Kinematics of a two-body decay [closed]

Question

I suspect a flaw in the reasoning below, but am unable to pinpoint it: Is there something inconsistent in terms of the application of conservation of momentum and energy? Thanks for any hints in this regard.

Let's consider the 2-body decay:

$$Y \to B^++B^-$$

where $m_Y=10.58\,\text{GeV}/c^2$ and $m_{B^{\pm}}=5.279\,\text{GeV}/c^2$. Let's suppose that the momentum of $Y$ (in the laboratory reference system) before the decay is given by:

$$\vec{p}_Y=(-p_Y,0,0), \quad p_Y=5.9\,\text{GeV}/c$$

Then the energy of $Y$ is given by:

$$E_Y=\sqrt{m_Y^2c^4+p_Y^2c^2}=12.1\,\text{GeV}$$

Now we ask ourselves if it is possible that $B^+$ is emitted with a momentum given by:

$$\vec{p}_{B^+}=(p_{B^+},0,0)$$

with $p_{B^+}>0$, namely that $B^+$ is emitted in the positive direction of x axis. Using conservation of total momentum we have:

$$\vec{p}_Y=\vec{p}_{B^+}+\vec{p}_{B^-} \quad \Rightarrow \quad \vec{p}_{B^-}=\vec{p}_Y-\vec{p}_{B^+}=(-p_Y-p_{B^+},0,0)$$

Then we have:

$$|\vec{p}_{B^-}|=p_{B^-}=p_Y+p_{B^+} \quad \Rightarrow \quad p_{B^+}=p_{B^-}-p_Y$$

By now we have only used the conservation of total momentum. Now let's apply the conservation of energy:

$$E_Y=E_{B^+}+E_{B^-} \quad \Rightarrow \quad E_Y=\sqrt{m_B^2c^4+p_{B^+}^2c^2}+\sqrt{m_B^2c^4+p_{B^-}^2c^2}$$

From this equation, with some calculation (I repeated the calculations several times carefully) and using the fact that $p_{B^+}=p_{B^-}-p_Y$, we find that:

$$(4m_Y^2c^6)p_{B^-}^2-(4p_Ym_Y^2c^6)p_{B^-}+(4m_Y^2m_B^2c^8+4p_Y^2m_B^2c^6-m_Y^4c^8)=0$$

This is a second degree equation in $p_{B^-}$, and solving it we find:

$$p_{B^-}=2.56\,\text{GeV}/c, \quad p_{B^-}=3.34\,\text{GeV}/c$$

Then if $p_{B^-}=3.34\,\text{GeV}/c$ we have:

$$p_{B^+}=p_{B^-}-p_Y=-2.56\,\text{GeV}/c$$

while if $p_{B^-}=2.56\,\text{GeV}/c$ we have:

$$p_{B^+}=p_{B^-}-p_Y=-3.34\,\text{GeV}/c$$

This is impossible, since $p_{B^+}$ must be positive. Then we conclude that $B^+$ can't be emitted in the positive direction of x axis, I guess. However the exercise I am doing tells me to suppose that $B^+$ is emitted in the positive direction of x axis.

This contradiction suggests a misunderstanding of something conceptual about the conservation laws. Thanks for any pointers.