- Email: [email protected]
Enhanced production of events at large x and Q2 at HERA and the meson cloud in the nucleon
11 September 1997
PHYSICS LElTERS 6
BISBVIBR
Physics Letters B 408 (1997) 275-280
Enhanced production of events at large x and Q2 at HERA and the meson cloud in the nucleon A. Szczurek, A. Budzanowski Institute of Nuclear Physics, ul. Radzikowskiego 152, PL-31-342 Krakow, Poland
Received 28 March 1997; revised manuscript received9 June 1997 Editor: PV. Landshoff
Abstract We examine to which degree the effect of the inclusion of target mass cotrections in the description at low-Q2 DIS and meson cloud effects may, after QCD evolution, modify DIS cross section at large x and Q2. This is of interest in the context of recently reported excess of events observed by Hl and ZEUS collaborations at HERA. We predict an enhanced production of events at large-x in comparison to standard sets of quark distributions with rather mild Q2-dependence. Our analysis leaves some room for more exotic effects beyond parton approach and/or Standard Model. Our large-x effects can be verified in the future when the HEXA luminosity will be increased. @ 1997 Elsevier Science B.V. PACS: 13.6O.Hb
1. Introduction
Recently both Hl [ 1 ] and ZEUS [ 21 collaborations at HERA have presented their results for the neutral current (positron-jet) and charged current (singlejet) cross sections accumulated during the years 1994 to 1996. A sizeable enhancement over predictions of improved parton approach based on Standard Model at large x and Q* region has been reported by both groups. This is in the region of phase space which is particularly well suited for searches of possible deviations from the Standard Model. At present the large x and Q* statistics based on the integrated sample of 20.1 pb-* (ZEUS) and 14.19 pb-’ (HI) is not sufficient to draw more definite conclusion about the discovery of a new particle or the quark substructure. Because no model can give reliable predictions for the properties of the new particle and many new scenarios
are possible a priori, one must rather wait for a better statistics and/or try to find limits on parameters of the candidate theories. In the present communication we analyze whether effects of the meson cloud and of the inclusion of kinematical target mass corrections in the description of low-Q* deep-inelastic scattering may, after QCD evolution of parton distributions, influence the large x and Q* region and in the consequence disturb in the future a reliable extraction of the signal of New Physics. The meson cloud effects have been known for some time to be of special importance in low energy physics due to spontaneus chiral symmetry breaking. It has been proven already long ago [3] that the pion contribution to DIS scales in the Bjorken limit. In last years the meson cloud effects have become crucial (see for instance [7] and references therein) in understanding the Gottfried Sum Rule violation [ 41, the Drell-
0370-2693/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PII SO370-2693(97)008 11-3
276
A. Szczurek, A. Budzanowski/Physics
Yan asymmetry in proton-proton and proton-deuteron collisions [5] and semi-inclusive production of fast neutrons at HERA [ 6 1. The inclusion of meson cloud effects and target mass corrections at low Q* leads to an enhancement of the quark distributions at large x [ 81. The enhancement survives after QCD evolution from low Q* to Q2 appropriate for the HERA large x and Q* region. This effect turned out recently to be very helpful [9] also in understanding the enhancement of the large-& di-jet production in protonantiproton collisions observed by the CDF collaboration [ lo], which may be an interesting alternative for the enhanced gluon distribution scenario proposed in Ref. [ 111. Can the same effects be responsible for the excess of events at large Q* and large x observed recently at HERA [ 1,2] ?
Letiers B 408 (1997) 275-280
The explicit y-dependence contained in Y+(y) functions is due to the helicity dependence of electroweak interactions (see for instance [ 121) . The introduced auxilliary calligraphic structure functions 3:(x,
Q*) = fi(x, Q*) f
+ &Q*) 3F(x,Q*) + &Q2)
~z(Q*hG2(x,
(0: + 4)H2(x,Q2)
Q2)
,
= dQ*)(-ar)xWx,Q*) (2~dxH3(x,
~2)
9
(5)
l'@(x,Q*) = ~,:(Q', , @(x,Q*) = TWf(Q',
(6)
are defined in terms of quark distributions 2. Neutral and charged current deep inelastic scattering
Fdx,Q*)
In the kinematical range in which the deep inelastic scattering process may be described within the parton picture the cross section can be written as a linear combination of parton densities f q/N
Wx,Q2)
d&*q 1fq,,&,Q*).
