A Strategic Study on Foreign Fund Utilization in Chinese Insurance Industry

2025-04-30 0 0 972.17KB 25 页 10玖币

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Investigation of production of neutral Higgs boson and two charged

charginos from electron-positron annihilation via different propagators

Sara Abdelrady Hassan1, Asmaa.A. A2,Sherif Yehia3, M.M. Ahmed3 and Mohammed

Said Mohammed Abu-Elmagd1

1Department of Engineering Mathematics and Physics, Higher Institute of

Engineering, El-Shorouk Academy, El-Shorouk City, Egypt

2Egyptian Organization for Standardization and Quality, Cairo, Egypt

3Department of Physics, Faculty of Science, Helwan University, Cairo, Egypt

* Fax: +2(02)26000039 E-mail: m.said@sha.edu.eg

Abstract

In the current work we investigated the production of neutral Higgs boson (

) and two charged Charginos

(



) owing to electron-positron annihilation via different propagators for the process 







 and in the Minimal Supersymmetric Standard Model (MSSM), the cross

sections for this interaction were estimated. Five groups of 180 probabilities from Feynman diagrams are

taken by different propagators. Group (I) when  and bosons are propagators, Group (II) when  and

 bosons are propagators, Group (III) whenand(Lightest Higgs boson) bosons are propagators, Group

(IV)  and  bosons are propagators and Group (V)  and  bosons are propagators where   

  .

We calculated the process's production cross-sections as a function of mass center energy, and determined

the best cross-section based on all considerations of the (MSSM), the process's mechanisms can be identified

as:

   

 in group IV

   

 in group II.

   

 in group III

   

 in group V

   

 in group I.

At S interval (1600- 3500) Gev, the best value of σ is  Pb in-group (IV). When masses of

Charginos are



, 



  and mass of neutral Higgs boson is 

 

Keywords: Higgs boson, Chargino and Neutralino

1. Introduction

The Supersymmetry Standard Model (SUSY) [1–7], suggests adding a new symmetry to particle physics'

Standard Model (SM), as well as a symmetry between bosons and fermions, and anticipates the presence of

potential partners for each Standard Model (SM) particle. This provides resolve for the hierarchy dilemma

[7-12] and a nominee for dark matter in the form of the lightest supersymmetric particle (LSP), which will

be static in the situation of conserved R-parity [13].

The SM's minimal supersymmetric extension (MSSM) [14, 15], The bino, the winos, and the Higgsino are

the superpartners of the U(1)Y and SU(2)L gauge fields, as well as the Higgs field. The mass terms for the

bino, wino, and Higgsino states are M1,M2, and, μ respectively. Since they not carry color charge, they can

only be produced through electroweak interactions or the decay of colored superpartners. Because

electroweak processes have smaller cross sections, the masses of these objects are observationally less limited

than the masses of colored SUSY particles. According to the mass spectrum. Through mixing of the

superpartners, chargino (

 ) and neutralino (

 ) mass eigenstates are created. These are known as

electroweakinos, and the subscripts imply increasing electroweakino mass. If the 

 is stable, for

example as the lightest supersymmetric particle (LSP) and R-parity conservation is postulated, it is a viable

dark-matter candidate [16, 17].

This paper calculates the cross sections (σ) as a function of center of mass energy a search for direct

production of neutral Higgs boson and two charged charginos from electron-positron annihilation via

different propagators for the process  





1.1 The Cross-section Scattering

In physics, the significance of cross section is an indicator of the probability that a particular process will

occur when a particular type of radiant excitation encounters a highly concentrated phenomenon. The

Rutherford cross-section, for example, is an indicator of the chance of an alpha particle being diverted by a

specific direction throughout an interaction with an atomic nucleus. σ (sigma) cross section and is measured

in term of area, specifically barns. In some ways, it can be compared to the size of the object that the excitation

must strike throughout order for the process to take place.

We have learned a lot about nuclear and atomic physics through scattering experiments, such as the discovery

of subatomic particles (such as quarks). Scattering phenomena, such as neutron, electron, and x-ray scattering,

are used to investigate solid state systems in low energy physics. As a main overview, it is therefore essential

in any advanced quantum mechanics course.

If the radiation is thought to be made up of quanta, The quantity of incident particles hitting the target's

surface per unit time per unit area is the flux, and the cross-section measures the scattering rate per unit

incident radiation flux. Calculating scattering cross-sections for long-wavelength electromagnetic radiation

means dividing the power of the scattered wave by the intensity of the incident wave. A cross-section

represents an area in dimensions, with its unit is barn, which has an area of 10−28 m2. Instead of a true

geometric cross-sectional area, a scattering cross-section can be interpreted as an effective area proportional

to the probability of interaction between the radiation and the target.

A differential cross section is the differential limit of a function of some final-state parameter, such as particle

angle or energy. A total cross section or integrated total cross section is a cross section that has been integrated

over all scattering angles. In a real scattering experiment, the different rates of scattering to different angles

provide information about the scatterer. Detectors are positioned at various angles (. The standard form

for an infinitely small solid angle is   . The total solid angle (all probable scatterings) is

   the area of a unit radius sphere.

The differential cross section, , is the part of the total number of scattered particles which emerge in

the solid angle , so the rate of particle scattering to this detector is , with n defined above as the

beam intensity. By integrating over all solid angles, we can obtain the total cross section from the differential.

 

 



 







The cross section is sensitive to the energy of the incoming particles.

1.2 Properties of Chargino:

Chargino are composed of Winos () and Higgsinos ()[17,18]. In nature, neutralino dark

matter is experimentally investigated indirect through the use of γ ray and neutrino telescopes or directly

through the utilizing laboratory experiment like those of Cryogenic dark matter search (CDMS) [19, 20].

