ULTRARELATIVISTIC COLLISIONS Theodore Tomaras University of Crete Motivation The relevance of classical gravity A slightly simpler model scalar radiation The local and the nonlocal source ID: 303703
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Slide1
GRAVITATIONAL BREMSSTRAHLUNG INULTRA-RELATIVISTIC COLLISIONS
Theodore Tomaras
University of CreteSlide2
MotivationThe relevance of classical gravityA slightly simpler model – scalar radiation
The local and the non-local source
Destructive interference The emitted energy4. Classical gravitational bremsstrahlung in M4 x Td5. Region of validity of the approximation6. Conclusion - Discussion
PLAN OF THE TALKSlide3
1. MOTIVATION
About 10% losses in
e+e- collisions at Z0 (Altarelli, Martinelli; Buccella; CED) Reasonable expectation: Even more important in transplanckian collisions.MOST NATURAL CONTEXT: TeV-SCALE GRAVITY with LARGE EXTRA DIMENSIONS
Characteristics of gravitational radiation per se
Useful checks of analogous computations
using different methods and computer simulations
3. Estimates of BH production cross-section ??Slide4
2. At transplanckian energies gravity is (a) dominant and (
b
) classical The qualitative argument
Classicality:
Also obtained for:
(
Giudice
,
Rattazzi
, Wells
Veneziano
,…)
A.D.D.:Slide5
Classical ultra-relativistic scattering = eikonal approximation
An explicit demonstration
(All mode summations converge)
GKST: 0903.3019 (JHEP)Slide6
(For d
=0
: Deibel, Schucher)
Cross-section
identical
to the one obtained
quantum
mechanically
in the
eikonal
approximation.
All orders in the QM sense.
ACV (1987)
Verlinde’s
(1992)
Kabat+Ortiz
(1992)Slide7
GRAVITATIONAL BREMSSTRAHLUNG IN TRANSPLANCKIAN COLLISIONS IN M4xT
d
Amati, Ciafaloni, VenezianoCardoso et alChoptuik and PretoriusChristodoulou D’Eath and PayneGiddings et alYoshino et al…………………………See our papers….PEDESTRIAN APPROACH: MASSIVE POINT PARTICLES (“STARS”)
GKST: 0908.0675 (PLB),
1003.2982 (JHEP); also to appear…
THE GENERAL FORM OF THE RADIATED ENERGY:Slide8
3. A SLIGHTLY SIMPLER MODEL: SCALAR BREMSSTRAHLUNG IN GRAVITY-MEDIATED U-R COLLISIONSSlide9
THE SOLUTION UP TO FIRST ORDER
The
LAB frameSlide10
THE SECOND ORDER EQUATION – SCALAR RADIATION
m
m
’
m
m
’Slide11
THE EMITTED ENERGY – GENERAL FORMULAESlide12
THE LOCAL SOURCE
(
p, l)
(
k
,
n
)
m
m
’
Expressed in terms of
hatted
Macdonald
K
n
(z
l
) functions
with argumentSlide13
Macdonald functions K(zL) fall-off exponentially for large zL.
Natural cut-off at
zL≈1
Effective number of interaction modes.
Convergence of summation.Slide14
Frequency and angular distribution of radiation
(b1) z≈1 and small angles:
(b2) z≈1 and large angles:
(SUPRESSED)
DOMINANTSlide15
Frequency and angular distributions - GRAPHS
Angular distribution of
Ez’ in D=4 for γ=1000 The frequency and angular distributions are very well localizedSlide16
Frequency distribution of Ez in
D=7 and for
γ=1000…so it is simple to obtain the powers of γSlide17
COUNTING POWERS OF γ IN THE EMITTED ENERGY
FROM THE LOCAL CURRENT ALONE:
THE EMITTED ENERGYSlide18
THE NON-LOCAL SOURCE
(
k
,
n
)
(
p-k
,
l-n
)
(
p
,
l
)
m
m
’
fSlide19
A USEFUL REPRESENTATIONSlide20
DESTRUCTIVE INTERFERENCE
In the regime:
The terms of O(
γ
)
and O(1)
in
ρ
n
and
σ
n
0
cancel in their sum.
For synchrotron in
d
=0: Gal’tsov
, Grats, Matyukhin (1980)Slide21
THE REMAINING SOURCE OF
Φ
-RADIATION Contains only Kα(z)Contains only Kα(z’)Slide22
(1)
(2)Slide23
(1)
THE COMPONENTS OF RADIATION
(1)(2)
Soft radiation is suppressed
(2)Slide24
Frequency distribution for Ez’
in D=4 for
γ=1000Slide25
Frequency and angular distributions - GRAPHS
Angular distribution of
Ez’ in D=4 for γ=1000Slide26
The unbeamed emission of E
z
’ in D=7 and for γ=1000Slide27
Frequency distribution of Ez in D=7 and for
γ
=1000Slide28
e.g. for the energy of the dominant components:
USING
jn=jnz + jnz’ AND INTEGRATINGTHE TOTAL ENERGYSlide29
4. GRAVITATIONAL BREMSSTRAHLUNG IN
M
4 X TdDIFFERENCES:GRAVITATIONAL RADIATION POLARIZATIONSCOUPLING TO THE PARTICLES GRAVITATIONAL
For
d
=0 see also K. Thorne and S. Kovacs, 1975 – 78Slide30
But e.g. ACV:
??Slide31
5. REGION OF VALIDITY OF THE APPROXIMATION
Mode sums to integrals Particle trajectories (Δθ<<θ, Δb<<b)
Weak field |
h
|<<1, and
small scattering angle
Classical radiation field –
Number of emitted quanta
DEPENDS ON THE RADIATION CHARACTERISTICS
AND THE KINEMATICS OF THE COLLISIONSlide32
AN EXAMPLE: THE GRAVITY CASE
(
NOT GOOD FOR m=0 !!)
FOR A
ROUGH ESTIMATE OF
Ε
FFICIENCY
: TAKE
b
SATISFIED
i
n a window
depending on
s
,
d
,
m
, M
*
e.g.
d
=2Slide33
A NEW SCALE ??
i.e.
For
FOR
Slide34
6. CONCLUSIONS - DISCUSSION
Strictly speaking
not reliable for collisions in the LHC. Improvement necessary (e.g. to remove bc). A potential test for computer simulations or limits of other analytical computations. Valid for MD as well as M4 x Td.
Practically interesting context:
TeV
-scale gravity with LED.
A
classical
calculation shows that in
transplanckian
collisions there
may be extreme gravitational
bremsstrahlung
with
ε=Ο(1)
for
b>>r
S. Back Reaction in such computations should be very important. Reliable for collisions of
massive particles and important for γ>>1.
Simulations with small γ not sensitive to such effects (Cardoso et al)
A final state of 10-20 50 GeV gravitons are lost in the QCD background. No
BHs in LHC?? Maybe the cross-section is much smaller….. Affect bounds on extra dimensions.