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Gravitons are heavier than 500 GeV! December 23, 2008

Posted by dorigo in news, personal, physics, science.
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About a year ago I reported here on a search performed by CDF for events featuring two Z bosons, both decaying to electron-positron pairs: I had been an internal reviewer of that analysis, and I discussed it in some detail after we approved it for publication. While the standard model expectation for electroweak production of two Z bosons is of about 1.5 pb, and the process has indeed been put in evidence in CDF and D0 Run II data, the analysis was rather focused on a search for heavy mass resonances decaying to the ZZ final state: new physics, that is, either in the form
of a heavy Higgs boson, or of a graviton (in the Randall-Sundrum scenario), or other still fancier (and improbable) beasts.

CDF has now repeated that search by increasing the dataset size by a factor of three, and by including mixed final states which include muon pairs and even jet pairs. This makes the analysis intrinsically interesting to me, since I have started a similar analysis with the CMS experiment, together with a PhD student in Padova, Mia Tosi. Mia and I will be looking for Higgs bosons in the dilepton plus dijet final state, with particular emphasis on the Z \to b \bar b decay, which is a signal with which we have quite some familiarity.

The new CDF search for high-mass ZZ events configures itself as a “signature-based” one: despite the reference to the Randall-Sundrum graviton, the analysis cuts are kept generic, such that a signal can be found for anything that decays to two Z bosons, and in case no signal is seen, a model-independent limit on the cross section can be set. The only limitation of the search is that the four-body mass is studied only above the minimum value of 300 GeV. Such a requirement allows to steer away from phase space regions where backgrounds dominate.

Once four objects (electrons, muons, and jets, with the specification that at most two jets are present) are selected with loose cuts, a statistical estimator is built to test the hypothesis that they originate from the decay X \to ZZ \to llll (lljj). It is a simple \chi^2 function, which utilizes the expected resolution on the two two-body masses and the resulting four-body mass to estimate how much the event departs from the tentative signal interpretation. Only in the case of jet pairs, an explicit cut is set on the dijet mass to lay between 65 and 120 GeV, to avoid accepting too many random jet combinations.

While the M_x>300 GeV region is the one where the signal is sought, the complementary region of the four-body mass is used as a control sample, to verify that background estimates obtained with Monte Carlo simulations are in agreement with the observed data. The nice thing about such a spectacular signature as the production of two Z bosons is that backgrounds are exclusively of electroweak nature: by having at least one Z \to ll decay in the final state, the signal cannot be mimicked easily by purely quantum chromodynamical processes, which plague most hadron collider searches with high rates. Besides regular ZZ pairs from standard model processes, backgrounds include WZ, WW, and Z+jets production. At high four-body mass, however, all of these are really small, and even in the 3 inverse femtobarns of proton-antiproton collisions analyzed by CDF for this search, they contribute only few events; only the dilepton+dijet signature accepts a few hundred events, because of the large cross-section of Z+2 jet production processes.

In the end, no signal is seen, and a cross-section limit is extracted as a function of the X mass. The limit is shown below, compared to the expected cross section for graviton production and decay to the ZZ final state. The comparison of upper limit (the red curve) with the theory hatched line allows to exclude gravitons with masses below 491 GeV, for a particular choice of model parameters k/M_p=0.1 (k is a warp factor for the extra dimensions, and M_p is the Planck mass).

As a by-product of this analysis, a new set of excellent standard-model-like ZZ decay candidates have been selected. I am unable to show any of the new event displays here, because they have not been approved for public consumption by CDF yet… So please see the lego plot of a ZZ \to eeee candidate below, extracted last year by the same authors. The two pairs of electrons make masses very close to that of the Z boson, as evidenced by the two pink numbers.

To read this graph, you have to know that the greek letter \eta is the pseudorapidity, basically a function of the angle that particles make with the beam axis. A pseudorapidity of zero means that the particle is emitted at 90 degrees from the beam, while positive and negative values indicate the proton and antiproton directions. The other coordinate, \phi, indicates the azimuthal angle in the transverse plane. The z axis (the height of the bars) indicates how much energy is deposited in the \eta - \phi interval span by the bars. In bright pink are shown the four electron candidates, as measured by the CDF calorimeter, and each bar is labeled by the energy in GeV measured for each.

I am only left with the pleasant task of congratulating my colleagues Antonio Boveia, Ben Brau, and David Stuart for this new result, which greatly extends the scope of the analysis I have reviewed last year. During my review I had encouraged them to pursue the other decay modes of ZZ pairs, and so they did. Well done, folks!

Hooman Davoudisal: Extra dimensions and the LHC May 25, 2008

Posted by dorigo in physics, science.
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Let me continue the long string of posts describing what I heard at the PPC 2008 conference last week with a report on a talk by Hooman Davoudisal, who gave a very clear and entertaining overview of the issue of Large Extra Dimensions, and their testability in the near future.

