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International Journal of Trend in Scientific Research and Development (IJTSRD) 


Special Issue on Modern Trends in Scientific Research and Development, Case of Asia 
Available Online: www.ijtsrd.com e-ISSN: 2456 - 6470 


Solution of Problems on Conservation 
Laws of Baryon and Lepton Charges 


Davletniyazov Salamat Paluaniyazovich 


Assistant of the Nukus State Pedagogical Institute Named After Ajiniyaz, Uzbekistan 


ABSTRACT 


This article is devoted to the conservation laws of 
Elementary Particle Physics, those have a universal and 
approximate nature, that is, some of them are enforced in 
all possible interactions and have a universal character, and 
some of them is enforced in some interactions only and 
violated in others, mainly to the conservation laws of 
baryons and leptons. 





KEYWORDS: elementary particle physics, the principle of 
intersubject interdisciplinary, baryonic and_ leptonic 
conservation laws 


I. INTRODUCTION 

Extensive research is being carried out to improve the 
efficiency of student’s development of Elementary Particle 
Physics on the basis of the principle of interdisciplinary 
communication [1-3]. For this, aspects of the conservation 
laws of Elementary Particle Physics were studied in relation 
to the application of other sections of physics and chemistry 
[2] and the role of this section in relation to other disciplines 
from the point of view of the object of research [3]. It is 
known that, unlike other branches of physics, the 
conservation laws in Elementary Particle Physics have a 
universal and approximate nature, that is, some of them are 
enforced in all kinds of interactions and have a universal 
character. some are preserved in some interactions, while in 
others they are violated, that is, they are approximate [4]. In 
this study, the laws of conservation of baryon and lepton 
charges, their great importance are described. Universal 
conservation laws are fulfilled in all basic interactions, and in 
approximate laws - only in some. 


Laws of conservation of energy, momentum, and angular 
momentum are universal conservation laws. The 
conservation laws of all charges also universal conservation 
laws (we will discuss them below) [5]. 


The need to introduce charges (other than electricity) was 
compared with experimental data, which could only explain 
the existence of charges of a non-electrical nature. Each of 
these charges describes a certain intrinsic property of the 
particle. 


Il. MATERIAL AND METHODS 

For elementary particles, much more conservation laws are 
satisfied than for macroscopic processes. All these laws are 
subdivided into exact and approximate ones. Exact 
conservation laws are fulfilled in all fundamental 
interactions, and approximate ones - only in some. 


The laws of conservation of energy, momentum and angular 
momentum are exact. The laws of conservation of all charges 
are also exact (we will talk about them below). 


The need for the introduction of charges (other than electric) 
was dictated by experimental facts, which could be explained 
only under the condition that there are charges of a non- 
electric nature, which are also conserved. Each of these 
charges characterizes some internal property of the particle. 


Five charges are established: electricQ, baryonic B, and 


three lepton ones L,, L,,, L,.Forall elementary particles, 


these charges have only integer values (Q charge is the 
number of units of elementary charge @€). 


Baryon charge. If baryons and anti baryons are assigned a 
baryon charge such that 


, 


aM - 1 for baryons (nucleons and hyperons) 


—1 for antibaryons 


and all other particles have a baryon charge B = 0), then for 
all processes involving baryons and antibaryons the total 
baryon charge will be conserved. This is called the baryonic 
charge conservation law. 


For example, this conservation law determines the stability 
of the lightest of baryons - the proton, inhibiting the process 


pre r+y 

which would ultimately lead to the annihilation of atoms, 
since the resulting positrons would annihilate with the 
electrons of the atomic shells. 

It follows from the same law that an antibaryon can be born 


only in a pair with its own baryon. For example, an 
antiproton is born in the reaction 


pt+p—>pt+ptptp 
The law of conservation of electric charge determines the 


stability of the lightest charged particle - an electron, 
forbidding, for example, the process 


e7yvt+yt+v 
although it is permitted by all other conservation laws. 


Lepton charges (numbers). There are three types of lepton 
charges: electronic L, (for e€ and V,), muon (// for and 


V,Jandtau L, (7 forand V,).Here V,, V,,, V, - electron, 





ID: IJTSRD37941 | Special Issue on Modern Trends in Scientific Research and Development, Case of Asia 


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International Journal of Trend in Scientific Research and Development (IJTSRD) @ www.ijtsrd.com eISSN: 2456-6470 


muon and tau neutrino, respectively. It follows from the 
experiment that these are different neutrinos. 


