Electroweak and Flavor Dynamics at Hadron Colliders–I

Home , Kenneth Lane (physicist), Technicolor (physics)

Electroweak and Flavor Dynamics at Hadron Colliders±I b Estia Eichtena and Kenneth Lane

a Fermi National Accelerator Laboratory, P.O. Box 500 Batavia, IL 60510

b Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA 02215

ABSTRACT technipions are listed for some simple models in Section 3. The most promising processes involve production of an isovector

This is the ®rst of two reports cataloging the principal sig-

technirho T resonance and its subsequent decay into technip-

pp pp

natures of electroweak and ¯avor dynamics at and col-

M < 2M

ion pairs. Walking technicolor suggests that ,in

T 1

liders. Here, we discuss some of the signatures of dynamical T

! W W W W

1 L L L T L which case T or, more likely, ,where is elecroweak and ¯avor symmetry breaking. The framework for a longitudinal weak boson. We also discuss a potentially impor-

dynamical symmetry breaking we assume is technicolor, with

T 1

tant new signal: the isoscalar T , degenerate with , and de-

a walking coupling TC, and extended technicolor. The re-

Z T

caying spectacularly to T and . The most important sub-

< s actions discussed occur mainly at subprocess energies ^

processes for colored technihadrons are discussed in Section 4. eV 1T . They include production of color-singlet and octet tech-

These involve a color-octet s-channel resonance with the same

nirhos and their decay into pairs of technipions, longitudinal

8 quantum numbers as the gluon; this technirho T dominates

weak bosons, or jets. Technipions, in turn, decay predominantly

M < 2M

colored technipion pair production. If ,then

T 8

into heavy fermions. T

! qq gg 8 T and , a resonance in dijet production. The main signatures of topcolor-assisted technicolor, top-

I. INTRODUCTION 0

V Z 8 pions t and the color-octet and singlet of broken topcolor This is the ®rst of two reports summarizing the major sig- gauge symmetries, are described in the following report, as are nals for dynamical electroweak and ¯avor symmetry breaking the signatures for quark and lepton substructure. At the end of in experiments at the Tevatron Collider and the Large Hadron the second report, we have provided a table which summarizes Collider. The division into two reports is done solely to ac- the main processes and sample cross sections at the Tevatron and comodate the length requirements imposed on contributions to LHC. Our reports are not intended to constitute a complete sur- the Snowmass '96 proceedings. In contrast, the motivations for vey of electroweak and ¯avor dynamics signatures accessible at these studies are clear: We do not know the mechanism of elec- hadron colliders. We have limited our discussion to processes troweak symmetry breaking nor the physics underlying ¯avor with the largest production cross sections and most promising and its symmetry breaking. The dynamical scenarios whose sig- signal-to-background ratios. Even for the processes we list, we nals we catalog provide an attractive theoretical alternative to have not provided detailed cross sections for signals and back- perturbative supersymmetry models. At the same time, they grounds. Signal rates depend on masses and model parameters;

p they and the backgrounds also depend strongly on detector capa- give experimentalists a set of high- T signatures that challenge heavy-¯avor tagging, tracking and calorimetryÐdetector sub- bilities. Experimenters in the detector collaborations will have systems somewhat complementary to those tested by supersym- to carry out these studies. metry searches. Finally, many of the most important signs of electroweak and ¯avor dynamics have sizable rates and are de- II. OVERVIEW OF TECHNICOLOR AND tected relatively easily in hadron collider experiments. Exten- EXTENDED TECHNICOLOR sive searches are underway in both Tevatron Collider collabora-

tions, CDF and Dé. We hope that these reports will inspire and TechnicolorÐa strong interaction of fermions and gauge

1TeV

help the ATLAS and CMS Collaborations to begin their studies. bosons at the scale TC Ðis a scenario for This report lists some of the major signals for dynamical elec- the dynamical breakdown of electroweak symmetry to troweak and ¯avor symmetry breaking in experiments at the electromagnetism[1]. Based on the similar phenomenon Tevatron Collider and the Large Hadron Collider. Section 2 of chiral symmetry breakdown in QCD, technicolor is explicitly contains a brief overview of technicolor and extended techni- de®ned and completely natural. To account for the masses color. This discussion includes summaries of the main ideas that of quarks, leptons, and Goldstone ªtechnipionsº in such a have developed over the past decade: walking technicolor, mul- scheme, technicolor, ordinary color, and ¯avor symmetries are tiscale technicolor, and topcolor-assisted technicolor. Hadron embedded in a larger gauge group, called extended technicolor

collider signals of technicolor involve production of technipi- (ETC)[2]. The ETC symmetry is broken down to technicolor

qq gg = O(100 TeV)

ons via annihilationand fusion. These technipions include and color at a scale ET C . Many signatures

