Music Therapy- Since stress is the root of many health problems, the relaxing effect of jazz music can have an incredible healing influence. It physically changes your body by lowering your heart and respiratory rate.

Stroke Recovery
Listening to music (jazz included) directly after a stroke improves verbal memory, focus and mood. In just 3 months after a stroke:

Music Listeners' verbal memory increased 60% and focused attention increased 17%.
Non-Listeners' verbal memory increased 29% and focused attention increased 0%.
Audio Book Listeners' verbal memory increased 18% and focused attention increased 0%.
Pain Relief
Listening to jazz has been shown to reduce time and intensity of both general and migraine headaches.
Study shows that listening to music (including jazz) can reduce chronic pain. After listening to jazz music for an hour every day for a week:

Music Listeners had a 21% decrease in pain.
Non-Listeners had a 2% increase in pain.
Music therapy is increasingly used for pain relief in hospitals to:

reduce need for medication during childbirth
decrease postoperative pain
complement use of anesthesia during surgery
Blood Pressure
Studies show that music (including jazz) and laughter can lower blood pressure by causing blood vessels to expand by up to 30%.
After 3 months of the music & laughter study:

music group decreased blood pressure by 6 mmHg
laughter group decreased blood pressure by 5 mmHg
control group had no change
Immediately after each session also revealed a short-term dip of 6 mmHg to 7 mmHg.
The range of decline is comparable with someone:

adopting a low-salt diet
losing 10 pounds
taking blood-pressure-lowering medication.
This change reduces risk of death from heart disease or stroke by up to 15%.

Immunity
Listening to jazz for 30 minutes boosts immunoglobulin A (IgA) levels. IgA resides in mucous linings of the body and acts as an antibody; preventing virus, bacteria, and infection. The effect on IgA levels continues for an additional 30 minutes after the music stops playing.