We agreed to consider that 


+1 for leptons 
e Ll T 


L =, =, = ; 
{" 1 for antileptons 


For all other elementary particles, lepton charges are taken 
to be zero. 


The law of conservation of the lepton charge requires that 
during neutron decay 


n> pte +V, 


together with the electron, an electron antineutrino was 
born, since the total lepton charge of these two particles is 
zero. 


The law of conservation of lepton charge explains the 
impossibility of the following processes: 


v,tperettn, wtp tn 


although they are permitted by other conservation laws. The 
processes 


ae + mo + 
Vitpoe tn, V, +p +n, 


satisfying the lepton charge conservation law were observed 
experimentally. After it was experimentally established that 


V, and V y are different particles, different lepton charges 
L, and Li, were introduced. Similarly, the situation was 


with the introduction of the tau lepton charge L, [6-7]. 


Ill. RESULTS 
We consider some problems below. 


Example1: Baryon number conservation. 


Based on the law of conservation of baryon number, which 
of the following reactions can occur? 


a) @ +poR +n+n +2°* 
b) p+p>pt+ptp 


Strategy 
Determine the total baryon number for the reactants and 
products, and require that this value does not change in the 
reaction. 


Solution 

For reaction (a), the net baryon number of the two reactants 
is 0+1=1 and the net baryon number of the four products 
is 0+1+0+0=1. 


Since the net baryon numbers of the reactants and products 
are equal, this reaction is allowed on the basis of the baryon 
number conservation law. 


For reaction (b), the net baryon number of the reactants is 
1+ (- 1) =0 and the net baryon number of the proposed 


products is 1+1+(—1)=1. Since the net baryon numbers of 


the reactants and proposed products are not equal, this 
reaction cannot occur. 


Significance 

Baryon number is conserved in the first reaction, but not in 
the second. Baryon number conservation constrains what 
reactions can and cannot occur in nature. 


Example2: Lepton number conservation 


Based on the law of conservation of lepton number, which of 
the following decays can occur? 


a) n> pte +V, 
b) a uw Ve 


Strategy 
Determine the total lepton number for the reactants and 
products, and require that this value does not change in the 
reaction. 


Solution 
For decay (a), the electron-lepton number of the neutron is 
0, and the net electron-lepton number of the decay products 


is O+14+(-1l)=0. 


Since the net electron-lepton numbers before and after the 
decay are the same, the decay is possible on the basis of the 
law of conservation of electron-lepton number. Also, since 
there are no muons or tau-leptons involved in this decay, the 
muon-lepton and tau-lepton numbers are conserved. 


For decay (b), the muon-lepton number ofthe 7 is 0, and 
the net muon-lepton number of the proposed decay products 


is 1+14+(-1)=1. 


Thus, on the basis of the law of conservation of muon-lepton 
number, this decay cannot occur. 


Significance 

Lepton number is conserved in the first reaction, but not in 
the second. Lepton number conservation constrains what 
reactions can and cannot occur in nature. 


IV. CONCLUSION 

Like the law of conservation of momentum, based on the 
isotropic nature of our ordinary space, a_ particular 
momentum-spin is conserved in all interactions. These 
conservation laws are fulfilled in all processes occurring 
with particles, and have the property of controlling all 
processes in the world of particles. When studying the 
physics of elementary particles, the analysis of the 
fulfillment of these conservation laws by the example of 
specific processes will undoubtedly help to increase the 
efficiency development of this field. To this end, the next task 
in studying the fundamentals of elementary particle physics 





ID: IJTSRD37941 | Special Issue on Modern Trends in Scientific Research and Development, Case of Asia 


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International Journal of Trend in Scientific Research and Development (IJTSRD) @ www.ijtsrd.com eISSN: 2456-6470 


is to create a database that unites various processes 


involving _ particles 


and_ provides _ interdisciplinary 


developments, control questions for their amplification, 
reflecting the mass, spin and other characteristics of 
particles. Viewed as 


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