Introduction • iQuarks Production at LHC • Prompt Annihilation (After Energy Loss) • Summary •

Some Phenomenology of iQCD

Tzu-Chiang Yuan (阮自強) Academia Sinica, Taipei

Collaborators: Kingman Cheung and Wai-Yee Keung

From LHC to the Universe

NTU-U.C. Davis Meeting

Dec. 15-18 (2008)

Outline

• Introduction

• iQuarks Production at LHC

• Prompt Annihilation (After Energy Loss)

• ^Summary

Quirky papers

• Kang and Luty, arXiv:0805.4642

• Jacoby and Nussinov, arXiv:0712.2681

• Kang, Luty and Nasri, JHEP 0809, 086 (2008) hep-ph/0611322

• Burdman, Chacko, Goh, Harnik and Krenke, PRD78:075028 (2008) [arXiv:0805.4667]

• Cheung, Keung and Yuan, Nucl.Phys. B in press [arXiv:0810.1524]

• Harnik and Wizansky, arXiv:0810.3948

• Cai, Cheng and Terning, arXiv:0812.0843

• Bjorken, SLAC-PUB-2372 (1979)

• Okun, JETP Lett. 31, 144 (1980); Nucl. Phys. B173, 1 (1980)

• Gupta and Quinn, PRD 25, 838 (1982)

Older papers

Introduction

Hidden Strongly Interacting Sector ?

Or New Physics NOT (directly) related to EW symmetry breaking ?

• A Familiar Example: Extra Z boson models

• Hidden Valley Models (Strassler)

• Unparticle (Georgi)

• Quirks and infracolor QCD (Luty)

Un-motivation

Nuclear Phystcs B173 (1980) 1-12

© North-Holland P u b h s h m g C o m p a n y

T H E T A P A R T I C L E S

L.B. O K U N

Institute of Theorettcal and Experimental Physics, Moscow, 117259 USSR Received 4 March 1980

The hypothesis is considered, according to whtch there exist elementary particles of a new type, theta parttcles, thetr gauge interaction being characterized by a macroscopic radius of confinement. The quanta of the corresponding gauge held, thetons, are massless vector parttcles, analogous to gluons. The bound systems of two or three thetons have macroscopic dimensions.

The existence of such objects is not excluded by experiment, as the Interaction of thetons wtth ordinary particles must be very weak. However, the production of heavy theta leptons and theta quarks at accelerators would open the way to intensive creataon of thetons and theta strings.

1. Introduction: what we call O-particles

. In a recent letter [1] a hypothesis was put forward on the existence of a new type of particle, the interaction of which has a macroscopic confinement radius. This interaction is caused by non-abelian gauge fields, whose quanta (we denote them 0 and call thetons) are massless neutral vector particles, analogous to gluons. At distances of the order of 1 G e V - 1 (we use units, in which h = ¢ = 1), the interaction between thetons is characterized by a coupling constant of the order of a ( a = - - I ) 137 "

The strength of this interaction, however, does not drop as two thetons go apart, and the interaction energy grows. This leads to a number of very unusual physical p h e n o m e n a which are displayed at macroscopic distances. The aim of this paper is to consider these p h e n o m e n a in more detail and to discuss the possibilmes of their experimental detection.

As we shall see, these possibilities crucially depend on whether other particles, besides thetons, exist, which possess 0 charges, that is, which can emit and absorb thetons. We shall consider two types of such particles: 0-1eptons (~0) and 0-quarks (q0). We define as 0-1eptons such hypothetical particles, which, like the ordinary leptons, interact with intermediate bosons (W, Z) and, if they are charged, with photons (y), but which, besides that, interact with thetons (0). The 0-quarks are coupled not only to W, Z, 7, 0, but to ordinary gluons as well. All the data obtained up to now at accelerators and m cosmic ray experiments do not exclude the existence of such particles if their masses are larger than ~ 15 GeV. If the masses of 0-1eptons and 0-quarks are close to this lower limit, these particles will be

2 L.B. Okun / Thetaparttcles

produced and observed when the energy of e + e - colliding beams becomes higher.

Of course, we may be not so lucky, if the masses of 0-fermions are higher, say, than 1 TeV.

One of the most exciting physical objects is the 0-strings. The radius of the string is equal to the confinement radius, but its length is unlimited. Such strings unlike gluonic strings, are absolutely unbreakable. They do not interact with ordinary matter and go freely through any material object, for instance, through the Earth.

It is very interesting that the most stringent lirmts on the possible properties of 0-particles are imposed by the big bang cosmology. We shall consider them at the end of this paper. As we shall see, these limits are so stringent that they practically leave no place for such particles as theta-neutrinos and not very heavy theta quarks.

2. Why a new local group S U ( N ) 0 is not implausible

As is well-known, the existing theory of electroweak [2] and strong [3, 4] interac- tions is based on gauge groups U ( 1 ) x SU(2)w! SU(3)¢, their quanta being 7, W, Z, g. Alongside these groups, a number of other groups is considered in literature: for instance, the so-called "technicolor" [5] S U ( N ) t ¢ with its tech- nigluons, and the so-called horizontal [6] group SU(N)h. A vast literature exasts on the so-called models of grand unification [7] SU(5),SO(10),SO(14) . . . . In the highest of these groups there are dozens and even hundreds of gauge particles. In this atmosphere the hypothesis on existence of another three (SU(2)s) or eight (SU(3)0) gauge particles does not look very courageous. So we postulate that the entire local group has the form:

U(1) ! SU(2)w ! SU(3)c ! . . . ! S U ( N ) a .

