Download Looking for Magnetic Monopoles AT The Large Hadron Collider

Looking for Magnetic
Monopoles
AT
The Large Hadron Collider
Vicente Vento
Universidad de Valencia-IFIC
martes 26 de junio de 12
· Luis Epele
· Huner Fanchiotti
· Carlos García Canal
· Vasiliki Mitsou
martes 26 de junio de 12
·
Introduction
· Monopoles
· Monopole Production and Detection
· Monopolium
· Monopolium Production and Detection
· Moedal
· Concluding Remarks
martes 26 de junio de 12
· Introduction
In 1984 Pierre Curie suggested that
magnetic monopoles could exist
martes 26 de junio de 12
Restores Electric-Magnetic Symmetry in
Maxwell’s Equations
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Monopoles
Dirac 1931 : Monopole and Quantum
Mechanics: Magnetic Coulomb Field:
B=gr/
2
r
Conflict when defining the vector potential
The solution of a Genius
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A particle with charge, say an electron,
traveling around some path P in a region with
zero magnetic field (B = 0 = ∇ x A) must acquire a
phase φ; given by:
.
The only way we would NOT see the Dirac
string is if the wave function of the electron
only acquired a “trivial phase” i.e. ∆Φ = 2π N
(n =1,2,3..). That is, if:
Charge Quantization
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Monopole Properties
·
The Dirac monopole is a point like particle
· magnetic charge g = 68.5 e and no electric
charge
· Monopoles accelerate along field lines
according to the Equivalent Lorentz Eqn.
F = gB + ep × B / γm0
· The monopole mass is not predicted within
the Dirac’s€ theory.
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Monopoles and Grand Unification
·
Grand Unified gauge theories predict Monopoles:
‘t Hooft and Polyakov (1974) discovered that
monopoles are fundamental solutions to nonAbelian gauge “GUT” theories
· These Monopoles have structure and no string
singularity.
· The field of the GUT monopole is B ~ g/r2 outside
· The Mass m(GUT)M ≥ mX/g > 1017 GeV. not
producible by particle accelerators
· primordial monopoles present in the Universe
· GUT monopoles can catalyze proton decay!
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There are models For “the desert” where
monopoles appear in a mass range accessible
to the LHC:
· The electroweak Cho-Maison monopole
· The Troost-Vinciarelli monopole
· The model of Weinberg et al.
· Superstring models
We shall take a phenomenological approach
and assume that the mass is a parameter
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Monopole Production and Detection
e -> β g
martes 26 de junio de 12
term to be sufficient, for our purposes. Guided by simplicity and phenomenological
inspiration we introduce an effective theory which is finite and well defined and we call
this proposal the β scheme.
Note that the Ginzburg-Schiller scheme and the β scheme are in some sense complementary. The former is valid below the monopole threshold, while the latter above
since β vanishes below threshold.
The aim here is to study possible signals of magnetic monopoles at LHC. According
to previous studies [?], the most promising mechanism is photon fusion. The elementary diagrams contributing to pair production are those in Fig. ??, where the explicit
couplings have been shown.
The photon-fusion elementary cross section is obtained from the well-known QED
electron-positron pair creation cross section [?], simply changing the coupling constant
(e → gβ ) and the electron mass by the monopole mass me → m, leading to
!
!
"
"
4
4
2
4
3−β
1+β
π g (1 − β ) β
2
σ(γ γ → mm) =
log
−
(2
−
β
) ,
(4)
2
2m
2β
1−β
Monopole Production
Σ!Ω"
where β is the monopole velocity, a function of the center-of-mass energy, E. In Fig. ??
we show the ω = E/2 m dependence of the adimensional functional form of Eq.(??) to
10.
show the effect of the β g coupling. The solid curve corresponds to the electron-positron
case, the dashed one to the monopole case
which
contains the β 4 factor. One should
!
"
e !e
1.
notice the large effect associated
with this factor in the vicinity of the threshold.
LHC detectors, apart from the MoEDAL experiment [?], have not been designed
m!m
0.1
4
0.01
0.001
1.0
1.5
2.0
3.0
5.0
7.0
10.0
Ω
Figure 3: Adimensional functional form of the elementary photon-fusion cross section
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Production from photon fusion at
Large Hadron Collider
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i) inelastic
p + p -> X + X + M
(photons radiated from partons)
ii)
iii)
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semielastic p + p -> p + X + M
(one photon from partons the other
from the other proton leaving the
proton intact)
elastic
p + p -> p + p + M
(both photons from protons)
andapq'(s)=
the choice ofdx)
Ge&
made
is
such
Q2=1
dx2total
dz)
maximum
the
value
of
to
be
the
mo
mentioned
above
cross
gedQtoscalars
there
pp
4m /sx& x&
4m /sx l
4m /s
%'ith
s
be
/4.
er
del
applicable.
cer
structure
function.
