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Diphoton resonance from D3-branes or closed strings

Fifteen hep-ph papers co-written by Dr *ang today

By December 21st, 43 hep-ph papers on the diphoton resonance seen at the LHC have been written (and released in three packages). Eight days later, the terrain is very different. After another package on Dec 22, the total number has jumped to 72 (like the number of virgins who wait for a terrorist in the Islamic hell), then to 80 (Dec 23), 89 (Dec 24), 98 (Dec 25), and by today, the total has reached 118 unless I have overlooked some papers.

At this rate, the number of papers on the \(750\GeV\) resonance may surpass 750 by April when the new collisions may start to show that all of this activity was focusing on a mirage – or not.



A Honda CB 750 redesigned by the holographic hammer. Motorbikes with 750 cc (cm3) completely dominate the Google Images search for "750".

Because it's Tuesday today – a strong day – and we've had the Christmas break, there are many papers on the arXiv. Hep-ph shows 99 entries including 44 newly posted papers. It's a lot but what I find even more amazing – a sign of the Asian century that many people expect – is that 15 newly posted hep-ph papers were written or co-written by Dr *ang. It's close to the number of papers written by authors with any name posted on an average day. ;-)




Using the arXiv's ID [1]-[44] for the new hep-ph papers, we may see papers with the following authors:

[3] Wang+Wang+1
[5] Wang+2
[22] Tang+Wang+4
[25] Tang+1
[26] Kang+2
[27] Wang
[28] Zhang
[31] Wang+Zhang+1
[32] Wang+Wang+Zhang+Yang+1
[33] Zhang+2
[34] Zhang+4
[38] Zhang+2
[40] Huang+Wang+7
[42] Huang+5
[43] Zhang+2
OK, your playful humble correspondent has spent about 5 minutes with this stuff. As Madonna sang and it rang true, the list is no prang (such as the spang Monty Python sketch) even if it makes your head bang once you hang the papers on the wall. I guess that some playful readers will appreciate this research that sheds completely new light on Yang-Mills theory – which suddenly looks like a single Asian-underrepresented projection of physics insights among a billion of similar insights. ;-)

Many of the papers seems very good but my overall impression still is that China is much more likely to beat the West in the quantity rather than the quality.




The 20 papers on the diphoton resonance are
5 11 18 19 22 24 25 28 31-34 37-44
The largest group of papers wants to explain the excess by models adding vector-like quarks and perhaps also leptons (aside from a new bosonic field); with seven papers [18], [24], [25], [28], [32], [33], [44] in just one day, you could almost say that the need for new vector-like particles in the explanation of the bump is almost a "consensus" in the literature. These new fermions may run in the loops which are the triangular Feynman diagrams with the new resonance \(S\) as well as two gluons \(gg\) (production) or two photons \(\gamma\gamma\) (final state) attached to the vertices.

Well, such "consensus" based on counting shouldn't ever be taken more seriously and this "consensus" has important loopholes, too. The paper [40], one of the *ang* papers, proposes to only add two new bosonic (scalar) fields, \(H'\) at \(750\GeV\) and \(s\) below \(2.6\GeV\). The latter, light scalar is pair-produced and decays to a pair of photons. In total, \(H'\) decays to four photons\[

H'\to ss\to \gamma\gamma\gamma\gamma

\] but the pairs of photons coming from each \(s\) are flying the nearly identical direction (they are "collimated") and can't be distinguished from the single photons at the LHC.

Also, [19] by Dermíšek and 3 non-Czech, Asian authors proposes a model with no new \(750\GeV\) boson at all. They claim that a bump-like profile may be obtained from a direct \(gg\to \gamma\gamma\) one-loop box diagram if a \(375\GeV\) particle runs in the loop.

But let me return to the vector-like fermions combined with a new boson for a while.

Vector-like fermions refer to full Dirac spinors with uniform couplings to bosonic fields. This condition means that the left-handed and right-handed two-component spinors carry the same charges and representations under non-Abelian groups as well so you don't need any \(\gamma_5\) in between the Dirac spinors to write the interactions with the gauge (vector) fields. This is to be contrasted with the \(V-A\) (vector minus axial vector) interactions of the chiral fermions in the electroweak theory.

The most explicit and elegant models involving new vector-like fermions are those working in the NMSSM, the next-to-minimal supersymmetric standard model, the "more natural" cousin of MSSM where the \(\mu\) coefficient of the Higgs-up-Higgs-down bilinear term in the superpotential is promoted to a whole new chiral superfield with a vev.