It may turn out that the 0-group may help to solve some problems on the way to grand unification, but we will not pursue this possibility here.

3. Why the existence of a large radius of confinement is not implausible

The main difference between the group S U ( N ) and other gauge groups, consid- ered in the literature, is that the 0-group has a very large and maybe even macroscopic radius of confinement. Let us show by tracing the analogy with QCD, that this assumption also does not look fantastic. As is well-known, confinement for QCD is not yet proved; nevertheless, the excellent quantitative agreement of QCD with experiment, and the absence [8] of free quarks around us (see, however, ref. [9]) make us believe that SU(3)c confines. Furthermore, QCD phenomenology suggests that A c is not far from 0.1 GeV, where 1 / A c is the confinement radius. It is this quantity which determines the scale of masses of light mesons and baryons (light means consisting of u- and d-quarks). It is essential, that the so-called

Infracolor QCD of Kang and Luty

New confining strong interaction with

In particular

Λ ^! ! TeV Λ ^! ! M ^Q

In QCD Λ

_QCD

> m

_π

, light quark-antiquark pairs can be easily created from the vacuum by string breaking

In infracolor QCD, there are no light quirks.

Heavy quirk-antiquirk pairs created from the vacuum by string breaking are exponentially suppressed.

In infracolor QCD, quarks becomes quirks, gluons becomes infracolor gluons.

Quirks carries both infracolor and SM quantum numbers

Unbreakable Strings Unbreakable Strings

Unbreakable Strings

Unconfined

Confined breakable string => Independent fragmentation

Confined unbreakable string

!

confinement radius

light quark pair creation

Tension ≈ Λ

^!2

Couloumb potential dominates for small r

Λ ! 2m ^q

(Λ ^! ! 2m ^Q )

Suppression of soft hadronization

[Bjorken (1979); Gupta and Quinn (1982)]

NP stringy effect is important, not suppressed at high Q squared

x

unbreakable string

QCD

iQCD

quirk ↔ iquark infracolor gluon ↔ igluon

infracolor glueball ↔ iglueball etc

Trendy names suggested

infracolor Object ↔ iObject

(e.g. iMesons, iBaryons, etc)

Size of the string

Phenomenology depends sensitively on size of string!

Kinetic Energy of iQuark ~ String Potential Energy

String potential energy ≈ Λ ^!2 L

L ≈ M _Q

Λ ^!2 ≈ 10 m

! M _Q TeV

" ! Λ ^!

100 eV

" ₋₂ K.E. = √

ˆs − 2M ^Q ∼ M ^Q

Macroscopic String

100 eV ≤ Λ ^! ≤ 10 keV <==> mm ≤ L ≤ 10 m

(Luty’s Talk)

Reconstruction algorithms fail to identify quirky tracks → Missing Energy quirky tracks

=> iQuarks pair not easily meet to form bound states.

But one single quirky track event is sufficient for its discovery.

Energy loss mechanism: bremsstrahlung, ionization, etc.

Quirks in the detector (Luty, Kang and Nasri) For values of ! of order 100 eV or less there is a

significant probability for quirks to enter the detector. The string tension causes their tracks to bend differently than those of muons and other charged particles. In such a scenario a single event might suffice for discovery!

String tension causes the quirky tracks bent differently from those SM charged particles

Large lever arm =>Angular momentum de-coherence

•

Too small to be resolved in detector but larger than atomic scale

•

iQuark-anti-iQuark pair appears as single particle in the detector

•

Matter interaction might be efficient to randomize angular momentum and prevent annihilation

•

Otherwise, might lead to displaced vertex before annihilation

Mesoscopic String

10 keV ≤ Λ ^! ≤ MeV ↔ A ≤ L ≤ mm

^o

Microscopic String

MeV ≤ Λ ^! ≤ GeV ↔ 100 fm ≤ L ≤ 100 A

K.E. ≈ M ^Q ↔ highly excited

iQuarks are confined into bound states Salient features:

J ≈ rp ≈ M _Q ⁻¹ M _Q ≈ 1

o

L ! Λ ^!−1 ↔ classical string

=> nearly spherical

Prompt annihilation of these highly excited states?

No large lever arm to randomize angular mom

Soft Energy Loss

QCD “brown muck” interactions energy loss

∆E ∼ GeV each crossing

Energy Loss when 2 iQuarks cross (Prevent Annihilation)

QCD/iQCD ``brown muck/imuck’’ NP interactions

==> Energy Loss

(i)glueballs

Fig. 9. Schematic depiction of hadronic fireball and hard annihilation into muons. Note that the the asymmetry of the muons and the fireball are in the same direction.

particle invariant mass distribution of the produced quirks. This gives an additional handle on these events.

5.7 Non-perturbative Infracolor Interactions

We now consider non-perturbative infracolor interactions of the quirks. There are many analogies with the non-perturbative QCD interactions of colored quirks dis- cussed in the previous subsection, so our discussion will be brief and highlight the important differences.

The infracolor “brown muck” has a geometrical cross section for interaction, so we also expect ∼ 1 interaction per classical crossing time. As argued in Subsection 3.3, radiation of infracolor glueballs takes place only while the quirk separation is less than or of order Λ⁻¹. The non-perturbative infracolor interactions will therefore give rise to the emission of only ∼ 1 infracolor gluons with total energy ∼ Λ.

