The Higgs boson decay into ZZ decaying to identical fermion pairs

0.54 MB·

by  Taras V. Zagoskin

The Higgs boson decay into ZZ decaying to identical fermion pairs
T.V. Zagoskin1, and A.Yu. Korchin1,2,
∗ †
1NSC “Kharkov Institute of Physics and Technology”, 61108 Kharkov, Ukraine
2V.N. Karazin Kharkov National University, 61022 Kharkov, Ukraine
In order to investigate various decay channels of the Higgs boson h or the hypothetical dilaton,
we consider a neutral particle X with zero spin and arbitrary CP parity. This particle can decay
into two off-mass-shell Z bosons (Z∗ and Z∗) decaying to identical fermion-antifermion pairs (ff¯):
1 2
X →Z∗Z∗ →ff¯ff¯. Wederiveanalyticalformulasforthefullydifferentialwidthofthisdecayand
1 2
for the fully differential width of h → Z∗Z∗ → 4ℓ (4ℓ stands for 4e, 4µ, or 2e2µ). Integration of
7 1 2
1
these formulas yields some Standard Model histogram distributions of the decay h → Z∗Z∗ → 4ℓ
0 1 2
2
which are compared with corresponding Monte Carlo simulated distributions obtained by ATLAS
n
a
and with ATLAS experimentaldata.
J

3
2

]
h
I. INTRODUCTION
p
-
p
e
h The boson h discovered [1] in 2012 by the CMS and ATLAS collaborations was reported to have a mass about
[

125 GeV and some decay modes predicted for the Standard Model (SM) Higgs boson. Since that time, the
1
v
observedparticle, called the Higgs boson, has been intensively studied (see, for example, papers [2]). A main goal
5
3
3 of experiments on the Higgs boson physics has been to prove or disprove the hypothesis that h is the SM Higgs
6
0 boson. Apart from the decay channels, the SM predicts that h has JCP = 0++. The followed thorough analysis
.
1
0 has fine-tuned the mass of h, which is 125.09 0.24 GeV according to Ref. [3], and has yielded some information
±
7
1 on its spin and its CP parity.
:
v
i In particular, the observation of the h ZZ and h W W+ modes (see, for example, Ref. [4]) means that
X → → −
r
the Higgs boson spin is 0, 1, or 2 while the fact that h decays [4] to γγ and the Landau-Yang theorem exclude the
a
spin-one variant. Further, the analyses presented in [5, 6] rule out many spin-two hypotheses at a 99% confidence
level(CL)orhigher. Therefore,weconcludethat the spinofthe Higgsbosonis 0witha probabilityofabout99%.
To clarifythe CP properties ofh, inRef. [7]we study the decayofa spin-zeroparticle X into twooff-mass-shell
Z bosons Z and Z . Since X is defined as an elementary neutral particle with zero spin, our study applies to the
1∗ 2∗
Higgs boson. Moreover,it can apply to the dilaton if this boson actually exists.
The amplitude of the decay X Z Z depends (see Eq. (4) in [7]) on 3 complex-valued functions of the
→ 1∗ 2∗
∗Electronicaddress: [email protected]
†Electronicaddress: [email protected]
2
invariant masses of Z and Z . These functions determine the CP properties of the boson X and are called the
1∗ 2∗
XZZ couplings. UsingtheCMSandATLASexperimentaldataonthedecayh Z Z 4ℓ(where4ℓstandsfor
→ 1∗ 2∗ →
4e, 4µ, or 2e2µ), these collaborations in Refs. [4–6] and we in Ref. [7] have obtained some constraints on the hZZ
couplings. TheseconstraintsdemonstratethathisnotaCP-oddstateanditmaybetheSMHiggsboson,another
CP-even state, or a boson with indefinite CP parity. Besides, as shown in [7], a non-zero imaginary part of the
hZZ couplings is not excluded, which can be related to small loop corrections and possibly to a non-Hermiticity
of the hZZ interaction.
