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GGI Firenze, 5.May 2009
Open String Amplitudes for StandardModel Quivers and their Application
for the LHC Dieter Lüst, LMU (Arnold Sommerfeld Center)
and MPI München
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Outline
● Stringy amplitudes for the LHC
(The LHC string hunter’s companion)
● Intersecting D-brane models
● Mass scales in D-brane models
GGI Firenze, 5.May 2009
![Page 3: Open String Amplitudes for Standard Model Quivers and ...GGI Firenze, 5.May 2009 Open String Amplitudes for Standard Model Quivers and their Application for the LHC Dieter Lüst, LMU](https://reader035.vdocuments.us/reader035/viewer/2022062915/5e95f81a8d767d2588000801/html5/thumbnails/3.jpg)
Outline
● Stringy amplitudes for the LHC
(The LHC string hunter’s companion)
● Intersecting D-brane models
● Mass scales in D-brane models
GGI Firenze, 5.May 2009
![Page 4: Open String Amplitudes for Standard Model Quivers and ...GGI Firenze, 5.May 2009 Open String Amplitudes for Standard Model Quivers and their Application for the LHC Dieter Lüst, LMU](https://reader035.vdocuments.us/reader035/viewer/2022062915/5e95f81a8d767d2588000801/html5/thumbnails/4.jpg)
GGI Firenze, 5.May 2009
II) (Intersecting) D-brane models:(Bachas (1995); Blumenhagen, Görlich, Körs, Lüst (2000); Angelantonj, Antoniadis, Dudas Sagnotti (2000); Ibanez,
Marchesano, Rabadan (2001); Cvetic, Shiu, Uranga (2001); ...)
Alternative constructions: heterotic strings
F-theory
(Braun, He, Ovrut, Pantev; Bouchard, Donagi; Buchmüller, Hamaguchi, Lebedev, Nilles, Ramos-Sanchez, Ratz, Vaudrevange; Groot Nibbelink, Held, Ruehle, Trapletti, Vaudrevange; Faraggi, Kounnas, Rizos; see talk by Stefan Groot Nibbelink)
(Beasly, Heckman, Marsano, Saulina, Schafer-Nameki, Vafa;Donagi, Wijnholt, ...)
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GGI Firenze, 5.May 2009
II) (Intersecting) D-brane models:(Bachas (1995); Blumenhagen, Görlich, Körs, Lüst (2000); Angelantonj, Antoniadis, Dudas Sagnotti (2000); Ibanez,
Marchesano, Rabadan (2001); Cvetic, Shiu, Uranga (2001); ...)
Consider open string compactifications with intersecting D-branes ➠ Type IIA/B orientifolds:
Alternative constructions: heterotic strings
F-theory
(Braun, He, Ovrut, Pantev; Bouchard, Donagi; Buchmüller, Hamaguchi, Lebedev, Nilles, Ramos-Sanchez, Ratz, Vaudrevange; Groot Nibbelink, Held, Ruehle, Trapletti, Vaudrevange; Faraggi, Kounnas, Rizos; see talk by Stefan Groot Nibbelink)
(Beasly, Heckman, Marsano, Saulina, Schafer-Nameki, Vafa;Donagi, Wijnholt, ...)
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GGI Firenze, 5.May 2009
II) (Intersecting) D-brane models:(Bachas (1995); Blumenhagen, Görlich, Körs, Lüst (2000); Angelantonj, Antoniadis, Dudas Sagnotti (2000); Ibanez,
Marchesano, Rabadan (2001); Cvetic, Shiu, Uranga (2001); ...)
Consider open string compactifications with intersecting D-branes ➠ Type IIA/B orientifolds:
Features:
Alternative constructions: heterotic strings
F-theory
(Braun, He, Ovrut, Pantev; Bouchard, Donagi; Buchmüller, Hamaguchi, Lebedev, Nilles, Ramos-Sanchez, Ratz, Vaudrevange; Groot Nibbelink, Held, Ruehle, Trapletti, Vaudrevange; Faraggi, Kounnas, Rizos; see talk by Stefan Groot Nibbelink)
(Beasly, Heckman, Marsano, Saulina, Schafer-Nameki, Vafa;Donagi, Wijnholt, ...)
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GGI Firenze, 5.May 2009
II) (Intersecting) D-brane models:(Bachas (1995); Blumenhagen, Görlich, Körs, Lüst (2000); Angelantonj, Antoniadis, Dudas Sagnotti (2000); Ibanez,
Marchesano, Rabadan (2001); Cvetic, Shiu, Uranga (2001); ...)
Consider open string compactifications with intersecting D-branes ➠ Type IIA/B orientifolds:
Features: ● Non-Abelian gauge bosons live as open strings on lower dimensional world volumes of D-branes.!
Alternative constructions: heterotic strings
F-theory
(Braun, He, Ovrut, Pantev; Bouchard, Donagi; Buchmüller, Hamaguchi, Lebedev, Nilles, Ramos-Sanchez, Ratz, Vaudrevange; Groot Nibbelink, Held, Ruehle, Trapletti, Vaudrevange; Faraggi, Kounnas, Rizos; see talk by Stefan Groot Nibbelink)
(Beasly, Heckman, Marsano, Saulina, Schafer-Nameki, Vafa;Donagi, Wijnholt, ...)
![Page 8: Open String Amplitudes for Standard Model Quivers and ...GGI Firenze, 5.May 2009 Open String Amplitudes for Standard Model Quivers and their Application for the LHC Dieter Lüst, LMU](https://reader035.vdocuments.us/reader035/viewer/2022062915/5e95f81a8d767d2588000801/html5/thumbnails/8.jpg)
GGI Firenze, 5.May 2009
II) (Intersecting) D-brane models:(Bachas (1995); Blumenhagen, Görlich, Körs, Lüst (2000); Angelantonj, Antoniadis, Dudas Sagnotti (2000); Ibanez,
Marchesano, Rabadan (2001); Cvetic, Shiu, Uranga (2001); ...)
Consider open string compactifications with intersecting D-branes ➠ Type IIA/B orientifolds:
Features: ● Non-Abelian gauge bosons live as open strings on lower dimensional world volumes of D-branes.!
