# How credible are CKM matrix limits on new physics?

• I
Gold Member
A pre-print of a conference paper from eleven months ago analyzes the extent to which the available data on the CKM matrix element values rules out beyond the Standard Model Physics.

It finds that in the most rigid model dependent analysis, that new physics are excluded up to a characteristic energy scale of about 500,000 TeV. There is no practical way that a human designed experiment could reach these energy scales from an engineering perspective. These are energy scales that haven't existed anywhere in the Universe since the early moments of the Big Bang.

If the assumptions of the model are relaxed, new physics are still excluded up to a characteristic energy scale of 114 TeV. This would take an accelerator on the order of ten times as powerful as the LHC or more to test.

To allow for new physics at a characteristic energy scale of 11 TeV which is the highest that there is a realistic chance that could be discovered at the LHC, one would have to abandon assumptions that are almost certainly correct based upon the available experimental evidence.

These limits are much more strict than the energy scale limitations established by direct searches for new particles at the LHC.

So, if this analysis of correct, the likelihood that we can experimentally observe any new physics that could tweak the parameters of the CKM matrix is dim indeed. But, how credible is this analysis? What loopholes remain for "relatively" low energy new beyond the Standard Model physics?

The paper is:

Unitarity Triangle Analysis in the Standard Model and Beyond
Cristiano Alpigiani, Adrian Bevan, Marcella Bona, Marco Ciuchini, Denis Derkach, Enrico Franco, Vittorio Lubicz, Guido Martinelli, Fabrizio Parodi,Maurizio Pierini, Luca Silvestrini, Viola Sordini, Achille Stocchi, Cecilia Tarantino, Vincenzo Vagnoni

(Submitted on 26 Oct 2017 (v1), last revised 27 Oct 2017 (this version, v2))

Flavour physics represents a unique test bench for the Standard Model (SM). New analyses performed at the LHC experiments are now providing unprecedented insights into CKM metrology and new evidences for rare decays. The CKM picture can provide very precise SM predictions through global analyses. We present here the results of the latest global SM analysis performed by the UTfit collaboration including all the most updated inputs from experiments, lattice QCD and phenomenological calculations. In addition, the Unitarity Triangle (UT) analysis can be used to constrain the parameter space in possible new physics (NP) scenarios. We update here also the UT analysis beyond the SM by the UTfit collaboration. All of the available experimental and theoretical information on ΔF=2 processes is reinterpreted including a model-independent NP parametrisation. We determine the allowed NP contributions in the kaon, D, Bd, and Bs sectors and, in various NP scenarios, we translate them into bounds for the NP scale as a function of NP couplings.

The pertinent language from the conclusion of the paper is as follows:

In the case of the general NP scenario, left plot in Fig. 6 shows the case of arbitrary NP flavour structures (|Fi | ∼ 1) with arbitrary phase and Li = 1 corresponding to strongly-interacting and/or tree-level NP. The overall constraint on the NP scale comes from the kaon sector (Im C 4 K in Fig. 6) and it is translated into Λgen > 5.0 · 105 TeV. As we are considering arbitrary NP flavour structures, the constraints on the NP scale are very tight due to the absence of the CKM or any flavour suppression.

In the NMFV case, the strongest bound is again obtained from the kaon sector (Im C 4 K in right plot in Fig. 6) and it translates into the weaker lower limit ΛNMFV > 114 TeV. In this latter case and in the current scenario, the Bs system also provides quite stringent constraints.

In conclusion, a loop suppression is needed in all scenarios to obtain NP scales that can be reached at the LHC. For NMFV models, an αW loop suppression might not be sufficient, since the resulting NP scale is still of the order of 11 TeV. The general model is out of reach even for αW (or stronger) loop suppression. Finally, the reader should keep in mind the possibility of accidental cancellations among the contribution of different operators, that might weaken the bounds we obtained.

Last edited:
Urs Schreiber

Urs Schreiber
Gold Member
When you say that energies around 500,000 TeV "haven't existed" since around the big bang, you are thinking of average energies, hence of temperature scale. But for single particles such energies are not out of the question.

