Large extra dimensional limit of gravity subject to proton decay

2020 ◽  
Author(s):  
Deep Bhattacharjee

D(p) Branes can range from any number of spatial dimensions extending from 1 to 10. Most of the force and matter fields are concentrated along the wall of the brane as a open strings thereby permitted to travel in higher dimensions however a typical type of bosonic force field called the gravitons extend beyond the boundary of our 4 dimensions and extend to (4 + n) dimensions with the value of (n ≤ 10). This peculiar property of gravitons exist as because there are always a closed strings with no ends attached to a D(p) branes. The energy required to detect gravity is at a close proximity of 10^16 GeV to 10^19 GeV making GUT or grand unified theories. However, the LED or large extra dimensions model reduce the energy scale to 1000 GeV or 1 TeV. However in this paper I will show that not only energy required equals to 1 TeV but an energy of much less than 1 TeV that is 10 GeV. Therefore, the gravity would be accessible at a much lower energy provided the dimension of the LED is equal to 1 mm. During a head to head collision of proton bombardment in LHC 'gravitons' appeared but remains undetected as they quickly appeared to higher dimensions at (4 + n) with (4 < ≤ 10). However when dimensions = 6 then a Calabi-Yau manifold is formed but here there is SED or 'small extra dimensions' instead of LED. Now, an open question that I want to ask to my readers is that, if gravity of 1 mm which is sufficiently small one a scale = 1 where the force actually disappears then if it got except in higher dimensions then the higher dimensions must have a value of D = 2mm > r = 1mm. So, the throat must be larger than the minimal length of gravity to swallow it whole. Therefore, if extra dimensions exist then they must be equal to or greater than 1mm. Another important thing to note is the proton decay where a proton decays into a neutral pions and a positron which ultimately decays into 2 gamma rays and the half-life time of the proton decay is around 10^34 years which is impossible to observe for the humans. Now, a proton having a mass parameter of 1800 times greater than the electrons have the effect of gravity comparatively significant than that of the lepton 'electron'. And that proton decay has a connection with GUT via magnetic monopoles provided the D(p)-1 Branes are extremely long. However, an alternative approach of the 'magnetic monopole' can be found from the Gauss's law of magnetism as (∇ • B = 4πρ) where magnetic charge density that is ρ.

2020 ◽  
Author(s):  
Deep Bhattacharjee

Gravity has been leaking in higher dimensions in the bulk. Gravity being a closed string is not attached or does not have any endpoints unlike photons to any Dirichlet (p)-Branes and therefore can travel inter-dimensional without any hindrance. In LHC, CERN, Gravitons are difficult to detect as they last for such a short span of time and in most of the cases invisible as because they can escape to higher spatial dimensions to the maximum of 10, as per 'M'-Theory. Gravity being one of the 4-Fundamental forces is weaker than all 3 (strong and weak nuclear force, electromagnetism) and therefore a famous problem has been made in particle physics called the 'hierarchy problem'. Through comprehensive analysis and research I have come to the conclusion that if dimension is 5 (or 4 if we neglect the temporal dimensions) then an old approach is there for the compactification of the dimensions as per Kaluza-Klein theory and the most important implications of this theory is that an unification of electromagnetism with gravitation occurs in the fifth dimensions, therefore we can conclude that both the charge (electric as well as magnetic and gravity) are dependent of each other in case of Dimensions greater than 4 (5 if time is added). Now, basic principles of electromagnetic theory states that the field-flux density through a closed surface like a T 2 Torus when integrated over the surface area leads to a zero flux. That means there is no flux outside this closed surface integral. However, if the surface is open then the field flux density is not zero and this preserves the concept of magnetic monopoles. However, in a paper in 1931,[1] Dirac approaches monopole theory of magnetism through a different perspectives that, if all the electrical charges of the universe is quantized[2] then there is a suitable (not yet proved though) existence of monopoles; however this are not well understood as of today's scenario. In condensed matter physics, plasma physics and magneto hydrodynamics, there are flux tubes and as the both ends of the flux tubes are independent of each other then the net flux through the cylinder is zero as the amount of field lines entering the tube on one side is equal to the amount of field lines exit from the other end. And in the sides of the cylinder or the flux tube there is no escape of field lines, hence, net flux is conserved. There also exists a type of 'Quasiparticles' that can act as a monopole.[3][4][5] Now, from the perspectives of the Guess law of electromagnetism, if there exists a magnetic monopole then the net charge or flux density over a surface is not zero rather the divergence of the flux density B is 4 [6]and an alternative approach of the 'monopole' can be achieved by increasing the spatial dimensions by a factor of 1 or more. The Gravity has no such poles and therefore can be considered as a unipolar flux density existing throughout the universe and is applicable to the inverse square law of decreasing magnitude via distance as 1/r 2. However, a magnet is always of bipolar with a north and South Pole. If a magnet can be broken then also the broken parts develop the other poles and become bipolar. However, there are tiny domains inside a magnet and if a magnet can be heated to approx. 700℃ then all the poles disappeared and if its cooled quickly, rather very quickly then the tiny domains inside the magnet would not get enough time to rearrange themselves and multipolar magnet is developed therefore to preserve the bipolar properties, the magnet should be cooled slowly allowing the time given to the tiny domains top rearrange themselves. Therefore, even multipole can be achieved quite easily but not the monopoles. So, the equation for a closed surface integral of a flux density without monopole is ∯(S) B dS = 0 or ∇ • B = 0 and that closed surface can be considered as 2 types namely (we will discuss about torus) as because in string theory compactification of higher spatial dimensions occurs in torus.


