Discovering New Interactions at Colliders 2 Kingman Cheung 1 and Robert M

Discovering New Interactions at Colliders 2 Kingman Cheung 1 and Robert M. Harris

1 University of Texas, Austin, TX 78712

2 Fermilab, Batavia, IL 60510 E

ABSTRACT neutrino to have more than 30 GeV of transverse energy, T .

E > 50

He required at least two jets in the event, one with T

We summarize results of the 1996 Snowmass workshop on fu-

E > 20 E T GeV, and the other with T GeV. The higher cut on

ture prospects for discovering dynamical electroweak symmetry

M>500 the two jets was optimized for a high mass W search ( breaking, compositeness, and anomalous couplings of quarks at GeV) and should be reduced for a lower mass technirho search.

colliders. We present the mass reach of the Tevatron to a color 1 The resulting W+dijet mass distribution from 110 pb of CDF singlet or octet technirho, and to a topgluon or topcolor Z0 from data was in good agreement with standard model predictions,

topcolor assisted technicolor. We explore the sensitivity of the

1 and was used to determine the 95% CL upper limit on the T Tevatron, LHC, NLC, and VLHC to contact interactions and ex- cross section, shown in Fig. 1. Here he assumed that the accep-

cited fermions. Finally we investigate the possibility of seeing 0

tance for a technirho was roughly the same as for a W .Theex-

anomalous couplings of quarks at the Tevatron and LHC. 1 trapolation to higher luminosities shows that TeV33 (30 fb ) should be able to exclude at 95% CL a color singlet technirho de- I. DYNAMICAL ELECTROWEAK caying to W plus dijets for technirho masses up to roughly 400 SYMMETRY BREAKING GeV. This covers the expected range in the one-family technicolor model. The mechanism of electroweak symmetry breaking is un- known. The possibility exists that electroweak symmetry is not broken by a fundamental higgs boson, but instead is broken through the dynamics of a new interaction. We explore the discovery potential of future accelerators, and luminosity upgrades to the Tevatron, for two models of dynamical electroweak symmetry breaking: one-family technicolor and topcolor assisted technicolor. A. One-Family Technicolor Eichten and Lane [1] have presented a one-family technicolor model with color triplet techniquarks and color singlet tech-

nileptons. The techniquarks will bind to form color singlet tech-

nirhos, and , with mass roughly in the range 200 to

T 1

T 1 400 GeV. Color singlet technirhos are produced in hadron col-

lisions through quark-antiquark annihilation. The expected de-

0 0 0

! W Z W Z !

cay modes are , , ,,and

T T T 1

T 1 T T

W W W

, , . Here the technipions, T , decay pre-

T T T

! cb tb bb

dominantly to heavy ¯avors: ! ,and , . Tech-

% Br( ! Wjj)

Figure 1: 95 CL upper limit of T vs. M .

T 0

niquarks will also bind to form color octet technirhos, , with

T 8

Br The solid line is the theoretically expected and assumes

mass roughly in the range 200 to 600 GeV. Color octet tech-

! WX ! Wjj = 100% 1

T . The dashed lines show pre-

1 1 1

nirhos are produced and decay via strong interactions. If the dicted limits for 110pb ,2fb and 30fb respectively. Note mass of the colored technipions is greater than half the mass of that we have assumed that the limits simply scale as the inverse the technirho, then the color octet technirho will decay predom-

of the square root of the luminosity

! gg 8 inantly to dijets: T . If colored technipions are light the

color octet technirho decays to pairs of either color triplet tech-

! W + bb 1

nipions (leptoquarks) or color octet technipions. 2. T at the Tevatron and LHC

q q ! ! 1

Womersley [3] has studied the process T

! W

T 1

1. + dijet at the Tevatron

W ! (l )(bb)

T , including the effect of tagging events with a

! WX X W Z b m = 210

The search for T ,where can be a , ,or ®nal state quark, for theparticular case of GeV and

= 115 W m

T , is suf®ciently similar to the search for a massive decay- GeV. He generates signal and background events

0 W ing to WZ, that Toback [2] has extrapolated the search to using ISAJET, and uses a fast simulation of the CMS detector higher luminositiesas an estimate of our sensitivity to color sin- at the LHC. After all simulation, events are required to have a

glet technirhos at the Tevatron. He considered the decay chain good W candidate, formed from an isolated charged lepton with

! WX ! e + E > 25 j j < 1:1 T T dijets, and required both the electron and GeV and pseudorapidity , a neutrino with

969

E > 25

T GeV, and their combined transverse mass in the range

T GeV. Further, events were required to have

E > 20 j j < 2:5

two jets with T GeV and , and the probability of tagging at least one of the two b quarks was assumed to be

50% with a mistag rate of 1% for light quarks. Figure 2 show

the reconstructed T peak in the signal sample, and that prior to b-tagging the signal is swamped by a large QCD W+dijet background. Figure 2 also shows that after b-tagging the signal to background is signi®cantly improved at both the Tevatron and the LHC. For this particular case of a light technirho the signal to background is better at the Tevatron although the rate at the LHC is considerably higher. Clearly, b-tagging is critical, and

makes possible the discovery of a 210 GeV color singlet tech- 1 nirho at the Tevatron in Run II (2 fb ).

