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Comments to B s -> m + m -

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- received comments on PRL draft during collab. review from 16 people
- mostly comments/suggestions to style
- almost all style suggestions are included in new PRL draft v4.2
- thank you very much to the collaboration for all your valuable comments and in particular many many thanks to the EB023.
- the list of all collected comments plus our answers is linked to the web page: http://www-d0.fnal.gov/~ralf/d0_private/bsMuMu.html
- In the following we will focus on the following comments
- comments to the method, i.e. how to treat Bd ?
- comments to detector/experiment/setup
- comments to the analysis
- comments to the limit setting
- comments to physics interpretation
- other misc. comments

Ralf Bernhard and Frank Lehner

U Zurich

September 09, 2004

- masses of Bs and Bd are only 90 MeV (our mass resolution for two-body decays) apart
- can not readily separate the two decays
- let R be the ratio R=BR(Bd)/BR(Bs) for the muonic decays of Bd and Bs
- in SM and MSSM (if minimal flavor violation holds)
- R~|Vtd/Vts|^2~0.045, i.e. Bd suppressed

- the general formula we use in the PRL:
- BR(Bs->mm) < Nul/NB+·BR1·BR2·(emmK/emm)·1/{fb->Bs /fb->Bd + R·(e(Bd)/e(Bs))}
- how to arrive to this equation, see next slide
- we set R=0 and derive a “conservative” limit. We do not subtract Bd
- Questions/comments were made: why bother with Bd at all? Put BR(Bd)=0, and use only simpler expression in PRL
- we think that full equation contains more experimental information
- if a theorist wants to better constrain his/her model by using a model dependent R value as input, the derived limit on Bs->mm can be improved
- all relevant values for this exercises are given in PRL
- e.g. using CKM-fitter values to calculate R, we could improve limit by 12%

- definition of pseudorapidity added
- pT better explained
- Q: expect (track) momentum resolution in PRL paper
- A: there is not really a final “official” number and we have not put any number in the paper. The mass resolution for two-body tracks is given and this matters much more for us.

- four separate dimuon triggers -> four versions of dimuon (…)
- trigger simulation software package -> trigger simulation
- changed from 30 MeV uncertainty to 30 MeV shift in tracker momentum scale and mention “shifted” now only once.

- Q: cut values for discriminating variables are given with too much precision – what is effect of rounding?
- A: there is no change in expected background and efficiencies if values are rounded

- Q: is the innermost SVX layer required ?
- A: no

- Q: why only 4 CFT hits ?
- A: this is mainly a fiducial cut, which keeps the acceptance higher. There are a few tracks with CFT<4. The requirement of SMT hits is more stringent.

- Q: background is unlikely to be faked muons:
- A: OK, drop this part

- Q: cone size for isolation large; what is with underlying event?
- A: cone size was introduced from the beginning of analysis, optimization is based on this

- Q: how well are discriminating variables reproduced in data for B+ normalization channel
- A: see plots next slide

Control plots for normalization

Channel B+ -> J/Psi K+

Opening angle

Transverse decay

length

Control plots for normalization

Channel B+ -> J/Psi K+

Isolation

pT of B+

- Q: how is normalization in the plots for the discriminating variables done?
- A: we have 38k sideband events and 10k signal MC events after preselection. Plots would contain basically all events. However, the decay length significance plots are not shown over the full range of the variables. Relative Normalization between MC and sideband data is the done for in this plot separately.
- Q: why does fitted line for background increase in B+ plot beyond 5.7 GeV/c2?
- A: background is 2nd order polynomial, which opens again towards larger mass values. Systematics of different background descriptions and signal function resolution is included as 3% effect on number of B+
- Q: Naively judging from the plots, I think a cut on 10 or 15 on the decay length significance would be better.
- A: we have optimized in three dimensions to obtain the best value of P. Judging only one plot (out of three) might simplify the three-dimensional problem too much

- Q: you should use multi-channels for a limit setting and the CLs method
- A: a limit obtained from several observation channels might be more powerful than simply counting events in the box. However, the search was designed from the beginning to be a single-channel experiment. Our optimization was also defined as single-channel counting (Punzi). The box is now opened and any change from a single-channel counting if data are “visible” is against the spirit of a “blind analysis”. In future, we will look at this. One remark: In case of one channel only, the CLs method gives exactly the same formula for the confidence limit than a Bayes’ approach with flat prior

- Q: why not use Poisson for background modeling in limit calculation
- A: the underlying statistics of event counting is a poisson one p(n), of course. The uncertainty sb of the expected background b however, is a so-called “nuisance”-parameter which is integrated over when calculating the limit. We thus need a continues function to integrate over the “true” (but unknown) nuisance parameters and create a new probability density q:
- q(n) ~ p(n) · exp(-(b-b’)2/2sb2) db’
- efficiency uncertainties are treated similar
- the limit is then calculated by sum_{n’=0}^{n’=nul} q(n’) = 1-a
- this procedure to deal with nuisance parameters is pretty much standard in most frequentist, bayes and semi-bayesian methods

- Q: “can we rule out something”, “should we be more specific on the SO(10) GUT model”
- after discussions with U. Nierste we think the best is to finish with a simple sentence: “This new limit can be used to constrain models of new physics beyond the SM.”
- The good thing on Bs-> mm is that it is useful for many many models beyond SM. The bad thing is that we are only scratching the parameter space of MSSM, mSUGRA and 2HDM. In order to say something more specific about SO(10) we need to define a set of arbitrary input parameters. Vivek has shown a nice example in his W&C talk.
- this is good/impressive for talks, but we think it is not worth (nor do we have the space) to make up such an (somewhat) arbitrary exclusion something for the PRL

- Q: Too much theoretical papers cited
- A: this shows only how multi-various the constraints coming from this rare decay to many models beyond SM are

- BR calculation in SM: hadronic uncertainties -> non-perturbative …
- Pre-selection or preselection ?
- Re-weighting or reweighting?
- decided in both cases w/o hyphen (“in dubio pro Gregorio L.”)

- dropped footnote with Bs-> J/ normalization
- dropped sentence with “..1/3 of data were used for optimization”
- dropped word “Punzi”
- moved sentence with “after opening the box we found 4 events …” before normalization discussion in order to keep flow: background estimation -> number of observed events -> limit setting. The plots are now in order: discriminating plots, opened box mass plot, normalization plot.