Adding xarray without creating additional dimensions

I'm not exactly sure how to phrase this, but an example makes this clear:

import xarray as xr
a = xr.DataArray(data=range(8), dims = ["measurement"], coords = {"measurement": range(8), "plant":("measurement",[0,0,0,0,1,1,1,1])})
b = xr.DataArray(data=[100, 200], dims = ["plant"], coords = {"plant": range(2)})

which gives

<xarray.DataArray (measurement: 8)>
array([0, 1, 2, 3, 4, 5, 6, 7])
Coordinates:
  * measurement  (measurement) int32 0 1 2 3 4 5 6 7
    plant        (measurement) int32 0 0 0 0 1 1 1 1
<xarray.DataArray (plant: 2)>
array([100, 200])
Coordinates:
  * plant    (plant) int32 0 1

I want to add the offsets per manufacturing plant from b to the measurements in a. But running a+b gives me

<xarray.DataArray (measurement: 8, plant: 2)>
array([[100, 200],
       [101, 201],
       [102, 202],
       [103, 203],
       [104, 204],
       [105, 205],
       [106, 206],
       [107, 207]])
Coordinates:
  * measurement  (measurement) int32 0 1 2 3 4 5 6 7
  * plant        (plant) int32 0 1

so it made all kind of extra data points.

I can make it in an ugly way:

def adder(x, y):
    return x + y.sel(plant = x.plant.values)

a.groupby("measurement").map(lambda x:adder(x,b))

which gives the desired answer

<xarray.DataArray (measurement: 8)>
array([100, 101, 102, 103, 204, 205, 206, 207])
Coordinates:
  * measurement  (measurement) int32 0 1 2 3 4 5 6 7
    plant        (measurement) int32 0 0 0 0 1 1 1 1

How do I make this in a nice way?