Muon g 2 Anomaly and Neutrino Magnetic Moments
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Muon g − 2 Anomaly and Neutrino Magnetic Moments
K.S. Babu,1, ∗ Sudip Jana,2, † Manfred Lindner,2, ‡ and Vishnu P.K.1, §
1
Department of Physics, Oklahoma State University, Stillwater, OK, 74078, USA
2
Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany
We show that a unified framework based on an SU (2)H horizontal symmetry which generates a
naturally large neutrino transition magnetic moment and explains the XENON1T electron recoil
excess also predicts a positive shift in the muon anomalous magnetic moment. This shift is of the
right magnitude to be consistent with the Brookhaven measurement as well as the recent Fermilab
measurement of the muon g − 2. A relatively light neutral scalar from a Higgs doublet with mass
near 100 GeV contributes to muon g − 2, while its charged partner induces the neutrino magnetic
moment. In contrast to other multi-scalar theories, in the model presented here there is no freedom
to control the sign and strength of the muon g − 2 contribution. We analyze the collider tests of
this framework and find that the HL-LHC can probe the entire parameter space of these models.
arXiv:2104.03291v3 [hep-ph] 10 Jan 2022
Introduction.– There has been considerable inter- [6, 7]. We find that within this class of models, an expla-
est in understanding the long-standing discrepancy be- nation of the XENON1T excess will necessarily lead to
tween the measured and predicted values of the anoma- a positive contribution to ∆aµ , which lies neatly within
lous magnetic moment of the muon, aµ . The Brookhaven the Brookhaven and the recent Fermilab measurements
Muon g-2 collaboration has measured it to be aµ (BNL) = of aµ [3]. This class of models is thus in accordance with
116592089(63) × 10−11 two decades ago [1], while Occam’s razor, explaining both anomalies in terms of the
theoretical predictions find it to be aµ (theory) = same new physics.
116591810(43) × 10−11 [2]. Taken at face value the dif- Model.– We focus on models that can generate siz-
ference, ∆aµ = aµ (experiment) − aµ (theory) ' 279 × able transition magnetic moments for the neutrinos while
10−11 , is a 3.7 sigma discrepancy, which may indicate keeping their masses naturally small. Models which gen-
new physics lurking around or below the TeV scale. erate a neutrino transition magnetic moment of order
Very recently the Fermilab Muon g-2 collaboration [3] 10−11 µB would typically also induce an unacceptably
has announced their findings, which measures it to be large neutrino mass of order 0.1 MeV. An SU (2)H family
aµ (FNAL) = 116592040(54) × 10−11 which confirms the symmetry acting on the electron and muon families can
Brookhaven measurement and increases the significance resolve this conundrum as it decouples the neutrino mag-
of the discrepancy to the level of 4.2 sigma. These results netic moment from the neutrino mass [7]. This follows
make the motivations for new physics explanation more from the different Lorentz structures of the transition
compelling. magnetic moment and mass operators. The magnetic
moment operator (νeT Cσµν νµ )F µν , being antisymmetric
The purpose of this paper is draw a connection be- in flavor is a singlet of SU (2)H , while the mass operator
tween new physics contributions to aµ and a possible (νeT Cνµ ), being symmetric in flavor, belongs to SU (2)H
neutrino transition magnetic moment µνµ νe . A sizable triplet and vanishes in the SU (2)H symmetric limit [6].
neutrino magnetic moment has been suggested as a pos- The class of models we study makes use of this symmetry
sible explanation for the excess in electron recoil events argument. New physics at the TeV scale is required to
observed in the (1 − 7) keV recoil energy range by the generate the magnetic moment of the desired magnitude.
XENON1T collaboration recently [4]. The neutrino mag- This should violate lepton number, since the transition
netic moment needed to explain this excess lies in the magnetic moment operator is a ∆L = 2 operator. This
range of (1.6 − 2.4) × 10−11 µB , where µB stands for the requirement naturally leads to the model of Ref. [5]. It
electron Bohr magneton [5]. Such a value would require is based on an SU (2)H extension of the Zee model of
new physics to exist around the TeV scale. As we shall neutrino mass [8] involving a second Higgs doublet and
show in this paper, models that induce neutrino magnetic a charged singlet η ± . The extension incorporates the
moments, while maintaining their small masses naturally, SU (2)H symmetry.
also predict observable shifts in the muon anomalous The class of models under study is based on the
magnetic moment. We focus on a specific class of mod- SM gauge group and an approximate SU (2)H horizon-
els based on an SU (2)H horizontal symmetry (or fam- tal symmetry acting on the electron and muon families
ily symmetry) acting on the electron and muon families [5, 7, 9]. The lepton fields transform under SU (2)L ×
that naturally leads to a large neutrino magnetic moment U (1)Y × SU (2)H as follows:2
νe νµ 1 ντ 1
ψL = ∼ (2, − )(2), ψR = (e µ)R ∼ (1, −1)(2), ψ3L = ∼ (2, − )(1), τR ∼ (1, −1)(1). (1)
e µ L 2 τ L 2
All quark fields transform as singlets of SU (2)H symme- try and will not be discussed further here. The scalar
sector of the model contains the following fields:
φ+
+ +
1 φ1 φ2 1
η = η1+ η2+ ∼ (1, 1)(2).