daeiN = c
+&Q*)l,
4
(1)
4
=x~e&(x,Q*)
Here, the factorization scale is chosen to be the virtuality Q*. Neglecting the longitudinal structure function the unpolarized differential cross section for neutral current (NC) I* + nucleon scattering is given as
=xX2 e,u,tq(x, Q2) + 4(x, Q*)
1
(~3 + a;) [q(x, Q*) + 3x9 Q*) 1 ,
H2(x,Q2) =xX 9
Gdx,Q*) =xX2 4
e,a,[q(xv Q*) - 4(x, Q*) 1 ,
H3(x,Q2) =xX2
uqaqtdx,Q2) - cHx,Q’)l
9
(7) for neutral
d*o*nc _ 2rff* xQ4
dxdQ*
x {Y+(yP;(x,Q*)
+Y-(~)3;f(x,Q*)}
(2)
and for charged current (CC) I* + nucleon scattering as
xWc(X,Q*) =Zxx[di(x,Q*)
-Ei(x,Q*)]
2m* d*a+ cc dxdQ* = -i@-
~wF(xvQ’)
-~i(x,Q*)]
x {Y+(YW,~CGQ~)
(8)
i
+ Y-(yW3f(x+Q2)}
1 (3)
where Y*(y)=lf(l-y)?
=2xC[ui(x9Q2)
,
(4)
and charged current DIS. The short hand notation has been used above ui s (u,c,t), di G (d,s,b). The Standard Model vector and axial vector weak coupling constants can be expressed in terms of weak isospin, electromagnetic charges and weak mixing angle: up =
A. Szczurek, A. Budzanowski/Physics
277
Letters B 408 (1997) 275-280
T3q- 2e,sin* (&), a4 = Tjqfor quarks and u, = Tsc 2e, sin*( 0,)) a, = Tse for positron or electron. The kinematical factors
MQ*>
=
Q2 4sin*(B,) cos*(&,) Q* + Mi 1
and
av(Q2) =
1 4sin*(&)
Q2 Q* + M$
contain the ratio of heavy boson to photon propagators. In the region of large x and Q* studied in Refs. [ 1,2] the parity-violating 55 term in Eq. (2) substantially reduces the efp and enhances the e-p NC cross scction.
3. Results and perspectives In this section we compare the results obtained with the set of quark distributions which take into account the target mass corrections and meson cloud effects at low Q* [8] with those obtained with typical standard quark distributions. Having checked that all sets of parton distributions available in the literature lead to very similar results (see also a detailed discussion in [ 1,2] ), in the following we shall show only results obtained with parton densities as given by simple parametrizations [ 16,171. In Fig. 1 we present the cross section for the neutral current e+p deep inelastic scattering obtained with the help of quark distributions from [ 171 (dashed) and [ 83 (solid), normalized arbitrarily to the cross section calculated with quark distributions from [ 161. In comparison to the standard sets of quark distributions [ 16,171 the quark distributions found in [ 81 produce a sizeable enhancement but only at invariant lepton-parton mass (M = 6) M > 200 GeV which corresponds to rather large Bjorken x > 0.6. In this calculation the cross sections have been integrated in the range of Q* > lo4 GeV*. The Zeus collaboration have reported that the enhancement is situated rather at large Q*. In Fig. 2 we present therefore the cross section as a function of Q2 integrated over x > xmin= 0.5, 0.6, 0.7 normalized as before to the calculation with quark distributions from [ 161. As seen from the figure the target mass corrections and meson cloud ef-
O‘,,,,,,,‘,I,,,,,,,~,,,,,,,,,,,,,,,,,,,~ 100 150 200
250
:
M (GeV) Fig. 1. The Q2-integrated ( Q2 > lo4 GeV2) cross section as a function of M normalized arbitrarilly to the calculation with quark distributions from [ 161. Different lines correspond to quark distributions from [ 161 (short-dashed), [ 171 (long-dashed), [ 81 (solid). Table 1 The number of event in e*p collisions for M > 180 and y > 0.4, which corresponds to the kinematical cuts of the Hl analysis [ 11. Reaction
GRV95
Owens
tmc
tmc+mc
Experiment
e+p,NC
2.65 0.54 7.21 10.01
2.64 0.59 7.29 10.02
2.63 0.59 7.23 9.97
2.84 0.67 7.34 10.23
7 -
e+p,
CC
e-p,
NC
e-p,
CC
fects lead to an enhancement of the cross section especially at larger ~ti,,. However, the increase is only slightly larger at larger Q*, not fully compatible with what is observed experimentally by Hl [ 11 and ZEUS [ 21 collaborations. The calculated number of events within kinematical cuts corresponding to the Hl selection of events are shown for different sets of quark distributions [ 8,17,16] in Table 1. In this calculation the integrated luminosity has been taken to be L = 14.19 pb-’ [ 11. The column marked by “tmc” corresponds to the set of quark distributions which include only target mass corrections and the column marked by “tmc,mc” both the target mass corrections and the meson cloud effects. Surprisingly similar results have been obtained with rather different sets of parton distributions (compare columns marked by GRV95,Owens91, “tmc”).