Figure 3: The mass reach for new particles decaying to dijets vs. integrated luminosity at the Tevatron. The mass reach of the

NLC for direct production is also shown.

gg ! Z Z ;W W

L L L 4. L at LHC Lee [6] has studied the production of longitudinal weak gauge boson pairs via gluon fusion in a one-family technicolor model [1] at the LHC. Fig. 4 shows that when the invariant mass

is above the threshold for production of pairs of colored techni-

W W Z Z

L L L pions, the L or signal cross section is greater than

the standard model background by over an order of magnitude.

Z Z L Assuming an integrated luminosity of 100 fb ,the L signal, over a thousand events with four leptons in the ®nal state

(e and ), will be easily observable. If one-family technicolor

! W + ! (l )(bb)

1 T Figure 2: T search. (upper left) Lead- exists, the LHC will see it in this channel. ing dijet invariant mass distributionfor signal at the LHC. (upper 100 100

right) Same for signal (dark) and background (light) at the Teva- |y|<2.5 |y|<1.5

1 tron before b-tagging. Vertical scale is events/10 GeV/2 fb . 10-1 10-1 (lower left) Same at the Tevatron after b-tagging. (lower right)

Same at the LHC after b-tagging. Vertical scale is events/10 10-2 10-2 1 GeV/0.5 fb . All horizontal scales are in GeV. 10-3 10-3

10-4 10-4

Cross section (pb/GeV) Cross section (pb/GeV)

! 8 3. T dijets at the Tevatron (a) (b) 10-5 10-5 Harris has determined the sensitivity at the Tevatron to di- 200 400 600 800 1000 200 400 600 800 1000 jet decays of color octet technirhos by extrapolating CDF Mzz(GeV) Mww(GeV)

searches [4] to higher luminosities. Here there are signi®cant

Z W L Figure 4: The cross sections for a) L -pair and b) -pair pro-

QCD backgrounds, so the cross section limits scale inversely as

E =14

duction via gluon fusion in proton collisions at c:m: TeV.

the square root of the luminosity. In reference [5] he compared

q The solid curves are for the q initiated backgrounds, and dot- the cross section limit to the theoretical prediction, to determine ted, dot-dashed, and dashed curves are for technipion masses of

the mass excluded at 95% CL, shown in ®g. 3. The mass reach

GeV 300 GeV 350 GeV

250 , ,and respectively. The thick dot-

:77

for color octet technirhos is 0 TeVforRunII(2fb )and

=0 m

dashed curves are for the chiral limit ( ).

:90

0 TeV for TeV33 (30 fb ), which is more than the expected

8 T mass in the one-family technicolor model.

970 B. Topcolor Assisted Technicolor Eichten and Lane [7] have recently discussed the phenomenol- ogy of the topcolor model of Hill and Parke [8], and Burdman has recently studied the scalar sector of the model [9]. Topcolor assisted technicolor [10] is a model of dynamical electroweak

symmetry breaking in which the top quark is heavy because of

SU (3)

a new dynamics. Topcolor replaces the C of QCD with

SU (3) SU (3) 2 1 for the third quark generation and for the ®rst

two generations. The additional SU(3) symmetry produces a <

t> t condensate which makes the top quark heavy, and gives rise

to a color octet gauge boson, the topgluon B. The topgluon is ex-

=M 0:3 0:7 M 0:5 2 pected to be wide ( ) and massive ( TeV). In hadron collisions it is produced through a small cou-

pling to the ®rst two generations, and then decays via a much

q ! B ! bb;tt

larger coupling to the third generation: q .

U (1)

Similarly, topcolor also replaces Y of the standard model

U (1) U (1)

1 Y 2

with Y for thethird generation and for the ®rst two (1) generations. The additional U keeps the bottom quark light,

and gives rise to a massive color singlet gauge boson, the top-

0 0

Z =M 0:01 0:1

color Z . The topcolor may be narrow ( )

and it couples predominantly to t .