φS = S ∼ (2, )(1), Φ= ∼ (2, )(2), (2)
φ0S 2 φ01 φ02 2
Here the φS field is the SM Higgs doublet which√acquires where the mixing angle α is defined as
a vacuum expectation value (VEV) hφ0S i = v/ 2, with √
v = 246 GeV. The Φ and η fields, which are doublets 2µv
tan 2α = 2 . (7)
of SU (2)H , are needed to generate transition magnetic mη − m2φ+
moments for the neutrino. Both fields are necessary in
order to break lepton number. The neutral components This mixing is essential for lepton number violation and
of the Φ field are assumed to not acquire any VEV. With the generation of magnetic moment of the neutrino. Note
this particle content, in the SU (2)H symmetric limit, the that the two copies of h+i are degenerate, as are the two
leptonic Yukawa couplings of the model are given by the Hi+ owing to SU (2)H symmetry.
Lagrangian [5] Muon anomalous magnetic moment and neu-
T
trino transition magnetic moment.– Fig. 1 shows
LYuk = h1 Tr ψ̄L φS ψR + h2 ψ̄3L φS τR + h3 ψ̄3L Φiτ2 ψR
T
τ2 Cψ3L + f 0 Tr ψ̄L Φ τR + H.c. (3)
+f ητ2 ψL
Eq. (3) would lead to the relation me = mµ , which
of course is unacceptable. This is evaded by allowing
for explicit but small SU (2)H breaking terms in the La-
grangian. In particular, the following Yukawa couplings
are necessary:
L0Yuk = δh1 [(Le φS eR ) − (Lµ φS µR )] + H.c. (4)
Figure 1. New physics affecting muon anomalous magnetic
Here LTe = (e νe )L , etc. With this term included, me√6= moment as well as νµ -magnetic moment.
mµ is realized, since now we√ have me = (h1 + δh1 )v/ 2
and mµ = (h1 − δh1 )v/ 2. While √ the violation of the connection between ∆aµ and µνµ νe in a generic
SU (2)H is small, δh1 = (me − mµ )/( 2v) ' 3 × 10−4 , it model. Fig. 2 has the explicit diagrams in the SU (2)H
is nevertheless significant in constraining the parameter symmetric models. We first focus on the new contribu-
space of the model, as we shall see. There are also other tions to the muon anomalous magnetic moment within
SU (2)H breaking terms in the Lagrangian of similar or- our framework. Both the neutral scalars and charged
der, but these terms will not play any significant role in scalars present in the model contribute to ∆aµ via one-
our discussions. loop diagrams shown in Fig. 2. Since chirality flip occurs
The scalar potential of the model contains SU (2)H on the external legs in these diagrams, the loop correc-
symmetric terms of the form [5]: tions mediated by the neutral scalars φ01 and φ02 con-
V ⊃ m2η (|η1 |2 + |η2 |2 ) + m2φ+ (|φ+ 2 + 2 tribute positively to aµ , whereas the corrections from the
1 | + |φ2 | )
charged scalars result in negative aµ . The full one-loop
+ m2φ0 (|φ01 |2 + |φ02 |2 ) + {µ η Φ† iτ2 φ∗S + H.c.} (5) contributions to ∆aµ are given by [10]
The cubic term in the Eq. (5) would lead to mixing be-
tween the charged scalars ηi+ and φ+ 0 m2µ
i (with i = 1, 2). The ∆aϕ |f 0 |2 + |h3 |2 Fϕ0 [mφ0 ],
µ = 2
(8)
corresponding mass eigenstates are denoted as h+ i (with
16π
mass m2h+ ) and Hi+ (with mass m2H + ) and are given by + m2µ
∆aϕ |f cos α|2 + |h3 sin α|2 Fϕ+ [mh+ ]
µ =
16π 2
h+ + +
i = cos α ηi + sin α φi , m2µ
|–f sin α|2 + |h3 cos α|2 Fϕ+ [mH + ], (9)
Hi+ = − sin α ηi+ + cos α φ+ +
i , (6) 16π 23
where the loop functions are given by
1
x2 (1 − x)
Z
Fϕ0 [mϕ0 ] = dx ,
0 m2µ x2 + m2ϕ0 (1 − x) + x(m2τ − m2µ )
(10)
1
x2 (x − 1)
Z
Fϕ+ [mϕ+ ] = dx . (11)
0 m2µ x2 + x(m2ϕ+ − m2µ )
Here mφ0 is the common mass mφ01 = mφ02 . In Eq. (8),
the two terms proportional to |f 0 |2 and |h3 |2 arise from
diagrams with φ02 and φ01 exchange respectively. The two
contributions in Eq. (9) arise from the exchange of h+
and H + .
