If I look back at the first times I discussed the important graph of the top quark versus W boson mass, nine years ago, I am amazed at observing how much progress we have made since then. The top quark mass in 2005 was known with 2-3 GeV precision, the W boson mass with 35 MeV precision, and we did not know where the Higgs boson was, or if there was one.

Today, the top quark mass is measured with a 770 MeV uncertainty and the W boson mass with a 15 MeV uncertainty. That alone is a reduction of a factor of 10 in the allowed phase space of those two parameters; but crucially, we no also know the Higgs mass with a 0.5% accuracy. This leaves very little space for the true parameters of the standard model. On the other hand, if the SM were to be enlarged to a minimal version of Supersymmetry, then the theory predictions would blow up considerably, as the MSSM allows much more freedom to those parameters as others (like squark masses) are varied.

The summary of the experimental situation is shown in the graph below, which Sven Heinemeyer produced today for this blog (thanks Sven). The graph summarizes calculations produced by Heinemeyer and his colleagues Hollik, Stockinger, Weiglein and Zeune. In the graph the horizontal axis shows possible values of the top quark mass, in the very restricted range allowed by the latest world's best CMS measurement; the vertical axis shows values of the W boson mass, in an even narrower range in absolute terms, thanks to precise measurements of that quantity performed by LEP2 and the Tevatron experiments. The experimental determination of those two parameters is symbolized by a grey ellipse which encompasses 68% of their probable values.

Then if we stay within the standard model, the Higgs boson mass measurements by the CERN experiments (+-0.7 GeV) force the two parameters to be bound to lie within the very narrow red line; if instead we take the MSSM as the true underlying theory, the whole green area is possible; different points of this area correspond to different value of other parameters (here a more liberal variation of the Higgs mass is taken, to cover more possibilities). The downward arrow symbolizes that as one increases the "mass scale" of the MSSM the allowed region moves closer to the SM line.

Note that in this graph the grey ellipse and the red line are the only experimental inputs; there is no "LEP indirect" oval here, as this would be too wide for the graph. In other words, the precision electroweak information from the Z boson studies of the nineties has become largely irrelevant in this particular view (it remains a formidable input to verify the general agreement of SM and data, if one studies other parameters).

So, what should we carry home from this graph ? I believe at least two things. One, that the SM likes the W mass to be a bit lower than what is currently measured, and the top quark to be a bit higher; the tension is however only mild -we are talking about just a bit more than one standard deviation for the disagreement. Two, that the MSSM is not killed by these measurements - it would live on regardless of the precise values of W and top masses, as the breadth of the green area shows.

Oh, and a third thing - the experimental measurements of these quantities rock!

Other considerations can be made, but I will stop here for tonight. Tomorrow I will be on a train at 6 in the morning, to participate in a 2-day open discussion organized by INFN in Rome, called "WHAT NEXT". A very interesting discussion on the long term plans of italian research based on the current status of particle physics, astrophysics, cosmology, and other fundamental investigations. I will have something to report on that later on...

Standard Model Or Minimal SUSY ?

## Comments

Hi T -- Is there a one sigma thickness to the standard model red line that has not been shown -- depending on one sigma range for Higgs mass? Or is the red line really that thin at the one sigma level?

Anonym (not verified) | 04/07/14 | 00:55 AM

- Link

Hi,

the red band is the 2-sigma SM band, where an experimental uncertainty of 0.35 GeV was used.

Looking at the plot one should keep in mind that the m_t value is purely the new one from CMS. A combined one from all existing measurements would be at slightly higher top mass values.

Cheers, Sven

the red band is the 2-sigma SM band, where an experimental uncertainty of 0.35 GeV was used.

Looking at the plot one should keep in mind that the m_t value is purely the new one from CMS. A combined one from all existing measurements would be at slightly higher top mass values.

Cheers, Sven

Sven (not verified) | 04/07/14 | 02:00 AM

Tommaso Dorigo | 04/07/14 | 12:48 PM

Tommaso,

How many parameters does the MSSM require one included beyond the tried & trusted ones from the SM? I find the flexibility of the beyond the standard model theorizing a bit frustrating, for whatever the experimental results are, the ubermodell will never die.

Cheers,

W

How many parameters does the MSSM require one included beyond the tried & trusted ones from the SM? I find the flexibility of the beyond the standard model theorizing a bit frustrating, for whatever the experimental results are, the ubermodell will never die.

Cheers,

W

West (not verified) | 04/07/14 | 16:22 PM

Tommaso Dorigo | 04/07/14 | 16:35 PM

Hi,

the number 105 is in principle correct. However, not all of them are relevant for all the observables (many are intergenerational mixing...) In order to produce the green MSSM area we varied about 14 free parameters, see http://arxiv.org/abs/1311.1663 . But also of those some are substatially less relevant than others.

