tag:blogger.com,1999:blog-7315236707728759521.post3677741960140386708..comments2024-03-28T21:52:52.100-06:00Comments on Dispatches From Turtle Island: Measuring The Strong Force Coupling ConstantAndrew Oh-Willekehttp://www.blogger.com/profile/02537151821869153861noreply@blogger.comBlogger15125tag:blogger.com,1999:blog-7315236707728759521.post-42510244960133565482015-08-19T18:36:04.162-06:002015-08-19T18:36:04.162-06:00For example, current electron dipole moment experi...For example, current electron dipole moment experiments naively constrain the SUSY scale to be about 10 TeV, which would be inconsistent with the SUSY scale range permitted based upon the running of the strong force coupling constant.andrewhttps://www.blogger.com/profile/08172964121659914379noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-61347505164365397402015-08-19T18:33:53.004-06:002015-08-19T18:33:53.004-06:00A new paper applies LHC data to gauge unification ...A new paper applies LHC data to gauge unification in the MSSM. It finds that the "SUSY Scale" at which SUSY effects should appear is 2.3 to 3.5 TeV with a best fit of 2.8 TeV.<br />http://arxiv.org/pdf/1508.04176.pdf This would imply gauge unification at 10^16 GeV and a unified coupling constant value of 1/25.83. This SUSY scale is high enough to be consistent with the fact that no SUSY phenomena have been observed so far.<br /><br />But, less notable than the minimum SUSY scale estimate, is the maximum. Strong force coupling constant running constrains SUSY scale from both the top and the bottom. The data in 1991 didn't strongly constrain this, with a range of 100 GeV to 10 TeV, but the LHC data provide a narrower range that combined with other SUSY searches could easily become over constrained, even with just LHC Run 2 data.<br /><br />Run I of the LHC provided strong force coupling constant experimental data up to 1.4 TeV, and the threshold will get higher in Run 2.andrewhttps://www.blogger.com/profile/08172964121659914379noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-5664015409768984292015-08-12T12:29:08.157-06:002015-08-12T12:29:08.157-06:00I suppose you have a point. Gauge unification is ...I suppose you have a point. Gauge unification is almost definitionally part of a GUT.<br /><br />On the other hand, if there are quantum gravity corrections to the beta functions, the "right" GUT without quantum gravity corrections, would not necessarily display gauge unification. Gauge unification in a GUT that is not a TOE, might be "too good to be true" evidence that actually hurts that particular theory.andrewhttps://www.blogger.com/profile/08172964121659914379noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-48626302659030516332015-08-12T04:57:41.122-06:002015-08-12T04:57:41.122-06:00*convergence, not convenience*convergence, not convenienceMitchellhttps://www.blogger.com/profile/10768655514143252049noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-9450846492808087012015-08-12T04:56:45.105-06:002015-08-12T04:56:45.105-06:00Basically, gauge unification is implied by GUT, no...Basically, gauge unification is implied by GUT, not by Susy. At the level of theory, MSSM doesn't imply gauge unification any more than SM does. What *is* true is that the measured couplings, evolving under SM beta functions, do not converge exactly, whereas they can do so in the MSSM, because of the influence of the extra particle species on the beta functions. But to explain this convenience at the level of theory, you still need a GUT. It's just that, having started with MSSM, it must be a GUT with susy added. <br /><br />Incidentally, because susy hasn't appeared, there is a small revival of non-susy GUTs happening. But this doesn't include original SU(5), it only includes more complex ones like SO(10).Mitchellhttps://www.blogger.com/profile/10768655514143252049noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-2159953479317164492015-08-12T04:37:37.911-06:002015-08-12T04:37:37.911-06:00Andrew, I think that in fact your procedure *is* v...Andrew, I think that in fact your procedure *is* valid for non-susy SU(5), although no-one actually reasoned that way. Instead, they just employed the fact that below the unification point, the beta functions are those of the SM, extrapolated all three couplings to high energies, and showed that they don't meet, as they should in SU(5). But certainly what you suggest could be done - only extrapolate electromagnetic and weak upwards, locate the unification scale, then extrapolate downwards to what the strong coupling should be.Mitchellhttps://www.blogger.com/profile/10768655514143252049noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-44414207244784212822015-08-11T14:03:21.958-06:002015-08-11T14:03:21.958-06:00In concrete terms, a SUSY theory is ruled out with...In concrete terms, a SUSY theory is ruled out with 95% confidence if the predicted strong force coupling constant value from the method above is not between 0.1173-0.1197 and is ruled out with 99% confidence if the predicted strong force coupling constant value is not between 0.1167-0.1203.