The discovery of the Higgs boson in 2012 rises new questions:

1º) Is it the SM Higgs or an impostor? It seems like a SM Higgs but…We don’t know yet for sure.

2º) Is it the ONLY Higgs-like particle or are there new Higgses? Circa November 2013 (2019 revision as well), it seems a minimal Higgs boson.

3º) Can we find new physics in the Higgs sector of the Standard Model? No new physics beyond the minimal Higgs-like SM boson was found.

In fact, the 123?124?125?126?127?128? GeV/c² Higgs boson mass is too low for many supersymmetric extensions of the Standard Model and not every parameter space below this mass have been excluded (to my knowledge). Therefore, some new light very weakly higgs boson exotics could be found in the future (indeed, LUX has proved that WIMPs below 33GeV are very unlikely unless they have very strange couplings).

What else is left to be found from SM predictions? Well, maybe nonperturbative effects like instanton effects, the Schwinger effect (pair production in strong fields) in Q.E.D., the sphaleron, and electroweak monopoles. Moreover, in the neutrino sector, we are yet seeking the neutrino CP violating phase after the discovery. Furthermore, our understanding of the vacuum in yet very poor! The most important “vacuum-related” parameters in the Standard Model are not explained with our current theories. Namely:

**1st. The strong CP problem.** The angle is known to be

This is the *QCD vacuum problem*.

**2nd. The cosmological constant problem.** Why ? That is, QFT predicts something like

where is the Planck mass. This is the *gravitational vacuum problem*.

And things get worst if we compared these stuff with the energy order of the “electroweak vacuum”. The electroweak scale lives around 100GeV, why is the QCD scale below 100GeV or why is the electroweak scale much lower than the fundamental (Planck) scale is completely unknown with our current theories. This last problem is the hierarchy problem. The little hierarchy problem is related to the neutrino mass scale with respect to the electroweak scale.

An important link to all these problems is the Higgs particle. We have entered a new phase in the study of the inner structure of matter and energy. The Higgs particle is not protected by any symmetry in the Standard Model, so it is a complete mystery why the Higgs particle we have found has the mass it seems to have. Indeed, QFT would suggest that the Higgs pole mass receives quantum corrections and the running Higgs mass should be far bigger than the one we have found. That is:

1st. Running Higgs mass is “low”.

2nd. Renormalon effects should be considered, and it makes this problem yet harder.

3rd. Why the Higgs pole mass we measure ( and the running Higgs mass) converges to a “light” value about is COMPLETELY UNKNOWN!

The Higgs signal we have found seems to be pretty consistent with a SM Higgs with quantum numbers . We have yet to check if the Higgs sector and the Higgs boson we found is the SM Higgs or a subtle variation from New Physics. This problem will be “solved” with more experiments in the forthcoming years.

Beyond the Standard Model (BSM) theories and beyond the SM Higgs we have built different models and theories that will be tested in the Large Hadrond Collider, the International Linear Collider (ILC) and future new colliders. Complementary searches will include:

1st. Neutrino masses measurements.

2nd. Dark matter searches (like LUX and others, e.g., AMS in the ISS).

3rd. Cosmic rays searches.

4th. Neutrino telescopes.

5th. WIMP/WISP searches.

6th. Gravitational wave searches.

7th. Exotic physics searches.

8th. Quantum gravity searches.

Two of the most important unsolved problems from the theoretical aside, the hierarchy problem and the flavor problem, are pushing forward in the experimental realm. Moreover, the naturalness of the SM has been put into question with the last discoveries and measurements. In the theoretical realm, the hierarchy problem had some good progress in the last decades. We had SUSY, extra dimensions, the Little Higgs models, the model building from superstring string theories or M-theory. However, the flavor problem had no similar advances. Indeed, current B-physics, the problem of neutrino masses and the puzzling mixing of quarks and leptons have left many unanswered questions and there are no models to treat them yet!

However, not everything is good or bad as I have exposed above. SUSY (supersymmetry) has also “flavor” problems. Whenever you break SUSY, you can obtain lots of new flavors and new particles. The introduction of “soft breaking” SUSY terms transforms or maps the minimal supersymmetric standard model (MSSM) into the cMSSM (constrained MSSM). SUGRA is also “flavor blind” mostly. Therefore, SUSY allows light Higgs mass in some region of their parameter space. The LHC alone is not enough to give up SUSY. And thus, a bayesian approach over the mMSSM implies that the light Higgs hypothesis if favored over the heavy alternative.