There
proton
is
a
epforinelastic
ferfermions.
duction
reads.
charged
These
off'shel
the
hf thethat
are
photons
sufficiently
~H+H
cross
for
L
semielastic
section
The
(L
in
m
We
choose
the
logarithm
to
be
pp
(4).
Eq.
=
=
Q
/Q2
ln(
(z
(z)
)
is
the
inelastic
where
structure
proton
2
F(2
deep
Q
&q
&q
r
r
50
2~
z
he choice
of
Ge&
made
the (4).
is
such
that
photo
Q2=1
1
1
1
of the logarithm
in the argument
in Eq.
W
dz,
dz,
dx,
—
form
as
in
more
a
compact
write
(3)given
able.
of
Ge& Xis1
is
Q2=1
by s/4
)pX
4mby/s m and4mthe/sxchoice
4m
/sx
z
l
l l
ale Q has been chosen throughout
cross sectionmodel
for1 ppto ~H+H
L )pX is1 given by
be applicable.
1 (L
=
dx2 cross
dz)for pp ~H+H
)fq.
dx)&~(x2,
semielastic
section
The Q
x2z, z2
~(x&,
(zz)8&r(x,
g
)fr&q(z,
)fry.
4m
4m /sx x&z&
4m
/sx
4m
/s
/sx&
x&
is
now
=Qsx,
subprocess
given
by
z2
energy
z,
l
F~2(x,
(4)
(z2)o
(z,
z,
,
F~2(x, , Q')f, (
dz,
dz,
dx,
o"
—
=
—
"'(s)=2f,
beeno obtained
4m
4m
/sx
z
elastic
spectrum
'„'&~(z)
/s
L*,
photon
dz, is the pi
',X and
f4meither
K
or /sx
e„='„ed4ml l/s dx,has
—,
1
l
4m /sx l ~~
4m /sx
use
an
ap
in
we
However,
form
of an
integral
[ll].
is=Qx&x2z&zzs.
the
inelastic
structure
function.
T
proton
F(2
deep
The structure functions have th
which
in
expression
given
analytic
ximate
[12]
2,
of
the
in
We
choose
)fy(z)
(z2)oyer(x)x2z)z2s),
logarithm
argument
)f),
(4).
Q
Eq.
with
is the
is The
inside
now
=Qsx,
photon
a
WQ
given
quark.
by spectrum
z2.
ergy
z,
+s
is
now
=Q
subprocess
given
by
f„&q
energy
with
2.
—
Th
results
about
10%.
to
exact
wn
to
reproduce
(5)
2
and
the
choice
of
Ge&
made
m
is
Q2=1
obtained
hasphoton
been
o
has such
been
spectrum
'„'&~(z)
=—
The
elastic
spectrum in'„'&~(z)
is
m
use
2
2
we
given
by
in
4)/$06.
00
2335
in [ll].
we
However,
form
of
an
the
integral
.use 50
toabout
be applicable.
an
apinthe[ll].
egral
choiceHowever,
of the2m
scaleswe
Q,
in
expression
given
analytic
proximate
~H+H
+
ue
of
the
momentum
transfer
cross
for
L [12]
given
semielastic
section
is
which
in
(L
cp- expression given
)p
[12]pp
—
results
about
to
exact
=
known
to
reproduce
off'shell
ently
for
the
quark-parton
z)
[1+(1
f'y'ip(z)
]
The
results
about
10%.
to
exact
ce
zs+m
)(s
)
is
27TZ
is
form we use given by
s/4
e
f
m
&
f
(z):f
f
o" "'(s)=2f,
f, f,
f
+s(x, z, s)
)f"~
Q')f,
f, f,f f, f,
f
2f,
+2
&
&
l
l
f =—
Q;„=
martes 26 de junio de 12
&
+s
—
+ [(s+m
f
Q;„=
—
5000
2
M σ(γγ)
4000
3000
2000
1000
0
0
5
10
15
20
E/M
gure 4: We show the photon fusion production cross section for monopolium (solid curve
r R = 1.5 and Γ̄M = 0.1, and for monopole-antimonopole (dotted curve) as a function of th
ergy
martes 26variable
de junio de 12 E = E/M .
monopole mass limit
martes 26 de junio de 12
Monopole Detection
ted) scattering given in fb/GeV as a function of the invariant mass
a LogLog
plot. The Higgs signal abov
m. We have assumed a monopole of mass 750 in
GeV,
chosen because
ns turned out to be close to the expected magnitude
Higgs toThe figures correspond t
makeofitthe
visible.