<br /><br />This means that in the universe of SUSY theories (and more generally triple gauge coupling unified theories) for which exact beta functions for the coupling constants are known, each could be tested against experiment and either found to be consistent with the data or ruled out, in something on the order of an hour or less, without further analysis. My sense is that this has not been done comprehensively, and that it would rule out a large share of classes of potential SUSY theories. <br /><br />For example, I know with some confidence that the exact beta functions of some of the most common SUSY theories (MSSM, NMSSM, CNMSSN) are known and therefore ought to be subject to quick and easy experimental testing by this means. I personally don't know if they would pass the test or not. I presume that MSSM would pass this test, but I am less clear about the others.andrewhttps://www.blogger.com/profile/08172964121659914379noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-60565412180931787812015-08-11T13:38:48.553-06:002015-08-11T13:38:48.553-06:00"I don't follow your scheme for getting h..."I don't follow your scheme for getting highly precise predictions for alpha_s from a GUT, susy or otherwise."<br /><br />You need the following:<br />1. The experimental world average of the electromagnetic coupling constant at a given energy scale.<br />2. The experimental world average of the weak force coupling constant at a give energy scale.<br />3. The exact beta function of the electromagnetic coupling constant.<br />4. The exact beta function of the weak force coupling constant.<br />5. The exact beta function of the strong force coupling constant.<br />6. Knowledge that the theory has gauge coupling unification at a single point from theoretical considerations, which is generically true in SUSY theories, but is not true in many other classes of theories. This procedure does not work in theories that do not include as a feature triple gauge coupling constant unification. Many non-SUSY GUT theories such as the one referenced in your comment do not have this feature and hence have three degrees of coupling constant freedom rather than two.<br />7. Key observation. The beta function of the coupling constants of a theory (such as the SM or MSSM or any other particular SUSY or GUT theory) can in principle be determined exactly without reference to the experimentally measured parameters of that theory. The parameters of the beta functions of these theories are not experimentally measured parameters of the theory.<br /><br />Process. Use 1-4, to determine the exact energy scale at which the electromagnetic force coupling constant and weak force coupling constant are identical (i.e. calculate the GUT scale of the theory), and the value of these coupling constants that that energy scale. As a consequence of 6, you can use 5 to reverse engineer the value of the strong force coupling constant at any value given knowledge of the energy scale and coupling constant value determined with 1-4.<br /><br />Result. The strong force coupling constant can be determined at any arbitrary energy scale with an uncertainty only equal to the uncertainty in the least accurately known of 1 and 2 (currently the weak force coupling constant which is known with precision roughly 100,000 times that of the strong force coupling constant).<br /><br />This sets out my reasoning which seems pretty much irrefutable if all of my assumptions are true. My assumption is that you doubt the veracity of 6 or 7, or at least, did not recognize that this process is limited to cases when 6 and 7 are true.<br /><br />Also, to be clear, I am not claiming that any particular SUSY theory or GUT theory is actually true. I am proposing an experimental test of the truth of any given theory of that type that meets assumptions 6 and 7. If 6 and 7 is true, and the predicted value of the strong force coupling constant differs materially from the measured value of the strong force coupling constant, then that theory is ruled out.andrewhttps://www.blogger.com/profile/08172964121659914379noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-74747203308295891992015-08-11T07:25:23.997-06:002015-08-11T07:25:23.997-06:00See this exposition of how it works in the simples...See <a href="http://users.uoa.gr/~dkatsinis/gut-pres.pdf" rel="nofollow">this exposition</a> of how