For all our electro-weak enthusiasts, this past week has been a very exciting time. The CMS Collaboration has just published our first study measuring the *W*^{+}*W*^{–} production cross section at 7 TeV. This study, titled *“Measurement of W*^{+}*W*^{–}* Production and Search for the Higgs Boson in pp Collisions at sqrt(s) = 7 TeV,”* is available on arXiv.org and has been accepted for publication by Physics Letters B (a peer-review journal for those who are wondering).

But before we delve into the paper proper, let’s take a moment and ask ourselves: “Why study *W*^{+}*W*^{– }production at all?”

For this answer, let’s take a page out of one of Flip Tanedo’s posts, “*An Idiosyncratic Introduction to the Higgs*,” and study the Higg’s Branching Ratios (or the percent of Higgs particles decaying by method X out of all possible decays Y). Now one question you might be asking is: “Do particles really decay in more then one way?”

The answer is, yes. The name of the game is that heavy particles always decay into lighter particles, unless a conservation law prevents it. And particles will decay by different methods based on probability; it’s all random and up to chance. However, some decay methods for a particle are *more* likely then others. Looking at the plot of the Branching Ratio for the Higgs boson (which I took from Flip), the curves that are above everything else in the plot represent the decay methods that are more likely then the others (So the Branching Ratio is also a statement about probability!).

The Higgs, being a theoretically massive particle (since we have yet to observe it in a collider), can decay in numerous ways. In the plot below, the possible ways the Higgs can decay are:

- A quark an anti-quark (b and the b with a bar over it; c and the c with a bar over it).
- Two W bosons (with opposite electric charged because the Higgs has zero electric charge).
- Two tau (ττ) leptons (with opposite electric charge).
- Two gluons (the gg symbol).
- Two Z bosons (the Z is also electrically neutral).
- Two photons (
*γγ*) - A Z and a photon

But, since the Higgs hasn’t been found yet experimentally, physicists are unsure of its actual mass (and thus what it will decay into). The theory does give us clues though (as do other experiments, more on this later).

But how do particle physicists look for a new particle? One way to find them is to search for peaks in a mass distribution.

Now since energy and mass are related, the more energetic an object is, the more mass it has. This doesn’t really matter in our everyday lives, because the increase is very, very small; but if you’re a sub-atomic particle (or an atomic scale particle) it matters a lot! As an example, when protons are accelerated in the LHC, they become several thousand times more massive to when they are at rest!

But how do you make a mass distribution? Well, physicists take two objects (say a *W*^{+}*W*^{–}, or a *μ*^{+}*μ*^{–}) and look at the sum of their masses. On the x-axis you plot the mass of the pair, and on the y-axis you plot the number of times you found a pair with that mass value. Here is an example of what you would get for a pair of muons (*μ*^{+}*μ*^{–}):

So in this plot of “Events” vs. “Muon Pair (*μ*^{+}*μ*^{–}) Mass” (read Y vs. X), we see three peaks! These peaks correspond to three different mesons (a meson is a class of particles made up of a quark and anti-quark); in order they are the Υ(1S), Υ(2S), and Υ(3S). Sadly in particle physics we started to run out of symbols. It is common now to name particles based on how the quarks bind together to form the particle, hence the (1S), (2S) and (3S) after the symbol “Υ”. These represent three different “bound-states” (and thus three different particles) of the quarks making up the Upsilon (“Υ”).

Anyway…

Now back to our Branching Ratio plot above. Notice how the *W*^{+}*W*^{– }line is above all the other lines for masses greater than ~130 GeV/c^{2}. This means that the Higgs has a higher probability of decaying into a *W*^{+}*W*^{–} pair for this region (mass > 130 GeV/c^{2})! Therefore, if you’re an experimentalist looking to find the Higgs, one of the best places to look is in events with a *W*^{+}*W*^{– }pair coming out of the proton-proton collision!!!

