Dear all,
I send this e-mail to better explain my remarks this morning on the ppmu
correction procedure, and to frame any conversation we have on the subject
this afternoon.
The ppmu correction is an essential step in extracting the singlet capture
rate from our measured muon disappearance rate. The size of the ppmu
correction depends upon two things:
(1) the method of calculating the correction (i.e. 1st moment
vs. best-fit), and
(2) the values of the ppmu parameters used in the calculation.
In this e-mail I am only addressing subject (1).
Below are the parameters that I use as inputs to my Monte Carlo program.
Note that I have used (approximately) Prod-50 statistics, and that I have
chosen to use the average experimental value of lambda_of=2.5e6 Hz, and
the theoretical value lambda_op=7.1e4 Hz, which lies midway between the
two existing experimental determinations.
double N = 1.95e9;
double B = 2000;
double lambda0 = 0.455160e-3; // (1/ns)
double Lambda_s = 730.*1e-9; // (1/ns)
double Lambda_t = 12.*1e-9; // (1/ns)
double phi = 0.0116;
double gamma_o = 1.009/2.;
double gamma_p = 1.143/2.;
double lambda_of = 2.5*1e-3; // (1/ns)
double lambda_pf = 0.0074*1e-3; // (1/ns)
double lambda_op = 7.1*1e-5; // (1/ns)
My MC program creates a "random" time distribution of decay electrons
according to the experimental parameters, and then fits it with a simple
exponential, just as we have done for Run8. The results are plotted in
the attached ROOT file. Of course, for a particular set of parameters,
the "ideal" first moment (which uses the closed-form analytic expression)
is always the same, while the exponential best-fit value varies due to the
Monte Carlo's simulations. In plot "hDelRmoment" you will find that
ideal_first_moment - lambda_0 - Lambda_S = -28 Hz (always)
In other words, the first moment calculation says that ppmu molecular
effects pull the muon disappearance rate down by 28 Hz from the desired
rate (lambda_0 + Lambda_S). In contrast, the best-fit results in
histogram "DelRfit" have a Gaussian distribution with mean
Mean(best-fit - lambda_0 - Lambda_S) = -22.7 Hz
This ~ 5 Hz difference between the two approaches suggests to me that we
should think carefully about the wisdom of applying a first-moment-based
ppmu correction to our experimental best-fit result. It seems possible
that our result should be something like 725 Hz, not 730 Hz; i.e. our
current number has been *over*-corrected, since it uses the larger first
moment number.
Of course, we won't resolve this before Peter's presentation, but we
should take it into consideration when composing our paper.
Regards,
Tom
Attachment:
ppmu-test.root
Description: Binary data