Predictions by string theory?

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Predictions by string theory?
f0(1500) ? 4p0 Suppressed
w/ C.I.Tan and S.Terashima, 0709.2208
Charge radius of Roper 0.73fm
w/ T.Sakai and S.Sugimoto, to appear
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ID of QCD glueball?
? Scalar glueball
(ex ? meson, ? baryon)
Lattice prediction of lightest glueball mass
1600MeV
0 state
We need theoretical description of glueball decay!
Perturbative QCD
Chiral perturbation
Difficult
Mixings?
Lattice QCD
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A Solution Holographic QCD
String theory
Step 1
4D gauge theory _at_ large Nc, large ?
10D classical gravity on curved background
Gauge/Gravity correspondence
Step 2
10D classical gravity flavor D-brane on
curved background
QCD _at_ large Nc, strong coupling
Holographic QCD
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D-branes giving the duality
Step 1
Quantizing Strings defined in 10D spacetime
Open string ? massless gauge field Closed
string ? massless graviton
D-branes Object on which open strings can end
Nc parallel Dp-branes
Source of closed strings Source of gravity
Extended blackhole blackbrane in 10D
Open string theory on the Dp-brane is SU(Nc)
gauge theory in p1 dimensions
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Nc open strings
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Gauge/Gravity correspondence
Black brane
Nc D-branes
Propagation of SU(Nc) gauge theory composite
states
Propagation of graviton in near-horizon
geometry of black p-brane
(glueball)
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Introducing quarks
Step 2
Nf flavor D-brane
SU(Nf) gauge fields in higher dim. D-brane on
curved background
Propagation of meson
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We get interacting hadrons from strings
Einstein action higher dim. YM action
on curved background in 10D
Decomposition by fields in 4 dimensions
Glueball Meson interacting action
No mixing, Coefficients computed explicitly
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Power of holography
Decay width
Experiments f0(1500) PDG
Decay branch
Holographic QCD
0.040
0.025
0.059
0.035
No decay
0.0090
0.0050
No decay
not seen
f0(1500) can be identified as a pure glueball
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(No Transcript)
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Decay width and branching ratios
Decay width of each branch
not produced
If we tune the glueball mass and eta mass by hand
so that it can fit the experimental data, then
Comparison In experiments, f0(1500) decays as
Our results are consistent
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What is the ID of Glueballs?
Glueballs Bound state consisting only of
Gluons, among many hadrons appearing
at low energy of QCD.
? Scalar glueball
(ex ? meson, ? baryon)
Mystery of Glueballs
Which is the glueball, among states observed with
?
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Difficulties in identifying the glueball

Diff.(1) Perturbative analysis is impossible due
to strong coupling at low energy of QCD.
This is related to the mass-gap problem in
YM, which is a millenium problem!
Diff.(2) Lattive QCD predicts that the lightest
glueball has and its mass should
be around 1600 MeV. But it cannot calculate
dynamical decay process, so no more
comparison is available.
Diff.(3) There are many hadrons having the same
quantum number , so the glueball is
mixed among mesons. Generally mass eigen
states are mixed.
Diff.(4) Chiral perturbation cannot be applied to
glueball dynamics, since glueballs live not
really in low energy.
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Glueball Decay in Holographic QCD
27th Nov., 2007 _at_ KEK

• Koji Hashimoto (RIKEN)

arXiv/0709.2208(hep-th) w/ Seiji Terashima(YITP)
and Chung-I Tan(Brown U)
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Plan of todays talk

• 1. Mystery of Glueballs
• 2. Holographic QCD
• From String Theory to Hadrons
• 3. Glueball Decay

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1. Mystery of Glueballs
What is the ID of Glueballs? Present status of
Glueball searches Power of Holographic QCD
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What is the ID of Glueballs?
Glueballs Bound state consisting only of
Gluons, among many hadrons appearing
at low energy of QCD.
? Scalar glueball
(ex ? meson, ? baryon)
Mystery of Glueballs
Which is the glueball, among states observed with
?
17
RefPDG data of decay of glueball candidates
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Difficulties in identifying the glueball