W Z L

the longitudinal weak bosons L and as well as the pseudo- of ETC are expected in the energy regime of 100 GeV to

Goldstone bosons T of dynamical symmetry breaking. The 1 TeV, the region covered by the Tevatron and Large Hadron

T are generally expected to have Higgs-boson-like couplings Colliders. For a review of technicolor developments up through to fermions and, therefore, to decay to heavy, long-lived quarks 1993, see Ref. [3]. The principal signals in hadron collider and leptons. experiments of ªclassicalº technicolor and extended technicolor The subprocess production cross sections for color-singlet were discussed in Ref. [4]. In the minimal technicolor model,

1001 containing just one technifermion doublet, the only prominent condensate models of electroweak symmetry breaking[10, 11], signals in high energy collider experiments are the modest en- almost all of the top quark mass arises from a new strong ªtop-

hancements in longitudinally-polarized weak boson production. colorº interaction. To maintain electroweak symmetry between

s m '

These are the -channel color-singlet technirho resonances near (left-handed) top and bottom quarks and yet not generate b

0 0

! W W ! W Z m SU (3)

1.5±2 TeV: and .Thesmall t , the topcolor gauge group is generally taken to be

T 1 L L T 1 L L

( ) U (1) U (1) O cross sections of these processes and the dif®culty of , with the providing the difference between top and

reconstructing weak-boson pairs with reasonable ef®ciency bottom quarks. Then, in order that topcolor interactions be m

make observing these enhancements a challenge. Nonminimal naturalÐi.e., that their energy scale not be far above t Ðand technicolor models are much more accessible because they have yet not introduce large weak isospin violation, it is necessary

a rich spectrum of lower energy technirho vector mesons and that electroweak symmetry breaking is still due mainly to tech-

technipion ( T ) states into which they may decay. In the one- nicolor interactions[12]. In TC2 models, ETC interactions are

family model, containing one isodoublet each of color-triplet still needed to generate the light and bottom quark masses, con-

(U; D ) (N; E) m

techniquarks and color-singlet technileptons ,tribute a few GeV to t , and give mass to the technipions.

(8) SU (8)

the technifermion chiral symmetry is SU .There The scale of ETC interactions still must be hundreds of TeV

are 63 T and , classi®ed according to how they transform to suppress FCNC and, so, the technicolor coupling must still

(3) SU (2)

under ordinary color SU times weak isospin .The walk. Two recent papers developing the TC2 scenario are in

00 0 0

2 (1; 1) W ;Z ; 2 (1; 3)

technipions are ; and ; Ref. [13]. Although the phenomenology of TC2 is in its infancy,

T L T

L T

2 (8; 1) ; 2 (8; 3)

color octets T and ; and color-triplet it is expected to share general features with multiscale techni-

T 8

; 2(3; 3) (3; 1) (3; 3) (3; 1)

leptoquarks .The color: many technihadron states, some carrying ordinary color,

QL LQ

T belong to the same representations. some within range of the Tevatron, and almost all easily pro- Because of the con¯ict between constraints on ¯avor- duced and detected at the LHC at moderate luminosities.

changing neutral currents and the magnitude of ETC-generated We assume throughout that the technicolor gauge group is

SU (N )

quark, lepton and technipion masses, classical technicolor was TC and that its gauge coupling walks. A minimal,

superseded a decade ago by ªwalkingº technicolor. In this one-doublet model can have a walking TC only if the tech-

kind of gauge theory, the strong technicolor coupling TC nifermions belong to a large non-fundamental representation. runs very slowly for a large range of momenta, possibly all the For nonminimalmodels, we generally consider the phenomenol-

way up to the ETC scaleÐwhich must be several 100 TeV to ogy of the lighter technifermions transforming according to the N suppress FCNC. This slowly-running coupling permits quark fundamental ( TC) representation; some of these may also be

and lepton masses as large as a few GeV to be generated from ordinary color triplets. In almost all respects, walking models (3) ETC interactions at this very high scale [5]. are very different from QCD with a few fundamental SU rep-

