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A phenomenological two-component picture of large transverse momentum production
Volume 63B, number 3
PHYSICS LETTERS
A PHENOMENOLOGICAL
TWO-COMPONENT PICTURE
OF LARGE TRANSVERSE
MOMENTUM PRODUCTION
2 August 1976
S. FREDRIKSSON Department of Theoretical Physics, Royal Institute of Technology, S-I O0 44 Stockholm 70, Sweden Received 27 May 1976 It is suggested that large-PT hadrons can be classified into two categories with completely different properties according to whether they contain a leading quark or just sea quarks from the initial projectile-target system. From simple quark counting we get relations between hadron ratios at large PT, which are consistent with data.
The aim of this note is to suggest a simple phenomenological two-component picture of large-p T hadron production in high-energy proton-proton and protonnucleus collisions. Separating the particle production mechanism in several components is a well-established way of treating inclusive longitudinal momentum spectra, but it seems also to be taken for granted in many models for transverse spectra that there are several completely different mechanisms at work. Parton model builders for instance usually assume, in an ad hoc way, that there is one small-p T mechanism (not specified by the model) dominating at PT ~ 1 GeV/c and one large-p T mechanism, often postulated to correspond to some specific parton diagram or set of diagrams [1, 2]. We suggest that there is an equally natural way of discriminating between medium- and very-large-p T parton processes. The small- and medium-p T parts of 90 ° hadron spectra are assumed to be dominated by hadrons that contain just sea ("wee") quarks from the colliding hadrons. This component is therefore equal for particle and antiparticle. The very-large-p T region is suggested to contain particles built up by at least one of the initial leading ("valence") partons. It is reasonable to assume that such a component in the spectrum of a hadron c is proportional to the number of "useful" leading partons in the initial state (a u quark is "useful" for n + production, a d quark for lr- etc). Let us start with a few trivial comments. Intuitively, it is clear that i f 9 0 ° hadrons can be classified like that, the second type will have considerably larger mean transverse momenta. What we do not know yet is if they will also dominate the spectrum in a large enough PT interval to be of interest. It is clear
however that very near the phase space boundary PT ~X/~, the spectrum must, for kinematical reasons, be built up entirely by exclusive events like pp (nTr+), pp ~ pp etc, which by definition belong to our second component. Even if the event structures in general are not as simple as that at very large PT, we suggest that the same kinds of parton subprocesses are present also in more complicated events. As far as we can see, our two-component picture is not related to any of the detailed parton models on the market, simply because we do not care about the particular parton diagrams that contribute to the two components. It might well be that gluon exchange, 7r-parton scattering, zrTrscattering, parton-parton scattering etc are important in both components. The qualitative support to our picture comes from the fact that there are clear differences between ~r~ , K ÷ and p production on one hand and K - and ~ production on the other, and that the only natural borderline we can find between these two groups is that the first four hadrons, in contrast to K - and ~, contain at least one u or d quark. The differences in PT spectra that we refer to have a tendency to set in above PT = 2 - 3 GeV/c or possibly above x T ----2PT/X/~ = 0.25 -- 0.35 (depending on how one parametrises data). To be specific, data from the Chicago-Princeton (CP) experiment [3] at Fermilab (proton-nucleus) and from the British-Scandinavian (BS) collaboration [4] at the CERN ISR (proton-proton) tell us that (i) the hadron ratios K-/Tr- and ~/zr- decrease with PT above PT ~ 2 GeV/c, while K+/rr + and p/rr + stay roughly constant in that PT region; (ii) K - [ z r - and ~/lr- increase somewhat with x/~ at fixed PT, while K+/Tr+ and p/•r + are constant or slightly falling with x/s-; 321
Volume 63B, number 3
PHYSICS LETTERS