One important difference with the QCD case is that the infracolor hadrons gen- erally do not interact after they are emitted, and therefore their angular position is probably not “measured” on time scales relevant for colliders. The cross section for an infracolor glueball with energy ∼ Λ to scatter e.g. via γg → γg is of order

σ ∼ 1 16π

Λ⁶

m⁸_Q ∼ 10⁻¹⁶σ_W

! Λ

GeV

"4! m_Q TeV

"₋₈

, (5.61)

where σ_W ∼ Λ²/16πM_W² is a typical weak cross section. However, even if we assume that quantum coherence is maintained between the angular wavefunction and the wavefunction of the emitted infracolor hadrons, we still expect the probability to find

34

hadronic fireball

∆E ∼ GeV or Λ

^!

per crossing

Bjorken’s picture

Angular Decoherence

each crossing Prob(J = 0) ∼ 1

√ N after crossings N Losing all kinetic energy to soft hadrons:

Prob ∼ (1 − P

⁰

)

!

1 − P

₀

√ 2

"

· · ·

!

1 − P

₀

√ 100

"

∼ 50%

N

_cross

∼ m

_Q

GeV ∼ 100

Hadronic “fireballs”

(Kang and Luty)

NP interaction effective up to l

_max

∼ M

^Q

/Λ ∼ 10

³

Total number of crossings ∼ M

^Q

/Λ ∼ 10

³

R ∼ Λ⁻¹ or Λ^"−1

Wave function overlapp (WKB)

Energy loss (visible or invisible)

photons

Soft stuff

hard SM stuff

Geometric cross section

Can iGlueballs detectable?

iGluons do not carry SM charge ==> Loop Effects

Fig. 1. Loop graphs contributing to the coupling of the standard model and infracolor sector.

The operator Eq. (2.1) mediates infracolor glueball decay, for example to photons or gluons. The rate is of order

Γ ∼ 1 8π

! g²g^!2 16π²m⁴_Q

"₂

Λ⁹. (2.2)

Note that this is very sensitive to both Λ and m_Q. We have cτ ∼ 10 m

# Λ

50 GeV

$−9# m_Q TeV

$₋₈

. (2.3)

We see that the infracolor glueballs can decay inside a particle detector for Λ >∼ 50 GeV, while the lifetime becomes longer than the age of the universe for Λ <∼ 50 MeV.

2.2 Star Cooling

Stars with temperature T >∼ Λ can potentially cool due to emission of infracolor glueballs. Due to the rapid decoupling of infracolor interactions from standard model interactions in Eq. (2.1), we find that this does not give interesting bounds.

We will focus on bounds from SN1987A, which has the highest temperature (T ∼ 30 MeV) of the astrophysical systems used to constrain light particles. We can estimate the bounds by comparing to axion cooling, which constrains the ax- ion decay constant f_a >∼ 10⁹ GeV. For both the axion and infracolor, the dominant energy loss mechanism is nuclear bremmstrahlung.

Below the QCD scale the coupling Eq. (2.1) gives rise to an effective coupling of infracolor gauge fields to nucleons:

L^eff ∼ g²g^!2Λ_QCD

16π²m⁴_Q N N F¯ _µν^!2. (2.4)

4

We will consider collider signals for string length scales ranging from the size of detectors (∼ 10 m) to microscopic scales.

This paper is organized as follows. In Section 2, we briefly discuss model-building issues such as naturalness and unification, as well as indirect constraints from precision electroweak data, cosmology, and astrophysics. In Section 3 we discuss production of quirks and strings. In Section 4 we discuss signals for macroscopic strings. In Section 5 we consider annihilation of quirks catalyzed by the string. In Section 6 we discuss the signals of mesoscopic strings, those that are too small to be resolved in a detector but large compared to atomic scales. In Section 7 we discuss the collider signals from microscopic strings. Section 8 contains our conclusions.

2 Models and Indirect Constraints

In this section, we discuss model-building issues such as naturalness and unification, as well as indirect constraints from precision electroweak constraints and cosmology.

This discussion is fairly standard, and our conclusion is that there are no strong model-independent constraints on quirks from these considerations.

2.1 Coupling to the Infracolor Sector

Because we assume that the scale of infracolor strong interactions is below the weak scale, the hadrons of the infracolor sector are kinematically accessible to existing ex- periments. However, the standard model is uncharged under infracolor, and therefore a quirk loop is required to couple the sectors. Since the quirks are heavy, this leads to highly suppressed couplings to the infracolor sector.

The leading coupling between the standard model and the infracolor sector at low energies arises from the diagram of Fig. 1a. This gives rise to the dimension-8 effective operator

L^eff ∼ g²g^!2

16π²m⁴_QF_µν² F_ρσ^!2. (2.1) The 2-loop diagram of Fig 1b can couple the infracolor gauge fields to dimension-3 fermion bilinears, but these have an additional helicity suppression in addition to the additional loop suppression, and are therefore suppressed. For m_Q >∼ 100 GeV this operator is far weaker than the weak interactions, so production of infracolor gauge bosons at colliders with energy below the quirk mass is completely negligible. Probing this sector at colliders requires sufficient energy to produce quirks directly.

3

Fig. 1. Loop graphs contributing to the coupling of the standard model and infracolor sector.

The operator Eq. (2.1) mediates infracolor glueball decay, for example to photons or gluons. The rate is of order

Γ ∼ 1 8π

! g²g^!2 16π²m⁴_Q

"2

Λ⁹. (2.2)

Note that this is very sensitive to both Λ and m_Q. We have cτ ∼ 10 m

# Λ

50 GeV

$−9 # m_Q TeV

$₋₈

. (2.3)

We see that the infracolor glueballs can decay inside a particle detector for Λ >∼ 50 GeV, while the lifetime becomes longer than the age of the universe for Λ <∼ 50 MeV.