In addition to these facts, and the issue of the large parameter space of SUSY theories ( about 100 new parameters, unless you reduce them due to symmetry and symmetry breaking), we also have the Flavor Changing Neutral Current (FCNC). It provides

The gauge mediation through some new (likely scalar) messenger particles between the Hidden SUSY breaking sector and the Standard Model Higgs sector is a elegant way to overcome many of these problems. Without going into technical reasons, this gauge mediation would allow for:

1st. Loop suppressions.

2nd. Solve the muon and B anomaly problems.

The issue of the tree level gauge mediation is already an experimental issue: theoretically it is a well studied problem, we have to find it only.

By the other hand, effective actions with higher dimensional operators are a known effect of any new physics or BSM theory. Effective theories provide the tools to parametrize our ignorance about the fundamental New Physics laws OR the new degrees of freedom that are not accessible yet to our experimental devices in the current energy/length domain. Some models can impose the positivity in the Higgs potential. Moreover, non minimal supersymmetrical standard model (NMSSM) extensions are also possible. The Higgs potential problem without SUSY has been also treated in the theoretical literature in the past: to protect the Higgs mass use additional symmetry (NOT SUSY!): technicolor and the little Higgs are known examples of these alternative theories.

Despite the fact that the Higgs-like particle we have found seems to neglect the idea of compositeness, that is not completely true. A strong dynamics could mimic the Higgs particle to some extent. Therefore, the Higgs boson itself could be the pseudo-Nambu-Goldstone boson of certain global symmetry. If this global symmetry is broken spontaneously, we would have the Little Higgs. If this global symmetry is broken dynamically, we would have some kind of superstrong dynamics. Strong scales have some energy scale . The absence of FCNC and electroweak corrections seems to point out towards a scale or larger, with .

Another known issue of the electroweak sector are the prediction of electroweak magnetic monopoles. The absence of a new fourth generation with magnetic charges is put into question with current data. The Callan-Rubakov effect implies a high mass quark effect for these exotic states. The problem are that we would expect neutrino to be massless, and that is not true. We need some enlarged/generalized mechanism to explain the absence of magnetic monopoles. Why are not other quarks so heavy like the top quark? The top quark is too much heavy. If there were not Higgs, we could have explained with some magnetic 4th generation. Now, why the top quark Yukawa is almost one with respect to the Higgs field coupling is one of the deepest mysteries in the Standard Model phenomenology. The signal of magnetic monopoles can be read from “fireballs” or lagrangian terms like these:

and

Remember: technicolor+U(1) magnetic hypercharges imply NO HIGGS boson at all.

More fantastic ideas have been guessed by theoretical physicists in the last years. Extra dimensions of space have been studied. Not only the classical Kaluza-Klein theories but also new models with warped (curved) geometries like the so called Randall-Sundrum (RS) models have been proposed. Imagine our Universe is a 3-brane living inside a stacked set of branes in the multiverse. A minimal idea is to imagine a new 3-brane communicating through some interactions with our 3-brane. Neutrino masses challenge exotic branes like RS once again. A solution is to put the hidden (dark) brane infinitely away. This idea brings heavy Higgses (about 1TeV or heavier) and Kaluza-Klein resonances we have not observed until now. The existence of naked singularities in the hidden brane puzzles as well some models.

Non-Commutative geometry defenders have tried to fit the new experimental status after the Higgs boson discovery last year. Schucker, Connes and other “predicted” some time ago that, based on some non-commutative geometry arguments, the Higgs particle should be about 170 GeV/c². Now, they have redone their calculation to fit the data. The problem they leave unanswered is that their prediction of the Higgs mass don’t make clear at what scale they are computing the…Pole-mass? In the end, this approach have not accomplished its promise, like the string theory approach itself.

Let me remark that the LHC discovery has been supported by the last Tevatron data. And it matters! We have some good confidence that the Higgs boson (or what it shows to be) is real.

The minimal flavor hypothesis (MFH) states that the Yukawa couplings ARE the ONLY sources for mass terms and the flavor origin. That is,

It implies that !!!!

and from this we can obtain that

Thus, constraints are harder for new physics operators with the framework of the MFH!

Indeed, IceCube could shed light into this problem. The PMNS matrix is the equivalent (complementary) matrix in the neutrino sector, so IceCube could discover (potentially) new effects in the flavor mixing (neutrino sector) in the next 5-10 years. Visible matter is OK with known particles but dark matter requires some new particle species OR a modified theory of gravity. Dark Matter (DM) seems to feel only gravity, but new physics could change it and introduce some new very weak forces and anomalous couplings. However, till now, any dark matter experiment has provided null results. It puzzles the relation between the dark matter particles and the electroweak sector (and the corresponding electroweak symmetry breaking).

What is beyond the Higgs boson physics? What will be found? That is what makes Science, specially Physics, so amazing!!!!!