Two decay channels h → γγ,
+ Zγ of the Standard Model–like Higgs in a left-right
+ symmetry model are investigated using recent experimental data. We show that
+ there exist one-loop contributions that affect the h
+ → Zγ amplitude, but not the
+ h → γγ amplitude. From numerical
+ investigations, we show that the signal strength μZγ
+ of the decay h → Zγ
+ is still constrained strictly by that of h → γγ,
+ namely |Δμγγ| < 38%
+ results in maximum |ΔμZγ| < 46%.
+ On the other hand, the future experimental sensitivity |Δ
+ μγγ| = 4% still
+ allows |ΔμZγ| to
+ reach values larger than the expected sensitivity of |Δ
+ μZγ| = 23%.
The Standard Model–like (SM-like) Higgs decay h
+ → Zγ is one of the most important
+ channels being researched experimentally [1].
+ Meanwhile, the experimental evidence of this loop-induced decay relating to the
+ effective coupling hZγ has been reported by ATLAS and CMS
+ recently [2,
+ 3], in agreement with the SM prediction within 1.9 standard deviations.
+ Experimental data show that the effective coupling hγγ
+ derived from h → γγ decay rates
+ is constrained very strictly [4]. In
+ contrast, the effective coupling hZγ in many models beyond
+ the SM (BSM) might differ considerably from the SM prediction, because the Z
+ couplings to new particles are less strict than those of the photon. Hence, studying
+ the effective hZγ couplings will be an indirect channel to
+ determine the properties of new particles. Controlled by the strict experimental
+ constraint of the decay h → γγ,
+ constraints of the SM-like Higgs decay h →
+ Zγ affected by new fermions and charged scalars were studied in
+ several BSMs such as 3-3-1 models [5,6], only Higgs extended SM versions [7–10], U(1)
+ gauge extensions from the SM [11,12], supersymmetric models [13–15], chiral extension
+ of the SM [16], etc. Previous studies of
+ h → Zγ in left-right symmetric
+ models ignored one-loop contributions relating to the diagrams consisting of both
+ virtual Higgs and gauge particles in the loops [17
+ ,18], where the h-Higgs–gauge
+ boson couplings were assumed to be suppressed.
+
The experimental results have been updated for the loop-induced Higgs decays
+ h → γγ [19–21] and h
+ → Zγ [22]. In the future of this project, the significant strength
+ of the decay h → Zγ,
+ denoted as μZγ, can reach Δμ
+ Zγ ≡ μZγ
+ − 1 = ±0.23, whereas that of the channel h → γγ
+ can reach around Δμγγ ≡ μ
+ γγ − 1 = ±0.04, as determined from two CMS
+ and ATLAS experiments [23]. In addition,
+ the ATLAS expected significance at the High-Luminosity Large Hadron Collider
+ (HL-LHC) for the
+
+
+ channel will be 4.9σ with 3000 fb−1. Also, the
+ Circular Electron Positron Collider (CEPC) [24]
+ can reach a sensitivity of μZγ = 1
+ ± 0.22 [25].
+
One interesting extension of the BSM models is an extension of the lepton sector.
+ Namely, the minimal left-right symmetry model (MLRSM) is constructed based on the
+ parity symmetry SU(2)
+ L
+ ⊗SU(2)
+ R
+ ⊗U(1)
+ B − L [26–28], which contains Higgs fields
+ included in two SU(2)
+ L
+ triplets denoted as Δ
+ L, R
+ and a bi-doublet field Φ
+ playing the SM Higgs role. Therefore, the MLRSM allows us to solve the parity
+ problem of the SM as well as the neutrino oscillation data through the seesaw
+ mechanism. Besides, it contains extended particles which may result in interesting
+ consequences for rare decays such as Higgs boson decay h
+ → Zγ.
+
This work is organized as follows. In Sect. 2,
+ we present an overview of the MLRSM, including the particle content and physical
+ states. In Sect. 3, we present the
+ necessary couplings that generate one-loop contributions to the decays h
+ → γγ, Zγ. We will also
+ collect analytic formulas to determine the decay rates, recapitulating some new
+ contributions that were not discussed previously. Numerical results will be
+ investigated in Sect. 4. Namely, we
+ will investigate the dependence of
+
+
+ on several important parameters in this model. Finally, a summary is given in
+ Sect. 5.
+
+
+
+ The MLRSM
+
+
+ Review of the model
+
All needed ingredients relevant to one-loop contributions to the decay amplitudes
+ h → Zγ, γγ
+ will be collected in this section. Most generally, the electric charge operator
+ can be written as [29,30]:
+
+
+
+
+
where
+
+
+ are the generators of the gauge groups SU(2)
+ L, R
+ ; B (
+ L) is the baryon (lepton) number defining the U(1)
+ B − L group in the MLRSM. The baryon and
+ lepton numbers of the fermions can be written as in Table 1.
+
+
+
+
Baryon and lepton numbers of fermions in the MLRSM.
+
+
+
+
+
+ f
+
+
e, μ, τ, ν
+ e
+ ,
+ νμ, ντ
+
+ u, c, t, s
+
+
+
+
+
+
+ L
+
+
1
+
0
+
+
+
+ B
+
+
0
+
+
+
+
+
+
+
+
+
+
With this information, we can write down the lepton and fermion representations
+ as follows:
+
+
+
+
+
+
+
+
+
where i = 1, 2, 3 is the flavor index.
