Studying the resonance production cross-section of the heavy vectors within Heavy Vector Triplet model
In the context of TeV-scale extensions of the Standard Model both the experimental data and the construction of phenomenological models for the new heavy bosons searches are used by us. Heavy particles are predicted by the Simplified Model to describe only the on-shell resonance, have to be compared...
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2023
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| Cite this: | Studying the resonance production cross-section of the heavy vectors within Heavy Vector Triplet model / T.V. Obikhod, I.A. Petrenko // Problems of Atomic Science and Technology. — 2023. — № 3. — С. 3-7. — Бібліогр.: 11 назв. — англ. |
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| citation_txt | Studying the resonance production cross-section of the heavy vectors within Heavy Vector Triplet model / T.V. Obikhod, I.A. Petrenko // Problems of Atomic Science and Technology. — 2023. — № 3. — С. 3-7. — Бібліогр.: 11 назв. — англ. |
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| description | In the context of TeV-scale extensions of the Standard Model both the experimental data and the construction of phenomenological models for the new heavy bosons searches are used by us. Heavy particles are predicted by the Simplified Model to describe only the on-shell resonance, have to be compared with LHC data. Bosons V’ created and decay according to the process pp‐>V’‐>Vh (V=W, Z) have certain properties that can be modeled within the Heavy Vector Triplet model using the Madgraph computer program. We have calculated the production cross sections of heavy particles using the experimental constraints in the parameter space (cₕ, cf) imposed on the benchmark scenario. The nature of the functional dependence of the cross section on the mass of the new boson, as well as the mechanism for the heavy particle production is studied with variation of the model parameters.
У контексті тераелектронвольтних розширень Стандартної моделі нами використовуються як експериментальні виміри, так і побудовані феноменологічні моделі для пошуку нових важких бозонів. Важкі частинки, що передбачені спрощеною моделлю, яка побудована для опису тільки резонансу на оболонці, необхідно порівнювати з даними на LHC. Бозони V’, що утворюються і розпадаються відповідно до процесу pp‐>V’‐>Vh (V=W, Z), мають певні властивості, які можна змоделювати в рамках Heavy Vector Triplet моделі за допомогою комп’ютерної програми Madgraph. Ми розрахували перерізи утворення важких частинок V’ з використанням експериментальних обмежень у просторі параметрів (cₕ, cf), які накладено на еталонний сценарій. Досліджено характер функціональної залежності перерізу при основних параметрах моделі від маси нового бозона, а також механізм народження таких частинок.
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ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №3(145) 3
NUCLEAR PHYSICS AND ELEMENTARY PARTICLES
https://doi.org/10.46813/2023-145-003
STUDYING THE RESONANCE PRODUCTION CROSS-SECTION OF
THE HEAVY VECTORS WITHIN HEAVY VECTOR TRIPLET MODEL
T.V. Obikhod, I.A. Petrenko
Institute for Nuclear Research NAS of Ukraine, Kyiv, Ukraine
E-mail: obikhod@kinr.kiev.ua
In the context of TeV-scale extensions of the Standard Model both the experimental data and the construction of
phenomenological models for the new heavy bosons searches are used by us. Heavy particles are predicted by the
Simplified Model to describe only the on-shell resonance, have to be compared with LHC data. Bosons V’ created
and decay according to the process pp->V’->Vh (V=W, Z) have certain properties that can be modeled within the
Heavy Vector Triplet model using the Madgraph computer program. We have calculated the production cross
sections of heavy particles using the experimental constraints in the parameter space (cH, cF) imposed on the
benchmark scenario. The nature of the functional dependence of the cross section on the mass of the new boson, as
well as the mechanism for the heavy particle production is studied with variation of the model parameters.