Diff.(1) Perturbative analysis is impossible due
to strong coupling at low energy of QCD.
This is related to the mass-gap problem in
YM, which is a millenium problem!
Diff.(2) Lattive QCD predicts that the lightest
glueball has and its mass should
be around 1600 MeV. But it cannot calculate
dynamical decay process, so no more
comparison is available.
Diff.(3) There are many hadrons having the same
quantum number , so the glueball is
mixed among mesons. Generally mass eigen
states are mixed.
Diff.(4) Chiral perturbation cannot be applied to
glueball dynamics, since glueballs live not
really in low energy.
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Present status of glueball ID proposal

PDG prediction is f0(1500)glueball
Reason
f0(1370) can be produced by 2? and thus composed
by charged quarks. f0(1710) decays mainly to 2K,
thus strangeness should be the main component.
But, no one could compute these. Not decisive!
Our motivation, and Result
Holographic QCDApplication of AdS/CFT to QCD
Holographic QCD enables us to compute spectra and
couplings of/among composite states of stronly
coupled QCD!
Decay products, width, branching ratios
Computable! (but at
large Nc)
Conclusion f0(1500) is the glueball
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2. Holographic QCD
AdS/CFT From AdS/CFT to QCD Sakai-Sugimoto
model The model and experimental data
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Very brief history of string theory and AdS/CFT
1960s70s String theory was born in hadron
physics
Regge trajectory, s-t channel duality, tHooft
large N, .
?
1970s80sString as quantum gravity and
unification
Standard model and superstrings, supergravity
Late in 1990sRevolution by D-branes and duality
Toward non-perturbative definition AdS/CFT
(gauge/string duality)
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AdS/CFT Equivalence of two ways to describe
D-branes
Maldacena(97)
Open string (gauge theory)
Closed string (gravity)
Closed string in blackbrane background of N
D3-branes
Low energy effective action of open strings on N
D3-branes
10 dim. supergravity in curved backgrounds
4dim. gauge theory
Corresp.
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Theories in correspondence
super Yang-Mills
Open string side
with the low energy limit
Supergravity on
Closed string side
Near horizon geometry of BPS black 3-brane
solution in 10 dimensions
This classical geometry is valid when
is required
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Physical quantities in correspondence

Correlation functions in gauge theory can be
computed by gravity theory.
Gubser-Klebanov-Polyakov Witten
Bulk fields in supergravity
Gauge invariant composite operators in YM theory
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Holographic QCD (AdS/QCD)
Philosophy
AdS/CFT deals with strongly coupled gauge
theories Then why not QCD?
Present status
It reproduces various characteristics of low
energy hadron physics and provides a new
viewpoint (paradigm), though with some
difficulties
Difficulties
Large N Decoupling of higher dimensional DoF
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Sakai-Sugimoto model (hep-th/0412141)
Open string side (D-branes)
Nc D4-branes wrap , and gauginos
satisfy anti-periodic boundary condition ?
4d pure Yang-Mills at low energy Nf D8-branes
intersect with the D4s ? Nf left-handed
massless quarks Nf anti-D8-branes intersect
with the D4s ? Nf right-handed massless
quarks
Witten
Massless QCD is brane-engineered at low energy
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Closed string side (gravity)
D8s are put there as probes (probe
approximation, valid at )
Near horizon geometry of black 4-brane solution
on which fermions satisfy the anti-periodic b.c.
is
Witten
Once the correspondence is applied
gravity ? bound states of gluons(Glueballs)
D8 ? bound states of quarks(Mesons, Baryons)
KK modes of gauge fields on the D8 ? Meson
D8-brane action ? Chiral lagrangian
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The role of the D8-branes

D4
D8
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Spontaneous chiral symmetry breaking
Chiral symmetry
Gauge symmetries on the D8 and anti D8

