interpret a p-value result as a significance of a linear regression in terms of sigmas

dear R community,

I am running a linear regression for my dataset between 2 variables 
(disk mass and velocities).
This is the result returned by the summary function onto the lm object 
for one of my dataset.

Call:
lm(formula = df$md1 ~ df$logV, data = df)

Residuals:
      Min       1Q   Median       3Q      Max
-0.64856 -0.16492  0.04127  0.18027  0.45727

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept)   6.2582     0.2682  23.333  < 2e-16 ***
df$logV       1.2926     0.2253   5.738  6.5e-06 ***
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Residual standard error: 0.3067 on 24 degrees of freedom
Multiple R-squared:  0.5784,    Adjusted R-squared:  0.5609
F-statistic: 32.93 on 1 and 24 DF,  p-value: 6.504e-06

I am interested to give the significance in terms of sigmas (as 
generally done in particle physics, see for instance the 7 \sigma 
discovery of the Higgs particle)
of my regression.
For this, if I understood well, I should look at the p-value for the 
F-statistic which is in this univariate linear regression the same as 
the one for logV.

My question is, am I right if I state that the significance in terms of 
sigmas (sign) is given by: p = 2*(1-pnorm(sign)) since I guess the 
p-value returned by R is for a two sided test (and assuming Gaussianity 
for my dataset)?

Otherwise is there any way to get the significance of this linear 
regression in terms of sigmas?

I would have a similar question also, as extension, for a multivariate 
linear regression for which the p-value associated to F statistics is 
not the same as the p-value for each variable of the regression.

Thanks in advance,

Best Regards

Jean-Philippe Fontaine