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

360 New Physics
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Figure 5-19. The lower and upper bounds on (b 2 0 ± b 2 ⊥)sin 2 φ as a function of ω⊥0. For curves b and c
we have assumed the following values for the observables: Λ00 =0.6, Λ⊥⊥ =0.16, y0 =0.60, y⊥ =0.74.
Curves a and d represent the corresponding case with no direct CP asymmetry (i.e., y0 = y⊥ =1.0). The
solutions for ω⊥0 for Λ⊥0 =0.2 and Σ⊥0 =0.2 are shown as vertical lines.
The bounds improve as more New Physics signals are included in the fits. This is logical. For a particular
New Physics signal, the bounds are weakest if that signal is zero. (Indeed, the bounds vanish if all New
Physics signals are zero.) If a nonzero value for that signal is found, the bound will improve. Similarly, the
bounds generally improve if additional observables are measured, even if they are not signals of New Physics.
This is simply because additional measurements imply additional constraints, which can only tighten bounds
on the theoretical parameters.
In addition to the bounds on the bλ and rλ, it is possible to find correlated numerical constraints on the ηλ,
as in Fig. 5-16. If these are combined with a measurement of 2 βmeas λ , one can then obtain a bound on β,
even though New Physics is present.
Finally, even if 2ωσλ is not measured directly, one can obtain its value (up to a four-fold ambiguity) through
measurements of two observables involving the interference of two helicity amplitudes (as well as the Λλλ
and Σλλ). These can be converted into bounds on the other New Physics parameters. If 2ωσλ is measured
directly, this reduces the discrete ambiguity to twofold, and improves the bounds.
We stress that we have not presented a complete list of constraints on the New Physics parameters – the
main aim of this paper was simply to show that such bounds exist. Our results have assumed that only
a subset of all observables has been measured, and the bounds vary depending on the New Physics signal
found. In practice, the constraints will be obtained by performing a numerical fit using all measurements.
If it is possible to measure all observables, one will obtain the strongest constraints possible.
As a specific application, we have noted the apparent discrepancy in the value of sin 2β as obtained from
measurements of B 0 (t) → J/ψ K 0 S and B 0 (t) → φK 0 S. In this case, the angular analyses of B 0 (t) → J/ψ K ∗
and B 0 (t) → φK ∗ would allow one to determine if New Physics is indeed present. If New Physics is confirmed,
the method described in this paper would allow one to put constraints on the New Physics parameters. If
New Physics is subsequently discovered in direct searches at the LHC or ILC, these bounds would indicate
whether this New Physics could be responsible for that seen in B decays.
N.S. and R.S. thank D.L. for the hospitality of the Université de Montréal, where part of this work was done.
The work of D.L. was financially supported by NSERC of Canada. The work of Nita Sinha was supported
by a project of the Department of Science and Technology, India, under the young scientist scheme.
The Discovery Potential of a Super B Factory
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