● Chiral fermions are open strings on the intersection locus of two D-branes: NF = Iab ! #(!a " !b) ! !a # !b
Alternative constructions: heterotic strings
F-theory
(Braun, He, Ovrut, Pantev; Bouchard, Donagi; Buchmüller, Hamaguchi, Lebedev, Nilles, Ramos-Sanchez, Ratz, Vaudrevange; Groot Nibbelink, Held, Ruehle, Trapletti, Vaudrevange; Faraggi, Kounnas, Rizos; see talk by Stefan Groot Nibbelink)
(Beasly, Heckman, Marsano, Saulina, Schafer-Nameki, Vafa;Donagi, Wijnholt, ...)
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GGI Firenze, 5.May 2009
(Review: Blumenhagen, Körs, Lüst, Stieberger, hep-th/0610327)
Perturbative type II orientifolds contain:
● Closed string 6-dimensional background geometry:
-Torus, orbifold, Calabi-Yau space, generalized spaces with torsion.
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GGI Firenze, 5.May 2009
(Review: Blumenhagen, Körs, Lüst, Stieberger, hep-th/0610327)
Perturbative type II orientifolds contain:
● Space-time filling D(3+p)-branes wrapped around internal p-cycles:
- Open string matter fields.
● Closed string 6-dimensional background geometry:
-Torus, orbifold, Calabi-Yau space, generalized spaces with torsion.
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GGI Firenze, 5.May 2009
(Review: Blumenhagen, Körs, Lüst, Stieberger, hep-th/0610327)
Perturbative type II orientifolds contain:
● Space-time filling D(3+p)-branes wrapped around internal p-cycles:
- Open string matter fields.
● Closed string 6-dimensional background geometry:
-Torus, orbifold, Calabi-Yau space, generalized spaces with torsion.
● Strong consistency conditions:
- tadpole cancellation with orientifold planes.
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GGI Firenze, 5.May 2009
Intersecting D6-brane models:
!
a
Na!a = !O6Tadpole condition:
!abD6 wrapped on 3-cycles , intersect at angles!a
Orientifold Compactifications
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GGI Firenze, 5.May 2009
HSSM
Intersecting D6-brane models:
!
a
Na!a = !O6Tadpole condition:
!abD6 wrapped on 3-cycles , intersect at angles!a
Orientifold Compactifications
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GGI Firenze, 5.May 2009
HSSM
Intersecting D6-brane models:
!
a
Na!a = !O6Tadpole condition:
!abD6 wrapped on 3-cycles , intersect at angles!a
Orientifold Compactifications
(Ibanez,Marchesano, Rabadan, hep-th/0105155;Blumenhagen, Körs, Lüst, Ott, hep-th/0107138)
l
W±
q
(a) baryonic
U(2)
(d) leptonic
U(1)R
(c) right
(b) left
e
u, d
U(3)
U(1)L
g
Standard Model Quiver:
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GGI Firenze, 5.May 2009
How many orientifold models exist which come close to the (spectrum of the) MSSM?
(Blumenhagen, Gmeiner, Honecker, Lüst, Stein, Weigand; related work: Dijkstra, Huiszoon, Schellekens, hep-th/0411129; Anastasopoulos, Dijkstra, Kiritsis, Schellekens, hep-th/0605226; Douglas, Taylor, hep-th/0606109; Dienes, Lennek, hep-th/0610319)
Example: IIA orientifold:M6 = T 6/(ZN ! ZM )Systematic computer search (NP complete problem):Look for solutions of a set of diophantic equations:
(Intersecting) D6-brane statistics
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GGI Firenze, 5.May 2009
Z6’-orientifold:
Millions of standard models!
(Gmeiner, Honecker, arXiv:0806.3039)
How many orientifold models exist which come close to the (spectrum of the) MSSM?
(Blumenhagen, Gmeiner, Honecker, Lüst, Stein, Weigand; related work: Dijkstra, Huiszoon, Schellekens, hep-th/0411129; Anastasopoulos, Dijkstra, Kiritsis, Schellekens, hep-th/0605226; Douglas, Taylor, hep-th/0606109; Dienes, Lennek, hep-th/0610319)
Example: IIA orientifold:M6 = T 6/(ZN ! ZM )Systematic computer search (NP complete problem):Look for solutions of a set of diophantic equations:
(Intersecting) D6-brane statistics
![Page 17: Open String Amplitudes for Standard Model Quivers and ...GGI Firenze, 5.May 2009 Open String Amplitudes for Standard Model Quivers and their Application for the LHC Dieter Lüst, LMU](https://reader035.vdocuments.us/reader035/viewer/2022062915/5e95f81a8d767d2588000801/html5/thumbnails/17.jpg)
GGI Firenze, 5.May 2009
Z6’-orientifold:
Millions of standard models!
(Gmeiner, Honecker, arXiv:0806.3039)
gen.
models
1
210
410
610
810
1010
1210
1410
1610
1810
2010
1 2 3
ABaABbBBaBBb
SM gauge group with # of generations
How many orientifold models exist which come close to the (spectrum of the) MSSM?
(Blumenhagen, Gmeiner, Honecker, Lüst, Stein, Weigand; related work: Dijkstra, Huiszoon, Schellekens, hep-th/0411129; Anastasopoulos, Dijkstra, Kiritsis, Schellekens, hep-th/0605226; Douglas, Taylor, hep-th/0606109; Dienes, Lennek, hep-th/0610319)
Example: IIA orientifold:M6 = T 6/(ZN ! ZM )Systematic computer search (NP complete problem):Look for solutions of a set of diophantic equations:
(Intersecting) D6-brane statistics
![Page 18: Open String Amplitudes for Standard Model Quivers and ...GGI Firenze, 5.May 2009 Open String Amplitudes for Standard Model Quivers and their Application for the LHC Dieter Lüst, LMU](https://reader035.vdocuments.us/reader035/viewer/2022062915/5e95f81a8d767d2588000801/html5/thumbnails/18.jpg)
GGI Firenze, 5.May 2009
Z6’-orientifold:
Millions of standard models!
(Gmeiner, Honecker, arXiv:0806.3039)
h
models
1
10
210
310
410
510
610
710
810
910
1010
1110
1210
1310
1410
1510
0 3 6 9 12 15 18 21
SM gauge group, 3 generations with # of Higgses
How many orientifold models exist which come close to the (spectrum of the) MSSM?
