Transcript Intersecting Brane Models and Phenomenology

Dynamical Supersymmetry
Breaking in String Models
Jason Kumar
University of California, Irvine
String Theory, Cosmology and
Phenomenology
• LHC is coming soon, WMAP is here, DM direct and indirect
– good chance to probe EWSB, SUSY, dark matter, inflation, etc.
• goal for string theory
– not necessarily to use LHC “prove or falsify string theory”
– instead, use string theory to provide insight about lower-energy physics
which you can probe at experiments
• string theory can access gravity, gauge, matter
– insights can connect to LHC, cosmology, phenomenology
• many string models
– don’t want to take one specific model and beat it to death
– instead, focus on lessons common to many models
• doesn’t give a “prediction of string theory”
– gives a motivated idea for what new physics might look like at the EFT
level
String models
• recent focus Type IIA/B
– non-perturbative physics gives many options
• gauge group, matter multiplicity and representations, etc.
– D-branes/open strings are the key
• need to get chiral matter
– branes at singularities
– intersecting brane models (IBMs)
• much work on both…
• we study IBMs
IBM Basic Idea
• compactify IIA/B on
orientifolded CY 3-fold
– 10D  4D ; N=8  N=1
• O-planes have spacetimefilling charge  need to cancel
(Gauss’ Law / RR-tadpoles)
• D-branes do the job (D6-brane
in IIA)
• open strings give gauge
theory, chiral matter
• Iab counts bifundamental chiral
matter
– sym., anti-sym from O-planes
• tower of string excitations also
• we want an SM-sector, plus
other sectors
• extra sectors are generic,
since we need to cancel
charge
• bifundamental matter is
generic, since 3-cycles on a 6manifold generally intersect
Standard Model example
SU(2)L
U(1)X
QL
LL
U(3)qcd
uR,dR
eR,nR
U(1)L
SU(2)R
•
general features we can use
– extra sectors with U(1)’s
– representations: bifundamental, symmetric, anti-symmetric
– SM particles not charged under U(1)X at tree-level
• pseudo-hidden sector
– generic chiral matter
• mixed anomalies canceled by Green-Schwarz mechanism
• cubic anomalies automatically cancel due to Gauss’ Law
– many excited string modes
A few different directions….
• general phenomenological issues….
– dynamical supersymmetry breaking
• arXiv:0710.4116
– mediation to Standard Model (w/ S. Kachru, E. Silverstein)
• LHC collider phenomenology
– coupling SM gauge bosons to extra U(1)
• arXiv:0707.3488 (w/ A. Rajaraman, J. Wells)
– modified trilinear WWZ couplings
• arxiv:0801.2891 (w/ AR, JW)
• cosmology
– inflation
• hep-th/0703278 (w/ B. Dutta, L. Leblond)
• non-gaussianity (w/ B. Dutta, L. Leblond)
– baryogenesis
• hep-th/0608188 (w/ B. Dutta)
– dark matter (w/ J. Feng)
Dynamical Supersymmetry
Breaking
•
would like to generate an exponentially low susy scale by dynamics
– not only explain why it’s stable, but why it’s low
•
standard way to generate low scale in EFT
– dimensional transmutation
– dynamics of non-abelian gauge group generates scale
• ISS; Kawano, Kitano, Ooguri, Ookouchi, etc.
•
difficulties in gauge mediation
–
–
–
–
•
gauge messengers could cause Landau poles [ SU(5)  NC > 5 – 10 ]
more scales (hierarchy between Ldyn and mq)
harder to arrange in simple IBM’s (get NF  NC)
nice to have other options anyway
AKS used D-instanton to generate low scale
– no non-Abelian dynamics
– inherently “stringy”
– fits in with branes at singularities
•
is there something similar for intersecting brane models?
Yukawa coupling
• in IBM setup, Yukawa
coupling arises from
worldsheet instantons
(Aldazabal, Franco, Ibanez, Rabadan, Uranga; Kachru, Katz,
Lawrence, McGreevy; Cremades, Ibanez, Marchesano; Cvetic,
Papadimitriou)
– l is exponentially
suppressed
– in large volume regime
(where moduli stabilization
is understood), we get
small number for free
• this is a stringy effect
– from EFT point of view, no
reason for l to be small
c
a
f1
f2
f3
W  123
e
A
l s2
b
Use small l to get a small scale
• D-terms will play a vital role
• start with a simple example 
3 intersecting branes
– gauge theories have nontrivial Fayet-Iliopoulos terms
– assume they are of some
“natural” scale (perhaps GUT)
which need not be small ~ x
– additional terms due to axions
• Green-Schwarz mechanism
• all superpotential terms are
non-perturbative
– dominated by some small l
g a2
g b2
2
1  2   a   2  3  b 2
VD 
2
2
g c2
3  1  c 2

