New threshold model for high-energy elastic scattering

llllllllml

i

PROCEEDINGS SUPPLEMENTS

Nuclear Physics B (Proc. Suppl.) 25B (1992) 70-76 North-Holland

NEW THRESHOLD MODEL FOR HIGH-ENERGY ELASTIC SCATrERING Kyungsik KANG Department of Physics, Brown University°, Providence, R102912, USA and Division de Physique Th~'orique*, IPN, 91406 Orsay Cedex and LPTPE, Universit~ Pierre et Marie Curie, 4 Place Jussieu 75252 Paris Cedex 05, France Alan R. WHrIE High Energy Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA

(pi'csented by Kyungsik Kang#) We show that a new threshold model with a threshold close to but below the UA4 energy is compatible with all forward elastic scanering data. Possible origin of the threshold and related new physics are also discussed.

1. INTRODUCTION There are two interesting experimental results from the hadmn colliders that, if confirmed by further experiments, might perhaps entail the beginning of new Physics beyond that expected from the standard picture of hadron inmractions. They are the large UA4 result I for the real part of the elastic p~ forward scattering amplitude and the more recent result 2 of the "low" p~ total cross-section at the Fonnilab tevawon energy reported by ET10. The UA4 result was the reason for a lot of theoretical discussion in the litera,'-a+"c3 but -'.~.eETI0 ~su!t ,~z~ sinc~ r ~ o v ~ d r~c.st of the theoretical explanations. In fact the large UA4 real part is difficult to reconcile with the E?10 result for the total cross-section in standard high-energy models. A new physics effect must be introduced in order to link these two results. This conclusion is further strengthened by the E710 result on the real part of the forward elastic scattering amplitude that4 we have just heard at ~his meeting. Also the CDF group has announced a preliminary result [5] for the total cross-section that confirms the low E710 result. In this talk I would like to report a theoretical model6

that can explain all scattering data for the total cross section and the real part including those of UA4 and E710. This model was suggested before 7 the low luminosityindependent E710 cross-section was known. Assuming the validity of the UA4 real part and examining the trend of the total cross-sections at the UA4 and tevatmn energies, we concluded that there must a new relatively small Diffractive Threshold Below the UA4 Energy. As we discussed in Ref. 7, such a threshold is even suggested by Cosmic Ray Experiments. The more recent E710 result necessitates a trivial and minimal modification to our model but the physical picture that we had in mind for our model is, if anything, further supported by the ET10 result on the real part that we have just heard, making our model to stand out as one of the few models, perhaps the only one, that can explain all elastic scattering data. The plan of the talk is as follows: In the next section, I will review briefly other theoretical attempts to explain the high energy elastic scattering data in order to motivate the new diffractive threshold model. In Sec. III, I present the new threshold model and discuss further implications of the

o Permanent address * Unit~ de Recherche des Universit~s Paris 11 et Paris 6 Associte au CNRS # at the International Conference on E]~tic and Diffractive Scattering (4th Blois Workshop), May 22-25, 1991, Isola d'Elba, Italy

0920-5632/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved.

K./fang, A.R. White/Threshold model for high-energy elastic scatteriag

71

model. In addition, I will touch upon a possible origin o f

introduce a new physics ingredienL

the threshold, i.e., the dynamical condensation o f sextetcolored quarks which can produce an axion-like particle "q6

which is slowly varying with In s, the real part fails to grow

that can be diffractively produced in hadron scattering.

big enough to be consistent with 0) unless there is a large

In general, in any model with a total cross-section

difference between the pp and pl5 total cross-sections, i.e, 2. THEORETICAL ATTEMPTS Interest in the high energy elastic scattering problem has

a large Odderon term. This can easily be seen from the quasilocal analytic derivative dispersion w,lation9

been renewed mainly due to the UA4 observation at the CERN S p a s collider that the ratio of the real to imaginary parts of the forward p~ elastic scattering amplitude at 4"s = 546 GeV is surprisingly large I, i.e.,

Re Ap~

P=lmA~

=

d

2dlns ~

s

,

= I O,n A.,_ s"

