Experimental status/test possibilities for baryon number conservation in LHC?

Question

Violation of baryon number is hypothesized e.g. for baryogenesis (more matter than antimatter from Big Bang) or Hawking radiation (baryons -> black hole -> massless radiation) - quite extreme conditions.

In contrast, unsuccessful search for proton decay is mainly focused on room temperature water - maybe we just need more extreme conditions? Like centers of neutron stars especially those producing orders of magnitude more energy than expected, e.g. X82 X-2: https://www.space.com/bizare-object-10-times-brighter-than-sun

More accessibly in high energy experiments like LHC - is there any experimental evidence pro/against violation of baryon number from LHC? If not, is it in reach to confirm or deny possibility of its violation?

For example here is a fresh from ALICE: https://cerncourier.com/a/balancing-matter-and-antimatter-in-pb-pb-collisions/ writing:

for every 1000 produced protons, approximately 986 ± 6 antiprotons are produced

But to check baryon number conservation we would also need to include other baryons, and subtract from initial Pb-Pb.

Answer 1

The paper whose press release you cite looks at a number of baryons and other hadrons:

In this Letter, we report the most precise estimation to date of $μ_B$ and $μ_Q$ obtained from a set of antiparticle-to-particle yield ratios. The analyzed species are charged pions, protons, $Ω^−$ baryons, and light (hyper)nuclei. (Anti)protons are the most abundantly produced (anti)baryons at midrapidity (≈ 35 and ≈ 2 protons on average in central and peripheral Pb–Pb collisions, respectively [45]). Consequently, the antiproton-to-proton yield ratio can probe the antibaryon-to-baryon imbalance [42, 46] with high precision. On the other hand, the sensitivity to baryon asymmetry is enhanced when light (hyper)nuclei are included because of their larger baryon content. In this work, $\rm ^3He$, its isobar $\rm ^3H$, and hypertriton $\rm ^3_ΛH$, which is a bound state of a proton, a neutron, and a Λ, along with their antimatter counterparts, are considered$^1$. The ratio of oppositely charged pions provides a precise constraint on the imbalance of electric charge, as the yield ratio depends predominantly on $μ_Q$. Finally, the dependence of antimatter-to-matter ratios on strangeness is probed with (anti)$Ω^−$ baryons, which, unlike (anti)Λ and (anti)$Ξ^−$, have negligible contamination coming from heavier hadron decays.

The number headlined in the press release, a proton-antiproton asymmetry of $0.986±0.006$, is one of of about thirty such ratios reported in Figure A.1 of the paper. I have only skimmed the paper, rather than trying to reproduce the analysis, but they report the "baryon chemical potential $\mu_B$," which is a measure of baryon-number nonconservation in the context of a statistical ensemble of particles and antiparticles, to be "compatible with zero within $1.6\sigma$." This is a result you would expect in somewhat more than one in twenty experiments if the actual baryon number violation were zero, just due to statistical fluctuations.

You contrast with cold proton decay experiments, but you may not have done the arithmetic. All of the processes in the Standard Model are happening all of the time, because our universe only has one vacuum state, and the Standard Model describes its symmetries and their particle-like properties. There are frequently situations where you can neglect some weak or rare process, but you can never turn these processes off. Compare with air resistance, which we frequently have intro-physics students ignore, whether that ignoring is appropriate or not. We usually don't teach the rule of thumb that air resistance becomes important when the mass of displaced air becomes comparable to the mass of the object that's moving. This is why you can ignore air resistance if you're juggling golf balls but not if you're playing golf; this is why you can say that interplanetary space is a vacuum, but also talk about the hydrodynamics of the solar wind and its effect on interplanetary dust.

The LHC can excite the vacuum to temperatures where we might hope to see signs of baryon-number violation in $10^{20\text{-ish}}$ interactions. (I don't actually know the size of the LHC dataset. The part-per-billion measurements that I've done needed $10^{19\text{-ish}}$ interactions to get the statistical noise small enough to be interesting; I remember suddenly realizing that I was analyzing the behavior of an entire microgram of free neutrons.) The proton-decay experiment at Super-Kamiokande looked at $10^{30\text{-ish}}$ protons for several years, setting a lower limit on baryon-number-violating decays at zero temperature somewhere above $10^{33}$ years. I don't know which result is more stringent, but I'm pretty sure it's the cold protons.

Answer 2

LHC events are too messy with too many missed or misidentified particles for direct baryon and anti-baryon counting to be an effective method to look for Baryon Number Violation (BNV), but limits can be set by using charged leptons to tag the baryon number in top quark production and decay. The CMS Collaboration has set limits as small as $10^{-8}$ for the fraction of top quark decays that violate baryon number conservation.