PACS: 12.60.−i, 14.80.−j
INTRODUCTION
As Higgs boson properties have been measured with
increasing precision, it has become an ideal tool to
conduct new-physics searches. There are several
questions related to the electroweak symmetry breaking
mechanism, for example to the radiative corrections to
Higgs boson mass and to an extended scalar sector of
Higgs boson. Such phenomena have been predicted in
many extensions of the Standard Model (SM), among
which are heavy vector bosons which couple to the
Higgs boson (as in models with warped extra
dimensions). Prominent examples of searches for heavy
vector bosons are direct searches for new heavy
particles (instead of W, Z bosons in Fig. 1) decaying
into Higgs boson.
Fig. 1. Feynman diagrams for left:
vector boson fusion (VBF) production process; right:
associated Higgs boson production process [1]
The purpose of our paper is the study of
characteristics of such new heavy particles in the
framework of new phenomenological model according
to the latest experimental restrictions.
1. EXPERIMENTAL DATA AND THE NEED
FOR A NEW THEORETICAL
INTERPRETATION
The experimental searches for new heavy particles
were performed by ATLAS [2, 3] and CMS [4, 5]. The
ATLAS collaboration recently released results of a
search for a new heavy particle decaying into a Higgs
and a W boson [6], Fig. 2.
Fig. 2. Expected and observed upper limits at 95% CL
on the production cross section for pp→W’→WH
and the theory curves for Models A (B)
with corresponding couplings gV = 1 (3)
There is the search for an excess in the invariant
mass distribution of the ℓνbb final state with excluded
Wʹ masses below 2.95 and 3.15 TeV for two benchmark
models. Processes of type pp → WH/ZH were
summarized and numerically discussed for the total
cross sections, taking into account all available higher-
order corrections of the strong QCD interactions, Fig. 3.
Fig. 3. Left: hadronic collisions, (leading order, LO)
are affected by large uncertainties arising from center:
higher-order QCD corrections to the production cross
section (the next-to-leading order, NLO), right: the
next-to-next-to-leading order NNLO, from [7]
The total cross section for the subprocess is obtained by
integrating over k
2
:
4 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №3(145)
,
ˆ/1
ˆ/12ˆ;,
ˆ;,
ˆ288
22
222
222/122
42
sM
sMsMM
sMMa
s
MG
VHqq
V
VHV
HVqq
VF
LO
.
where the reduced quark couplings to the gauge bosons
are given in terms of the electric charge and the weak
isospin of the fermion as:
233 42,2 Wqqqqq sQIIa , V=Z;
2 qq a , V=W;
2 2 21 sin .W W Ws c
The impact of QCD corrections quantified by
calculating the K-factor is defined as the ratio of the
cross sections for the process at HO (NLO or NNLO),
over the cross section at LO:
( )
.
( )
HO
HO
LO
pp HV X
K
pp HV
The NLO K-factor is increasing as function of Higgs
mass from KNLO = 1.27 to KNLO = 1.29. The NNLO
contributions increase the K-factor by 1% - 3.5% for the
high value of Higgs mass, [7].
So, the experimental and modeled data of such
processes show a significant increase to the cross
section from the loop corrections and, accordingly,
require modification of the coupling constants. Such
requirements provide some models of theoretical
interpretations of the results and restrict benchmark
regions of the parameter space. It is clear that precise
predictions must be made in TeV-scale simplified
extensions of SM which have to be compared with LHC
data. Some qualitative predictions could be interpreted
in the context of the heavy vector triplet (HVT) model
parameterized on the new coupling constant and
connected with the existence of a set of new heavy
particles.
2. HEAVY VECTOR TRIPLET MODEL
AND CHARACTERISTICS OF HEAVY
PARTICLES
HVT is the type of particle with high mass and the
set of three vectors, 0, VV
= 1,2,3, spin-1 bosons (two
charged and one neutral):
,,
2
30
21
VV
iVV
V
which can describe 0, VV
system notated as W’/Z’.