(Blumenhagen, Gmeiner, Honecker, Lüst, Stein, Weigand; related work: Dijkstra, Huiszoon, Schellekens, hep-th/0411129; Anastasopoulos, Dijkstra, Kiritsis, Schellekens, hep-th/0605226; Douglas, Taylor, hep-th/0606109; Dienes, Lennek, hep-th/0610319)
Example: IIA orientifold:M6 = T 6/(ZN ! ZM )Systematic computer search (NP complete problem):Look for solutions of a set of diophantic equations:
(Intersecting) D6-brane statistics
![Page 19: Open String Amplitudes for Standard Model Quivers and ...GGI Firenze, 5.May 2009 Open String Amplitudes for Standard Model Quivers and their Application for the LHC Dieter Lüst, LMU](https://reader035.vdocuments.us/reader035/viewer/2022062915/5e95f81a8d767d2588000801/html5/thumbnails/19.jpg)
GGI Firenze, 5.May 2009
Z6’-orientifold:
Millions of standard models!
(Gmeiner, Honecker, arXiv:0806.3039)
!
P(models)
-710
-610
-510
-410
-310
-210
-110
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
SM gauge group, 3 generations with # of chiral exotics
How many orientifold models exist which come close to the (spectrum of the) MSSM?
(Blumenhagen, Gmeiner, Honecker, Lüst, Stein, Weigand; related work: Dijkstra, Huiszoon, Schellekens, hep-th/0411129; Anastasopoulos, Dijkstra, Kiritsis, Schellekens, hep-th/0605226; Douglas, Taylor, hep-th/0606109; Dienes, Lennek, hep-th/0610319)
Example: IIA orientifold:M6 = T 6/(ZN ! ZM )Systematic computer search (NP complete problem):Look for solutions of a set of diophantic equations:
(Intersecting) D6-brane statistics
![Page 20: Open String Amplitudes for Standard Model Quivers and ...GGI Firenze, 5.May 2009 Open String Amplitudes for Standard Model Quivers and their Application for the LHC Dieter Lüst, LMU](https://reader035.vdocuments.us/reader035/viewer/2022062915/5e95f81a8d767d2588000801/html5/thumbnails/20.jpg)
GGI Firenze, 5.May 2009
Z6’-orientifold:
Millions of standard models!
(Gmeiner, Honecker, arXiv:0806.3039)
!
P(models)
-710
-610
-510
-410
-310
-210
-110
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
SM gauge group, 3 generations with # of chiral exotics
ISB models with no chiral exotics
are possible!
How many orientifold models exist which come close to the (spectrum of the) MSSM?
(Blumenhagen, Gmeiner, Honecker, Lüst, Stein, Weigand; related work: Dijkstra, Huiszoon, Schellekens, hep-th/0411129; Anastasopoulos, Dijkstra, Kiritsis, Schellekens, hep-th/0605226; Douglas, Taylor, hep-th/0606109; Dienes, Lennek, hep-th/0610319)
Example: IIA orientifold:M6 = T 6/(ZN ! ZM )Systematic computer search (NP complete problem):Look for solutions of a set of diophantic equations:
(Intersecting) D6-brane statistics
![Page 21: Open String Amplitudes for Standard Model Quivers and ...GGI Firenze, 5.May 2009 Open String Amplitudes for Standard Model Quivers and their Application for the LHC Dieter Lüst, LMU](https://reader035.vdocuments.us/reader035/viewer/2022062915/5e95f81a8d767d2588000801/html5/thumbnails/21.jpg)
Outline
(The LHC string hunter’s companion)
● Intersecting D-brane models
● Mass scales in D-brane models
● Stringy amplitudes for the LHC
GGI Firenze, 5.May 2009
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GGI Firenze, 5.May 2009
III) Mass scales in D-brane models:
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GGI Firenze, 5.May 2009
There are 3 basic mass scales in D-brane compactifications:
III) Mass scales in D-brane models:
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GGI Firenze, 5.May 2009
There are 3 basic mass scales in D-brane compactifications:
III) Mass scales in D-brane models:
(1) : Ms =1!!!String scale:
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GGI Firenze, 5.May 2009
There are 3 basic mass scales in D-brane compactifications:
III) Mass scales in D-brane models:
(1) : Ms =1!!!String scale:
(2) : M6 =1
V 1/66
Compactification scale:
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GGI Firenze, 5.May 2009
There are 3 basic mass scales in D-brane compactifications:
III) Mass scales in D-brane models:
(1) : Ms =1!!!String scale:
(2) : M6 =1
V 1/66
Compactification scale:
(3) : M!p =
1
(V !p )1/p
, (3!) : M"6#p =
1(V "
6#p)1/(6#p)
V6 = V !p V "
6#p
Scale of wrapped D(p+3)-branes (e.g. IIB: p=0,4), (IIA: p=3):
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GGI Firenze, 5.May 2009
There are 2 basic 4D observables:
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GGI Firenze, 5.May 2009
There are 2 basic 4D observables:Strength of 4D gravitational interactions:
(A) : M2Planck !M8
s V6 ! 1019 GeV
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GGI Firenze, 5.May 2009
There are 2 basic 4D observables:Strength of 4D gravitational interactions:
(A) : M2Planck !M8
s V6 ! 1019 GeV
Strength of 4D gauge interactions:
=! (V !p )"1/p "Ms
(B) : g!2Dp !Mp
s V "p ! O(1)
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GGI Firenze, 5.May 2009
There are 2 basic 4D observables:
is a free parameter in D-brane compactifications ! Ms
(A) and (B): leave one free parameter.
Strength of 4D gravitational interactions:
(A) : M2Planck !M8
s V6 ! 1019 GeV
Strength of 4D gauge interactions:
=! (V !p )"1/p "Ms
(B) : g!2Dp !Mp
s V "p ! O(1)
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GGI Firenze, 5.May 2009
There are 4 natural scenarios for the string scale:
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GGI Firenze, 5.May 2009
There are 4 natural scenarios for the string scale:
(o) Planck scale scenario:
Ms !MPlanck " 1019 GeV
Gauge coupling unification at the Planck scales needs further effects (string threshold corrections, ...)
is the gravitational 4D Planck scale Ms
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GGI Firenze, 5.May 2009
Alternatively relate the string scale to particles physics mass scales.
Ms !MGUT " 1016 GeV
MGUT = MSM exp!
g!2Dp(MSM )!g!2
Dp(MGUT )
bp
"
(i) GUT scale scenario:
is the 4D scale of gauge coupling unificationMs
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GGI Firenze, 5.May 2009
Alternatively relate the string scale to particles physics mass scales.