2.2 Star Cooling

Stars with temperature T >∼ Λ can potentially cool due to emission of infracolor glueballs. Due to the rapid decoupling of infracolor interactions from standard model interactions in Eq. (2.1), we find that this does not give interesting bounds.

We will focus on bounds from SN1987A, which has the highest temperature (T ∼ 30 MeV) of the astrophysical systems used to constrain light particles. We can estimate the bounds by comparing to axion cooling, which constrains the ax- ion decay constant f_a >

∼ 10⁹ GeV. For both the axion and infracolor, the dominant energy loss mechanism is nuclear bremmstrahlung.

Below the QCD scale the coupling Eq. (2.1) gives rise to an effective coupling of infracolor gauge fields to nucleons:

L^eff ∼ g²g^!2Λ_QCD

16π²m⁴_Q N N F¯ _µν^!2. (2.4)

4

Fig. 1. Loop graphs contributing to the coupling of the standard model and infracolor sector.

The operator Eq. (2.1) mediates infracolor glueball decay, for example to photons or gluons. The rate is of order

Γ ∼ 1 8π

! g²g^!2 16π²m⁴_Q

"₂

Λ⁹. (2.2)

Note that this is very sensitive to both Λ and m_Q. We have cτ ∼ 10 m

# Λ

50 GeV

$₋₉ # m_Q TeV

$₋₈

. (2.3)

We see that the infracolor glueballs can decay inside a particle detector for Λ >∼ 50 GeV, while the lifetime becomes longer than the age of the universe for Λ <∼ 50 MeV.

2.2 Star Cooling

Stars with temperature T >∼ Λ can potentially cool due to emission of infracolor glueballs. Due to the rapid decoupling of infracolor interactions from standard model interactions in Eq. (2.1), we find that this does not give interesting bounds.

We will focus on bounds from SN1987A, which has the highest temperature (T ∼ 30 MeV) of the astrophysical systems used to constrain light particles. We can estimate the bounds by comparing to axion cooling, which constrains the ax- ion decay constant f_a >∼ 10⁹ GeV. For both the axion and infracolor, the dominant energy loss mechanism is nuclear bremmstrahlung.

Below the QCD scale the coupling Eq. (2.1) gives rise to an effective coupling of infracolor gauge fields to nucleons:

L^eff ∼ g²g^!2Λ_QCD

16π²m⁴_Q N N F¯ _µν^!2 . (2.4)

4

Λ^! ≥ 50 GeV, iglueball decays inside detector

Needs 2 loop to couple

to SM fermions

Soft photons of this energy can be picked up by the

tracking system, as seen in this picture from the ATLAS event display.

(Cheu and Parnell-Lampen)

Taken from Chacko’s talk

Electromagnetic Shower

a)

-800 -400 0 400 800

0 1 2 3 4 5 6

b)

-800 -400 0 400 800

0 1 2 3 4 5 6

z

!

c)

-800 -400 0 400 800

0 1 2 3 4 5 6

Figure 5: Calorimeter energy deposition in the toy detector simulation. The distribution is shown for (a) bound state radiation with 100% of the energy released in photons, (b) bound state radiation with 10% of the energy in photons and (c) a minimum bias event. Brighter squares indicate a higher energy deposition in the cell, however, the scale itself is arbitrary for each figure separately.

in photons, the average amount of energy deposited in our toy calorimeter is approximately 550 GeV for a squirk mass of 500 GeV. For comparison, in the average (modified) min-bias event the average was below a 100 GeV. Our modification of the min bias events (see section 4.1), which was geared toward generating conservative backgrounds for pattern recognition (see below), may have increased the later number, but it may be taken as a ballpark figure.

In this work we will focus on amore distinct “smoking gun” feature of our signal, the angular

“anntena” pattern of soft energy. Identifying this pattern provides a unique data analysis challenge since most triggering and clustering algorithms are geared toward the identification of hard objects.

A promising way to quantify the angular correlations of any function defined on a 2-sphere is to use a multipole decomposition, as was shown to be very effective in studies of the cosmic background

19

Harnik and Wizansky [arXiv:0810.3948]

CMB-like analysis

100 % energy loss to photons 10 % energy loss to photons 90 % to invisible

SM background

Cartoon from Harnik and Wizansky [arXiv:0810.3948]

Figure 1: A schematic cartoon of the initial and final states of an LHC event with squirk production via an s-channel W^±. The two protons are incoming along the horizontal axis. The squirks are produced and oscillate along the dashed axis. The final state includes an antenna pattern of soft photons (two cone like shapes aligned with the squirk production axis) and a pair of hard annihilation products, W γ in this case. The search strategy will first involve discovering a resonance in W γ and then searching for signals of patterns of soft photons in the candidate signal events.

excited bound state will emit soft radiation, and decay to the ground state, emitting many quanta.

Some of these quanta will be soft photons which are emitted in a particular angular distribution.

The ground state will then annihilate into a hard final state, for example a hard W^± and a hard photon. The invariant mass of the W +photon system reconstructs to the mass of the ground state meson (again, at several hundred GeV). All of the processes discussed above are prompt on collider time scales. A cartoon initial and final states of these events are depicted in Figure 1.