Walking technicolor models require a large number of tech- resentations. Thus, arguments based on naive scaling from QCD

N TC

and on large- certainly are suspect. In TC2, there is no need nifermions in order that TC runs slowly. These fermions may belong to many copies of the fundamental representation of the for large isospin splitting in the technifermion sector associated technicolor gauge group, to a few higher dimensional represen- with the top-bottommass difference. This simpli®es our discus- tations, or to both. This fact inspired a new kind of model, ªmul- sion greatly. tiscale technicolorº, and a very different phenomenology[6]. In multiscale models, there typically are two widely separated III. COLOR-SINGLET TECHNIPION

scales of electroweak symmetry breaking, with the upper scale PRODUCTION

F = 246 GeV

set by the weak decay constant . Technihadrons

+ 0

! W W W Z 1 associated with the lower scale may be so light that they are The T and signatures of the mini- within reach of the Tevatron collider; they certainly are readily mal model were discussed in Ref. [4]. The principal change

produced and detected at the LHC. An important consequence due to the large representation and walking is that scaling the

1 T T

of walking technicolor is that technipion masses are enhanced T coupling from QCD is questionable. It

T T

so that T decay channels may be closed. If this hap- may be smaller than usually assumed and lead to a narrower

! W W W !

T 1 L L L T T 8 1

pens, then or and dijets. If the T . There is also the possibility that, because of its large mass

T T 1 channels are open, they are resonantly produced at large (naively, 1.5±2 TeV), the T has a sizable branching ratio to ratesÐof order 10 pb at the Tevatron and several nanobarns at four-weak-boson ®nal states. To our knowledge, neither of these the LHCÐand, given the recent successes and coming advances possibilities has been investigated. in heavy ¯avor detection, many of these technipions should be From now on, we consider only nonminimal models which, reconstructable in the hadron collider environment. we believe, are much more likely to lead to a satisfactory walk- Another major advance in technicolor came in the past two ing model. They have a rich phenomenology with many diverse, years with the discovery of the top quark[7]. Theorists have relatively accessible signals. The masses of technipions in these concluded that ETC models cannot explain the top quark's large models arise from broken ETC and ordinary color interactions. mass without running afoul of either cherished notions of nat- In walking models we have studied, they lie in the range 100±

uralness or experimental constraints from the parameter and 600 GeV; technirho vector meson masses are expected to lie be-

! bb the Z decay rate[8, 9]. This state of affairs has led tween 200 and 1000 GeV (see, e.g., Ref. [6]). to ªtopcolor-assisted technicolorº (TC2). In TC2, as in top- Color-singlet technipions, including longitudinal weak

1002

W Z Q T

L i 3i

bosons L and , are pair-produced via the Drell-Yan pro- Here, and are the electric charge and third component of

O ( ) q

cess in hadron collisions. Their production rates at the weak isospin for iL;R . Production rates of several picobarns in- Tevatron and LHC are probably unobservably small compared crease by factors of 5±10 at the LHC; see the table in the follow- to backgrounds unless there are fairly strong color-singlet ing Report II. technirho resonances not far above threshold. To parameterize If the isospin of technifermions is approximately conserved,

the cross sections simply, we consider a model containing

T 1

there is an isoscalar partner T of the that is nearly degener-

0 Z

two isotriplets of technipions which mix W , with a L

L ate with it and may be produced at a comparable rate. The walk-

;0 triplet of mass-eigenstate technipions [6, 14]. We assume

T ing technicolor enhancement of technipion masses almost cer-

that the lighter isotriplet T decays into pairs of the state

! !

tainly closes off the isospin-conserving decay T .