In fact, amusingly enough, both NMSSM papers explaining the diphoton excess with vector-like fermions belong to the list of the *ang* papers at the top. You need to solve a simple one-minute exercise in comparative literature to see that despite the similarities in the content and the author names, the two groups of authors are disjoint:
[25] NMSSM extended with vector-like particles and the diphoton excess on the LHC, by Yi-Lei Tang, Shou-hua Zhu
[32] Interpreting 750 GeV Diphoton Resonance in the NMSSM with Vector-like Particles, by Fei Wang, Wenyu Wang, Lei Wu, Jin Min Yang, Mengchao Zhang
The PhD degree in comparative literature should be either automatically granted along with particle physics PhDs or required as a prerequisite before the physics PhD defense. ;-)

The NMSSM paper [25] postulates that the vector-like fermions transform in\[

{\bf 5}\oplus \bar{\bf 5}\quad {\rm or}\quad {\bf 10}\oplus \bar{\bf 10}

\] of an \(SU(5)\) grand unified gauge group. People generally prefer full representations of the \(SU(5)\) because that's how the SUSY-GUT gauge coupling unification may remain accurate. The first among the two direct sums arises from a \({\bf 10}\) of the \(SO(10)\) grand unified group which arguably makes it more likely, especially because this representation arises from the decomposition of a standard \(E_6\) GUT family\[

{\bf 27} = {\bf 16}\oplus {\bf 10}\oplus {\bf 1}

\] under the \(SO(10)\) subgroup. So the \(E_6\)-based grand unification could naturally have the particles required to explain the three well-known Standard Model generations of fermions as well as the new vector-like fermions needed to explain the diphoton excess. Such an explanation sounds elegant and thrifty, but so do the explanations based on the sgoldstino (or the radion and a few others).

While the paper [25] spends more time with the representation theory of the new fermions, the paper [32] spends more time with the new bosons. There are two new bosons nearly degenerate around \(750\GeV\), as in other models.



After the release of 950 and 950 XL, rumors suggest that Lumia 750 is one of the likely models that Microsoft is completing right now.

Aside from resonances supplemented with vector-like fermions, there are some papers about isolated creatures. Jihn Kim [37] (not to be confused with John Kom or Jahn Kam) discusses the heavy axion theory – or, more precisely, the axizilla. An axizilla is an off-spring of Godzilla and a Betsy Devine's detergent. Additional papers such as [5], [11], [22] try to explain the diphoton anomaly along with the dark matter. [33] uses extra dimensions and resembles the previously discussed radion models.

Even more stringy models than ever before

I want to start with Jonathan Heckman's explanation of the diphoton resonance using the F-theory model building although it appeared in the previous package of hep-ph explanations of the bump. Jonathan works with a type IIB model with intersecting D7-branes. The Standard Model fields live at the intersections of the D7-brane stacks – its fields arise from the 7-7 open strings. Just to be sure, the two digits in 7-7 indicate that both endpoints of the open string terminate on a D7-brane.

However, F-theory generically predicted possible new fields arising from the open 3-7 strings stretched between the Standard-Model-carrying D7-branes and some new "probe" D3-branes that are flying around (those D3-branes are ordinary spacetime-filling but points in the extra 6 dimensions). Heckman identifies the new \(750\GeV\) resonance with the scalar measuring the transverse distance of the D3-brane point from the locus of the D7-branes. And the new 3-7 strings give rise to the "messenger" states that play the same role as the vector-like fermions discussed in the models above.

But the 3-7 strings are not exactly "a stringy embedding of the same" vector-like fermions. Heckman is a bit ambiguous about the mass of the messenger 3-7 strings – anything between the LHC and GUT scale seems possible a priori and the gauge coupling unification may be preserved for all those options. For example, he can calculate that the effect of his 3-7 open strings are 2.2 times larger than the effect of a \({\bf 5}\oplus \bar{\bf 5}\) vector-like fermions discussed above. The fact that 2.2 is greater than 1 is encouraging because one seems to need a bit stronger signal than the vector-like models typically give. But the "integrating out" of the new messenger fields produces the same kind of a cubic interaction between the new scalar resonance and two gluons (or two photons) as the vector-like models.

Most importantly, Jonathan mentions that these extra 3-7 strings were viewed as a "redundant exotic prediction" of many F-theory models. In this sense, people may have been more self-confident about this piece and formulate it as a prediction of F-theory model building – a prediction that could be confirmed by the possible discovery in 2016. Of course, the bold prediction wasn't made in this way because the people weren't "quite" certain about their F-theory models.

Postdictions always look less impressive because one may adjust his explanations after the fact. However, from a logical perspective, it's obvious that the chronology of the discoveries and human statements is a matter of history and sociology, not pure scientific evidence, so if one assumes that the scientists are almost totally objective, postdictions should matter almost as much as "true" predictions.