Thus,theCP parityoftheHiggsbosonisnotyetfullyascertained. Moreover,insomesupersymmetricextensions
of the SM there are [8–10] neutral bosons with negative or indefinite CP parity. That is why it is now important
to establish the CP properties of the Higgs boson.
Aimingatthat,weconsiderthedecayoftheparticleX intoZ andZ whichthendecaytofermion-antifermion
1∗ 2∗
pairs f f¯ and f f¯ respectively. While in Ref. [7] we study in detail the decays with the non-identical fermions,
1 1 2 2
f = f , in the present paper the case f = f is under investigation. The masses of the fermions f and f is
1 2 1 2 1 2
6
neglected in both papers.
We are motivated to consider the decay into identical fermions by the following. In Refs. [5, 6] the CMS and
ATLAS collaborations analyze 95 decays h Z Z 4ℓ. 53 of them are the decays to identical leptons, namely
→ 1∗ 2∗ →
to 4e or 4µ. In spite of the fact that the decays to the identical leptons make up about 55% of the measured
decays h Z Z 4ℓ, the distributions of the former decays have not been properly analytically studied. The
→ 1∗ 2∗ →
SM total widths of the decays into identical fermions are studied in Refs. [11, 12] and are calculated in [13]. Some
distributions of the decay X Z Z 4ℓ are plotted in [5, 6] for the SM Higgs boson and some spin-zero states
→ 1∗ 2∗ →
beyondtheSM.InthepresentpaperweperformamoregeneralstudyandconsiderthedecayX Z Z ff¯ff¯
→ 1∗ 2∗ →
with allowance for all the possible CP properties of the particle X.
In Sec. II we derive an analytical formula for the fully differential width of the decay to identical fermions.
SectionIII showsacomparisonofsomedistributions ofthe decayto identicalleptonswith thosefor the decayinto
non-identical ones. For this comparison we obtain an exact analytical formula for a certain differential width of
the decay to non-identicalfermions (see Appendix B). We analyze the usefulness of all the compareddistributions
for obtaining constraints on the hZZ couplings. In Sec. IV we derive some SM histogram distributions of the
decay h Z Z 4ℓ by Monte Carlo (MC) integration and compare them with the corresponding simulations
→ 1∗ 2∗ →
presented in Ref. [5] and with the experimental distributions from [5].
3
II. THE FULLY DIFFERENTIAL WIDTH
We consider a neutral particle X with zero spin and arbitrary CP parity. It can decay into two fermion-
antifermion pairs, f f¯ and f f¯, through the two off-mass-shell Z bosons (Z and Z ):
1 1 2 2 1∗ 2∗
X Z Z f f¯f f¯. (1)
→ 1∗ 2∗ → 1 1 2 2
If m (4m ,2m ] (m is the mass of the particle X, m is the mass of the b quark, m is the mass of the t
X b t X b t
∈
quark), which holds for X = h, then f = e ,µ ,τ ,ν ,ν ,ν ,u,c,d,s,b. If m > 4m , which is possible [14] if
j − − − e µ τ X t
X is the dilaton, then f can be the top quark as well.
j
In Ref. [7] we considered decays
X Z Z f f¯f f¯, f =f (2)
→ 1∗ 2∗ → 1 1 2 2 1 6 2
at the tree level.
The present paper shows our analysis of decay (1) in the case of the identical fermions, f =f f:
1 2
≡
X Z Z ff¯ff¯. (3)
→ 1∗ 2∗ →
The matrix element of decay (3) is
M =M M˜, (4)
iden
−
where the matrix elements M and M˜ correspond to the diagrams (a) and (b) in Fig. 1 respectively. Namely,
f,k f,k
1 1
f,k f,k
1′ 2′
Z ,p Z ,p˜
1∗ 1 1∗ 1
X X
Z ,p Z ,p˜
2∗ 2 2∗ 2
f,k f,k
2 2
f,k f,k
2′ 1′
a b
Figure 1: The Feynmandiagrams contributing tothe matrix element of decay (3).