+
Gauge boson and fermion masses are originated from the following scalar sector,
+ consisting of a bi-doublet and two triplet scalar fields Δ
+ L, R
+ satisfying
+
+
+
+
+
The Higgs components develop vacuum expectation values (VEVs) defined as
+
+
+
+
+
where the neutral Higgs components are expanded as follows:
+
+
+
+
+
The symmetry-breaking pattern in MLRSM happens in the two following steps:
+
+ ,
+ which corresponds to the reasonable limits that v
+ R
+ ≫ k
+ 1, k2 ≫ v
+ L
+ . Only new gauge bosons will be
+ massive after the first step. The second step is the SM symmetry-breaking
+ generating masses for the SM particles. When the symmetry is broken in step two,
+ only U(1)
+ Q
+ remains unbroken, where
+ Q is the quantifier. As a result, the photon A
+ μ has no mass. We stress that the MLRSM contains no more than three
+ scalar multiplets (ϕ, Δ
+ L, R
+ ). The physical spectrum and
+ masses of all particles in the model under consideration are summarized as
+ follows.
+
+
+
+ Fermions
+
Physical fermion states and their masses always relate to the Yukawa
+ interactions, which are included in the following Lagrangian parts for leptons
+ and quarks:
+
+
+
+
+
Then, the mass terms for leptons and quarks are computed. We will use the results
+ for fermion masses and mixing presented in Refs. [29,30], i.e. all
+ the original and the physical states of fermions are the same. They are
+ identified with the SM ones and will be denoted as e
+ aL, R
+ , u
+ aL, R
+ , and d
+ aL, R
+ in this work. The mass
+ matrices Mℓ and M
+ u, d
+ for charged leptons and up
+ and down quarks are
+
+
+
+
+
where
+
+
+
+
+
As we will show below, the matching condition to the SM leads to k
+ = 246 GeV and the Yukawa couplings of quarks defined in the SM can be
+ seen as follows:
+
+
+ ,
+
+ ,
+ and
+
+ .
+ Here, we fix α = 0 so that the value of t
+ β = sβ/c
+ β can be small, namely tβ
+ ≥ 1.2 [31]. The three above
+ fermion mass matrices are denoted as M
+ f
+ with f
+ = ℓ, u, d and can be diagonalized by two unitary
+ transformations
+
+
+ and
+
+
+ as follows:
+
+ .
+ Here m
+ f, i
+ with i
+ = 1, 2, 3 and f = ℓ, u, d
+ denotes the physical masses of charged leptons and of up and down quarks. The
+ transformation between the flavor basis
+
+
+ and the mass basis
+
+
+ is
+
+ .
+ As we will show below, the couplings of the SM-like Higgs boson with charged
+ leptons and quarks are the same as the SM results.
+
+
+
+ Gauge bosons
+
The covariant derivative corresponding to the symmetry of the MLRSM is defined as
+ [29]:
+
+
+
+
+
where g
+ L, R
+ and g′
+ are the SU(2)
+ L, R
+ and U(1)
+ B − L gauge couplings, respectively.
+
The Lagrangian for scalar kinetic parts is written as
+
+
+
+
+
The particular forms of covariant derivatives for the scalar multiplets are
+
+
+
+
+
where X = L, R, σ
+ a
+ is the Pauli matrix
+ corresponding to the SU(2) doublet representation of
+
+
+ with a = 1, 2, 3. Therefore, the mass terms of gauge
+ bosons are derived from the VEVs of Higgs components as follows:
+
+
+
+
+
where k is defined as in Eq. (9). The mass terms of the neutral
+ and charged gauge bosons read:
+
+
+
+
+
where
+
+
+ with X = L, R. The mixing angle
+ ξ between two singly charged gauge bosons
+
+
+ and
+
+
+ is determined by the following formula:
+
+
+
+
+
Using the approximation that tan 2ξ ≪
+ 1⇒tan 2ξ ≈ sin 2ξ ≈
+ 2sin ξ ≈ 2ξ, and v
+ L
+ ≪ k
+ 1, k2 ≪ v
+ R
+ , the W
+ L
+ − W
+ R
+ mixing angle ξ is
+
+
+
+
+
The singly charged gauge bosons
+
+
+ can be written as functions of the mass basis (
+
+ )
+ as follows:
+
+
+
+
+
where cξ ≡ cos ξ and
+ sξ ≡ sin ξ. The respective
+ charged gauge boson masses are found to be
+
+
+
+
+
Identifying that
+
+
+ in the SM, we get
+
+
+ .
+
The original neutral gauge basis
+
+
+ is expressed in terms of the mass basis (Aμ,
+ Z1μ, Z2μ) as
+ follows:
+
+
+
+
+
where
+
+
+
+
+
and the mixing angles
+
+
+ are given by
+
+
+
+
+
State synchronization with the SM is as follows:
+
+
+ , Z1μ ≡ Z
+ μ in the limits
+
+ ,
+ then we also have
+
+
+
+
+
The Weinberg angle θ
+ W
+ is identified from the
+ definition
+
+ .
