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I am reading The Elegant Universe by Brian Greene.

In many places it's directly/indirectly mentioned that the LHC may not be able to detect (with the current technology) heavy particles to prove Super-Symmetry.

What prevents such accelerators from detecting such heavy particles?

I always thought it would be the opposite as heavy particles can make a stronger impression on detectors than light particles.

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    $\begingroup$ Oh, and I thought Super-Symmetry was just around the corner ... xD $\endgroup$ – image Sep 24 '17 at 14:37
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It's not detecting the particles that is hard, it's making them in the collisions.

Although the LHC collision energy is 14TeV, collisions aren't between the protons but rather between individual quarks inside the protons. Since the energy is shared between the three quarks in a proton the actual quark-quark collision energy is a lot less than 14TeV. Even then, for various reasons to do with conservation of momentum not all that energy can go into creating new particles. The end result is that it's hard to create particles much about above a TeV in weight. More on this in What is the maximal particle mass one can create via the LHC? Can we create dark-matter particles via the LHC? if you want to pursue this further.

The upshot is that if the heavy particles have a mass much greater than a TeV the LHC can't create them, and obviously if they can't be created they can't be detected. All is not completely lost since we might be able to detect heavy particles indirectly by the influence they have on the collisions we can detect. Even so the upper mass limit is still restricted.

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    $\begingroup$ +1 for your optimism. But actually all is lost. $\endgroup$ – lalala Sep 24 '17 at 10:01
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    $\begingroup$ Sadly it is looking that way ... $\endgroup$ – John Rennie Sep 24 '17 at 10:02
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    $\begingroup$ This is way worse actually: if we were to discover a new particle rather light particle through direct production or a heavier one through comparison with loop corrections, how would we know it has anything to do with SUSY? Most papers out there start from MSSM or NMSSM and try to work out a prediction but what matters is the reverse: how many and what kind of particles do we need to observe to confirm some of SUSY? And then of course, validating (N)MSSM is not validating superstrings, not by a long shot. $\endgroup$ – user154997 Sep 24 '17 at 10:48
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    $\begingroup$ Supersymmetric partners are always a couple of hundred GeV away: Implications of Initial LHC Searches for Supersymmetry (2011), The Smell of SUSY (2012), $\endgroup$ – David Tonhofer Sep 24 '17 at 20:34
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    $\begingroup$ For the sake of the future of particle physics, please lobby your politicians to found the International Linear Collider (ILC)! $\endgroup$ – user154997 Sep 25 '17 at 11:27
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As a consequence of $E=mc^2$, to create a heavy particle (i.e. large $m$) requires a large amount of energy ($E$). Since the LHC only generates a finite amount of energy in the collisions, there may be particles that are too heavy to be produced. This looks likely to be the case for superpartners (if they exist).

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