The goal of the LHC search for this model would be to first establish that new physics is seen using standard hard physics objects emitted in the hard annihilation, and then to extract information about the nature of the new physics. In particular, detection of the unusual “antenna pattern” of soft photons in addition to the hard resonance will be a smoking gun signal of the strong dynamics and the presence of a bound state. What is a possible strategy to making these discoveries? In this case the existence of new physics may be demonstrated by a standard hard search. However, the correlation of new physics events with anomalous underlying event may teach us about the nature of the new physics, and perhaps enhance the confidence in the original discovery. A rough sketch of a search is shown in Figure 2 and described below.

1. Establish the existence of an excess of events from new physics.

Signal events will pass triggers with high efficiency due to the hard photon and lepton/jets from the annihilation. A promising search is to look for a peak in the W +photon invariant mass (or rather transverse mass) for leptonic W decays [13]. Due to the clean final state and the mass peak a signal-to-background ratio of order 1 may be achieved¹.

1The signal to background ratio of order 1 may be achieved even when the transverse mass peak is smeared due

3

`Antenna Pattern’

iQuark Production at LHC

most of their kinetic energy and angular momenta by emitting infracolor glueballs and/or light QCD hadrons like pions before annihilation. In the latter case in which quirks are QCD-colored, it leads to a hadronic fireball along with the other SM decay products of the quirkonium. In particular, in the context of folded supersymmetry it is pointed out in Ref.[4] that production of the squirk-antisquirk pair ˜ Q ˜ Q

^∗

at the large hadron collider (LHC) would quickly lose their excitation energy by bremsstrahlung and relax to the ground state of the scalar quirkonium. However, the energy loss due to infracolor glueball emissions is harder to estimate.

In this work, we consider vector-like quirks with respect to the electroweak gauge group but without carrying the QCD color. However, quirk carries a new color degree of freedom of SU

_C^!

(N

_IC

). Thus, quirks do not mix with SM quarks or leptons since the latter do not carry the new color degrees of freedom. These quirks are the θ-leptons in Okun’s terminology [1]. We also assume MeV ≤ Λ

^"

" M

^Q

so that the strings are microscopic but yet unbreakable. In analogous to the case of folded supersymmetry [4], the bound states formed by the quirk-antiquirk pairs will annihilate promptly into SM particles. Let Q denotes a heavy quirk doublet. The quantum number assignment for the quirk doublet Q under SU

^C!

(N

_IC

) × SU

^C

(3) × SU

^L

(2) × U

^Y

(1) is given by

Q

^L,R

=







U D







L,R

∼

'

N

_IC

, 1, 2, 1 3

(

. (1)

The gauge interactions are given by

L

^gauge

= − g

_s^"

G

^"_µ^a

Qγ

^µ

T

^a

Q − eA

^µ

⁾ e

^U

Uγ

^µ

U + e

^D

Dγ

^µ

D ^*

− g

cos θ

_W

Z

_µ

⁾ v

^U

Uγ

^µ

U + v

^D

Dγ

^µ

D ^* − g

√ 2

) W

_µ⁺

Uγ

^µ

D + W

_µ⁻

Dγ

^µ

U ^* (2) where we have suppressed generation indices and ignored possible mixings among quirks.

T

^a

(a = 1, · · · , N

IC²

− 1) are the generators of the SU

^C!

(N

_IC

) in the defining representation where each quirk lives and g

_s^"

is its coupling. For vector quirk Q = U or D, we have

v

_Q

= 1

2 (T

₃

(Q

_L

) + T

₃

(Q

_R

)) − e

^Q

sin

²

θ

_W

. (3) Here T

₃

(Q

_L,R

) is the third-component of the weak isospin for the left- (right-) handed quirk Q. Since we assume vector quirks, T

₃

(Q

_L

) = T

₃

(Q

_R

), they have the same value for each component of Q. For each vectorial quirk doublet, we can also have a Dirac bare mass

3

most of their kinetic energy and angular momenta by emitting infracolor glueballs and/or light QCD hadrons like pions before annihilation. In the latter case in which quirks are QCD-colored, it leads to a hadronic fireball along with the other SM decay products of the quirkonium. In particular, in the context of folded supersymmetry it is pointed out in Ref.[4] that production of the squirk-antisquirk pair ˜ Q ˜ Q

^∗

at the large hadron collider (LHC) would quickly lose their excitation energy by bremsstrahlung and relax to the ground state of the scalar quirkonium. However, the energy loss due to infracolor glueball emissions is harder to estimate.

In this work, we consider vector-like quirks with respect to the electroweak gauge group but without carrying the QCD color. However, quirk carries a new color degree of freedom of SU

_C^!

(N

IC

). Thus, quirks do not mix with SM quarks or leptons since the latter do not carry the new color degrees of freedom. These quirks are the θ-leptons in Okun’s terminology [1]. We also assume MeV ≤ Λ

^"

" M

^Q

so that the strings are microscopic but yet unbreakable. In analogous to the case of folded supersymmetry [4], the bound states formed by the quirk-antiquirk pairs will annihilate promptly into SM particles. Let Q denotes a heavy quirk doublet. The quantum number assignment for the quirk doublet Q under SU

^C!

(N

IC

) × SU

^C

(3) × SU

^L

(2) × U

^Y

(1) is given by

Q

^L,R

=







U D







L,R

∼

'

N

IC

, 1, 2, 1 3

(

. (1)

The gauge interactions are given by

L

^gauge

= − g

s^"

G

^"_µ^a

Qγ

^µ

T

^a

Q − eA

^{µ )}

e

^U

Uγ

^µ

U + e

^D

Dγ

^µ

D

^*

− g

cos θ

_W

Z

_µ ⁾

v

^U

Uγ

^µ

U + v

^D

Dγ

^µ

D

^*

− g

√ 2

)

W

_µ⁺

Uγ

^µ

D + W

µ⁻

Dγ

^µ

U

^*

(2) where we have suppressed generation indices and ignored possible mixings among quirks.

