There are few involved in the investigation of the Chakras. Below are some of the better know researchers who have attempted to prove their existence, although as you can see, this list is by no means exhaustive.
Dr Hiroshi Motoyama
"…We may define the chakra as an energy centre which spins like a wheel and opens like a flower. Metaphysical concepts, however, do not belong purely to the world of spiritual experience; scientific enquiry has in many cases confirmed age-old beliefs.
Dr Hiroshi Motoyama bridges the world of the scientific and the spiritual with dual authority. He is both a scientist and a Shinto priest. Motoyama is the founder of the International Association for Religion and Parapsychology. In 1974 he was recognised by UNESCO [United Nations Educational, Scientific and Cultural Organization] as one of the world's ten foremost parapsychologists. He is especially interested to verify scientifically the claims put forward by proponents of spiritual practices. Several significant experiments have been conducted under his auspices.
He has specifically developed a Chakra Instrument which is designed to detect minute electrical, magnetic and optical changes which occur in the immediate environment of the experimental subject. In a typical experimental situation, the subject sat in an electrostatically secure room which was internally lined with aluminium sheeting and shielded by lead sheeting embedded in the walls. A round copper electrode and photo-electric cell were placed in front of the body, level with the location of a supposed chakra. During one test on the centres of the stomach and heart, the subject was monitored for a period of three minutes at each of the two locations. Separate readings were taken one minute before a state of concentration, during concentration, and one minute after concentration.
Curiously, when an advanced yoga practitioner was tested, the two centres gave quite different results. The stomach centre showed no change in measurable activity during the three-minute monitoring period. However, the heart centre showed a considerable intensification of measurable activity during the period of concentration. This difference corresponded to the subject's regular spiritual practice. He regularly meditated on the heart centre during meditation. The subject did not as a rule use the solar plexus chakra as a focal point for meditation as he suffered from a serious digestive disorder.
When working with another subject, Motoyama found that the increased activity of the heart chakra was sufficient to produce a measurable effect which was detected by the photo-electric cell. In other words the activity of the heart chakra was enough to produce a weak but measurable physical light. Moreover the subject was asked to press a button whenever she thought that she experienced the emission of psi-energy. The subjective feelings corresponded to the objectively measured periods of activity. It was experiments like these which were conducted with 100 subjects which led Motoyama to conclude 'that mental concentration on a chakra activates it' [Motoyama, The Theories of the Chakras, p.274]."