The new phenomenological Lagrangian incorporates
kinetic terms, SM interactions and HVT interactions
cba
abcVVV
V
a
F
a
F
V
aa
HV
aaVaa
V
VDVVc
g
JVc
g
g
HDHVcig
VV
m
VDVDL
2
24
1
2
2
2 ,
2
a a a b c
V VVHH VVW abc
g
g c V V H H c W V V
where
33,2/ JVcJVcJVcJVc qqllFF
aa
currents with different couplings to leptons, light quarks
and the third quark family. There is the parameterization
of the interaction terms V, H and fermionic fields with a
coupling gV. Similarly, the insertion of W is weighted
by coupling g. The first line of the above equation
contains the V kinetic and mass terms, plus trilinear and
quadrilinear interactions with the vector bosons from
the covariant derivatives,
,,][
cbabcaaaaa
VWgVVDVDVDVD
the second line contains direct interactions of V with the
Higgs current,
HHiDHDiHHDiH
aaa
and with the SM left-handed fermionic currents, a
FJ
,
(cH controls the V interactions with the SM vectors and
with the Higgs and in particular its decays into bosonic
channels, cF describes interaction with fermions, which
is responsible for both the resonance production by
Drell-Yan (DY) and for its fermionic decays).
The third-fourth lines contain 3 new operators and
free parameters, cVVV , cVVHH and cVVW and they do not
contribute directly to V decays and production
processes.
For the HVT, there are two overarching models,
termed Model A and Model B. Model A is the extended
gauge symmetry whereas Model B is more likely to be a
composite Higgs. The dominant branching ratio in the
Model B and the subdominant in Model A is the decay
into Higgs boson and a Vector boson, (Fig. 4).
Fig. 4. Feynman diagram for hadronic decay of the
heavy vector boson, W’
The neutral mass eigenvalues of heavy vector boson
0
V are expressed through the SM Z boson and one
heavy vector of mass M0
2
0
22
2
0
22 ,
MmMDet
MmMTr
ZN
ZN
In the charged sector the mass eigenvalues of charged
heavy vector boson are expressed through the SM W
boson and one heavy vector of mass M+
222
222 ,
MmMDet
MmMTr
WC
WС
In the following, we will use two models A [8] and
B [9], describing the heavy vectors, with fixed c
for A model: 1~,/~ 22
FVH cggc ;
for B model: ~ ~1,H Fc c
.
.
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №3(145) 5
and free parameters – the resonance coupling gV and its
mass MV.
Two main production processes of the new vectors
V’in proton-proton collision are DY and VBF. The
purpose of our paper is to calculate production cross-
sections of heavy vectors at different parameters and to
compare them with known results.
3. RESULTS OF CALCULATIONS
Experimental data, presented in Fig. 2 show the
upper limits on the production cross-section for
pp → W' times the branching fraction of W' →WH
process at 13 TeV. The masses below 2.95 TeV are
excluded with coupling constant gV = 1 for the HVT
benchmark Model A. For Model B masses below
3.15 TeV are excluded with coupling constant gV = 3.
Taking into account the experimental constrains in the
(cH , cF ) plane for the benchmark points at MV = 2 TeV
[10], we calculated the production cross sections for
heavy particles (Table 1), taking into account the
benchmark scenario for A and B models.
Table 1
Production cross sections for pp→V
’
→Vh (V=W, Z)
processes at 14 TeV
Channels Model Production cross
sections, (pb)
p
p
→
W
„
→
W
h
p
p
→
Z
’ →
Z
h
A: сH= - 0.5 cq= -1
c3= -1, cl= -1
0.6793 ± 0.0007
B: сH= - 0.7 cq= 1
c3= 1, cl= 1
0.6874 ± 0.00078
A: сH= - 0.5 cq= -1
c3= -1, cl= -1
0.5917 ± 0.00061
B: сH= - 0.7 cq= 1
c3= 1, cl= 1
0.5969 ± 0.00064
p
p
→
W
„
→
W
h
p
p
→
Z
’ →
Z
h
A: сH= 0 cq= -1
c3= -1, cl= -1
0.6775 ± 0.00068
B: сH= - 1 cq= 1
c3= 1, cl= 1
0.6853 ± 0.00072
A: сH= 0 cq= -1
c3= -1, cl= -1
0.5909 ± 0.00061
B: сH= - 1 cq= 1
c3= 1, cl= 1
0.5951 ± 0.00058
From Table 1 we do not see a significant difference
in the values of the cross sections for the production
processes of V’(W’ or Z’) for model A and model B,
although quantitatively the cross section for the
production of a boson Z’ is somewhat smaller than that
of a boson W’.