T

^a

(a = 1, · · · , N

IC²

− 1) are the generators of the SU

^C!

(N

_IC

) in the defining representation where each quirk lives and g

_s^"

is its coupling. For vector quirk Q = U or D, we have

v

_Q

= 1

2 (T

3

(Q

_L

) + T

3

(Q

_R

)) − e

^Q

sin

²

θ

_W

. (3) Here T

3

(Q

_L,R

) is the third-component of the weak isospin for the left- (right-) handed quirk Q. Since we assume vector quirks, T

3

(Q

_L

) = T

3

(Q

_R

), they have the same value for each component of Q. For each vectorial quirk doublet, we can also have a Dirac bare mass

3

most of their kinetic energy and angular momenta by emitting infracolor glueballs and/or light QCD hadrons like pions before annihilation. In the latter case in which quirks are QCD-colored, it leads to a hadronic fireball along with the other SM decay products of the quirkonium. In particular, in the context of folded supersymmetry it is pointed out in Ref.[4] that production of the squirk-antisquirk pair ˜ Q ˜ Q

^∗

at the large hadron collider (LHC) would quickly lose their excitation energy by bremsstrahlung and relax to the ground state of the scalar quirkonium. However, the energy loss due to infracolor glueball emissions is harder to estimate.

In this work, we consider vector-like quirks with respect to the electroweak gauge group but without carrying the QCD color. However, quirk carries a new color degree of freedom of SU

_C^!

(N

_IC

). Thus, quirks do not mix with SM quarks or leptons since the latter do not carry the new color degrees of freedom. These quirks are the θ-leptons in Okun’s terminology [1]. We also assume MeV ≤ Λ

^"

" M

^Q

so that the strings are microscopic but yet unbreakable. In analogous to the case of folded supersymmetry [4], the bound states formed by the quirk-antiquirk pairs will annihilate promptly into SM particles. Let Q denotes a heavy quirk doublet. The quantum number assignment for the quirk doublet Q under SU

^C!

(N

IC

) × SU

^C

(3) × SU

^L

(2) × U

^Y

(1) is given by

Q

^L,R

=







U D







L,R

∼

'

N

_IC

, 1, 2, 1 3

(

. (1)

The gauge interactions are given by

L

^gauge

= − g

s^"

G

^"_µ^a

Qγ

^µ

T

^a

Q − eA

^{µ )}

e

^U

Uγ

^µ

U + e

^D

Dγ

^µ

D

^*

− g

cos θ

_W

Z

_µ ⁾

v

^U

Uγ

^µ

U + v

^D

Dγ

^µ

D

^*

− g

√ 2

)

W

_µ⁺

Uγ

^µ

D + W

µ⁻

Dγ

^µ

U

^*

(2) where we have suppressed generation indices and ignored possible mixings among quirks.

T

^a

(a = 1, · · · , N

IC²

− 1) are the generators of the SU

^C!

(N

_IC

) in the defining representation where each quirk lives and g

_s^"

is its coupling. For vector quirk Q = U or D, we have

v

_Q

= 1

2 (T

₃

(Q

_L

) + T

₃

(Q

_R

)) − e

^Q

sin

²

θ

_W

. (3) Here T

3

(Q

_L,R

) is the third-component of the weak isospin for the left- (right-) handed quirk Q. Since we assume vector quirks, T

3

(Q

_L

) = T

3

(Q

_R

), they have the same value for each component of Q. For each vectorial quirk doublet, we can also have a Dirac bare mass

3

most of their kinetic energy and angular momenta by emitting infracolor glueballs and/or light QCD hadrons like pions before annihilation. In the latter case in which quirks are QCD-colored, it leads to a hadronic fireball along with the other SM decay products of the quirkonium. In particular, in the context of folded supersymmetry it is pointed out in Ref.[4] that production of the squirk-antisquirk pair ˜ Q ˜ Q

^∗

at the large hadron collider (LHC) would quickly lose their excitation energy by bremsstrahlung and relax to the ground state of the scalar quirkonium. However, the energy loss due to infracolor glueball emissions is harder to estimate.

In this work, we consider vector-like quirks with respect to the electroweak gauge group but without carrying the QCD color. However, quirk carries a new color degree of freedom of SU

_C^!

(N

_IC

). Thus, quirks do not mix with SM quarks or leptons since the latter do not carry the new color degrees of freedom. These quirks are the θ-leptons in Okun’s terminology [1]. We also assume MeV ≤ Λ

^"

" M

^Q

so that the strings are microscopic but yet unbreakable. In analogous to the case of folded supersymmetry [4], the bound states formed by the quirk-antiquirk pairs will annihilate promptly into SM particles. Let Q denotes a heavy quirk doublet. The quantum number assignment for the quirk doublet Q under SU

^C!

(N

_IC

) × SU

^C

(3) × SU

^L

(2) × U

^Y

(1) is given by

Q

^L,R

=







U D







L,R

∼

'

N

_IC

, 1, 2, 1 3

(

. (1)

The gauge interactions are given by

L

^gauge

= − g

s^"

G

^"_µ^a

Qγ

^µ

T

^a

Q − eA

^{µ )}

e

^U

Uγ

^µ

U + e

^D

Dγ

^µ

D

^*

− g

cos θ

_W

Z

_µ ⁾

v

^U

Uγ

^µ

U + v

^D

Dγ

^µ

D

^*

− g

√ 2

)

W

_µ⁺

Uγ

^µ

D + W

µ⁻

Dγ

^µ

U

^*

(2) where we have suppressed generation indices and ignored possible mixings among quirks.