+ Then, the neutral gauge boson masses of Z1,
+ Z2, and the photon A are given by
+
+
+
+
+
In addition, Z1 ≡ Z and
+ Z2 ≡ Z′ are, respectively,
+ the SM gauge boson Z found experimentally, and the heavy one
+ appearing in the MLRSM.
+
+
+
+ Higgs bosons
+
The MLRSM scalar potential is written as [29
+ ]:
+
+
+
+
+
From the minimal conditions of the Higgs potential given in Eq. (24), three parameters
+
+
+ ,
+
+ ,
+ and
+
+
+ are expressed as functions of other independent parameters. Inserting them into
+ the Higgs potential (24), we
+ can determine all Higgs boson masses and physical states. Firstly, the original
+ and the mass base of neutral CP-even Higgs bosons are related to each other as
+ follows:
+
+
+
+
+
We note that Eq. (25)
+ does not use the the limit k1 ≫ k
+ 2 mentioned in Ref. [29], which
+ gives
+
+
+ ,
+
+
+ , sβ ≈ 1, and ϵ1
+ ≡ k1/v
+ R
+ , ϵ2 ≡
+ k2/k1. Besides that, from
+ Eq. (25) we get the same
+ result as in Ref. [29] in this
+ limit. In this study, the SM-like Higgs mass is calculated approximately to the
+ order
+
+ ,
+ namely
+
+
+
+
+
The SM-like Higgs property appears in Eq. (26) as
+
+
+ because
+
+
+ when
+
+ .
+ In this limit,
+
+
+ can be identified with the SM-like Higgs boson with mass m
+ h
+ = 125.38 GeV confirmed
+ experimentally [1]. Then the Higgs
+ self-coupling λ1 is expressed as follows:
+
+
+
+
+
We note that Eq. (26) for
+ SM-like Higgs mass is consistent with Refs. [32–34], implying that the m
+ h
+ value is still at the
+ electroweak scale even in the case of large tβ.
+ Therefore, a value of tβ ≥ 1.2 is
+ still allowed to get the SM-like Higgs mass consistent with the experiment.
+
Regarding the SM-like Higgs couplings with charged leptons and fermions, using
+ Eq. (25) for the Yukawa
+ Lagrangian in Eq. (7), we derive easily that
+
+
+
+
+
where
+
+ ,
+ and the transformation in Eq. (
+ 28) is based on discussion relating to Eq. (8). Therefore, the SM-like Higgs
+ couplings with charged fermions can be identified with the SM results.
+
Similarly, the original and mass states of the singly charged Higgs bosons have
+ the following relations:
+
+
+
+
+
where
+
+
+ is massless, corresponding to the Goldstone boson eaten up by
+
+ ,
+ and the remaining squared masses of singly charged Higgs bosons are
+
+
+
+
+
Besides that, two components (
+
+ )
+ are also physical states with the following masses:
From the above Higgs potential and the discussion on the masses and mixing of
+ Higgs bosons, all Higgs self-couplings of h giving one-loop
+ contributions to the decays h
+ → γγ, Zγ can be
+ derived analytically. From the general notations in the interacting Lagrangian:
+
+ ,
+ the Feynman rule −iλ
+ hSS
+ corresponds to the vertex
+ hSS. All nonzero factors λ
+ hSS
+ are given in Table 2. We note that the vertex factors in
+ Table 2 are derived following
+ the general notation defined in Ref. [35],
+ so that we can use the analytic formulas to compute the partial decay widths of
+ h → γγ, Zγ
+ in the MLRSM mentioned in this work.
+
+
+
+
Feynman rules for the SM-like Higgs boson couplings with charged Higgs
+ bosons.
+
+
+
+
+
Vertex
+
Coupling: λ
+ hSS
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
[α1 + sβ
+ (4α2cβ
+ + α3sβ
+ )]v
+
+
+
+
+
+
+
+
[α1 + sβ
+ (4α2cβ
+ + α3sβ
+ )]v
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
The couplings of h with SM fermions can be determined using the
+ Yukawa Lagrangians given in Eq. (7), where the Feynman rule is
+
+
+ for each vertex
+
+ .
+ Because this model does not have exotic charged fermions and the couplings of SM
+ leptons to neutral Higgs/gauge bosons (
+
+ )
+ are defined as in the SM [
+ 36–38], we will use the SM results for one-loop fermion
+ contributions to the decay amplitudes of h
+ → Zγ, γγ.
+
The Higgs–gauge boson couplings giving one-loop contributions to the
+ decays h → Zγ,
+ γγ are derived from the kinetic Lagrangian of the Higgs bosons,
+ namely
+
+
+
+
+
where
+
+
+ denote charged Higgs bosons in the MLRSM. The Feynman rules for the h
+ couplings to at least one charged gauge boson are shown in Table 3. The momenta appearing in the vertex
+ factors are ∂μh
+ → −ip0μh
+ and ∂μS
+ i, j
+
+ → −ipμS
+ i, j
+ , where p
+ 0, p± are incoming momenta.
+
+
+
+
Feynman rules for couplings of the SM-like Higgs boson to charged Higgs
+ and gauge bosons.
+
+
+
+
+
Vertex
+
Coupling
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
The Feynman rules for Z couplings to charged Higgs and gauge
+ bosons as in Eq. (32)
+ are given in Table 4. The
+ couplings
+
+
+ are zero in the MLRSM.