Figure 6: Same as Fig. 5 for t decays of topgluons.

b 1. Topgluons decaying to b at the Tevatron

Harris [11] has used a full simulation of topgluon production

and decay to , and an extrapolation of the b-tagged dijet mass t 2. Topgluons decaying to t at the Tevatron

data [12], to estimate the topgluon discovery mass reach in a

Harris [14] has used a parton level prediction for produc- b b resonance search. Fig. 5 displays the results for three differ-

ent widths of the topgluon. The topgluon discovery mass reach, tion from QCD and topgluons, together with theprojected exper-

imental ef®ciency for reconstructing t , to estimate the topgluon

:77 0:95 1:0 1:2

0 TeV for Run II and TeV for TeV33, covers

discovery mass reach in a t resonance search. Fig. 6 dis-

0:5 2 a signi®cant part of the expected mass range ( TeV).

plays the results for three different widths of the topgluon. The

:0 1:1

topgluon discovery mass reach, 1 TeV for Run II and

:3 1:4

1 TeV for TeV33, covers a signi®cant part of the expected

0:5 2

mass range ( TeV). The mass reach estimated using

t the total t cross section, shown in Fig. 7, is similar to that for

the resonance search, providing an important check. This mass

reach is better than in the b channel, discussed in the previous

t section, because backgrounds in the t channel are smaller. If topgluons exist, there is a good chance we will ®nd them at the

Tevatron.

t t

3. Topcolor Z decaying to at the Tevatron

0 !

Tollefson [15] has considered the decay chain topcolor Z

t ! (Wb)(W b) ! l bbjj t . She uses the PYTHIA Monte Carlo [16] and a CDF detector simulation for both the signal and

background. As in the CDF top quark mass analysis [17], she re-

E > 20

quires a central charged lepton with T GeV, a neutrino

E > 20 E > 15 j j < 2 T

with T GeV, 3 jets with GeV and , one

E > 8 j j < 2:4

jet with T GeV and and requires that at least b

two of the four jets be tagged as a quark. She reconstructs the b

Figure 5: The mass reach for b decays of topgluons of width

t a) 0.3 M, b) 0.5 M, and c) 0.7 M. The cross section for topglu- t mass with the following mass constraints: the charged lepton and neutrino reconstruct to the mass of a W, the two jets recon-

ons (points) is compared to the 5 discovery reach of the Teva-

1 1

tron with a luminosity of 2 fb (dashed) and 30 fb (solid). d) struct to the mass of a W, and the mass of each reconstructed top

quark be 175 GeV. This results in t mass resolution of 6% and

SU (3)

Topgluon width as a function of mixing angle between 1

an acceptance of 6.5% for the signal. From a binned maximum

SU (3)

and 2 for 3 topgluon masses (curves). The vertical dashed

t lines are the theoretically preferred range of mixing angle [13]. likelihood ®t of the simulated t mass distribution, she deter-

mines what resonance cross section would produce a 5 signal,

971 0

and compares that to the expected topcolor Z cross section in 0

Fig. 8. The resulting mass reach for a narrow topcolor Z at the

:9 1:1

Tevatron is 0 TeV for Run II (2 fb )and TeV for TeV33 1 (30 fb ).

II. COMPOSITE FERMIONS The repetition of the three generations of quarks and leptons strongly suggests that they are composite structures made up of more fundamental fermions, which are often called ªpreonsº in the literature. There have been a lot of theoretical efforts to con- struct realistic models for composite fermions, but no obviously correct or compelling model exists. Nor do we know the energy

scale which characterizes the interactions of preons.

A. Contact Interactions Deviations from the Standard Model (SM) in low energy phe- nomena can be systematically studied using the effective La- grangian approach. In this approach, an effective Lagrangian,

which obeys the low energy SM symmetries, is constructed out

t Figure 7: The fractional difference between the t cross section of the SM ®elds. The leading terms are simply given by the SM, and the QCD prediction is shown for topgluons (solid curves), while the higher order terms consist of higher-dimension oper-

CDF data (solid circle), and D0 data (open box). The projected ators and are suppressed by powers of the scale of the new

5 uncertainty (dashed lines) and 95% CL (dotted lines) on the physics.

t measured t cross section can be compared with the topgluon The existence of quark and lepton substructure will be sig-

prediction to determine the discovery reach and exclusion reach naled by the appearance of the four-fermion contact interactions

1 of the Tevatron at the luminosities of 1, 10 and 100 fb . at energies below [18]. Eichten and Lane have reviewed these

contact interactions [7]. They arise from the exchanges of preon

(3) SU (2) U (1) bound states, and they must be SU invariant because they are generated by forces operating at or above the electroweak scale. The lowest order four-fermion contact inter-

actions are of dim-6, which means that they are suppressed by

= Min σ∗B(X→tt) for a resonance 1 . The general Lagrangian of four-fermion contact interac-

to be observed at the 5σ level. tions, up to dimension 6, can be written as

-1

1 fb g

L q q + F ` ` q q + F ` `

` ` (1)