T T

j i = sin jW i + cos j i

L T

T , leading to the processes

W W Z

Even the triply-suppressed mode L has little or no

L L

M 300 GeV

0 0 0 0

0 phase space for . Thus, we may expect the

q q ! W ! ! W Z ; W ; Z ;

L T L T

0 0

T 1 L L T T

! ! Z

main decays to be T , ,and .Interms

T T T T

+ +

0 0

q ! ; Z ! ! W W ; W ; :

q (1)

T 1

L L L T T T

! ! Z Z L

of mass eigenstates, these modes are T , , ,

T T

+ +

0 00

0 1

ZZ Z W W W

L;, ;and , , . It is not pos-

T T

L L T L T T

s 1 The -dependent T partial widths are given by (assuming no

other channels, such as colored techipion pairs, are open) sible to estimate the relative magnitudes of the decay ampli- !

tudes without an explicit model of the T 's constituent tech-

3 2

p 2 C

nifermions. Judging from the decays of the ordinary ,weex-

AB AB

; ( ! ; s)=

0 00 0 00 1 A B

T (2)

! ! ( ) Z ( )

T s

3 pect , to dominate, with the former

T T T T

mode favored by phase space.

p C = sin

where AB is the technipion momentum and ,

2 4

The T is produced in hadron collisions just as the ,via

T 1

2 sin cos cos = W W W + W

B L L L T T L

, for A , ,

Z M '

its vector-meson-dominance coupling to and .For !

T T 1 T T

T , respectively. The coupling obtained

M ! T

,the production cross section should be approximately

T 1

=2:91 (3=N ) TC

by naive scaling from QCD is [4] .

2 0

jQ + Q j Q

D U;D

U times the rate, where are the electric 1

Technipion decays are mainly induced by ETC interactions T !

which couple them to quarks and leptons. These couplings are charges of the T 's constituent technifermions. The principal

! + bb ` `

Higgs-like, and so technipions are expected to decay into heavy signatures for T production, then, are and (or )

+bb M = M

, with . T fermion pairs: bb

In the one-family and other models containing colored as well

bb M < 2m

0 if ,

! (3) as color-singlet technifermions, there are singlet and octet tech-

tt M > 2m

00 t

if ; T

nipions that are electroweak isosinglets commonly denoted

cb or cs; M

T +

t b

if ,and . These are singly-produced in gluon fusion. Depending

tb M >m +m

t b

if .on the technipion's mass, it is expected to decay to (and, pos-

0 00

gg tt =

sibly, )orto [4, 16]. With or T , and with con-

An important caveat to this rule applies to TC2 models. There, T N

stituent technifermions transforming according to the TC rep-

only a few GeV of the top mass arises from ETC interactions.

SU (N )

resentation of TC , the decay rates are

b tt cb cs

Then, the b mode competes with for ; or compete

+ +

b t ! b

with t for . Note that, since the decay is strongly

T T

2 2

2 2 3

m M

C N M

q q

S TC 0

suppressed in TC2 models, the can be much lighter than the 0

( !gg)= ; ( ! qq )= :

2 2

F 16F

top quark. 128

T T

1 A B

The T cross sections are well-approximated by (6)

= 1 4m =M SU (3)

Here, is the quark velocity. The -

d^ (q q ! ! )

i j A B

T 1

= C

color factor is determined by the triangle-anomaly graph for

! gg C =

. In the one-family model, for the sin-

4 2

2 3

M (1 z )

T 1

AB 2

O (1)

; (^s)C

A glet and for the octet ;valuesof are expected in T

(4) 3

5=2 2 2 2

3^s (^s M ) +^s

T 1 T1

other models. The technipion decay constant T is discussed

below. The dimensionless factor q allows for model depen-

s^ z = cos

where is the subprocess energy, is the A produc- qq

dence in the technipions' couplings to . In classical ETC

T 1

tion angle, and is the -dependent total width of .Ig-

T 1

j j = O (1) j j =

;0 q

models, we expect q . In TC2 models, =

noring Kobayashi-Maskawa mixing angles, the factors A

O (1) b j j =

for the light quarks and, possibly, the -quark, but t

ij are

tt O (few GeV =m ) 1 T

t ; there will be no enhancement of

2 production in topcolor-assisted technicolor.

1 s^

A =

2 4

The gluon fusion cross section for production and decay of

s^ M

4 sin

2 cos 2 s^

A = Q + (T Q sin )

i 3i i W 2

2 1

! ! Z ZZ

s^ M

sin 2

L L

The modes T , were considered for a one-doublet techni-

color model in Ref. [15]. We have estimated the branchingratios for the isospin-

0 0

2Q cos 2 sin s^

W i W

! Z 1

violating decays T , and found them to be negligible unless the

T T

+ Q :

i (5)

2 2

mixing angle is very small.

s^ M

sin 2

W Z

1003

because the fusing gluons are at low x (see the table in Report II).

