Obtaining physics results from the SLD CRID

Nuclear Instruments and Methods in Physics Research A 371 (1996) 195-199

NUCLEAR INSTRUMENTS a METMODS IN PHVSICS

ELSEVlER

Obtaining physics results from the SLD CRID K. Abe”, P. Antilogusb, D. Astonb”‘*, K. Baird”, C. Baltayd, A. Bean’, R. Ben-Davidd, T. Bienzb, F. Birdb, D.O. Caldwell’, M. Cavalli-Sforza’, J. Coller”, P. Coyle’, D. Coyne’, S. Dasub, M. Dimah, A. d’oliveira’, J. Duboscq’, W. Dunwoodieb, G. Hallewellb, K. Hasegawaa, Y. Hasegawaa, J. Huber”, Y. Iwasaki”, P. Jacques”, R.A. Johnson’, M. Kalelkar’, H. Kawaharab, Y. Kwonb, D.W.G.S. Leithb, X. Liuf, A. Lu”, S. Manlyd, J. Martinez’, L. Mathys”, S. McHugh”, B. Meadows’, G. Miillerb, D. Mullerb, T. Nagamineb, S. Narita”, M. Nussbaume, T.J. Pavelb, R. Piano’, B. Ratcliffb, P. Rensingb, A.K.S. Santha’, D. Schultzb, S. Send, J.T. Shankg, S. Shapirob, C. Simopoulosb, J. Snyder”, E. Solodovb, P. Stamerc, I. Stockdale’, F. Suekane”, N. Togeb, J. Turkd, J. Va’vrab, J.S. Whitakerg, D.A. Williams , S.H. Williamsh, S. Willocqd, . e h c a R . J . Wilson 7 G . Word 3 S . Yell,: , H . Yuta “Department

of Physics,

“Stanford ‘Grin

Physics Laboratory, ‘Department ‘Department

‘Santa

Linear

Cru;

of Physics, Particle

“Department ‘Department ‘Department

Rutgers

of Physics,

Inst. for

Tohoku

of Physics.

Center,

lJniversi@,

Universit?,

Boston

Universie

Sendai

980, Japan

CA 94.309,

New Haven.

of California.

Unir,ersity

Colorado

Aramaki. Stanford.

USA

P.O. B(I.Y 849. Piscataway.

Yale University,

Physics.

of Physics,

of Physics,

University,

Accelerator

Santa Barbara,

of Californiu.

University,

State University, of Cincinnati.

Boston,

NJ 088.5.7. USA

CT 06.511, USA CA 9_3106. USA

Santa Cruz. CA 9.5064. USA MA

0.?2/5,

Fort Collins. Cincinnati.

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CO 8052-3. USA

Ohio 45E1.

USA

Abstract We describe the likelihood ratio method used for particle identification in the SLD CRID, which allows the use of the entire momentum range covered by the liquid and gas radiators, including the threshold regions. Its application to two preliminary physics analyses is also described.

1. Introduction Operation and performance of the SLD CRID has been described elsewhere at this workshop [l]. The resolution obtained in both liquid and gas radiators, and the understanding of backgrounds, is now good enough to allow a general particle identification to work well, without requiring explicit fits to Cherenkov rings. In this paper, we give some hetails of the algorithm developed for particle identification in the CRID (21. which has not previously been published. We then give a brief description of preliminary physics analyses which make use of it [3,4], paying particular attention to the measurement of identification efficiency and understanding of systematic errors. Although our algorithm is general and

’ Speaker. * Corresponding author. 016%9002/96/$15.00 SSDI

0

1996

0168.9002(95)01156-O

has the great advantage of smoothness at thresholds and the ability to combine gas and liquid radiator information, it is not optimal in cases where resolution is the key (as in r/K separation at the highest momenta), unless all systematic errors have been removed from the detector alignment.

