Context : Recently , diffuse and extended sources in TeV \gamma -rays as well as in X-rays have been detected in the direction of the Galactic globular cluster ( GC ) Terzan 5 .
Remarkably , this is among the brightest GCs detected in the GeV regime .
The nature of neither the TeV nor the diffuse X-ray signal from Terzan 5 is not yet settled .
These emissions most likely indicate the presence of several non-thermal radiation processes in addition to those that give rise to the GeV signal .

Aims : The aim of this work is to search for diffuse X-ray emission from all GeV-detected GCs where appropriate X-ray observations are available , and to compare the obtained results with the signal detected from Terzan 5 .
This study will help to determine whether Terzan 5 stands out among other GC or whether a whole population of globular clusters feature similar properties .

Methods : After assessing all archival X-ray observations of GeV detected GCs , we analyzed the data of six Chandra observations pointed toward M 62 , NGC 6388 , NGC 6541 , M 28 , M 80 , and NGC 6139 .
For each GC we characterized the diffuse X-ray emission using the same analysis techniques as for Terzan 5 .
To study the emission on the same relative scales we used the half-mass radius as a scale parameter to determine the extent of the potential emission region .

Results : None of the six GCs show significant diffuse X-ray emission above the particle and diffuse galactic X-ray background components .
The derived upper limits allow to assess the validity of different models that were discussed in the interpretation of the multi-wavelength data of Terzan 5 .
A scenario based on synchrotron emission from relativistic leptons provided by the millisecond pulsar population can not be securely rejected if a comparable magnetic field strength as in Terzan 5 is assumed for every GC .
However , such a scenario seems to be unlikely for NGC 6388 , and M 62 .
An inverse-Compton scenario relying on the presence of a putative GRB remnant with the same properties as proposed for Terzan 5 can be ruled out for all six GCs .
Finally , the assumption that each GC hosts a source with the same luminosity as in Terzan 5 is ruled out for all GCs but NGC 6139 .

Conclusions :