Let’s consider new range of parameter space and
new energies at the LHC for the calculations of
production cross sections and masses of new heavy
particles. Using Madgraph_aMC@NLO program [11]
and corresponding parameter space, we calculated
production cross sections for pp → W’ → Wh process
at the fixed cH=1, presented below in Table 2.
Table 2
Production cross sections for pp → W’ → Wh
process at 14 TeV
The two main production mechanisms of the new
vectors are DY and VBF. DY is the dominant
production mechanism as the partonic cross-section is
large when the V’ coupling to fermions is much larger
than the one to vector bosons in all regions of parameter
space. VBF process has a chance of being comparable
to DY if cH is not suppressed. If the coupling to
fermions is suppressed, cF ≈ 0, VBF becomes the
dominant production mechanism, the fermionic decays
are suppressed and thus the total resonance width is
twice the di-boson one. This makes VBF more
interesting at the LHC at 14 TeV, to explore specific
scenarios with suppressed coupling to fermions. In
Fig. 5 we show the ratio of the production cross-section
by DY and VBF as a function of the cF/cH ratio, for
different processes (pp → V’ → Vh (V=W, Z)) at the
LHC at 14 TeV (cF is expressed in values of cq, cl, c3 ).
Fig. 5. The ratio of DY and VBF production cross-
sections as a function of the cF/cH ratio for up:
MV=2 TeV, cH=1; down: results from [10]
cF (cq, cl, c3) Production cross sections, (pb)
1 0.5969±0.00062±systematics
2 0.5987±0.00064±systematics
3 0.5992±0.00062±systematics
4 0.5991±0.00059±systematics
5 0.6003±0.00072±systematics
6 0.6±0.0006±systematics
7 0.5989±0.00054±systematics
8 0.5974±0.00069±systematics
9 0.596±0.00058±systematics
10 0.5927±0.00069±systematics
6 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №3(145)
Comparison of the calculated results shows that if in
region cF/cH ~ 1 there is an approximate coincidence of
the quantitative and qualitative behavior of the cross
sections, then with an increase in the ratio cF/cH, we
observe a peak and a decrease in the dependence curve.
In addition, the process with the W boson has a
significantly larger DY cross section compared to the Z
boson. At large cF/cH~10, we see the predominance of
the VBF process of production of a heavy boson above
DY one.
The study of the properties of a heavy boson is
associated with the determination of its mass as a key
parameter included in the calculation of observable
quantities. We have calculated the V’ boson masses at
energies of 14 and 100 TeV. The corresponding results
are shown in Fig. 6.
Fig. 6. Production cross section of heavy boson W
’
as
a function of its mass with different parameter space
at the energies: up – 14 TeV; down – 100 TeV
Comparison of the performed calculations presented
in Fig. 6 shows the same nature of the growth of cross
sections for different sets of parameters and energies,
however quantitatively at 100 TeV the cross section
grows by an order of magnitude and after 5 TeV there is
a tendency to reach saturation. We also calculated the
dependence of the cross section on the mass Z’ for the
restricted experimental data presented in the parameter
space (cH, cF) [10], presented in Fig. 7.
The obtained results are approximately the same one
as for the case shown in Fig. 6, but the production cross
section for Z’ boson is smaller than for heavy boson W’.