2
~
W   123

~
2
2
2
2
2
2
VF   2 1 2  2 3  3 1
 
W1   i e ai i
i

 
W2   i , j e ak i j
i, j
Scaling of VF and VD
• of course, if l=0 we can
set VF=VD=0 by sitting on
a D-flat direction
– take xa,c > 0, xb < 0
• D-flat direction - r
• naturally get l  g
– i.e., g small, l
exponentially small
– VD  VF  x2
– moving on r is not a
runaway direction for VF
1
2
2
2
3
2
 2 
  a  O 2 
 g 
 2 
 O 2 
 g 
 2 
  b  O 2 
 g 
 a ,b , c ~ 
g a ,b , c ~ g
 1   2   3  r
2
2
2
 4 2 
VD ~ O 2 
 g 
VF ~ O 2 2


Basic points
• not dependent on specific form of potential or brane
configuration
• W coefficients exponentially suppressed
– end up on D-flat direction “corrected” by F-terms
• more F-term equations than D-flat directions
• F-term runaway direction is generically not a D-flat
direction
• VD  VF , but VF exponentially suppressed
• x depends on “hypermultiplet” moduli
– need to stabilize to avoid runaway to supersymmetric vacuum
– but we need to stabilize closed string moduli anyway for
phenomenological reasons
• we will assume closed string moduli stabilized
How to mediate to SM?
• consider an SU(5) GUT setup
10
U(5)GUT
– extra U(1) brane
5
• 5 from bifundamental
• 10 from antisymmetric
• generic bifund. matter
– gauge mediation natural
• want to include both the SU(5)
sector and DSB sector
– need to add a few extra
branes for anomaly
cancellation
– also to make sure generic
superpotential involves all
fields
• M1,2  gauge messengers
U(1)
• assume xGUT = 0 to avoid
breaking GUT at higher scale
– needed in any case,
independent of DSB mech.
• assume one limit for simplicity
• factors which affect pheno.
– scale of F
– scale of messenger masses
– scale of R-symmetry breaking
• gaugino masses
• each controlled by a different
Yukawa in this setup
• involves interplay between Dterm and F-term
– would be nice to find a version
with only F-term dynamics, ala
AKS
– working on this now….
W  11M 1M 2  2123  i31i 3  4  i42i 1 2
a, f  0
b , c , e , g  0
22 c  32 g  24  f  0
F 2  4  0
F3  2  0
mM1, 2  1
W  3 s 3
W  3
Dark Matter
• couple of interesting features inherent to IBM scenario
– many hidden gauge sectors
– gauge mediation between open string sectors generic (via
bifundamental matter)
• can have stable particles charged only under hidden
sector
– left over discrete symmetries could stabilize
• possible dark matter candidates?
– no SM charge
– if stable, they contribute to dark matter
• could be either good, or bad
• what are the general dark matter implications for this
type of scenario?
Setup
•
•
•
•
one sector breaks SUSY
gauge mediation to multiple sectors,
including SM sector
unbroken discrete symmetries
not a detailed IBM scenario
–
–
•
not worrying about details of genericity,
# of sectors, size of Yukawas, discrete
symmetries, etc.
looking at a motivated EFT scenario
in each sector, low-energy scale set by
contribution to fermion/scalar splitting
due to gauge interactions
–
–
–
SUSY
vector-like matter can be expected to
get mass at high (GUT) scale
non-vectorlike matter has no mass
scale, except that generated by gauge
mediation
much as susy-breaking scale in MSSM
sets the EWSB scale and everything
else (up to small Yukawas)
hidden
MSSM
Gauge mediation
• “WIMP miracle”
– stable matter with weak group coupling and EWSB
scale mass would lead to approximately the right relic
density for dark matter
– R-parity can stabilize the LSP
• expect to be couple with SU(2) strength and with mass ~
EWSB scale in gravity mediation
• in gauge mediation, gravitino is LSP (very light)
– no good DM candidate  gravitino DM density too large
– WIMP miracle points to gravity mediation and
conserved R-parity
• lots of work connecting dark matter and the EWSB scale
– but is the miracle really so miraculous?
Scaling
• we assume that F and Mmess
are set by the dynamics of
susy-breaking sector
– same for all gauge sectors
• in each sector, ratio of gauge
coupling to scalar mass is
approximately fixed
• same ratio determines
annihilation cross-section via
gauge interactions
– determines relic density
– if MSSM gets it right, so does
every other sector
g 4 N mess.  F 
2


