The Higgs boson (H0) is the last lacking piece in the Standard
Model puzzle. It may be produced at LEP via the Bjorken process, i.e., a rare
decay of the Z0:
e+e- ---> Z0 --->
Z0H0
If the Z0 of the final state decays into an
e+e- pair we have the electron channel. The muon channel
(Z0-->mu+mu-) and the invisible channel
(Z0-->nunu~) have also been studied.
The present limit on the Higgs boson mass (Bruxelles, 1995) is:
m(H0) > 65.2 GeV (CL=95%)
This limit has been calculated combining 12 analyses (3 channels × 4
experiments) and take into account almost all LEP1 data.
At LEP2 there are two big changes with respect to LEP1:
Here there are some values of cross section of the Bjorken process, calculated by PYTHIA (pb):
+-------------------------------+
(pb) | SQRT(s) (GeV) |
| 161 175 192 205 |
+----------+-------------------------------+
| 20 | 3.30 2.43 1.75 1.405 |
| 30 | 2.82 2.10 1.544 1.243 |
| m(H0) 40 | 2.32 1.83 1.367 1.109 |
| 50 | 1.77 1.521 1.199 0.993 |
| 60 | 1.123 1.212 1.036 0.877 |
| (GeV) 70 | 0.180 0.848 0.847 0.759 |
| 80 | 0.019 0.372 0.650 0.632 |
| 90 | 0.006 0.020 0.418 0.493 |
+----------+-------------------------------+
These are the values for the whole Bjorken process; for the electron channel
the cross section must be multiplyed by
BR(Z0-->e+e-) = 3.366%.
The analysis of this channel consists mainly in the identification of the pair e+e-. They must become from an on-shell Z0 (this was not the case at LEP1!), so they must have very high momentum, some isolation, great opening angle and invariant mass. Then there must be at leat two jets, coming from H0.
If m(H0) lies in the range accesible by LEP2, the Higgs boson decays mainly in two hadronic jets. These are the branching ratios (see Z. Phys. C 63 (1994) 417, and erratum Z. Phys. C 66 (1995) 321):
+----------+----------------------------------------------------+ |m(H0)(GeV)| bb~ tau+tau- cc~ gg W+W- Z0Z0 gammagamma | +----------+----------------------------------------------------+ | 50 | 86.4 8.5 2.8 2.3 --- --- --- | | 60 | 85.6 8.7 2.8 2.9 --- --- --- | | 70 | 84.6 8.9 2.7 3.8 --- --- --- | | 80 | 83.3 9.0 2.7 4.8 0.1 --- 0.1 | | 90 | 82.0 9.1 2.6 5.9 0.2 --- 0.2 | | 100 | 79.8 9.1 2.5 7.1 1.2 0.1 0.2 | | 110 | 74.7 8.7 2.5 8.2 5.3 0.5 0.2 | +----------+----------------------------------------------------+
DAFNE itself contains some quality cuts. None of the default values have been changed (see DAFNE manual).
The signal must have an e+e- pair, and the Higgs boson decays in two hadronic jets (>90%) or in a tau+tau- pair (<10%): in this second case there is some probability to have a multi-prong decay. So there is a preselection on charged multiplicity:
In the following (points C,D,E) the routine searches for the e+e- pair. So, when I introduce a cut, I mean: the event is tagged if there are at least two charged tracks passing this cuts.
The electrons must be well-reconstructed tracks, coming from the vertex. This lead to four cuts:
We search for an e+e- pair coming from an on-shell Z0, i.e., tracks with high momentum and some isolation. The first cut is:
Regarding the isolation, we know the troubled path of electrons inside matter, because of their low mass. So there are some problems with low energy tracks near the electron (these often comes from reconstruction). The cut is:
Having found a pair of isolated tracks with high momentum, is this an e+e- pair? The routine doesn't make a tight identification (e.g. doesn't use the RICH information). The philosophy is to reject backgrounds (mainly from mu+mu- events), so the cuts have high efficiency and some redundancy. First of all, an electromagnetic calorimeters acceptance must be defined. These zones are considered dead:
Then there is an electromagnetic energy cut:
The measurement of dE/dX by the TPC must be not contrary to the electron hypothesis:
DAFNE provide a very good muon identification. Some test on MC data reveal that the rare misidentifications are made for pion, kaons, sometimes protons, but I have found only one case of electron identified as a muon. So the cut is:
An electron have seldom hadronic energy, unless it crosses a dead zone in electromagnetic calorimeters:
If two electrons have been found, they must have opposite charges; the cut on momentum is something low, so there is a requirement on momentum of one track; then the opening angle and the invariant mass of the pair must confirm the Z0 hypothesis. Here there are the four cuts:
The two electrons are skipped, and a call to PUCLUS (all defaults) is made to search for two jets. If two jets have been found, they must have:
At LEP2 we are no more under the Z0 peak; a production of a Z0 decaying into a pair ff~ is still the most likely process, but its cross section is decreased by two order of magnitude. This process can lead to a 4-fermion process, which was the harder background to reject at LEP1; so at LEP2 we can increase the efficiency. The other backgrounds are: Bhabha, gammagamma (QCD+QPM+VDM), Wenu, W+W-, Z0e+e-, Z0Z0.
The last one is the so-called irreducible background , because it can lead to all the final states of the Bjorken process. Besides, if the Higgs boson will be found at LEP2, its mass will be close to m(Z0): so the final cuts will be unuseful. In this case the Higgs boson can be revealed by an unexpected rate of Z0Z0 processes, and the b-tagging will be very useful. However, this process will become important beyond 180 GeV and will never have a high cross section.