4
i
M =
(a m2 +im Γ )(a m2 +im Γ )×
1− Z Z Z 2− Z Z Z
× AX→Z1∗Z2∗(p1,p2,λ1,λ2)AZ→ff¯(k1,k1′,λf1,λf¯1,λ1)AZ→ff¯(k2,k2′,λf2,λf¯2,λ2),
λ1,λ2X=−1,0,1
i
M˜ =
(a˜ m2 +im Γ )(a˜ m2 +im Γ )×
1− Z Z Z 2− Z Z Z
× AX→Z1∗Z2∗(p˜1,p˜2,λ1,λ2)AZ→ff¯(k1,k2′,λf1,λf¯2,λ1)AZ→ff¯(k2,k1′,λf2,λf¯1,λ2), (5)
λ1,λ2X=−1,0,1
where
k and k (k and k ) are the 4-momenta of the particles f and f¯ (f and f¯) in the rest frame of X;
• 1 1′ 2 2′ 1 1 2 2
p k +k andp k +k arethe4-momentaofZ andZ respectivelyintherestframeofX indiagram
• 1 ≡ 1 1′ 2 ≡ 2 2′ 1∗ 2∗
Fig. 1 (a);
a p2;
• j ≡ j
m and Γ are respectively the pole mass and the total width of the Z boson;
Z Z
•
• AX→Z1∗Z2∗(p1,p2,λ1,λ2) is the amplitude of the decay X → Z1∗Z2∗ where pj and λj are respectively the
momentum and the helicity of the boson Z in the rest frame of X;
j∗
• AZ→ff¯(k,k′,λf,λf¯,λ) is the amplitude of the decay Z → ff¯where k and λf (k′ and λf¯) are respectively
the momentum and the polarization of f (f¯) in the rest frame of Z, λ is the helicity of decaying Z;
p˜ k +k andp˜ k +k arethe4-momentaofZ andZ respectivelyintherestframeofX indiagram
• 1 ≡ 1 2′ 2 ≡ 2 1′ 1∗ 2∗
Fig. 1 (b);
a˜ p˜2.
• j ≡ j
From the conservation of the energy-momentum 4-vectors we find all the possible values of a and a :
1 2
4m2 <a <(m 2m )2, 4m2 <a <(m √a )2, (6)
f1 1 X − f2 f2 2 X − 1
where m is the mass of the fermion f .
fj j
The amplitude AX→Z1∗Z2∗(p1,p2,λ1,λ2) is [7]
b (a ,a )
Z 1 2
AX→Z1∗Z2∗(p1,p2,λ1,λ2)=gZ aZ(a1,a2)(e∗1·e∗2)+ m2X (e∗1·pX)(e∗2·pX)
c (a ,a )
+i Z 1 2 ε pµ(pν pν)(eρ) (eσ) , (7)
m2X µνρσ X 1 − 2 1 ∗ 2 ∗!
where g 2 √2G m2, G is the Fermi constant, a (a ,a ), b (a ,a ), and c (a ,a ) are some complex-
Z ≡ F Z F Z 1 2 Z 1 2 Z 1 2
p
valued dimensionless functions of a and a , e e(p ,λ ), e(p,λ) is the polarization4-vectorof the Z boson with
1 2 j j j
≡
5
a momentum p and a helicity λ, p p +p =p˜ +p˜ =(m ,~0) is the 4-momentum of the boson X in its own
X 1 2 1 2 X
≡
rest frame, ε is the Levi-Civita symbol (ε =1).
µνρσ 0123
The values of the couplings a , b , and c reflect the CP properties of the particle X. Specifically, at the tree
Z Z Z
level the correspondence shown in Table I takes place.
Table I: The CP parity of theparticle X for various valuesof aZ, bZ, and cZ.