Another stringy scenario of the diphoton resonance was discussed by Mirjam Cvetič and two co-authors who have surveyed 89,964 quiver diagrams arising from a class of type II string braneworlds. It's quite a comprehensive analysis of a large number of possibilities. The anti-string crackpots love to talk about a large number of possibilities as a flaw – and perhaps string theorists' personal failure. But it is not really a flaw, the number of models is whatever it is, it is a piece of knowledge to be learned, and technically powerful string theorists may sometimes analyze 89,964 models in one paper. In this sense, they may be doing 100,000 times more work for the same salary than a narrow-minded non-stringy phenomenologist. My main point is that the number of a priori possible detailed models going beyond the Standard Model is large – whether you think in terms of string theory or not – and one simply has to live with the fact and the research must adapt to this fact accordingly. Good theorists simply can't be stuck at a random small place (one tree) of this large forest; they must preserve their ability to see the whole forest or at least a non-negligible fraction of it! One random tree in a forest with zillions of trees is a very specific ("predictive") object but it is very unlikely that it is the right one. Before we climb to a specific tree, we should spend time with efforts to study the whole forest and comparisons of trees and their groups so that we only spend time by climbing the promising enough trees (or with methods to climb groups of trees simultaneously).

Finally, a new paper
[42] \(750\GeV\) diphotons from closed string states
by Dieter Lüst and 5 co-authors (including one Huang) discusses a stringy explanation of the diphoton resonance in terms of a closed string. Note that Heckman's scalar identified with the bump was a 3-3 open string. They investigate the possibility to describe the Standard Model as a stringy braneworld in the large extra dimensions (ADD) paradigm. When they adjust the string scale to be as low as allowed by the existing LHC exclusion limit – the string scale has to be above \(7\TeV\) or so – they find out that it is indeed possible to explain the diphoton bump as a closed string excitation (one freed from the D-branes, living in the bulk) that nevertheless couples to the gauge kinetic terms strongly enough.

The new particle of mass \(750\GeV\) could very well be the second example of a particle (after the graviton; and the first massive one) that is liberated from the D-branes on which we are stuck.

You see that the number of qualitatively different, interesting ideas proposed to explain the \(750\GeV\) diphoton resonance has become rather large. They differ in the technical preferences – what sort of particles, forces, representations, interactions, extra symmetries, SUSY breaking if any, extra dimensions, or their shapes are more natural. One of them could be right which would be a total revolution.

But more conceptually, the papers also differ in the depth to which the authors are willing to analyze more far-reaching hypothetical consequences. Some (intrinsically bottom-up, bound to experiments) authors only discuss a possible addition of a couple of new fields to the effective field theory, thus superseding the Standard Model. Others (authors who are naturally top-down theorists) aren't ashamed to link the "modest" new signal to SUSY breaking if not extra dimensions if not the whole structure of a string theory scenario with Hagedorn towers and geometries of D-branes predicted along the way.

The particular scenarios sketched by the latter, top-down authors may be slightly less likely than the particular extensions of the effective field theory considered by the first, bottom-up group. But they are much more interesting and potentially predictive. That's why I am much more excited about them and I am surely not the only one. And at the end, if a model is found to fulfill some Planck-scale consistency criteria, such a model may become more likely than a "simple" effective field theory, too.

In fact, the comparison of the two groups is ironic. The haters of science often like to pick string theorists (and, to a lesser extent, grand unification and supersymmetry model builders) as people who make no predictions and only describe what has already been seen. But if you compare the predictive power of the papers about the diphoton bump, you may see that the truth is closer to the opposite one. The mundane bottom-up model builders are only adding new fields and interactions once they are forced to do so by the observations at the LHC. They never really predict anything truly new simply because it isn't really possible to make predictions about more accurate, higher-energy-scale effective field theories from a lower-energy effective field theory.

On the other hand, extra-dimensional, supersymmetric, and especially stringy models have a very rich yet rigid structure with numerous interesting "qualitatively new" ingredients that go beyond the conventional effective field theories and that's why these models have the potential to produce "more original" but also "more constrained and unambiguous" predictions than the mundane bottom-up builders. No one can be sure that truly convincing characteristic signs of string physics will be discovered in 2016. But it isn't quite excluded, either. And if that happened, it would be a stunner, indeed.

The discovery of an otherwise "generic" new particle species beyond the Standard Model, another particle that "no one has ordered", would be fascinating but it would be vastly less fascinating than the discovery of some physical phenomena that would overthrow the business-as-usual routine based on the effective quantum field theories with some bosonic and fermionic fields and their Lagrangian-given interactions.

From some viewpoints, the continuation of the Lagrangian-based QFT model building is terribly boring even if it happened to go beyond the Standard Model by Summer 2016. Signs of string theory physics would be way cooler than that, of course. And an experimental discovery of stringy, beyond-QFT physics would arguably be the greatest event in physics of all time. This conditional proposition is no hype; it's a cold fact.

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