In 2012, July 4th…We had the Higgsdependence day! A SM Higgs-like resonance was discovered at the LHC and was announced to the world. Today, we celebrate this discovery of the Higgs-like thing or particle almost 3 years ago. So let me talk you about what were the expectations and especulations (some of these are yet discussed!) about finding or not the Higgs boson!

Facts: there was some SM exclusions from previous experimental data at the Tevatron and theoretical hints that if the Higgs existed, it should be relatively light (this was assumed taking into account the precision measurements in the SM and certain solid theoretical principles). More ore less, the Higgs shoould be excluded around the 160-170 GeV window (the top quark is near that energy, curiously). The vacuum understanding of the SM is, however, too low. In fact, something weird happens with the Higgs…Even when experimental data and some principles hinted that it should be light, no symmetry in the SM avoided that the Higgs mass received radiative corrections to the mass through virtual loops. Roughly, a single calculation with Feynman graphs provides in the SM:

\[\Delta M_H^2\simeq \Lambda^2\left(\dfrac{3(2M_W^2+M_Z^2+m_h^2-4m_t^2)}{32\pi^2 v^2}\right)\]

Plug the numbers and observe what you get! Things get worse if you include more loops with gauge bosons and fermions…The SM predicts its own fall with this phenomenon! Otherwise, we don’t understand QFT and how to make calculations that have provided to be very predictive. Theories beyond the SM include extra loops to cancel these contributions but it is not known if we can solve this issue without some amount of fine tuning…For instance, SUSY models include logarithmic corrections to these terms just as the inclusion of antiparticles solved the problem of the electron charge and mass in Quantum Electrodynamics. Renormalization and renormalizability of any QFT theory ARE important features! However, their origin is yet a mystery…Could we build a finite theory without the need of renormalization and regularization?

In fact, there is some problem with this, since the cosmological constant, roughly the vacuum energy we observe from cosmology, does not fit with the Higgs mass or more precisely with the minimum of the Higgs potential in the context of the SM. To make things worse…We have $\Lambda\sim 10^{-123}M_P^4$ as gravitational vacuum. In the QCD sector of the SM, moreover, another BIG issue is the strong CP problem, or why the CP violating term that is allowed by the theory and parametrized by the so called theta QCD angle is really tiny, about $\theta_{QCD}\leq 10^{-10}$. Back in time to the pre-2012 Higgs discovery era, the electroweak vacuum was known to be around the W, Z masses, roughly 100 GeV, and the Higgs should not be too far from them without dangerous or risky issues for the whole SM picture. Thus, the discovery of the SM Higgs was an important challenge for all the theoretical physics community!

What was to be found? The “pole mass” of the Higgs, since it was known to be a resonant or unstable particle/state…Masses are generally running, and the best behaviour of the mass is for pole masses: more “convergent” in some sense, easy to calculate renormalon effects and to show the finiteness of the theory, but as it happens with the W or the Z masses, where the Higgs mass was in energy was completely unknown. The SM alone does NOT fix the value of the Higgs mass and its coupling $\lambda$ to the SM particles, much unlike the Z mass, related to the W mass through some mathematical relationships and the Weinberg angle $\theta_W$. How to find the Higgs signal? Well, it is not like find a bat-signal but it is pretty similar in some points. Firstly we searched for a peak in the energy, showing the resonant state production (pole mass signal) plus another quantum numbers (like spin, helicity, parity, …some of which are not completely established now in 2015!). Finally, we should check if it is REALLY a SM Higgs particle or some subtle impostor that mimics him very, very well…That is another unsolved question but, at least with some great confidence, people believe the discovered $\sim 125GeV$ particle is some class of Higgs-like particle,…If it is composite or another cool impostor is yet to be analyzed! Assuming it is a SM Higgs, the 125 GeV particle should be a $0^+$ state or something very close to it in order to fit all the current data. Particles and resonances are usually classified by angular moment and spin, and it is denoted by $J^P$ in the particle data group and its reviews.

