Three Little-Known Equalities in Food For TheorDev

  • Context: Graduate 
  • Thread starter Thread starter arivero
  • Start date Start date
  • Tags Tags
    Food
Click For Summary
SUMMARY

The discussion centers on three lesser-known equalities in theoretical physics, specifically related to particle physics. The equalities presented include Smirnov's equations involving the angles θ_sun and θ_cabibbo, and De Vries' logarithmic relationship between the masses of the tau and muon particles. Additionally, a secondary formula for the electron-muon relationship is provided by De Vries. The conversation also touches on the potential for expressing these equalities using hyperbolic functions, although this approach does not yield further clarity.

PREREQUISITES
  • Understanding of particle physics concepts, including the Cabibbo angle.
  • Familiarity with logarithmic functions and their applications in physics.
  • Knowledge of hyperbolic functions and their mathematical properties.
  • Basic grasp of mass relationships among elementary particles, specifically muons and tau particles.
NEXT STEPS
  • Research the implications of the Cabibbo angle in particle interactions.
  • Explore the mathematical derivation of the relationships between particle masses.
  • Study hyperbolic functions and their applications in theoretical physics.
  • Investigate the significance of the equalities presented in the context of current particle physics theories.
USEFUL FOR

The discussion is beneficial for theoretical physicists, particle physicists, and advanced students in physics who are interested in the mathematical relationships governing particle interactions and mass ratios.

arivero
Gold Member
Messages
3,481
Reaction score
187
Three little known equalities:

From Smirnov:
\theta_{\mbox{sun}} + \theta_{\mbox{cabibbo}} = {\pi \over 4}

From De Vries:
\ln {m_\tau \over m_\mu} = \pi - {1 \over \pi}

From Smirnov again:
\sqrt {m_\mu \over m_\tau} \sim \sin \theta_{\mbox{Cab.} }

Can anyone predict them?

de Vries has a secondary formula for the electron-muon relationship, namely
ln(mu/me) / (2pi-3/pi) = 1.000627.

In principle one could recast them in terms of hyperbolic cosines and sines, for instance 1pi-1/pi= 2 sinh(ln(pi)) but it does not clarify the situation.

See also:
https://www.physicsforums.com/showthread.php?t=36624
http://arxiv.org/abs/hep-ph/0405088
http://www.chip-architect.com/news/2004_07_27_The_Electron.html
 
Last edited by a moderator:
Physics news on Phys.org
For instance, taking logarithms we have

\ln (\sin \theta_C) \sim - \sinh (\ln \pi)
 

Similar threads

  • Poll Poll
Graduate All the lepton masses from G, pi, e
  • · Replies 492 ·
17
Replies
492
Views
158K