1 2

L=R L=R B (pb) -1

σ∗ 10 fb =

where we have suppressed the generation and color indices,

1 F

,and ` is inserted to allow for different quark and lepton (1) -1 couplings but is expected to be O . It is conventional to de®ne

100 fb 2

=4 s^ -1 g , so that the interaction isde®ned to be strong when ap- 10

proaches . These contact interactions can affect jet production,

the Drell-Yan process, lepton scattering, etc. Since compared to

s= ^

the SM the contact interaction amplitudes are of order S

s= ^

or em , the effects of the contact interactions will be most s important in the phase space region with large ^. Therefore, the -2 10 TopColor Z‘, Γ=1.2% four-fermion contact interactions are often searched for at the ‘

Γ E

TopColor Z , =10% high T region in jet and lepton-pair production. So far, the con- 400 500 600 700 800 900 1000 tact interaction used most to parameterize the substructure scale 2

, is the product of two left-handed electroweak isoscalar quark Mtt GeV/c

and lepton currents.

:B (X ! t t ) t

Figure 8: t vs. mass. The minimum cross sec-

0 0

tion to observe a excess of events in a sample with 1, 10 and

l ! q q l l ! l l

1. l and Contact 1

100 fb (lines) is compared to the expected cross section for a

0 0

``q q ``` `

0 Cheung, Godfrey, and Hewett [19] studied the and

=M = :012 =M = :1

topcolor Z with width (triangles) and

+ +

e (squares). contact interactions at future e and colliders, and de-

rived limits on the compositeness mass scale using the reac-

972

cos distribution for the theory with a ®nite . An acceptance

Table I: 95% CL lower bounds on at lepton colliders, as a func-

cos j < 0:9 cos cut j was imposed and the whole distribution

tion of center of mass energy and integrated luminosity, shown is divided into 10 equal bins. The ef®ciencies in detecting the ®-

= 60% b c

for each possible helicity of the interaction. nal state are for quarks, 35% for quarks, and 100%

+ for leptons. The limits on at 95% CL that can be obtained by e

e Colliders

+ +

various processes at future e and colliders are tabu-

L s in TeV

lated in Table I. Very substantial improvements in probing the

LL LR RL RR

TeV fb Process + e

compositeness mass scale can be achieved. A 0.5 TeV e

+ +

e e ! 1 0.5 50 19 16 16 18

collider with a 50 fb luminosity can probe up to around 20

e ! bb e 24 18 5.5 16

TeV, which is better than Run II of the Tevatron. Up to about 40,

e ! cc

e 20 4.2 5.6 17

=1:0;1:5

60, and 160 TeV can be probed at s , and 5.0 TeV

+ +

e e !

1.0 200 37 33 33 36 +

e machines, respectively. A 4 TeV collider, which is

e ! bb e 48 36 11 33

under intensive study, can probe up to about 140 TeV. Slightly

e e ! cc

5.1 8.3 11 5.9

better results can be obtained by using polarized e beams with

+ +

e !

1.5 200 e 45 40 40 44 the same luminosity [19].

e ! bb

e 59 44 17 41

e ! cc

e 7.7 12 16 8.9

q q ! l l

+ +

2. Contact

e !

5.0 1000 e 120 110 110 120

e ! bb

e 160 120 54 110 P. de Barbaro et al [20] have studied the effect of a left-handed

e ! cc

e 26 40 51 29 contact interaction between quarks and leptons at the Tevatron.

+ Using 110 pb of CDF data on dielectron production, they re-

Colliders

+ +

(q q ! e e ) 3:4

port preliminary limits of TeV and

0.5 0.7 6.3 5.7 5.7 6.1 LL

(q q ! e e ) 2:4

TeV at 95% CL. They also report lim-

! bb

8.0 6.3 4.3 6.1 LL +

its for the dimuon channel and the combined dielectron+dimuon

! cc

6.9 3.5 4.0 2.7

+ +

channels; the latter is approximately 0 TeV more stringent than

0.5 50 19 16 16 18

with electrons alone. Using a Monte Carlo procedure they esti-

! bb

24 18 5.5 16 +

mate the sensitivity of the Tevatron with higher luminosities.