it works in the simplest case, non-susy SU(5). The GUT has one fundamental coupling constant, g5. The SM couplings at the energy scale where GUT symmetry breaking occurs can all be written in terms of g5, and at lower energies they run as in the SM. But this GUT breaking scale itself depends on several free parameters, appearing in the interaction Lagrangian for the superheavy Higgs that does the breaking. This simplest case doesn't work anyway, since the SM couplings simply don't meet, though they come close. Therefore people have considered susy, or non-susy SO(10) with an intermediate scale of Pati-Salam partial unification, etc.Mitchellhttps://www.blogger.com/profile/10768655514143252049noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-26984606203118777952015-08-11T07:09:49.070-06:002015-08-11T07:09:49.070-06:00I don't follow your scheme for getting highly ...I don't follow your scheme for getting highly precise predictions for alpha_s from a GUT, susy or otherwise... A supersymmetric GUT, in particular, will have many free parameters. The measured coupling constants are constraints on the possible values of those parameters, as is the absence of proton decay, as are various other measurements, and all these things taken together can even rule out certain GUT possibilities, as there is nowhere in the GUT parameter space consistent with observed reality. But I simply don't see a way to do what you describe.Mitchellhttps://www.blogger.com/profile/10768655514143252049noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-9227891097562970872015-08-10T21:21:00.101-06:002015-08-10T21:21:00.101-06:00A good survey of the physics of how quantum gravit...A good survey of the physics of how quantum gravity could impact the running of other coupling constants can be found <a href="http://www.ihes.fr/~vanhove/Slides/Donoghue-ihes-mars2011.pdf" rel="nofollow">here</a>. A <a href="https://en.wikipedia.org/wiki/Physics_applications_of_asymptotically_safe_gravity" rel="nofollow">Wikipedia article</a> notes the existence of a quantum gravity correction to the running of the fine structure constant in the asymptotically safe gravity approach to quantum gravity.andrewhttps://www.blogger.com/profile/08172964121659914379noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-5178165081959560082015-08-10T18:21:38.578-06:002015-08-10T18:21:38.578-06:00The pre-print from last April is here.The pre-print from last April is <a href="http://arxiv.org/abs/1504.00662" rel="nofollow">here</a>.andrewhttps://www.blogger.com/profile/08172964121659914379noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-70715014254212952712015-08-10T18:15:57.909-06:002015-08-10T18:15:57.909-06:00In other news, a precision extra-solar test of the...In other news, a <a href="http://www.sciencedaily.com/releases/2015/08/150806144557.htm" rel="nofollow">precision extra-solar test of the gravitational constant</a> from a white dwarf-pulsar system 3,750 light years away, confirms that Newton's constant, G, is the same there as it is here, although the press release does not make clear the precision of the extra-solar measurement.andrewhttps://www.blogger.com/profile/08172964121659914379noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-89555498307681168942015-08-10T18:08:53.413-06:002015-08-10T18:08:53.413-06:00Quantum gravity (or, for that matter, any new forc...Quantum gravity (or, for that matter, any new force or particle) automatically adds a new term into the renormalization group formula applies to the Standard Model Lagrangian which is used to compute the beta function for each of the other three forces.<br /><br />Also, at the GUT scale, the energy density of the interacting particles becomes so great that gravitational effects can't be ignored.<br /><br />And, keep in mind that the amount of tweak required isn't huge. You are talking about adjustments on the order of 1% over the entire 16 order of magnitude range for one of the beta functions, or less spread over all three, to make this happen.andrewhttps://www.blogger.com/profile/08172964121659914379noreply@blogger.comtag:blogger.com,1999:blog-7315236707728759521.post-25389039651527856192015-08-10T15:33:17.749-06:002015-08-10T15:33:17.749-06:00"the three Standard Model force coupling cons..."the three Standard Model force coupling constants do actually converge at a GUT scale, but that this happens only once quantum gravity effects on the ultraviolet running of these constants are considered, which the Standard Model beta functions do not."<br /><br />Seriously? <br /><br />Why would there be any quantum gravity effects on the ultraviolet running of those constants?Karl_Khttps://www.blogger.com/profile/10388217053237956318noreply@blogger.com