An update of the HLS estimate of the muon g−2 Benayoun, M.; David, P.; DelBuono, L. ...
The European physical journal. C, Particles and fields,
06/2013, Volume:
73, Issue:
6
Journal Article
Peer reviewed
Open access
A global fit of parameters allows us to pin down the Hidden Local Symmetry (HLS) effective Lagrangian, which we apply for the prediction of the leading hadronic vacuum polarization contribution to ...the muon
g
−2. The latter is dominated by the annihilation channel
e
+
e
−
→
π
+
π
−
, for which data are available by scan (CMD-2 & SND) and ISR (KLOE-2008, KLOE-2010 & BaBar) experiments. It is well known that the different data sets are not in satisfactory agreement. In fact it is possible to fix the model parameters without using the
π
+
π
−
data, by using instead the dipion spectra measured in the
τ
-decays together with experimental spectra for the
π
0
γ
,
ηγ
,
π
+
π
−
π
0
,
K
+
K
−
,
final states, supplemented by specific meson decay properties. Among these, the accepted decay width for
ρ
0
→
e
+
e
−
and the partial widths and phase information for the
ω
/
ϕ
→
π
+
π
−
transitions, are considered. It is then shown that, relying on this global data set, the HLS model, appropriately broken, allows to predict accurately the pion form factor below 1.05 GeV. It is shown that the data samples provided by CMD-2, SND and KLOE-2010 behave consistently with each other and with the other considered data. Consistency problems with the KLOE-2008 and BaBar data samples are substantiated. “All data” global fits are investigated by applying reweighting the conflicting data sets. Constraining to our best fit, the broken HLS model yields
associated with a very good global fit probability. Correspondingly, we find that
exhibits a significance ranging between 4.7 and 4.9
σ
.
Previous studies have shown that the Hidden Local Symmetry (HLS) model, supplied with appropriate symmetry breaking mechanisms, provides an effective Lagrangian (Broken Hidden Local Symmetry, BHLS) ...which encompasses a large number of processes within a unified framework. Based on it, a global fit procedure allows for a simultaneous description of the
e
+
e
-
annihilation into six final states—
π
+
π
-
,
π
0
γ
,
η
γ
,
π
+
π
-
π
0
,
K
+
K
-
,
K
L
K
S
—and includes the dipion spectrum in the
τ
decay and some more light meson decay partial widths. The contribution to the muon anomalous magnetic moment
a
μ
th
of these annihilation channels over the range of validity of the HLS model (up to 1.05 GeV) is found much improved in comparison to the standard approach of integrating the measured spectra directly. However, because most spectra for the annihilation process
e
+
e
-
→
π
+
π
-
undergo overall scale uncertainties which dominate the other sources, one may suspect some bias in the dipion contribution to
a
μ
th
, which could question the reliability of the global fit method. However, an iterated global fit algorithm, shown to lead to unbiased results by a Monte Carlo study, is defined and applied successfully to the
e
+
e
-
→
π
+
π
-
data samples from CMD2, SND, KLOE, BaBar, and BESSIII. The iterated fit solution is shown to further improve the prediction for
a
μ
, which we find to deviate from its experimental value above the
4
σ
level. The contribution to
a
μ
of the
π
+
π
-
intermediate state up to 1.05 GeV has an uncertainty about 3 times smaller than the corresponding usual estimate. Therefore, global fit techniques are shown to work and lead to improved unbiased results.
The departure of the latest FNAL experimental average for the muon anomalous magnetic moment
a
μ
=
(
g
μ
-
2
)
/
2
measurements, having increased from
4.2
σ
(Abi et al. in Measurement of the positive ...muon anomalous magnetic moment to 0.46 ppm,
arXiv:2104.03281
, 2021) to
5.0
σ
(Muon g-2, D.P. Aguillard et al. in Measurement of the positive muon anomalous magnetic moment to 0.20 ppm,
arXiv:2308.06230
, 2023) with respect to the white paper (WP) consensus (Aoyama et al. in Phys Rep 887:1,
arXiv:2006.04822
, 2020), may indicate a hint for new physics. As the most delicate piece of
a
μ
is its leading-order hadronic vacuum polarization (HVP) part
a
μ
H
V
P
-
L
O
, methods to ascertain its theoretical value are crucial to appropriately interpreting this departure from the measurement. We, therefore, propose to closely examine the dipion spectra from the
η
/
η
′
→
π
+
π
-
γ
decays in the hidden local symmetry (HLS) context using its BHLS
2
broken variant. We thus have at our disposal a framework where the close relationship of the dipion spectra from the
η
/
η
′
and
τ
decays and of the
e
+
e
-
→
π
+
π
-
annihilation can be simultaneously considered. A special focus is given to the high-statistics dipion spectra from the
η
decay collected by the KLOE/KLOE2 Collaboration and
η
′
decay collected by the BESIII Collaboration, and it is shown that the BHLS
2
framework provides a fair account of their dipion spectra. More precisely, it is first proven that a single Omnès representation real polynomial is required, common to both the
η
and
η
′
dipion spectra. Moreover, it is shown that fits involving the
η
/
η
′
/
τ
dipion spectra, and excluding the
e
+
e
-
→
π
+
π
-
annihilation data, allow for a prediction of the pion vector form factor data
F
π
(
s
)
which agrees fairly well with the usual dipion spectra collected in the
e
+
e
-
→
π
+
π
-
annihilation channel. Even if more precise
η
/
η
′
/
τ
dipion spectra would help to be fully conclusive, this confirms the dispersive approach results for
a
μ
H
V
P
-
L
O
and points toward a common non-experimentally dependent origin to this tension with the now well-accepted LQCD result.