He started by saying that the topic he was given to report on is narrow, but hundreds of papers have been written on the matter of large extra dimensions (LED) theories. He thus had to pick a few things to discuss about this widely studied topic.

Extra dimensions are not a new idea – they date back on an attempt by G.Nordstrom in 1914, who tried to unify pre-general relativity gravity and electromagnetism in a 5-dimensional world. This was followed by the work of Kaluza in 1921, and Klein in 1926. More recently, string theory has been recognized to require 10 or 11 dimension. The extra ones are compactified at a fundamental scale. This is motivated by the hierarchy problem, that is the fact that there is a very small ratio between electroweak scale and the Planck mass: M_W/M_P = 10^{-17}.

Arkadi-Hamed, Dimopoulos, and Dvali in 1998 studied the case of N compact extra dimensions to stabilize the hierarchy: the fundamental scale is now of the universe is of the order of a TeV. Extra dimensions are large in units of the fundamental scale.  Their scales range from a fermi to a millimeter.  The standard model particles are localized on a “3-brane”, which is a four-dimensional sheet in the multi-dimensional space. Gravity propagates in all dimensions, and therefore gets diluted by the extra dimensions. Kaluza-Klein modes are quantized momenta in the extra dimensions. They correspond to our picture of particles in a box: if you took a course in quantum mechanics, you know that particles confined in a box get their energy levels quantized.

Hooman said that the key signal for LED detection is, what do you know, missing energy! [Apparently, if LHC does not find anything in its missing energy spectrum it will put on the road string theorists, SUSY phenomenologists, and LED aficionados all together: quite a democratic turn of events, if you ask me].  Kaluza-Klein (KK) gravitons escape in the “bulk” -the extra dimensions- and they leave behind the energy bill to pay. KK gravitons could be produced by quark-antiquark annihilation. Also, spin-2 “towers” of KK gravitons  can give rise to spin-2 mediated angular distributions of the final state particles. Further, a possibility is black hole production. When you bring the Planck scale down, you can create  black holes in reasonably sized particle accelerators, such as the LHC -it does not fit in your living-room, but it is smaller than the solar system after all.

The signature of black hole production would be potentially spectacular signals, with energetic  multijets, multi-lepton events. However, this picture is under debate. Meade and Randall say  that this turn of events is difficult at LHC.

For large extra dimensions, searches have been done at the Tevatron and LEP. LEP has a better bound for few additional extra dimensions (well above a TeV), while for many extra dimensions -4 and above- the Tevatron wins, and has limits just below one TeV. These are extracted from both the jet plus missing  energy signature and the photon plus missing energy signature.

A more generic framework is that of universal extra dimensions (UED). This scenario entails Lorentz violation along the extra dimensions, and the lightest Kaluza-Klein particle  is stable. The resulting pheonomenology has the potential of mimicking supersymmetry at the LHC. If you are a believer, you may expect a huge debate going off between UED and SUSY aficionados as soon as ATLAS and CMS start observing missing energy signatures.

Hooman pointed out that the latest UED limit was obtained at CDF using Run 1 data! The lower limit is at 280 GeV. I rushed to check and by jove, he is right: what a jolly gathering of lazy bums CDF is! No results from Run II have been produced [and may I say, I see none in preparation either… Maybe D0 does ?]


The Randall-Sundrum model with a 4-dimensional Standard Model (1999) has its pros: a natural Planck-weak hierarchy, and striking signals. However, the fundamental cut-off is of the order of a TeV, and this is dangerous. [There follows a sentence I cannot make much sense of… Explanations by experts is appreciated here:] Standard Model flavor from a warped bulk: it was realized by placing the SM in the 5-dimensional bulk; the bulk has all SM particles in it. One wants to keep the Higgs boson localized  to the 4-D brane. Localizing the zero-mode of fermions, and fermions have fundamental scale which gives  a higher effective scale. This modifies the RS phenomenology quite a bit because now couplings get diluted. To place the collider reaches in perspective, assume bulk profiles for fermions, realistic flavor. KK gluon exchange contribution: one is required M_{KK}>20 TeV, 1-2 TeV is not favored by these  bulk models. So if you want to explain flavor and other things in these models you are  pushed to higher scales. [Ok, back to better understood sentences.]

In conclusion, Hooman explained that extra dimensions offer the possibility to solve the hierarchy problem, and shed light on the flavor sector of the SM. New phenomena can be discovered at TeV scale. He asked the audience to acknowledge that a discovery of extra dimensions would be a fundamental revolution in science, and as far as I could detect, nobody objected. He concluded by saying that various scenarios can be tested at the LHC.  The original Randall-Sundrum model had rosier signals, but once one introduces more sophistication, signals may become more elusive. This is true also for LED, where black hole signals could be less obvious or likely.