2 21m A~,p+lm App] __4.L_ J

0.24 _+0.04

(1)

subject to OT(I + p2) = 63.3+1.5 mb to fix the absolute

)+

(4)

+ higher derivatives

normalization of the differential cross-section8. While it is not difficult to explain the total cross-section OT = 60+_2 mb

renormalized Pomeron and exchange-degenerate Reggeon

at the CERN energy, most high-energy models fail to

terms can give at most an increase of 4.4 mb for Re Aft,/s

explain (1) as it is about 3 standard deviations away from

from the ISR m the UA4 energy from (4), whereby leaving

the prediction based on conventional models. This has

about 10 mb deficit to be consistent with the UA4 result

stimulated a lot of theoretical speculation3.

(1). Therefore if the real part is as large as (1), either there

There is another experimental surprise that confronts

Typical models such as the one containing a

must be a locally non-smoath region for the total cross-

any theoretical attempt now, i.e., the low luminosity-

section as a function of Ins between the ISR and the UA4

independent ~p total cross-section2 measured by E710 at

energies or there must be an extraordinarily large Odderon

the Fermilab tevatron energy 4-~ = 1.8 TeV,

term. Indeed, both possibilities, i.e., threshold m,~iel and resurrection l0 of the earlier Oddemn model 11. were tried.

OT = 72.14-3.3 mb

(2)

The models and their predictions can be summarized as follows.

The E710 group has just reported at this meeting on their preliminary measurement4 of p at 4"g = 1.8 TeV;

(A) Conventional Models 12 This is the case when the UA4 real part is viewed as

p = 0.126-+0.067 subject to o T = 73.3 4- 3.0 mb

(3) and B = 17.02 -+ 0.46

(GeV/c) -2, B being the usual nuclear slope parameter of the diffraction peak of the differential cross-section. Also the preliminary CDF result 5 on the total cross-section is OT = 72.0"£'-3.6 mb which is consistent with the E710 result. The low value of the total cross-section at 4g = 1.8 TeV serves

temporary and therefore not strictly imposed on. Typical models are those mentioned above involving a renormalized Pomeron. They can give aT-- 63 rob, p = 0.15 at the UA4 energy and GT--- 80 rob, p -- 0.16 at the tevatron energy. The so-called minijet models have essentially similar values. Any model in this class predicts ~ slowly varying OT and gives p smaller than (I) and slowly varying thereafter.

to eliminate many theoretical models that are designed to

(B) Odderon Model 10-13

explain (1). More importantly, it is difficult to reconcile

In this case, one assumes a large contribution from the odd-

such a large real part as (1) at ¢'g = 546 GeV with a low

signatured amplitude A_ = App - A~,. Indeed such a

cross-section like (2) at ~ = 1.8 TeV without having to

possibility was suggested 14 in 1975 based on an analytic

K. Kaag, A.R. White/Threshold model for high-energy elastic scattering

72

representation of the high-energy scattering amplitude

• +conc!~de that the threshold must be at a lower energy than

obtained as a solution of quasi-local derivative dispersion

546 GeV. Subsequent publication o f the luminosity independent GT by E710 has only strengthened, if

roAations satisfying the maximal saturation of the asymptotic bounds and the UA4 results resurrected this idea. The odderon model updated 10 by the UA4 data predicts oT = 77

anything, our New Threshold Model.

mb and p = 0.24 at ~ -- 1.8 TeV compared to the Tevatron

3. NEW THRESHOLD MODEL6,7

data (2) and (3). Therefore if the E710 data is proved to be valid by further experimental an~ysis, the maximal odderon

