What is the "Doppler mismatch"? In the paper

Coherent Optical Detection of Highly Excited Rydberg States Using Electromagnetically Induced Transparency. A. K. Mohapatra, T. R. Jackson and C. S. Adams. Phys. Rev. Lett. 98, 113003 (2007), U Durham eprint.

the authors state the following:

[...] due to the Doppler mismatch between the probe and coupling lasers, the hyperfine splitting of the $5p^2 P_{3/2}$ state is scaled by a factor of $1-\lambda_c/\lambda_p$ , and the fine structure splitting of the $nd$ state by $\lambda_c/\lambda_p$.

What is the Doppler mismatch of laser beams? (I presume it is related to the Doppler effect, but I don't know how.) How does it lead to the scaling of the hyperfine energy-levels?

For further visual aid:
The experimental setup can be seen in the figure below and represents two laser beams, a probe and a coupling beam, counterpropagating in a Rb vapour cell. To its left is the "Energy level diagram of the ${}^{85}$Rb ladder system".

 A: As shown in the diagram, the probe and coupling lasers propagate in opposite directions. This means that the Doppler effect works in opposite directions for the two beams: if the atom is moving up (as in the diagram), then the probe beam is blue-shifted and the coupling beam is red-shifted, and vice-versa.
A: This question had puzzled me for hours too. Actually, I am reading this paper right now. I used to think that EIT peak locates at the two photon resonance($\Delta_p+\Delta_c=0$, where $\Delta_p,\ \Delta_c$ correspond to detuning of probe and coupling light ) which is actually right, but in the hot atom surroundings something differs.
In the hot cell, atoms have different velocity which satisfies Gaussian distribution. This distribution is so wide in the room temperature that the number of atoms with a velocity of 0 is almost same to the velocity which causes the Doppler shift with hundreds MHz. So, the probe light with small $\Delta_p$(MHz) will excite the atom with velocity $v_0$, where $k_p v_0=-\Delta_p$. That means the atoms which actually join our light atom interaction has a velocity distribution which is Gaussian but the mean value is $v_0$ not 0. So, we have the two photon resonance condition(counter-propagation): $\Delta_p+\Delta_c+k_p v_0-k_c v_0=0\Rightarrow \Delta_c=k_c v_0=-\dfrac{\lambda_p}{\lambda_c}\Delta_p$. That is all of the story. The new two-photon resonance condition($\Delta_c=-\dfrac{\lambda_p}{\lambda_c}\Delta_p$) is the Doppler mismatch which can interpret the 6 peaks in the paper. I think the energy scaling of HFS and FS of Rydberg states is the same thing, I think the author wants to tell you the origins of the 6 pecks in the scaling energy way.
I am so happy you asked the question. Because of your question, I decided to figure out the Doppler mismatch.
Finally, my native language is not English. If there is something about English puzzling you please tell me.