A. Szczurek.
278
A. l3u&amwski/
Physics
s 8 ill.5 %
s
@l.O
% p) 1.0
g 3
3 ,d 0.5 2
275-280
g
,a05 z 0.0
2. The same
0.0
as
in Fig. 1 but as a function of Q2. The cross section has been integrated in the range x > X,in ( .q,,in = 0.5,
Table 2 The expected number of events in NC DIS e+p collisions for different cuts on Qz compared to the ZEUS and Hl data [ 1.21. Nple is a theoretical prediction of the ZEUS collaboration. The numbers of events calculated hem ~VMCM do include 81% efficiency of the ZEUS aparatus. N& is a number of events obtained by the HI collaboration recalculated to the luminosity of the ZEUS sample
Qfi,
B 408 (1997)
p.5 %
a
Fig.
Letters
(aV2)
NZEUS
Yt,
Npre
&CM
172.8
196.5
192.37
5000
191
10000
33
28.33
15000 20000 25000 30000 35000
12 5 3 2 2
17.00 7.08 2.83
32.18 8.66 2.76 1.01 0.37 0.145
34.03 9.97 3.59 1.44 0.61 0.26
0.6, 0.7).
This demonstrates that the region of interest is rather insensitive to the details of quark distributions provided the latter give a good description of large body of hard scattering data at smaller Q2. The inclusion of the meson cloud effects (column “tmcfmc”) results in onlv mild N 10% enhancement of the number of events. All the quark distributions predict below 3 events versus 7 events observed experimentally. Is this more than a statistical fluctuation. ; Table 2 compares our predictions with the ZEUS data Nznus [ 21 (L = 20.1 pb-’ ) for different lower bounds Q,$, on Q2. The numbers calculated in the last column do include 8 1% efficiency of data selecting [ 21. In column N& we have placed for comparison the HI data recalculated from HI to ZEUS integrated luminosity. At
A. Szczurek, A. Budzanowski/Physics
circles:
ul
“d 100
Letters B 408 (1997~275-280
279
ZEUS
triangles:
F
Hl i
0.1 11 0
lOdOs,
Q
2odQp
(GeV
>
30000
40000
Fig.
3. The Q2-dependenceof the cross section. The result obtained with the quark distributions which take into account both the meson cloud effects explicitly and tatget mass corrections at low Q2 (solid line) is compared against the ZEUS and Hl experimental data. The dashed curve represents the original result obtained by the ZEUS collaboration.
large Q2 the effects of meson cloud and target mass correction (&CM) cause a sizeable enhancement in comparison to a standard set of parton distributions (N,,) taken from Ref. [2] (see also Fig. 3). Thus the inclusion of the meson cloud effects and target mass corrections at low Q2 leaves less room for more exotic effects beyond the Standard Model. A more close inspection of Table 2 and Fig. 3 exhibits, however, a small but systematical excess at Q,& rv 3. IO4 GeV2 and can hardly be explained as a statistical fluctuation. It has been emphasized in Ref. [ 1] that all the excess events are placed in a tight region arround M x 200 GeV The average mass obtained from 7 selected events (Table 6 in [ 1 ] ) practically does not de nd -K7) on the method used: @,H’*7) = 199.00 GeV, M,, ' = 201.71 GeV , fi’Hr,7) = 203.57 GeV. This could e+Jel suggest a new resonance effect in the parton-lepton s-channel. We wish to empasize that such an interpretation of the observation will require a bit of caution. First of all similar average calculated from 4 selected ZEUS events (Table 2 in ]2]) is: @y*4) = 24 1.65 GeV, I@~“~*~) = 229.20 GeV. Secondly, specific kinematical cuts applied in the off-line analysis lead to a creation of such a resonance-like structure. In Fig. 4 we show the cross section for the e+p NC deep inelastic scattering integrated over Q2 > Q&, for
Fig. 4. Distribution in invariant quark-lepton mass (M) for different cuts on Q2: se*, -/& dQ2. The solid line corresponds to the calculation withze quark distributions found in Ref. [ 81, the long-dashed line to the GRV95 quark distributions [ 171 and the short-dashed line to those from Ref. [ 161.