CP a b c
X Z Z Z
1 any any 0
−1 0 0 6= 0
indefinite 6= 0 any 6= 0
any 6=0 6=0
For the SM Higgs boson the loop corrections change slightly the tree-level values a = 1, b = 0, c = 0 (see,
Z Z Z
for example, Refs. [6, 15–17]). In particular,the SM electroweakradiative diagramstune the value of the coupling
b , beginning from the next-to-leading order, while a contribution to c appears at the three-loop level. Physics
Z Z
beyond the SM is the additional source of a possible deviation from the values a =1, b =0, c =0.
Z Z Z
Calculating Lorentz-invariantamplitude (7) in the rest frame of X, we derive that
k
AX→Z1∗Z2∗(p1,p2,±1,±1)=gZ aZ(a1,a2)±cZ(a1,a2)m2 ,
(cid:18) X(cid:19)
m2 a a k2
AX→Z1∗Z2∗(p1,p2,0,0)=−gZ(cid:18)aZ(a1,a2) X2−√a11a−2 2 +bZ(a1,a2)4m2X√a1a2(cid:19),
AX→Z1∗Z2∗(p1,p2,λ1,λ2)=0, λ1 6=λ2, (8)
where k(a ,a ) λ1/2(m2 ,a ,a ), λ(x,y,z) x2+y2+z2 2xy 2xz 2yz.
1 2 ≡ X 1 2 ≡ − − −
We take the amplitude AZ ff¯(k,k′,λf,λf¯,λ) from the SM (see, for example, Ref. [18]).
→
ϕ
f
1
θ1 f2 θ2
¯ Z1∗ X Z2∗ f¯2
f
1
Figure 2: The kinematics of decay (1). We show the momenta of Z∗ and Z∗ in the rest frame of X while the momenta of
1 2
f1 and f¯1 (f2 and f¯2) are shown in the rest frame of Z1∗ (Z2∗).
Further, to describe decay (1), let us introduce the following angles (see Fig. 2): θ (θ ) is the angle between
1 2
6
the momentum of Z (Z ) in the rest frame of X and the momentum of f (f ) in the rest frame of Z (Z ) (in
1∗ 2∗ 1 2 1∗ 2∗
other words, θ (θ ) is the polar angle of the fermion f (f )) and ϕ is the azimuthal angle between the planes of
1 2 1 2
the decaysZ f f¯ and Z f f¯. For decay (3), we can arbitrarilychoosethe Z boson whichwe will call Z ,
1∗ → 1 1 2∗ → 2 2 1∗
and then we will refer to the other Z boson as Z .
2∗
As for a˜ and a˜ , an explicit calculation yields
1 2
a˜ = m2X −a1−a2(1 cosθ cosθ )+ √a1a2 sinθ sinθ cosφ+ k(cosθ cosθ ),
1 1 2 1 2 1 2
4 − 2 4 −
a˜ = m2X −a1−a2(1 cosθ cosθ )+ √a1a2 sinθ sinθ cosφ+ k(cosθ cosθ ). (9)
2 1 2 1 2 2 1
4 − 2 4 −
The expression for the amplitude AX→Z1∗Z2∗(p˜1,p˜2,λ1,λ2) is analogous to Eq. (7):
b (a˜ ,a˜ )
Z 1 2
AX→Z1∗Z2∗(p˜1,p˜2,λ1,λ2)=gZ aZ(a˜1,a˜2)(E1∗·E2∗)+ m2X (E1∗·pX)(E2∗·pX)
c (a˜ ,a˜ )
+i Z m12X 2 εµνρσpµX(p˜ν1 −p˜ν2)(E1ρ)∗(E2σ)∗!, (10)
where e˜j =e(p˜j,λj). Calculating AX→Z1∗Z2∗(p˜1,p˜2,λ1,λ2) in the rest frame of X, we get
2
AX→Z1∗Z2∗(p˜1,p˜2,±1,±1)=gZ(cid:18)aZ(a˜1,a˜2)±cZ(a˜1,a˜2)mX|k1+k′2|(cid:19),
g
AX→Z1∗Z2∗(p˜1,p˜2,0,0)=−4√a˜Z1a˜2 aZ(a˜1,a˜2) m2X +a1+a2+(m2X −a1−a2)cosθ1cosθ2
(cid:16)
−2√a1a2sinθ1sinθ2cosφ +bZ(a˜1,a˜2)·4|k1+k′2|2!,
(cid:17)
AX→Z1∗Z2∗(p˜1,p˜2,λ1,λ2)=0, λ1 6=λ2, (11)
where
|k1+k′2|2 = a1+4 a2 − √a21a2 sinθ1sinθ2cosφ+ 16km22 (cos2θ1+cos2θ2)+ cos8θm1c2osθ2(m4X −(a1−a2)2).