The New Threshold Model 7 was suggested when we had the earlier E710 result, o T (1.8 TeV) = 78.3 + 5.9 rob,

explanation will have to be abandoned also, For the moment, however, one is based on the Z2-fitfing of the data

consistent with this ET10 result if the threshold lies below

based on the obsarvaCJ= :hat the UA4 real part (1) can be

for its validity, which invites certain (subjective) decisions 15 on the weight of the l I A r data v~ lh~t of t~h@

but close to the UA4 energy. As we noted above, since

low-energy darns and on the selection of the data sets and

lower than the earlier re,suit. This necessitates a minor

errors when there are conflicting darns (such as ¢ ~ at ~ =

modification6 of our model. What is more significant with

9.987 G e ~ and , ~ = 23.764 GeV, t ~

at 4~= 52.8 GeV

the new E710 result is that the viability of our picture is

and ppp atv~- = 16.83 GeV). in addition, it has been shown

further enhanced by this: It appears that a threshold below

that 16 it is not easy to build a dynamically meaningful and

the UA4 energy is just about the only way to explain

yet QCD-mofivated model that can give the maximal

simultaneously the large UA4 real part and the low E710

then, there has been the new E710 result (2) which is even

odderon behavior. Also there seems to be theoretical

total cross-section at the Tevatron energy. Although

difficulty 17 for the three gluon exchange odderons 18

dramatic in its own implications, a new threshold

obtained in perturbative QCD calculations with confinement

interpretation of the combined results (!) and (2) is, in many

when one tries to apply it in forward elastic scattering.

ways, more attractive than the assumption o f a large

(C) "!nreshold Models 19

Odderon amplitude. A particularly simple model which fits

One natural possibility to explain the large UA4 real part was to assume a threshold. Since the total cross-section appears to be more or less as expected from the extrapolation of the ISR energies, one naturally assumed such an effective threshold to open up above the UA4

the data well enough for our general discussion is obtained by writing OT = O0 + O01 = lm Ai7p (s)/s

(5)

where

energy. Then it turned out that no threshold model could be constructed such that p (546 GeV) is big enough to be

OT = 37 + 8 0 / ~ + 6.5 In (~/25) mb

(6)

consistent with (!) and yet 01" (1.8 TeV) is moderate to be

Olh = 9 [ 1- (520)2 / s] !/2 0( s - (520)2)mb

(7)

consistent with the E710 results without making p (1.8 TeV) enormous. In fact one can get20 fairly general bounds

and a dispersion relation

75.51 mb < OT (1.8 TeV) < 127.08 mb f or a class of threshold models that have the threshold energy larger than ~46 GeV and when the UA4 real part is imposed. The

a~p = ~2E2 [°°dx

Im A~p(X)/[xlx 2- E~I

(8)

~l'fl

lower bound comes from the best fitted conventional amplitude involving the renormalized Pomeron and

to construct the real part of the forward amplitude. In (5)

exchange-degenerate Regge terms. Though one may have

and (6), 4~ is in units of GeV and E = 2 ~ - m in (8), m

many possible parameters that can give aT (1.8 TeV) close to the lower bound, they all give an even bigger p at 1.8

being the mass of the proton or antiproton. The results for OT and p are shown in Figs. 1 and 2. We stress that the

TeV than the UA4 value. This observation has led us 7 to

sharpness of the peak in p would be smoothed out in a

K. Kang, A.R. White/Threshold model for high-energy elastic scattering

too

I

l llJliT I

i i llitit[

[ ,lilnlt

73

I

I api5 OCT~

80--

70--

~

60 --

UA4 ~]~ if"

E

__

~ ' ~ ' -

50 ~

aol

~

_.,..,~ UA5

v V,VV!lll

10

I V,VVvlll

102

10 a

I I Ivv..

v

2x103

~ s (GeV)

FIGURE 1 The energy dependence of oT given by the model of F,qs. (5)-(6)

conventionally assumed value (0.15) and is in agreement

more physically realistic model which spreads the threshold

with the preliminary E710 result (3). The projected new measurements21 at CERN by the

behavior over a variety of processes at slightly different energies. However in order to achieve a relatively lew OT at

