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### How to discover new physics

The biggest news at CIPANP 2012 for particle physicists seems to be coming from the “low” energy frontier, at energies in the ballpark of 10GeV and lower. This may come as a surprise to some people, after all we’ve had experiments working at these energies for a few decades now, and there’s a tendency to think that higher energies mean more potential for discovery. The lower energy experiments have a great advantage over the giants at LHC and Tevatron, and this is richer collection of analyses.

There’s a big difference between discovering a new phenomenon and discovering new physics, which is something that most people (including physicists!) don’t appreciate enough. Whenever a claim of new physics is made we need to look at the wider implications of the idea. For example, let’s say that we see the decay of a $$\tau$$ lepton to an proton and a $$\pi^0$$ meson. The Feynman diagram would look something like this:

tau lepton decay to a proton and a neutral pion, mediated by a leptoquark

The “X” particle is a leptoquark, and it turns leptons into quarks and vice versa. Now for this decay to happen at an observable rate we need something like this leptoquark to exist. There is no Standard Model process for $$\tau\to p\pi^0$$ since it violates baryon number (a process which is only allowed under very special conditions). So suppose someone claims to see this decay, does this mean that they’ve discovered new physics? The answer is a resounding “No”, because if they make a claim of new physics they need to look elsewhere for similar effects. For example, if the leptoquark existed the proton could decay with this process:

proton decay to an electron and neutral pion, mediated by a leptoquark

We have very stringent tests on the lifetime of the proton, and the lower limits are currently about 20 orders of magnitude longer than the age the universe. Just take a second to appreciate the size of that limit on the lifetime. The proton lasts for at least 20 orders of magnitude longer than the age of the universe itself. So if someone is going to claim that they have proven the leptoquark exists we need to check that what they have seen is consistent with the proton lifetime measurements. A claim of new physics is stronger than a claim of a new phenomena, because it must be consistent with all the current data, not just the part we’re working.

How does all this relate to CIPANP 2012 and the low energy experiments? Well it turns out that there are a handful of large disagreements in this regime that all tend to involve the same particles. The $$B$$ meson can decay to several lighter particles and the BaBar experiment has seen the decays to the $$\tau$$ lepton are higher than they should be. The disagreement is more than $$3\sigma$$ disagreement with the Standard Model predictions for $$B\to D^{(*)}\tau\nu$$, which is interesting because it involves the heaviest quarks in bound states, and the heaviest lepton. It suggests that if there is a new particle or process, that it favors coupling to heavy particles.

Standard model decays of the B mesons to τν, Dτν, and D*τν final states

In another area of $$B$$ physics we find that the branching fraction $$\mathcal{B}(B\to\tau\nu)$$ is about twice as large as we expect from the Standard Model. You can see the disagreement in the following plot, which compares two measurements ($$\mathcal{B}(B\to\tau\nu)$$ and $$\sin 2\beta$$) to what we expect given everything else. The distance between the data point and the most favored region (center of the colored region) is very large, about $$3\sigma$$ in total!

The disagreement between B→τν, sin2β and the rest of the unitary triangle measurements (CKMFitter)

Theorists love to combine these measurements using colorful diagrams, and the best known example is the unitary triangle. If the CKM mechanism describes all the quark mixing processes then all of the measurements should agree, and they should converge on a single apex of the triangle (at the angle labeled $$\alpha$$). Each colored band corresponds to a different kind of process, and if you look closely you can see some small disagreements between the various measurements:

The unitary triangle after Moriond 2012 (CKMFitter)

The blue $$\sin 2\beta$$ measurement is pulling the apex down slightly, and green $$|V_{ub}|$$ measurement is pulling it in the other direction. This tension shows some interesting properties when we try to investigate it further. If we remove the $$\sin 2\beta$$ measurement and then work out what we expect based on the other measurements, we find that the new “derived” value of $$\sin 2\beta$$ is far off what is actually measured. The channel used for analysis of $$\sin 2\beta$$ is often called the golden channel, and it has been the main focus of both BaBar and Belle experiments since their creation. The results for $$\sin2\beta$$ are some of the best in the world and they have been checked and rechecked, so maybe the problem is not associated with $$\sin 2\beta$$.

Moving our attention to $$|V_{ub}|$$ the theorists at CKMFitter decided to split up the contributions based on the semileptonic inclusive and exclusive decays, and from $$\mathcal{B}(B\to\tau\nu)$$. When this happens we find that the biggest disagreement comes from $$\mathcal{B}(B\to\tau\nu)$$ compared to the rest. The uncertainties get smaller when $$\mathcal{B}(B\to\tau\nu)$$ is combined with the $$B$$ mixing parameter, $$\Delta m_d$$, which is well understood in terms of top quark interactions, but these results still disagree with everything else!:

Disagreement between B→τν, Δmd and the rest of the unitary triangle measurments (CKMFitter)

What this is seeming to tell us is that there could be a new process that affects $$B$$ meson interactions, enhancing decays with $$\tau$$ leptons in the final state. If this is the case then we need to look at other processes that could be affected by these kinds of processes. The most obvious signal to look for at the LHC is something like production of $$b$$ quarks and $$\tau$$ leptons. Third generation leptoquarks would be a good candidate, as long as they cannot mediate proton decay in any way. Searching for a new particle of a new effect is the job of the experimentalist, but creating a model that accommodates the discoveries we make is the job of a theorist.