Q,$, = 2. lo4 GeV’ (panel a) and Q&, = 3. lo4 GeV2 (panel b) . The effect of the kinematical cut leads to a resonance-like structure situated at Q* N 180-200 GeV. No significant effect due to the choice of parton distributions is observed. Summarizing, even parton distributions which include the meson cloud effects and target mass corrections are not able to produce sufficient enhancement of the cross section in the region of large Q2 and x in comparison to that observed in [ 1,2]. Because the two-dimensional distributions (x, Q2> are strongly decreasing functions of both Q2 and x, on the experimental side the excess of events could be understood
A. Szczurek,
280
A. Budzanowski/
Physics
Letters
B 408 (1997)
275-280
R&(Q’;xmin)
d
provided the experimental methods used lead to a systematical overestimation of extracted Q* and/or x in the interesting region. Beyond the Standard Model, the excess at high Q* and/or high h4 could be for instance due to the creation of leptoquarks [ 131 or squarks [ 141 (see also [ 151) in the quark-lepton s-channel or possible substructure of quark/lepton due to the contact interaction. In the lepto-quark scenario rather different effects are expected in the e+p and e-p reactions [ 131 in contrast to the quarkllepton substructure scenario. Therefore before any speculation about New Physics can be made, it seems particularly interesting and helpful to study in addition to
cross sections. Having results of both reactions would be much more restrictive on the choice of the Standard Model extension. The measurement with sufficient statistics appears to be feasible experimentally as in the region of interest the cross sections for both neutral current and charged current e-p deep inelastic scattering are substantially larger than for the e+p scattering, especially for the charged current (CC) case. In order to demonstrate this enhancement in Fig. 5 we show the ratios of cross sections integrated over x > xdn defined as _ =-
+
dzF 2
(Q
*;Xmi”)
/
“d;z 2
cQ
*; xmin)
3
R&(Q*; xmin) _
‘1;'(Q
=cc
2
+ *;&in)
/
d,q;p(Q *; hi”) .
+-
(9)
The ratios shown in Fig. 5 have been calculated with quark distributions from Ref. [ 81 which include both target mass corrections and meson cloud effects. The enhancement only weakly depends on the lower integration limit .xhn. Acknowledgements
We are indebted to our collegues from the Hl and ZEUS collaborations for providing us with details of their experiments.
R&(Q2;
X,tn) defined in Eq. (9)
calculatedwith quark distributions from Ref. [ 81 for different xmia: 0.1 (solid), 0.3 (long-dashed), 0.5 (short-dashed).
References [ 11 C. Adloff et al.(Hl), DESY 97-024, hep-ex/9702012. ]2] J. Breihveg et al.(ZEUS), DESY 97-025, hep-ex/9702015. [3] J.D. Sullivan, Phys. Rev. D 5 (1972) 1732. [4] F! Amaudmz et al., Phys. Rev. Lea. 66 (1991) 2712; M. Arneodo et al., Phys. Rev. D 50 ( 1994) Rl. [5] A. Baldit et al., Phys. Lett. B 332 ( 1994) 244. [6] M. Derrick et al., (ZEUS), Phys. Len. B 384 (1996) 388. [7] H. Holtmann, A. Szczurek and J. Speth, Nucl. Phys. A 596 (1996) 631; H. Holtmann, N.N. Nikolaev, J. Speth and A. Szczurek, Z. Phys. A 353 (1996) 411; A. Szczurek, M. Eticson, H. Holtmann and J. Speth, Nucl. Phys. A 596 (1996) 397; H. Holtmann, G. Levman, N.N. Nikolaev, A. Szczurek and J. Speth, Phys. Lett. B 338 (1994) 363; M. Przybycietl, A. Szczurek and G. Ingelman, DESY 96073, in print in Z. Phys. C. [8] A. Szczumk, V. Uleschenko, H. Holtmann and J. Speth, to be published in Nucl. Phys. A. [9] A. Szczurek and A. Budzanowski, in print in Phys. Lett. B. 101 E Abe et al., Phys. Rev. Lett. 77 (1996) 438. 111 J. Huston, E. Kovacs, S. Kuhlmann, H.L. Lai, J.F. Owens, D. Soper and W.K. Tung, Phys. Rev. Lett. 77 ( 1996) 444. 121 G. Ingelman and R. Riickl, Phys. Lett. B 201 (1988) 369. 131 W. Buchmiiller, R. Rilckl and D. Wyler, Phys. Len B 191 (1987) 442. 141 D. Choudhury and S. Raychaudhuri, CERN-TH/97-26, hepphl9702392. [ 151 G. Altarelli, J. Ellis, G.F. Giudice, S. Lola and M.L. Mangano, CERN-‘D-I/97-40, hep-ph/9703276. [ 161 J.F. Owens, Phys. Len B 266 (1991) 126. [ 171 M. Glilck, E. Reya and A. Vogt, Z. Phys. C 67 (1995) 433.