We now turn to the transition magnetic moment of the
neutrino in our framework and show its correlation with
∆aµ . The diagrams generating sizeable µνµ νe are shown
Figure 2. The dominant contributions to ∆aµ (top) and neu-
trino magnetic moment (bottom) are shown. For the neutrino
in Fig. 2, bottom panel. Owing to the SU (2)H symmetry
magnetic moment, the outgoing photon can be emitted also of the model, the two diagrams add in their contributions
from the τ lepton line. There are other diagrams, which are to the magnetic moment, while they subtract in their
subleading. contributions to neutrino mass when the photon line is
removed from these diagrams (for details, see Ref. [5, 9]).
The resulting neutrino magnetic moment is given by [5, 9]
ff0 m2h+ m2H +
1 1
µνµ νe = mτ sin 2α ln 2 − 1 − 2 ln −1 . (12)
8π 2 m2h+ mτ mH + m2τ
Comparing Eq. (12) with Eqs. (8) and (9) we see that from me 6= mµ is found to be
∆aµ and µνµ νe are dependent on the same set of param-
|f |2 (m2µ − m2e )
eters. To see their correlation quantitatively, we have to δm2η ' (14)
take into account the various constraints that exist on 16π 2
these parameters, which we now address. which does not induce large neutrino mass, even for |f | ∼
First of all, for µνµ νe to be in the range of (1.6 − 1. (Eq. (14) should replace Eq. (4.35) of Ref. [5], which
3.4)×10−11 µB so that the XENON1T excess is explained, is incorrect.) However, the coupling |f | is constrained
one needs |f f 0 sin 2α| ≥ (1 − 8) × 10−3 , corresponding from the universality limits from τ decay. In Ref. [5]
to mh+ = (100 − 300) GeV. The coupling |f | can be it was shown that the leptonic decay rate of the τ will
constrained from the induced neutrino masses from the receive additional contributions from the charged scalars
SU (2)H breaking effects. The cancellation that occurs leading to the modification Γ(τ → e) = ΓSM × (1 + τ )2 ,
among the two diagrams in the bottom panel of Fig. 2 where
f2 2 cos φ sin2 φ
2
in neutrino mass is valid only in the strict SU (2)H limit.
Since me 6= mµ is necessary, one should examine neutrino τ = 2 mW + 2 . (15)
g m2h+ mH +
masses including SU (2)H breaking effects. The resulting
neutrino mass is given by [5] A limit of τ ≤ 0.004 can be derived at 2 σ from the con-
" # straint gτ /gµ = 1.0011 ± 0.0015 [14] obtained by compar-
f f 0 mτ sin 2α δm2η δm2φ m2φ ing τ decay rate into muon with muon decay rate. This
mν ' − 2 + 2(δα) cot 2αln 2 . leads to the constraint |f | ≤ (0.05 − 0.25) for h+ mass in
16π 2 m2η mφ mη
the range of (100 − 500) GeV. As a result, the charged
(13) scalar contributions to the muon anomalous magnetic
Here δm2η is the squared mass splitting between the two moment turn out to be not significant.
The coupling h3 is constrained from the induced tau
charged scalars η1+ and η2+ arising from SU (2)H breaking
neutrino mass within the model, which is given by
effects. Similarly, δα is the shift in the common mixing 2
angle α that parametrizes η1+ − φ+ +
1 mixing and η2 − φ2
+ h3 f sin 2α mh+
mντ = mµ ln . (16)
mixing. The mass splitting among charged scalars arising 32π 2 m2H +4
1.0 of the model for neutrino magnetic moment and muon
0.8 g − 2. We also note that the model predicts a deviation
in the anomalous magnetic moment of the electron, ae ,
0.6 which is calculable owing to the SU (2)H symmetry. We
LEP
HL-LHC
find it to be ∆ae = ∆aµ (me /mµ )2 ≈ 6 × 10−14 . This
2 )μ T
| f '|
0.4 - n1 predicted deviation is consistent with the current mea-
(g e no surements [15, 16], but may serve as a future test of the
X
model.