That, in a nutshell is the difference between discovering a new phenomenon and discovering new physics. Anyone can find a bump in a spectrum, or even discover a new particle, but forming a consistent model of new physics takes a long time and a lot of input from all different kinds of experiments. The latest news from BaBar, Belle, CLEO and LHCb are giving us hints that there is something new lurking in the data. I can’t wait to see wait to see what our theorist colleagues do with these measurements. If they can create a model which explains anomalously high branching fractions $$\mathcal{B}(B\to\tau\nu)$$, $$\mathcal{B}(B\to D\tau\nu)$$, and $$\mathcal{B}(B\to D^*\tau\nu)$$, which tells us where else to look then we’re in for an exciting year at LHC. We could see something more exciting than the Higgs in our data!

(CKMFitter images kindly provided by the CKMfitter Group (J. Charles et al.), Eur. Phys. J. C41, 1-131 (2005) [hep-ph/0406184], updated results and plots available at: http://ckmfitter.in2p3.fr)

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### 7 Responses to “How to discover new physics”

2. John Carter says:

In the CKM fitter plot, what is the variance ( 1, 2, 3-sigma) among the various measurements? It would seem that new physics would only be considered if the ‘sweet spot’ (union of all measurements) becomes non-overlapping at 5-sigma.

• Hi John, from what I understand the colored regions show 1sigma and the red region around the apex is also 1sigma. The apex of the triangle (or “sweet spot”) should converge at a single point in the Standard Model scenario, but it’s not as simple as requiring a 5sigma disagreement before we declare new physics. If there are more than two apexes then how do we measure the disagreement between them all? There are several processes which are very sensitive to new physics or new particles, so the nature of the disagreement will give us hints about where to look. A 3sigma disagreement would be enough to encourage further study of that particular process and related processes, and that way we can be guided where to look for a new particle, long before the unitary triangle shoes a 5sigma disagreement between its various measurements. The CKM fit is a sort of map of heavy flavor physics, rather than a tool for direct discovery. If we do see a 5sigma disagreement in the fit the response would be more like “Huh?” than “Aha!”

3. Derrell Durrett says:

The new physics could be part of a larger system that suppresses proton decay. Analogously to suppression of kaon decay because of the coincidence (?) of charm/bottom masses. If there is some other channel that adds to the proposed leptoquark decay of protons to inhibit that but that doesn’t suppress tau decay, you could see one (or possibly the B to tau states described above),, but not the other. Might even bear on CPT violation as well….

• Hi Derrell, that’s a good point, but one that I have to disagree with for the following reason. At the moment proton decay is completely forbidden in the Standard Model, and the limits we have seem to support this absolute suppression. So far I have not seen a model which allows “dangerous” leptoquarks which mediate proton decay, and then has other particles which cancel out all of the dangerous processes. I would be very interested to see how the effects of leptoquarks cancel out exactly for proton decay, but not for tau decay. Essentially this comes down to the difference between a relatively forbidden process and an absolutely forbidden process. Thanks for your comment!

• Derrell Durrett says:

Aidan–

I realize that any effect has to be extraordinarily “tuned” in order to be consistent with the data. But (and this is without knowing the limits on τ→pπ0) it seems fairly obvious that the fact that another quark to lepton channel has an incomprehensible error is a possible clue. That the tuning might seem too “perfect” is something for philosophers. I’m too lazy (and a few years too removed from QFT) to bother trying to figure out how to calculate it, but the analogy to CKM seems just too apropos. For quite a few years after we knew K0 decays were weird, we thought “how could this be?” And you’re correct, the “level” of forbiddenness is what’s at issue. The notion of “absolute”, if it’s still only one of degree, is at risk of being over-turned. The notion of absolute, if one of “ruled out by every model we can conceive that’s consistent with the data” is far too slippery. I say, until we actually understand the Higgs sector, we’re so confused, we’d best just admit we’re guessing.

• Hi Derrell, to be honest I’m making a jump from 10^33 years to an infinite amount of time, which I shouldn’t technically be doing, but I think we can agree that it’s a very stringent limit on the lifetime. Just for reference the branching fraction limit for τ→pπ0 is <1.5e-5. I deliberately picked these two examples exactly because one of them is so stringent that any model that accommodated both measurements (in the case of non-zero B(τ→pπ0)) would have an almost incomprehensibly small amount of parameter space to fit into. The point of the post was just to point out that any model that explains a new phenomenon must be consistent with existing measurements, and then turn attention to some existing measurements that are hinting at some new physics, rather than to make any useful statement about leptoquarks and proton decay. Experimentalists are often keen to show off a bump or anomaly, only to have their enthusiasm shot down by theorists who point out the problems with a particular interpretation of the data.

Out of curiosity what is the quark to lepton channel that has an incomprehensible error?

Thanks for the comment!