X X
(12)
Using Eqs. (4), (5), (8), (9), and (11), we derive Eq. (A1) (see Appendix A).
III. INVARIANT MASS AND ANGULAR DISTRIBUTIONS
IntegratingEq.(A1)numerically,wecanobtainsomedistributionsofdecay(3). Moreover,numericalintegration
of Eq. (5) in Ref. [7] yields distributions for decay (2). In Figs. 3 and 4 we compare certain distributions of (3)
with those of (2). We define the weak mixing angle as θ arcsin 1 m2 /m2, where m is the mass of the
W ≡ − W Z W
p
W boson, and use the values of the constants in Table II neglecting their experimental uncertainties.
First, we show the SM distribution 1 d2Γ for any decay h Z Z f f¯f f¯ with f different from f
Γda1da2 → 1∗ 2∗ → 1 1 2 2 1 2
(see Fig. 3a) and that for any decay h Z Z 4l where l stands for e, µ, or τ (see Fig. 3b). We see peaks
→ 1∗ 2∗ →
at √a1 = mZ or √a2 = mZ and a flat surface outside the peaks for either dependence. For the decay into
7
Table II: Thevalues of the Fermiconstant, of themasses of h, Z, W,and of thetotal width of Z from Ref. [19].
GF =1.1663787(6)×10−5 GeV−2
m =125.7(4) GeV
h
mZ =91.1876(21) GeV
mW =80.385(15) GeV
ΓZ =2.4952(23) GeV
non-identical fermions the SM values of 1 d2Γ on the peaks are about 120 times greater than the values on the
Γda1da2
“plateau” (the square√a ,√a .50GeV). However,forthe decayinto identicalleptons this ratiovariesfrom3 to
1 2
55 if we take √a =m , √a = 1(m m ) as the indicative point on the peak and on the plateau we consider
1 Z 2 2 h− Z
the points on the line √a = √a from √a = 1 GeV to √a = 59 GeV. Moreover, the SM probability that in a
1 2 1 1
decay h Z Z f f¯f f¯ either Z boson has an invariant mass less than 50 GeV is
→ 1∗ 2∗ → 1 1 2 2
(50 GeV)2 (50 GeV)2
1 d2Γ
da1 da2 f16=f2 2.4% (13)
Γ da da ≈
f16=f2|SM Z0 Z0 1 2 (cid:12)(cid:12)SM
(cid:12)
while the corresponding probability for the decay h Z Z 4l is much(cid:12)higher, of about 21%.
→ 1∗ 2∗ →
Figure4showsthe distributions 1dΓ, 1 1dΓ, and 1dΓ for the decayto non-identicalleptons andthe decayto
Γda sinθΓdθ Γdφ
identicalones. The definitions andexplicit formulasfor the differentialwidths dΓ and dΓ are givenin Appendix C
da dθ
(see Eqs. (C1), (C9), (C10), and (C15)).
