In recent years, water-absorbent resins having excellent water absorbency are developed and widely used mainly for disposable uses, as absorbent articles (e.g. disposable diapers and sanitary napkins), and further water-retaining agents in agricultural and horticultural fields and water-holding materials in engineering works fields. 
The above water-absorbent resins are made water-swellable and water-insoluble by slightly crosslinking hydrophilic polymers.  Generally, as to the production process thereof, they have been obtained as powders by a process including the steps of: carrying out polymerization of water-soluble unsaturated monomers such as acrylic acid; and crosslinking the resultant polymers during or after the polymerization.  Accordingly, many polymerization methods for obtaining powdery water-absorbent resins (e.g. reversed-phase suspension polymerization, aqueous solution polymerization, and further precipitation polymerization which involves precipitating a polymer in a solvent, bulk polymerization which involves polymerization substantially in the absence of a solvent, and spray polymerization which involves polymerization in gas phase) have been proposed hitherto.  Among these polymerization methods, the aqueous solution polymerization and reversed-phase suspension polymerization are mainly used in view of performance and easiness of controlling the polymerization. 
The reversed-phase suspension polymerization is a polymerization method which involves dispersing an aqueous monomer solution in a hydrophobic organic solvent in the form of particles having particle diameters of about 1 to about 0.1 mm, and has the advantage of obtaining gel particles having particle diameters of products at the same time as the polymerization (for example, as is mentioned in such as specifications of U.S. Pat.  Nos.  4,093,776, 4,367,323, 4,446,261, and 4,683,274, and especially refer to the following patent document 1.). 
However, the control of the polymerization temperature is difficult in the reversed-phase suspension polymerization which is carried out by being dispersed in a large quantity of solvent.  Especially, there is danger of explosion during the polymerization when the concentration is raised (for example, the concentration of the aqueous monomer solution is not less than 40 weight %).  Therefore, there are problems such that the productivity in an increasing scale cannot be improved sufficiently. 
In addition, the aqueous solution polymerization is a method which involves polymerizing an aqueous monomer solution without using a dispersible solvent, and is excellent in costs, productivity, and safety of products because the polymerization can be carried out by using water only.  These aqueous solution polymerizations are further roughly divided into a method which involves static polymerization such as belt polymerization (for example, as is mentioned in such as specifications of U.S. Pat.  Nos.  6,174,978 and 4,857,610, and especially refer to the following patent document 2.),  and a method which involves polymerization while being stirred with such as kneaders (stirring polymerization).  In the above aqueous solution polymerization that is different from the reversed-phase suspension polymerization, obtained is a massive gel having a size of far larger than particle diameters of products.  Therefore, the fine division of the gel is necessary for drying and production.  When polymerization vessels having shearing force (e.g. kneaders) are used as polymerization machines in the above stirring polymerization, the gel is finely divided at the same time as the polymerization.  Therefore, a step of finely dividing the gel after the polymerization is unnecessary, and the specific surface area of the gel is large during the polymerization.  Accordingly, the stirring polymerization has the advantage of easily removing polymerization heat and also having high productivity. 
The above stirring polymerization carried out by using such as kneaders is a production process for a water-absorbent resin, comprising a polymerization step including the steps of: supplying an aqueous solution of a water-soluble unsaturated monomer to a polymerization vessel having shearing force to carry out polymerization involving crosslinking; and at the same time finely dividing the resultant hydrogel (for example, as is exemplified in such as: specifications of U.S. Pat.  Nos.  4,625,001, 4,985,514, and 5,124,416 filed by Nippon Shokubai Co., Ltd.; and a pamphlet of WO 01/38402 and specifications of U.S. Pat.  Nos.  5,149,750, 4,769,427, and 4,873,299 filed by BASF, and especially refer to the following patent documents 3 and 4.). 
However, in the above production process for a water-absorbent resin, comprising a polymerization step including the steps of: carrying out polymerization including crosslinking; and at the same time finely dividing the resultant gel, the gel is finely divided into pieces having particle diameters of about 1 mm during the polymerization, but there are many cases where the fine division of the gel carried out at the same time as the polymerization takes longer time than the polymerization time.  Therefore, there are cases where the polymerization time is unnecessarily prolonged for carrying out the fine division sufficiently, or where the lowering of properties is caused because of the longtime fine division (shearing) of the gel. 
Furthermore, the hydrogel as discharged from the polymerization vessel in this way is finely divided into a particulate gel having a size of a few millimeter (favorably about 1 to about 3 mm) by shearing force during the polymerization, but the fine division of the gel during the polymerization is usually difficult to completely carry out.  There are cases where the resultant finely divided gel is contaminated with such a coarse gel as has a size of larger than a few centimeters in an amount of a few to about 10 weight %. 
Particularly, the side-production of the coarse gel tends to increase if an attempt is made to raise the temperature when the polymerization is initiated, or to raise the concentration of the water-soluble unsaturated monomer, or to decrease the extractable content of the water-absorbent resin.  Accordingly, in the above production process for a water-absorbent resin, comprising a polymerization step including the steps of: carrying out polymerization involving crosslinking; and at the same time finely dividing the resultant gel, there is a case where: when an attempt is made to decrease the extractable content of the water-absorbent resin, or to raise the temperature when the polymerization is initiated or the concentration of the water-soluble unsaturated monomer in order to improve productivity or properties, the restriction occurs that the coarse gel is side-produced. 
In addition, the drying time of the finely divided gel depends upon its specific surface area.  Therefore, the contamination with the coarse gel in only a few percents has problems such that: not only the drying rate of the entire finely divided gel is greatly lowered and the longtime drying is necessary, but also the above unnecessarily drying causes the properties to lower, or the properties after the drying are changed or lowered in proportion to the gel particle diameter.  In addition, there is a case where the above coarse gel in an amount of few percents is an undried product even after the drying, and there is also a case where the procedure such as pulverization or classification after the drying cannot be carried out (e.g. the pulverization step or classification step after the drying is stopped.)  because of the adhesion of the undried product (gel) with which the dried product is contaminated. 
Accordingly, as to the coarse gel with which the finely divided gel is contaminated, a method which involves removing the coarse gel by classification after polymerization (for example, as is mentioned in such as a gazette of JP-A-107800/1994, and especially refer to the following patent document 5.)  and a method which involves classifying an undried product after drying (for example, as is mentioned in such as a specification of U.S. Pat.  No.  6,291,636, and especially refer to the following patent document 6.)  are also proposed.  However, in the above methods which involve removing the coarse gel or undried product after the polymerization, not only the apparatuses are complicated and the classification efficiency is also low, but also are caused the problems of waste derived from the classified coarse gel and the lowering of yield accompanying the abandonment. 
In addition, as to other problems, in the case of carrying out high-temperature polymerization or polymerization in the presence of a transition metal, which includes the reversed-phase suspension polymerization and the static polymerization such as belt polymerization, there have problems such that the stability of monomers is lowered even before the polymerization or during the preparation.  In addition, there are also problems of coloring in the water-absorbent resin as obtained. 
[Patent Document 1]
Specification of U.S. Pat.  No.  5,244,735
[Patent Document 2]
Specification of U.S. Pat.  No.  6,241,928
[Patent Document 3]
Specification of U.S. Pat.  No.  5,250,640
[Patent Document 4]
Gazette of Japanese Patent No.  2966539
[Patent document 5]
Gazette of JP-A-142612/1994
[Patent Document 6]
Pamphlet of WO 00/24810