Testing C Invariance at the Collider M. Longo 11/97 The general idea here is to compare inclusive production of a particle in the proton hemisphere with its antiparticle in the p-bar hemisphere. This could be done over a wide range of x and pt, and for different particle species. Since we don't have particle identification for charged particles we would be comparing a mix of species with the anti-mix. For neutrals we would have an admixture of the neutrons and antineutrons, but this would be dominated for high energies by neutrons in the proton hemisphere and antineutrons in the anti-proton hemisphere. The admixture only dilutes a C-violating effect a bit. Experimentally this, of course, means we would have to make measurements in both the p-bar and the proton direction, then compare the charge-conjugate yields. The normalization can either be done via luminosity or, probably better, using ratios to C-symmetric quantities like pizeros or sums of positive and negative yields. I did a literature search. A good "theory" paper is "Notes on Antibaryon Interactions" by A. Pais in PRL, Vol 1,p 242, way back in 1959. He notes that actually you need to do a Charge conjugation plus Reflection. Also, pretty much the same prediction results from CP. (See below.) There have been few experimental tests of C in strong interactions. Most involve eta and omega decays. (See PDG, long version, section on Tests of Conservation Laws.) I did find one test in pbar-p interactions by Dobrzynski et al., Phys. Letters 22, 105 (1966). They used a few hundred events in a hydrogen bubble chamber to compare pbar + p --> K* + Kbar + n(pi) with pbar + p -> Kbar* + K + n (pi) at 1.2 GeV. I think they are comparing the phi distri- bution of the K from the K+ with that of the Kbar from the Kbar*. They see no violations of C (or CP or P). As far as I can see, no one has simply compared the inclusive yields of particles on the proton side with antiparticles on the pbar side. Of course, at low pbar energies this doesn't make much sense as the distributions are fairly isotropic in angle, so there's no proton and antiproton "hemispheres". As Larry Jones points out, CDF/D0 could in principle do this. I don't think they have, and I don't think it is nearly as interesting at large angles. I am not expert on the theory. To me the most telling argument against the possibility of C-violation is that it also implies a CP violation (since CPT is sacred). There have been more searches for CP violation, of course. It may be a little hard to concoct a scenario with a smallish C violation in strong interactions which does not give large CP violations in the K0 system. My guess is that it is perfectly possible, especially if the C-violating effect only occurs for relatively large momentum transfers, either transverse or longitudinal. As far as I can see, no one has ever done a comprehensive test of C violation in strong interactions at momentum transfers > 0.4 GeV or so. I'm on less sure grounds in saying there does not seem to be any strong theoretical argument against a moderately large violation that only shows up at momentum transfers >> 0.5 GeV. On the philosophical side, I find it disconcerting that we go along for decades taking all these things for granted. Nevertheless it may be hard to convince the PAC this is worth doing. I think we should try.