Now, suppose it is the SM or a subtle impostor…How do we go beyond the SM? How to go BSM? Well, as we all know, if you read this blog or similar sources, there are some pretty solid hints of BSM physics:

**1st. Neutrino masses and oscillations.** Neutrino masses are too tiny with respect the rest of the SM particles. Indeed, the SM prediction for neutrino masses is ZERO provided there is no flavor oscillations…However, neutrino change its flavor through big distances…What kind of neutral spinor is a neutrino if it is not a Weyl neutrino? Even if you can fit them with new vacuum expectation values through the Higgs field and the spontaneous symmetry breaking, supposing that the neutrino is a Dirac field, some physicists work out the idea that the neutrino mass hierarchy and its origin is different from the SM particles. If neutrino were Majorana particles (equal to their antiparticles) the neutrino field would be even more special… The little hierarchy problem, or why the neutrino masses are lower than other SM fields could be solved with the aid of the mechanism called the seesaw. However, there are other ways to generate neutrino masses without seesaws. Even you can be conservative and take Dirac neutrinos and the SM way via the Higgs and vev to generate neutrino masses, if you give away some naturalness…

**2nd. The SM fine tuning of the masses and couplings** is another well known problem that has no explanation with the tools of the SM. Beyond the little hierarchy problem stated above, we have the hierarchy problem (why the electroweak scale is so different from the Planck scale). Is there a desert between the electroweak and the Planck scale? Can we test it?

**3rd. The flavor problem.** Why 3 generations and 6 flavors? Nobody knows…

The hierarchy problem has been one of the guiding principles to build BSM theories. In the past 40 years we have thought or study loopholes and ways to solve that gap: supersymmetry (SUSY) and supergravity (SUGRA), superstrings/M-theory, TeV-scale gravity, preonic models, extra dimensions of space (and time, but it is not mainstream), little Higgses (or theories with extra gauge bosons in which the Higgs particle is the Nambu-Goldstone pseudoboson particle), and lots of model building with the framework of the braneworlds during the last 2 decades. The advent of the LHC has changed some too optimistic expectations (fiction-science?) and I believe some big classes of the models in the last list has gone to the trash…Literally.

Sadly, there is another big problem not too known for the public…The flavor problem, that has not received the required attention those years…Or at least, it has not made big advances ultimately. Without progress, there is no science…So the LHC is going to shed light to this one much more than, perhaps, the hierarchy problem…B physics (physics related to the B quarks) is putting strong bounds on new physics BSM and, indirectly, paving the way to…A desert? The explanation of the neutrino masses? We have no idea yet, but understanding the pattern in the mixing of the quarks and neutral leptons, neutrinos, is VERY important. In fact, the mixing of the quarks is minimal to some extent, since the CKM matrix is almost diagonal, while the mixing of the neutrinos is close to be maximal, since the PMNS matrix has the matrix elements “very mixed” or “rotated”.

The attack to the flavor methods with SUSY has provided to be awful and terrible. In fact, the breaking of SUSY produces lots of flavors, much more than we observe. In fact, this is used to put stringent bounds on SUSY models (Oh, yeah! But you should NOT talk too much about this with SUSY specialists or stringers if you don’t want to be into trouble with them!). Roughly, soft terms in the MSSM and the constrained MSSM (or MSUGRA) drive us into the question: is SUGRA flavor blind? Moreover, in this to equilibrate the discussion with stringers and SUSY fans, some regions in the parameter space of these models DO contain light higgs masses as the one we have discovered…Indeed, some bayesian and mMSSM tools applied to them produce the following result (also expected from the pure SM view and precision data): light Higgs masses are favored over heavy scalar masses.

The flavor problem contains another subtle concept: the flavor changing neutral currents (FCNC). These are very dangerous “beasts”. However, they can also be friendly: FCNC can help to reduce the 100 free parameter space in some of the monstrous models above. Flavor changing neutral currents in the SM are very suppressed and hints of such an event could shed light to what kind of theory stands beyond the SM. These currents can modify the “order zero” CKM expectation of quasi-diagonal matrix, i.e., $m_q^2\sim m^2\delta_{ij}$. Of course, the relevant part of this is “almost”.

