## Thursday, 19 November 2015

### Leptoquarks strike back

Leptoquarks are hypothetical scalar particles that carry both color and electroweak charges. Nothing like that exists in the Standard Model, where the only scalar is the Higgs who is a color singlet. In the particle community, leptoquarks enjoy the similar status as Nickelback in music: everybody's heard of them, but no one likes them.  It is not completely clear why... maybe they are confused with leprechauns, maybe  because they sometimes lead to proton decay, or maybe because they rarely arise in cherished models of new physics.  However,  recently there has been some renewed interest in leptoquarks.  The reason is that these particles seem well equipped to address the hottest topic of this year - the B meson anomalies.

There are at least 3 distinct B-meson anomalies that are currently intriguing:
1.  A few sigma (2 to 4, depending who you ask) deviation in differential distribution of B → K*μμ decays,
2.  2.6 sigma violation of  lepton flavor universality in  B → Kμμ vs B → Kee decays,
3.  3.5 sigma violation of lepton flavor universality, but this time in  B → Dτν vs B → Dμν decays.
Now, leptoquarks with masses in the TeV ballpark can explain either of these anomalies.  How? In analogy to the Higgs, leptoquarks may interact with the Standard Model fermions via Yukawa couplings. Which interactions  are possible is determined by  its color and electroweak charges. For example, this paper proposed a leptoquark transforming as (3,2,1/6) under the Standard Model gauge symmetry (color SU(3) triplet like quarks, weak SU(2) doublet like Higgs,  hypercharge 1/6).  Such particle can have the following Yukawa couplings with b- and s-quarks and muons:
If both  λb and λs  are non-zero then a tree-level leptoquark exchange can mediate the b-quark decay  b → s μ μ.  This contribution  adds up to the Standard Model amplitudes  mediated by loops of W bosons, and thus affects the B-meson observables. It turns out that the first two anomalies listed above can be fit if the leptoquark mass is in the 1-50 TeV range, depending on the magnitude of λb and λs.

Also the 3rd anomaly above can be easily  explained by leptoquarks. One example from this paper is a leptoquark transforming as (3,1,-1/3) and coupling to matter as

This particle contributes to  b → c τ ν, adding up to the tree-level W boson contribution, and is capable of explaining the apparent excess of semi-leptonic B meson decays into D mesons and tau leptons observed by the BaBar, Belle, and LHCb experiments. The difference to the previous case is that this leptoquark has to be less massive, closer to the TeV scale, because it has to compete with the tree-level contribution in the Standard Model.

There are more kinds of leptoquarks with different charges that allow for Yukawa couplings to matter. Some of them could also explain the 3 sigma discrepancy of the experimentally measured muon anomalous magnetic moment with the Standard Model prediction. Actually, a recent paper says that the (3,1,-1/3) leptoquark discussed above can explain all B-meson and muon g-2 anomalies simultaneously, through a combination of tree-level and loop effects.  In any case, this is something to look out for in this and next year's data.  If a leptoquark is indeed the culprit for the B → Dτν excess, it should be within reach of the 13 TeV run (for the 1st two anomalies it may well be too heavy to produce at the LHC).   The current reach for leptoquarks is up to 1 TeV mass (strongly depending on model details),  see e.g. the recent ATLAS and CMS analyses. So far these searches have provoked little public interest, but that may change soon...

Xezlec said...

I'll miss my protons.

StevieB said...

Obviously, the scalar leptoquark is consistent with the Jester Exclusion principle. This alone weighs in its favor.

Philippe said...

But what would be the implications for proton decay?

Jester said...

That of course would be catastrophic for our health :) However, in simple models discussed in this post , baryon number is conserved and proton decay does not occur. Proton decay will happen if a leptoquark has Yukawa couplings with 2 quarks of the 1st generation, but that is not needed to address the B-meson anomalies and it is consistent to assume such couplings are zero.

Philippe said...

I see. So it is coupled only to heavier quarks to solve this problem. My mistake. When I read "leptoquark", I immediately started thinking about all our old dreams, like SU(5). Thank you for your explanation.

