production in rare meson decays, and the angular accep-
tance function for FASER are given in Appendices A, B,
and C, respectively.
II. PROPERTIES OF AXIONLIKE PARTICLES
We consider a low-energy effective theory in which an
ALP a couples to vector bosons through the dimension-5
interactions
L
int
¼ −
1
4
g
aBB
aB
μν
˜
B
μν
−
1
4
g
aWW
aW
A
μν
˜
W
A;μν
; ð1Þ
where B
μν
and W
A
μν
are the Uð1Þ
Y
and SUð2Þ
L
field strength
tensors, respectively, and g
aBB
and g
aWW
are the corre-
sponding coupling constants with dimension GeV
−1
.If
such interactions are generated by physics with coupling α
that was integrated out at some heavy scale f, one expects
g
aBB
;g
aWW
∼
α
2πf
: ð2Þ
This is the case for axions [23–26], for example, and more
generally for pseudo-Goldstone bosons with nonvanishing
axial anomalies.
After electroweak symmetry breaking, the couplings
g
aBB
and g
aWW
induce couplings of the ALP to γγ , γZ,
ZZ, and W
þ
W
−
. In this study, we focus on the γγ coupling
and neglect the others. The other couplings typically have a
small effect on our signal; for example, the subdominant
production process of ALPs from meson decays can be
enhanced by W
þ
W
−
couplings [32]. More important are
their effects on other observables. For example, a non-
vanishing γZ coupling induces the exotic decay Z → aγ.
Although this process does not contribute significantly to
the ALP production rate in the far-forward region, it can
be searched for in high-p
T
experiments at the LHC. (See
Refs. [27,33] for some future projections.)
ALPs may also couple through dimension-5 operators to
gluons and fermions, as well as through dimension-6
couplings to the Higgs boson. For a recent review see,
e.g., Ref. [27]. In this study, we assume that the effects of
these other couplings on our signal processes are negli-
gible. This is the case when these couplings are relatively
small, or, for example, when the couplings are to heavy
particles, such as third-generation fermions, and so their
impact on ALP production and decay is suppressed. It is
important to note, however, that gluon and fermion cou-
plings generate diphoton couplings through loops and vice
versa, and so to analyze a specific underlying ALP model in
detail, one would in general have to include all of these
couplings in a unified way. Here, we take a more model-
independent, phenomenological approach.
With these simplifying assumptions, we therefore focus
on the ALP effective Lagrangian
L ⊃
1
2
∂
μ
a∂
μ
a −
1
2
m
2
a
a
2
−
1
4
g
aγγ
aF
μν
˜
F
μν
; ð3Þ
where F
μν
is the field strength tensor of electromagnetism.
The resulting parameter space is very simple, as it is
spanned by two parameters: the ALP mass m
a
and the
diphoton coupling g
aγγ
.
With this Lagrangian, the ALP decay width is
Γ
a
≡ Γða → γγÞ¼
g
2
aγγ
m
3
a
64π
: ð4Þ
The cubic dependence on m
a
, resulting from the fact that
the decay is mediated by a dimension-5 operator, implies
that, as the ALP mass decreases, the ALP lifetime increases
rapidly. The ALP decay length is
¯
d
a
¼
c
Γ
a
γ
a
β
a
≈ 630 m
10
−4
GeV
−1
g
aγγ
2
p
a
TeV
50 MeV
m
a
4
;
ð5Þ
where we have normalized to currently viable values of g
aγγ
and m
a
. For these values and ALP momenta p
a
∼ TeV, the
ALP decay length is naturally hundreds of meters, i.e., in
the range relevant for FASER searches for LLPs.
Although the ALP decays primarily into pairs of
photons, it is possible that one of the photons converts
into an electron pair leading to the decay a → e
þ
e
−
γ. The
branching fraction for this decay is [34]
Bða → e
þ
e
−
γÞ¼
e
2
6π
Z
m
2
a
4m
2
e
dq
2
q
2
jF ðq
2
Þj
2
1 −
4 m
2
e
q
2
1
2
×
1 þ
2 m
2
e
q
2
1 −
q
2
m
2
a
3
; ð6Þ
where q
2
is the invariant mass of the electron pair, and
Fðq
2
Þ ≈ 1. For ALP masses between m
a
¼ 10 MeV and
1 GeV, the branching fraction ranges from Bða →
e
þ
e
−
γÞ¼0.4% to 1.7%. Note that this branching fraction
peaks at low q
2
, implying that most of the ALP energy will
be carried by the photon, while the electrons will typically
be softer.
III. ALP PRODUCTION AND DECAY IN FASER
A. Mechanisms for ALP production
in the forward region
In the dominant ALP-photon coupling scenario, ALPs
can be produced in any process involving photons by
radiating an ALP off a photon line. However, for FASER,
we are primarily interested in the production of highly
energetic ALPs in the very forward region. The dominant
production mechanism is then the Primakoff process, in
which a photon converts into an ALP when colliding with a
nucleus. This can happen when photons produced at the
AXIONLIKE PARTICLES AT FASER: THE LHC AS A … PHYS. REV. D 98, 055021 (2018)
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