+
+
+
+
Feynman rules of couplings of Z to charged Higgs and
+ gauge bosons. Notations p+ and
+ p− are incoming momenta.
+
+
+
+
+
Vertex
+
Coupling
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
The triple gauge couplings of Z and photon to
+
+
+ are derived from the kinetic Lagrangian of the non-Abelian gauge bosons
+
+
+
+
+
where
+
+ ,
+ and
+
+
+ are the SU(2) structure constants. The respective Z
+ couplings to
+
+
+ are included in the following part:
+
+
+
+
+
Then, the vertex factors corresponding to particular couplings are defined as
+
+
+
+
+
where Γμνλ(p0,
+ p+, p−) ≡
+ gμν(p0 −
+ p+)λ + g
+ νλ(p+ − p
+ −)μ + g
+ λμ(p− − p
+ 0)λ, and i, j = 1, 2. The photon
+ always couples to two identical particles as the consequence of the Ward
+ Identity [39], see the second line of
+ Eq. (35). The nonzero
+ factors for triple couplings of Z with charged gauge bosons are
+ collected in Table 5.
+
+
+
+
Feynman rules for triple gauge couplings relating with the decay
+ h → Zγ.
+
+
+
+
+
Vertex
+
Coupling
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
To end this section, we emphasize that all couplings determined in this
+ section do not use the assumption k1 ≫
+ k2, equivalently tβ
+ ≫ 1 as used in Refs. [29,30].
+
+
+
+ Partial decay widths and signal strengths of the decays <italic>h</italic>
+ → <italic>Z</italic>γ, γγ
+
In the MLRSM framework, one-loop three-point Feynman diagrams giving
+ contributions to the decay amplitude
+
+
+ are shown in Fig. 1, where the
+ unitary gauge is applied to determine the gauge boson contributions. The fermion
+ contributions to the amplitude of the decay h
+ → Zγ coincide with the SM results
+ calculated in Refs. [36,37]. Using the general calculation
+ introduced in Ref. [35], we can write
+ these contributions as follows:
+
+
+
+
+
where all form factors
+
+
+ are written in terms of the Passarino–Veltman (PV) notations [40].
+
+
+
+
One-loop three-point Feynman diagrams contributing to the decay
+
+
+ in the unitary gauge, where f
+ i, j
+ are the SM
+ fermions,
+
+
+ ,
+
+
+ .
+
+
+
+
Similarly, the contribution from the charged Higgs bosons can be given as
+
+
+
+
+
The charged gauge boson contributions
+
+
+ to the h → Zγ
+ amplitude are
+
+
+
+
+
Similarly, the contribution from the charged Higgs and gauge bosons arising from
+ diagrams 3 and 4 in Fig. 1 can be
+ given as
+
+
+
+
+
where
+
+
+
+
+
+
+
+
+
Now, the h → Zγ
+ partial decay width is [41,42]:
+
+
+
+
+
where the scalar factors
+
+
+ are derived as follows [35]:
+
+
+
+
+
We note that
+
+
+ were omitted in some previous works [5
+ ,17,
+ 18] because their contributions were expected to be much smaller than the
+ contributions from the SM and are still far from the sensitivity of recent
+ experiments. However, since collider sensitivities have recently been improved
+ and new scales have been established, these contributions are necessary. The
+ branching ratio BrLR(h →
+ Zγ) in the MLRSM framework is
+
+
+
+
+
where
+
+
+ is the total decay width of the SM-like Higgs boson h [41,42].
+ Although experimental measurements of the SM-like Higgs boson productions and
+ decays are available [43], we focus
+ only on the Higgs production through the gluon fusion process ggF
+ at the LHC, in which the respective signal strengths predicted by the two models
+ SM and MLRSM are equal. Then the signal strength corresponding to the decay mode
+ h → Zγ predicted by the
+ MLRSM is:
+
+
+
+
+
where BrSM(h → Zγ)
+ is the SM branching ratio of the decay h
+ → Zγ. The recent ggF
+ → h → Zγ
+ signal strength is μZγ = 2.4
+ ± 0.9 at 2.7σ (standard deviation) [2,3].
+
Similarly, the partial decay width and signal strength of the decay h → γγ
+ can be calculated as [35,42]:
+
+
+
+
+
where
+
+
+
+
+
and
+
+
+
+
+
Here we have used notations to the effect that [
+ 6]:
+
+
+
+
+
where X2 = C12
+ + C22 + C2
+ and
+
+
+ are PV functions [40] with x
+ = f, s, v implying fermions, charged Higgs, and gauge
+ bosons, respectively. Particular forms given in Eq. (49) are defined precisely in Ref.
+ [6]. In the following section, the
+ numerical results will be evaluated using LoopTools [44].
In this section, we use the following quantities fixed from experiments [45]: m
+ h
+ = 125.38 GeV, m
+ W
+ , m
+ Z
+ , well-known fermion masses,
+ v ≃ 246 GeV, the SU(2)
+ L
+ gauge coupling g
+ 2 ≃ 0.651, αem = 1/137,
+
+
+ ,
+
+
+ .
