Physics Letters B 738 (2014) 123–127
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
The muon anomalous magnetic moment and the pion polarizability
Kevin T. Engel
a
, Michael J. Ramsey-Musolf
b,c,∗
a
University of Maryland, College Park, MD 20742, USA
b
Physics Department, University of Massachusetts Amherst, Amherst, MA 01003, USA
c
Kellogg Radiation Laboratory, California Institute of Technology, Pasadena, CA 91125, USA
a r t i c l e i n f o a b s t r a c t
Article history:
Received
4 April 2014
Received
in revised form 13 August 2014
Accepted
3 September 2014
Available
online 6 September 2014
Editor:
W. Haxton
We compute the charged pion loop contribution to the muon anomalous magnetic moment a
μ
, taking
into account the previously omitted effect of the charged pion polarizability, (α
1
− β
1
)
π
+
. We evaluate
this contribution using two different models that are consistent with the requirements of chiral symmetry
in the low-momentum regime and perturbative quantum chromodynamics in the asymptotic region. The
result may increase the disagreement between the present experimental value for a
μ
and the theoretical,
Standard Model prediction by as much as ∼60 × 10
−11
, depending on the value of (α
1
−β
1
)
π
+
and the
choice of the model. The planned determination of (α
1
− β
1
)
π
+
at Jefferson Laboratory will eliminate
the dominant parametric error, leaving a theoretical model uncertainty commensurate with the error
expected from planned Fermilab measurement of a
μ
.
© 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
.
The measurement of the muon anomalous magnetic moment,
a
μ
, provides one of the most powerful tests of the Standard Model
of particle physics and probes of physics that may lie beyond it.
The present experimental value obtained by the E821 Collabo-
ration
[1–3] a
exp
μ
= 116592089(63) × 10
−11
disagrees with the
most widely quoted theoretical SM predictions by 3.6σ : a
SM
μ
=
116591802(49) ×10
−11
(for recent reviews, see Refs. [4–6] as well
as references therein). This difference may point to physics beyond
the Standard Model (BSM) such as weak scale supersymmetry or
very light, weakly coupled neutral gauge bosons [7–10]. A next
generation experiment planned for Fermilab would reduce the ex-
perimental
uncertainty by a factor of four [11]. If a corresponding
reduction in the theoretical, SM uncertainty were achieved, the
muon anomalous moment could provide an even more powerful
indirect probe of BSM physics.
The
dominant sources of theoretical uncertainty are associ-
ated
with non-perturbative strong interaction effects that enter
the leading order hadronic vacuum polarization (HVP) and the
hadronic light-by-light (HLBL) contributions: δa
HVP
μ
(LO) =±42 ×
10
−11
and δa
HLBL
μ
=±26 × 10
−11
[12] (other authors give some-
what
different error estimates for the latter [13–27], but we will
refer to these numbers as points of reference; see [28] for a re-
view).
In recent years, considerable scrutiny has been applied to
the determination of a
HVP
μ
(LO) from data on σ (e
+
e
−
→ hadrons)
*
Corresponding author.
and hadronic τ decays. A significant reduction in this HVP error
will be needed if the levels of theoretical and future experimental
precision are to be comparable.
In
this Letter, we concentrate on the more theoretically-
challenging
a
HLBL
μ
, computing the previously omitted contribution
from the charged pion polarizability and estimating the associated
parametric and model-dependent uncertainties. At leading order
in the expansion of the number of colors N
C
, a
HLBL
μ
is generated
by the pseudoscalar pole contributions that in practice turn out
to be numerically largest. The contribution arising from charged
pion loops is subleading in N
C
, yet the associated error is now
commensurate with the uncertainty typically quoted for the pseu-
doscalar
pole terms. Both uncertainties are similar in magnitude
to the goal experimental error for the proposed Fermilab measure-
ment.
Thus, it is of interest to revisit previous computations of the
charged pion loop contribution, scrutinize the presently quoted er-
ror,
and determine how it might be reduced.
In
previously reported work [29], we completed a step in this
direction by computing the amplitude Π
μναβ
for light-by-light
scattering for low-momentum off-shell photons. In this regime,
Chiral Perturbation Theory (χPT) provides a first principles, effec-
tive
field theory description of strong interaction dynamics that
incorporates the approximate chiral symmetry of quantum chro-
modynamics
(QCD) for light quarks. Long-distance hadronic effects
can be computed order-by-order in an expansion of p /Λ
χ
, where
p is a typical energy scale (such as the pion mass m
π
or mo-
mentum)
and Λ
χ
= 4π F
π
∼ 1GeVis the hadronic scale with
F
π
= 92.4MeVbeing the pion decay constant. At each order in
http://dx.doi.org/10.1016/j.physletb.2014.09.006
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
.