PHYSICS LElTERS 6
BISBVIBR
Physics Letters B 408 (1997) 275-280
Enhanced production of events at large x and Q2 at HERA and the meson cloud in the nucleon A. Szczurek, A. Budzanowski Institute of Nuclear Physics, ul. Radzikowskiego 152, PL-31-342 Krakow, Poland
Received 28 March 1997; revised manuscript received9 June 1997 Editor: PV. Landshoff
Abstract We examine to which degree the effect of the inclusion of target mass cotrections in the description at low-Q2 DIS and meson cloud effects may, after QCD evolution, modify DIS cross section at large x and Q2. This is of interest in the context of recently reported excess of events observed by Hl and ZEUS collaborations at HERA. We predict an enhanced production of events at large-x in comparison to standard sets of quark distributions with rather mild Q2-dependence. Our analysis leaves some room for more exotic effects beyond parton approach and/or Standard Model. Our large-x effects can be verified in the future when the HEXA luminosity will be increased. @ 1997 Elsevier Science B.V. PACS: 13.6O.Hb
1. Introduction
Recently both Hl [ 1 ] and ZEUS [ 21 collaborations at HERA have presented their results for the neutral current (positron-jet) and charged current (singlejet) cross sections accumulated during the years 1994 to 1996. A sizeable enhancement over predictions of improved parton approach based on Standard Model at large x and Q* region has been reported by both groups. This is in the region of phase space which is particularly well suited for searches of possible deviations from the Standard Model. At present the large x and Q* statistics based on the integrated sample of 20.1 pb-* (ZEUS) and 14.19 pb-’ (HI) is not sufficient to draw more definite conclusion about the discovery of a new particle or the quark substructure. Because no model can give reliable predictions for the properties of the new particle and many new scenarios
are possible a priori, one must rather wait for a better statistics and/or try to find limits on parameters of the candidate theories. In the present communication we analyze whether effects of the meson cloud and of the inclusion of kinematical target mass corrections in the description of low-Q* deep-inelastic scattering may, after QCD evolution of parton distributions, influence the large x and Q* region and in the consequence disturb in the future a reliable extraction of the signal of New Physics. The meson cloud effects have been known for some time to be of special importance in low energy physics due to spontaneus chiral symmetry breaking. It has been proven already long ago [3] that the pion contribution to DIS scales in the Bjorken limit. In last years the meson cloud effects have become crucial (see for instance [7] and references therein) in understanding the Gottfried Sum Rule violation [ 41, the Drell-
0370-2693/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PII SO370-2693(97)008 11-3
276
A. Szczurek, A. Budzanowski/Physics
Yan asymmetry in proton-proton and proton-deuteron collisions [5] and semi-inclusive production of fast neutrons at HERA [ 6 1. The inclusion of meson cloud effects and target mass corrections at low Q* leads to an enhancement of the quark distributions at large x [ 81. The enhancement survives after QCD evolution from low Q* to Q2 appropriate for the HERA large x and Q* region. This effect turned out recently to be very helpful [9] also in understanding the enhancement of the large-& di-jet production in protonantiproton collisions observed by the CDF collaboration [ lo], which may be an interesting alternative for the enhanced gluon distribution scenario proposed in Ref. [ 111. Can the same effects be responsible for the excess of events at large Q* and large x observed recently at HERA [ 1,2] ?
Letiers B 408 (1997) 275-280
The explicit y-dependence contained in Y+(y) functions is due to the helicity dependence of electroweak interactions (see for instance [ 121) . The introduced auxilliary calligraphic structure functions 3:(x,
Q*) = fi(x, Q*) f
+ &Q*) 3F(x,Q*) + &Q2)
~z(Q*hG2(x,
(0: + 4)H2(x,Q2)
Q2)
,
= dQ*)(-ar)xWx,Q*) (2~dxH3(x,
~2)
9
(5)
l'@(x,Q*) = ~,:(Q', , @(x,Q*) = TWf(Q',
(6)
are defined in terms of quark distributions 2. Neutral and charged current deep inelastic scattering
Fdx,Q*)
In the kinematical range in which the deep inelastic scattering process may be described within the parton picture the cross section can be written as a linear combination of parton densities f q/N
Wx,Q2)
d&*q 1fq,,&,Q*).