C D R

Table I: The factors R and in Eq. 9 for the one-family

T An interesting feature of this cross section is that the T in- model (O) and a multiscale model (M).

variant mass distribution peaks near the color-triplet and octet

C C D D

8 3 8

3 technipion thresholds, which can be well above . It is pos-

Model T

16 4

2 2

W Z

10=3 1=3 M M

sible that mixed modes such as and L are also pro-

T T

(O) L

3 8

9 9

32 16

2 2

M M 8=3 4=3

duced by gluon fusion, with the rates involving mixing angles

Q Q (M)

Q Q

3 8

9 9

2 2

(2M M ) 8 0 0

such as in Eq. 4.

L L (M)

L L

3 T

IV. COLOR-OCTET TECHNIRHO qq to heavy is isotropic:

PRODUCTION AND DECAY TO JETS

0 0 0

N d^ (gg ! ! qq ) ( ! gg) ( ! qq )

C AND TECHNIPIONS

= ;

2 2

dz 32 (^s M ) +^s

(7) Models with an electroweak doublet of color-triplet techni-

(U; D ) I =0 8

quarks have an octet of technirhos, T , with

N =1 T

where C (8) for ( ). The decay rates and cross

the same quantum numbers as the gluon. The T is produced F

sections are contolled by the technipion decay constant T .In

qq gg

strongly in and collisions. Assuming the one-family

F = 123 GeV

the standard one-family model, T and the en-

model for simplicity, there are the 63 technipions listed in Sec- qq hancements in productionare never large enough to see above

tion 2. The color-singlet and octet technipions decay as in Eq. 3 N

background (unless TC is unreasonably large). In multiscale

above. The leptoquark decay modes are expected to be F

models and, we expect, in TC2 models, T may be consider-

ably smaller. For example, in the multiscale model considered

c M

F =30 50 GeV

! b ; ! ;

in Ref. [6], ±; in the TC2 model of Ref. [13],

D N U N

t M >m

F = 80 GeV

T . Since the total hadronic cross section,

c M

+ if

2 0 0

!b ; ! :

( ! gg) ( ! qq )

(11)

DE U E

t M >m

(pp ! ! qq ) '

2s M

Z M

M The caveat regarding technipion decays to top quarks in TC2

p p

B B

p p

d f e f e ;

B (8) g

g models still applies.

s s

There are two possibilities for T decays [6]. If walking

2 =F scales as 1 , small decay constants may lead to observable

T technicolor enhancements of the technipion masses close off the

enhancements of tt production in standard multiscale techni-

! qq; gg ! jets

T T 8

T channels, then .Thecolor-

color and in bb production in TC2. Sample rates are given in the

( ) averaged O cross sections are given by

table in Report II. S

2 2 2

u^ + t d^ (q q ! q q ) 2

In models containing colored technifermions, color-singlet 2

i i i i

= D

=0 2

technipions are also pair-produced in the isospin I channel

dz 9^s s^

2 2

via gluon fusion. This process involves intermediate states of 2

u^ s^ +^u

Re D + ;

color-triplet and octet technipions. Again, the subprocess cross gg

^ ^

st t

section is isotropic; it is given by[17] ^

2 2 2

u^ + t 2 d^(q q ! q q )

i i j j

0 0 2

D = ;

gg d^ (gg ! )

d^(gg ! )

T T S

T T

dz 9^s s^

=2 = T (R)

15 3

dz dz 2 F s^

2 T

64 4 d^ (gg ! q q ) d^ (q q ! gg)

i i i i

= =

2 2 2 2

dz 9 dz 3^s

C s^ (2M + M ) + D 1+ 2I(M : ;s^)

R R

(9)

R R

3 T

2 2

^ ^ ^

2^ut t u^ + t u^

D 1 + + ;

2 2

s^ u^ s^

=2p= s^

Here, is the technipion velocity. The sum is over

^ ^

9 u^t ts^ s^u^ d^(gg ! gg)