+
The unknown Higgs self-couplings of the MLRSM are ρ1, 2, 3, 4,
+ α1, 2, 3, 4, 5, 6, λ2, 3, 4. The dependent
+ parameter λ1 is given by Eq. (27). Some Higgs self-couplings
+ are expressed as functions of the heavy Higgs boson masses, namely
+
+
+
+
+
Choosing the masses of
+
+
+ ,
+
+ ,
+ and
+
+
+ as free parameters we get
+
+
+
+
+
The other free parameters are λ2,3,4,
+
+ ,
+ hence the mixing angle and the gauge boson masses will be at the orders of
+
+
+ :
+
+
+
+
+
We note here that the relations given in Eq. (52) are consistent with the SM
+ because the two couplings hW+W
+ − and ZW+W
+ − are consistent with the SM predictions.
+
Apart from the limit g
+ L
+ = g
+ R
+ chosen in Eq. (52), in various discussions for
+ the more general case g
+ R
+ ≠ g
+ L
+ , which showed that this ratio
+ is allowed in the following range [46,47]:
+
+
+
+
+
where the lower bound v
+ R
+ > 10 TeV.
+
A recent study showed a lower bound of
+
+
+ TeV is still allowed [31], which gives
+ v
+ R
+ ≥ 17 TeV in this case.
+ On the other hand, the constraint of tβ
+ ≥ 1.2 is allowed, while no lower bounds of charged Higgs masses were
+ given; especially in the limit of the phase, α given in Eq. (6) is zero. Various works discuss
+ the constraints of Higgs masses indirectly [48],
+ or directly from the LHC for doubly charged Higgs bosons [49]. The lower bounds are
+
+
+ GeV. Theoretical constraints were discussed in Ref. [33] for Higgs self-couplings satisfying unitarity bounds
+ and vacuum stability criteria, which will be applied in our numerical
+ investigation.
+
Based on the above discussion for investigating the significant strengths of the
+ two decays h → γγ, Zγ,
+ the values of unknown independent parameters that we choose here will be scanned
+ in the following ranges:
+
+
+
+
+
where the Higgs self-couplings satisfy all theoretical constraints discussed in
+ Ref. [33].
+
+
+
+ Results and discussions
+
To express the differences of prediction between the SM and the MLRSM, we define
+ a quantity ΔμZγ as in
+ Ref. [6]:
+
+
+
+
+
which is constrained by recent experiments as ΔμZ
+ γ = 1.4 ± 0.9 [2
+ ,3], implying the following 1σ
+ deviation:
+
+
+
+
+
The 1σ constraint from h → γγ
+ decay originating from ggF fusion is defined as
+
+ ,
+ leading to the respective 2σ deviation as follows:
+
+
+
+
+
The numerical results we discuss in the following will always satisfy this
+ constraint. We have checked numerically that the MLRSM always contains regions
+ of the parameter space where both values of ΔμZ
+ γ, Δμγγ → 0,
+ implying consistency with the SM results. Considering the special case of
+ g
+ L
+ = g
+ R
+ , we discuss firstly the
+ dependence of
+
+
+ on
+
+ ,
+ which is illustrated in Fig. 2. We
+ just focus on the region satisfying
+
+
+ in order to collect interesting points that may support the 1σ range
+ given in Eq. (56). It
+ can be seen that
+
+
+ is constrained strictly by
+
+ ,
+ i.e.
+
+
+ in the range of 2σ deviation given in Eq. (57). It is noted that negative
+ values of
+
+
+ can give larger
+
+
+ than the positive ones. The largest values of
+
+
+ are still much smaller than the 1σ deviation given by recent experimental
+ data.
+
+
+
+
Correlations between
+
+
+ and
+
+
+ with g
+ L
+ =
+ g
+ R
+ .
+
+
+
+
We comment here to make the point that the future sensitivities are
+
+
+ and
+
+ ,
+ respectively [23]. In the model under
+ consideration, large values of
+
+
+ are not allowed with g
+ L
+ = g
+ R
+ .
+
For completeness in the case of g
+ L
+ = g
+ R
+ , we discuss the dependence of
+
+
+ on tβ and v
+ R
+ , which are shown in
+ Fig. 3. We can see that
+
+
+ depends weakly on v
+ R
+ , but strongly on t
+ β. Namely, all values of v
+ R
+ can give large
+
+ ,
+ while needing small tβ
+ → 1.2.
+
+
+
+
Correlations between
+
+
+ and different values of tβ and
+ v
+ R
+ with g
+ R
+ =
+ g
+ L
+ .
+
+
+
+
The correlations between
+
+
+ and charged Higgs boson masses are shown in Fig. 4. The results show that all charged Higgs masses do not
+ affect strongly the values of
+
+
+ .
+
+
+
+
Correlations between
+
+
+ and charged Higgs boson masses with g
+ R
+ =
+ g
+ L
+ .
+
+
+
+
Finally, we consider the general case of g
+ R
+ with allowed values given in
+ Eq. (53). Numerical
+ results for important correlations of
+
+
+ with
+
+
+ and g
+ R
+ are depicted in Fig. 5. It can be seen clearly that large
+
+
+ corresponds to large g
+ R
+ , which is consistent with the
+ property that new contributions consist of the factor g
+ R
+ in the Feynman rules shown in
+ Sect. 3. We emphasize that large
+ g
+ R
+ is necessary for large
+
+
+ that can reach a value of 46%, very close to the recent experimental
+ sensitivity. Furthermore, the expected sensitivity of
+
+
+ does not affect large values of
+
+
+ that are visible for the incoming experimental sensitivity of 23%.