! cc

20 4.2 5.6 17

+ +

For standard model production of dielectrons they simulate

4.0 1000 110 99 99 110

one hundred experiments with 2 fb and one hundred exper-

! bb

140 110 44 100

1 +

iments with 30 fb , each measuring the dielectron mass spec-

! cc 20 33 42 24 trum. For each experiment they calculate a likelihood as a func-

tion of of that experiment coming from the standard model

plus a contact interaction of strength . To minimize ¯uctua-

` ! f f f = ; ; b; c ` = e; ` 6= f ) tions ` ,where and ( .

tions in the shape of the likelihood function, they average the

Z These reactions proceed via s-channel exchanges of , ,and

likelihood functions from the 100 experiments. In Figure 9 they f

the ``f contact interaction. The polarized differential cross

plot the log likelihood as a function of ,where is the sign

e ! f f cos

sections for e versus ,where is the scat- L=R

tering angle in the CM frame, are given by of the contact interaction. From Fig. 9 a Tevatron experiment

1 +

(q q ! e e ) 10

with 2 fb would exclude TeV and

+ 1

(q q ! e e ) 6:5

C d f

L TeV, and 30 fb would exclude

2 2 2 2 LL

= jC j (1 + cos ) + jC j (1 cos )

+ +

LL LR

(q q ! e e ) 20 (q q ! e e ) 14

cos 4s

d TeV and TeV.

LL LL

= 1 (2) The sensitivity is always greater for , because this corre-

where sponds to constructive interference between the standard model

f and the contact interaction, and hence a larger number of dielec-

C C s s

L L

= Q + +

C trons. f

LL (3)

2 2 2

c s s M + i M 2

Z Z

w w

qq ! qq

f 3. Contact

C C

s s

C = Q + + f

LR (4)

2 E

2 2 2

An excess of events with high jet T in hadron collisions is a

c s M + i M 2 s

Z Z

w w

! qq

well known signature for a qq contact interaction. How-

f f

2 2

= T Q s = Q s C C C = 3(1) f

3f f f

and , , f for being ever, signi®cant uncertainties in the parton momentum distribu-

w w

L R

s c w

a quark (lepton), w and are, respectively, the sine and co- tions within the proton, ambiguities in QCD calculations, and

d =d cos

sine of the weak mixing angle. The expressions for R , systematic uncertainties in jet energy measurement, make it dif-

C C L $ R RL RR ,and can be obtained by interchanging .The ®cult to discover a signal. This is apparent from the recent CDF

unpolarized differential cross section is simply given by the av- measurement of the inclusive jet cross section [21], and the phe-

d =d cos d =d cos R

erage of L and . Other observables, e.g., nomenological papers which followed [22]. Some progress has

A ;A cos LR FB , can be obtained from these distributions. been made at the Snowmass workshop on quantifyingthe uncer-

To obtain the sensitivity to the compositeness scale they as- tainties in the parton distributions [23], however, more work is

qq ! qq sume that the SM is correct and perform a analysis of the clearly necessary. Another signal of a contact interac-

973 6

Figure 10: Event rate for isolated events with invariant

3 min pp

masses larger than M at a 60 TeV collider scaled to a lu-

minosity of 100 fb . The solid curves is the SM case while

( )= 3 the top dotted curve corresponds to + TeV in the left (right) ®gure. Each subsequent dotted curve corresponds to an

increase in by 1 TeV. In either case we have applied the cuts

p j j 1 500

GeV and . t 0

-1 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 destructively with the SM contribution. It is clear that the con-

tact interaction in (5) affects the parton cross section most in the s region with large ^, and thus it causes the cross section to be

Figure 9: The change in the log likelihood function from the less peaked in the forward and backward directions and gener-

1= ee

maximum plotted as a function of for channel with ates more central and higher T photons. It also enhances the

1 1 M

2fb (circles) and 30 fb (squares). The 95% CL one sided production rate at high diphoton invariant mass .

limit occurs where the solid line at 1.34 intersects the points. Figure 10 shows the integrated event rates for isolated dipho-

min pp

ton events with invariant mass larger than M at a 60 TeV

collider with a 100 fb luminosity. It clearly shows that the

tion, which is not very sensitive to theoretical or jet energy mea- contact interaction of Eq.(5) changes the cross sections most in min

the high M region. In order to obtain the sensitivity to the

surement, is a dijet angular distribution which is more isotropic 1 than predicted by QCD. Using 110 pb of data at the Teva- contact interaction, we can assume that there is no event excess

tron, CDF has recently measured the dijet angular distribution over the SM predictions in various future collider experiments,

2 and found good agreement with QCD predictions, thereby ex- and then we can put limits on using a simple analysis.

cluding a contact interaction among up and down type quarks The results for various future collider experiments are tabulated