The distributions in Fig. 4 are presented at the following four sets of values of the couplings a , b , and c :
Z Z Z
a =1, b =0, c =0,
Z Z Z
| |
a =1, b =0, c =0.5,
Z Z Z
a =1, b =0, c =0.5i,
Z Z Z
a =1, b = 0.5, c =0. (14)
Z Z Z
−
InRef. [7]sets (14) areshownto be consistentwith the availableLHC data and arechosenforan analysisofsome
observables sensitive to the hZZ couplings.
The dependences in the upper plot of Fig.4a are calculatedusing Eq. (A2) from Ref. [7] and Eq. (B2) fromthis
paper. The dots in the two other plots of Fig. 4a present the results of MC integrations of Eq. (A2). The lines
shown in these plots fit the corresponding dots according to the method of least squares.
The dots in Fig. 4b are obtainedby means of MC integrationofEq. (A1). The lines in the upper plot ofFig. 4b
consist of cubic parabolas joining the neighboring dots, since we have not been able to properly fit the dots of
this plot with the method of least squares. The lines in the two other plots of Fig. 4b are least-squares fits to the
corresponding dots.
The dependences plotted in Fig. 4 almost coincide at all four sets (14). For this reason, we can get significant
8
a
b
Figure 3: The distribution Γ1dad12dΓa2 in the SM for the decays h → Z1∗Z2∗ → f1f¯1f2f¯2 with f1 6= f2 (a) and for the decays
h→Z∗Z∗ →4l with l=e,µ,τ (b).
1 2
constraintson a , b , and c via measurementof the distributions 1dΓ, 1 1dΓ, and 1dΓ only if these distribu-
Z Z Z Γda sinθΓdθ Γdφ
tions are measured at very high precision. That is why in order to constrain the hZZ couplings, we should try to
define observables sensitive to these couplings, like it is done in [7] for decay (2).
The distinctions between the distributions 1dΓ for the decay into non-identical leptons (Fig. 4a) and those for
Γda
identical leptons (Fig. 4b) are due to greater values of the SM distribution 1 d2Γ on the plateau for the decay
Γda1da2
h → Z1∗Z2∗ → 4l and smaller values of this distribution at the peaks √a1 = mZ and √a2 = mZ (see Fig. 3).
However,these distinctions are insubstantial.
The dissimilarity between the functions 1 1dΓ and 1dΓ in Figs. 4a and 4b is much more appreciable. The
sinθΓdθ Γdφ
global maximum of 1 1dΓ at θ = π/2 in Fig. 4a becomes a local minimum in Fig. 4b, and the values near the
sinθΓdθ
points θ = 0 and θ = π increase. Analogous distinctions take place between the dependences of 1dΓ in Figs. 4a
Γdφ
and 4b.
9
G1ddGa,10-4Ge1V2 G1ddGa,10-4Ge1V2
7 7
6 6
5 5
4 4
3 3
2 2
1 1
20 40 60 80 100 120 a,GeV 0 20 40 60 80 100 120 a,GeV
1 1dG 1 1dG
sinΘGdΘ sinΘGdΘ
0.6 0.6
0.5 0.5
0.4 0.4
0.3 0.3
0.2 0.2
0.1 0.1
0.00 Π4 Π2 34Π ΠΘ 0 Π4 Π2 34Π Π Θ
1dG 1dG
GdΦ GdΦ
0.25 0.25
0.20 0.20
0.15 0.15
0.10 0.10
0.05 0.05
Φ Φ
0 Π Π 3Π 2Π 0 Π Π 3Π 2Π
2 2 2 2
a b
Figure 4: The distributions Γ1ddΓa, sin1θΓ1ddΓθ, and Γ1ddΓφ for the decays h→Z1∗Z2∗ →l1−l1+l2−l2+; lj =e,µ,τ in the cases l1 6=l2
(a) and l1=l2 (b). The blue, purple,yellow, and green lines and dots correspond to sets (14) respectively.