Z decay
In Fig. 4 we have shown a direct correlation between
0.2
the muon anomalous magnetic moment and neutrino
magnetic moment within our framework. As noted be-
50 100 200 500 fore, the dominant contribution to ∆aµ solely depends
on the Yukawa coupling f 0 and the neutral scalar mass
mϕ0 [GeV] mφ0 . The transition magnetic moment of the neutrino
µνµ νe depends on the same Yukawa coupling f 0 as well
Figure 3. The 2σ allowed range (in green) for the muon as the charged scalar masses. The measurement of the
anomalous magnetic moment measurement [3] at the Fermi- e+ e− → τ + τ − process at the LEP experiment [12] im-
lab in the |f 0 |-mφ0 plane. The region labelled XENON1T ex- poses a strong limit on the Yukawa coupling f 0 as a func-
plains the electron recoil excess at 90% C.L [4]. The dashed tion of the neutral scalar mass mφ0 . Therefore, in Fig. 4,
line indicate the limit on neutrino magnetic moment from
we vary the Yukawa coupling f 0 in such a way that the
the BOREXINO experiment [11]. The shaded regions denote
the excluded parameter space from various experiments: the parameters are consistent with these constraints. An op-
light pink shaded region from the LEP experiment [12] and timal scenario is realized when the neutral scalar is light,
the yellow shaded region from the Z-decay width measure- with its mass not lower than 45 GeV so as to be consistent
ments [12, 13]. Here we have fixed f = 10−2 , sin α = 0.35, with Z decay constraint [13]. The mass splitting between
mh+ = mφ0 + 50 GeV and mH + = mh+ + 350 GeV. the lightest charged scalar and neutral scalar is set to be
50 GeV in order to satisfy the charged Higgs mass limit of
∼95 GeV (for detail see Ref. [17]) from collider searches.
Demanding mντ ≤ 0.05 eV, while also requiring µνµ νe ∼ As for the charged scalar masses which have a strong im-
1.6 × 10−11 µB one obtains a limit |h3 | < 10−2 . Conse- pact on the neutrino magnetic moment, but little effect
quently, the neutral φ01 exchange of Fig. 2 to the muon on the muon g − 2, we note that these masses cannot be
anomalous magnetic moment is negligible. Thus we ar- arbitrary, as the mass splittings between the charged and
rive at the model prediction that ∆aµ receives significant neutral scalars are tightly bounded from the electroweak
contributions only from φ02 exchange diagram. precision data [13, 17]. Therefore, it follows that there
In Fig. 3 we show the parameter space in the Yukawa is no extra room to control the strength and the sign of
coupling |f 0 | versus the mass of the neutral scalar (mφ0 ) the muon g − 2 in our setup. The parameter space which
plane consistent with the observed muon anomalous mag- predicts large neutrino magnetic moment leads to a pos-
netic moment measurement ∆aµ = (251 ± 59) × 10−11 at itive contribution to muon g − 2. Thus, the measurement
Fermilab [3] as indicated by green band. Here we have of muon g − 2 by the Fermilab experiment can be an in-
fixed the charged scalar masses at mh+ = mφ0 + 50 GeV direct and novel test of the neutrino magnetic moment
and mH + = mh+ + 350 GeV, a choice consistent with hypothesis, which can be as sensitive as other ongoing
electroweak T parameter constraint. A lower bound on neutrino/dark matter experiments.
the neutral scalar mass is obtained from the decay width There are strong astrophysical constraints on neu-
measurements of the Z boson: mφ0 & 45 GeV [12, 13], trino magnetic moments from red giants and horizon-
which is indicated by the yellow shaded region. The tal branch stars, since photons in the plasma of these
Yukawa coupling f 0 leads to additional contributions to environments can decay into neutrino pairs [18, 19]. A
the e+ e− → τ + τ − process at the LEP experiment [12] limit |µν | ≤ 1.5 × 10−12 µB (95% CL) has been derived
via t−channel neutral scalar exchange. This leads to an from the evolutionary studies of horizontal branch stars
upper limit on f 0 which is depicted by the pink shaded [20–22]. This would be in contradiction with the µνe νµ
region. Moreover, our model leads to the most promis- needed to explain the XENON1T anomaly. However, this
ing signal pp → φ0i φ∗0 i → µ µ τ τ
− + − +
at the LHC where constraint can be evaded if νµ has a matter-dependent
different flavored leptons can be easily reconstructed as mass, which can arise from its weak coupling to a new
a resonance. The collider phenomenology of this model light scalar, as shown in Ref. [23] and adopted in Ref.
has been studied in detail in Ref. [5]. The blue dashed [5]. Note that the transition magnetic moment µνe νµ
line represents the 5σ sensitivity of the neutral scalar of would lead to plasmon decay into νe + νµ , which would
mass 398 GeV [5] at the HL-LHC with an integrated lu- be kinematically suppressed inside red giants and hori-
minosity of L = 1 ab−1 . This can be a promising test zontal branch stars if the matter-dependent mass of νµ is5
230
Fermilab '21
Exp. avg.