UA4-2 collaboration as well as the worl~ in progress at

1.8 TeV to be consistent with the E710 result, an essentially

Fermilab by E710 to analyse the elastic scattering data at ~E

local explanation of the UA4 result is unavoidable: the total

= 540 GeV and ~ = 1 TeV should soon determine whether p varies in a manner at all resembling the dramatic encrgy

cross-section must vary locally fast enough to cause a substantial contributio, to the real p-~--,~,v.4thout making CT

behavior of Fig. 2. If both (i) and (2) are. cnnfirmed ~ d .',cf

large. This require~ ¢Ythto be a weak effect and the

p is shown to vary smoothly with energy, then there must

threshold to be close to and below the UA4 energy wherewe know that the real part is large. Note that 00 increases

be a large odderon amplitude. However this may not asymptotic Odderon approach, whether maximal or not,

slower than the conventional fits to the total cross-section and the contribution of ¢Ythdisappears rapidly w~th energy.

because a physical threshold, if it exists, need not be

I~: addition we see that our p (1.8 TeV) is smaller than the

necessarily be a. confirmation o f the conventional

;~

K. Kang, A.R. White/Threshold model for high-energy elastic scattering

o.3 n-rn-j--

0.2-

0.t

'

o _....k

pp • • A ~r D 0

~p ' f Ftgey el al. lgS7 II Faiar~ et al. 1981 @ Amos el al. 1985 ).4 UA 4

-0.2 - ,~

-o.3 ~ ! , . ,]

Foley et al, 1967 Bezn~ikhet a t 1972 nartenev et at. 1973 ,Aw~ltl~et aL 1977 Purq el at, l g ~ . Amos et al. 1985

. . . . . . . .

I . . . . . . . . 10 2 ~ s (GeV)

l 10 3

. . . . . . . .

I 10 4

FIGURE 2 The energy depende~e of p given by the model of F_.qs.(5)-(8). The preliminary E710 data (ref.4) is also shown for comparison

confined to just the even signature amplitude. Thus we may say that as long as lm A_ = Im A p p - l m ,~p remains

consistently interpreted as the hadronic and two-photon decays of the same short lived particle with a mass around

unmeasured at collider energies, the odderon can never be

30 GcV, which is produced diffractively causing a

ruled out phenomenologically. In contrast to the odderon,

diffractive hadronic threshold of the type that we depict in

however,

our model. Based on the cosmic ray events, one may expect

our

new

zhreshold

model

can

be

straightforwardly confirmed or ruled out by projected

that there could be about 2 m b cross sections at the

collider experiments within the near future.

Tcvatron for diffractive production o f this new particle that

To this end we may ask if there is any evidence for such

would h~v¢ decayed into two photons. In fact the CDF

a new threshold and what could be the new physics that might be involved. The details of the speculations are given

group has launched the measurement of this new particle "116" through its two photon decays. Then what is the

elsewhere 7. Basically, we believe that there is substantial

dynamical origin of 116 ? We have speculated that "q6 might

evidence for a diffractive threshold in the energy range of = 400-5G0 GeT in cosmic ray experiments. In

be an axion associated with the axial LI(l) ehiral symmetry

particular, mini-eentauros and Geminions can be

doublet of sextet quarks. The sextet quark theory o f

in a dynamical symmetry breaking model involving a flavor

K. Kang, A.R. White/Threshold model for high-energy elastic scattering electroweak symmetry breaking requires a flavor doublet of quarks with conventional charges. In fact the nontrivial solution of the Schwinger-Dyson zquation |or the sextet quark propagator was studied recently by Fukazawa et al.22

75

REFERENCES 1.

UA4 Collab., D. Bernard et al., Phys. I.,¢m B198 (1987) 583.

2.

ETlO Collab., N. Amos et al., Phys. Lett. B243 (1990) 158.

3.

See Proc. 2nd Biois Workshop, K. Goulianos, Ed., (Editions Fronti~res 1998) and Proc. 3rd Blois Workshop, M.M. Block and A.R. White, Eds., Nucl. Phys. B (Proc. Suppl.) VoL 12 0990).

4.

See. S. Shukla in this Proc.

5.

See. S. White in this Proc.

6.

K. Kang and A.R. White, _n.,~-wn-!'~-'T-805,ANI.,~ HEP -PR-91-32, Phys.Lett. B (in press).

7.