2004 ◽  
Vol 19 (29) ◽  
pp. 4899-4951 ◽  
Author(s):  
PANAGIOTA KANTI

We start by reviewing the existing literature on the creation of black holes during high-energy particle collisions, both in the absence and in the presence of extra, compact, spacelike dimensions. Then, we discuss in detail the properties of the produced higher-dimensional black holes, namely the horizon radius, temperature and life-time, as well as the physics that governs the evaporation of these objects, through the emission of Hawking radiation. We first study the emission of visible Hawking radiation on the brane: we derive a master equation for the propagation of fields with arbitrary spin in the induced-on-the-brane black hole background, and we review all existing results in the literature for the emission of scalars, fermions and gauge bosons during the spin-down and Schwarzschild phases of the life of the black hole. Both analytical and numerical results for the graybody factors and radiation spectra are reviewed and exact results for the number and type of fields emitted on the brane as a function of the dimensionality of space–time are discussed. We finally study the emission of Hawking radiation in the bulk: graybody factors and radiation spectra are presented for the emission of scalar modes, and the ratio of the missing energy over the visible one is calculated for different values of the number of extra dimensions.


2001 ◽  
Vol 16 (13) ◽  
pp. 2399-2410 ◽  
Author(s):  
FRED C. ADAMS ◽  
GORDON L. KANE ◽  
MANASSE MBONYE ◽  
MALCOLM J. PERRY

We consider proton decay in theories that contain large extra dimensions. If virtual black hole states are allowed by the theory, as is generally the case, then proton decay can proceed via virtual black holes. The experimental limits on the proton lifetime place strong constraints on the quantum gravity scale M qg (the effective Planck mass). For most theories, this implies a lower bound of M qg >1016 GeV. The corresponding bound on the size of large extra dimensions is ℓ<106/n×10-30 cm, where n is the number of such dimensions. Regrettably, for most theories this limit rules out the possibility of observing large extra dimensions at accelerators or in millimeter scale gravity experiments. Conversely, proton decay could be dominated by virtual black holes, providing an experimental probe to study stringy quantum gravity physics.


2004 ◽  
Vol 13 (01) ◽  
pp. 367-370 ◽  
Author(s):  
MAREK GÓŹDŹ ◽  
WIESŁAW A. KAMIŃSKI

We present the possible influence on the half-life of neutrinoless double beta decay coming from the existence of n extra spatial dimensions. The half-life in question depends on the mass of the electron neutrino. We base our analysis on the Majorana neutrino mass mechanism in Arkani-Hamed–Dimopoulos–Dvali model.


2007 ◽  
Vol 2007 (11) ◽  
pp. 089-089 ◽  
Author(s):  
Benjamin C Allanach ◽  
Jordan P Skittrall ◽  
K Sridhar

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