scholarly journals Time Dilation in Relativistic Quantum Decay Laws of Moving Unstable Particles

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Filippo Giraldi
Keyword(s):  
Decay Rate ◽  
Effective Mass ◽  
Survival Probability ◽  
Relativistic Quantum ◽  
Scaling Law ◽  
Power Laws ◽  
Time Dilation ◽  
Linear Momentum ◽  
Unstable Particle ◽  
Unstable Particles

The relativistic quantum decay laws of moving unstable particles are analyzed for a general class of mass distribution densities which behave as power laws near the (nonvanishing) lower bound μ0 of the mass spectrum. The survival probability Pp(t), the instantaneous mass Mp(t), and the instantaneous decay rate Γp(t) of the moving unstable particle are evaluated over short and long times for an arbitrary value p of the (constant) linear momentum. The ultrarelativistic and nonrelativistic limits are studied. Over long times, the survival probability Pp(t) is approximately related to the survival probability at rest P0(t) by a scaling law. The scaling law can be interpreted as the effect of the relativistic time dilation if the asymptotic value Mp∞ of the instantaneous mass is considered as the effective mass of the unstable particle over long times. The effective mass has magnitude μ0 at rest and moves with linear momentum p or, equivalently, with constant velocity 1/1+μ02/p2. The instantaneous decay rate Γp(t) is approximately independent of the linear momentum p, over long times, and, consequently, is approximately invariant by changing reference frame.

scholarly journals Invisible neutrino decay: first vs second oscillation maximum

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Kaustav Chakraborty ◽  
Debajyoti Dutta ◽  
Srubabati Goswami ◽  
Dipyaman Pramanik
Keyword(s):  
Decay Rate ◽  
Survival Probability ◽  
Mixing Angle ◽  
Decay Lifetime ◽  
Long Baseline ◽  
Physics Potential ◽  
Normal Mass ◽  
Compare And Contrast ◽  
Neutrino Decay ◽  
Oscillation Maximum

Abstract We study the physics potential of the long-baseline experiments T2HK, T2HKK and ESSνSB in the context of invisible neutrino decay. We consider normal mass ordering and assume the state ν3 as unstable, decaying into sterile states during the flight and obtain constraints on the neutrino decay lifetime (τ3). We find that T2HK, T2HKK and ESSνSB are sensitive to the decay-rate of ν3 for τ3/m3 ≤ 2.72 × 10−11s/eV, τ3/m3 ≤ 4.36 × 10−11s/eV and τ3/m3 ≤ 2.43 × 10−11s/eV respectively at 3σ C.L. We compare and contrast the sensitivities of the three experiments and specially investigate the role played by the mixing angle θ23. It is seen that for experiments with flux peak near the second oscillation maxima, the poorer sensitivity to θ23 results in weaker constraints on the decay lifetime. Although, T2HKK has one detector close to the second oscillation maxima, having another detector at the first oscillation maxima results in superior sensitivity to decay. In addition, we find a synergy between the two baselines of the T2HKK experiment which helps in giving a better sensitivity to decay for θ23 in the higher octant. We discuss the octant sensitivity in presence of decay and show that there is an enhancement in sensitivity which occurs due to the contribution from the survival probability Pμμ is more pronounced for the experiments at the second oscillation maxima. We also obtain the combined sensitivity of T2HK+ESSνSB and T2HKK+ESSνSB as τ3/m3 ≤ 4.36 × 10−11s/eV and τ3/m3 ≤ 5.53 × 10−11s/eV respectively at 3σ C.L.

scholarly journals Unstable particles in non-relativistic quantum mechanics?

2011 ◽  
Author(s):  
H. Hernandez-Coronado ◽  
Luis Arturo Ureña-López ◽  
Hugo Aurelio Morales-Técotl ◽  
Román Linares-Romero ◽  
Elí Santos-Rodríguez ◽  
...  
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Unstable Particles

scholarly journals Moving Unstable Particles and Special Relativity

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Eugene V. Stefanovich
Keyword(s):  
Special Relativity ◽  
Reference Frame ◽  
Unstable Particle ◽  
Internal Variables ◽  
Dirac Theory ◽  
Decay Probability ◽  
Unstable Particles ◽  
Interacting Systems

In Poincaré-Wigner-Dirac theory of relativistic interactions, boosts are dynamical. This means that, just like time translations, boost transformations have a nontrivial effect on internal variables of interacting systems. In this respect, boosts are different from space translations and rotations, whose actions are always universal, trivial, and interaction-independent. Applying this theory to unstable particles viewed from a moving reference frame, we prove that the decay probability cannot be invariant with respect to boosts. Different moving observers may see different internal compositions of the same unstable particle. Unfortunately, this effect is too small to be noticeable in modern experiments.