BNLE821
220
210
ref
aμ - a
200
XENON1T
BOREXINO
TEXONO
4.2σ
BBN
10-10
190
180 SM prediction
2006.04822
170
160
0.1 0.5 1 5 10 50
μνμ νe [ 10μ-11
B
]
Figure 4. Theoretical predictions and experimental measurements of the muon anomalous magnetic moment and the neutrino
transition magnetic moment. Purple, cyan, light blue, blue, green, yellow, orange and red scattered points depict the correlated
predictions for the muon magnetic moment (aµ ) and neutrino magnetic moment (µνµ νe ) in our framework for different ranges
of mass splittings between the charged scalars: mH + − mh+ = 20, 50, 100, 200, 300, 500, 800 and 1000 GeV. Here we choose
different ranges of parameters as {f 0 ∈ (0.001 − 1), mφ0 ∈ (45 − 500) GeV, and mH + − mh+ ∈ (20 GeV - 1 TeV)} consistent
with the theoretical and experimental limits discussed in text. The lower black dotted point with error bar indicates the
updated SM prediction [2] for aµ (see other previous analyses (in chronological order) as: HMNT06 [29], DHMZ10 [30], JS11
[31], HLMNT11 [32], DHMZ17 [33], KNT18 [34]) , and others [35–51]). The upper dotted data points with error bars represent
different experimental measurements: BNLE821 [1], Fermilab [3], and the the combined experimental average of the BNL [1]
and Fermilab [3] results. These evaluations and measurements of aµ are independent of neutrino magnetic moment values. The
current uncertainty on the measurement of aµ at the Fermilab [3] is given by the light brown band at 1σ level. The purple
band represents the SM prediction from Ref. [2] with 1σ value and the light green band indicates the combined experimental
average of the BNL [1] and Fermilab [3] results at 1σ level. Here we choose the reference value aref = 11659000. The orange
band labelled with XENON1T denotes the preferred range µνe νµ ∈ (1.65 − 3.42) × 10−11 µB to explain the electron recoil excess
at 90% C.L [4]. The vertical lines indicate the limits on neutrino magnetic moment from various measurements: blue solid
line from TEXONO [52], dark green solid line from BBN [53], light green solid line from BOREXINO [11], and cyan dashed
line from globular clusters [20]. The astrophysical limits on neutrino magnetic moment shown by the dashed cyan line can be
evaded by utilizing a neutrino trapping mechanism [5] (see discussions in text).
of order few keV. This would not suppress the standard in a class of models that generates naturally large tran-
νe emission, which could have modified the evolution of sition magnetic moment for the neutrino needed to ex-
these stars significantly [24, 25]. The modifications to plain the XENON1T electron recoil excess. These mod-
neutrino emissivity will only affect νµ ν µ emissions me- els are based on an approximate SU (2)H symmetry that
diated through neutral currents. Following Ref. [26], suppresses the neutrino mass while allowing for a large
we estimate that the neutrino emissivity changes by only neutrino transition magnetic moment. We have shown
∼ 0.3% in our scenario compared to the standard case. that the new scalars present in the theory with masses
This shift is small owing to the dominance of the vector- around 100 GeV can yield the right sign and magnitude
couplings of the electrons to the Z boson, which is how- for the muon g − 2 which has been confirmed recently
ever suppressed by a factor (1 − 4 sin2 θW ). The contri- by the Fermilab collaboration. Such a correlation be-
bution of the axial-vector current is always negligible for tween muon g − 2 and the neutrino magnetic moment
all conditions of astrophysical interest [27, 28]. is generic in models employing leptonic family symmetry
Conclusions.– In this paper we have analyzed new to explain a naturally large µνµ νe . We have also outlined
contributions to the muon anomalous magnetic moment various other experimental tests of these models at col-6
liders. The entire parameter space of the model can be [15] R. H. Parker, C. Yu, W. Zhong, B. Estey, and
explored at the HL-LHC through the pair production of H. Müller, “Measurement of the fine-structure constant
neutral scalars and their subsequent decays into eτ and as a test of the standard model,” Science 360 no. 6385,
µτ final states. (Apr, 2018) 191–195.
