Letter from Wolfram Kittel

Wolfram Kittel

Schlossgasse 9

3422 Hadersfeld

Austria

wolfram@hef.ru.nl

April 22, 2012

Dear Rudy,

Even though I am quite late to congratulate you to your 80st anniversary, I wish you and Helen all of the best for the coming years! What I find absolutely remarkable and admirable is that you are thinking about retirement only now, and that even only officially. So I see you continuing inofficially even further. Since I am not able to join you during your retirement fest to come, I will try to dig into my memory in order to be with you that way. Of course, you will have to excuse me if that memory turns out to be wrong on one point or the other. In addition, this memory is restricted to your contributions to multihadron dynamics, a field where our interest overlapped. I realize that your own interests are much wider than that and extend to other fields, as well. I am sure they will get their proper recognition by other scientists.

As far as I remember, the first time we met (of many times to come) was the Multiparticle Dynamics Symposium in Tábor, Czechia, back in 1978, when you came over from Rutherford Lab. I was impressed by the quark recombination model you had developed together with Das in 1977 and were busy extending, e.g. by including resonance decays with Roberts and Matsuda (1978) or by the choice of a proper recombination function with Chang (1979). To my knowledge, it was in fact the first detailed model based on the recombination idea. While a large number of physicists joined you on these efforts, you again pioneered with your valon model of constituent valence quarks (with Chang, Zahir, Eilam, Yang and Lam), which reveal universal parton structure when probed at sufficiently high momentum transfer. The model was successfully tested on hadron fragmentation data (e.g. by the Nijmegen student Gatignon). Together with Roberts, you showed how the recombination picture can be used to determine the valence quark distribution in mesons, for which no direct information from deep inelastic lepton interactions exists. Most importantly, the success of your approach e.g. in K fragmentation affirmed that the hadron quark structure is playing a role also in soft hadronic processes.

As a further progress I remember geometrical branching (with Chen in the late 1980ies) successfully describing e.g. the widening of the multiplicity distribution with increasing energy (1986) and, based on that, your eikonal cascade model ECCO (with Pan in the early 1990ies). There, the first step is the eikonal formalism in which the geometrical size of the colliding hadrons plays an essential role. The next step is a cut-pomeron expansion, where you make contact with the S-matrix approach to multiparticle production. In both cases, the summation of a series of terms exponentiates the probability of no inelastic collision and imposes unitarity. Each pomeron is then treated in the model as a branching process. The basic difference between GBM-ECCO and DPM or FRITIOF was that in the former you assumed the existence of partons in the hadrons before their collision, as one does in the parton model. The partons already there rearrange themselves through short-range interaction (in rapidity) into colorless clusters and undergo successive branchings. The fluctuation in the impact parameter from event to event leads to fluctuations in the transverse momentum. Furthermore, the successive branching is a random process giving rise to fluctuations, in particular to higher-order multiplicity fluctuations.

To study these fluctuations and to see whether multiparticle fluctuations possess (multi)fractal properties, you suggested in 1990 (then joined by Chiu and Florkowski, 1991) the so-called G-moments (or frequency moments), later elegantly extended by you (1995, see also Dremin 1994, Duclos and Meunier 1994) to factorial moments of continuous order, with the statistical fluctuations filtered out as in the integer-order ones. Both approaches led to interesting experimental applications and analyses. In 1990, you also had been among those who showed that the intermittency indices were related to the anomalous (or co-) dimensions giving the deviation from an integer dimension.

With Białas (1991) you drew the attention to order-independent anomalous dimensions, i.e. monofractal behaviour, as a possible signature for a quark-gluon plasma second-order phase transition. After first indications in heavy-ion data, later and more accurate data, however, gave evidence against such a transition. With Nazirov (1892) and Lesniak (1992) and on your own (1993/94), you, therefore, dropped the original simple Ising model approach and studied intermittency in the framework of the Ginzburg-Landau theory. In that model the anomalous dimension is not constant, but follows a precisely defined and universal order dependence. In quantum optics, where γ production at the threshold of lasing is describable as a second-order phase transition, you succeeded to verify this universal order dependence to high precision (with Young, Qu, and Singh, 1994) . On the other hand, hadron production in hadron-hadron as well as in heavy-ion collisions significantly deviates from the universal law. So you gave clear evidence against the assumption of a second-order phase transition in heavy-ion hadron production. Nevertheless, to be really sure, you suggested an extension (1998) of the use of fluctuations in the search for a second-order phase transition in terms of multiplicity difference correlators.

To understand multiplicity distributions of final-state hadrons, the difference between quark jets and gluon jets had to be understood. Hadron production can be assumed to be due to a shower of bremsstrahlung processes, followed by hadronization. The former is directly proportional to the coupling of the radiated gluon to the radiator (quark or gluon). Neglecting gluon splitting into quark-antiquark pairs, the ratio of the gluon multiplicity radiated from a gluon to that radiated from a quark is, therefore, expected to approach, to leading order and asymptotically, the ratio 9/4 of the QCD color factors. Together with Dremin you were involved in the calculation of analytical corrections to next-to-next-to-leading order (NNLO) and to energy conservation (1994).

Together with Cao (1995 - 2000), you generalized factorial F moments to so-called C moments defined as the sample average of the pth power of an F moment of order q, divided by the pth power of the sample average of that F moment, where the power p need not be integer. The advantage over the conventional intermittency analysis in terms of F moments is that the C moments for 0<p<2 already reveal a lot of information not probed by the former. One can then search for scaling in the latter. To distinguish that from intermittency, it is referred to as ‘erraticity’ of the system. In particular in heavy-ion collisions the experimental results deviate strongly from statistical fluctuations, thus indicating that event-to-event fluctuations are mainly dynamical and become more erratic with increasing order.

When the event multiplicity is low, the gaps between neighbouring particles carry more information about an event than multiplicity spikes. In order to obtain complementary information from the low multiplicities, you (with Zhang and Wu, 1999, 2000) suggested to extend the analysis to that of rapidity gaps. Again, the experimental application to hadron-hadron and heavy-ion collisions shows that fluctuations are far from statistical fluctuations and increase with increasing order.

In all that, you have stayed particularly close to experiment, checking your manifold ideas and suggestions on experimental data, both already existing and specially extracted according to your suggestions. It is encouraging to see that in more recent publications (with Yang) you have been continuing this approach with respect to the LHC. There, literally hundreds of people are crowding on so-called hot topics, while only too few are brave enough to execute the more service-like jobs on the underlying hadronic events.

Besides meeting you and Helen and learning from you at several of the successful International Multiparticle Dynamics Symposia and several other occasions, the series of workshops on Multiparticle Production stick out. You were involved in the organization and publication of the proceedings of all of them, including the one in Nijmegen, which you were kind enough to also summarize in the closing lecture. The first and particularly exciting one in these series was organized by you, Meng Er-xi, Wang Chen-rui, and Xie Qu-bing in Jinan, Shandong, China, in 1987. We exchanged a lot of new multiparticle results there, but you

also took the advantage of being there, to show us your country in an unequalled post-conference tour of sights carefully selected by you and Helen and presented by expert local tourist guides. This tour was the most impressive experience for Susi and myself until now.

Wolfram Kittel