Context : Stars form surrounded by gas and dust rich protoplanetary discs .
Generally , these discs dissipate over a few ( 3–10 ) Myr , leaving a faint tenuous debris disc composed of second generation dust produced by the attrition of larger bodies formed in the protoplanetary disc .
Giant planets detected in radial velocity and transit surveys of main sequence stars also form within the protoplanetary disc , whilst super-Earths now detectable may form once the gas has dissipated .
Our own Solar system , with its eight planets and two debris belts is a prime example of an end state of this process .

Aims : The Herschel DEBRIS , DUNES and GT programmes observed 37 exoplanet host stars within 25 pc at 70 , 100 and 160 \mu m with the sensitivity to detect far-infrared excess emission at flux density levels only an order of magnitude greater than that of the Solar system ’ s Edgeworth-Kuiper belt .
Here we present an analysis of that sample , using it to more accurately determine the ( possible ) level of dust emission from these exoplanet host stars and thereafter determine the links between the various components of these exoplanetary systems through statistical analysis .

Methods : We have fitted the flux densities measured from recent Herschel observations with a simple two parameter ( T _ { d } , L _ { IR } / L _ { \star } ) black body model ( or to the 3- \sigma upper limits at 100 \mu m ) .
From this uniform approach we calculate the fractional luminosity , radial extent , dust temperature and disc mass .
We then plotted the calculated dust luminosity or upper limits against the stellar properties , e.g .
effective temperature , metallicity , age , and identified correlations between these parameters .

Results : A total of eleven debris discs are identified around the 37 stars in the sample .
An incidence of ten cool debris discs around the Sun-like exoplanet host stars ( 29 \pm 9 % ) is consistent with the detection rate found by DUNES ( 20.2 \pm 2.0 % ) .
For the debris disc systems , the dust temperatures range from 20 to 80 K , and fractional luminosities ( L _ { IR } / L _ { \star } ) between 2.4 \times 10 ^ { -6 } and 4.1 \times 10 ^ { -4 } .
In the case of non-detections , we calculated typical 3- \sigma upper limits to the dust fractional luminosities of a few \times 10 ^ { -6 } .

Conclusions : We recover the previously identified correlation between stellar metallicity and hot Jupiter planets in our data set .
We find a correlation between the increased presence of dust , lower planet masses and lower stellar metallicities .
This confirms the recently identified correlation between cold debris discs and low mass planets in the context of planet formation by core accretion .