1 Introduction - Caltech High Energy Physics - California Institute of ...

42 Rare Decays
analyses [134, 51, 131, 139]:
m pole
c /m pole
b ⇒ m MS
c (µ)/m pole
b , µ ∈ [mc,mb]. (2.30)
Numerically, the shift from mpole c /m pole
b =0.29 ± 0.02 to mMS c (µ)/m pole
b =0.22 ± 0.04 is rather important
and leads to a +11% shift of the central value of the B → Xsγ branching ratio. Since the matrix element
starts at NLL order and, thus, the renormalization scheme for mc is an NNLL issue, one should regard the
choice of the MS scheme as an educated guess of the NNLL corrections. Nevertheless, the new choice is
guided by the experience gained from many higher order calculations in perturbation theory. Moreover, the
MS mass of the charm quark is also a short-distance quantity which does not suffer from nonperturbative
ambiguities, in contrast to its pole mass. Therefore the central value resulting within this scheme is definitely
favored. However, one has to argue for a theoretical uncertainty in mMS c (µ)/m pole
b , which also includes the
value of mpole c . This is done in the above theoretical predictions by using a large asymmetric error in mc/mb
that fully covers any value of mc/mb compatible with any of these two determinations:
mc
mb
=0.23 +0.08
−0.05 . (2.31)
The dominant uncertainty due to the renormalization scheme dependence is a perturbative error that could
be significantly reduced by a NNLL QCD calculation. Such a calculation would also further reduce the scale
uncertainty given in the theoretical predictions above. Needless to say, the parametric error can also be
further reduced by independent experiments. Thus, a theoretical error around 5% seems possible. At that
stage a further study of the nonperturbative corrections seems to be appropriate in order to make sure that
they are under control at this level of accuracy.
The uncertainty regarding the fraction of the B → Xsγ events above the chosen lower photon energy cut-off
Eγ quoted in the experimental measurement, also often cited as model dependence, should be regarded as
a purely theoretical uncertainty: in contrast to the ‘total’ branching ratio of B → Xsγ, the photon energy
spectrum cannot be calculated directly using the heavy mass expansion, because the OPE breaks down in
the high-energy part of the spectrum, where Eγ ≈ mb/2. However, a partial resummation of an infinite
number of leading-twist corrections into a nonperturbative universal shape function is possible. At present
this function cannot be calculated, but there is at least some information on the moments of the shape
function, which are related to the forward matrix elements of local operators. An important observation is
that the shape of the photon spectrum is practically insensitive to physics beyond the Standard Model (see
Fig. fig:Toymodel. This implies that we do not have to assume the correctness of the Standard Model in the
experimental analysis. A precise measurement of the photon spectrum would allow a determination of the
parameters of the shape function. Moreover, the universality of the shape function, valid to lowest order in
ΛQCD/mb, allows us to compare information from the endpoint region of the B → Xsγ photon spectrum
and of the B → Xuℓν charged-lepton spectrum up to higher 1/mb corrections. Thus, one of the main aims
in the future should therefore be a precise measurement of the photon spectrum. It is clear, that a lower
experimental cut in the photon spectrum within the measurement of B → Xsγ decreases the sensitivity to
the parameters of the shape function and that the ideal energy cut would be 1.6 GeV. In this case, however,
a better understanding of the BB background is necessary. In the last Belle measurement the photon cut
was already pushed to 1.8 GeV [48].
The important role of the B → Xsγ decay in the search for New Physics cannot be overemphasized (for a
recent review, see [41]), as it already leads to stringent bounds on various supersymmetric extensions of the
Standard Model (see for example [56, 57, 140, 141, 142, 143]). Also, in the long run, after New Physics has
been discovered via the direct search, this inclusive decay mode will play an even more important role in
analyzing in greater detail the new underlying dynamics.
The Discovery Potential of a Super B Factory