1:6 1:4

with scale TeV or TeV at 95% CL [24]. in Table II. From the table we can see that colliders are bet-

q q

For a ¯avor symmetric contact interaction among all quarks the ter than pp colliders because there are more luminosities in

pp pp

:2 exclusions are 0 TeV more. Although with further luminos- than in . The limits can be pushed to about 7±13 TeV at a ity this exclusion will improve somewhat, comparing this limit 60 TeV machine, and about 16±33 TeV at a 200 TeV one. withthat obtained from the UA1 experiment [25], we see that the

compositeness scale reach of a hadron collider is roughly equal p

to its center of mass energy, s . This is con®rmed by studies of

q q

Table II: 95% CL bounds on the scale of the contact in-

15 the LHC [26], where the predicted reach is TeV. min

teraction at future hadron colliders. Here, p is the minimum t

transverse momentum of each of the photons in GeV, L is the

q !

4. q Contact Interaction

machine integrated luminosity in fb ,and is the lower

q ! Rizzo has previously studied the effects of a q contact bound on the scale in TeV.

interaction at the Tevatron and the LHC [27] and here he extends

these results to a Very Larger Hadron Collider (VLHC) [28]. min

p j j L

Machine ;max t The lowest dimension gauge invariant operator involving two TeV 15 1 2 0.75 0.71

fermions and two photons is a dimension-8 operator, which in- LHC 200 1,2.5 100 2.8 2.9

duces a q contact interaction. This interaction, assuming

' 9:5 ' 6:5 60 TeV (pp) 500 1 100

parity and CP conservation, is given by

p ' 13:5 '

60 TeV (p ) 500 1 100 10.5

pp ' 23 ' 16

2 200 TeV ( ) 1000 1 1000

2ie

pp ' 33 ' 26

L = Q F F q @ q;

(5) 200 TeV ( ) 1000 1 1000

where e is the electromagnetic coupling, and is the associated B. Excited Quarks mass scale. The observation of the signatures associated with

this operator would be a clear signal of compositeness. The mass Although it is expected that the ®rst evidence for quark and/or scale indicates that the limits obtained below will depend lepton substructure would arise from the affects of contact inter- upon whether the contact operator interferes constructively or actions, conclusive evidence would be provided by observation

974 of excitations of the preon bound state. If quarks are composite The effective Lagrangian for the interactions between a quark

particles then excited quarks are expected. Harris [29] has in- and a gluon that include the CEDM and CMDM form factors is

vestigated the prospects for discovering an excited quark [30],

a d a a 5 a

u or with spin 1/2 and weak isospin 1/2, at hadron collid-

G + L = g qT G G q:

e s

4m 4m

qg ! q ! qg q ers. He considers the process , and does a lowest q

order calculation of the dijet resonance signal and QCD back- (6)

=2m =~ 2m q q ground assuming an experimental dijet mass resolution of 10%. where q ( ) is the CMDM (CEDM) of the quark .

The above Lagrangian is valid for both light and heavy quarks.

0:94

The estimated 5 discovery mass reach at the Tevatron is

1 1

The Lagrangian in Eq. (6) gives an effective qqg vertex, and also

TeV for Run II (2 fb )and1 TeV for TeV33 (30 fb ). The

induces a qqgg interaction, which is absent in the SM. We shall

:3 mass reach at the LHC is 6 TeV for 100 fb . The discovery mass reach at a Very Large Hadron Collider (VLHC) is shown use a short-hand notation:

in Fig. 11 for 3 different machine energies as a function of in-

0 0

= ; ~ =

tegrated luminosity. At a VLHC with a center of mass energy (7)

2m 2m q

of (50) 200 TeV the mass reach is 25 TeV (78 TeV) for an inte- q

4 1

10 1 grated luminosity of fb . However, an excited quark with which are given in units of (GeV) .

a mass of 25 TeV would be discovered at a hadron collider with

1 = 100 s TeV and an integrated luminosity of only 13 fb : A. Prompt Photon Production here a factor of 2 increase in energy from a 50 TeV to a 100

TeV machine is worth a factor of 1000 increase in luminosity Cheung and Silverman have studied the effects of anomalous at a ®xed machine energy of 50 TeV. CMDM and CEDM of light quarks on prompt photon production [35]. Prompt photon production is sensitive to the gluon luminosity inside a hadron because it is mainly produced by quark-gluon scattering. For the same reason this process is also sensitive to the anomalous couplings of quarks to gluons. The

contributing subprocesses for prompt photon production are:

(q)g ! q(q) q q ! g

q and . The spin- and color-averaged

q (p )g (p ) ! (k )q (k )

2 1 2

amplitude for 1 is given by

2 2

16 Q

0 0

s + t

s em

2 2 2

= 2u( +~ )

jMj (8)