[16] L. Morel, Z. Yao, P. Cladé, and S. Guellati-Khélifa,
Acknowledgments.– We thank Evgeny Akhmedov “Determination of the fine-structure constant with an
for discussions. The work of KSB and VPK is in part accuracy of 81 parts per trillion,” Nature 588 no. 7836,
(2020) 61–65.
supported by US Department of Energy Grant Number [17] K. S. Babu, P. S. B. Dev, S. Jana, and A. Thapa,
DE-SC 0016013 and by a Fermilab Neutrino Theory Net- “Non-Standard Interactions in Radiative Neutrino Mass
work grant. Models,” JHEP 03 (2020) 006, arXiv:1907.09498
[hep-ph].
∗
E-mail: babu@okstate.edu [18] J. Bernstein, M. Ruderman, and G. Feinberg,
†
E-mail:sudip.jana@mpi-hd.mpg.de “Electromagnetic Properties of the neutrino,” Phys.
‡
E-mail:lindner@mpi-hd.mpg.de Rev. 132 (1963) 1227–1233.
§
E-mail:vipadma@okstate.edu [19] G. G. Raffelt, “Particle physics from stars,” Ann. Rev.
[1] Muon g-2 Collaboration, G. W. Bennett et al., “Final Nucl. Part. Sci. 49 (1999) 163–216,
Report of the Muon E821 Anomalous Magnetic arXiv:hep-ph/9903472.
Moment Measurement at BNL,” Phys. Rev. D 73 [20] N. Viaux, M. Catelan, P. B. Stetson, G. Raffelt,
(2006) 072003, arXiv:hep-ex/0602035. J. Redondo, A. A. R. Valcarce, and A. Weiss, “Neutrino
[2] T. Aoyama et al., “The anomalous magnetic moment of and axion bounds from the globular cluster M5 (NGC
the muon in the Standard Model,” Phys. Rept. 887 5904),” Phys. Rev. Lett. 111 (2013) 231301,
(2020) 1–166, arXiv:2006.04822 [hep-ph]. arXiv:1311.1669 [astro-ph.SR].
[3] B. Abi et al., “Measurement of the Positive Muon [21] N. Viaux, M. Catelan, P. B. Stetson, G. Raffelt,
Anomalous Magnetic Moment to 0.46 ppm,” J. Redondo, A. A. R. Valcarce, and A. Weiss,
arXiv:2104.03281 [hep-ex]. “Particle-physics constraints from the globular cluster
[4] XENON Collaboration, E. Aprile et al., “Excess M5: Neutrino Dipole Moments,” Astron. Astrophys.
electronic recoil events in XENON1T,” Phys. Rev. D 558 (2013) A12, arXiv:1308.4627 [astro-ph.SR].
102 no. 7, (2020) 072004, arXiv:2006.09721 [hep-ex]. [22] F. Capozzi and G. Raffelt, “Axion and neutrino bounds
[5] K. S. Babu, S. Jana, and M. Lindner, “Large Neutrino improved with new calibrations of the tip of the
Magnetic Moments in the Light of Recent red-giant branch using geometric distance
Experiments,” JHEP 10 (2020) 040, arXiv:2007.04291 determinations,” Phys. Rev. D 102 no. 8, (2020)
[hep-ph]. 083007, arXiv:2007.03694 [astro-ph.SR].
[6] M. B. Voloshin, “On Compatibility of Small Mass with [23] K. S. Babu, G. Chauhan, and P. S. Bhupal Dev,
Large Magnetic Moment of Neutrino,” Sov. J. Nucl. “Neutrino nonstandard interactions via light scalars in
Phys. 48 (1988) 512. the Earth, Sun, supernovae, and the early Universe,”
[7] K. S. Babu and R. N. Mohapatra, “Model for Large Phys. Rev. D 101 no. 9, (2020) 095029,
Transition Magnetic Moment of the νe ,” Phys. Rev. arXiv:1912.13488 [hep-ph].
Lett. 63 (1989) 228. [24] B. Ahlgren, T. Ohlsson, and S. Zhou, “Comment on “Is
[8] A. Zee, “A Theory of Lepton Number Violation, Dark Matter with Long-Range Interactions a Solution
Neutrino Majorana Mass, and Oscillation,” Phys. Lett. to All Small-Scale Problems of Λ Cold Dark Matter
B 93 (1980) 389. [Erratum: Phys.Lett.B 95, 461 (1980)]. Cosmology?”,” Phys. Rev. Lett. 111 no. 19, (2013)
[9] K. S. Babu and R. N. Mohapatra, “Large transition 199001, arXiv:1309.0991 [hep-ph].
