Method of Studying $\Lambda_b^0$ decays with one missing particle

A new technique is discussed that can be applied to $\Lambda_b^0$ baryon decays where decays with one missing particle can be discerned from background and their branching fractions determined, along with other properties of the decays. Applications include measurements of the CKM elements $|V_{ub}|$ and $|V_{cb}|$, selected charmless decays, and detection of any exotic objects coupling to $b\to s$ decays, such as the inflaton.


Introduction
where E and − → p indicate energy and three-momentum, respectively. Peaks in m 2 x would 12 be indicative of single missing particles in the B hadron decay. 13 A related example is charm semileptonic decays with a missing neutrino. Determinations 14 of branching fractions and form-factors have been carried out in fixed target experiments, 15 exploiting the measured direction of the charmed hadron and assuming that the missing 16 particle has zero mass, which leads to a two-fold ambiguity in the neutrino momentum 17 calculation [1]. If the charm decay particle is a D 0 , extra constraints can be imposed on 18 its decay requiring it to be produced from a D * + in the decay D * + → π + D 0 . This leads 19 to more constraints than unknowns, and is quite useful for rejecting backgrounds [2]. inside the detection apparatus. One example of such a possibly long-lived particle is the 26 "inflaton." This particle couples to a scalar field and is responsible for cosmological inflaton.

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In a specific model, Bezrukov and Gorbunov predicted branching fractions and decay 28 modes of inflatons, χ, in B meson decays [3]. For B → χX s decays the branching fraction where X s stands for strange meson channels mostly saturated by a sum of pseudoscalar 31 and vector kaons, m χ and m t , the inflaton and top quark masses, respectively, and θ, 32 β and β 0 are model parameters, where β/β 0 ≈ O(1). Their inflaton branching fraction 33 predictions are shown in Fig. 1(a). The branching fractions are quite similar for Λ 0 b decays.

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The Λ 0 b → pK − χ channel would seem to be the most favorable, since the Λ 0 b decay point 35 could be accurately determined from the pK − vertex. The inflaton decay mode predictions, 36 which depend on inflaton mass, are shown in Fig. 1    were possible to find a way to estimate the Λ 0 b momentum. The Λ 0 b direction is measured 49 by using its finite decay distance. To get an estimate of the Λ 0 b energy we can decay. Then and after some algebraic manipulations we find where cos θ is the measured angle between the pion and the  Table 1.
Although there is no measurement of the relative Σ one might imagine that the production ratio would be close to unity. The pions from the 68 Σ ( * )± b decays have relatively low momenta, so their detection efficiencies could be small.

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Although CDF does not report a value for the production ratio, the number of seen signal 70 events gives an observed value of r ΣΛ equal to 13%. This is certainly a useful sample.

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Backgrounds will be an issue, however, as the CDF data do show a substantial amount of 72   this procedure, the neutrino mass is set to zero, where X represents the sum of Λ + c and − energies and momenta. Eq. (3) and Eq. (5) can 88 be used as two constraint equations with one unknown variable |p Λ b |.

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Measurement of |V ub | using Λ b → p − ν decays is subject to the uncertainty on B(Λ + c → 90 pK − π + ) , but here the current precision of 5% on this branching fraction is sufficient.

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Theoretical calculations of the decay width from the lattice, done in a limited four-92 momentum transfer range [12], light cone sum rules [13,14], and QCD sum rules