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What is new with Koide sum rules?

  1. Aug 9, 2017 #161
    Just for gigs, I created this abomination to check whether it actually works out

    Code (Text):
    #!/usr/bin/python
    import math
    from math import sqrt

    # experimental quark masses, MeV
    md=4.7
    mu=2.2
    ms=96
    mc=1280
    mb=4180
    mt=173500

    print "Square roots of experimental quark masses, MeV"
    rmd=sqrt(md)
    rmu=sqrt(mu)
    rms=sqrt(ms)
    rmc=sqrt(mc)
    rmb=sqrt(mb)
    rmt=sqrt(mt)
    print "dn: %.4f %.4f %.4f" % (rmd,rms,rmb)
    print "up: %.4f %.4f %.4f" % (rmu,rmc,rmt)

    print "Unit-length vectors built of those (divided by norm)"
    nu=sqrt(mu+mc+mt)
    nd=sqrt(md+ms+mb)
    nmd=rmd/nd
    nmu=rmu/nu
    nms=rms/nd
    nmc=rmc/nu
    nmb=rmb/nd
    nmt=rmt/nu
    print "dn: %.4f %.4f %.4f" % (nmd,nms,nmb)
    print "up: %.4f %.4f %.4f" % (nmu,nmc,nmt)

    print "Kohzo Nishida says that (normed_sqrt_up_masses) = CKM * (normed_sqrt_down_masses)"
    c11=0.97435  ;c12=-0.2287 ;c13=0.005641
    c21=0.2286   ;c22=0.9712  ;c23=-0.06700
    c31=0.009846 ;c32=0.06652 ;c33=0.9977
    u1 = c11*nmd + c12*nms + c13*nmb
    u2 = c21*nmd + c22*nms + c23*nmb
    u3 = c31*nmd + c32*nms + c33*nmb
    print "rc: %.4f %.4f %.4f" % (u1,u2,u3)
    Output:

    Code (Text):

    Square roots of experimental quark masses, MeV
    dn: 2.1679 9.7980 64.6529
    up: 1.4832 35.7771 416.5333
    Unit-length vectors built of those (divided by norm)
    dn: 0.0331 0.1498 0.9882
    up: 0.0035 0.0856 0.9963
    Kohzo Nishida says that (normed_sqrt_up_masses) = CKM * (normed_sqrt_down_masses)
    rc: 0.0036 0.0868 0.9962
     
  2. Aug 9, 2017 #162

    ohwilleke

    User Avatar
    Gold Member

    If you really wanted to go large, you could do a crude Monte Carlo error analysis by having a program do the same thing for every combination of +1 sigma, the best fit vale and -1 sigma, for all of the input values based on the Particle Data Group error bars.
     
  3. Aug 10, 2017 #163
    That would amount to reimplementing CKM Fitter code from scratch :)

    I assume CKM Fitter people, if not already grappling with the possibilities opened by this paper, to do so Real Soon.
     
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