Ms !MGUT " 1016 GeV
MGUT = MSM exp!
g!2Dp(MSM )!g!2
Dp(MGUT )
bp
"
(i) GUT scale scenario:
is the 4D scale of gauge coupling unificationMs
Recent GUT string model building in F-theory and IIB orientifolds: (Beasly, Heckman, Marsano, Saulina, Schafer-Nameki, Vafa;
Donagi, Wijnholt; Blumenhagen, Braun, Grimm, Weigand; Andreas, Curio)
● D7-branes wrapped on del Pezzo surfaces● GUT gauge group is broken by flux U(1)Y
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GGI Firenze, 5.May 2009
Ms !MSUSY " 1011 GeV
MSUSY !"
MSMMPlanck
(ii) SUSY breaking scenario:
is the intermediate 4D scale of supersymmetry breaking
Ms
Gravity mediation:
(No natural gauge coupling unification!)
(Balasubramanian, Conlon, Quevedo, Suruliz, ...)
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GGI Firenze, 5.May 2009
Ms !MSM " 103 GeV
(iii) Low string scale scenario:(Antoniadis, Arkani-Hamed, Dimopoulos, Dvali)
is the Standard Model (TeV) scale:Ms
(No natural gauge coupling unification!)
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GGI Firenze, 5.May 2009
Ms !MSM " 103 GeV
(iii) Low string scale scenario:(Antoniadis, Arkani-Hamed, Dimopoulos, Dvali)
Table 1: The three di!erent mass scales in D-brane models
Ms (GeV) Ls (m) M6 = V !1/66 (GeV) V 1/6
6 (m) M"2 = (V "2 )!1/2 (GeV) (V "2 )1/2 (m)
(o) 1019 10!35 1019 10!35 1019 10!35
(i) 1016 10!32 1015 10!31 1013 10!29
(ii) 1011 10!27 106!7 10!(22!23) 103 10!19
(iii) 103 10!19 10!14/6 10!14 10!13 10!3
Dimensionless volume in string units:
V!6 = V6M6
s = M2PlanckM2
s= 1, 106, 1016, 1032
SUMMARY:
is the Standard Model (TeV) scale:Ms
(No natural gauge coupling unification!)
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GGI Firenze, 5.May 2009
There are 3 generic type of particles:
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GGI Firenze, 5.May 2009
There are 3 generic type of particles:
Open string excitations: completely universal (model independent), carry SM gauge quantum numbers
MRegge = Ms = MPlanck!V !
6
M2n = M2
s
!n"
k=1
!µ!k!!
k ! 1
#= (n! 1) M2
s , (n = 1, . . . ,")
(i) Stringy Regge excitations:
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GGI Firenze, 5.May 2009
MT =MPlanck
(V !6)3/2
= 1019, 1010, 10"5, 10"29 GeV
Problem: the very light mass causes a fifth force.
(ii) Overall volume modulus:
Closed string, model independent, neutral under the SM, interacts only gravitationally
Would rule out TeV string scale !
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GGI Firenze, 5.May 2009
MT =MPlanck
(V !6)3/2
= 1019, 1010, 10"5, 10"29 GeV
Problem: the very light mass causes a fifth force.
(ii) Overall volume modulus:
Closed string, model independent, neutral under the SM, interacts only gravitationally
Would rule out TeV string scale !
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GGI Firenze, 5.May 2009
MT =MPlanck
(V !6)3/2
= 1019, 1010, 10"5, 10"29 GeV
Problem: the very light mass causes a fifth force.
(ii) Overall volume modulus:
Closed string, model independent, neutral under the SM, interacts only gravitationally
Would rule out TeV string scale !
!MT !< Tµ
µ Tµµ >
M2Planck
! M4s
M2Planck
! 10!13 GeV
But one expects a mass shift by radiative corrections:
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GGI Firenze, 5.May 2009
M!KK =
1
(V !p )1/p
!Ms =MPlanck
(V "6)1/2
Open strings, depend on the details of the internal geometry, carry SM gauge quantum numbers
(iii) D-brane cycle Kaluza Klein excitations:
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GGI Firenze, 5.May 2009
SUMMARY:The string Regge excitations (i) and the D-brane cycle KK modes (iii) are charged under the SM and have massof order ➠ can they be seen at LHC ?! Ms
M!KK =
1
(V !p )1/p
!Ms =MPlanck
(V "6)1/2
Open strings, depend on the details of the internal geometry, carry SM gauge quantum numbers
(iii) D-brane cycle Kaluza Klein excitations:
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GGI Firenze, 5.May 2009
Type IIB orientifolds: Realization of low string scale compatifications on „Swiss Cheese“ Manifolds:
(Abdussalam, Allanach, Balasubramanian, Berglund, Cicoli, Conlon, Kom, Quevedo, Suruliz; Blumenhagen, Moster, Plauschinn;
for model building and phenomenological aspects see: Conlon, Maharana, Quevedo, arXiv:0810.5660)
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GGI Firenze, 5.May 2009
Type IIB orientifolds: Realization of low string scale compatifications on „Swiss Cheese“ Manifolds:
(Abdussalam, Allanach, Balasubramanian, Berglund, Cicoli, Conlon, Kom, Quevedo, Suruliz; Blumenhagen, Moster, Plauschinn;
for model building and phenomenological aspects see: Conlon, Maharana, Quevedo, arXiv:0810.5660)
QL
Q
eLU(2)
U(3)
R
U(1)
U(1)
eR
BULKBLOW!UP
- SM lives on D7-branes around small cycles of the CY. One needs at least one blow-up mode (resolves point like singularity).
2 requirements: - Negative Euler number.
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GGI Firenze, 5.May 2009
Type IIB orientifolds: Realization of low string scale compatifications on „Swiss Cheese“ Manifolds:
(Abdussalam, Allanach, Balasubramanian, Berglund, Cicoli, Conlon, Kom, Quevedo, Suruliz; Blumenhagen, Moster, Plauschinn;
for model building and phenomenological aspects see: Conlon, Maharana, Quevedo, arXiv:0810.5660)
QL
Q
eLU(2)
U(3)
R
U(1)
U(1)
eR
BULKBLOW!UP
- SM lives on D7-branes around small cycles of the CY. One needs at least one blow-up mode (resolves point like singularity).
2 requirements: - Negative Euler number.
Moduli potential:
Kähler potential: K = Kcs ! 2 log!
V6 +!
2g32s
"
Superpotential: W = Wcs +!
