2014.07.039
0370-2693/
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by
SCOAP
3
.