The generic hidden local symmetry (HLS) model has recently given rise to its
variant, defined by introducing symmetry breaking mostly in the vector meson sector; the central mechanism is a ...modification of the covariant derivative at the root of the HLS approach. However, the description of the
dipion spectra, especially the Belle one, is not fully satisfactory, whereas the simultaneous dealing with its annihilation sector (
) is optimum. We show that this issue is solved by means of an additional breaking term which also allows us to consistently include the mixing properties of the
system within this extended
(
) scope. This mechanism, an extension of the usual 't Hooft determinant term, only affects the kinetic energy part of the
Lagrangian. One thus obtains a fair account for the
dipion spectra which complements the fair account of the annihilation channels already reached. The Belle dipion spectrum is found to provide evidence in favor of a violation of the conserved vector current (CVC) in the
lepton decay; this evidence is enforced by imposing the conditions
on
axial current matrix elements.
is found to recover the usual (completed) formulae for the
mixing parameters, and the global fits return mixing parameter values in agreement with expectations and better uncertainties. Updating the muon hadronic vacuum polarization (HVP), one also argues that the strong tension between the KLOE and BaBar pion form factors imposes to provide two solutions, namely
and
, in units of
, rather than some combination of these. Taking into account common systematics, their differences from the experimental BNL-FNAL average value exhibit significance
(KLOE) and
(BaBar), with fit probabilities favoring the former.
The generic hidden local symmetry (HLS) model has recently given rise to its
BHLS
2
variant, defined by introducing symmetry breaking mostly in the vector meson sector; the central mechanism is a ...modification of the covariant derivative at the root of the HLS approach. However, the description of the
τ
dipion spectra, especially the Belle one, is not fully satisfactory, whereas the simultaneous dealing with its annihilation sector (
e
+
e
-
→
π
+
π
-
/
π
+
π
-
π
0
/
π
0
γ
/
η
γ
/
K
+
K
-
/
K
L
K
S
) is optimum. We show that this issue is solved by means of an additional breaking term which also allows us to consistently include the mixing properties of the
π
0
,
η
,
η
′
system within this extended
BHLS
2
(
EBHLS
2
) scope. This mechanism, an extension of the usual ’t Hooft determinant term, only affects the kinetic energy part of the
BHLS
2
Lagrangian. One thus obtains a fair account for the
τ
dipion spectra which complements the fair account of the annihilation channels already reached. The Belle dipion spectrum is found to provide evidence in favor of a violation of the conserved vector current (CVC) in the
τ
lepton decay; this evidence is enforced by imposing the conditions
<
0
|
J
μ
q
|
q
′
q
′
¯
(
p
)
>
=
i
p
μ
f
q
δ
q
q
′
,
{
q
q
¯
,
q
=
u
,
d
,
s
}
on
EBHLS
2
axial current matrix elements.
EBHLS
2
is found to recover the usual (completed) formulae for the
π
0
,
η
,
η
′
mixing parameters, and the global fits return mixing parameter values in agreement with expectations and better uncertainties. Updating the muon hadronic vacuum polarization (HVP), one also argues that the strong tension between the KLOE and BaBar pion form factors imposes to provide two solutions, namely
a
μ
H
V
P
-
L
O
(
KLOE
)
=
687.48
±
2.93
and
a
μ
H
V
P
-
L
O
(
BaBar
)
=
692.53
±
2.95
, in units of
10
-
10
, rather than some combination of these. Taking into account common systematics, their differences from the experimental BNL-FNAL average value exhibit significance
>
5.4
σ
(KLOE) and
>
4.1
σ
(BaBar), with fit probabilities favoring the former.