The cross section of backgrounds can be calculated by PYTHIA:
+-------------------------------------+
(pb) | SQRT(s) (GeV) |
| 161 175 192 205 |
+----------------------+-------------------------------------+
| Bhabha (theta>11deg) | 1870 1590 1334 1195 |
| Bhabha (theta>37deg) | 118.9 104.1 88.7 79.3 |
| ff~ | 221 174 134.5 115.0 |
| gammagamma (m>30GeV) | 20.5 22.6 24.8 26.5 |
| Wenu | 0.523 0.686 0.909 1.088 |
| W+W- | 4.28 14.47 17.7 18.1 |
| Z0e+e- | 1.532 1.69 1.87 2.00 |
| Z0Z0 | 0.449 0.451 1.186 1.414 |
+----------------------+-------------------------------------+
compare them with the cross section of the Bjorken process, listed in the introduction of this page.
Many events have been simulated at various energies: here I resume the performance on the signal (efficiency) and on the backgrounds (purity).
The sample of MC data is made by:
In these ranges, the efficiency depends nor from SQRT(s), neither from
m(H0); its value is:
epsilon(H0e+e-) = (46.86 +- 0.54)%
Note that the efficiency on this channel was ~20% in the last period of LEP1,
because of the background coming from the Z0 peak, and because of
the off-shell final state Z0 (see the introduction). So it will be easier searching the Higgs boson
at LEP2 with respect to LEP1.
Other channels of the Bjorken process have been simulated. There is some probability (0.019%) to tag the H0mu+mu-, because of a misidentification of the pair mu+mu-; some processes with a pair tau+tau-, coming from H0 or Z0 decay, are also tagged (a tau can decay into an electron, so in this case the identification is correct). However, these channels cannot increase the efficiency on the signal beyond the statistical error: so, they are not taken into account.
Many events have been simulated for all of the backgrounds listed before. Only three of them can be tagged by the routine, with very low probability. So we may say to have a high purity routine: I have preferred to increase purity in despite of efficiency, because the signal is a rare process.
Below are listed, for each background, the number of events in the MC sample, the corresponding integrated luminosity (compare it with 25 pb-1, the goal at 161 GeV), the number of events tagged by the routine, and the efficiency:
+------------------+--------+----------+----------+----------------+ | Background | sample | L (pb-1) | # tagged | efficiency (%) | +------------------+--------+----------+----------+----------------+ | Bhabha | 15719 | 10 | 0 | 0 | | ff~ | 45374 | 200 | 1 | 0.0022 | | qq~ | 48000 | 300 | 0 | 0 | | gammagamma (QCD) | 33689 | 15 | 0 | 0 | | gammagamma (QPM) | 29444 | 31 | 0 | 0 | | gammagamma (VDM) | 76401 | 11 | 0 | 0 | | Wenu | 1997 | 3700 | 0 | 0 | | W+W- | 27517 | 6100 | 6 | 0.0218 | | Z0e+e- | 1656 | 240 | 0 | 0 | | Z0Z0 | 252 | 550 | 1 | 0.40 | +------------------+--------+----------+----------+----------------+
The high energy run of November 1995, 6 pb-1 at SQRT(s) = 130-140 GeV, has produced the first real data beyond the Z0 peak. At this energy, the Higgs boson could be found only if m(H0) < 40 GeV, so there were no hope to find anything; however, we can use this data to test the behaviour of the routine on real backgrounds, which for the first time are no more dominated by the ff~ process. No candidates have been found, and the number of events passing each cut is compatible with the number expected using the MC sample. So the routine can reject a real background, and the MC sample covers all the real processes.
The run at 161 GeV should reach 25 pb-1. From the efficiency and the purity we can calculate the number of events we expect to tag per pb-1, and the total number of events we expect to tag, in the 25 pb-1 hypothesis. These are the results:
+-------+--------------+--------------+ | m(H0) | # ev. tagged | # ev. tagged | | (GeV) | (1 pb-1) | (25 pb-1) | +-------+--------------+--------------+ | 40 | 0.04 | 0.91 | | 50 | 0.03 | 0.70 | | 60 | 0.02 | 0.44 | | 70 | 0.003 | 0.07 | | 80 | 0.0003 | 0.008 | | 90 | 0.0001 | 0.002 | +-------+--------------+--------------+
+------------+--------------+--------------+ | Background | # ev. tagged | # ev. tagged | | | (1 pb-1) | (25 pb-1) | +------------+--------------+--------------+ | ff~ | 0.005 | 0.12 | | W+W- | 0.001 | 0.02 | | Z0Z0 | 0.002 | 0.05 | +------------+--------------+--------------+ | Total | 0.008 | 0.19 | +------------+--------------+--------------+
In conclusion, the routine can distinguish the signal from the backgrounds if SQRT(s) > m(H0) + 100 GeV, i.e., until the Bjorken process is on-shell. But this is a rare process, so we are handling with little numbers: a conclusion is impossible due to statistical fluctuations. Nevertheless this is not the only way to find the Higgs boson: the electron channel covers only 3.366% of cases. We can do some hypothesis, all of them very conservative (except, perhaps, for the first):
With these hypothesys, the 161 GeV run can provide a limit on m(H0). This limit depends on the number of candidates, and it is m(H0) > 61.8, 58.4, or 52.8 GeV at 95% confidence level if 0, 1, or 2 events are tagged respectively. This limit could be very close to the LEP1 limit (65.2 GeV): a few months against six years. So LEP2 seems to be a very exciting period for all the Higgs Searchers!
In the case you have doubts then contact the expert: Nicola Gagliolo