magnetic moment of the neutrino from horizontal [25] O. Straniero, C. Pallanca, E. Dalessandro,
symmetry,” Phys. Rev. D 42 (1990) 3778–3793. I. Dominguez, F. R. Ferraro, M. Giannotti, A. Mirizzi,
[10] J. P. Leveille, “The Second Order Weak Correction to and L. Piersanti, “The RGB tip of galactic globular
(G-2) of the Muon in Arbitrary Gauge Models,” Nucl. clusters and the revision of the axion-electron coupling
Phys. B 137 (1978) 63–76. bound,” Astron. Astrophys. 644 (2020) A166,
[11] Borexino Collaboration, M. Agostini et al., “Limiting arXiv:2010.03833 [astro-ph.SR].
neutrino magnetic moments with Borexino Phase-II [26] E. Braaten and D. Segel, “Neutrino energy loss from the
solar neutrino data,” Phys. Rev. D 96 no. 9, (2017) plasma process at all temperatures and densities,” Phys.
091103, arXiv:1707.09355 [hep-ex]. Rev. D 48 (1993) 1478–1491, arXiv:hep-ph/9302213.
[12] LEP, ALEPH, DELPHI, L3, OPAL, LEP [27] Y. Kohyama, N. Itoh, and H. Munakata, “Neutrino
Electroweak Working Group, SLD Electroweak Energy Loss in Stellar Interiors. II. Axial-Vector
Group, SLD Heavy Flavor Group Collaboration, Contribution to the Plasma Neutrino Energy Loss
t. S. Electroweak, “A Combination of preliminary Rate,” Astrophys. J. 310 (Nov., 1986) 815.
electroweak measurements and constraints on the [28] G. G. Raffelt, Stars as laboratories for fundamental
standard model,” arXiv:hep-ex/0312023. physics: The astrophysics of neutrinos, axions, and
[13] Particle Data Group Collaboration, M. Tanabashi other weakly interacting particles. 5, 1996.
et al., “Review of Particle Physics,” Phys. Rev. D 98 [29] K. Hagiwara, A. D. Martin, D. Nomura, and
no. 3, (2018) 030001. T. Teubner, “Improved predictions for g-2 of the muon
[14] A. Pich, “Precision Tau Physics,” Prog. Part. Nucl. and alpha(QED) (M**2(Z)),” Phys. Lett. B 649 (2007)
Phys. 75 (2014) 41–85, arXiv:1310.7922 [hep-ph]. 173–179, arXiv:hep-ph/0611102.
[30] M. Davier, A. Hoecker, B. Malaescu, and Z. Zhang,7
“Reevaluation of the Hadronic Contributions to the light-by-light scattering: two-pion contributions,” JHEP
Muon g-2 and to alpha(MZ),” Eur. Phys. J. C 71 04 (2017) 161, arXiv:1702.07347 [hep-ph].
(2011) 1515, arXiv:1010.4180 [hep-ph]. [Erratum: [43] M. Hoferichter, B.-L. Hoid, B. Kubis, S. Leupold, and
Eur.Phys.J.C 72, 1874 (2012)]. S. P. Schneider, “Dispersion relation for hadronic
[31] F. Jegerlehner and R. Szafron, “ρ0 − γ mixing in the light-by-light scattering: pion pole,” JHEP 10 (2018)
neutral channel pion form factor Fπe and its role in 141, arXiv:1808.04823 [hep-ph].
comparing e+ e− with τ spectral functions,” Eur. Phys. [44] A. Gérardin, H. B. Meyer, and A. Nyffeler, “Lattice
J. C 71 (2011) 1632, arXiv:1101.2872 [hep-ph]. calculation of the pion transition form factor with
[32] K. Hagiwara, R. Liao, A. D. Martin, D. Nomura, and Nf = 2 + 1 Wilson quarks,” Phys. Rev. D 100 no. 3,
T. Teubner, “(g − 2)µ and α(MZ2 ) re-evaluated using (2019) 034520, arXiv:1903.09471 [hep-lat].
new precise data,” J. Phys. G 38 (2011) 085003, [45] J. Bijnens, N. Hermansson-Truedsson, and
arXiv:1105.3149 [hep-ph]. A. Rodrı́guez-Sánchez, “Short-distance constraints for
[33] M. Davier, A. Hoecker, B. Malaescu, and Z. Zhang, the HLbL contribution to the muon anomalous
“Reevaluation of the hadronic vacuum polarisation magnetic moment,” Phys. Lett. B 798 (2019) 134994,
contributions to the Standard Model predictions of the arXiv:1908.03331 [hep-ph].
muon g − 2 and α(m2Z ) using newest hadronic [46] G. Colangelo, F. Hagelstein, M. Hoferichter, L. Laub,
cross-section data,” Eur. Phys. J. C 77 no. 12, (2017) and P. Stoffer, “Longitudinal short-distance constraints
827, arXiv:1706.09436 [hep-ph]. for the hadronic light-by-light contribution to (g − 2)µ
[34] A. Keshavarzi, D. Nomura, and T. Teubner, “Muon with large-Nc Regge models,” JHEP 03 (2020) 101,
g − 2 and α(MZ2 ): a new data-based analysis,” Phys. arXiv:1910.13432 [hep-ph].
