Reproduction steps:
1. Create a new HDRP Template project
2. Add a Particle System (GameObject -> Effects -> Particle System)
3. Create a new Material (HDRP/Lit) and assign it to the Renderer module of the Particle System
4. Set Motions Vectors to Camera Motion Only (Particle System Renderer module)
5. Enter Play Mode

Expected result: Motion Vectors are applied and visible in both Game and Scene view
Actual result: in the Game view Particles are transparent and producing visual artifacts/trails

Reproducible with: HDRP 4.10.0 (2018.4.15f1), HDRP 6.9.2 (2019.2.17f1), HDRP 7.1.7 (2019.3.0f4, 2020.1.0a18)

Notes:
1. Reproducible in both Build & Editor
2. In 2018.4 + HDRP 4.10.0 the issue reproduces in both Game and Scene view
3. Reproducible only when using only HDRP Lit Material
4. Could not test with URP (there is no option in Particle Renderer module for Motion Vectors)