Fig. 7. Production cross section of heavy boson Z
’
formation as a function of its mass at the energy 14 TeV
CONCLUSIONS
We have done the production cross sections
calculations of heavy bosons, their masses and
dependence on the certain benchmark scenario for cF
and cH. We have found different values of the cross
sections for different parameters and showed that
qualitatively the character of behavior of the cross
section from mass remains the same for different
particles (W’ or Z’) and different energies, although
quantitatively the cross sections for the production of
heavy bosons are 10 times larger at 100 TeV compared
to similar calculations at 14 TeV. We compared the
cross section ratio DY/VBF with previous calculations
by D. Pappadopulo, A. Thamm, R. Torre and A. Wulzer
and found a numerical agreement in the same parameter
range. However, further study of the nature of the cross
section showed the predominance of the process VBF at
cF/cH~10.
REFERENCES
1. URL: https://en.wikipedia.org/wiki/Higgs_boson
#cite_ref-HprodLHC_107-3.
2. ATLAS Collaboration. Search for W Z resonances
in the fully leptonic channel using pp collisions at
s = 8 TeV with the ATLAS detector //
arXiv:1406.4456.
3. ATLAS Collaboration. Search for new phenomena
in the dijet mass distribution using pp collision data
at s = 8 TeV with the ATLAS detector //
arXiv:1407.1376.
4. CMS Collaboration. Search for narrow t + b
resonances in the leptonic final state at √ s = 8 TeV
// CMS-PAS-B2G-12-010.
5. CMS Collaboration. Search for new resonances
decaying via WZ to leptons in proton-proton
collisions at s = 8 TeV // arXiv:1407.3476.
6. ATLAS Collaboration. Search for heavy resonances
decaying into a W boson and a Higgs boson in final
states with leptons and b-jets in 139 fb
−1
of pp
collisions at s = 13 TeV with the ATLAS detector //
ATLAS-CONF-2021-026.
7. O. Brein, A. Djouadi, R. Harlander. NNLO QCD
corrections to the Higgs-strahlung processes at
hadron colliders // arXiv:hep-ph/0307206.
https://en.wikipedia.org/wiki/Higgs_
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №3(145) 7
8. V. Barger, W.Y. Keung, and Ernest Ma. Gauge
model with light W and Z bosons // Phys. Rev. 1980,
D 22, p. 727.
9. R. Contino, D. Marzocca, D. Pappadopulo, and
R. Rattazzi. On the effect of resonances in
composite Higgs phenomenology // JHEP. 2011,
v. 10 081, arXiv:1109.1570.
10. D. Pappadopulo, A. Thamm, R. Torre, A. Wulzer.
Heavy Vector Triplets: Bridging Theory and Data //
arXiv:1402.4431 [hep-ph].
11. J. Alwall et al. The automated computation of tree-
level and next-to-leading order differential cross
sections, and their matching to parton shower
simulations // arXiv:1405.0301 [hep-ph].
Article received 06.03.2023
ВИЗНАЧЕННЯ ПЕРЕРІЗУ РЕЗОНАНСНОГО УТВОРЕННЯ ВАЖКИХ ВЕКТОРІВ
У HEAVY VECTOR TRIPLET МОДЕЛІ
Т.В. Обіход, Є.О. Петренко
У контексті тераелектронвольтних розширень Стандартної моделі нами використовуються як
експериментальні виміри, так і побудовані феноменологічні моделі для пошуку нових важких бозонів.
Важкі частинки, що передбачені спрощеною моделлю, яка побудована для опису тільки резонансу на
оболонці, необхідно порівнювати з даними на LHC. Бозони V’, що утворюються і розпадаються відповідно
до процесу pp->V’->Vh (V=W, Z), мають певні властивості, які можна змоделювати в рамках Heavy Vector
Triplet моделі за допомогою комп'ютерної програми Madgraph. Ми розрахували перерізи утворення важких
частинок V’ з використанням експериментальних обмежень у просторі параметрів (cH, cF), які накладено на
еталонний сценарій. Досліджено характер функціональної залежності перерізу при основних параметрах
моделі від маси нового бозона, а також механізм народження таких частинок.
