I've just discovered that the right side of my embouchure is not vibrating when I am buzzing without the mouthpiece. It is leaking air as well.

I think it's because of the small mouthpiece mark on the right side of my lips. There is a small depression on the right of my embouchure because I have always been playing with my stand on my right so that the bell will not block the score. It seems that I have been tilting my trombone to the stand unconsciously as well. The leaking is not causing any evident problem when I play the trombone with the mouthpiece as the rim of the mouthpiece rests on the mouthpiece mark. But this will most probably be a great impedance for reaching higher registers because half of my embouchure's muscles are not working effectively.

Now the questions is how to cure my embouchure, to make the right side vibrate again. So does anyone have any effective solution to this?

Thanks in advance!

You may not have as bad a problem as you think.
Let me tell you now if you try and change your embouchre you will sound horrible and miss many of your notes.

Just because the right side of your embouchre isn't vibrating without the mouthpiece doesn't mean you will be restricted in range. Your lips muscles have probably adjusted to the lack of movement and the center of your embouchre has now moved to the left. Because of teeth issues many people do not have the center of their embouchre in the center of their lips. And professional musicians who I have worked with who had BellPalsy seizures often favor one side of the embouchre during and after recovery.

So. Don't try and change your embouchre . . . . yet.
Decide how you are going to be playing. If you are going to keep the trombone to the side of the stand then continue that way. If your tone has turned to crap and you have no range then we can address the issue. Otherwise you may be just fine. I would be more concerned about the ratio and relationship of your top lip to your bottom lip.

If you are really concerned then let me offer you an option.
Get in your normal playing position and play some regular easy music. Have someone take a photo of you from the front, the back, and both sides. The photo should include at least from your hips up to the top of your head. You can send them to me via the PM here on 8notes and I will evaluate what you can do, if anyhting is needed, to improve any weaknesses you think you might have.

John

Thanks for your advice! I think the problem isn't serious though, I can still reach the all the notes required at my level of playing. I was worried about if the embouchure not being centred is going to prevent me getting higher.

However I think it is important to mend the dent on my embouchure. It leaks air when I play in higher registers, when the muscles on the embouchure tense up and embouchure becomes hard. My friend who switched from playing trombone to tuba had the same embouchure problem when he first played the tuba (tuba needs a larger embouchure, so the embouchure problem vecame evident). He consciously used the side that was leaking and solved the problem in a few months. Do you think this will work for me as well?

I do not encourage changing the embouchre directly as you suggest.
The problem with chanigng the embouchre yourself is that you may just be forcing other muscles to compensate for something that is already mis-adjusted. And then you will have problems with range, stamina, and tone quality.
You really need to have someone who knows what is going on, and that being said there are many professionals and top teachers who are great, but they themselves don't understand all the mechanics behind the embouchre.

If you are going to do it yourself then start with your hips. Make sure your hips are aligned. Make sure your back is relatively straight. There should be jusst the slightest curve and this should swope directly into the neck and jaw. Your head should not be pushed forward and your neck should not be criked to the left or right. Nor should you be turning to the left or right.

With all these major muscle groups aligned properly your embouchre will be more natural and correct. This will also allow for better air support. And playing is all about air. High range is all about faster air (well not ALL about faster air). And tone is strongly affected by volume of air.

So, don't work on the lips themselves. Very few of us can actually control these. There are lots of muscles there and we can't really tell each one what we want it to do. If you try and patch the hole you will be using more pressure than needed, and thats a bad thing. That or you will end up pinching, which will result in a bad tone. Get the rest of your body in proper shape and alignment and the embouchre will be forced to take care of itself.

ok, I will try to change my embouchure in the way as you've suggested. I'll be wary about any change in my tone and range.

Thank you so much for your help!