sage
发表文章数: 1125
武功等级: 天山六阳掌
(第六重)
内力值: 535/535
Higgs boson mass and detection
1) Discoving massive W and Z particle does not imply the existence of
Higgs. It shows
1a) there is a electroweak phase transition in which electroweak
symmetry is broken. Otherwise, W and Z would be massless.
1b) there are additional degrees of freedoms, Goldstones, being eaten
by the gauge boson, because massive gauge boson have 1 more degree of
freedom than the massless one.
However, none of this leads to the conclusion of the existence of a
Higgs. The Higgs boson as a new degree of freedom only exist if there
are additional bosonic states in the electroweak symmetry breaking
sector.
1c) The standard model with 1 Higgs doublet is an example where there
is one additional degree of freedom we call Higgs boson.
1d) On the other hand, there are models of electroweak symmetry
breaking where we do not have a Higgs boson at all. Technicolor is one
of such models.
2) Now let's move on with the assumption that there is a Higgs
boson. IF there is such a state, how do we know it is there.
Of course, it is a state in the theory. Therefore, it will come in
through in the loop corrections to parameters in the theory, such
as masses and couplings. Therefore, even we do not see it fly in
front of our eyes, we should tell its existence by just looking at
its contribution to the radiative corrections of various Standard
Model parameters. This is certainly true and has been pursued for
quite a while already. It has the name electroweak precision
tests. From that, assuming Standard Model with one Higgs boson, we
already know that Higgs boson should be lighter than 200 GeV.
However, these are INDIRECT evidences of Higgs boson and its
properties. How do we know a Higgs boson really exists? How do we
know the effect we see in the electroweak precision tests are not
from some other stuff?
3) There is only one way to be sure. We have to produce the Higgs and
measure it properties. By 'produce', we mean that we have to have
enough energy to produce a Higgs on-shell and measure its decay
products.
Notice that just like W and Z bosons, Higgs is not stable. It will
decay to other particles right away. Therefore, existence of Higgs
means the existence of such a state in the Hilbert space of the
theory. it does mean, however, we can just go and collect them in
nature. We have to have enough energy to excite such an heavy
state.
4) Now I am going to talk about the details of producing and detecting
Higgs. However, for the impatients, here is the summary. Because it
mass and (mainly) its couplings, producing and detecting a Higgs is
much much harder than W and Z. The best limit we have now on the
Higgs mass is about 115 GeV from LEP. (see details below point 5 )
5) Now, when do we give up searching for a Higgs? With all the
difficulties above, LHC could still probe Higgs mass all the way up
to about 1 TeV = 1000 GeV. Upto that point, if we still do not see
the Higgs, I will at least give up the simple model with 1 Higgs
boson, because we do not expect Higgs mass to be very different
from W and Z, certainly not more than one order of magnitude.
On the other hand, there we have puzzle of how the electroweak
symmetry is borken. We will have to build more powerful colliders
to find out. In general, the mechanism resposible for electroweak
symmetry breaking should not be very far away from the weak scale,
and we should be able to find out in the next couple generations of
colliders.
It is very important to realize that in a collider, any new particle
do not come out with a little flag on it saying that 'hey, my name is
....'. Most of the particles, like Higgs or W/Z, decay before it reach
any detector. Therefore, we only see their decay products. A usual
practice is to detect the decay products, from them, we infer the
production of a 'mother' particle.
In order to see a particle, we have to have enough energy to produce
it. What is enough depends not only on the particle mass, but also on
the production processes.
For W and Z, since they couple directly to standard model fermions
with gauge couplings, we can directly producing them by colliding
Standard model fermions together. For example, we can directly produce
a Z boson by annhilation of an electron and a positron with enough
energy:
e^(-) + e^(+) ---> Z
Therefore, order to produce Z, the energy we need for a
electron-positron collider is E>m_Z. Similarly, in order to produce
a W, we could have a proton-antiproton collider with the process
u + dbar ---> W^(+)
with energy E>m_W. I remind you that m_W is about 80 GeV and m_Z is
about 90 GeV.
(by the way, these processes are usually called Drell-Yan processes)
On the other hand, how do we produce a Higgs? In principle, Higgs will
couple to Standard Model fermions with Yukawa couplings. However, in
the Standard Model, because higgs Yukawa couplings are also
responsible for generating the fermion masses, the size of yukawa
couplings are proportional to the fermion mass. This makes them
typically very small. For example, higgs-electron-electron Yukawa
coulping is about m_e/v which is about 10^(-2) to 10^(-3). Therefore,
it is very hard to produce Higgs through annihilation of fermions.
There are many other processes which produces higgs. Let me just
mention one which is more relevant for lepton colliders and low energy
Hadron colliders. IT is the process
f + fbar ---> W(Z)* ---> W(Z) + h
the * means that the W, Z intermediate state is virtual. One
immediately see that this is very different from W/Z production. The
Energy required for this process is m_W(or m_Z)+m_h !! this meaning
producing a Higgs is much much harder than producing W and Z.
LEP, an electron-positron collider, has center of mass energy of about
200 GeV. Therefore, it has an limit on Higgs mass as 115 GeV (It is
the highest mass they can probe!).
It is also very important to realize that we have no control to select
one kind of particle to produce. We product all of them according to
certain probabilities. Therefore, in order to single out a channel, we
have to go above the background, ie, other particle productions.
This is particularly relevant for LHC which is a proton-proton
collider which produces a lot of junks.
Now, for W and Z, they can decay to quarks as well as leptons. leptons
are in general much easier to be observed than quarks.
Higgs particle, on the other hand, couples to fermion through Yukawa
couplings, which proportional to the fermion mass. Therefore, it will
usually prefer to go to heavier fermions. therefore, electron and
muons are not among the common decay products of the Higgs. A Higgs
with mass about 115 GeV will typically go to a pair of bottom
quarks. This is in general harder to see than leptons.
(detecting a Higgs signal is a very big subject of active research. I
only covered the very surface of it here. I could go into details if
anyone is interested in it.)
| 发表时间：2005-06-21, 13:20:13 |
 作者资料
|
元江
发表文章数: 228
武功等级: 逍遥拳
(第五重)
内力值: 200/200
Re: Higgs boson mass and detection
Thanks, sage, this is a nice introduction about how the Higgs particle is going to be searched. I am pretty naive about the experiment of high energy physics (even others too). I will read it more carefully.
If I were a congressman, I would agree to give money for high energy collider now:-)
道可道非常道
名可名非常名
| 发表时间：2005-06-21, 13:43:33 |
作者资料
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可见光
发表文章数: 421
武功等级: 拈花指
(第八重)
内力值: 405/405
Re: Higgs boson mass and detection
谢谢sage哥（还有昌海哥），让我们方便快捷地了解知识。
detecting a Higgs signal is a very big subject of active research. I
only covered the very surface of it here. I could go into details if
anyone is interested in it.
在LHC即将横空出世之际，愿闻其详。另外，Higgs机制之外的替代方案好象也有不少，不妨顺便也介绍一些，令我们更有一个立体感。
生活充满七彩阳光，是为可见光
宇宙无限，爱心永恒！
| 发表时间：2005-06-22, 00:27:22 |
作者资料
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georgecsh