T

^a

(a = 1, · · · , N

IC²

− 1) are the generators of the SU

^C!

(N

_IC

) in the defining representation where each quirk lives and g

_s^"

is its coupling. For vector quirk Q = U or D, we have

v

_Q

= 1

2 (T

3

(Q

_L

) + T

3

(Q

_R

)) − e

^Q

sin

²

θ

_W

. (3) Here T

3

(Q

_L,R

) is the third-component of the weak isospin for the left- (right-) handed quirk Q. Since we assume vector quirks, T

₃

(Q

_L

) = T

₃

(Q

_R

), they have the same value for each component of Q. For each vectorial quirk doublet, we can also have a Dirac bare mass

3

A Simple Model

Vectorial

Vectorial => Escape constraints from LEP EW precision data

But a Dirac bare mass term is possible

Assume MeV ≤ Λ

^!

" M

^Q

Fractional charged θ-leptons of Okun

No Yukawa coupling with SM Higgs

(Microscopic string scenario)

[Cheung, Keung and TCY, 0810.1524]

Quarkonium Production

Plus fragmentation, color octet mechanism as well.

Colored/Uncolored iQuarks are produced via QCD/Electroweak hard processes

q

q’ iQ

iQ’

photon,Z,W

unbreakable string

QCD: gluon

Λ ^! ! M

EW:

via electroweak interactions rather than QCD. For M^U_,D around 100 − 200 GeV the cross sections are of order O(1) − O(10) pb. In contrast with QCD, due to the unbroken string flux tube, the two quirks do not hadronize individually to form isolated jets. Since we assume the quirk doublet is vector-like, the β-decay between doublet members is suppressed by small mass splittings due to radiative corrections. Instead these initially flying-apart quirk-antiquirk pair will come back close to each other to form quirkonium after losing their kinetic energies by radiating off infracolor glueballs and photons [3]. Essentially, in the case of microscopic Λ^! all open quirk pairs will, at the end, come together to form a quirkonium.

This is in sharp contrast to the normal quarkonium, in which we have to force them to go together in the same direction (e.g. by radiating a gluon) and in roughly the same velocity in order to form a quarkonium. Therefore, the quirkonium production rates are not inferior to the quarkonium, although quirks are only produced via electroweak interactions. We will discuss more about these interesting phenomena in the next section.

10^-3 10^-2 10^-1 10⁰ 10¹

100 200 300 400 500 600 700 800

Cross Sections (pb)

M_U or M_D (GeV) LHC

U D

-

D U

-

U U

-

D D

-

FIG. 1: Production cross sections for pp → UU, DD, UD and DU at the LHC. The label M^U on the x-axis is for UU, UD and DU production while M^D is for DD production. We assume M^U − M^D = 10 GeV and set NIC = 3.

6

Open production cross section for iQuarks at LHC

[Cheung, Keung and TCY, 0810.1524]

for the first time the collider phenomenology associated with the production of heavy quark partners in this scenario. The charge assignments and strong dynamics effects will lead to signals that are very different from either supersymmetric or generic hidden valley models.

Theories with a QCD^! sector where there is a large hierarchy between the masses of the matter fields and the QCD^! scale, m_q^! ! Λ^!, give rise to very unusual dynamics [8][7][9][10]. For this reason the quarks (or scalar quarks) of such a sector have been dubbed quirks (or squirks) [9]. To understand this, let us first recall the dynamics of normal QCD. Consider two heavy quarks that are produced back-to-back in a hard process. As the two quarks get farther apart and their distance approaches Λ⁻¹, confining dynamics sets in and some of their energy is lost to a gluonic flux tube extending between them. When the local energy density in the flux tube is high enough it is energetically favorable to pair create a light quark anti-quark pair, ripping the tube. This mechanism of soft hadronization allows the two heavy quarks to hadronize separately.

In quirky QCD, on the other hand, such a soft hadronization mechanism is absent because there are no quarks with mass less than or comparable to Λ^!. The energy density in the QCD flux tube, or more simply, the tension of the QCD string cannot exceed Λ^!2 which is far less than the m_q^! per Compton wavelength needed to create a heavy quirk anti-quirk pair. The splitting of the QCD string by a quirk anti-quirk pair is exponentially suppressed as exp(−m²_q^!/Λ^!2) [8]. In fact, one may view the entire process as single production of a highly excited bound state, squirkonium. All of the kinetic energy that the quirks posses at production, √

ˆs − 2m^q!, which is typically of order m_q^!, can be interpreted as squirkonium excitation energy. This energy is radiated away into glueballs of QCD^! and photons. Eventually the two quirks pair-annihilate back into lighter states.

From the above discussion it is clear that the char- acteristic collider signatures of folded supersymmetry are determined by the final states that the squirks annihilate into. In what follows we calculate the cross- section for production of these particles at the LHC, and evaluate the branching ratios for pair-annihilation into various final states. The possibility of discovering the soft photons from the loss of excitation energy will be discussed elsewhere [11]. We then focus on the most promising annihilation channel for detection, which is W + photon, and demonstrate the reach for this search at the LHC. Some qualitative features of our analysis also apply to the supersymmetric model of Babu, Gogoladze and Kolda [12], which also predicts quirky behaviour at the weak scale.