The 500,000 TeV that you name is 0.5 EeV, and particles of energy a few EeV are observed, rarely but regularly, to hit earth's atmosphere, as seen by the Auger Observatory, see e. g.

"Ultra-high energy cosmic rays"
arxiv.org:1612.08188

Observing such natural events can conceivably shed light on BSM physics.

In fact such a claim was made just four days ago (this particular claim may or may not hold water, but it shows that the general possibility exists):

The ANITA Anomalous Events as Signatures of a Beyond Standard Model Particle, and Supporting Observations from IceCube

arxiv.org:1809.09615

Derek B. Fox, Steinn Sigurdsson,Sarah Shandera, Peter Mészáros,Kohta Murase, Miguel Mostafá,Stephane Coutu
(Submitted on 25 Sep 2018)

Abstract:
The ANITA collaboration have reported observation of two anomalous events that appear to be εcr≈0.6 EeV cosmic ray showers emerging from the Earth with exit angles of 27∘ and 35∘, respectively. While EeV-scale upgoing showers have been anticipated as a result of astrophysical tau neutrinos converting to tau leptons during Earth passage, the observed exit angles are much steeper than expected in Standard Model (SM) scenarios. Indeed, under conservative extrapolations of the SM interactions, there is no particle that can propagate through the Earth with probability p>10−6 at these energies and exit angles. We explore here whether "beyond the Standard Model" (BSM) particles are required to explain the ANITA events, if correctly interpreted, and conclude that they are.

mfb
Mentor
The center of mass energies of collisions of these particles are much lower. A 500,000 TeV particle colliding with a proton leads to a center of mass energy of just 30 TeV - not too much above the LHC energy. Take into account that the collision is better described by a collision with a parton and the energy gets even lower.

Urs Schreiber
Gold Member
Ultra-high cosmic rays hitting our atmosphere hardly provide a substitute for particle accelerator-like experiments, but they do show that ultra-high energy processes are common in the present epoch of the universe, and not confined to the "early moments of the big bang". There are some processes out there which could plausibly show signatures of BSM physics, even under very pessimistic assumptions.

There is a certain problem that I have. How is the CKM matrix affected by mass renormalization? Strictly speaking, it is renormalization of the coefficient matrices for the interaction terms of the elementary fermions and the Higgs particle(s).

I have come up with a hand-wavy guess as to what the renormalization-group equations look like for these coefficients. They have form ##y^I_{ia}##, where I is up or down, i is the ur-generation index of the left-handed quarks, and a is the ur-generation index of the right-handed quarks. I say "ur-generation" to distinguish this kind of generation from the generations that one observes. The RGE's look like this:
$$\frac{d y^I_{ia}}{dt} = C_I y^I_{ia} + C_{IJ} y^J_{ib} {\bar y^J_{jb}} y^I_{ja} + C_{IJK} y^J_{ib} {\bar y^J_{jb}} y^K_{jc} {\bar y^K_{kc}}y^I_{ka} + \cdots$$
where t = log(momentum/energy) and the C's include gauge-field contributions. Left-hand indices are shared by up-like and down-like quarks, but right-hand indices are not.

We can find a simpler expression by taking a sort of matrix square: ##Y^I_{ij} = y^I_{ia} {\bar y^I_{ja}}## or ##Y = y y^\dagger##. This form was chosen to put the left-hand indices on the outside. The RGE's become
$$\frac{d Y^I}{dt} =2 C_I Y^I + C_{IJ} (Y^J Y^I + Y^I Y^J) + C_{IJK} (Y^J Y^K Y^I + Y^I Y^K Y^J) + \cdots$$
To lowest order, this gives the result that the Y eigenvalues are proportional to (energy)some power and that the CKM matrices are unchanged, thus giving familiar mass-renormalization behavior. But the next terms are likely to change the CKM matrices, especially the parts involving the top quark, with its great mass.