Anthropologically, there are no human races, period.
From one perspective; biologically, human races are undefined and hence for definition's sake
do not exist. To say "there are multiple races which can not be defined" scientifically is basically accepting the concept of all of humanity being a melting-pot and thus, while doubtlessely having races, doesn't have races that can be defined and thus for all practical purposes has no races. Because no human strain of people has ever been split from another long enough to be defined, without a doubt or misconception, as a race. Here's what the History and Geography of Human Genes (1996) had to say on it:
"The classification into races has proved to be a futile exercise for
reasons that were already clear to Darwin. Human races are still extremely
unstable entities in the hands of modern taxonomists, who define from 3 to
60 or more races. To some extent, this latitude depends on the personal
preference of taxonomists, who may choose to be 'lumpers' or 'spliters.'
Although there is no doubt that there is only one human species, there are
clearly no objective reasons for stopping at any particular level of
taxonomic splitting. In fact, the analysis we carry out in chapter 2 for
purposes of evolutionary study shows that the level at which we stop our
classification is completely arbitrary. Explanations are statistical,
geographic, and historica. Statistically, genetic variation within clusters
is large compared witht hat between clusters.
All populations or population clusters overlap when single genes are
considered, and in almost all populations, all alleles are present but in
different frequencies. No single gene is therefore sufficient for
classifying human populations into systematic categories." p. 19
However, because of the melting-pot-thing, the human race is unefineable in the biological sense outside of certain strains of taxonomy:
"A race is a biological subspecies, or variety of a species, consisting of a more or less distinct population with anatomical traits that distinguish it clearly from other races. This biologist's definition does not fit the reality of human genetic variation today. We are biologically an extremely homogenous species. As a matter of fact, all humans today are 99.9% genetically identical, and most of the variation that does occur is in the difference between males and females and our unique personal traits. This homogeneity is very unusual in the animal kingdom. Even our closest relatives, the chimpanzees have 2-3 times more genetic variation than people. Orangutans have 8-10 times more variation.
It is now clear that our human "races" are cultural creations, not biological realities. The concept of human biological races is based on the false assumption that anatomical traits, such as skin color and specific facial characteristics, cluster together in single distinct groups of people. They do not. There are no clearly distinct "black", "white", or other races."
http://anthro.palomar.edu/ethnicity/ethnic_1.htm
The subject is sensitive one because of the obvious problem of racism. Anthropologists have accepted that there are no human races. Biologists have their debates. However, whether or not you accept the existance of human races (which many biologists do not), the problem states way above in which taxonomy can't make a definitive decision on human races erradicates any possibility of debating the subject from "scientific grounds"
PS: if you'd notice, by the way, I noted before that there's "only one human race, Homo sapiens sapiens" If I were talking about species, I wouldn't have added the second sapiens. Just saying.