Thursday, October 8, 2020

Current Experimental Exclusions On BSM Particles

One of the most widely examined beyond the Standard Model theories is called supersymmetry (SUSY) and its quantum gravity extension called supergravity (SUGRA). There are also a variety of other widely studied potential beyond the Standard Model theories that give rise to new particles.

The current experimental exclusions on Supersymmetric Particles, on fourth generation Standard Model Particles, and on other select beyond the Standard Model particles, according to the Particle Data Group can be summarized as follows after a list of some common reference points to provide context.

Background Context For Particle Physics Masses

For context, the heaviest fundamental fermions of the Standard Model (the third generation fundamental charged fermions and the heaviest Standard Model neutrino mass) are the top quark which is about 173 GeV, the bottom quark which is about 4.2 GeV, the tau lepton which is about 1.78 GeV, and the heaviest Standard Model neutrino which is probably about 0.1 eV although direct experimental measurements only exclude heaviest neutrino masses up to 18.2 MeV. 

The other eight fundamental fermions of the Standard Model are less massive. In the second generation of fundamental fermions, the charm quark is about 1.28 GeV, the strange quark is about 0.1 GeV, the muon is about 0.1 GeV, the up quark is about 0.0025 GevV, the down quark is about 0.005 GeV, the electron is about 0.000511 GeV, and the two lightest neutrino masses are each less than about 1 eV based upon direct measurements and less than 0.0000000001 GeV based upon reasonable indirect measurements and astronomy observations.

There are three massive fundamental bosons in the Standard Model, the Higgs boson is about 125 GeV, the Z boson is about 91.2 GeV and the W boson is about 80.4 GeV. Photons and gluons have zero rest mass in the Standard Model, and the hypothetical graviton in most quantum gravity theories also has zero rest mass. The vacuum expectation value of the Higgs field associated with the Higgs boson is about 246 GeV. The Higgs vacuum expectation value is also sometimes known as the "electroweak scale" and is the energy scale at which the early inventors of supersymmetry theories expected to see supersymmetric phenomena - something that the Large Hadron Collider and other experiments have now largely ruled out.

Protons and neutrons have masses of a little less than 0.94 GeV each. The lightest composite particle in the Standard Model (which is the main carrier of the residual strong force that binds protons and neutrons in atomic nuclei together) has a mass of a bit less than 0.14 GeV. The heaviest composite particles consisting of quarks bound directly by gluons (or bound states of gluons only), which are called hadrons ever actually produced experimentally in particle colliders, is about 6 GeV although it is theoretically possible to create hadrons with masses of up to about 14 GeV (or perhaps even up to about 30 GeV for hadrons such as tetraquarks, pentaquarks or hexaquarks).

The Large Hadron Collider can produce collisions with energies of up to about 14 TeV (14,000 GeV), but it isn't usually possible for collisions of those energies to produce individual particles of that mass sufficient to make a statistically significant discovery of it.

Supersymmetric Particles (including extended Higgs boson sectors)

In more minimal supersymmetric theories, each Standard Model fundamental particle has a supersymmetric partner, but the correspondence is not exact because some supersymmetric particles "blend" into each other. There are also additional electromagnetically neutral and charged Higgs bosons. There are less minimal supersymmetric theories in which there are even more particles, and there are "supergravity" theories in which there is a graviton and its supersymmetric partner, the gravitino, in addition to the usual supersymmetric particle zoo.

To oversimplify, in R-Parity conserving supersymmetric models, there is a new quantum number called R-Parity that is conserved so that the net number of supersymmetric particles less the net number of supersymmetric antiparticles in an interaction is conserved. So, the lightest supersymmetric particle (LSP) is stable, since there is no lighter supersymmetric particle to which it can decay, and the LSP is a strong dark matter candidate. 

In contrast, in R-Parity violating supersymmetric models, it is possible for a supersymmetric particle to decay entirely to non-supersymmetric particles by means other than matter-antimatter annihilation between supersymmetric particles and supersymmetric antiparticles. More generally, more interactions between Standard Model particles and supersymmetric particles are possible. This models would less naturally provide a dark matter candidate, and would also be easier to detect experimentally (something that hasn't happened so far), so if supersymmetry is a correct theory of nature, Baysean reasoning favors R-Parity conserving models over R-Parity violating models.

The excluded masses provided by the Particle Data Group, moreover, are really just minimal values. They don't include any global analysis, the list doesn't actually incorporate every experimental exclusion result, and many exclusions involve more than one value in a parameter space that trade off against each other with this list only reporting complete exclusions (many of which are displayed in a Particle Data Group review article).

Similarly, these numbers don't illustrate the magnitude of supersymmetric particle masses suggested if the muon g-2 discrepancy is not just an experimental or QCD calculation error within the Standard Model.

The list below also does not address some additional supersymmetry parameters (discussed, in part, in a Particle Data Group review article regarding supersymmetry theories focused on the minimal supersymmetric extension of the Standard Model) for which there are exclusion ranges other than beyond the Standard Model supersymmetric particle masses.