on above background. The cross sections are wide,
gaussian,
fromalmost
the curves
that monopole-antimonop
g softly just above threshold (1500 GeV). LHC detectors are blind for
of the cross section above the background
ng and have black spots due to construction features in the non-forward
expected
from Standard Mo
o not allow for a full detection of photons. Therefore
in orderbackground
to obtain
Eγ 1 TeV.
timation of the observable cross section we take region
the right-angle
crossHence the required selec
ltiply it by 4π. This differential cross section is thus
the smallest
possible. of the photon pairs pro
the majority
from threshold, it corresponds quite well to a realistic
since,
Thus estimate,
the search
for monopole-antimonop
n, the elementary differential cross section drops fast with angle and
at the LHC.
hould consider an efficiency factor for the various detectors.
400
4
300 H # ΓΓ %x 50&
dΣ #
2
200
100
1
0
1500
GeV
3
fb
GeV
dΣ #
fb
$
$
5
m $ m # ΓΓ
2000
2500
3000
EΓ !GeV"
3500
4000
0
200
400
600
800
1000 1200 1400
EΓ !GeV"
ward (solid) and the right-angle cross sections forFigure
a monopole
of mass
12: Comparison
of the γγ monopol
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Dirac (1934)
“…The attractive force between two magnetic
poles is 4692 1/4 time that between the electron
and the proton. This very large force may perhaps
account for why the monopoles have never been
separated...”
- Monopolium -
martes 26 de junio de 12
Monopolium production
Monopolium is a monopole - antimonopole
boundstate
rm
−g
martes 26 de junio de 12
rm
-g2/r
+g
Monopolium production from photon fusion
at Large Hadron Collider
M
martes 26 de junio de 12
i) inelastic
p + p -> X + X + M
(photons radiated from partons)
ii)
iii)
martes 26 de junio de 12
semielastic p + p -> p + X + M
(one photon from partons the other
from the other proton leaving the
proton intact)
elastic
p + p -> p + p + M
(both photons from protons)
andapq'(s)=
the choice ofdx)
Ge&
made
is
such
Q2=1
dx2total
dz)
maximum
the
value
of
to
be
the
mom
mentioned
above
cross
gedQtoscalars
there
4m pp
4m /sx l
4m /s
/sx& x&
%'ith
s
be
/4.
er
del
applicable.
cer
structure
function.
There
proton
is
a
epforinelastic
ferfermions.
duction
reads.
charged
These
off'shel
the
hf the
that
are
photons
sufficiently
~H+H
cross
for
L
semielastic
section
The
(L
in
m
We
choose
the
logarithm
to
be
pp
(4).
Eq.
=
=
Q
/Q2
ln(
(z
(z)
)
is
the
inelastic
where
structure
proton
2
F(2
deep
Q
&q
&q
r
r
50
2~
z
he choice
of
Ge&
made
the (4).
is
such
that
photo
Q2=1
1
1
1
of the logarithm
in the argument
in Eq.
W
dz,
dz,
dx,
—
form
as
in
more
a
compact
write
(3)given
able.
Ge& Xis1
m and4mthe/sxchoice of
is
Q2=1
by s/4
)pX
by
4m
4m
/sx
z
/s
l
l l
ale Q has been chosen throughout
cross sectionmodel
for1 ppto ~H+H
L )pX is1 given by
be applicable.
1 (L
=
dx2 cross
dz)for pp ~H+H
)fq.
dx)&~(x2,
semielastic
section
The Q
x2z, z2
~(x&,
(zz)8&r(x,
g
)fr&q(z,
)fry.
4m
4m /sx x&z&
4m
/sx
4m
/s
/sx&
x&
is
now
=Qsx,
subprocess
given
by
z2
energy
z,
.
l
F~2(x,
(4)
(z2)o
(z,
z,
,
F~2(x, , Q')f, (
dz,
dz,
dx,
o"
—
=
—
"'(s)=2f,
beeno obtained
4m
4m
/sx
z
elastic
spectrum
'„'&~(z)
/s
L*,
photon
dz, is the pi
',X and
f4meither
K
or /sx
e„='„ed4ml l/s dx,has
—,
1
l
4m /sx l ~~
4m /sx
use
an
ap
in
we
However,
form
of an
integral
[ll].
is=Qx&x2z&zzs.
the
inelastic
structure
function.
T
proton
F(2
deep
The structure functions have th
which
in
expression
given
analytic
ximate
[12]
2,
of
the
in
We
choose
)fy(z)
(z2)oyer(x)x2z)z2s),
logarithm
argument
)f),
(4).
Q
Eq.
with
is the
is The
inside
now
=Qsx,
photon
a
WQ
given
quark.
by spectrum
z2.
ergy
z,
+s
is
now
=Q
subprocess
given
by
f„&q
energy
with
2.
