and my question is why arduino detecing LOW of pin(INPUT_PULLUP) in circuit wich is not connected to anything
Yes, a lower value (external) pull-up resistor may help...It could be picking-up noise (usually 50/60Hz electromagnetic radiation from your house wiring). There is a certain small-amount of energy being picked-up, depending the length of the wires, shielding (if any) and the location (how close they are to the power wiring) and orientation of the wires, etc. If you've ever touched an audio input connection and heard a "buzz", that's the same thing, with your body acting as an antenna instead of a long unshielded wire. "Energy" (more accurately power) is measured as Watts (or micro-watts in this case) and power is calculated as Voltage x Current. With a given amount of energy (microwatts) you'll get higher voltage into a higher impedance. You could easily get 1 volt or more if you touch a high impedance Arduino input because with high impedance you don't get much current. With lower impedance (or lower resistance) the voltage (from the noise) drops because a very-small amount of current is flowing through a lower resistance (Ohms Law). There isn't enough energy picked-up to get "high" voltage and "high" current at the same time. Since the High/Low is determined by voltage, lowering the impedance/resistance lowers the noise-voltage, making it more immune to noise. In this application, an external 1K pull-up resistor is fine and hopefully the noise problem will go-away. 5V and 1K only requires 5mA, which your doorbell switches and power supply can easily handle.
then i unpluged everything from arduino and then i connect short wire 100mm to pin(INPUT_PULLUP) and second end to common GND of that switches remeber this common gnd is not connected to gnd of arduino rhight now this circuit with switches is connected to nothing. and digitalRead sometimes return LOW when i stick cable from input_pullup to this common gnd of switches wich is not connected to gnd.and my question is why arduino detecing LOW of pin(INPUT_PULLUP) in circuit wich is not connected to anything