K. Kang and A.R. White, Phys. Rw. D42 (1990) 835; in Proc. 4th Asia-Pacific Physics Conf. Yonsei Univ., Seoul, Korea, 1990; in Proc. 20th Ira.Syrup. Multiparticle Physics, Gut Holmecke, Germany, 1990.

8.

UA4 Collab., M. Bozzo et al., Phys. L,ett. 147B (1984) 392.

production of sextet quarks with mass >_ 250 GeV is less than 1 picobarn at CDF making "q6 hard to be seen in hard

9.

K. Kang and S. Hadjitheodoridis, Proc. 2rid Blois

collisions. It could be seen at LEP as a rare radiative Z0 decay eventually if LEP accumulates enough Z0s.

10.

D. Bernard, P. Gauron and B. Nicolescu, Phys. Left. 199B (1989) 125.

However, diffractive production of heavy flavors, and of the ~16 in particular, will be large because of the Pomeron

11.

couplings in QCD. We have also argued that a strongly interacting sextet quark sector might absorb e+e- production providing an explanation of the muon-rich photon showers

K. Kang and B. Nicolescu, Phys. Rev. D! I (1975) 2461. See also L.Lukaszuk and B. Nicolescu, Nuovo Cim. Lett. 8 (1973) 405.

12.

See M.M. Block, F. Halzen and K. Kang in Proc. 3rd Blois Workshop.

and the wide range of anomalous shower development seen in high-energy cosmic ray events.

13.

P. Gauron and B. Nicolescu, Phys. Lett. B258 (1991) 482.

In short, the new threshold model to explain the large

14.

K. Kang and B. Nicolescu (Ref. 11).

UA4 real part and lower E710 total cross-section at the Tevatron energy is compatible with all forward elastic

15.

We thank P. Gauron and B. Nicolescu for numerous discussions on this point.

scattering data. If these results are confirmed by further

16.

J. Finkelstein, H.M. Fried, K. Kang and C-I Tan, Phys. Lett. B232 (1989) 257

17.

See. A.R. White in this Proc.

18.

J. Kwiecinski and M. Praszalowicz, Phys. LeR. B94 (1980) 413: L. Lip~tov, Phys. Lett. B251 (1990) 284.

19.

See K. Kaag and S. Hadjitheodoridis, A. Martin, P. Kluit in Proc. 2nd Blois Workshop.

20.

K. Kang and S. Hadjitheodoridis, Phys. Lett. B208 (!988) 135.

which showed in the strong coupEng regime the sextet quark mass to be in the range of 300-400 GeV for the tquark mass range of 77-160 GeV. It was shown that the sextet quark condensates acquire a large anomalous dimension triggering spontaneous symmetry breaking of SU(2) x U(I). Though there would be new sextet hadrons the central point is that them is a sextet eta,'q6, which is left unabsorbed by any gauge bosons. The ~6 will acquire its mass from the higher order sextet quark interactions of the four-fermion type with a full sextet/triplet instanton interaction. Since these operators are also exp:c:zd. :~ have a large anomalous dimension in the strong coupling regime, it can easily induce a large mass for the ¢16 perhaps as large as 30 GeV. The life-time of the ¢16 is estimated to be very close to that of x0. The cross-section for perturbative QCD

Workshop.

experiments, they could imply a beginning of new physics involving a new quark sector. This work is supported in part by the U.S. Department of Energy. We would iike to acknowledge useful discussion with A. Martin, E. Leader, M.M. Block and B. Nicolescu. In addition, one of us (KK) would like to thank R. Vinh Mau for kind hospitality extended to him at IPN and LPTPE during the summer of 1991.

T6 21.

E. Kang, A.R. White~Threshold model for high-energy elastic scattering See M. Hagenauer in this Proc.

22.

K. Fukuzawa et al., Prog. Theor. Phys. 85 (1991) 111; T. Muta, in Proc. 25th Int. Conf. High-Energy Physics, Singapore (1990).