+
+
+
+
Correlations between
+
+
+ and
+
+
+ (g
+ R
+ ) in the left
+ (right) panel with 0.65 ≤ g
+ R
+ ≤ 1.6.
+
+
+
+
Finally, we focus on the correlations of
+
+
+ with tβ, v
+ R
+ , and all charged Higgs masses,
+ which are depicted in Fig. 6. It
+ is seen again that large
+
+
+ requires small tβ. In contrast,
+
+
+ depends weakly on charged Higgs boson masses and v
+ R
+ as given in Eq. (54).
+
+
+
+
Correlations of
+
+
+ with tβ, v
+ R
+ , and charged
+ Higgs masses with 0.65 ≤ g
+ R
+ ≤ 1.6.
+
+
+
+
+
+
+
+ Conclusions
+
We have studied all one-loop contributions to the SM-like Higgs decays h
+ → γγ, Zγ in the MLRSM
+ framework. Interesting properties of the new gauge and Higgs bosons were explored.
+ Namely, the SM-like Higgs couplings were identified with the SM prediction and
+ experimental data. All masses, physical states of gauge and Higgs bosons, and their
+ mixing were presented clearly so that all couplings related to one-loop
+ contributions to the decay amplitudes h
+ → γγ, Zγ are derived
+ analytically. From this, the decays h
+ → γγ, Zγ in the MLRSM
+ have been discussed using the relevant recent experimental results. The one-loop
+ contributions from the diagrams containing both gauge and Higgs mediation were
+ included in the decay amplitude h → Zγ.
+ These contributions were ignored in previous studies, although they may enhance the
+ h → Zγ amplitude, but do not
+ affect the h → γγ one, leading
+ to the possibility that large ΔμZγ
+ may be allowed under the strict experimental constraint of Δμ
+ γγ. We have shown that the mentioned h decay
+ rates depend weakly on tβ, the SU
+ (2)
+ R
+ vacuum scale v
+ R
+ . The 2σ deviation of μ
+ γγ results in a rather strict constraint
+
+ .
+ On the other hand, large values of
+
+
+ can appear under the very strict constraint of
+
+
+ corresponding to the future experimental sensitivities, provided the two
+ requirements of sufficiently small tβ and large
+ g
+ R
+ are met. Therefore, the future
+ experimental searches of the two decays mentioned in this work will be important to
+ constrain the parameter space of the MLRSM.
+
+
+
+
+ Funding
+
This research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM)
+ under grant number C2022-16-06. Open Access funding: SCOAP3.
+
+
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\ No newline at end of file
diff --git a/tests/units/oup/test_oup_parser.py b/tests/units/oup/test_oup_parser.py
index 6114fafb..2266795b 100644
--- a/tests/units/oup/test_oup_parser.py
+++ b/tests/units/oup/test_oup_parser.py
@@ -619,3 +619,98 @@ def test_collections(parsed_articles):
article["collections"][0] for article in parsed_articles
]
assert set(collections) == set(collections_parsed_article)
+
+
+@fixture
+def article_with_orcid(parser, shared_datadir):
+ with open(os.path.join(shared_datadir, "oup_orcid.xml")) as file:
+ content = parse_without_names_spaces(file.read())
+ article = parser._publisher_specific_parsing(content)
+ yield parser._generic_parsing(article)
+
+
+def test_authors_parsing_with_orcid(article_with_orcid):
+ expected_output = [
+ {
+ "surname": "Hong",
+ "given_names": "T T",
+ "affiliations": [
+ {
+ "institution": "An Giang University",
+ "country": "Vietnam"
+ },
+ {
+ "institution": "Vietnam National University",
+ "country": "Vietnam"
+ }
+ ],
+ "orcid": "0000-0002-7719-4160",
+ "full_name": "Hong, T T"
+ },
+ {
+ "surname": "Le",
+ "given_names": "V K",
+ "affiliations": [
+ {
+ "institution": "An Giang University",
+ "country": "Vietnam"
+ },
+ {
+ "institution": "Binh Thuy Junior High School",
+ "country": "Vietnam"
+ }
+ ],
+ "full_name": "Le, V K"
+ },
+ {
+ "surname": "Phuong",
+ "given_names": "L T T",
+ "affiliations": [
+ {
+ "institution": "An Giang University",
+ "country": "Vietnam"
+ }
+ ],
+ "full_name": "Phuong, L T T"
+ },
+ {
+ "surname": "Hoi",