Previous studies have shown that the Hidden Local Symmetry (HLS) Model, supplied with appropriate symmetry breaking mechanisms, provides an Effective Lagrangian (BHLS) able to encompass a large ...number of processes within a unified framework. This allowed one to design a global fit procedure which provides a fair simultaneous description of the
e
+
e
-
annihilation into six final states (
π
+
π
-
,
π
0
γ
,
η
γ
,
π
+
π
-
π
0
,
K
+
K
-
,
K
L
K
S
), the dipion spectrum in the
τ
decay and some more light meson decay partial widths. In this paper, additional breaking schemes are defined which improve the BHLS working and extend its scope so as to absorb spacelike processes within a new framework (
BHLS
2
). The phenomenology previously explored with BHLS is fully revisited in the
BHLS
2
context with special emphasis on the
ϕ
mass region using all available data samples. It is shown that
BHLS
2
addresses perfectly the close spacelike region covered by NA7 and Fermilab data; it is also shown that the recent lattice QCD (LQCD) information on the pion form factor are accurately
predicted
by the
BHLS
2
fit functions derived from fits to
only
annihilation data. The contribution to the muon anomalous magnetic moment
a
μ
th
of these annihilation channels over the range of validity of
BHLS
2
(up to
≃
1.05 GeV) is updated within the new
BHLS
2
framework and shown to strongly reduce the former BHLS systematics. The uncertainty on
a
μ
th
(
s
<
1.05
GeV
) is much improved compared to standard approaches relying on direct integration methods of measured spectra. Using the
BHLS
2
results, the leading-order HVP contribution to the muon anomalous moment is
a
μ
HVP
-
LO
=
686.65
±
3.01
+
(
+
1.16
,
-
0.75
)
syst
in units of
10
-
10
. Using a conservative estimate for the light-by-light contribution, our evaluation for the muon anomalous magnetic moment is
a
μ
th
=
11
659
175.96
±
4.17
+
(
+
1.16
,
-
0.75
)
syst
×
10
-
10
. The relationship between the dispersive and LQCD approaches to the
ρ
0
–
γ
mixing is also discussed which may amount to a shift of
δ
a
μ
π
π
ρ
γ
=
+
(
3.10
±
0.31
)
×
10
-
10
at LO+NLO, presently treated as additional systematics. Taking also this shift into account, the difference
a
μ
th
-
a
μ
BNL
exhibits a significance not smaller than
3.8
σ
.
The muon anomalous magnetic moment
a
μ
and the hadronic vacuum polarization are examined using data analyzed within the framework of a suitably broken HLS model. The analysis relies on all available ...scan data samples and leaves provisionally aside the existing ISR data. Our HLS model based global fit approach allows for a better check of consistency between data sets and we investigate how results depend on different strategies which may be followed. Relying on global fit qualities, we find several acceptable solutions leading to ambiguities in the reconstructed value for (
a
μ
)
th
. Among these, the most conservative solution is
and (
a
μ
)
th
=11 659 175.37(5.31)×10
−10
corresponding to a 4.1
σ
significance for the difference Δ
a
μ
=(
a
μ
)
exp
−(
a
μ
)
th
. It is also shown that the various contributions accessible through the model yield uniformly a factor 2 improvement of their uncertainty. The breaking procedure implemented in the HLS model is an extension of the former procedure based on a mechanism defined by Bando, Kugo and Yamawaki (BKY). This yields a quite satisfactory simultaneous description of most
e
+
e
−
annihilation channels up to and including the
ϕ
meson (
π
+
π
−
,
π
0
γ
,
ηγ
,
π
+
π
−
π
0
,
K
+
K
−
,
) and of a set of 10 (mostly radiative) decay widths of light mesons. It also allows to achieve the proof of consistency between the
e
+
e
−
→
π
+
π
−
annihilation and the
τ
±
→
π
±
π
0
ν
decay and gives a solution to the reported problem concerning the measured partial width ratio
. Prospects for improving the VMD based estimates of
a
μ
are emphasized.