Ai exp(!aiti)
Minima: Large hierarchical scales with V6M6s = 1016, 1032
Moduli stabilization ➣
(Becker,Becker, Haack, Louis)
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Outline
(The LHC string hunter’s companion)
(D. Lüst, S. Stieberger, T. Taylor, arXiv:0807.3333; L. Anchordoqui, H. Goldberg, D. Lüst, S. Nawata, S. Stieberger, T. Taylor, arXiv:0808.0497 [hep-ph]; arXiv:0904.3547 [hep-ph]D. Härtl, D. Lüst, O. Schlotterer, S. Stieberger, T. Taylor, to appear)
● Intersecting D-brane models
● Mass scales in D-brane models
● Stringy amplitudes for the LHC
GGI Firenze, 5.May 2009
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GGI Firenze, 5.May 2009
III) The LHC String Hunter‘s Companion:
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GGI Firenze, 5.May 2009
Test of D-brane models at the LHC:(New stringy physics of beyond the SM)
III) The LHC String Hunter‘s Companion:
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GGI Firenze, 5.May 2009
Test of D-brane models at the LHC:(New stringy physics of beyond the SM)
III) The LHC String Hunter‘s Companion:
New massive particles at string scale :Ms
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GGI Firenze, 5.May 2009
Test of D-brane models at the LHC:(New stringy physics of beyond the SM)
III) The LHC String Hunter‘s Companion:
New massive particles at string scale :Ms
- Massive extra (anomalous) U(1) gauge bosons Z !
(Abel, Goodsell, Jäckel, Khoze, Ringwald, arXiv: 0803.1449)
(also kinetic mixing of with photon and milli-charged particles)
Z !
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GGI Firenze, 5.May 2009
Test of D-brane models at the LHC:(New stringy physics of beyond the SM)
- Massive black holes (for strong string coupling)
III) The LHC String Hunter‘s Companion:
New massive particles at string scale :Ms
- Massive extra (anomalous) U(1) gauge bosons Z !
(Abel, Goodsell, Jäckel, Khoze, Ringwald, arXiv: 0803.1449)
(also kinetic mixing of with photon and milli-charged particles)
Z !
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GGI Firenze, 5.May 2009
Test of D-brane models at the LHC:(New stringy physics of beyond the SM)
- Regge excitations of higher spin
- Massive black holes (for strong string coupling)
III) The LHC String Hunter‘s Companion:
New massive particles at string scale :Ms
- Massive extra (anomalous) U(1) gauge bosons Z !
(Abel, Goodsell, Jäckel, Khoze, Ringwald, arXiv: 0803.1449)
(also kinetic mixing of with photon and milli-charged particles)
Z !
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GGI Firenze, 5.May 2009
Test of D-brane models at the LHC:(New stringy physics of beyond the SM)
- Regge excitations of higher spin
- Kaluza Klein (KK) (and winding) modes
- Massive black holes (for strong string coupling)
III) The LHC String Hunter‘s Companion:
New massive particles at string scale :Ms
- Massive extra (anomalous) U(1) gauge bosons Z !
(Abel, Goodsell, Jäckel, Khoze, Ringwald, arXiv: 0803.1449)
(also kinetic mixing of with photon and milli-charged particles)
Z !
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GGI Firenze, 5.May 2009
Test of D-brane models at the LHC:(New stringy physics of beyond the SM)
- Regge excitations of higher spin
- Kaluza Klein (KK) (and winding) modes
- Massive black holes (for strong string coupling)
III) The LHC String Hunter‘s Companion:
New massive particles at string scale :Ms
One has to compute the parton model cross sections of SM fields into new stringy states !
- Massive extra (anomalous) U(1) gauge bosons Z !
(Abel, Goodsell, Jäckel, Khoze, Ringwald, arXiv: 0803.1449)
(also kinetic mixing of with photon and milli-charged particles)
Z !
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l
W±
q
(a) baryonic
U(2)
(d) leptonic
U(1)R
(c) right
(b) left
e
u, d
U(3)
U(1)L
g
Open string Standard Model Quiver:
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l
W±
q
(a) baryonic
U(2)
(d) leptonic
U(1)R
(c) right
(b) left
e
u, d
U(3)
U(1)L
g
Open string Standard Model Quiver:
We want to compute all n-point, g-loop string amplitudes of SM model open string fields.
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l
W±
q
(a) baryonic
U(2)
(d) leptonic
U(1)R
(c) right
(b) left
e
u, d
U(3)
U(1)L
g
Open string Standard Model Quiver:
We want to compute all n-point, g-loop string amplitudes of SM model open string fields.
So far: n=4,5; g=0
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Parton model cross sections of SM-fields:
A(!1,!2,!3,!4) =< V!1(z1) V!2(z2) V!3(z3) V!4(z4) >disk
Disk amplitude among n external SM fields :(q, l, g, !, Z0, W±)
n = 4 :
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Parton model cross sections of SM-fields:
These amplitudes are dominated by the following poles:
A(!1,!2,!3,!4) =< V!1(z1) V!2(z2) V!3(z3) V!4(z4) >disk
Disk amplitude among n external SM fields :(q, l, g, !, Z0, W±)
n = 4 :
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Parton model cross sections of SM-fields:
These amplitudes are dominated by the following poles: ● Exchange of SM fields
A(!1,!2,!3,!4) =< V!1(z1) V!2(z2) V!3(z3) V!4(z4) >disk
Disk amplitude among n external SM fields :(q, l, g, !, Z0, W±)
n = 4 :
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Parton model cross sections of SM-fields:
These amplitudes are dominated by the following poles: ● Exchange of SM fields
A(!1,!2,!3,!4) =< V!1(z1) V!2(z2) V!3(z3) V!4(z4) >disk
Disk amplitude among n external SM fields :(q, l, g, !, Z0, W±)
n = 4 :
● Exchange of string Regge resonances (Veneziano like ampl.) ⇒ new contact interactions:
k1
k2
k3
k4
| k; n !!!2 "(2) trF 4!!2⇒
A(k1, k2, k3, k4;!!) ! "!("!!s) !(1" !!u)
!("!!s" !!u)=
"!
n=0
"(n)s"M2
n
! t
s" #2
6tu (!!)2 + . . .
