Context : Mass loss is one of the fundamental properties of asymptotic giant branch ( AGB ) stars , but for stars with initial masses below \sim 1 M _ { \odot } , the mass loss on the first red giant branch ( RGB ) actually dominates mass loss on the AGB .
Nevertheless , mass loss on the RGB is still often parameterised by a simple Reimers law in stellar evolution models .

Aims : To study the infrared excess and mass loss of a sample of nearby RGB stars with reliably measured Hipparcos parallaxes and compare the mass loss to that derived for luminous stars in clusters .

Methods : The spectral energy distributions of a well-defined sample of 54 RGB stars are constructed , and fitted with the dust radiative transfer model DUSTY .
The central stars are modelled by MARCS model atmospheres .
In a first step , the best-fit MARCS model is derived , basically determining the effective temperature .
In a second step , models with a finite dust optical depth are fitted and it is determined whether the reduction in \chi ^ { 2 } in such models with one additional free parameter is statistically significant .

Results : Among the 54 stars , 23 stars are found to have a significant infrared excess , which is interpreted as mass loss .
The most luminous star with L = 1860 \mbox { $L _ { \odot } $ } is found to undergo mass loss , while none of the 5 stars with L < 262 \mbox { $L _ { \odot } $ } display evidence of mass loss .
In the range 265 < L < 1500 \mbox { $L _ { \odot } $ } , 22 stars out of 48 experience mass loss , which supports the notion of episodic mass loss .
It is the first time that excess emission is found in stars fainter than \sim 600 L _ { \odot } .
The dust optical depths are translated into mass-loss rates assuming a typical expansion velocity of 10 km s ^ { -1 } and a dust-to-gas ratio of 0.005 .
In this case , fits to the stars with an excess result in \log \dot { M } ( M _ { \odot } yr ^ { -1 } ) = ( 1.4 \pm 0.4 ) \log L + ( -13.2 \pm 1.2 ) and \log \dot { M } ( M _ { \odot } yr ^ { -1 } ) = ( 0.9 \pm 0.3 ) \log ( L R / M ) + ( -13.4 \pm 1.3 ) assuming a mass of 1.1 M _ { \odot } for all objects .
We caution that if the expansion velocity and dust-to-gas ratio have different values from those assumed , the constants in the fit will change .
If these parameters are also functions of luminosity , then this would affect both the slopes and the offsets .
The mass-loss rates are compared to those derived for luminous stars in globular clusters , by fitting both the infrared excess , as in the present paper , and the chromospheric lines .
There is excellent agreement between these values and the mass-loss rates derived from the chromospheric activity .
There is a systematic difference with the literature mass-loss rates derived from modelling the infrared excess , and this has been traced to technical details on how the DUSTY radiative transfer model is run .
If the present results are combined with those from modelling the chromospheric emission lines , we obtain the fits \log \dot { M } ( M _ { \odot } yr ^ { -1 } ) = ( 1.0 \pm 0.3 ) \log L + ( -12.0 \pm 0.9 ) and \log \dot { M } ( M _ { \odot } yr ^ { -1 } ) = ( 0.6 \pm 0.2 ) \log ( L R / M ) + ( -11.9 \pm 0.9 ) , and find that the metallicity dependence is weak at best .
The predictions of these mass-loss rate formula are tested against the recent RGB mass loss determination in NGC 6791 .
Using a scaling factor of \sim 8 \pm \sim 5 , both relations can fit this value .
That the scaling factor is larger than unity suggests that the expansion velocity and/or dust-to-gas ratio , or even the dust opacities , are different from the values adopted .
Angular diameters are presented for the sample .
They may serve as calibrators in interferometric observations .

Conclusions :