mscalar 
4 
m
4   mess. 
2
2
g h4  mmess. 

  const.
mh2  F 
1
 g h4 
 F 
1


  2   
v  mh 
m
 mess. 
2
Upshot
• we find in this scenario, a generic charged stable particle should
have the right density (order of magnitude) to be dark matter
• maybe WIMP miracle isn’t that miraculous … any gauge sector with
any coupling would have worked
• in fact, it should have worked for the MSSM in gauge-mediation
– two stable particles  the LSP and the electron
– first accident  electron Yukawa coupling is extremely (perhaps
unnaturally) small
• mass much lighter than normal scale
• a “natural” mass would be mtop
• if electron mass were ~ mtop, would have the right relic density
– second accident  in gauge mediation, the LSP is not gauge charged
• but in any other sector, a discrete symmetry can stabilize a hidden
sector gauge charged particle
– in the right ball-park for dark matter
– distinct from gravity mediated result, where it really is a miracle
But what about detection?
• if hidden sector not coupled to
visible sector, all DM
annihilations could be invisible
SM
SM
Y
– in this case, could not detect
DM by direct, indirect or
collider
• only by astronomical
observation
• but if hidden sector couples to
SM sector, very interesting
detection scenarios
X
X
SM
– could couple to SM particles
via Yukawa or gauge
couplings
– Yukawa coupling especially
interesting, as it could be O(1)
SM
'
• assume fewer SM final states
X
X
Indirect Detection possibilities
•
•
dark matter at galactic center
annihilates to SM particles, which
emit photons detected at gamma
ray telescopes
– photon flux scales as (# density)2
– larger signal at small MX
take scenario with Yukawa
coupling to SM
– X is the light hidden sector scalar
• stabilized by discrete symmetry
• mass ~ 5 GeV
– Y is a fermion with both hidden
and SM charge
• gains mass from both hidden and
SM gauge interactions
• mass ~ 1 TeV
•
coupled to SM up-quarks
– W = lXYLQL + lXYRuR +mYLYR
– l is O(1)
• with this scenario, GLAST
could probe for halo density
J ~ 3 , l ~ 0.3
– this is the lower end of
what various theories
predict
– most dark matter models
do not allow one to probe
this region
 
 Ethr   7 109 cm2 s 1 4 J
Direct Detection limits
•
•
•
need to see if this is ruled out by direct
detection bounds
DM passing through earthbound
detector transfers momentum to
nucleus via elastic scattering
expect not bounded
–
–
•
direct detection sensitivity scales with
number density
goes bad ~ 10 GeV
can compute direct detection limits
  4 685 pb 
–
•
for l and MX in our range, not ruled out
by direct detection
note, could have coupled to t instead
of up-quark
–
–
then indirect detection sensitivity is
basically the same
but no direct detection possibility
Dan Hooper
SUSY ‘07
Conclusion
• string theory can be a powerful generator of
ideas for new physics
– the tight constraints of consistent quantum gravity can
illustrate new scenarios and features which otherwise
would be less noticed
• phenomenology, collider physics, cosmology
– ideas aren’t exclusive to string theory (and thus
neither prove nor falsify), but the question is if they
satisfy the “usefulness” test
• much more to learn ….