Wednesday, October 26, 2011

Theoretical calculation of Cabibbo and Weinberg angles



The Mission Statement for LHC was stated by CERN as below.

“Although in the popular imagination the goal of the LHC is to discover the Higgs boson, the scope of the LHC is really much broader: it is the scientific exploration of the TeV scale. A major part of this enterprise is to answer one of the most intriguing open questions in physics: “Why is it that the W and Z-bosons and the top quark have masses of around 100 times that of the proton, whereas the photon is massless?” In technical terms this is “to discover the mechanism of electroweak symmetry breaking”. Discovering a light Higgs boson as predicted by the Standard Model is just one of the possible outcomes of this endeavour.”


That is, the true purpose of LHC is to discover the “particles’ rest mass rising mechanism”.  In Standard Model (SM), the Higgs mechanism is the only pathway for this end. Thus, the Higgs boson searching becomes the first mission for LHC. After two years of searching, the fate of SM Higgs is not good. But, by all means, Higgs search is only the first step. The W and Z-bosons’ masses are calculated with some mixing angles, such as, the Cabibbo angle (θc) with a measured value of  c)   = 13.04 degrees, and the Weinberg angle (θW ) with the measured value ranges from 28.8 to 30°.  Both Cabibbo angle and Weinberg angle are measured perimeters, and they cannot be derived theoretically in Standard Model. Thus, the true “Mission of LHC” is to discover the theoretical foundation for calculating these two mixing angles. 


Even if a SM Higgs were discovered, it will still take many years of works at LHC to understand the way of calculating these two mixing angles theoretically. On the other hand, with the Fictitious Universe physics (http://prebabel.blogspot.com/2011/10/super-unified-theory-via-new.html ), we can calculate these two mixing angles with ease.

First, we have derived a unit angle, A (0) equals to 1.4788425146211 degrees [57.29577951 * .051621342/2]. How A(0) is calculated was described in detail on the page 36 of the book “Super Unified Theory” (ISBN 0-916713-02-4, Copyright # TX 1-323-231, Library of Congress Catalog Card Number 84-90325). It is also available in many of my articles online; thus, I will not repeat it here.

With A(0), we get A(1) = [360 - 24 * A(0)]/24 = 13.5211574853 degrees, and this is very close to the Cabibbo angle (θc).

With A(0) and A(1), we get A(2) = 2 * [360 - A(1) - A(0)]/24 = 28.75 degree, and this is almost the same as the measured Weinberg angle (θW ).

In this Fictitious Universe physics, it has two steps.
1. Constructing a Fictitious Universe by selecting (not discovering) a set of physics laws. Why A(0),  A(1) and A(2) take these equations? They are the results of this Fictitious Universe physics.

2. Comparing these laws and their derived phenomena with the Nature universe.


Now, two greatest mysteries of Standard Model (the theoretical foundation for calculating both the Cabibbo and Weinberg  angles) are easily resolved in this Fictitious Universe physics.  What does this tell us? 

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