As above with a few twists.
Vit K is essential for blood clotting. Babies are prone to being deficient (a design flaw IMO). Formula is supplemented. Breast milk is not ergo. Breast fed babies are more at risk of problems.
The problems is a condition called Haemorrhagic disease of the Newborn which can cause devastating bleeds inside babies brains (like a stroke). The consequences can be lifelong, life limiting and sometimes life threatening.
Vitamin K supplementation prevents against this. The data shows that worldwide no babies given IM vitamin K have had a bleed. Several babies who received oral vitamin K have had a bleed (primarily because effective oral supplementation requires 3 doses to be taken spaced apart, therefore a signficant minority of children don't receive the full protective course of oral vitamin K).
There was a furore about Vitamin K historically being associated with some childhood malignancies but this was disproven a really long time ago but the stigma still hangs on.
Personally my kids would get IM Vitamin K. As a HCP I personally wouldn't worry about 'traumatising' a small infant who has just been born - much better to keep them safe but this is my opinion and I respect the views of those who disagree I would just ask you to think carefully about why it is given and the admittedly rare but devestating consequences that can arise if it is not given.
I've seen 3 babies in my short careers suffer from an intracranial bleed. One died. All 3 were in the UK. Birth trauma etc. is not a major risk factor for the bleeds they tend to happen spontaneously and the most serious ones happen late (between 2 weeks and 2 months of age).
Trusted link information is available here:
www.nlm.nih.gov/medlineplus/ency/article/007320.htm