|
| id | nasplib_isofts_kiev_ua-123456789-196129 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:03:01Z |
| publishDate | 2023 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Obikhod, T.V. Petrenko, I.A. 2023-12-10T16:46:38Z 2023-12-10T16:46:38Z 2023 Studying the resonance production cross-section of the heavy vectors within Heavy Vector Triplet model / T.V. Obikhod, I.A. Petrenko // Problems of Atomic Science and Technology. — 2023. — № 3. — С. 3-7. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 12.60.−i, 14.80.−j DOI: https://doi.org/10.46813/2023-145-003 https://nasplib.isofts.kiev.ua/handle/123456789/196129 In the context of TeV-scale extensions of the Standard Model both the experimental data and the construction of phenomenological models for the new heavy bosons searches are used by us. Heavy particles are predicted by the Simplified Model to describe only the on-shell resonance, have to be compared with LHC data. Bosons V’ created and decay according to the process pp‐>V’‐>Vh (V=W, Z) have certain properties that can be modeled within the Heavy Vector Triplet model using the Madgraph computer program. We have calculated the production cross sections of heavy particles using the experimental constraints in the parameter space (cₕ, cf) imposed on the benchmark scenario. The nature of the functional dependence of the cross section on the mass of the new boson, as well as the mechanism for the heavy particle production is studied with variation of the model parameters. У контексті тераелектронвольтних розширень Стандартної моделі нами використовуються як експериментальні виміри, так і побудовані феноменологічні моделі для пошуку нових важких бозонів. Важкі частинки, що передбачені спрощеною моделлю, яка побудована для опису тільки резонансу на оболонці, необхідно порівнювати з даними на LHC. Бозони V’, що утворюються і розпадаються відповідно до процесу pp‐>V’‐>Vh (V=W, Z), мають певні властивості, які можна змоделювати в рамках Heavy Vector Triplet моделі за допомогою комп’ютерної програми Madgraph. Ми розрахували перерізи утворення важких частинок V’ з використанням експериментальних обмежень у просторі параметрів (cₕ, cf), які накладено на еталонний сценарій. Досліджено характер функціональної залежності перерізу при основних параметрах моделі від маси нового бозона, а також механізм народження таких частинок. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Problems of Atomic Science and Technology Nuclear physics and elementary particles Studying the resonance production cross-section of the heavy vectors within Heavy Vector Triplet model Визначення перерізу резонансного утворення важких векторів у Heavy Vector Triplet моделі Article published earlier |
| spellingShingle | Studying the resonance production cross-section of the heavy vectors within Heavy Vector Triplet model Obikhod, T.V. Petrenko, I.A. Nuclear physics and elementary particles |
| title | Studying the resonance production cross-section of the heavy vectors within Heavy Vector Triplet model |
| title_alt | Визначення перерізу резонансного утворення важких векторів у Heavy Vector Triplet моделі |
| title_full | Studying the resonance production cross-section of the heavy vectors within Heavy Vector Triplet model |
| title_fullStr | Studying the resonance production cross-section of the heavy vectors within Heavy Vector Triplet model |
| title_full_unstemmed | Studying the resonance production cross-section of the heavy vectors within Heavy Vector Triplet model |
| title_short | Studying the resonance production cross-section of the heavy vectors within Heavy Vector Triplet model |
| title_sort | studying the resonance production cross-section of the heavy vectors within heavy vector triplet model |
| topic | Nuclear physics and elementary particles |
| topic_facet | Nuclear physics and elementary particles |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/196129 |
| work_keys_str_mv | AT obikhodtv studyingtheresonanceproductioncrosssectionoftheheavyvectorswithinheavyvectortripletmodel AT petrenkoia studyingtheresonanceproductioncrosssectionoftheheavyvectorswithinheavyvectortripletmodel AT obikhodtv viznačennâpererízurezonansnogoutvorennâvažkihvektorívuheavyvectortripletmodelí AT petrenkoia viznačennâpererízurezonansnogoutvorennâvažkihvektorívuheavyvectortripletmodelí |