(iii) 7r+/lr- increases slowly, while K+/K - and p/~ increase rapidly with PT; (iv) the exponent N(XT) in the well-known parametrisation
E doc/d3p190 ° = pT N f(XT) increases roughly linearly with x T but has in addition a clear leveling-off above x T ~ 0.3 in n ±, K + and p production, which is not present in K - and ~ spectra; (v) the exponent ot(pT) in the parametrisation
E dOc/d3p[ 90° =AUg(pT) of inclusive spectra from proton-nucleus collisions [3] (A = nuclear mass number) has the same characteristic features as N in point (iv); it increases linearly with PT for K - and ~ but has a clear "plateau" above PT = 3 - 4 GeV/c in 7r-, + K + and p spectra. All those trends give us the impression that there is some kind of large-p T component in 7r-+, K + and p production that cannot contribute to the production of K - and ~ at any energy or transverse momentum. We will not try to find the x/~"and PT structure of the two components because experimental data are too crude to allow any finer analysis. Instead we restrict our quantitative investigation to point (iii) above, since here we can get some predictions from the mere definition o f the model. We use the abbreviation fc = E dtrc/d3p] 90° and start by defining S~r, 2L~r, S K and 2L K to be the small-p T and large-p T components in 7r+ and K + production in pp collisions. By definition and by just "counting quarks" we get: fn + = Sir + 2Lit,
fir- = Sn +Llr,
fK + = SK + 2LK,
fK-
= SK
in proton-proton collisions, and fTr+ =STr + 1.75L~,
fTr- =S,r + l'25L~r,
fK + = SK + 1.75LK,
fK- = SK
in proton-nucleus collisions assuming that the target nucleus contains an approximately equal amount of protons and neutrons. From CPdata on ~r+/Tr- we now estimate the ratio L n / S n. We start with the parametrisation 7r+hr- I pA = 1 + B x t ,
where B = 0.6 --- 0.1, which is good for 300 and 400 322
2 August 1976
GeV/c data at 0 <~ x T ~ 0.5. It is not absolutely clear that x T is a "better" variable than PT to use here. A parametrisation with CPTinstead o f B x T above would however also give predictions in agreement with data. From our first result
L J S n = BXT/(0.5 - 1.25BXT) we see that the very-large-p T component starts to dominate in 7r+ production above x T = 0.30 -+ 0.05 and in 7r- production above x T = 0.35 -+ 0.05, which is consistent with the various "breaks" found in other largePT data. The formula is naturally not valid above x T 0.5. By using this form for L , / S ~ we get 7r+/Tr- I pp
=
(2 + 3BXT)/(2 -- BXT).
In the region x T <~ 0.2, where there are data from the ISR [4], this can be approximated with /r+/'tr-]pp = 1 +(1.3 + 0 . 3 ) x T, to be compared with the experimental trend 7r+/Tr- exp pp = 1 +(1.6 + 0 . 3 ) x r . TO get further and estimate K÷/K - from lr+/lr - we must make the extr~assumption that
L K / S K =Ln/S n. Such an equality is indeed natural in our approach. As a K + differs from a 7r÷ just through the presence of an ~"quark instead of a d quark, both coming from the initial sea, we suggest that the production of the antiquark in a hadron will influence the two components S and L in the same way, so that a "sea quark probability factor" is divided out in the ratio L/S. We must however restrict our analysis to a PT region where all quark masses can be neglected (at PT ~" 0.5 GeV/c say), since there is no reason to believe that also the purely kinematical mass dependence is the same (and factorizable) in L and S. Perhaps it would be wise to try to take this into account by comparing K and 7r c ~ nents at the same single particle energy, E = x/(p~ + mc), but this gives some extra troubles in the data reduction [5]. The prediction K + / K - I p A = (1 + BxT)/(1 - 2.5BXT) is compared with CP data in fig. 1. It can be seen that this form is everywhere consistent with data. Although error bars are large, it is encouraging to find that the sharp increase with x T is correctly repro-
Volume 63, number 3
t 7 61
/k ~ O [3
PHYSICS LETTERS
pW 300 GeV/c pW 400 GeV/c pBe 300GeV/c pTi aooGeV/c
'v -x. ,¢,
0
01
0,2
0.3
04
05
06
07
XT Fig. 1. The inclusive hadron ratio K+/K- at large PT as a function ofx T -= 2PT/x/s-in proton-nucleus collisions. Data points are extracted from [3]. Some typical error bars are indicated. The area between the lines corresponds to the prediction from our model, as described in the text.