+ "given_names": "N C",
+ "affiliations": [
+ {
+ "institution": "An Giang University",
+ "country": "Vietnam"
+ }
+ ],
+ "full_name": "Hoi, N C"
+ },
+ {
+ "surname": "Ngan",
+ "given_names": "N T K",
+ "affiliations": [
+ {
+ "institution": "Department of Physics, Can Tho University",
+ "country": "Vietnam"
+ }
+ ],
+ "full_name": "Ngan, N T K"
+ },
+ {
+ "surname": "Nha",
+ "given_names": "N H T",
+ "email": "nguyenhuathanhnha@vlu.edu.vn",
+ "affiliations": [
+ {
+ "institution": "Subatomic Physics Research Group, Science and Technology Advanced Institute, Van Lang University",
+ "country": "Vietnam"
+ },
+ {
+ "institution": "Faculty of Applied Technology, School of Engineering and Technology, Van Lang University",
+ "country": "Vietnam"
+ }
+ ],
+ "orcid": "0009-0005-5993-6895",
+ "full_name": "Nha, N H T"
+ }
+ ]
+ assert article_with_orcid["authors"] == expected_output
diff --git a/tests/units/springer/test_parser.py b/tests/units/springer/test_parser.py
index 257b84b1..77146de0 100644
--- a/tests/units/springer/test_parser.py
+++ b/tests/units/springer/test_parser.py
@@ -132,7 +132,7 @@ def test_authors(parsed_articles):
for author in authors:
for aff in author.get("affiliations", []):
- if aff.get("country") is "Korea":
+ if aff.get("country") == "Korea":
aff["country"] = "South Korea"
assert Enhancer()("Springer", parsed_article)["authors"] == authors
@@ -328,3 +328,95 @@ def test_abstract(parsed_articles):
for abstract, article in zip(abstracts, parsed_articles):
assert "abstract" in article
assert article["abstract"] == abstract
+
+
+@fixture
+def article_with_orcid(parser, datadir):
+ with open(datadir / "s10052-024-12692-y.xml") as file:
+ yield parser._generic_parsing(parser._publisher_specific_parsing(ET.fromstring(file.read())))
+
+
+def test_article_with_cleaned_orcid(article_with_orcid):
+ expected_output = [{
+ "surname": "Hong",
+ "given_names": "T.",
+ "email": "tthong@agu.edu.vn",
+ "affiliations": [
+ {
+ "value": "An Giang University, Long Xuyen, 880000, Vietnam",
+ "organization": "An Giang University",
+ "country": "Vietnam"
+ },
+ {
+ "value": "Vietnam National University, Ho Chi Minh City, 700000, Vietnam",
+ "organization": "Vietnam National University",
+ "country": "Vietnam"
+ }
+ ],
+ "full_name": "Hong, T."
+ },
+ {
+ "surname": "Tran",
+ "given_names": "Q.",
+ "email": "tqduyet@agu.edu.vn",
+ "affiliations": [
+ {
+ "value": "An Giang University, Long Xuyen, 880000, Vietnam",
+ "organization": "An Giang University",
+ "country": "Vietnam"
+ },
+ {
+ "value": "Vietnam National University, Ho Chi Minh City, 700000, Vietnam",
+ "organization": "Vietnam National University",
+ "country": "Vietnam"
+ }
+ ],
+ "full_name": "Tran, Q."
+ },
+ {
+ "surname": "Nguyen",
+ "given_names": "T.",
+ "email": "thanhphong@ctu.edu.vn",
+ "affiliations": [
+ {
+ "value": "Department of Physics, Can Tho University, 3/2 Street, Can Tho, Vietnam",
+ "organization": "Can Tho University",
+ "country": "Vietnam"
+ }
+ ],
+ "full_name": "Nguyen, T."
+ },
+ {
+ "surname": "Hue",
+ "given_names": "L.",
+ "email": "lethohue@vlu.edu.vn",
+ "affiliations": [
+ {
+ "value": "Subatomic Physics Research Group, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam",
+ "organization": "Van Lang University",
+ "country": "Vietnam"
+ }
+ ],
+ "full_name": "Hue, L."
+ },
+ {
+ "orcid": "0009-0005-5993-6895",
+ "surname": "Nha",
+ "given_names": "N.",
+ "email": "nguyenhuathanhnha@vlu.edu.vn",
+ "affiliations": [
+ {
+ "value": "Subatomic Physics Research Group, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam",
+ "organization": "Van Lang University",
+ "country": "Vietnam"
+ },
+ {
+ "value": "Faculty of Applied Technology, School of Technology, Van Lang University, Ho Chi Minh City, Vietnam",
+ "organization": "Van Lang University",
+ "country": "Vietnam"
+ }
+ ],
+ "full_name": "Nha, N."
