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D0 decays to K+/K- (CKM suppression)

  1. Jun 15, 2015 #1

    ChrisVer

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    I was looking at the [itex]D^0 \rightarrow K^+ \pi^-[/itex] and [itex]D^0 \rightarrow K^- \pi^+[/itex].

    The first is doubly Cabbibo suppressed whereas the other is Cabibbo favored.
    I got the ratio:
    [itex]A= \frac{Br( D^0 \rightarrow K^+ \pi^-)}{Br(D^0 \rightarrow K^- \pi^+)} = \frac{|V_{cd}|^2 |V_{us}|^2}{|V_{cs}|^2 |V_{ud}|^2} \approx 0.002863(12)[/itex]
    I used the values given for [itex]V_{ij}[/itex] from wikipedia .
    I then checked the pdg for the appropriate decay rates :
    [itex]Br( D^0 \rightarrow K^+ \pi^-)= 1.380(28) \times 10^{-4}[/itex]
    [itex]Br( D^0 \rightarrow K^- \pi^+)= 3.88(5) \times 10^{-2}[/itex]
    From which I got their ratio:
    [itex]A \approx 0.00356(9)[/itex]

    I was wondering why these ratios are not equal?
     
  2. jcsd
  3. Jun 15, 2015 #2

    mfb

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    For an exact calculation you have to consider higher orders. Those are very messy for charm decays.
    For experimental observations, you also have to take mixing into account. The ##D^0## can go to ##\overline {D^0}## and then decay via the Cabibbo favored decay, which looks exactly like the suppressed decay. Then you also add interference between mixing and decay and you get a parabolic shape of this measured branching ratio as function of time.

    LHCb has the most sensitive measurement so far.
    Publication 1
    Publication 2
    Overview note
     
  4. Jun 15, 2015 #3

    ChrisVer

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    So you think that the pdg's values take into account the [itex]D^0 (\rightarrow \bar{D}^0 )\rightarrow K^+ \pi^-[/itex]?
    I'll have a look at your citations.
     
  5. Jun 15, 2015 #4

    mfb

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    They have separate groups for the rare decay: total, via DCS, via ##\overline {D^0}##. Not sure how they handle interference.

    Where is the point in the non-interactive version:
    http://pdg8.lbl.gov/rpp2014v1/pdgLive/Particle.action?node=S032 [Broken]
    http://pdg8.lbl.gov/rpp2014v1/pdgLive/BranchingRatio.action?parCode=S032&desig=50 [Broken]

    Looks like the LHCb estimate is not included yet. You can also have a look at the Heavy Flavor Averaging Group.
     
    Last edited by a moderator: May 7, 2017
  6. Jun 15, 2015 #5

    ChrisVer

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    Judging from the LHCb results, the ratio ##R(t)## has a minimum value ##R_D## which is still larger (##3.568 \times 10^{-3}##) and that gets larger with time because of the D-Dbar oscillations. So in fact the oscillations would lead in a higher [itex]A[/itex] than the one I obtained from pdg...and so even larger from the one I obtained from the CKM... So I guess the main difference is because of higher order contributions to those diagrams...
     
  7. Jun 16, 2015 #6

    Hepth

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    If you also include approximations to the theoretical predictions, like the zero recoil form factors for the transitions (assuming factorization), then you have in addition to the CKM ratios, ##\left(\frac{f_{D\pi}}{f_{DK}} \frac{f_K}{f_{\pi}}\right)^2##

    from http://arxiv.org/pdf/0907.2842v1.pdf and decay constant ratios from PDG vals http://pdg.lbl.gov/2014/reviews/rpp2014-rev-pseudoscalar-meson-decay-cons.pdf

    I get ##0.00309508 \pm 0.000428392##

    Then theres factorization violating stuff too.
     
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