Vt(!!) =!(1! s/M2
string)!(1! u/M2string)
!(1! t/M2string)
= 1! "2
6M"4
stringsu! #(3)M"6stringstu + · · ·" 1|!!#0
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Parton model cross sections of SM-fields:
These amplitudes are dominated by the following poles: ● Exchange of SM fields
A(!1,!2,!3,!4) =< V!1(z1) V!2(z2) V!3(z3) V!4(z4) >disk
Disk amplitude among n external SM fields :(q, l, g, !, Z0, W±)
n = 4 :
● Exchange of string Regge resonances (Veneziano like ampl.) ⇒ new contact interactions:
k1
k2
k3
k4
| k; n !!!2 "(2) trF 4!!2⇒
A(k1, k2, k3, k4;!!) ! "!("!!s) !(1" !!u)
!("!!s" !!u)=
"!
n=0
"(n)s"M2
n
! t
s" #2
6tu (!!)2 + . . .
Vt(!!) =!(1! s/M2
string)!(1! u/M2string)
!(1! t/M2string)
= 1! "2
6M"4
stringsu! #(3)M"6stringstu + · · ·" 1|!!#0
!(n) =tM4!2n
s
su n!
n!
J=1
(u + M2s J)
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Parton model cross sections of SM-fields:
These amplitudes are dominated by the following poles: ● Exchange of SM fields
● Exchange of KK and winding modes (model dependent)
A(!1,!2,!3,!4) =< V!1(z1) V!2(z2) V!3(z3) V!4(z4) >disk
Disk amplitude among n external SM fields :(q, l, g, !, Z0, W±)
n = 4 :
● Exchange of string Regge resonances (Veneziano like ampl.) ⇒ new contact interactions:
k1
k2
k3
k4
| k; n !!!2 "(2) trF 4!!2⇒
A(k1, k2, k3, k4;!!) ! "!("!!s) !(1" !!u)
!("!!s" !!u)=
"!
n=0
"(n)s"M2
n
! t
s" #2
6tu (!!)2 + . . .
Vt(!!) =!(1! s/M2
string)!(1! u/M2string)
!(1! t/M2string)
= 1! "2
6M"4
stringsu! #(3)M"6stringstu + · · ·" 1|!!#0
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The string scattering amplitudes exhibit some interesting properties:
● Interesting mathematical structure
(ii) They contain stringy corrections.
● They go beyond the N=4 Yang-Mills amplitudes:
(i) The contain quarks & leptons in fundamental repr.
Quark, lepton vertex operators:
Fermions: boundary changing (twist) operators!
Vq,l(z, u, k) = u!S!(z)!a!b(z)e""(z)/2eik·X(z)
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(i) Four point scattering amplitudes (2 jet events):
4 gluons:
2 gluons, 2 quarks:
Field theory factors:
!ij" = (!i)!(!j)!
Striking relation between quark and gluon amplitudes:
z4
Aa3Aa2
Aa1
a
a
z3
a
a
z1
z2
Aa4
A(g!1 , g!2 , g+3 , g+
4 ) = V (4)(!", ki)!M(4)YM
M(4)YM =
4g2YM!12"4
!12"!23"!34"!41"
N (4)YM =
4g2YM!14"!13"3
!12"!23"!34"!41"
A(g!1 , g+2 , q!3 , q+
4 ) = V (4)(!", ki)!N (4)YM
(Stieberger, Taylor)
(Lüst, Stieberger, Taylor)
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(i) Four point scattering amplitudes (2 jet events):
4 gluons:
2 gluons, 2 quarks:
Field theory factors:
!ij" = (!i)!(!j)!
Striking relation between quark and gluon amplitudes:
z4
Aa3Aa2
Aa1
a
a
z3
a
a
z1
z2
Aa4
A(g!1 , g!2 , g+3 , g+
4 )!!"0 !M(4)YM ,
!V (4) = 1 + !(2)O("#2)
"
M(4)YM =
4g2YM!12"4
!12"!23"!34"!41"
N (4)YM =
4g2YM!14"!13"3
!12"!23"!34"!41"
A(g!1 , g+2 , q!3 , q+
4 ) = V (4)(!", ki)!N (4)YM
(Stieberger, Taylor)
(Lüst, Stieberger, Taylor)
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(i) Four point scattering amplitudes (2 jet events):
4 gluons:
2 gluons, 2 quarks:
Field theory factors:
!ij" = (!i)!(!j)!
Striking relation between quark and gluon amplitudes:
z4
Aa3Aa2
Aa1
a
a
z3
a
a
z1
z2
Aa4
A(g!1 , g!2 , g+3 , g+
4 )!!"0 !M(4)YM ,
!V (4) = 1 + !(2)O("#2)
"
M(4)YM =
4g2YM!12"4
!12"!23"!34"!41"
N (4)YM =
4g2YM!14"!13"3
!12"!23"!34"!41"
A(g!1 , g+2 , q!3 , q+
4 )!!"0 ! N (4)YM
(Stieberger, Taylor)
(Lüst, Stieberger, Taylor)
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GGI Firenze, 5.May 2009
Any null-vector k2i = 0 can be written in terms of two spinors (!, !)
Momentum kµi !" Dirac spinor
!u+(ki)!
u!(ki)!
"!
!(!i)!
(!i)!
"
with choice u+(k) =1!2
!
""#
!k+
!k! ei!!
k+!
k! ei!
$
%%& , u!(k) =1!2
!
""#
!k! e!i!
"!
k+!
k! e!i!!
k+
$
%%&
k± = k0 ± k3
e±i! =k1 ± ik2
!k+k!
Define | i±! = u±(ki) , "i± | = u±(ki)
Spinor products:
!ij" := !i!|j+" = u!(ki) u+(kj) # !!" ("i)! ("j)" =!
kikj ei#ij ,
[ij] := !i+|j!" = u+(ki) u!(kj) # !!" ("i)! ("j)" = $!
kikj e!i#ij
u(k) = Dirac spinor, helicity states u±(k) = (1± !5) u(k)
=! "ij#[ji] = $kikj
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(ii) Five point scattering amplitudes (3 jet events):z2
a
z3
a
a
a
z1
z4z5
Aa5
Aa1 Aa3
Aa4
Aa2
a
z2
a
z3
b
a
a
z1
z4z5
!"5
#5
Aa1 Aa3
!#4
"4
Aa2
a
5 gluons:
3 gluons, 2 quarks:
Field theory factors:
(Stieberger, Taylor (2006))
(D. Lüst, O. Schlotterer, S. Stieberger, T. Taylor, work in progress).