3 st

where

2 2 2

s =(p +p ) ;t=(p k ) ;u=(p k ) ;

2 1 1 1 2

1 (9)

Q q

and q is the electric charge of the quark in units of proton

charge. Similarly, the spin- and color-averaged amplitude for

q (p )q(p ) ! (k )g(k )

2 1 2

1 is given by

2 2

128 Q

0 0

t + u

s em

2 2

Figure 11: The discovery mass reach, for excited quarks de- 2

+2s( +~ ) : =

jMj (10) ut

caying to dijets, is shown as a function of integrated luminosity 9

p =50 for a VLHC with s TeV, 100 TeV and 200 TeV (solid curves). The horizontal dashed line demonstrates what luminos- The differential cross section for prompt photon production ver- ity is necessary to discover a 25 TeV excited quark. sus the transverse momentum of the photon is shown in Fig. 12a.

The LO QCD curve has to be multiplied by a K -factor of about

III. ANOMALOUS COUPLINGS OF QUARKS 1.3 to best ®t the CDF data. Figure 12a also shows curves with 0

nonzero values of CMDM. It is clear that nonzero will in-

The lowest order interaction between a quark and a gluon is crease the total and the differential cross sections, especially in

t T tG p ( ) T

a dimension-4 operator, a . Among all the dimension-5 the large region. The effects due to nonzero CEDM will

operators, the most interesting ones involvingquarks and gluons be the same because the increase in cross section is proportional

0 0

2 2

+~ ) are the chromomagnetic (CMDM) and chromoelectric (CEDM) to ( . dipole moment couplings of quarks. These dipole moment cou- The fractional difference from pure QCD for nonzero CMDM

plings are important not only because they are only suppressed is shown in Fig. 12b. The data are from CDF [36] and D0 [37].

p ( )

by one power of but also because a nonzero value for the The anomalous behavior at low T has already been resolved

CEDM is a clean signal for CP violation. The effects of these by including initial and ®nal state shower radiation, therefore, p

anomalous couplings have been studied quite extensively, e.g., only the large T region is relevant. Since in Eqs. (8) and (10)

0 0

t bb ~ in t production [31, 32, 33], in production [31], and in inclu- the role of and are the same, one of them is kept zero when sive jet production [34]. bounding on the other. From these curves it is clear that the CDF

975

> 0:0045

and D0 data would be inconsistent with , therefore, E

Table III: Table of High T Bins at 10% Statistical Error and 1-

giving a bound of

Sensitivity for in that Bin, is shown as a function of machine

0 energy, integrated luminosity, and bin width.

0:0045 GeV

(11) E

Int. Bin T Jets Photons

on the CMDM of light quarks. Similarly, a bound of ~

E E E

cm Lum. Width

T T

:0045 GeV 1 0 on the CEDM of light quarks is valid as well. TeV fb GeV GeV TeV GeV TeV

We compare this with the results obtained in Ref.[34] for jet pro- 1.8 0.1 10 360 1.8 140 0.7 0 duction. The value of obtained in ®tting to the CDF[21] trans- 2.0 2 20 490 2.8 260 1.5

verse energy distribution of the inclusive jet production is[34] 2.0 10 20 540 3.3 325 1.9

0 3

=(1:00:3) 10 GeV which is consistent with the 2.0 30 20 575 3.5 370 2.1 bound in Eq. (11) 14 10 100 2500 13 1000 4.5 14 100 100 3100 17 1400 6.3

the top pair production threshold region, and have much higher sensitivities to the CMDM.

Figures 13a and 13c show the modi®cations in the SM expec-

d =dM d =dp t tations for both tt and , respectively, for differ-

ent values of of the top quark. Perhaps more revealing, Fig-

ures 13b and 13d show the ratio of the modi®ed distributions to

d =p d

Figure 12: (a) Transverse momentum distribution T in the corresponding SM ones. One can see that a non-zero leads

prompt photon production for pure QCD and nonzero values of

i p M ii tt

to ( ) enhanced cross sections at large t and ,and( )the 0

. The data points are from CDF; (b) fractional difference from shapes of thedistributionsare altered, i.e., the effect is not just an

0 0

~ QCD for various values of and . Both D0 and CDF data are overall change in normalization. The sensitivities of these dis- shown. tributions to nonzero are also estimated using a Monte Carlo approach, taking into account a reasonable size of systematic er- rors. Assuming the SM is the correct theory, the 95% CL al-

B. Sensitivities in Future Collider Experiments

0:09 0:10

lowed regions of of the top quark are

M 0:06 0:06 p T Silverman and Cheung [38] have estimated the sensitivity of from the tt distribution and from the the Tevatron and LHC to the anomalous chromomagnetic dipole distribution. moment of light quarks. A lowest order parton level calculation was used, and only the statistical sensitivity of the experiments was considered. The criterion, in the spirit of reference [26], is

to take bins of appropriate size for the energy range being exam-

E E

ined, and ®nd the T called at which the QCD cross section T statistical error bars are 10%. These will be bins with 100 QCD events. Then the cross section due to QCD plus the anomalous

chromomagnetic moment contributionwill be explored, and the

value of or is determined where the excess over

QCD is 10% at this E .These and are shown in Table III.