II. PRODUCTION AND ENERGY LOSS

In a folded supersymmetric model, the scalar quirks have exactly the same electroweak quantum numbers as

200 400 600 800

squirk mass (GeV) 1e-05

0.0001 0.001 0.01 0.1 1

! (pb)

FIG. 1: The total cross-section for production of first generation squirk anti-squirk pairs via an s-channel W⁺ (top curve) and W⁻ (bottom curve) at the LHC as a function of the squirk mass. The up and down squirks have been taken to be degenerate.

the corresponding quarks, but are charged under QCD^!, not under QCD. Specifically, under SU(3)_C^! × SU(3)^C × SU(2)_L × U(1)^Y, where SU(3)_C^! corresponds to QCD^!, the quantum numbers of the squirks are

Q˜ [3, 1, 2, (1/3)]

D˜^c [¯3, 1, 1, (2/3)]

U˜^c [¯3, 1, 1, −(4/3)] (2) Therefore, at a collider squirks are only weakly produced.

This could happen through the Drell-Yan process via an off-shell photon, Z, or W , or alternatively by gauge boson fusion. Production through the photon or the Z typically does not result in an observable signal, since the primary annihilation channel is to glueballs of QCD^!, which are invisible ^∗. In the simple analysis of this paper we focus on production of squirks through s-channel W^±†. In this case the conservation of electric charge implies that squirk annihilation must result in the emission of at least one charged particle.

Figure 1 shows the production cross-section for first generation SU(2) doublet up-down squirk anti-squirk pairs through s-channel W⁺ and W⁻ as a function of the squirk mass. In folded supersymmetry the second generation squirks are expected to be nearly degenerate

∗ Although glueballs of QCD^# decay back to SM states, giving rise to potentially observable signals [7], in the parameter range of interest this generally happens outside the detector [6].

† It should be pointed out that weak boson fusion may dominate over Drell-Yan production at high squirk mass [13] and may require further study.

2

Open squirk (siquark) production in folded SUSY

(Burdman, Chacko, Goh, Harnik and Krenke, arXiv:0805.4667)

iQuark has larger production rate than scalar iQuark!

Figure 1: Total cross-sections vs. mass of top quirk

top quirk mass M_XT = 800 GeV, about one hundred events with quirk pairs can be produced.

8 Conclusion

In this paper, we have displayed a quirky little Higgs model and used a color-neutral top quirk to cancel the quadratic divergence from the top quark loop. The top quirk and top quark are related by an SU(6) bulk gauge symmetry in which their respective confining gauge groups are embedded. The Higgs in this model is a pseudo-Nambu-Goldstone boson and its mass parameter is protected by an SU(3)_W symmetry. The collective breaking of the little Higgs mechanism occurs on two separate branes, which leads to finite results for the Higgs mass. Since the mass spectrum is mainly determined by the radius of extra dimension, precision electroweak tests only put stringent constraints on 1/R. This is quite different from the original little Higgs model, there the mass of the

15

Open production of top quirk in Quirky Little Higgs Model

(Cai, Cheng and Terning 0812.0843)

Prompt Annihilation

(After Energy Loss)

the charged

¹

S

0

quirkonium. On the other hand, the leading mode for the charged

³

S

1

quirkonium is nonzero, and we list the formulas in the appendix. We include the W g

^!

g

^!

in the decay branching ratio.

C. Decay patterns

We present the decay branching ratios of the S-wave

¹

S

0

and

³

S

1

quirkonium of UU, DD, and the charged UD in Figs. 2 – 4. In these plots, we have set N

^IC

= 3 and give a small mass difference of M

^U

− M

^D

= 10 GeV for the cases of charged quirkonium.

0.01 0.1 1

100 150 200 250 300 350 400 450 500

Branching Ratios

M (GeV) U U

-

¹_S

0 quirkonium

g’ g’ (!’=10 MeV)

W⁺ W^-

Z Z

" "

Z "

0.001 0.01 0.1 1

100 150 200 250 300 350 400 450 500

Branching Ratios

M (GeV) D D

-

¹_S

0 quirkonium

g’ g’ (!’=10 MeV)

W⁺ W^- Z Z

Z "

" "

FIG. 2: Branching fractions of the quirkonium of (a) ¹S₀(UU) and (b) ¹S₀(DD) versus the quirko- nium mass M . We have chosen n_Q = 1 and Λ^! = 10 MeV in the running α^!_s.

0.01 0.1 1

100 150 200 250 300 350 400 450 500

Branching Ratios

M (GeV) U U

-

³_S

1 quirkonium

# $ $- _{# l}⁺ _l^-

u u- _{+ c c}- ^{d d}- _{+ s s}- _{+ b b}-

W⁺ W^- t t-

g’ g’ g’

" g’ g’ Z g’ g’ 0.001

0.01 0.1 1

100 150 200 250 300 350 400 450 500

Branching Ratios

M (GeV) D D

-

³_S

1 quirkonium

# $ $-

# l⁺ l^-

u u- _{+ c c}- ^{d d}

- _{+ s s}- _{+ b b}-

W⁺ W^-

t t-

g’ g’ g’

" g’ g’

Z g’ g’

FIG. 3: Branching fractions of the quirkonium of (a) ³S₁(UU) and (b) ³S₁(DD) versus the quirko- nium mass M . We have chosen n_Q = 1 and Λ^! = 10 MeV in the running α^!_s.

13

1 S ₀ neutral iquarkonium

Dominant Decay Mode: Invisible g ^! g ^! mode