Antonio (AKA "Un físico") said...

Thanks Jester: it is the first time I heard about leptoquarks. Now, I wonder if those three B-meson annomalies could be explained only by W bosons (and Z bosons) with different loop orders.

Anonymous said...

Hi Jester -- Not sure if your response to Phillipe needs a bit of a revision. Even if lepto-quarks in your examples were to couple to first generation, still Baryon number seems to be conserved -- the way the hypercharge and SU(3)_c quantum numbers are chosen for the models you mentioned. I am not sure if any higher scale suppressed non-renormalizable terms are any more dangerous than in std model -- maybe not. An issue is of course having light leptoquark scalars requires finetuning owing to Hierarchy problem.

Jester said...

I meant Yukawa couplings with 2 quarks, like \phi^\dagger u^c d^c . This would violate baryon number. Couplings to the first generation like \phi^\dagger Q_1 L_1 that conserve baryon number are of course no problem.

Avelino said...

Nice post, Jester.

You may be interested in 1505.05164 as well. They also propose a leptoquark explanation to the B anomalies. In fact, the authors of this paper claim that with the vector leptoquark V = (3,1,-2/3) one can in principle address all of them (and in this case at tree-level, in contrast to the paper by Bauer and Neubert).

Jester said...

Thx Avelino, I haven't read that yet, I'll do it soon.
Antonio, one cannot explain these anomalies by W and Z bosons alone; if the effect is real, it must be due to a new fairly light particle.

Anonymous said...

I think the hypercharge assignments of \phi prevent Baryon number violating Yukawa terms like \phi^\dagger u^c d^c -- just like in std model -- may occur at higher powers.

Jester said...

In my notation u^c and d^c are 2-component Weyl fermions corresponding to charge conjugate of the right-handed up and down quarks (sorry everyone else for the Chinese ;) ). So u^c transforms as (3bar,1,-2/3) and d^c as (3bar,1,1/3). With \phi^\dagger transforming as (3bar,1,1/3) \phi^\dagger u^c d^c is allowed by the gauge symmetry. You may be thinking about susy theories where this term would be forbidden by holomorphy.

Anonymous said...

Thanks Jester.  I was taking the Hypercharge (Y) values to be given by Q_em = I_3L + Y/2, so for u^c and d^c I had them as -4/3 and 2/3 respectively, as is the usual convention.  So it didn't work. But in your post the Hypercharge values are given by the convention Q_em = I_3L + Y. Else we wont have the term  (Q_3 L_3 \phi^\dagger).   Yeah so B violating terms are permitted by Gauge symmetry like you say.  I guess B would then have to be explicitly introduced as a global symmetry that remains unbroken.

Alex Small said...

Nickelback's first hit, "How You Remind Me", was solid stuff. The problem is that the band then decayed into a long-lived degenerate state that made a large contribution to the background noise.

RBS said...

Jester, how would such a possibility position itself against prospects of SUSY in this run and in general (pro, contra or orthogonal, etc)?

Jester said...

This is mostly orthogonal. Depending on the quantum numbers couplings to matter, some leptoquarks can be interpreted as squarks in R-parity violating SUSY. But, in general, finding leptoquarks does not make the case for SUSY stronger or weaker.

Anonymous said...

Just wanted to point out that CERN searched their 13 TeV data for narrow resonances and found nothing so far: http://cds.cern.ch/record/2110669

David Brown said...

"Proton decay will happen if a leptoquark has Yukawa couplings with 2 quarks of the 1st generation ..." Does that mean that LHC has a good chance of discovering such proton decay if such leptoquarks exist?

David Brown said...

Is the following publication likely to be relevant to leptoquarks?
"Intersecting Branes, SUSY Breaking and the 2TeV Excess at the LHC" by Ralph Blumenhagen, 2015

Anonymous said...

You say leptoquarks aren't theoretically popular. I thought they were a mostly guaranteed particle in most GUTs. Is this not so? I saw a comment languishing SU(5), but how does this look, say, in the popular Pati-Salam model? Is this good news? Is there any reason to suggest a GUT that also requires SUSY to explain this?