T T

Varying the bin size by a factor of two makes only a small change

j j

in the value of E or . The limits in used are 0.9 for the T

Tevatron, and 1.0 for the LHC. From table III one can see that

sensitivity scales roughly as the beam energy.

t C. Effects on t Production at the LHC Top quark production at hadronic colliders is the most obvi-

ous place to probe the anomalous coupling of top quarks to glu- t Figure 13: (a) t invariant mass distribution at the LHC for var-

ons. There have been quite a few studies [31, 32, 33] on this sub-

m = 180

ious values of assuming t GeV. (b) The same distri-

ject at the Tevatron energies. Rizzo has extended the study to the

t tp

bution scaled to the SM result. (c) t distribution at the LHC

LHC [39]. The contributing subprocesses to top pair production and (d) the same distribution scaled to the SM. In all cases, the

q; gg ! tt are q . The existence of a nonzero chromomagnetic SM is represented by the solid curve whereas the upper(lower) dipole moment of the top quark will change both the total and pairs of dotted, dashed, and dash-dotted curves corresponds to

differential cross sections. Since higher partonic center-of-mass = 0.5(-0.5), 0.25(-0.25), and 0.125( -0.125), respectively. energies become accessible at the LHC , one can probe beyond

976 Table IV: The mass reach and discovery potential, for particles from one-family technicolor or topcolor, at the Tevatron as a function of integrated luminosity

Channel Run I Run II TeV33

1 1 1

(.1 fb ) (2 fb ) (30 fb )

! W 400 1 T + dijet No Mass No Mass GeV

(no b-tagging) Reach Reach at 95% CL

! W 1

T + dijet Discovery for Better than

M = 210 M = 115

(with b-tagging) ? GeV no b-tag

! 0:25

8 T dijet TeV TeV TeV

at 95% CL at 95% CL at 95% CL

! bb 0:77 0:95 1:0 1:2

Topgluon B Search in TeV TeV

:3 < =M<0:7 5 5

( 0 )Progress at at

! tt 0:97 1:11 1:3 1:4

Topgluon B Search in TeV TeV

:3 < =M<0:7 5 5

( 0 )Progress at at

! tt

TopC Z Search in 920 GeV 1150 GeV

=M = :012 5 5 ( ) Progress at at

Table V: Mass and energy reach in TeV for new interactions at colliders. The symbol ªº indicates a guess based on scaling from lower energy machines. ªFoundº indicates the collider will discover the particle if it exists, and ªAlready Foundº indicates the particle would have already been discovered by a earlier collider. The symbol ª±º means not applicable, and ª?º means we don't

know. The numbers in square brackets are either con®dence levels in % or RMS deviations in units of , indicating the statistical size of the effect corresponding to the mass or energy reach.

Particle Collider

or TeV33 LHC VLHC NLC Muon

+ +

p pp pp e e

Interaction 2TeV,p 14 TeV, 200 TeV, .5 TeV, 4TeV,

1 1 1 1 1

fb fb fb fb

Scale 30 fb 100 1000 50 1000

> 1 1:5 6:7 10 1

Technicolor T .4 [95%] ? [ ]

! 8

Techni T dijet Found Already Found

! tt 5

Topcolor Z 1.1 [ ] Found Already Found

! bb; tt 5

Topgluon B 1.4 [ ] Found Already Found

0 0

(l l ! l l ) 19

LL ± ± ± [95%] 110 [95%]

(qq ! qq) 2 15 200

LL ± ±

(q q $ l l ) 100 1000

LL 20 [95%] 24 [95%] 140 [95%]

q q ! )

( 0.9 [95%] 3 [95%] 20 [95%] ± ±

5 5 0:45 3

Excited Quark 1.1 [5 ] 6.3 [ ] 78 [ ]

> 1 > 1

CMDM (dijets) 3.5 [ ] 17 [ ] ? ± ±

> 1 > 1

CMDM ( +jet) 2.1 [ ] 6.3 [ ] ? ± ± y from reference [26] from reference [40]

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