duced. The slight underestimates in both our tests can be fully compensated for either by giving less weight to the proton-tungsten data when fitting the parameter B (that would result in a larger B value) or by taking into account that tungsten consists of around 60% (and not 50%) neutrons (that would result in factors 1.7 and 1.3 instead of 1.75 and 1.25 in front of L in the expressions for f~r and fK). Unfortunately, we are not able to repeat our analysis for the ratio p/~, because here it is not possible to apply our simple probabilistic considerations; a produced large-p T proton can get more than one of its constituents from the set o f initial leading partons. It is clear though, that p/~ should fulfil p/~ >> rr+/rr - and p/~) > K+/K - , which is in qualitative agreement with data. We conclude this note with a number of more or
2 August 1976
less straight-forward predictions from the model: (i) As x T grows, it+fir - ~ 2 in pp and ~ 1.4 in pA collisions, K+/K - and p/~ -~ 0% K+fir + ~ constant > 0, K - / l r - and ~/lr- -~ 0, all in qualitative agreement with data. The increase in K÷/rr ÷, K - / r r - , ~/lrand p/rr + with x T at x T < 0.2 is in our model a typical low-p T mass effect; an opinion that also has some "direct" support in data [5]. (ii) The large-PT correlations should change character as x T increases beyond 0.3. We attribute the increase with PT in associated multiplicity, found in the Pisa-Stony Brook experiment [6] at the ISR, to the S component and expect a gradual decrease at larger PT. A fall-off, or possibly a leveling-off, is indeed visible in the associated multiplicity when the PT of the trigger n ° (i.e. photon) exceeds 3 GeV/c. Eventual jet structures should most likely appear in the L and not in the S component, but here we cannot be very precise. We are more confident when suggesting that the number of outgoing protons correlated to for instance a largePT rr+ will change with increasing PT of the trigger. At small PT the number of protons will be the same as in an average event, while at very large PT, where L dominates, there will be a more than 50% chance that one of the protons "redresses" to a neutron. Alternatively, one might trigger (in a large solid angle) on two outgoing protons. Such a selection criterion will reduce the components L~r and L K by more than 50% but leave S~r and S K unchanged, with due consequences for the various large-PT spectra. I would like to thank the Swedish Atomic Research Council for financial support.
References [1] D. Sivers, S.J. Brodsky and R. Blankenbecler, Phys. Reports 23C (1976) 1. [2] S.D. Ellis, in Proc. XVII Int. Conf. on High energy physics, London, 1974. [3] J.W. Cronin et al., Phys. Rev. Dll (1975) 3105. [4] B. Alper et al., Nucl. Phys. B100 (1975) 237. [5] S. Fredriksson, Nucl. Phys. B84 (1975) 234. [6] G. Finocchiaro et al., Phys. Lett. 50B (1974) 396.
323
PHYSICS LETTERS
A PHENOMENOLOGICAL
TWO-COMPONENT PICTURE
OF LARGE TRANSVERSE
MOMENTUM PRODUCTION
2 August 1976
S. FREDRIKSSON Department of Theoretical Physics, Royal Institute of Technology, S-I O0 44 Stockholm 70, Sweden Received 27 May 1976 It is suggested that large-PT hadrons can be classified into two categories with completely different properties according to whether they contain a leading quark or just sea quarks from the initial projectile-target system. From simple quark counting we get relations between hadron ratios at large PT, which are consistent with data.
The aim of this note is to suggest a simple phenomenological two-component picture of large-p T hadron production in high-energy proton-proton and protonnucleus collisions. Separating the particle production mechanism in several components is a well-established way of treating inclusive longitudinal momentum spectra, but it seems also to be taken for granted in many models for transverse spectra that there are several completely different mechanisms at work. Parton model builders for instance usually assume, in an ad hoc way, that there is one small-p T mechanism (not specified by the model) dominating at PT ~ 1 GeV/c and one large-p T mechanism, often postulated to correspond to some specific parton diagram or set of diagrams [1, 2]. We suggest that there is an equally natural way of discriminating between medium- and very-large-p T parton processes. The small- and medium-p T parts of 90 ° hadron spectra are assumed to be dominated by hadrons that contain just sea ("wee") quarks from the colliding hadrons. This component is therefore equal for particle and antiparticle. The very-large-p T region is suggested to contain particles built up by at least one of the initial leading ("valence") partons. It is reasonable to assume that such a component in the spectrum of a hadron c is proportional to the number of "useful" leading partons in the initial state (a u quark is "useful" for n + production, a d quark for lr- etc). Let us start with a few trivial comments. Intuitively, it is clear that i f 9 0 ° hadrons can be classified like that, the second type will have considerably larger mean transverse momenta. What we do not know yet is if they will also dominate the spectrum in a large enough PT interval to be of interest. It is clear
