Physics Letters B 789 (2019) 598–602
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Determination of α
s
from static QCD potential with renormalon
subtraction
H. Takaura
a,∗
, T. Kaneko
b
, Y. Kiyo
c
, Y. Sumino
d
a
Department of Physics, Kyushu University, Fukuoka, 819-0395, Japan
b
Theory Center, KEK, Tsukuba, Ibaraki, 305-0801, Japan
c
Department of Physics, Juntendo University, Inzai, 270-1695, Japan
d
Department of Physics, Tohoku University, Sendai, 980-8578, Japan
a r t i c l e i n f o a b s t r a c t
Article history:
Received
19 October 2018
Received
in revised form 26 November 2018
Accepted
25 December 2018
Available
online 28 December 2018
Editor:
J. Hisano
We determine the strong coupling constant α
s
(M
Z
) from the static QCD potential by matching a lattice
result and a theoretical calculation. We use a new theoretical framework based on operator product
expansion (OPE), where renormalons are subtracted from the leading Wilson coefficient. We find that
our OPE prediction can explain the lattice data at
QCD
r 0.8. This allows us to use a larger window in
matching, which leads to a more reliable determination. We obtain α
s
(M
Z
) = 0.1179
+0.0015
−0.0014
.
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
Today, facing frontier experiments of particle physics such as
those at LHC and super B Factory, there exist increasing demands
for more accurate theoretical predictions based on QCD on various
phenomena of the strong interaction. Precise determination of the
strong coupling constant α
s
sets a benchmark for such predictions.
For instance, a precise value of α
s
will play crucial roles in mea-
surements
of Higgs boson properties, in searches for new physics,
in high-precision flavor physics, etc.
The
current value of α
s
, given as the world-combined result by
the Particle Data Group (PDG), reads α
s
(M
Z
) = 0.1181 ±0.0011 [1].
Dominant contributions to this value come from determinations by
lattice QCD, which have smaller errors than other determinations
using more direct experimental inputs. Nevertheless, most lattice
QCD determinations have the “window problem” in an explicit or
implicit way, as pointed out in the Flavor Lattice Averaging Group
(FLAG) report [2]: It is difficult to find a region where both lat-
tice
QCD and perturbative QCD predictions are accurate. At short
distances (Q
QCD
), where perturbation theory is accurate, lat-
tice
data are distorted by ultraviolet (UV) cutoff effects due to the
finite lattice spacing a, whereas at larger distances (Q ∼
QCD
),
where finite a effects are suppressed, perturbation theory is not
reliable.
The
method of the finite volume scheme combined with step-
scaling
was proposed to solve this problem [3,4]. This method
enlarges reliable energy region of lattice simulation. As a result,
*
Corresponding author.
E-mail
address: takaura@phys.kyushu-u.ac.jp (H. Takaura).
matching with perturbative prediction can be taken in a wide
range at high energy, 10–100 GeV.
In
this Letter, we propose an alternative approach to the win-
dow
problem: We enlarge the validity range of theoretical predic-
tion
to the region where lattice calculations are accurate, Q a
−1
.
To this end we use operator product expansion (OPE) with sub-
traction
of renormalons. Accuracy of a perturbative prediction has
a limitation due to renormalons (which specify certain divergent
behaviors of perturbative series), and an O(
n
QCD
/Q
n
)-error is in-
evitable,
for a dimensionless observable with typical scale Q . In
OPE, the O(
n
QCD
/Q
n
)-term is described by a nonperturbative ma-
trix
element (ME). Hence, we can enlarge validity range of theoret-
ical
prediction to lower energy by subtracting renormalons appro-
priately
from perturbative prediction in the framework of OPE.
Although
OPE is a good and well-known framework, there is
a difficulty in practical calculations. There has not been an es-
tablished
way to factorize the two components of OPE, Wilson
coefficients and nonperturbative MEs, which are conceptually UV
and infrared (IR) quantities, respectively. Although one may find
in the literature that Wilson coefficients are calculated in usual
perturbation theory, this procedure is not desirable since loop inte-
grals
in dimensional regularization contain both UV and IR modes.
In particular, IR contributions cause renormalon uncertainties in a
Wilson coefficient, which makes it practically impossible to distin-
guish
a nonperturbative ME from the renormalon uncertainties.
In
Refs. [5,6], a formulation to separate UV and IR contributions
in OPE has been proposed. A Wilson coefficient is constructed as a
UV quantity, free from renormalon uncertainties (i.e., renormalons
https://doi.org/10.1016/j.physletb.2018.12.060
0370-2693/
© 2018 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.