Perhaps its also interesting to take a look at the current constraints placed on the Higgs mass. The LHC’s ancestor, the Large Electron Positron (LEP) Collider, has placed a lower limit on the Standard Model (SM) Higgs Boson mass of 114.4 GeV/c^{2} with a 95% Confidence Level (C.L.). Previous precision electroweak measurements have constrained the SM Higgs mass to be less than 185 GeV/c^{2} (95% C.L.). And the US’s Tevatron Collider has excluded the mass range of 158-175 GeV/c^{2} (95% C.L.). In summary, the current unexplored regions of the SM Higgs mass are 114.4-158 GeV/c^{2} and 175-185 GeV/c^{2}. Or more precisely, if the SM Higgs boson does exist, then it will most likely have a mass between 114.4-158 GeV/c^{2} or 175-185 GeV/c^2, and for some portions of these ranges the Higgs will decay over 90% of the time to a *W*^{+}*W*^{– } Pair!!!

As a note on book keeping, this study used **all** of the data collected by the CMS Detector in 2010!

* *

So, what did my colleagues in the electro-weak sector of CMS look for? Since a W will decay into a charged lepton and the corresponding lepton-neutrino, (i.e. *W*^{±}* → l*^{±}*v*_{l}); CMS Physicists looked for events containing e^{+}e^{–}, μ^{+}μ^{–}, e^{+}μ- (or e^{–}μ^{+}) pairs which have a large component of their momentum in the plane perpendicular to the two proton beams. In addition, CMS Physicists also looked for events containing large missing transverse energy.

Since two neutrinos are present in these *W*^{+}*W*^{– }events; and the CMS Detector cannot detect neutrinos directly (they just interact too *weakly!*), physicists must infer their presence by looking for this “missing transverse energy”.

But what is missing transverse energy? To measure missing transverse energy, we look at the energy coming out in all directions in the transverse plane, the plane perpendicular to the beam pipe where the protons collide. If the energy going out in one direction does not balance the energy going out in the opposite direction, we know that a particle escaped detection.

Or more simply, Ta-da, a neutrino went that-a-way. This is also how we would detect other particles that do not interact with matter in an ordinary way.

Now that’s the basics of Event Selection, the full details can be found in section 3 of the paper (and if anyone has any questions I will try to answer them!), but let’s move on for now.

CMS Researchers found 13 events total, in which a *W*^{+}*W*^{– }pair was produced (this is in agreement with simulation, where 13.5 events where found). Now, let’s take a moment to ponder this. Researchers looked at *all of the data* from 2010, and only found **13 events!** This shows that *W*^{+}*W*^{– }production is an *incredibly* rare process!

Now, for some results! Experimentalists have found the *W*^{+}*W*^{–} production cross-section at a center of mass energy of 7 TeV in proton-proton collisions to be *σ =* 41.1 ± 15.3 ± 5.8 ± 4.5 pico-barn (pb, for an idea of what a barn is, see this post by Ken Bloom). The uncertainties listed on this cross-section value are due to statistical, systematic, and luminosity factors, respectively.

So what!? Well, this is in agreement with the theoretical prediction given by the Standard Model (SM) at Next-to-Leading Order (NLO). The SM prediction was 43.0 ± 2.0 pb.

So our theory is correct! It matches the experimental data!

Also, to reduce uncertainties, CMS Physicists also took the ratio of the *W*^{+}*W*^{–} to *W*^{± }production cross sections. In this case, the uncertainty in the proton beam’s luminosity cancels out. The experimental ratio of these two cross sections was found to be 4.46 ± 1.66 ± 0.64 ·10^{-4 }(uncertainties are again due to statistical & systematic factors, respectively), whereas the theoretical value of this ratio was given to be 4.45 ± 0.30 · 10^{-4}. *Now this is even better agreement! *Which is why experimentalists choose to compare these two ratios instead.

Now onto the “Glorious Higgs!” The process we are now interested in is:

H → *W*^{+}*W*^{–} → 2*l *2*v*_{l}

Where: *l *is a lepton, and *v*_{l }is the corresponding neutrino.

CMS Physicists modified the event selection slightly for this. The theory tells us when the Higgs decays into a *W*^{+}*W*^{– }pair the angle between the two outgoing oppositely charged (electric) leptons is very small (close to zero degrees), whereas when we are just looking at background processes (such as pure *W*^{+}*W*^{– }production, top quark events, ect…) the angle is very large (close to 180 degrees). So experimentalists made a measurement of the angle between these two leptons to get an idea if a Higgs boson had decayed into a *W*^{+}*W*^{– }pair, shown here:

So in this plot we have our 13 selected *W*^{+}*W*^{– }events, they are the black experimental data points (and their uncertainties), the colored portions are the theoretical predictions given by the SM for various known processes.