To further simplify the chart above, the 95% confidence level exclusions by particle, incorporating all evidence and using the least restrictive limits are:

R-Party conserving limits

Gluino > 2000 GeV

Heavy Neutral Higgs (scalar or pseudoscalar) > 1496 GeV

First and Second Generation Squark > 1250 GeV

Charged Higgs > 1103 GeV

Double Charged Higgs > 723 GeV (and here)

Neutralino > 580 GeV

Selectron > 107 GeV

Sneutrino > 94 GeV

Chargino > 94 GeV

Smuon > 94 GeV

Stau > 81.9 GeV

Gravitino > 0.00035 eV

R-Parity violating limits

Gluino > 2260 GeV

First and Second Generation Squark > 1600 GeV

Heavy Neutral Higgs (scalar or pseudoscalar) > 1496 GeV

Stop > 1190 GeV

Charged Higgs > 1103 GeV

Double Charged Higgs > 723 GeV (and here)

Neutralino > 580 GeV

Smuon > 410 GeV

Selectron > 410 GeV

Sbottom > 370 GeV

Sneutrino > 94 GeV

Chargino > 94 GeV

Stau > 81.9 GeV

Gravitino > 0.00035 eV

With Respect to Fourth Generation Standard Model Charged Particles

There are theoretical reasons in the Standard Model that there must be a fourth generation of each Standard Model fermion if there is a fourth generation of any Standard Model fermions.

b' > 1530 GeV

t' > 1280 GeV

tau' > 100.8 GeV

An extension of Koide's rule provides a reasonable theoretical expectation for what these masses might be if fourth generation Standard Model fermions existed. The predicted b' mass would be 3,563 GeV and the predicted t' mass would be about 83.75 TeV (i.e. 83,750 GeV). These fourth generation quark masses are not  currently experimentally excluded. 

The Koide's rule extension for charged leptons (a muon, tau, tau prime triple), however, would imply a 43.7 GeV tau prime, which is clearly ruled out experimentally.

With Respect to Fourth Generation Standard Model Neutrinos

Number of active neutrinos:

The invisible Z width estimate doesn't exclude fourth generation Standard Model neutrinos which are more than 45 GeV (45,000 MeV or 45,000,000,000 eV). 

But direct measurements exclude a heaviest of the three Standard Model neutrino masses of more than 18.2 MeV, and indirect limitations from neutrino oscillations and cosmology data strongly favor a heaviest Standard Model neutrino mass of less than 0.1 eV. 

So, if there was a fourth generation active neutrino it would have to have a mass roughly 450 billion times that of the heaviest of the three Standard Model neutrinos, a mass gap between generations which is far in excess of all eight of the other Standard Model fermion generation mass gaps. The top quark mass (which is the largest fundamental particle mass in the Standard Model) is only about 338 thousand times the mass of the electron (the smallest non-neutrino fundamental particle mass in the Standard Model).

Astrophysical data also rules out a fourth generation of neutrinos under about 1-10 eV in mass. This exclusion includes any neutrino type that oscillates with Standard Model neutrinos, whether or not it has weak force interactions (as "active neutrinos" do). So, it also excludes light sterile neutrinos that oscillate with Standard Model neutrinos. A neutrino with a mass of 45 GeV or more, however, would not impact the effective number of astrophysical neutrinos measured by this data, even if it had all of the properties of a fourth generation Standard Model neutrino, and would not be ruled out by neutrino oscillation data if the mixing angle between it and the other three Standard Model neutrinos was very small. 

naive extension of Koide's formula to neutrinos with an electron neutrino of near zero mass would lead to a fourth generation neutrino of about 0.05 eV and it could have a mass of up to 11.6 eV in a nearly degenerate neutrino mass hierarchy.

The exclusion of a fourth generation Standard Model neutrino can be taken much further, however, because a fourth generation Standard Model neutrino of 45 GeV or more, however, would be indistinguishable from a hypothetical dark matter particle known as a WIMP (weakly interacting massive particle) that had a weak force cross section of interaction with ordinary matter identical to that of ordinary neutrinos.

Dark dark matter detection experiments have ruled out particles that make up most of hypothetical dark matter particles having weak force interaction coupling constants equal to Standard Model neutrinos at masses of up to about 10 TeV (i.e. 10,000 GeV). In the chart below, that cross section is the blue dotted line marked "Z portal C(x)=1" by a factor of 1,000,000. So, even if the flux of 45 GeV+ Standard Model neutrinos were a million times smaller than the hypothetical flux of dark matter particles through Earth, they would be ruled out by the direct detection experiments up to about 10 TeV.

So, while a fourth generation of Standard Model particles is not definitively ruled out experimentally to infinitely high masses, and the direct experimental exclusions for fourth generation up quarks, down quarks and electrons is not so terribly high, the fact that a fourth generation of Standard Model particles would have to include a fourth generation neutrino, and the experimental exclusion of such particles, subject to reasonable assumptions up to about 100 trillion times the mass of the heaviest known Standard Model neutrino, very strongly disfavors their existence.

Limits on Next Generation or Parallel Gauge Bosons

Axigluons > 6100 GeV

Diquarks > 6000 GeV

W' > 5200 GeV

Z' > 4500 GeV

Leptoquarks > 1755 GeV

Right handed W bosons > 715 GeV

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