however that very near the phase space boundary PT ~X/~, the spectrum must, for kinematical reasons, be built up entirely by exclusive events like pp (nTr+), pp ~ pp etc, which by definition belong to our second component. Even if the event structures in general are not as simple as that at very large PT, we suggest that the same kinds of parton subprocesses are present also in more complicated events. As far as we can see, our two-component picture is not related to any of the detailed parton models on the market, simply because we do not care about the particular parton diagrams that contribute to the two components. It might well be that gluon exchange, 7r-parton scattering, zrTrscattering, parton-parton scattering etc are important in both components. The qualitative support to our picture comes from the fact that there are clear differences between ~r~ , K ÷ and p production on one hand and K - and ~ production on the other, and that the only natural borderline we can find between these two groups is that the first four hadrons, in contrast to K - and ~, contain at least one u or d quark. The differences in PT spectra that we refer to have a tendency to set in above PT = 2 - 3 GeV/c or possibly above x T ----2PT/X/~ = 0.25 -- 0.35 (depending on how one parametrises data). To be specific, data from the Chicago-Princeton (CP) experiment [3] at Fermilab (proton-nucleus) and from the British-Scandinavian (BS) collaboration [4] at the CERN ISR (proton-proton) tell us that (i) the hadron ratios K-/Tr- and ~/zr- decrease with PT above PT ~ 2 GeV/c, while K+/rr + and p/rr + stay roughly constant in that PT region; (ii) K - [ z r - and ~/lr- increase somewhat with x/~ at fixed PT, while K+/Tr+ and p/•r + are constant or slightly falling with x/s-; 321
Volume 63B, number 3
PHYSICS LETTERS
(iii) 7r+/lr- increases slowly, while K+/K - and p/~ increase rapidly with PT; (iv) the exponent N(XT) in the well-known parametrisation
E doc/d3p190 ° = pT N f(XT) increases roughly linearly with x T but has in addition a clear leveling-off above x T ~ 0.3 in n ±, K + and p production, which is not present in K - and ~ spectra; (v) the exponent ot(pT) in the parametrisation
E dOc/d3p[ 90° =AUg(pT) of inclusive spectra from proton-nucleus collisions [3] (A = nuclear mass number) has the same characteristic features as N in point (iv); it increases linearly with PT for K - and ~ but has a clear "plateau" above PT = 3 - 4 GeV/c in 7r-, + K + and p spectra. All those trends give us the impression that there is some kind of large-p T component in 7r-+, K + and p production that cannot contribute to the production of K - and ~ at any energy or transverse momentum. We will not try to find the x/~"and PT structure of the two components because experimental data are too crude to allow any finer analysis. Instead we restrict our quantitative investigation to point (iii) above, since here we can get some predictions from the mere definition o f the model. We use the abbreviation fc = E dtrc/d3p] 90° and start by defining S~r, 2L~r, S K and 2L K to be the small-p T and large-p T components in 7r+ and K + production in pp collisions. By definition and by just "counting quarks" we get: fn + = Sir + 2Lit,
fir- = Sn +Llr,
fK + = SK + 2LK,
fK-
= SK
in proton-proton collisions, and fTr+ =STr + 1.75L~,
fTr- =S,r + l'25L~r,
fK + = SK + 1.75LK,
fK- = SK
in proton-nucleus collisions assuming that the target nucleus contains an approximately equal amount of protons and neutrons. From CPdata on ~r+/Tr- we now estimate the ratio L n / S n. We start with the parametrisation 7r+hr- I pA = 1 + B x t ,
where B = 0.6 --- 0.1, which is good for 300 and 400 322
2 August 1976
GeV/c data at 0 <~ x T ~ 0.5. It is not absolutely clear that x T is a "better" variable than PT to use here. A parametrisation with CPTinstead o f B x T above would however also give predictions in agreement with data. From our first result
L J S n = BXT/(0.5 - 1.25BXT) we see that the very-large-p T component starts to dominate in 7r+ production above x T = 0.30 -+ 0.05 and in 7r- production above x T = 0.35 -+ 0.05, which is consistent with the various "breaks" found in other largePT data. The formula is naturally not valid above x T 0.5. By using this form for L , / S ~ we get 7r+/Tr- I pp
=
(2 + 3BXT)/(2 -- BXT).