Time Dilation and the Velocity of Unstable Particles

1999 ◽  
Vol 12 (4) ◽  
pp. 669-670
Author(s):  
Robert J. Hannon
Keyword(s):  
Time Dilation ◽  
Unstable Particles

Gravity currents with residual trapping

2008 ◽  
Vol 611 ◽  
pp. 35-60 ◽  
Author(s):  
M. A. HESSE ◽  
F. M. ORR ◽  
H. A. TCHELEPI
Keyword(s):  
Scaling Law ◽  
Leading Edge ◽  
Power Laws ◽  
Gravity Currents ◽  
Sharp Interface Model ◽  
Current Volume ◽  
Residual Trapping ◽  
Self Similar ◽  
Loss Term ◽  
Structural Closure

Motivated by geological carbon dioxide (CO2) storage, we present a vertical-equilibrium sharp-interface model for the migration of immiscible gravity currents with constant residual trapping in a two-dimensional confined aquifer. The residual acts as a loss term that reduces the current volume continuously. In the limit of a horizontal aquifer, the interface shape is self-similar at early and at late times. The spreading of the current and the decay of its volume are governed by power-laws. At early times the exponent of the scaling law is independent of the residual, but at late times it decreases with increasing loss. Owing to the self-similar nature of the current the volume does not become zero, and the current continues to spread. In the hyperbolic limit, the leading edge of the current is given by a rarefaction and the trailing edge by a shock. In the presence of residual trapping, the current volume is reduced to zero in finite time. Expressions for the up-dip migration distance and the final migration time are obtained. Comparison with numerical results shows that the hyperbolic limit is a good approximation for currents with large mobility ratios even far from the hyperbolic limit. In gently sloping aquifers, the current evolution is divided into an initial near-parabolic stage, with power-law decrease of volume, and a later near-hyperbolic stage, characterized by a rapid decay of the plume volume. Our results suggest that the efficient residual trapping in dipping aquifers may allow CO2 storage in aquifers lacking structural closure, if CO2 is injected far enough from the outcrop of the aquifer.

scholarly journals Complex-Mass Definition and the Structure of Unstable Particle’s Propagator

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Vladimir Kuksa
Keyword(s):  
Spectral Function ◽  
Unstable Particle ◽  
Unstable Particles ◽  
Spinor Fields ◽  
Complex Mass ◽  
Special Case ◽  
Mass Definition

The propagators of unstable particles are considered in framework of the convolution representation. Spectral function is found for a special case when the propagator of scalar unstable particle has Breit-Wigner form. The expressions for the dressed propagators of unstable vector and spinor fields are derived in an analytical way for this case. We obtain the propagators in modified Breit-Wigner forms which correspond to the complex-mass definition.

scholarly journals INHOMOGENEOUS FIXED POINT ENSEMBLES REVISITED

2010 ◽  
Vol 24 (12n13) ◽  
pp. 1811-1822 ◽  
Author(s):  
Franz J. Wegner
Keyword(s):  
Fixed Point ◽  
Density Of States ◽  
Disordered Systems ◽  
Scaling Law ◽  
Localization Length ◽  
Power Laws ◽  
Real Space ◽  
Group Approach ◽  
Real Space Renormalization Group ◽  
Renormalization Group Approach

The density of states of disordered systems in the Wigner–Dyson classes approaches some finite non-zero value at the mobility edge, whereas the density of states in systems of the chiral and Bogolubov-de Gennes classes shows a divergent or vanishing behavior in the band centre. Such types of behavior were classified as homogeneous and inhomogeneous fixed point ensembles within a real-space renormalization group approach. For the latter ensembles, the scaling law µ = dν-1 was derived for the power laws of the density of states ρ ∝ |E|µ and of the localization length ξ ∝ |E|-ν. This prediction from 1976 is checked against explicit results obtained meanwhile.

scholarly journals FACTORIZED FORMULA FOR THE CROSS-SECTION OF TWO-PARTICLE SCATTERING

2008 ◽  
Vol 23 (27n28) ◽  
pp. 4509-4516 ◽  
Author(s):  
V. I. KUKSA
Keyword(s):  
Cross Section ◽  
Intermediate State ◽  
Factorization Method ◽  
Phenomenological Analysis ◽  
Unstable Particle ◽  
Specific Structure ◽  
Particle Scattering ◽  
Unstable Particles ◽  
The Cross ◽  
Exact Factorization

We applied the factorization method to the processes of two-particle scattering with an unstable particle in the intermediate state. It was shown, that in the framework of this method, the cross-section can be represented in the universal factorized form for an arbitrary set of particles. An exact factorization is caused by a specific structure of unstable particles propagators. Phenomenological analysis of the factorization effect is performed.

scholarly journals Direct Relativistic Extension of the Madelung-de-Broglie-Bohm Reformulations of Quantum Mechanics and Quantum Hydrodynamics

2021 ◽  
Author(s):  
Arquimedes Ruiz-Columbié ◽  
Luis Grave de Peralta
Keyword(s):  
Quantum Mechanics ◽  
Kinetic Energy ◽  
Relativistic Quantum ◽  
Free Particle ◽  
Linear Momentum ◽  
Relativistic Quantum Mechanics ◽  
Quantum Hydrodynamics ◽  
Relativistic Extension ◽  
Basic Equations ◽  
De Broglie Bohm

Abstract Using a Schrödinger-like equation, which describes a particle with mass and spin-0 and with the correct relativistic relation between its linear momentum and kinetic energy, the basic equations of the non-relativistic quantum mechanics with trajectories and quantum hydrodynamics are extended to the relativistic domain. Some simple but instructive free particle examples are discussed.

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