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Papers on an "excited quark" bump could be even cooler than the cernette

CMS was the first one to have killed the \(750\GeV\) diphoton resonance. ATLAS' paper will be released on Monday.

Because the particle apparently doesn't exist, the most likely prediction for the 2016 dataset was that it disappears completely. It did. And even though CMS was against the publication of its new diphoton paper after it was for it ;-), we saw the paper with the new graphs in time, as I discussed in the previous blog post.

I encourage all particle phenomenologists who have mostly completed a model explaining the \(750\GeV\) not to send it to the arXiv. Instead, submit it to the competing – it should be an easy process – for you to have a nice, arXiv-like URL and for the viXra amateur scientists to have a nice company, competition, and perhaps inspiration. (Well, most of them won't get inspired because they believe that they are brighter than you are LOL.)

Alternatively, you may just change the title and a few words, submit to arXiv and conferences, and pretend that your paper didn't depend on the diphoton excess. ;-)

There isn't anything to be excited about in the diphoton channel now. The new largest current bumps \(620,900,1300\GeV\) of CMS are small and disjoint with the small but largest \(975\GeV\) bump that ATLAS will probably show tonight. Update 4pm: See the new ATLAS plots, a press release, and the paper.

As the previous blog post mentioned, the highest new significance seen by the CMS is an excited quark (see Page 5, Figure 2) whose mass is almost exactly \(2.0\TeV\) and whose excess only appears in one bin of width of \(70\GeV\) or so. But locally, it's a cool 3.7-sigma excess, assuming a low \(f\sim 0.1\), which is a cubic coupling constant of the excited quarks to the SM gauge fields, and that still translates to a 2.84-sigma excess (see page 7) globally.

Can you see an ATLAS talk on this channel? A related ATLAS paper based on the 2015 data sees nothing around \(2\TeV\). Just for the fun of it, imagine that ATLAS will announce the same 3.7-sigma (locally) excess at the mass \(2\TeV\) soon. It is unlikely. But I still have the freedom to speculate.

What would it imply?

First, the combined local significance would be \(3.7\times \sqrt{2}\sim \)=5.2 sigma. Even when you take care of the 30 bins to compute the global significance, it would be some 4.6 sigma. Not bad. Despite the disappointing experience with the \(750\GeV\) diphoton excess, people could start to write lots of papers attempting to explain this possible signal.

What theories could you invent? Quarks could be composite (a bound state of several point-like particles). There may be preons and other kinds of substructure. But all these models are rather contrived and unnatural and they have problems with the right spectrum of particles, viable flavor-changing processes etc. If you search for an "excited quark" and "string theory", you will find e.g. this paper by Blumenhagen, Deser, and Lüst from 2010. Already on page 2, they tell you that a very natural explanation for an excited quark \(q^*\) or an excited gluon \(g^*\) is simply an excited string with the string scale equal to\[

M_{q^*,g^*} = M_s = \sqrt{\frac{1}{\alpha'}} = 2.0\TeV.

\] For your convenience and excitement, I included the precise value of the string scale measured by the LHC. Now, string models with this accessibly low string scale can't be old-fashioned heterotic string models or any vacua explaining the Standard Model as closed strings. They have to be all about open strings – and these open strings have to be stuck on branes within a much larger compactification manifold. As sketched by ADD, Arkani-Hamed, Dimopoulos, and Dvali in 1998 ("old large dimensions").

You may literally think that the quark state \(\ket{q}\) is an open string state of a low-lying vibration of an open string whose one end point is stuck at one D-brane stack, the other on another D-brane stack, and the whole open string – which doesn't want to grow too long because it costs energy – is therefore confined to the vicinity of the intersection of the two D-brane stacks.

The \(2.0\TeV\) excited string would probably be the state similar to\[

\ket{q^*} = \alpha_{-1}^{\mu} \ket{q},\quad \mu\in\{x,y\}

\] I've simply added the lowest non-trivial string oscillator Fourier mode of \(X^{x/y}(\sigma,\tau)\) because I wanted to keep all the internal quantum numbers as well as the statistics. But the addition of this \(\alpha^\mu_{-1}\) oscillator to an open string simply increases \(m^2\) by\[

\Delta (m^2) = \frac{1}{\alpha'}.

\] Cool. So there could be additional excitations of these open strings. Their masses would be very close to \(\sqrt{n}\times 2.0\TeV\) for integer values of \(n\in\ZZ\). So the following one would be about \(2.8\TeV\). However, there could be new objects where \(n\) is a fractional number, a multiple of one-half or (because of the omnipresence of \(\ZZ_3\) orbifolds in simple enough orbifold compactifications) one-third or one-sixth.

You have the homework to list all interesting, low enough values of \(\sqrt{p/6}\times 2.0\TeV\) for \(p\in\ZZ\). For example, the lightest \(p=1\) massive state could be \(\sqrt{1/6}\times 2.0\TeV\sim 816\GeV\). Different levels of this kind could contain different exotic states. With an increasing \(p\), the spacing between the levels shrinks. So if you build a \(100\TeV\) Mao collider, you may in principle probe the excited string states up to \(p\sim 1000\) or more. If one could know the list of all particle species at each level, he could probably extract the appropriate orbifold compactification (assuming it would be simple enough) uniquely.

Let me point out that the closed strings need left-moving and right-moving oscillators. The pair \(\alpha_{-1}^\kappa \tilde \alpha_{-1}^\lambda\) of creation oscillators adds \(4/ \alpha'\) to the closed string's \(m^2\), about \(16\TeV^2\). The first excited closed string sits at \(m\sim 4\TeV\). But the division by \(\sqrt{6}\) etc. may be plausible here, too.

The \(2.0\TeV\) excited quark probably doesn't really exist. But even speculating about possible explanations of such conceivable discoveries from the LHC shows how well-motivated, predictive, and interesting the stringy explanations of such effects are relatively to things you could think about if you knew nothing about string theory.

Note that if \[

\alpha' = \frac{1}{(2\TeV)^2}

\] and \(g_s\sim 0.1\), you get \[

G_4 \sim\frac{ g_s^2(\alpha')^4 }{V^6}

\] which implies \(V\sim 10^6\sqrt{\alpha'}\) or so. Assuming six large dimensions, their common radius would be a bit longer than the radius of the proton. There even might be a (holographic style?) reason why the QCD scale is linked to the Kaluza-Klein scale. These possibilities seem unlikely but imagine how terribly far-reaching the consequences would be. The LHC could easily start to discover the detailed shape of extra dimensions and excited strings.

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