A(g!1 , g!2 , g+3 , g+
4 , g+5 ) =
!V (5)(!", ki)! 2i"(1, 2, 3, 4)P (5)(!", ki)
""M(5)
YM
A(g!1 , g+2 , g+
3 , q!4 , q+5 ) =
!V (5)(!", ki)! 2i"(1, 2, 3, 4)P (5)(!", ki)
""N (5)
YM
N (5)YM =
4g3YM!15"!14"3
!12"!23" . . . !51"
M(5)YM =
4g3YM!12"4
!12"!23" . . . !51"
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(ii) Five point scattering amplitudes (3 jet events):z2
a
z3
a
a
a
z1
z4z5
Aa5
Aa1 Aa3
Aa4
Aa2
a
z2
a
z3
b
a
a
z1
z4z5
!"5
#5
Aa1 Aa3
!#4
"4
Aa2
a
5 gluons:
3 gluons, 2 quarks:
Field theory factors:
(Stieberger, Taylor (2006))
(D. Lüst, O. Schlotterer, S. Stieberger, T. Taylor, work in progress).
A(g!1 , g!2 , g+3 , g+
4 , g+5 )!!"0 !M(5)
YM ,!V (5) = 1 + !(2)O("#2) , P (5) = !(2)O("#2)
"
A(g!1 , g+2 , g+
3 , q!4 , q+5 ) =
!V (5)(!", ki)! 2i"(1, 2, 3, 4)P (5)(!", ki)
""N (5)
YM
N (5)YM =
4g3YM!15"!14"3
!12"!23" . . . !51"
M(5)YM =
4g3YM!12"4
!12"!23" . . . !51"
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(ii) Five point scattering amplitudes (3 jet events):z2
a
z3
a
a
a
z1
z4z5
Aa5
Aa1 Aa3
Aa4
Aa2
a
z2
a
z3
b
a
a
z1
z4z5
!"5
#5
Aa1 Aa3
!#4
"4
Aa2
a
5 gluons:
3 gluons, 2 quarks:
Field theory factors:
(Stieberger, Taylor (2006))
(D. Lüst, O. Schlotterer, S. Stieberger, T. Taylor, work in progress).
A(g!1 , g!2 , g+3 , g+
4 , g+5 )!!"0 !M(5)
YM ,!V (5) = 1 + !(2)O("#2) , P (5) = !(2)O("#2)
"
A(g!1 , g+2 , g+
3 , q!4 , q+5 )!!"0 ! N (5)
YM
N (5)YM =
4g3YM!15"!14"3
!12"!23" . . . !51"
M(5)YM =
4g3YM!12"4
!12"!23" . . . !51"
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k3
k2
k1
k4
k5
| k; n ! | k"; n" !
k3
k2
k1
k4
k5
| k; n !
The two kinds of amplitudes are universal: the same Regge states are exchanged:
● n-point tree amplitudes with 0 or 2 open string fermions (quarks, leptons) and n or n-2 gauge bosons (gluons) are completely model independent.
⇒ Information about the string Regge spectrum.
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4 gauge boson amplitudes:
z4
Aa3Aa2
Aa1
a
a
z3
a
a
z1
z2
Aa4
Only string Regge resonances are exchanged ⇒This amplitude is completely model independent!
Examples for squared amplitudes:
Disk amplitude:
⇒ dijet events
(Anchordoqui,Goldberg,Nawata, Taylor, arXiv:0712.0386)Observable at LHC for Mstring = 3 TeV
|A(gg ! gg)|2 = g43
! 1s2
+1t2
+1u2
"#94s2V 2
s (!!)" 13( sVs(!!))2 + (s# t) + (s# u)
$
|A(gg ! g!(Z0))|2 = g4356Q2
A
! 1s2
+1t2
+1u2
"( sVs("!) + tVt("!) + uVu("!) )2
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4 gauge boson amplitudes:
z4
Aa3Aa2
Aa1
a
a
z3
a
a
z1
z2
Aa4
Only string Regge resonances are exchanged ⇒This amplitude is completely model independent!
Examples for squared amplitudes:
Disk amplitude:
agreement with SM!!! ! 0 :|A(gg ! gg)|2!!!0 !
! 1s2
+1t2
+1u2
"94#s2 + t2 + u2
$
|A(gg ! !(Z0))|2!!!0 ! 0
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2 gauge boson - two fermion amplitude:
Only string Regge resonances are exchanged ⇒These amplitudes are completely model independent!
Note: Cullen, Perelstein, Peskin (2000)considered:
e+e! ! !!
z3
z4
z1z2
a b
a
!!4
"4
!"3!3
Aa Ab
z4!
!4
"4
!"3!3Aa
Aa
b
b
a
z3
a
a
z1
z2
⇒ dijet events
|A(qg ! q!(Z0))|2 = "13g43Q2
As2 + u2
sut2(sVs("!) + uVu("!))2
|A(qg ! qg)|2 = g43s2 + u2
t2
!Vs(!!)Vu(!!)" 4
91su
(sVs(!!) + uVu(!!))2"
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2 gauge boson - two fermion amplitude:
Only string Regge resonances are exchanged ⇒These amplitudes are completely model independent!
Note: Cullen, Perelstein, Peskin (2000)considered:
e+e! ! !!
z3
z4
z1z2
a b
a
!!4
"4
!"3!3
Aa Ab
z4!
!4
"4
!"3!3Aa
Aa
b
b
a
z3
a
a
z1
z2
!! ! 0 : agreement with SM !
|A(qg ! qg)|2!!!0 = g43s2 + u2
t2
!1" 4
91su
(s + u)2"
|A(qg ! q!(Z0))|2!!!0 = "13g43Q2
As2 + u2
sut2(s + u)2
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4 fermion amplitudes:
These amplitudes are more model dependent and test the internal CY geometry.
Exchange of Regge, KK and winding resonances.
Constrained by FCNC’s and/or proton decay.
E.g.
d
z2
!!4
"4
!#3!3
z1z4
b
z3
!"1$1
c
a
d
X1X4
!!4
"4
a
%4
c
%2
X2
d
b
X z
!$2
#2
!"1$1
X3
!#3!3
%3 %2
%1%4
!$2
#2
%1
%3
(Klebanov, Witten, hep-th/0304079; Abel, Lebedev, Santiago, hep-th/0312157)
depend on internal geometry
|A(qq ! qq)|2 =29
1t2
!"sF bb
tu (!!)#2 +
"sF cc
tu (!!)#2 +
"uGbc
ts(!!)
#2 +"uGcb
ts(!!)
#2$
+29
1u2
!"sF bb
ut (!!)
#2
+"sF cc
ut (!!)