daeiN = c
+&Q*)l,
4
(1)
4
=x~e&(x,Q*)
Here, the factorization scale is chosen to be the virtuality Q*. Neglecting the longitudinal structure function the unpolarized differential cross section for neutral current (NC) I* + nucleon scattering is given as
=xX2 e,u,tq(x, Q2) + 4(x, Q*)
1
(~3 + a;) [q(x, Q*) + 3x9 Q*) 1 ,
H2(x,Q2) =xX 9
Gdx,Q*) =xX2 4
e,a,[q(xv Q*) - 4(x, Q*) 1 ,
H3(x,Q2) =xX2
uqaqtdx,Q2) - cHx,Q’)l
9
(7) for neutral
d*o*nc _ 2rff* xQ4
dxdQ*
x {Y+(yP;(x,Q*)
+Y-(~)3;f(x,Q*)}
(2)
and for charged current (CC) I* + nucleon scattering as
xWc(X,Q*) =Zxx[di(x,Q*)
-Ei(x,Q*)]
2m* d*a+ cc dxdQ* = -i@-
~wF(xvQ’)
-~i(x,Q*)]
x {Y+(YW,~CGQ~)
(8)
i
+ Y-(yW3f(x+Q2)}
1 (3)
where Y*(y)=lf(l-y)?
=2xC[ui(x9Q2)
,
(4)
and charged current DIS. The short hand notation has been used above ui s (u,c,t), di G (d,s,b). The Standard Model vector and axial vector weak coupling constants can be expressed in terms of weak isospin, electromagnetic charges and weak mixing angle: up =
A. Szczurek, A. Budzanowski/Physics
277
Letters B 408 (1997) 275-280
T3q- 2e,sin* (&), a4 = Tjqfor quarks and u, = Tsc 2e, sin*( 0,)) a, = Tse for positron or electron. The kinematical factors
MQ*>
=
Q2 4sin*(B,) cos*(&,) Q* + Mi 1
and
av(Q2) =
1 4sin*(&)
Q2 Q* + M$
contain the ratio of heavy boson to photon propagators. In the region of large x and Q* studied in Refs. [ 1,2] the parity-violating 55 term in Eq. (2) substantially reduces the efp and enhances the e-p NC cross scction.
3. Results and perspectives In this section we compare the results obtained with the set of quark distributions which take into account the target mass corrections and meson cloud effects at low Q* [8] with those obtained with typical standard quark distributions. Having checked that all sets of parton distributions available in the literature lead to very similar results (see also a detailed discussion in [ 1,2] ), in the following we shall show only results obtained with parton densities as given by simple parametrizations [ 16,171. In Fig. 1 we present the cross section for the neutral current e+p deep inelastic scattering obtained with the help of quark distributions from [ 171 (dashed) and [ 83 (solid), normalized arbitrarily to the cross section calculated with quark distributions from [ 161. In comparison to the standard sets of quark distributions [ 16,171 the quark distributions found in [ 81 produce a sizeable enhancement but only at invariant lepton-parton mass (M = 6) M > 200 GeV which corresponds to rather large Bjorken x > 0.6. In this calculation the cross sections have been integrated in the range of Q* > lo4 GeV*. The Zeus collaboration have reported that the enhancement is situated rather at large Q*. In Fig. 2 we present therefore the cross section as a function of Q2 integrated over x > xmin= 0.5, 0.6, 0.7 normalized as before to the calculation with quark distributions from [ 161. As seen from the figure the target mass corrections and meson cloud ef-
O‘,,,,,,,‘,I,,,,,,,~,,,,,,,,,,,,,,,,,,,~ 100 150 200
250
:
M (GeV) Fig. 1. The Q2-integrated ( Q2 > lo4 GeV2) cross section as a function of M normalized arbitrarilly to the calculation with quark distributions from [ 161. Different lines correspond to quark distributions from [ 161 (short-dashed), [ 171 (long-dashed), [ 81 (solid). Table 1 The number of event in e*p collisions for M > 180 and y > 0.4, which corresponds to the kinematical cuts of the Hl analysis [ 11. Reaction
GRV95
Owens
tmc
tmc+mc
Experiment
e+p,NC
2.65 0.54 7.21 10.01
2.64 0.59 7.29 10.02
2.63 0.59 7.23 9.97
2.84 0.67 7.34 10.23
7 -
e+p,
CC
e-p,
NC
e-p,
CC
fects lead to an enhancement of the cross section especially at larger ~ti,,. However, the increase is only slightly larger at larger Q*, not fully compatible with what is observed experimentally by Hl [ 11 and ZEUS [ 21 collaborations. The calculated number of events within kinematical cuts corresponding to the Hl selection of events are shown for different sets of quark distributions [ 8,17,16] in Table 1. In this calculation the integrated luminosity has been taken to be L = 14.19 pb-’ [ 11. The column marked by “tmc” corresponds to the set of quark distributions which include only target mass corrections and the column marked by “tmc,mc” both the target mass corrections and the meson cloud effects. Surprisingly similar results have been obtained with rather different sets of parton distributions (compare columns marked by GRV95,Owens91, “tmc”).