Abstract
Previous studies have shown that the Hidden Local Symmetry (HLS) Model, supplied with appropriate symmetry breaking mechanisms, provides an Effective Lagrangian (BHLS) able to encompass a ...large number of processes within a unified framework. This allowed one to design a global fit procedure which provides a fair simultaneous description of the
$$e^+ e^-$$
e
+
e
-
annihilation into six final states (
$$\pi ^+\pi ^-$$
π
+
π
-
,
$$\pi ^0\gamma $$
π
0
γ
,
$$\eta \gamma $$
η
γ
,
$$\pi ^+\pi ^-\pi ^0$$
π
+
π
-
π
0
,
$$K^+K^-$$
K
+
K
-
,
$$K_L K_S$$
K
L
K
S
), the dipion spectrum in the
$$\tau $$
τ
decay and some more light meson decay partial widths. In this paper, additional breaking schemes are defined which improve the BHLS working and extend its scope so as to absorb spacelike processes within a new framework (
$${\hbox {BHLS}}_2$$
BHLS
2
). The phenomenology previously explored with BHLS is fully revisited in the
$${\hbox {BHLS}}_2$$
BHLS
2
context with special emphasis on the
$$\phi $$
ϕ
mass region using all available data samples. It is shown that
$${\hbox {BHLS}}_2$$
BHLS
2
addresses perfectly the close spacelike region covered by NA7 and Fermilab data; it is also shown that the recent lattice QCD (LQCD) information on the pion form factor are accurately
predicted
by the
$${\hbox {BHLS}}_2$$
BHLS
2
fit functions derived from fits to
only
annihilation data. The contribution to the muon anomalous magnetic moment
$$a_\mu ^{\mathrm{th}}$$
a
μ
th
of these annihilation channels over the range of validity of
$${\hbox {BHLS}}_2$$
BHLS
2
(up to
$$\simeq $$
≃
1.05 GeV) is updated within the new
$${\hbox {BHLS}}_2$$
BHLS
2
framework and shown to strongly reduce the former BHLS systematics. The uncertainty on
$$a_\mu ^{\mathrm{th}}(\sqrt{s}< 1.05 \, \hbox {GeV}$$
a
μ
th
(
s
<
1.05
GeV
) is much improved compared to standard approaches relying on direct integration methods of measured spectra. Using the
$${\hbox {BHLS}}_2$$
BHLS
2
results, the leading-order HVP contribution to the muon anomalous moment is
$$a_\mu ^{\mathrm{HVP-LO}}= 686.65 \pm 3.01 +(+1.16,-0.75)_{\mathrm{syst}}$$
a
μ
HVP
-
LO
=
686.65
±
3.01
+
(
+
1.16
,
-
0.75
)
syst
in units of
$$10^{-10}$$
10
-
10
. Using a conservative estimate for the light-by-light contribution, our evaluation for the muon anomalous magnetic moment is
$$a_\mu ^{\mathrm{th}}=\left 11\,659\,175.96 \pm 4.17 +(+1.16,-0.75)_{\mathrm{syst}}\right \times 10^{-10}$$
a
μ
th
=
11
659
175.96
±
4.17
+
(
+
1.16
,
-
0.75
)
syst
×
10
-
10
. The relationship between the dispersive and LQCD approaches to the
$$\rho ^0$$
ρ
0
–
$$\gamma $$
γ
mixing is also discussed which may amount to a shift of
$$\delta a_\mu \pi \pi _{\rho \gamma }=+(3.10\pm 0.31) \times 10^{-10}$$
δ
a
μ
π
π
ρ
γ
=
+
(
3.10
±
0.31
)
×
10
-
10
at LO+NLO, presently treated as additional systematics. Taking also this shift into account, the difference
$$a_\mu ^{\mathrm{th}}-a_\mu ^{\mathrm{BNL}}$$
a
μ
th
-
a
μ
BNL
exhibits a significance not smaller than
$$3.8 \sigma $$
3.8
σ
.
BACKGROUND AND PURPOSETransient loss of consciousness is commonly evaluated in the emergency department. Although typically caused by epileptic seizure, syncope, or psychogenic nonepileptic seizure, ...the underlying etiology is frequently misdiagnosed. Lateral tongue bites are reportedly a specific clinical finding of seizure. We have observed tongue signal abnormality suggesting bite injury on brain MR imaging after seizures. We hypothesized an association between tongue signal abnormality and seizure diagnosis among patients in the emergency department imaged for transient loss of consciousness. Our purposes were to determine the prevalence of tongue signal abnormality among this population and the predictive performance for seizure diagnosis. MATERIALS AND METHODSFor this retrospective study including 82 brain MR imaging examinations, 2 readers independently assessed tongue signal abnormality on T2-weighted and T2-weighted FLAIR images. Discrepancies were resolved by consensus, and interrater reliability (Cohen κ) was calculated. The final diagnosis was recorded. Proportions were compared using the Fisher exact test. RESULTSTongue signal abnormality was present on 19/82 (23%) MR imaging examinations. Interrater reliability was "substantial" (κ = 0.77). Seizure was diagnosed among 18/19 (95%) patients with tongue signal abnormality and 29/63 (46%) patients without it (P < .001). In our cohort, tongue signal abnormality conveyed 97% specificity, 95% positive predictive value, and 63% accuracy for seizure diagnosis. CONCLUSIONSTongue signal abnormality was observed in 23% of the study cohort and conveyed 97% specificity and 95% positive predictive value for seizure diagnosis. By assessing and reporting tongue signal abnormality, radiologists may facilitate a timely and accurate diagnosis of seizure among patients imaged for transient loss of consciousness.
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