+ }]
+
+ assert expected_output == article_with_orcid["authors"]
diff --git a/tests/units/springer/test_parser/s10052-024-12692-y.xml b/tests/units/springer/test_parser/s10052-024-12692-y.xml
new file mode 100644
index 00000000..c99a7c13
--- /dev/null
+++ b/tests/units/springer/test_parser/s10052-024-12692-y.xml
@@ -0,0 +1,493 @@
+
+
+
+
+ Springer Berlin Heidelberg
+ Berlin/Heidelberg
+ Springer
+
+
+
+ 10052
+ 10.1007/10052.1434-6052
+ 1434-6052
+ 30312819
+ The European Physical Journal C
+ Particles and Fields
+ Eur. Phys. J. C
+
+ Physics
+ Elementary Particles,
+ Quantum Field Theory
+ Nuclear Physics, Heavy
+ Ions, Hadrons
+ Quantum Field Theories,
+ String Theory
+ Measurement Science and
+ Instrumentation
+ Astronomy, Astrophysics
+ and Cosmology
+ Nuclear Energy
+ Physics and Astronomy
+
+
+
+
+ 84
+ 84
+ 12
+
+
+
+ 3
+ 3
+ 128
+
+
+ 2024
+ 5
+ 7
+
+
+ 2024
+ 3
+
+ 2024
+
+
+ EDP Sciences, Societa Italiana di Fisica (SIF) and
+ Springer-Verlag GmbH, DE, part of Springer Nature
+ 2024
+
+
+
+
+ 12692
+ 10.1140/epjc/s10052-024-12692-y
+ 338
+ 125
+
+ 10.1140/epjc/s10052-024-12783-w
+
+
+
+
+
+
+
+
+ anomalies and decays
+
+
+
+
+
+ ,
+
+
+
+
+ ,
+ and
+
+
+
+
+
+ in a two Higgs doublet model with inverse seesaw neutrinos
+ Regular Article - Theoretical Physics
+ 1
+ 30
+
+
+ 2024
+ 3
+ 20
+
+
+ 2023
+ 12
+ 21
+
+
+ 2024
+ 3
+ 20
+
+
+ 2024
+ 3
+ 30
+
+
+
+
+
+ 2024
+ 5
+ 3
+
+
+ An Erratum to this paper has been published:
+ https://doi.org/10.1140/epjc/s10052-024-12783-w
+
+
+
+
+
+
+
+
+ Vietnam National University HoChiMinh City
+ C2022-16-06
+
+
+
+ The Author(s)
+ 2024
+ corrected publication 2024
+
+
+ Open Access This article is licensed
+ under a Creative Commons Attribution 4.0 International License, which
+ permits use, sharing, adaptation, distribution and reproduction in any
+ medium or format, as long as you give appropriate credit to the original
+ author(s) and the source, provide a link to the Creative Commons licence,
+ and indicate if changes were made. The images or other third party
+ material in this article are included in the article’s Creative Commons
+ licence, unless indicated otherwise in a credit line to the material. If
+ material is not included in the article’s Creative Commons licence and
+ your intended use is not permitted by statutory regulation or exceeds the
+ permitted use, you will need to obtain permission directly from the
+ copyright holder. To view a copy of this licence, visit
+ http://creativecommons.org/licenses/by/4.0/
+
+ .
+ Funded by SCOAP3.
+
+
+
+
+
+
+
+
+
+
+
+ 10052
+ 84
+ 84
+ 3
+ 3
+
+
+
+
+
+
+ T.
+ T.
+ Hong
+
+
+ tthong@agu.edu.vn
+
+
+
+
+ Q.
+ Duyet
+ Tran
+
+
+ tqduyet@agu.edu.vn
+
+
+
+
+ T.
+ Phong
+ Nguyen
+
+
+ thanhphong@ctu.edu.vn
+
+
+
+
+ L.
+ T.
+ Hue
+
+
+ lethohue@vlu.edu.vn
+
+
+
+
+ N.
+ H.
+ T.
+ Nha
+
+
+ nguyenhuathanhnha@vlu.edu.vn
+
+
+
+ https://ror.org/023pm6532
+ grid.448947.2
+ 0000 0000 9828 7134
+ An Giang University
+
+ Long Xuyen
+ 880000
+ Vietnam
+
+
+
+ grid.444808.4
+ 0000 0001 2037 434X
+ Vietnam National University
+
+ Ho Chi Minh City
+ 700000
+ Vietnam
+
+
+
+ https://ror.org/0071qz696
+ grid.25488.33
+ 0000 0004 0643 0300
+ Department of Physics
+ Can Tho University
+
+ 3/2 Street
+ Can Tho
+ Vietnam
+
+
+
+ https://ror.org/02ryrf141
+ grid.444823.d
+ 0000 0004 9337 4676
+ Subatomic Physics Research Group, Science and Technology
+ Advanced Institute
+ Van Lang University
+
+ Ho Chi Minh City
+ Vietnam
+
+
+
+ https://ror.org/02ryrf141
+ grid.444823.d
+ 0000 0004 9337 4676
+ Faculty of Applied Technology, School of Technology
+ Van Lang University
+
+ Ho Chi Minh City
+ Vietnam
+
+
+
+
+ Abstract
+ The lepton flavor violating decays
+
+
+
+
+
+ ,
+
+
+
+
+ ,
+ and
+
+
+
+
+
+ will be discussed in the framework of the Two Higgs doublet model with
+ presence of new inverse seesaw neutrinos and a singly charged Higgs boson
+ that accommodate both
+
+
+
+
+
+ experimental data of
+
+
+
+
+
+ anomalies of the muon and electron. Numerical results indicate that there
+ exist regions of the parameter space supporting all experimental data of
+
+
+
+
+
+ as well as the promising LFV signals corresponding to the future
+ experimental sensitivities.
+
+
+ The original online version of this article was revised: the
+ affiliation details for Author Nguyen Hua Thanh Nha were incorrectly given
+ as ‘Faculty of Applied Technology, School of Engineering and Technology, Van
+ Lang University, Ho Chi Minh City, Vietnam’ but should have been ‘Faculty of
+ Applied Technology, School of Technology, Van Lang University, Ho Chi Minh
+ City, Vietnam’.
+
+
+ An erratum to this article is available online at
+ https://doi.org/10.1140/epjc/s10052-024-12783-w
+
+ .
+
+
+
+
+
+
+
+
\ No newline at end of file