A. Szczurek.
278
A. l3u&amwski/
Physics
s 8 ill.5 %
s
@l.O
% p) 1.0
g 3
3 ,d 0.5 2
275-280
g
,a05 z 0.0
2. The same
0.0
as
in Fig. 1 but as a function of Q2. The cross section has been integrated in the range x > X,in ( .q,,in = 0.5,
Table 2 The expected number of events in NC DIS e+p collisions for different cuts on Qz compared to the ZEUS and Hl data [ 1.21. Nple is a theoretical prediction of the ZEUS collaboration. The numbers of events calculated hem ~VMCM do include 81% efficiency of the ZEUS aparatus. N& is a number of events obtained by the HI collaboration recalculated to the luminosity of the ZEUS sample
Qfi,
B 408 (1997)
p.5 %
a
Fig.
Letters
(aV2)
NZEUS
Yt,
Npre
&CM
172.8
196.5
192.37
5000
191
10000
33
28.33
15000 20000 25000 30000 35000
12 5 3 2 2
17.00 7.08 2.83
32.18 8.66 2.76 1.01 0.37 0.145
34.03 9.97 3.59 1.44 0.61 0.26
0.6, 0.7).
This demonstrates that the region of interest is rather insensitive to the details of quark distributions provided the latter give a good description of large body of hard scattering data at smaller Q2. The inclusion of the meson cloud effects (column “tmcfmc”) results in onlv mild N 10% enhancement of the number of events. All the quark distributions predict below 3 events versus 7 events observed experimentally. Is this more than a statistical fluctuation. ; Table 2 compares our predictions with the ZEUS data Nznus [ 21 (L = 20.1 pb-’ ) for different lower bounds Q,$, on Q2. The numbers calculated in the last column do include 8 1% efficiency of data selecting [ 21. In column N& we have placed for comparison the HI data recalculated from HI to ZEUS integrated luminosity. At
A. Szczurek, A. Budzanowski/Physics
circles:
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triangles:
F
Hl i
0.1 11 0
lOdOs,
Q
2odQp
(GeV
>
30000
40000
Fig.
3. The Q2-dependenceof the cross section. The result obtained with the quark distributions which take into account both the meson cloud effects explicitly and tatget mass corrections at low Q2 (solid line) is compared against the ZEUS and Hl experimental data. The dashed curve represents the original result obtained by the ZEUS collaboration.
large Q2 the effects of meson cloud and target mass correction (&CM) cause a sizeable enhancement in comparison to a standard set of parton distributions (N,,) taken from Ref. [2] (see also Fig. 3). Thus the inclusion of the meson cloud effects and target mass corrections at low Q2 leaves less room for more exotic effects beyond the Standard Model. A more close inspection of Table 2 and Fig. 3 exhibits, however, a small but systematical excess at Q,& rv 3. IO4 GeV2 and can hardly be explained as a statistical fluctuation. It has been emphasized in Ref. [ 1] that all the excess events are placed in a tight region arround M x 200 GeV The average mass obtained from 7 selected events (Table 6 in [ 1 ] ) practically does not de nd -K7) on the method used: @,H’*7) = 199.00 GeV, M,, ' = 201.71 GeV , fi’Hr,7) = 203.57 GeV. This could e+Jel suggest a new resonance effect in the parton-lepton s-channel. We wish to empasize that such an interpretation of the observation will require a bit of caution. First of all similar average calculated from 4 selected ZEUS events (Table 2 in ]2]) is: @y*4) = 24 1.65 GeV, I@~“~*~) = 229.20 GeV. Secondly, specific kinematical cuts applied in the off-line analysis lead to a creation of such a resonance-like structure. In Fig. 4 we show the cross section for the e+p NC deep inelastic scattering integrated over Q2 > Q&, for
Fig. 4. Distribution in invariant quark-lepton mass (M) for different cuts on Q2: se*, -/& dQ2. The solid line corresponds to the calculation withze quark distributions found in Ref. [ 81, the long-dashed line to the GRV95 quark distributions [ 171 and the short-dashed line to those from Ref. [ 161.