**4th. Dark matter (DM).** Galactic rotation curves does not fit the Kepler laws/Universal gravitation/GR expectation. Some galactic cluster observations do support the idea of having more mass in galaxies that the mass we can see with light. However, where is this matter? How is it distributed? And more…What particle/s are dark matter? DM can not be any SM particle. That is a fact. However, it introduces the possibility of finding new particles and interactions at the LHC, the ILC and their successors. Many physicists think that the whole dark matter is likely not a single particle but a completely new set of new particles (of course, you could be minimal and conservative and set the dark energy density of the universe with a single new field as well!) and their interactions. These new interactions should be restricted to gravity, maybe the weak force and a really weakly or feeble coupling to the SM (if any!). Thus, you have lots of models with dark matter out there. For instance, gauge mediated models introduce “messenger particles” that connect the hidden SUSY breaking scale (or the new physics scale) with the SM or some subsector of the MSSM that reproduces the SM. However, problems arise again: we need loop suppressions in the calculations of the masses and problems with the so called couplings of the superpotential. Perhaps some models sith tree level gauge mediation are possible in order to recover the SM fields through interactions of Z’ and Z with heavy neutrinos and other mediators. The SM is thought to be an effective theory valid up to some energy scale. If you put the energy-cut off at the Planck scale, you find a wonderful fine tuning of the parameters or some class of symmetry should protect the Higgs (and other extra scalars that effective SUSY models produce, for instance) to get heavier and make your brain boils like water…Effective field theories (even superstring theory and M-theory are effective despite the fact their fans don’t use to know it) require the expansion around some energy scale (with the aid of perturbation theory) and higher dimensional (quantum) operators. These operators are tools used to parametrize our ignorance about New Physics and the true “final theory”. New Physics involves some new degrees of freedom in general. New fields, new interactions. However, many of these models of new physics does not fix our Higgs potential ambiguity or they do not impose positivity in the (scalar/super) potential. A class of these models is the NMSSM. Please, note that the usually adored MSSM plus effective approaches produces problems. So, what about giving up SUSY after all? How to solve the hierarchy problem without SUSY/SUSY breaking? Compositeness theories like technicolor theories or preonic models are known examples of all this…But the recipe is very similar to that with SUSY…Use additional symmetries to protect the Higgs mass (and other likely scalar particles/new particles). This compositeness theories involve generally new ultrastrong dynamics. It is tied to certain class of models called little Higgses: Higgs as pseudo-Nambu-Goldstone particle of broken symmetry. Compare this situation with the breaking of chiral symmetry in QCD. A new superstrong energy scale is usually introduced. The absence of FCNC plus electroweak corrections provide a rough idea of this superQCD dynamics energy scale. It should be around 3 TeV. Early ideas that the SM is effective up to a few TeVs is managed with these models. However, some fine tuning of the parameters is required…

**Before the LHC**, the flavor problem made us to wonder about new generations of heavy particles (quarks and leptons). Even technicolor and other ideas would try to explain what would happen were the Higgs not been detected:

What about a fourth generation with weird quantum numbers? What about magnetic monopoles or dyons -particles with both electric and magnetic charges? Electric and magnetic supercharges have been known in the physics literature. However, again, there are some problems. For instance, in the presence of magnetic monopoles (or magnetic charges), baryon number (and even angular moment) can change and catalyze baryon decay (e.g. proton decays!). Protons are very stable, since current bounds say that $\tau(p)>10^{33-34}yrs$, so any BSM theory including magnetic monopoles can get into trouble quickly if you don’t avoid this event. The Callan-Rubakov effect and the Witten effect are also related to this issue. You generally require high mass quark effects because of QCD. Skyrmions (certain QCD configurations) can decay due to magnetic monopoles at low energy but certain topological baryon number is conserved instead. Neutrinos are also neglected in this picture due to the fact they are almost massless. However, it is believed that in order to get magnetic monopoles interact with neutrinos, some enlarged or generalized mechanism should be invented. Thus, the question of why there are not other heavy quarks beyond the top quark -or the quarks of the second/third generations is easily solved by compositeness. There is no Higgs but a new superstrong dynamics, but there should be a magnetic charge! Magnetic monopoles produce striking signals at some detectors (fireballs or “rainbow” cascades, even they produce entire gap leaps in superconducting devices-recall the unreproduced Cabrera monopole in 1982, 14th February). In summary, technicolor plus some magnetic charges in a hidden U(1) theory would not need a (fundalmental) Higgs at all.

