1 00:00:05,310 --> 00:00:07,320 MARKUS KLUTE: Welcome back to 8.701. 2 00:00:07,320 --> 00:00:09,300 So in this short video, we'll talking 3 00:00:09,300 --> 00:00:12,480 about the effects of renormalization 4 00:00:12,480 --> 00:00:14,790 and higher-order QED diagrams. 5 00:00:14,790 --> 00:00:17,010 And we have already seen that when 6 00:00:17,010 --> 00:00:23,580 we perform the integration of a matrix element over q, 7 00:00:23,580 --> 00:00:25,230 that there's infinities. 8 00:00:25,230 --> 00:00:28,200 And those infinities can be gotten around 9 00:00:28,200 --> 00:00:31,320 with by introducing a cut-off scale, 10 00:00:31,320 --> 00:00:36,690 and then only integrating up to this cut-off scale, 11 00:00:36,690 --> 00:00:41,280 and in effect renormalize or redefine 12 00:00:41,280 --> 00:00:44,260 masses and couplings involved. 13 00:00:44,260 --> 00:00:47,880 So the first of such an effect or effective higher 14 00:00:47,880 --> 00:00:51,450 order is the so-called vacuum polarization. 15 00:00:51,450 --> 00:00:54,460 So you have high-order contribution 16 00:00:54,460 --> 00:00:57,490 which may look like this, an additional loop, which 17 00:00:57,490 --> 00:01:01,480 you can think about in the photon is so energetic that it 18 00:01:01,480 --> 00:01:03,620 can polarize the vacuum and produce 19 00:01:03,620 --> 00:01:06,130 a particle-antiparticle pair. 20 00:01:06,130 --> 00:01:09,760 And that particle and antiparticle pair 21 00:01:09,760 --> 00:01:12,640 then provides kind of a screening of the charge 22 00:01:12,640 --> 00:01:13,900 you want to probe. 23 00:01:13,900 --> 00:01:17,710 So I mentioned this particle here emits a photon 24 00:01:17,710 --> 00:01:22,770 and wants to probe the electric charge of this particle. 25 00:01:22,770 --> 00:01:27,110 The fact that there is this vacuum polarization going on 26 00:01:27,110 --> 00:01:29,800 screens the charge you actually want to probe. 27 00:01:29,800 --> 00:01:34,100 So effectively, you see a charge which is either 28 00:01:34,100 --> 00:01:37,010 reduced or increased, depending on the impact, 29 00:01:37,010 --> 00:01:39,470 on the sort of impact. 30 00:01:39,470 --> 00:01:42,860 So the fine structure constant, remember, alpha, 31 00:01:42,860 --> 00:01:47,310 is 1/137 [INAUDIBLE] at 0. 32 00:01:47,310 --> 00:01:52,730 We measure that the value of alpha slightly increases as we 33 00:01:52,730 --> 00:01:54,630 go to higher and higher energies. 34 00:01:54,630 --> 00:01:56,540 And so this has been measured in many places, 35 00:01:56,540 --> 00:01:58,910 experimentally confirmed, for example, 36 00:01:58,910 --> 00:02:02,030 at lab where, at the [INAUDIBLE] of the W 37 00:02:02,030 --> 00:02:05,150 or the scale of the W mass, the value of alpha 38 00:02:05,150 --> 00:02:07,850 has been measured to 1/128. 39 00:02:07,850 --> 00:02:09,560 And you can do this analytically. 40 00:02:09,560 --> 00:02:13,670 You can calculate what the scale of effect is and plot this. 41 00:02:13,670 --> 00:02:17,390 So you see here the running of alpha QED as a function 42 00:02:17,390 --> 00:02:18,510 of the energy scale. 43 00:02:18,510 --> 00:02:20,900 And you see this increase here. 44 00:02:20,900 --> 00:02:22,580 There's another interesting point. 45 00:02:22,580 --> 00:02:29,260 As you open up new particles of higher masses, quark 46 00:02:29,260 --> 00:02:31,970 and antiquark pairs, you find this kind 47 00:02:31,970 --> 00:02:33,950 of stepping approach here-- 48 00:02:33,950 --> 00:02:35,360 the new particles, for example. 49 00:02:35,360 --> 00:02:38,480 The muon, antimuon, and the quarks and antiquarks 50 00:02:38,480 --> 00:02:42,070 are [INAUDIBLE]. 51 00:02:42,070 --> 00:02:42,640 All right. 52 00:02:42,640 --> 00:02:46,010 So this is the first effect, vacuum polarization. 53 00:02:46,010 --> 00:02:49,150 The second effect is very interesting-- probably one 54 00:02:49,150 --> 00:02:53,530 of the most famous higher-order processes in QED. 55 00:02:53,530 --> 00:02:56,890 And it has to do with the anomalous magnetic moment. 56 00:02:56,890 --> 00:02:59,980 The magnetic moment is defined as the factor 57 00:02:59,980 --> 00:03:04,930 g times e over 2m times S, the spin of the particle. 58 00:03:04,930 --> 00:03:08,820 Diagrams of this form here modify the vertex. 59 00:03:08,820 --> 00:03:12,660 So instead of having a vertex like this, 60 00:03:12,660 --> 00:03:15,180 you have higher orders which modify the [INAUDIBLE].. 61 00:03:15,180 --> 00:03:22,020 This leads, then, to a modified magnetic moment 62 00:03:22,020 --> 00:03:24,710 of the fermion involved-- in this case, an electron, 63 00:03:24,710 --> 00:03:29,060 but it can also [INAUDIBLE] muon or tau or another form. 64 00:03:29,060 --> 00:03:33,420 So this was shown by Schwinger already in 1948, 65 00:03:33,420 --> 00:03:36,360 and then experimentally confirmed many times after. 66 00:03:36,360 --> 00:03:40,830 This g minus [INAUDIBLE],, which is 2, leading order, 67 00:03:40,830 --> 00:03:47,170 is modified to 2 plus pi over alpha in next leading order. 68 00:03:47,170 --> 00:03:49,830 We can calculate this to many orders, 69 00:03:49,830 --> 00:03:53,780 and with mind-blowing precision. 70 00:03:53,780 --> 00:03:56,480 So the precision is better than 10 to the minus 12 pi now. 71 00:03:56,480 --> 00:04:00,730 I think it's 1.7 [INAUDIBLE] at this stage. 72 00:04:00,730 --> 00:04:02,470 And experiments have tried to measure 73 00:04:02,470 --> 00:04:04,290 this to find new effects. 74 00:04:04,290 --> 00:04:06,700 I mentioned you can have new particles which 75 00:04:06,700 --> 00:04:11,450 make modifications to the magnetic moment here. 76 00:04:11,450 --> 00:04:13,520 And you would have sensitivity by making 77 00:04:13,520 --> 00:04:14,730 experimental measurements. 78 00:04:14,730 --> 00:04:17,630 So the electrons [INAUDIBLE] muon g minus 2 79 00:04:17,630 --> 00:04:20,329 has been measured with very high precision. 80 00:04:20,329 --> 00:04:21,890 No new physics have been observed, 81 00:04:21,890 --> 00:04:28,340 but some differences are small differences 82 00:04:28,340 --> 00:04:32,630 that have caused quite some excitement 83 00:04:32,630 --> 00:04:35,810 about further improvements in g minus 2 measurements 84 00:04:35,810 --> 00:04:37,170 specifically for the muon. 85 00:04:37,170 --> 00:04:40,000 So they're ongoing at this point.