2. The likelihood ratio method During development of the particle identification algorithm. the principal goals were: _ to maximise the use of available information; _ to give equal treatment to liquid and gas radiators; _ to give smooth behaviour at thresholds. In order to satisfy these requirements, it was necessary to develop a realistic model of the backgrounds, including allowance for photoelectrons (pe’s) generated by other

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K. Abe et al. I Nucl. Znstr. and h4eth. in Phys. Rex A 371 (1996) 195-199

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tracks in the event. The method uses as a basis the observed density of pe’s in real space (n, y, z) and transforms to “Cherenkov space” (0, 4, t) where, for a given charged track (0, 4) are the spherical polar coordinates of the photon with respect to the track and t is the depth in the photon detector measured along the ray. The transformation between these systems and the Jacobian which relates them: a(@ 4, I) 5=

a(4 y7 z)

can be calculated without too much trouble. Suppose E is the expected number of pe’s in the detector and n is the actual number (obviously fi depends on the hypotheses for the tracks). Then the probability of n given fi is ti”e-“ln!. In addition to getting the correct number of pe’s, the hypotheses for the various tracks must give the correct distribution. Let P(r) = P(x, y, z) be the probability of a given photoelectron being in a small volume d7r, then G’(r) is the expected number of photoelectrons in d3r. The overall probability of there being n points and those points distributed as they were found is the “likelihood” 9’ which, taking into account all the permutations, can he expressed as

ring, and @ is the allowable a’~range (which for gas is usually 2~). Actually there are generally several terms in P~,~, corresponding to gas, liquid and quartz sources, and each term should have its own M,,,, which may be zero. For simplicity, we will leave this fact implicit. At present 5’ depends explicitly on the hypotheses of all tracks, and this is a combinatorial explosion that we cannot deal with. However, there is an obvious simplification. Let us allow the hypothesis for track k to vary while keeping all hypotheses for other tracks, j, constant at h,. Then we can write YkLh= e-M,,, El (4 + p,.,(ri)) . and B,, has now been redefined as the background that would be present if there were no Cherenkov radiation, with addition of the contribution expected from other tracks: B,=B+C Jfk

P,,,.I’

and the product i runs over only those pe’s for which at least one of the five hypotheses leads to a finite P~,~. Since the B, are now independent of the hypothesis for track k, ratios of likelihoods are unchanged by the replacement

,=I

where i runs over all the pe’s. If p(r) is the density of points under the assumption of a given set of hypotheses for the tracks and background, we can simply relate it to P(r) = p(r)d3rlA. Since we are only concerned with likelihood ratios between 9’ for different sets of hypotheses, we can remove the awkward factors of d”r from 9’ to get _!T=em” fi p(r,). ,=I

It is convenient

to break

p(r)

explicitly

into two terms as

p(r) = B(r) + C p,.,,(r) ,

t

where B(r) Cherenkov hypothesis amounts to highest 9.

is the expected background in the absence of pe’s and the p,.,,(r) are the densities due to h, of track k. The “likelihood” method choosing as the best hypotheses those with

Now Pk.h is most conveniently expressed in “Cherenkov space” and converted into a density using the Jacobian YZ

In this form, it is obvious that the larger Bk is at a given point, the less effect a pe at that point has on the likelihood ratio. By the simplifications we have made, we have lost the ability to compare the hypotheses of two different tracks, but achieved the main goal of calculating the likelihood ratios for the several hypotheses of a given track. In practice, the computation of _Yk,, is an iterative procedure, since the B, are dependent on the choice of hypotheses for other tracks (we use the current best overall hypothesis, defaulting to a), but the procedure always converges very quickly. We compute the likelihood ratios for liquid and gas radiators separately, though they can be simply combined. In our background model we include liquid, gas and quartz source terms from all tracks, and use pe’s which have no reasonable assignment to any track as a basis for a constant background density term at the liquid and gas sides of each TPC.

3. Obtaining

where A is the photon attenuation length, (T is the expected error in the Cherenkov angle (which may be itself a rather complicated function), 0, is the expected Cherenkov angle for hypothesis h, M,,, is the number of photoelectrons expected in the allowable 4 range from the hypothesised

physics results

There are now preliminary results from two analyses which make use of the method described above. The first [3] is a measurement of hadronic particle fractions, for which the Monte Carlo (MC) is used to produce a complete efficiency matrix of rr, K and p identification and misidentification probabilities. We use a log-likelihood

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K. Abe et al. I Nucl. Instr. and Meth. in Phys. Res. A 371 (1996) 195-199

difference (A) of 5 as the criterion for identification. Fig. 1 shows the elements of the matrix for the liquid and gas radiators as a function of momentum. We have used rrf from KY decays to check the IT (mis)identification column of the matrix. The agreement is satisfactory, and the errors in Fig. I have been increased to cover possible discrepancies. Qualitatively, the behaviour is as expected; as a threshold is crossed, the identified fraction rises rapidly to a plateau typically 280%. then declines as the ring radius becomes indistinguishable from the next heavier or lighter species. Misidentification is critically dependent on backgrounds, particularly in the Cherenkov veto regions, and can be as high as -7%. Because of the lack of a tracking detector after the barrel CRID. it includes a component from tracks which interact or decay in the CRID and therefore cannot be properly identified. Leptons are not distinguished from pions in this analysis, but are corrected for in the MC. An advantage of this method, which obtains