**Extra dimensions** have been very popular in Physics, not only in Science-Fiction in the last centuries! Modern superstring theory/M-theory relates the Newton constant, the string scale and the Kaluza-Klein scale in clever ways. The second superstring revolution and the new braneworlds models have shifted the attention to some usually assumed as true facts. In old Kaluza-Klein theories (KK theories for short), the string scale was about the KK scale. That is not necessarily true anymore. Up to a numerical constant, we have:

\[\dfrac{1}{G_N}=\dfrac{M_s^8}{M^2_{KK}}\approx 10^{38}GeV\]

Old KK arguments implied that $M_s\sim M_{KK}$ and then $M_s\sim M_p\sim 10^{19}$ GeV. Current theories put some fields in the “TeV”-scale and other in the bulk (extradimensional space). The bulk is connected with the SM 3-brane with some fields depending on some fine tuning and clever model building. The radion, the dilaton and other extra fields propagate under certain subspaces. Even you have other braneworld models like that by Randall and Sundrum where you get weak gravity in the SM 3-brane but strong gravity at the parallel brane due to a cool and clever non factorizable metric! Anyway, standard KK methods work: you get the light plus heavier higgses in general plus whole sets of KK resonances. You can also have higher spin particles with care (specially if you require SUSY!).

Another unsolved question by the SM is its own geometrical origin. Some smart people (Schucker, Connes,…) tried in the last decades to formulate the SM and its messy lagrangian from solid and strong geometrical foundations. Indeed, they managed it…However, they were not successful with the Higgs mass prediction. However, non-commutative geometry has provided its power to derive the SM lagrangian from the spectral action principle (see the works by Connes et alii, like Ali Chamseddine, Matilde Marcolli, …). One good thing about the NC construction of the SM is that it predicts a single Higgs. Gauge groups are restricted and the fermions are in the fundamental representation. However, it was a pity they failed in the Higgs mass prediction…That M. Shaposhnikov guessed around 2010 using asymptotically safety gravity+SM! His only addition were 3 right-handed heavy/very heavey new neutrinos…I am not going to discuss this idea in this post, but I should say that predicting a Higgs mass about 128 GeV without SUSY is quite an statement!!!!

What if…no Higgs or Higgslike partice had been found? Then, we would have been into trouble…But troubles are fun sometimes. We have fun with this Higgs-like state and the questions we have know are yet pretty similar to those we would have had in the case of no Higgs. That is: is the Higgs gaugephobic for some of the SM fields? Is there some unHiggs particle or some conformal hidden sector BSM? What is the state of art with extra dimensions and NC with the current data? In any case, we should watch all the data with care…To solve the flavor problem, the minimal solution is to introduce the Yukawa as the only sources of FCNC through some dimension 6 operators. Essentially, the effective lagrangian should contain two pieces: the SM piece and some piece involving dimension 6 operators or higher. The scale induced is larger that roughly 11 TeV (maybe more with the last data but I am not updated in this subject)! Thus, flavor physics, as I stated above, constraints harder the scale of new physics! With neutrinos, Ice Cube will be studying high energy neutrinos, neutrinos with energies much much larger than ANY accelerator can produce in a human lifetime and likely in the next centuries. We are lucky that Nature produces naturally such amount of highly energy neutrinos that we could not even produce with current technologies! Maybe, some FCNC hints could be discovered in 5-10 years of data taking in some neutrino detectors. Who knows?

Dark matter is yet mysterious…Dark energy is yet even more mysterious…And are they related to the electroweak SSBthrough some hidden portal? There is no conclusive answer yet. In principle, interactions between the DM or hidden sector with the SM are possible, but highly suppressed…Otherwise, we would have noticed it!!!

What lies beyond the SM?

See you in my next blog post!!!!

PS: From the SM and beyond in a few pics…

Shaposhnikov’s model: the “almost desert/nightmare” of theoretical physics (asymptotically safe gravity is also suggested)

From the light to the dark side of the Universe using braneworlds…

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