#2 +"tGbc
us(!!)
#2 +"tGcb
us(!!)
#2$" 4
27s2
tuF
bb
tu(!!)F bb
ut (!!) + F cc
tu (!!)F ccut (!
!)#
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4 fermion amplitudes:
These amplitudes are more model dependent and test the internal CY geometry.
Exchange of Regge, KK and winding resonances.
Constrained by FCNC’s and/or proton decay.
E.g.
d
z2
!!4
"4
!#3!3
z1z4
b
z3
!"1$1
c
a
d
X1X4
!!4
"4
a
%4
c
%2
X2
d
b
X z
!$2
#2
!"1$1
X3
!#3!3
%3 %2
%1%4
!$2
#2
%1
%3
(Klebanov, Witten, hep-th/0304079; Abel, Lebedev, Santiago, hep-th/0312157)
!! ! 0 : agreement with SM !
|A(qq ! qq)|2!!!0 !49
!s2 + u2
t2
"+
49
!s2 + t2
u2
"" 8
27s2
tu
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● Discovery of Regge excitations: these stringy corrections can be seen in dijet events at LHC:
(Anchordoqui, Goldberg, Lüst, Nawata, Stieberger, Taylor, arXiv:0808.0497[hep-ph]arXiv:0904.3547 [hep-ph])
!Regge = 15! 150 GeV
Widths can be computed in a model independent way !
(Anchordoqui, Goldberg, Taylor, arXiv:0806.3420)
MRegge = 2 TeV
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● Discovery of Regge excitations: these stringy corrections can be seen in dijet events at LHC:
(Anchordoqui, Goldberg, Lüst, Nawata, Stieberger, Taylor, arXiv:0808.0497[hep-ph]arXiv:0904.3547 [hep-ph])
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● Discovery of Regge excitations: these stringy corrections can be seen in dijet events at LHC:
There are possible also stringy Drell-Yan processes like
qq ! ll
(Anchordoqui, Goldberg, Lüst, Nawata, Stieberger, Taylor, arXiv:0808.0497[hep-ph]arXiv:0904.3547 [hep-ph])
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● KK modes are seen in scattering processes with more than 2 fermions.
⇒ Information about the internal geometry.KK modes are exchanged in t- and u-channel processes and exhibit an interesting angular distribution.
(L. Anchordoqui, H. Goldberg, D. Lüst, S. Nawata, S. Stieberger, T. Taylor, arXiv:0904.3547 [hep-ph])
|A(qq ! qq)|2 =29
1t2
!"sF bb
tu (!!)#2 +
"sF cc
tu (!!)#2 +
"uGbc
ts(!!)
#2 +"uGcb
ts(!!)
#2$
+29
1u2
!"sF bb
ut (!!)
#2
+"sF cc
ut (!!)
#2 +"tGbc
us(!!)
#2 +"tGcb
us(!!)
#2$" 4
27s2
tuF
bb
tu(!!)F bb
ut (!!) + F cc
tu (!!)F ccut (!
!)#
Squared 4-quark amplitude with identical flavors:
Squared 4-quark amplitude with different flavors:
|A(qq! ! qq!)|2 =29
1t2
!"sF bb
tu (!!)#2 +
"sGcc!
tu (!!)#2 +
"uGbc
ts(!!)
#2 +"uGbc!
ts (!!)#2
$
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where, e.g.:
F bbtu = t Vabab(!t/M2
s ,!u/M2s )
Vabab(t, u) = 2!gs
! 1
0dx xt!1(1! x)u!1 I(x)
"
pa,pb"Ze!Sba
inst.(x)
Quantum part Instanton contribution from wrapped D-branes
2 kind of (unphysical) poles:
(i) x! 1 :(ii) x! 0 :
Pole in t
Pole in u
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Dominant contribution (after Poisson resummation at x=0):
F bbtu = 1 +
g2b t
g2au
+g2
b t
g2a
Np !u!M2
ab
! ! e!M2ab/M2
sM2ab = (M (b)
KK)2 + (M (a)wind.)
2 ,
Np : Np = 3Degeneracy of KK-states; take
! : Thickness of D-branes
KK of SU(2) branes and winding modes of SU(3) branes:
Mab :Mab = 0.7Ms
Gbctu = Gbc
tu = 1
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Dijet angular contribution by t-channel exchange:
CMS detector simulation:
1fb!1 10fb!1Luminosity
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GGI Firenze, 5.May 2009
Conclusions
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GGI Firenze, 5.May 2009
Conclusions ● There exists many ISB models with SM like spectra without chiral exotics.
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GGI Firenze, 5.May 2009
Conclusions ● There exists many ISB models with SM like spectra without chiral exotics.● One can make some model independent predictions:
String tree level, 4-point processes with 2 or 4 gluons ☛ observable at LHC ?? -
(Independent of amount of (unbroken) supersymmetry!)
Mstring??
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GGI Firenze, 5.May 2009
Conclusions ● There exists many ISB models with SM like spectra without chiral exotics.
Computations done at weak string coupling ! Black holes are heavier than Regge states: Mb.h. =
Mstring
gstring
● One can make some model independent predictions:
String tree level, 4-point processes with 2 or 4 gluons ☛ observable at LHC ?? -
(Independent of amount of (unbroken) supersymmetry!)
Mstring??
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GGI Firenze, 5.May 2009
Conclusions ● There exists many ISB models with SM like spectra without chiral exotics.
Computations done at weak string coupling ! Black holes are heavier than Regge states: Mb.h. =
Mstring
gstring
Question: do loop and non-perturbative corrections change tree level signatures? Onset of n.p. physics: Mb.h.
● One can make some model independent predictions:
String tree level, 4-point processes with 2 or 4 gluons ☛ observable at LHC ?? -
(Independent of amount of (unbroken) supersymmetry!)
Mstring??
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GGI Firenze, 5.May 2009
Conclusions ● There exists many ISB models with SM like spectra without chiral exotics.
Computations done at weak string coupling ! Black holes are heavier than Regge states: Mb.h. =
Mstring
gstring
Question: do loop and non-perturbative corrections change tree level signatures? Onset of n.p. physics: Mb.h.
● One can make some model independent predictions:
String tree level, 4-point processes with 2 or 4 gluons ☛ observable at LHC ?? -
(Independent of amount of (unbroken) supersymmetry!)
Mstring??
INTERESTING TIMES FOR STRING PHENOMENOLOGY ARE AHEAD OF US.
THANK YOU !!