Now for our Higgs search, *W*^{+}*W*^{– }*is a background (shown in brown)! *Our other backgrounds being:

- Dark Blue: production of a Z boson plus jets (hadronic activity).
- Pink: top quark pair production or single top quark with a W boson production
- Green: di-boson production, like WZ, or ZZ, or γZ, etc…
- Light Blue: W plus jets (hadronic activity).

Now if we assume the Higgs Boson has a mass of 160 GeV/c^{2} then the theoretical prediction of the angle between the two charged leptons in our events is shown as the solid black line *(which has a peak near zero, the angle between the outgoing leptons is small for Higgs production)*** . **So from this plot, we see that we haven’t found any evidence that a Higgs Boson with a mass of 160 GeV/c

^{2}has been found (i.e. there are not a lot of points near the peak in the black solid line).

But that was just one value for the Higgs mass. What about the others? As particle physicists we need to look at all possible ranges for the mass of the Higgs. CMS Physicists decided to look at a large range, of 120-600 GeV/c^{2}. This is shown here:

So this is a very colorful plot, but what does it mean?

The Y-Axis is the Higgs production cross section multiplied by the Higgs Branching Ratio to *W*^{+}*W*^{– }pairs. The X-axis is the Higgs Mass. The blue line is experimental observation. This is the region of the “phase-space” we where able to see with this study. The “phase-space” is the possible ways something can happen. When you’re playing Monopoly, and you roll two dice, the most likely outcome for the sum of the dice roll is 7. This has a large phase space….you can make 7 with a (1,6), or (2,5) or (3,4) on each dice. Whereas having both dice add to 12 has a very small phase space, this only happens when each die comes up 6.

So the blue line represents how much of the phase space we were able to see. The green and yellow lines are the 95% C.L. bands on the blue lines.

The solid red line near the bottom of the graph is the theoretical prediction given by the current Standard Model for how the Higgs boson’s “phase space” may behave. Notice the experimental blue line, and the theoretical red line are *nowhere near each other! *Since we didn’t see many data points in the Higgs (160 GeV/c^{2}) region in the graph of the angle between our two charged leptons above, it shouldn’t shock us that the blue line is nowhere near the solid red line (at 160 GeV/c^{2}). But this doesn’t mean that there was anything wrong with the experiment. On the contrary, what this means is that CMS Physicists did not have conclusive evidence to say whether or not the Higgs will or will not decay into a *W*^{+}*W*^{– }pair (based on a statistically significant dataset).

So the current theory (the Standard Model) tells us that the Higgs can decay into a *W*^{+}*W*^{–} pair; but with the current data CMS Physicists where unable to prove or disprove the Standard Model’s theoretical prediction.

But, the final line is, what I think, the most interesting. This is the red portion with the criss-crossing pattern around it (second item on the legend in the above graph).

Currently in the Standard Model there are three generations of quarks that have been experimentally confirmed. Theorists have often wondered if this is the full story. Meaning, could a possible 4th generation of quarks/leptons exist and we just haven’t seen them yet? This criss-crossing red line gives the phase space for how the Higgs would decay if this 4th generation did exist.

Now notice the blue line is underneath the criss-crossed red line for a Higgs mass of 144-207 GeV/c^{2 }when you assume there is a 4th generation of quarks/leptons.

The fact that the blue line is under the criss-crossed red line means that we were conclusively able to probe this portion of the phase space for the 4th generation hypothesis. Since we did not see any conclusive evidence (again, reference angle between our charged leptons in the graph above) of Higgs decaying into a *W*^{+}*W*^{–} pair for the mass region of 144-207 GeV/c^{2}, we were able to make a definitive statement:

If the Standard Model has a 4th Generation of Quarks/Leptons, and the Higgs boson has a mass between 144-207 GeV/c^{2}, the it does not decay to a *W*^{+}*W*^{– }pair.

But the jury is still out on the current three generation cases. We weren’t able to probe that region of the phase space (blue line nowhere near solid red line). As is often the case in all fields of science, **we need more data**.

Until next time,

-Brian

(I would like to thank Kathryn Grim for her helpful advice regarding the presentation of this material)