# How to force Mathematica to plot the function near zero?

I have the code of the function

InversedsToGeV = 1/(1.5*10^24);
GammatotalBInInverseds = (1.638*10^-12)^-1;
GammatotalB = GammatotalBInInverseds*InversedsToGeV
mB = 5.279;
mK = 0.493;
mPi = 0.14;
vhiggs = 240;
ebs = 3.6*10^-4;
ebd = 7.9*10^-5;
fBK = 0.33;
fBpi = 0.258;
MBpole = Sqrt;
msquark = 0.09;
mbquark = 4.65;
BKFormFactor[S_] = fBK/(1 - S/MBpole^2);
BpiFormFactor[S_] = fBpi/(1 - S/MBpole^2);
BrscalarBtoK[MS_] =
Piecewise[{{1/(8*Pi) 1/(
mB GammatotalB) (mbquark/vhiggs*BKFormFactor[MS^2]*
ebs*(mB^2 - mK^2)/(mbquark - msquark))^2 (1 + MS^4/mB^4 +
mK^4/mB^4 - 2*MS^2*mK^2/mB^4 - 2*mK^2/mB^2 - 2*MS^2/mB^2)^(
1/2)/2, MS < mB - mK}, {0, True}}];


I try to plot the function BrscalarBtoK with the code

LogPlot[{BrscalarBtoK[m\[Phi]]}, {m\[Phi], 0.21, 10},
FrameLabel -> {"\!$$\*SubscriptBox[\(m$$, $$\[Phi]$$]\) [GeV]",
"\!$$\*SubscriptBox[\(P$$, $$meson$$]\)/\!$$\*SuperscriptBox[\(\ \[Theta]$$, $$2$$]\)"}, Frame -> True,
FrameStyle -> Directive[Black, 35],
PlotRange -> {{0, 10}, {10^-5, 5}},
PlotStyle -> {{Thick, Blue, Thickness[0.005]}},
GridLines -> Automatic, ImageSize -> Large]


The result is on the left picture below. However, I want it to be like on the right picture below and don't understand what is the reason for this incorrect plotting. Can you please help me with this problem? • Try increasing PlotPoints or MaxRecursion? – user202729 Jun 28 '18 at 12:52
• Maybe change the value of the piecewise function above the threshold to 10^-9 rather than zero (which is difficult to show in a log plot). The option Exclusions -> None could help. – b.gates.you.know.what Jun 28 '18 at 12:57
• @b.gatessucks : thank you, your advice helped! – John Taylor Jun 28 '18 at 13:06

Add a second plot that is focused on the region you want, with increased PlotPoints to help the sampling:
plot2 = LogPlot[{BrscalarBtoK[m\[Phi]]}, {m\[Phi], mB - mK - 10^-2, 