Cheers, Sven

the number 105 is in principle correct. However, not all of them are relevant for all the observables (many are intergenerational mixing...) In order to produce the green MSSM area we varied about 14 free parameters, see http://arxiv.org/abs/1311.1663 . But also of those some are substatially less relevant than others.

Cheers, Sven

Sven (not verified) | 04/08/14 | 00:07 AM

Sven,

If I am understanding the paper correctly, albeit from a quick scan, the parameter estimates look to be from marginalized posteriors. Is this correct? If this is the case, does this software also produce global likelihoods (evidence) for both the SM and the MSSM? Would love to know what the ratio of those global likelihoods.

My guess is that the ratio of evidences strongly prefers the SM given the existing experimental data.

If I am understanding the paper correctly, albeit from a quick scan, the parameter estimates look to be from marginalized posteriors. Is this correct? If this is the case, does this software also produce global likelihoods (evidence) for both the SM and the MSSM? Would love to know what the ratio of those global likelihoods.

My guess is that the ratio of evidences strongly prefers the SM given the existing experimental data.

West (not verified) | 04/08/14 | 13:42 PM

Hi West,

you are assuming too much of our scan. We simply varied the parameters randomly (flat in the given rages) and marked green the area where the points appeared. There is no probability interpretation. For that you need more observables, see e.g. here: http://arxiv.org/abs/1312.5250 .

Cheers, Sven

you are assuming too much of our scan. We simply varied the parameters randomly (flat in the given rages) and marked green the area where the points appeared. There is no probability interpretation. For that you need more observables, see e.g. here: http://arxiv.org/abs/1312.5250 .

Cheers, Sven

Sven (not verified) | 04/08/14 | 15:43 PM

Thanks Sven for the quick and succinct response.

May I say that using a Bayesian posterior sampling method (MultiNest) to compute frequentist confidence intervals makes me twitch, but whatever. Since the code exists to crunch the numbers, what would be really nice is to see the relevant Bayes factor comparing the marginal likelihood for the (C)MSSM to that from the SM. Once we then have the posterior odds ratio p(H_{mssm}|Data)/p(H_{SM}|Data), we can ask at what odds are people willing to use as a threshold for giving up on some subset of SUSY models.

People writing "my gut says that SUSY is 80% likely to be true" and then justify it with hand-waving is baffling. Sorry to get animated, but statistics and model comparison is an important but under-appreciated task. And the lack of solid quantification of uncertainty means one gets a lot of theoretical airy cheerleading.

May I say that using a Bayesian posterior sampling method (MultiNest) to compute frequentist confidence intervals makes me twitch, but whatever. Since the code exists to crunch the numbers, what would be really nice is to see the relevant Bayes factor comparing the marginal likelihood for the (C)MSSM to that from the SM. Once we then have the posterior odds ratio p(H_{mssm}|Data)/p(H_{SM}|Data), we can ask at what odds are people willing to use as a threshold for giving up on some subset of SUSY models.

People writing "my gut says that SUSY is 80% likely to be true" and then justify it with hand-waving is baffling. Sorry to get animated, but statistics and model comparison is an important but under-appreciated task. And the lack of solid quantification of uncertainty means one gets a lot of theoretical airy cheerleading.

West (not verified) | 04/08/14 | 18:15 PM

Tommaso Dorigo | 04/09/14 | 00:19 AM

Hi Tommaso

I don't fault Sven (and his collaborators) for not providing a very particular statistic in the two papers he linked to in this thread. I wanted to know if someone out there was producing those sort of results. And now knowing that the big collaborations are doing just that makes me feel a bit better. Could you provide an arxiv link or just a the take away line?

My apologies if my own frustration was inadvertently projected onto you both in the above responses.

Cheers,

W

I don't fault Sven (and his collaborators) for not providing a very particular statistic in the two papers he linked to in this thread. I wanted to know if someone out there was producing those sort of results. And now knowing that the big collaborations are doing just that makes me feel a bit better. Could you provide an arxiv link or just a the take away line?

My apologies if my own frustration was inadvertently projected onto you both in the above responses.

Cheers,

W

West (not verified) | 04/09/14 | 15:09 PM

Hi West,

see if you can read this - I am not sure the link works for non-CMS members:

https://cds.cern.ch/record/1693148/files/?ln=it

T.

see if you can read this - I am not sure the link works for non-CMS members:

https://cds.cern.ch/record/1693148/files/?ln=it

T.

Tommaso Dorigo | 04/09/14 | 15:18 PM

Hi Tommaso,

Was able to download the PDF without issue. Looks like there is a lot of stuff publicly available via https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResults

Cheers,

W

Was able to download the PDF without issue. Looks like there is a lot of stuff publicly available via https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResults

Cheers,

W

West (not verified) | 04/09/14 | 20:48 PM