Massless QCD (weak coupling description)
Replacing the D4 by its gravity solution
Spontaneous chiral SB at strong coupling
D8s are connected, and gauge symmetry is
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Meson sector in the SS model
D8-brane action on the curved background
Metric induced on the D8 by the D4-brane graviy
solution is
Redefinition of coordinates
KK decomposition of this YM theory on the curved
background is the meson lagrangian
AdS/CFT
KK modes of ? Vector mesons A KK mode of
? Pion
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Action is evaluated as
KK modes of gauge field
Eigen equation for the modes
Pion is given by the zeroth mode of the
decomposition
Higher modes are absorbed by field redefinition

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Final lagrangian quadratic in KK modes is
Eigenvalues correpond to masses of vector mesons.
Comparison with observed data
Meson interactions can be computed from YM
interactions.
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3. Glueball Decay
Summary We describe decay of lightest
glueball in QCD by using AdS/CFT. The computed
decay products and width are consistent with a
hadron f0(1500) which is a glueball candidate.
arXiv/0709.2208(hep-th) Seiji Terashima(YITP) and
Chung-I Tan(Brown)
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Our strategy
Using holographic QCD, we compute analytically
interactions between Glueballs and Mesons /
photons, calculate the decay products and
widths, and compare them with experimental data.
Gauge (QCD) side
Gravity side
Our work
Gravity fluctuations around near horizon
geometry of non -BPS black 4-brane(Witten)
We compute couplings between the two sectors in
the gravity side, and describe the glueball decay
Gluon sector (Glueballs)
Csaki,Ooguri,Oz,Terning(98) Brower,Mathur,Tan(00)
Gauge fluctuation on the probe D8
(Sakai-Sugimoto)
Quark sector (Mesons)
Sakai,Sugimoto(04,05)
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Review Computing Glueball spectrum via AdS/CFT

Gravity background dual to 4d pure YM(Witten)
Wrap a D4-brane around a circle, and impose
anti-periodic boundary condition for the fermions
to break the SUSY
Supergravity fluctuation ocrresponding to the
lightest glueball (ConstableMyers,
BrowerMathurTan)
eigenfunction in higher dim
Glueball field
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Glueball spectrum obtained in AdS/CFT
Lattice calculation (SU(3) pure YM)
(BrowerMathurTan,2003)
(MorningstarPeardon,1999)
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Computing the coupling between glueballs and
mesons
Glueball ? Gravity Meson ? Gauge (on D8)
? correspondence
? In string theory, all the interactions between
gravity and D8 gauge fields are encoded in
D8-brane action
We substitute gravity and D8 gauge
fluctuations representing the mesons and
glueballs, and perform the integration of higher
dimensional space
We obtain interacting lagrangian of glueball /
meson fields
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Result
Glueball , Pion ,?meson
Kinetic terms
No mixing between mesons and lightest glueball
Interaction terms
(This expression is for a single flavor, for
simplicity)
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Possible decay process of the lightest glueball

Interaction terms obtained via AdS/CFT
YM
? CS
Among these, (ii)(iii) includes more than 5 pions
after the decay and so are negligible. Possible
decay processes are
These reproduces decay products of f0(1500)
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Decay width and branching ratios
Decay width of each branch
not produced
If we tune the glueball mass and eta mass by hand
so that it can fit the experimental data, then
Comparison In experiments, f0(1500) decays as
Our results are consistent
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4. Summary and Prediction
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Summary
Holographic QCD can really help computing
interactions among hadrons. It enables us to
compute glueball interactions analytically, and
f0(1500) can be identified as a scalar glueball.
Other results
Other decay process No decay to 2? ?
f0(1370) is not a glueball Small decay width
to 2K? f0(1710) is not a glueball Prediction No
decay of f0(1500) to 4 p0
Many more can be computed similarly
Interactions of heavier glueballs (with different
spins etc) Glueball-glueball interactions
Glueballs in finite temperature, finite baryon
density,