Q,$, = 2. lo4 GeV’ (panel a) and Q&, = 3. lo4 GeV2 (panel b) . The effect of the kinematical cut leads to a resonance-like structure situated at Q* N 180-200 GeV. No significant effect due to the choice of parton distributions is observed. Summarizing, even parton distributions which include the meson cloud effects and target mass corrections are not able to produce sufficient enhancement of the cross section in the region of large Q2 and x in comparison to that observed in [ 1,2]. Because the two-dimensional distributions (x, Q2> are strongly decreasing functions of both Q2 and x, on the experimental side the excess of events could be understood
A. Szczurek,
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Physics
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B 408 (1997)
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R&(Q’;xmin)
d
provided the experimental methods used lead to a systematical overestimation of extracted Q* and/or x in the interesting region. Beyond the Standard Model, the excess at high Q* and/or high h4 could be for instance due to the creation of leptoquarks [ 131 or squarks [ 141 (see also [ 151) in the quark-lepton s-channel or possible substructure of quark/lepton due to the contact interaction. In the lepto-quark scenario rather different effects are expected in the e+p and e-p reactions [ 131 in contrast to the quarkllepton substructure scenario. Therefore before any speculation about New Physics can be made, it seems particularly interesting and helpful to study in addition to
cross sections. Having results of both reactions would be much more restrictive on the choice of the Standard Model extension. The measurement with sufficient statistics appears to be feasible experimentally as in the region of interest the cross sections for both neutral current and charged current e-p deep inelastic scattering are substantially larger than for the e+p scattering, especially for the charged current (CC) case. In order to demonstrate this enhancement in Fig. 5 we show the ratios of cross sections integrated over x > xdn defined as _ =-
+
dzF 2
(Q
*;Xmi”)
/
“d;z 2
cQ
*; xmin)
3
R&(Q*; xmin) _
‘1;'(Q
=cc
2
+ *;&in)
/
d,q;p(Q *; hi”) .
+-
(9)
The ratios shown in Fig. 5 have been calculated with quark distributions from Ref. [ 81 which include both target mass corrections and meson cloud effects. The enhancement only weakly depends on the lower integration limit .xhn. Acknowledgements
We are indebted to our collegues from the Hl and ZEUS collaborations for providing us with details of their experiments.
R&(Q2;
X,tn) defined in Eq. (9)
calculatedwith quark distributions from Ref. [ 81 for different xmia: 0.1 (solid), 0.3 (long-dashed), 0.5 (short-dashed).
References [ 11 C. Adloff et al.(Hl), DESY 97-024, hep-ex/9702012. ]2] J. Breihveg et al.(ZEUS), DESY 97-025, hep-ex/9702015. [3] J.D. Sullivan, Phys. Rev. D 5 (1972) 1732. [4] F! Amaudmz et al., Phys. Rev. Lea. 66 (1991) 2712; M. Arneodo et al., Phys. Rev. D 50 ( 1994) Rl. [5] A. Baldit et al., Phys. Lett. B 332 ( 1994) 244. [6] M. Derrick et al., (ZEUS), Phys. Len. B 384 (1996) 388. [7] H. Holtmann, A. Szczurek and J. Speth, Nucl. Phys. A 596 (1996) 631; H. Holtmann, N.N. Nikolaev, J. Speth and A. Szczurek, Z. Phys. A 353 (1996) 411; A. Szczurek, M. Eticson, H. Holtmann and J. Speth, Nucl. Phys. A 596 (1996) 397; H. Holtmann, G. Levman, N.N. Nikolaev, A. Szczurek and J. Speth, Phys. Lett. B 338 (1994) 363; M. Przybycietl, A. Szczurek and G. Ingelman, DESY 96073, in print in Z. Phys. C. [8] A. Szczumk, V. Uleschenko, H. Holtmann and J. Speth, to be published in Nucl. Phys. A. [9] A. Szczurek and A. Budzanowski, in print in Phys. Lett. B. 101 E Abe et al., Phys. Rev. Lett. 77 (1996) 438. 111 J. Huston, E. Kovacs, S. Kuhlmann, H.L. Lai, J.F. Owens, D. Soper and W.K. Tung, Phys. Rev. Lett. 77 ( 1996) 444. 121 G. Ingelman and R. Riickl, Phys. Lett. B 201 (1988) 369. 131 W. Buchmiiller, R. Rilckl and D. Wyler, Phys. Len B 191 (1987) 442. 141 D. Choudhury and S. Raychaudhuri, CERN-TH/97-26, hepphl9702392. [ 151 G. Altarelli, J. Ellis, G.F. Giudice, S. Lola and M.L. Mangano, CERN-‘D-I/97-40, hep-ph/9703276. [ 161 J.F. Owens, Phys. Len B 266 (1991) 126. [ 171 M. Glilck, E. Reya and A. Vogt, Z. Phys. C 67 (1995) 433.