Heavier neutralinos usually disintegrate to lighter neutralinos via a neutral Z boson or a via charged W boson

to a light chargino. [21]. It is created in pairs through s-channel  exchange [22, 23]. The lightest neutralino



 is heavier than the lightest chargino 

.

The mean lifetime (



) of 

 is expressed in the form of 

, which is customarily in the range of a

nanosecond. Charginos have a lifetime ranging from 0.1 to 10 ns [24]. The charginos disintegrate to the

lightest neutralino 

, that is believed to be stable, and a two fermions (f) consisting of quarks and antiquarks

or leptons and neutrinos [25]. The lightest chargino with a mass larger than 103.5 GeV [26].There are three

variables or soft terms in the chargino mass matrix (,  and ) and the neutralino mass matrix has four

soft terms ( , ,  and ).

1.3 Higgs boson:

The Standard Model (SM) of elementary particles describes strong and electroweak interactions between

quarks and leptons by exchanging force carriers, such as photons for electromagnetic interactions, W and Z

bosons for weak interactions, and gluons for strong interactions. Quarks and leptons serve as the fundamental

components of matter in the SM. The electroweak hypothesis unifies the electromagnetic and weak

interactions. The SM's predictions have been amply verified because they are remarkably compatible with

the majority of accurate measurements up to the energies now available, but it is still unclear how the W and

Z gauge bosons pick up mass while the photon stays massless. It was postulated almost 50 years ago that the

introduction of a scalar field may lead to spontaneous symmetry breaking in gauge theories. The W and Z

masses are produced as a result of applying this method to the electroweak theory through a complex scalar

doublet field, and the SM Higgs boson's existence is predicted (H).Through the Yukawa interaction, the scalar

field also provides mass to the fundamental fermions [27, 28].

1.3.1 Higgs Field

In the Standard Model, no particle has a mass when it first appears. This may be the case for photons,

however the W and Z have mass that is close to 100 times greater than that of a proton. A solution was

offered by Peter Higgs to this issue. The W and Z are given mass by the Brout-Englert-Higgs process,

which interacts with an ethereal field that is now known as the Higgs field. The Higgs field was initially

zero after the big bang, but when the cosmos cooled and the temperature dipped to a crucial point, it

developed spontaneously, giving any particle interacting with it a mass. A particle becomes heavier as

it interacts more with this field. The photon and other particles that do not interact with it have no mass

at all. The Higgs boson is a particle that is connected to the Higgs field, like all other fundamental fields.

1.3.2 Properties of Higgs boson

The Higgs boson has no spin, has zero electric and color charge and it is also its own antiparticle.

1.3.3 The Higgs boson production and decay

The Higgs boson can be produced at the Large Hadron Collider (LHC) through gluon-gluon fusion (ggF)

87% of the time, accompanied by vector boson fusion (VBF, 7%), associated top-antitop production (ttH,

1%), which is known as the top fusion process because it includes two colliding gluons, where every decay

into a heavy quark-antiquark pair. Each pair's quark and antiquark can then merge to create a Higgs

particle.[29]

1.4 Two-Higgs-doublet model

Following the breakthrough of the Standard Model (SM) Brout-Englert-Higgs boson at the Large Hadron

Collider (LHC), the concern of whether there are more particles within experimental reach remains open.

One straightforward possibility is that a second Higgs doublet has the same quantum numbers as the SM

Higgs [30]. The Two-Higgs-Doublet Model (2HDM) is the most basic evolution of the Standard Model (SM),

containing one extra scalar doublet with more physical neutral and charged Higgs fields.

There are five physical scalar states with the second Higgs doublet, including the CP even neutral Higgs

bosons h and H (where H is heavier than h), the CP odd pseudoscalar A, and two charged Higgs bosons H±.

The Higgs boson detected is measured to be CP even. Six physical parameters, including four Higgs masses

(), the ratio of the two vacuum expectation values (), and the mixing angle ()

that diagonalizes the mass matrix of the neutral CP even Higgses, can be used to characterise such a model.

The mass of the Higgs particle and its vacuum expectation value are the only two parameters used by the SM.



 





 









  



  



  

  



  



The Higgs potential that is composed of quadratic terms and quadratic interaction terms, governs the Higgs

characteristics of the MSSM. Supersymmetric gauge couplings directly impact the strength of the interaction

terms. The Higgs spectrum, an angle (which represents the degree of mixing of the original   Higgs

doublet states in the physical CP-even scalars), and the Higgs boson couplings are all determined by 

and one Higgs mass ().

2. Rules of Calculation Cross sections in (Pb):

Initial states have momenta  and their masses  , while three-body final states have

momenta and their masses .

  (1)

  (2)

The cross section () for the process  



 can be

expressed in writing as

  



Where M is the matrix element, by using Feynman rules this allows us to write the M-matrix as well as the

trace thermos needed to compute the square matrix (  ), with the integration carried out by a

straightforward approximation produced by an enhanced Weizsacker-Williamson approach [31, 32]. Where:

  

 (4)

Then, the integration limit and integration simplification which done by using the Mathematica application

are.









 (5)









 (6)

 

 (7)

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InvestigationofproductionofneutralHiggsbosonandtwochargedcharginosfromelectron-positronannihilationviadifferentpropagatorsSaraAbdelradyHassan1,Asmaa.A.A2,SherifYehia3,M.M.Ahmed3andMohammedSaidMohammedAbu-Elmagd11DepartmentofEngineeringMathematicsandPhysics,HigherInstituteofEngineering,El-ShoroukAcad...

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