IV. COMPARISON WITH EXPERIMENTAL DATA
A. ATLAS and CMS results
In Ref. [5] the ATLAS collaboration presents experimental distributions of the decay h Z Z 4ℓ and
→ 1∗ 2∗ →
corresponding distributions derived with MC simulations in the SM. We take the same kinematic limitations
and the bin widths as ATLAS and use Eqs. (A1) and (A2) to derive the SM histogram distributions of the decay
h Z Z 4ℓwhichappearin[5]. ComparisonofourdistributionswiththeATLASexperimentalandtheoretical
→ 1∗ 2∗ →
ones will determine the usefulness of Eq. (A1).
CMS has shownexperimental distributions for the decay h VV 4ℓ (VV =ZZ, Zγ,γγ) and corresponding
→ →
MC simulations in the SM in Ref. [6]. Taking the same kinematic limitations and the same bin widths as CMS,
we integrate Eqs. (A1) and (A2) in the SM to obtain distributions for the decay h Z Z 4ℓ.
→ 1∗ 2∗ →
We introduce the four following variables: m (m ) is the invariant mass of the Z boson which is produced in
12 34
10
a decay h Z Z 4ℓ and whose mass is closest to (most distant from) m , θ (θ ) is the polar angle of the
→ 1∗ 2∗ → Z 1′ 2′
fermion whose parent Z boson has the invariant mass closest to (most distant from) m . From the definitions of
Z
m and m it follows that
12 34
m m < m m . (15)
12 Z 34 Z
| − | | − |
However,sincem <2m ,thequantitym (m )canbeequivalentlydefinedastheinvariantmassoftheheaviest
h Z 12 34
(lightest) Z boson produced in a decay h Z Z 4ℓ (m >m ).
→ 1∗ 2∗ → 12 34
In Ref. [5] ATLAS shows distributions of m , m , cosθ , and φ (a distribution of cosθ is not presented).
12 34 1′ 2′
ATLAS selects decays h Z Z 4ℓ wherein
→ 1∗ 2∗ →
m (50 GeV,106 GeV), m (12 GeV,115 GeV), η ( 2.47,2.47), η ( 2.7,2.7). (16)
12 34 e µ
∈ ∈ ∈ − ∈ −
Here η (η ) is the pseudorapidity of the electron (muon):
e µ
θ
i
η (θ ) lntan , i=e,µ, (17)
i i
≡− 2
where θ (θ ) is the polar angle of the electron (muon).
e µ
CMS paper [6] presents distributions of m , m , cosθ , cosθ , and φ for the decay h VV 4ℓ with
12 34 1′ 2′ → →
m (40 GeV,120 GeV), m (12 GeV,120 GeV), η ( 2.5,2.5), η ( 2.4,2.4). (18)
12 34 e µ
∈ ∈ ∈ − ∈ −
Constraints (16) and (18) determine the fractions of decays selected by ATLAS or CMS in the corresponding
decay modes. These fractions are given by the left-hand sides of Eqs. (D1) and (D9). We have calculated the
corresponding percentages in the SM (see Table III).
Table III:The SMpercentages PSM of decaysselected bytheCMS and ATLAScollaborations, for various decay modes.
Decay mode PSM
CMS ATLAS
h→Z∗Z∗ →4e 84.6 % 75.6 %
1 2
h→Z∗Z∗ →4µ 84.1 % 76.4 %
1 2
h→Z∗Z∗ →2e2µ 86.5 % 85.1 %
1 2
h→Z∗Z∗ →4ℓ 85.5 % 81.1 %
1 2
B. A discussion of plots
IntegratingEq.(D10)withaMCmethod,wederivesomeSMhistogramdistributionsofthedecayh Z Z
→ 1∗ 2∗ →
4ℓ (see the blue lines in Figs. 5 and 6). The bin widths in Fig. 5 are taken from Ref. [5] while those in Fig. 6 are
taken from [6].