Rev. D 97 no. 11, (2018) 114025, arXiv:1802.02995 [47] G. Colangelo, M. Hoferichter, A. Nyffeler, M. Passera,
[hep-ph]. and P. Stoffer, “Remarks on higher-order hadronic
[35] G. Colangelo, M. Hoferichter, and P. Stoffer, “Two-pion corrections to the muon g−2,” Phys. Lett. B 735 (2014)
contribution to hadronic vacuum polarization,” JHEP 90–91, arXiv:1403.7512 [hep-ph].
02 (2019) 006, arXiv:1810.00007 [hep-ph]. [48] T. Blum, N. Christ, M. Hayakawa, T. Izubuchi, L. Jin,
[36] M. Hoferichter, B.-L. Hoid, and B. Kubis, “Three-pion C. Jung, and C. Lehner, “Hadronic Light-by-Light
contribution to hadronic vacuum polarization,” JHEP Scattering Contribution to the Muon Anomalous
08 (2019) 137, arXiv:1907.01556 [hep-ph]. Magnetic Moment from Lattice QCD,” Phys. Rev. Lett.
[37] M. Davier, A. Hoecker, B. Malaescu, and Z. Zhang, “A 124 no. 13, (2020) 132002, arXiv:1911.08123
new evaluation of the hadronic vacuum polarisation [hep-lat].
contributions to the muon anomalous magnetic moment [49] T. Aoyama, M. Hayakawa, T. Kinoshita, and M. Nio,
and to α(m2Z ),” Eur. Phys. J. C 80 no. 3, (2020) 241, “Complete Tenth-Order QED Contribution to the
arXiv:1908.00921 [hep-ph]. [Erratum: Eur.Phys.J.C Muon g-2,” Phys. Rev. Lett. 109 (2012) 111808,
80, 410 (2020)]. arXiv:1205.5370 [hep-ph].
[38] A. Keshavarzi, D. Nomura, and T. Teubner, “g − 2 of [50] A. Czarnecki, W. J. Marciano, and A. Vainshtein,
charged leptons, α(MZ2 ) , and the hyperfine splitting of “Refinements in electroweak contributions to the muon
muonium,” Phys. Rev. D 101 no. 1, (2020) 014029, anomalous magnetic moment,” Phys. Rev. D 67 (2003)
arXiv:1911.00367 [hep-ph]. 073006, arXiv:hep-ph/0212229. [Erratum: Phys.Rev.D
[39] A. Kurz, T. Liu, P. Marquard, and M. Steinhauser, 73, 119901 (2006)].
“Hadronic contribution to the muon anomalous [51] C. Gnendiger, D. Stöckinger, and H. Stöckinger-Kim,
magnetic moment to next-to-next-to-leading order,” “The electroweak contributions to (g − 2)µ after the
Phys. Lett. B 734 (2014) 144–147, arXiv:1403.6400 Higgs boson mass measurement,” Phys. Rev. D 88
[hep-ph]. (2013) 053005, arXiv:1306.5546 [hep-ph].
[40] K. Melnikov and A. Vainshtein, “Hadronic light-by-light [52] TEXONO Collaboration, M. Deniz et al.,
scattering contribution to the muon anomalous “Measurement of Nu(e)-bar -Electron Scattering
magnetic moment revisited,” Phys. Rev. D 70 (2004) Cross-Section with a CsI(Tl) Scintillating Crystal Array
113006, arXiv:hep-ph/0312226. at the Kuo-Sheng Nuclear Power Reactor,” Phys. Rev.
[41] P. Masjuan and P. Sanchez-Puertas, “Pseudoscalar-pole D 81 (2010) 072001, arXiv:0911.1597 [hep-ex].
contribution to the (gµ − 2): a rational approach,” [53] N. Vassh, E. Grohs, A. B. Balantekin, and G. M. Fuller,
Phys. Rev. D 95 no. 5, (2017) 054026, “Majorana Neutrino Magnetic Moment and Neutrino
arXiv:1701.05829 [hep-ph]. Decoupling in Big Bang Nucleosynthesis,” Phys. Rev. D
[42] G. Colangelo, M. Hoferichter, M. Procura, and 92 no. 12, (2015) 125020, arXiv:1510.00428
P. Stoffer, “Dispersion relation for hadronic [astro-ph.CO].You can also read