SU (3) R =3;8 T (R)

representations of the and is the trace S

= 3

2 2

SU (3) T (R)= ^

dz 4^s s^ u^

of the square of their -generator matrices: for t

d(R)=3 d(R)=8 2

triplets (dimension ), 3 for octets ( ). The 2

u^ t

1 1

Re(D 1) ; D 1

remaining factors are given in Table I. The integral is +

gg gg

4 4

u^t

d^ (q q ! q q ) d^ (q q ! q q ) d^ (q q ! q q )

i j i j i j i j i j i j

(1 x y ) I (M ;s) dx dy

= =

xy s M + i

dz dz dz

h i

2 2 2

2 s^ +^u

2 2

M =2s 2 arctan 4M =s 1 s<4M

= if ;

9^s

2 =

(10):

1+ 14M =s

2 2

d^(q q !q q ) d^ (q q ! q q )

M =2s ln i s>4M

i i i i i i i i

: if

1 14M =s

dz dz

2 2 2 2 2 2

2 s^ +^u s^ +^u

The rates at the Tevatron are at most comparable to those en- t

= ; +

2 ^

hanced by technirhos; they are considerably greater at the LHC ^

9^s s^

u^t t

1004

d^ (g q ! g q ) d^ (gq ! gq )

i i i

i [2] S. Dimopoulos and L. Susskind, Nucl. Phys. B155, 237 (1979);

= dz

dz E. Eichten and K. Lane, Phys. Lett. 90B, 125 (1980).

4 1

2 2

S [3] K. Lane, An Introduction to Technicolor, Lectures given at the

(^s +^u ) :

= (12)

2^s 9^su^

t 1993 Theoretical Advanced Studies Institute, University of Col-

orado, Boulder, published in ªThe Building Blocks of Creationº,

1 1

= cos t = s^(1 z ) u^ = s^(1 + z )

Here, z , , and it is 2

2 edited by S. Raby and T. Walker, p. 381, World Scienti®c (1994).

q 6= q = u; d; c; s; b j understood that i contribute to dijet events. [4] E. Eichten, I. Hinchliffe, K. Lane and C. Quigg, Rev. Mod. Phys.

Only the s-channel gluonpropagator was modi®ed to includethe 56, 579 (1984); Phys. Rev. D34, 1547 (1986).

8 T resonance. Here and below, we use the dimensionless prop-

[5] B. Holdom, Phys. Rev. D24, 1441 (1981); Phys. Lett. 150B, 301

D = 1+( (^s)= )D

gg S

agator factors g and T T (1985); T. Appelquist, D. Karabali and L. C. R. Wijewardhana,

Phys.Rev.Lett.57, 957 (1986); T. Appelquist and L. C. R. Wije-

D = :

g (13)

T wardhana, Phys. Rev. D36, 568 (1987); K. Yamawaki, M. Bando

s^(1 (^s)= s ) M + i (^s)

T T 8 8

T and K. Matumoto, Phys. Rev. Lett. 56, 1335 (1986); T. Akiba and

M s 2M

< T. Yanagida, Phys. Lett. 169B, 432 (1986).

T 8

If ,the -dependent width is the sum of

T 8 T

(allowing for multijet tt ®nal states, assumed light compared to [6] K. Lane and E. Eichten, Phys. Lett. B222, 274 (1989); K. Lane p

s ) and M. V. Ramana, Phys. Rev. D44, 2678 (1991).

6 [7] F. Abe, et al., The CDF Collaboration, Phys. Rev. Lett. 73, 225

3 (s)

S (1994); Phys. Rev. D50, 2966 (1994); Phys. Rev. Lett. 74, 2626

( ! gg)= s: ( ! q q )=

T 8 8 i i

T (14)

T (1995) ; S. Abachi, et al., The Dé Collaboration, Phys. Rev. Lett. =1

i 74, 2632 (1995).