Theoretical Background

For Grand Unified Theories where baryon number violation is mediated by a boson with (very large) mass $M_{BNV}$, the higher energy of the LHC is grossly insufficient to compete with proton decay experiments. BNV production and decay rates would be $$\sigma_{BNV}\sim \hbar^2 c^2 \frac{s}{M_{BNV}^4}\qquad \mathrm{and} \qquad \tau_{BNV}\sim \hbar \frac{M_{BNV}^4}{Q^5}$$ where $Q$ is the decay energy, $s$ is the centre-of-mass energy squared, $\hbar$ is the reduced Planck constant, and $c$ is the speed of light. The existing lower bound on the proton lifetime of $\tau_p > 9\times10^{29}$ years for $Q\sim m_p$ implies that at the LHC ($\sqrt{s}\sim14$ TeV) $$\sigma_{BNV}<\frac{\hbar^3 c^2 s}{\tau_p m_p^5}\sim 10^{-39}\,\mathrm{fb}$$ To see even one such event would take many, many orders of magnitude longer than the age of the universe.

What is relevant at the LHC is baryon number violation via Standard Model sphaleron/instanton tunnelling between different vacuum states. Such processes are exponentially suppressed at low temperatures but might be observable at the LHC if the potential barrier separating the vacua is not too much above the Electroweak Scale. (The processes are non-perturbative and hence hard to calculate.) More theoretical details can, for example, be found in:

• "Proton Lifetime and Baryon Number Violating Signatures at the LHC in Gauge Extended Models" (2005)
• "Baryon number violation at the LHC: the top option" (2012)

CMS Experimental Limits

The CMS limits come from searching for BNV production processes such as $ud\rightarrow \bar{t}e^+$ or BNV violating decays such as $t\rightarrow b\mu^+\nu_\mu$ or $\bar{t}\rightarrow \bar{b}e^-\bar{\nu}_e$. Most theoretical models for baryon number (B) violation also violate lepton number (L), but conserve B-L, so CMS uses the sign of the charged lepton in semileptonic decays to distinguish $t$ and $\bar{t}$ quarks. These CMS top BNV limits are

• $\lt 0.15\%$, from "Search for baryon number violation in top-quark decays" (2014).
• from $\lesssim 10^{-8}$ for $t\rightarrow ud (e/\mu)$ to $\lesssim 10^{-6}$ for $t\rightarrow bc (e/\mu)$, from "Search for baryon number violation in top quark production and decay using proton-proton collisions at √s = 13 TeV" (2024).

The following CMS paper does not look directly for baryon number violation, but gives a limit on sphaleron production based on event topology.

• Sphaleron limit $\lt 2.1\%$, "Search for black holes and sphalerons in high-multiplicity final states in proton-proton collisions at s√= 13 TeV" (2018).

In principle, limits on top quark BNV production and decays without lepton number violation could be set by searching for processes such as $ud\rightarrow \bar{t}\bar{b}\bar{c}c$ or $t\rightarrow \bar{b}\bar{c}\bar{b}\bar{c}c$, but identifying such events would be a daunting challenge.

Answer 3

1. The most important thing to keep in mind is that the LHC cannot directly check baryon conservation because of limited kinematic coverage of the detectors (many fragments fly down the beam pipe), and the difficulty in detecting neutral baryons (such as neutrons). The closest thing one can do is look for specific baryon number violating decays that involve distinct final states.

2. The Alice experiment measures a small net-proton excess at central rapidity (longitudinal momentum), where the detector has coverage. This is not surprising -- a bigger excess was observed at RHIC. The mechanism is related to the fact that most baryons at central rapidity are produced by hadronization of pair produced quarks and anti-quarks, but some are produced by stopping of baryons in the original nuclei (which obviously have an excess of baryons over anti-baryons). The effect is bigger at lower energy (RHIC), because the nuclei have smaller energy, and projectile baryons are easier to stop.

3. There is a mechanism for baryon number violation in the standard model (related to electroweak instantons, see for example this question). This rate is unobservably small under ordinary conditions, but at some point there were suggestions that the rate grows with energy, and that the effect could be observable at the LHC (see, e.g. Arnold and Mattis). The idea was that these events would be unusual in many ways (democratic in quark and lepton flavor, many W's produced, most at central rapidity), so that events can be detected without complete kinematic coverage. This is now considered extremely unlikely.

4. I think you can safely ignore the X-82 story (this is about details of the accretion mechanism in neutron stars).