the fractions directly by inversion of the efficiency matrix, is that their sum, which is not constrained to unity, acts as an additional check. Since the efficiency matrix is derived by making cuts on A, directly comparing the data and MC distributions of A is also very useful. Fig. 2 shows this comparison for one momentum byte in the liquid and gas identification regions. The relative data/MC normalisation is unimportant since it depends on details of the hadronisation model used in the MC (which we are trying to validate); the spikes at iA/ -45 are artifacts of our software, which forces 3 to lie within that range: but it is important to have a qualitative understanding of the other features. In Fig. 2(b) the bump around zero is caused by protons which are below threshold and are equally badly described as either n or K; it is also clear that the efficiency for identification of n or K is not sensitive to the value of A chosen but, in contrast, Fig. 2(d) shows that identification of K is (this is the gas veto

P (GeV) Fig. I. Preliminary simulated efficiency matrix for charged -rr, K and p to be (mis)identified by the liquid (solid dots) and gas (open squares) as a function of momentum with a cut A = 5. The errors are dominated by systematic separation up to about 3f GeVlc in the liquid and 20 GeVlc in the gas.

effects as described

in the text. We obtain good T/K

V. PHYSICS

RESULTS

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K. Abe et al. I Nucl. Instr. and Meth. in Phys. Res. A 371 (1996) 195-199

0.8 < p c 1.5 GeV (liquid)

800

4
’

600

800

Fig. 2. Distributions of 7-K log-likelihood difference (A,,) for tracks in the momentum range 0.8-I .5 GeVlc in liquid (a, b). and 4-8 GeVlc in the gas (c,d). Data are shown as points and the MC is the solid histogram. In (b) and (d), the actual MC pions are shown as the dashed histogram at the right and in (b) the MC kaons are the dashed histogram to the left.

region). Figs. 2(a) and 2(c) show reasonable qualitative agreement between the data and MC distributions, but there is evidence that the 7~ separation in the data is “too good” in the liquid and “not good enough” in the gas. We have found that an understanding of plots such as these is very helpful in tuning the MC and even in finding bugs in the algorithm! A second preliminary analysis .using the CRID to do charged K tagging in the gas region in a measurement of A, has also been presented recently [4]. Although work remains to be done in understanding the systematics of the particle identification, the measurement is competitive with other methods and the systematic error is dominated by unknowns in the B decay mode1 itself, not by the CRID.

improve the Cherenkov angle resolution, but we could improve n/K separation at the highest momenta in the gas and n/K/p separation in the gas veto region by using explicit ring fits to remove detector alignment systematics, and improve the effective gas and liquid angle resolutions where the ring radius is the critical parameter. In a sense, we already have a preliminary answer to the technically most challenging measurement using the CRID-determination of particle fractions over a wide range of momenta. As our understanding improves and more high-polarisation data is obtained, we expect to attack a wide range of physics topics topics including: polarised s-quark asymmetry; quark/gluon jet differences; leading baryons ‘and baryon correlations.

4. Conclusions

Acknowledgements

The general CRID particle identification algorithm is now quite well understood and can be used in both ring and threshold regions for doing physics. Further work on detector alignment and systematics is still needed to

This work was supported by Department of Energy contract DE-AC03-76SFOO515 and other DOE and NSF grants. The speaker gratefully acknowledges the financial support of the RICH95 organisers.

K. Abe et al. I Nucl. btstr. and Meth. in Phys. Res. A 371 (1996) 195-199

References I1 J D. Aston representing the SLD CRID group, these Proceedings (1995 Int. Workshop on Ring Imaging Cherenkov Detectors. Uppsala, Sweden) Nucl. Instr. and Meth. A 371 ( 1996) 8. [2] S. Yellin. Finding Cherenkov Angles and Testing Hypotheses, CRID memo #49, 1993 (unpublished),

199

131 K. Baird, representing the SLD Collaboration, The Production of ni, KT, D,K” and 12” in Hadronic 2” Decays, SLAC-PUB95-6933, presented at the 30th Rencontres de Moriond. March 1995. [4] SLD Collaboration, Measurement of A, at the 2” Resonance Using Identified Charged Kaons, Contributed Paper eps-251 to the Brussels EPS Meeting, July 1995.