8 A search for the dijet signal of T has been carried out by [8] A. Blondel, Rapporteur talk at the International Conference on the CDF Collaboration; see Ref. [18] for a detailed discus- High Energy Physics, Warsaw (July 1996). sion of expected signal and background rates. Rough signal-to- background estimates are given in the table in Report II. They [9] R. S. Chivukula, S. B. Selipsky, and E. H. Simmons, Phys. Rev. Lett. 69 575, (1992);R. S. Chivukula, E. H. Simmons, and J. Tern- are sizable at the Tevatron and LHC, but are sensitive to jet en- ing, Phys. Lett. B331 383, (1994), and references therein. ergy resolutions. Colored technipions are pair-produced in hadron collisions [10] Y. Nambu, in New Theories in Physics, Proceedings of the XI International Symposium on Elementary Particle Physics, Kaz- through quark-antiquark annihilation and gluon fusion. If the

imierz, Poland, 1988, edited by Z. Adjuk, S. Pokorski and

8 T T T decay channels are open, this production is reso- A. Trautmann (World Scienti®c, Singapore, 1989); Enrico Fermi

nantly enhanced. The subprocess cross sections, averaged over Institute Report EFI 89-08 (unpublished);V.A. Miransky, M. Tan- C initial colors and summed over the colors B , of technipions, abashi and K. Yamawaki, Phys. Lett. 221B, 177 (1989); Mod. are given by Phys. Lett. A4, 1043 (1989);W. A. Bardeen, C. T. Hill and

M. Lindner, Phys. Rev. D41, 1647 (1990).

2 3

d^ (q q ! ) (^s)

i i B C

S 2

= S T (R) 1 z D T

[11] C. T. Hill, Phys. Lett. 266B, 419 (1991) ;S. P. Martin, Phys.

dz 9^s

B;C Rev. D45, 4283 (1992); ibid D46, 2197 (1992); Nucl. Phys.

B398, 359 (1993); M. Lindner and D. Ross, Nucl. Phys. B370,

(^s) 3 d^ (gg ! )

B C

S 2 2

= S T (R) z D T

30 (1992);R. BÈonisch, Phys. Lett. 268B, 394 (1991);C. T. Hill,

dz s^ 32

B;C D. Kennedy, T. Onogi, H. L. Yu, Phys. Rev. D47, 2940 (1993).

2 2 2 2

2 (1 z ) (1 z ) [12] C. T. Hill, Phys. Lett. 345B, 483 (1995).

Re (D )+2

2 2 2 2

z 1 z

1 [13] K. Lane and E. Eichten, Phys. Lett. B352, 382 (1995) ;K. Lane,

2 4 2 2

2 Phys. Rev. D54, 2204 (1996).

T (R) 3 (1 ) + (1 z )

;

+ (15)

2 2

2 [14] E. Eichten and K. Lane, ªLow-Scale Technicolor at the Tevatronº,

(R) 32 (1 z )

d FERMILAB-PUB-96/075-T, BUHEP-96-9, hep-ph/9607213; to

z = cos D =

where is the technipion velocity, and T appear in Physics Letters B.

D + D S =1

g gg . The symmetry factor for each channel

T [15] R. S. Chivukula and M. Golden, Phys. Rev. D41, 2795 (1990).

S =

of and for ; for the identical-particle

LQ QL

T 8 T 8

2 [16] E. Farhi and L. Susskind Phys. Rev. D20 (1979) 3404;S. Di-

0 0

SU (3) T (R) T

®nal states, and T .The group factors

T 8 8

T mopoulos, Nucl. Phys. B168, 69 (1980);T. Appelquist and G. Tri-

(R) R =3;8

and d for were de®ned above at Eq. 9. The tech- antaphyllou, Phys. Rev. Lett. 69,2750 (1992) ;T. Appelquist and

qq gg

nirho width is now the sum of the and partial widths and J. Terning, Phys. Rev. D50, 2116 (1994);E. Eichten and K. Lane,

( ! )= S T(R)p =3s

1 B C is given by T .As

T Phys. Lett. B327, 129 (1994);K. Lane, Phys. Rev. D52, 1546 B;C indicated in the table in Report II, pair-production rates for col- (1995). ored technipions with masses of a few hundred GeV are several [17] K. Lane, Phys. Lett. B357, 624 (1995);also see T. Lee, Talk pre- picobarns at the Tevatron, rising to a few nanobarns at the LHC. sented at International Symposium on Particle Theory and Phe- nomenology, Ames, IA, May 22-24, 1995, FERMILAB-CONF- V. REFERENCES 96-019-T, hep-ph/9601304, (1996). [18] F. Abe, et al., The CDF Collaboration, Phys. Rev. Lett. 74, 3538 [1] S. Weinberg, Phys. Rev. D19, 1277 (1979); L. Susskind, Phys. (1995). Rev. D20, 2619 (1979).

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