—
Th
results
about
10%.
to
exact
wn
to
reproduce
(5)
2
and
the
choice
of
Ge&
made
m
is
Q2=1
obtained
hasphoton
been
o
has such
been
spectrum
'„'&~(z)
=—
The
elastic
spectrum in'„'&~(z)
is
m
use
2
2
we
given
by
in
4)/$06.
00
2335
in [ll].
we
However,
form
of
an
the
integral
.use 50
toabout
be applicable.
an
apinthe[ll].
egral
choiceHowever,
of the2m
scaleswe
Q,
in
expression
given
analytic
proximate
~H+H
+
ue
of
the
momentum
transfer
cross
for
L [12]
given
semielastic
section
is
which
in
(L
c expression given
)p
[12]pp
p—
results
about
to
exact
=
known
to
reproduce
off'shell
ently
for
the
quark-parton
z)
[1+(1
f'y'ip(z)
]
The
results
about
10%.
to
exact
ce
zs+m
)(s
)
is
27TZ
is
form we use given by
s/4
f
m
&
f
(z):f
f
o" "'(s)=2f,
f, f,
f
+s(x, z, s)
)f"~
Q')f,
f, f,f f, f,
f
2f,
+2
&
&
&
l
l
f =—
Q;„=
martes 26 de junio de 12
+s
—
+ [(s+m
f
Q;„=
—
Monopolium photon coupling
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Monopolium wave function
· The monopole has been regarded as possessing some
spatial extension that avoids the singularity at the
origin.
rm
−g
martes 26 de junio de 12
rm
-g2/r
+g
We have represented this complex scenario by a potential
which behaves like a magnetic Coulomb for r >> 2 rclassical
and is finite at the origin.
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Excited Coulomb states
Texto
n > 13 well defined
ρ=
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Two parameters : M , m
M
m-m
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Small Binding
Large Binding
=2m/M
Lower mass threshold M < 2m
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Binding Effect
Threshold effect
Example: for m = 1 TeV and M= 1 TeV at LHC for
100 fb-1 106 monopoles and 108 monopolia.
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Total cross section for monopolium production at LHC with
3.5 TeV beams and monopole masses ranging from 500 to
1000 GeV, with binding energies 2 m/15 and widths 10 GeV.
martes 26 de junio de 12
Monopolium detection at LHC with diphoton
events
ΨM
martes 26 de junio de 12
ΨM
Mass effect
m= 750 GeV
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M= 1400 GeV
ΓM = 10 GeV
Moedal
martes 26 de junio de 12
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toughts...
i) near threshold (grounstate -> l= 0)
γ
M
γ
· β small -> elastic multiparticle collisions
· In presence of magnetic fields huge polarizability
d ̴ rM3 B ̴ (α Ebinding)-3 B
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ii) boundstate -> excited states -> l > 0
multipoles
-> bending (photon emission)
-> excitation and ionization
martes 26 de junio de 12
iii) Monopolium (weak binding and/or excited states)
-> (capturing electrons or protons) -> Dions
D
−e
+g
M
−g
+e
martes 26 de junio de 12
D̄
M
D
D̄
martes 26 de junio de 12
Concluding remarks
Dirac felt that he "would be surprised if Nature had
made no use of it". It, being the Magnetic Monopole.
· Ed Witten once asserted in his Loeb Lecture at
Harvard, “almost all theoretical physicists believe in
the existence of magnetic monopoles, or at least hope
that there is one.”
·
·
· Joseph Polchinski, a string-theorist, described the
existence of monopoles as "one of the safest bets
that one can make about physics not yet seen" and
that “their existence seems inevitable in any
framework that explains the quantization of electric
charge. Of course their mass scale and abundance
are highly uncertain,... ”
martes 26 de junio de 12
· We have shown that if non relic monopoles exist
and their masses are in the TeV region they are
soon to be found either as
m - m pairs or monopolium
much effort is going to go both in the more
traditional schemes, Atlas and CMS, and in Moedal.
Magnetic monopoles can be detected by their high
ionization, their binding to conventional particles and
nuclei, diphoton events, ...
martes 26 de junio de 12
· Monopolium groud state a very heavy neutral
object
-> good diphoton signal (Z0, W±, ...)
-> large magnetic polarizability (in the presence
of large B-fields)
-> naively : difficult object for Moedal (?? elastic
collisions)
· Monopolium excitations
-> multiphoton processes (pseudo-polynomial
trajectories)
-> excitation and ionization (multipole interactions)
· Dion formation
-> good Moedal candidates
martes 26 de junio de 12
Thank you for your attention!
martes 26 de junio de 12