In the region x T <~ 0.2, where there are data from the ISR [4], this can be approximated with /r+/'tr-]pp = 1 +(1.3 + 0 . 3 ) x T, to be compared with the experimental trend 7r+/Tr- exp pp = 1 +(1.6 + 0 . 3 ) x r . TO get further and estimate K÷/K - from lr+/lr - we must make the extr~assumption that
L K / S K =Ln/S n. Such an equality is indeed natural in our approach. As a K + differs from a 7r÷ just through the presence of an ~"quark instead of a d quark, both coming from the initial sea, we suggest that the production of the antiquark in a hadron will influence the two components S and L in the same way, so that a "sea quark probability factor" is divided out in the ratio L/S. We must however restrict our analysis to a PT region where all quark masses can be neglected (at PT ~" 0.5 GeV/c say), since there is no reason to believe that also the purely kinematical mass dependence is the same (and factorizable) in L and S. Perhaps it would be wise to try to take this into account by comparing K and 7r c ~ nents at the same single particle energy, E = x/(p~ + mc), but this gives some extra troubles in the data reduction [5]. The prediction K + / K - I p A = (1 + BxT)/(1 - 2.5BXT) is compared with CP data in fig. 1. It can be seen that this form is everywhere consistent with data. Although error bars are large, it is encouraging to find that the sharp increase with x T is correctly repro-
Volume 63, number 3
t 7 61
/k ~ O [3
PHYSICS LETTERS
pW 300 GeV/c pW 400 GeV/c pBe 300GeV/c pTi aooGeV/c
'v -x. ,¢,
0
01
0,2
0.3
04
05
06
07
XT Fig. 1. The inclusive hadron ratio K+/K- at large PT as a function ofx T -= 2PT/x/s-in proton-nucleus collisions. Data points are extracted from [3]. Some typical error bars are indicated. The area between the lines corresponds to the prediction from our model, as described in the text.
duced. The slight underestimates in both our tests can be fully compensated for either by giving less weight to the proton-tungsten data when fitting the parameter B (that would result in a larger B value) or by taking into account that tungsten consists of around 60% (and not 50%) neutrons (that would result in factors 1.7 and 1.3 instead of 1.75 and 1.25 in front of L in the expressions for f~r and fK). Unfortunately, we are not able to repeat our analysis for the ratio p/~, because here it is not possible to apply our simple probabilistic considerations; a produced large-p T proton can get more than one of its constituents from the set o f initial leading partons. It is clear though, that p/~ should fulfil p/~ >> rr+/rr - and p/~) > K+/K - , which is in qualitative agreement with data. We conclude this note with a number of more or
2 August 1976
less straight-forward predictions from the model: (i) As x T grows, it+fir - ~ 2 in pp and ~ 1.4 in pA collisions, K+/K - and p/~ -~ 0% K+fir + ~ constant > 0, K - / l r - and ~/lr- -~ 0, all in qualitative agreement with data. The increase in K÷/rr ÷, K - / r r - , ~/lrand p/rr + with x T at x T < 0.2 is in our model a typical low-p T mass effect; an opinion that also has some "direct" support in data [5]. (ii) The large-PT correlations should change character as x T increases beyond 0.3. We attribute the increase with PT in associated multiplicity, found in the Pisa-Stony Brook experiment [6] at the ISR, to the S component and expect a gradual decrease at larger PT. A fall-off, or possibly a leveling-off, is indeed visible in the associated multiplicity when the PT of the trigger n ° (i.e. photon) exceeds 3 GeV/c. Eventual jet structures should most likely appear in the L and not in the S component, but here we cannot be very precise. We are more confident when suggesting that the number of outgoing protons correlated to for instance a largePT rr+ will change with increasing PT of the trigger. At small PT the number of protons will be the same as in an average event, while at very large PT, where L dominates, there will be a more than 50% chance that one of the protons "redresses" to a neutron. Alternatively, one might trigger (in a large solid angle) on two outgoing protons. Such a selection criterion will reduce the components L~r and L K by more than 50% but leave S~r and S K unchanged, with due consequences for the various large-PT spectra. I would like to thank the Swedish Atomic Research Council for financial support.
References [1] D. Sivers, S.J. Brodsky and R. Blankenbecler, Phys. Reports 23C (1976) 1. [2] S.D. Ellis, in Proc. XVII Int. Conf. on High energy physics, London, 1974. [3] J.W. Cronin et al., Phys. Rev. Dll (1975) 3105. [4] B. Alper et al., Nucl. Phys. B100 (1975) 237. [5] S. Fredriksson, Nucl. Phys. B84 (1975) 234. [6] G. Finocchiaro et al., Phys. Lett. 50B (1974) 396.
323