## Nagel: Equality And Partiality X

Chapter Fifteen

It may be impossible to meet Nagel’s suggested legitimacy through unanimity approach because some value systems may be so opposed that they cannot allow each other without compromising themselves. Nagel’s two examples are abortion and Israel. [Interesting that both of these turn on religion, which is protected against discrimination’ by him in the same way as sex and race. An obvious solution presents itself, along with the further question as to how many such intractable problems are caused by religion. This would appear to be a significant number in the US at least.]

Justice cannot regulate the differences between parties as to the correct form of justice. [This must be true at some level, in that there could not be a just solution to a 50/50 split on the correct way to decide questions of justice. But people could vote on constitutional reform, including for example on the independence of the judiciary and the way of electing representatives — and these events frequently happen.] But this may require a higher order moral’ ideal.

The problem cannot be solved globally but is still difficult even on a national basis. [True, but some nations exhibit more cultural unity than others. Could it be that those are the ones with less religion and in addition, fewer different religious sects? To be fair to Nagel, he does cite religious xenophobia’ as one of the issues here. Note that this term means fear of the unknown’ though rather than fear of the different’.]

Extreme inequality may also make a solution unobtainable. [Nagel is clear here he does mean globally, but since he has just abandoned even the idea of finding a global solution, it is unclear what agenda he is pursuing here. A case can be made that the situation has improved since he wrote, but as it would be at best an improvement in the absolute conditions of the poorest countries combined with a relative decline, or perhaps a minor reduction in inequality, he probably would not accept it. He would also welcome the global financial crisis, since it has affected wealthy countries much more severely.]

Revolution and minor aid for the poor at the expense of the rich may both be legitimately rejected by the obvious parties and thus are not legitimate for Nagel. The reasonable rejection’ criterion is satisfied in both cases by the amount one party has to lose. However, this does not generate reasonable rejectability in all cases, with the example being slave-owners. Even though these would lose a great deal from abolition, they still may not enforce their system. [Nozick has a counter-example to the idea that absolute prohibition of slavery is the correct approach, based on the supremacy of consent. He considers a situation where someone has a terminally ill child, with medicine available from only one quarter. Presumably this medicine is extremely expensive, and so it is available only on the condition that the parent sign themselves into slavery. Nozick thinks we should be permitted to make this exchange, and I agree. Those unsure should consider the further modification that perhaps the medicine does not yet exist, and the extraordinary costs of research and production can only be met by say 100 parents agreeing to become slaves. Are we sure we should prevent them if they all agree?]

Nevertheless, the impersonal renders irrelevant’ the personal here. [While we can all agree that slavery is either completely impermissible or only to be admitted under exceptional circumstances such as those outlined above, this is a different question as to whether we should ever allow the mythical impersonal to so trump the personal as to eliminate it entirely. Nagel does not argue for this but claims to have derived it from finding it to be true in this one example.]

The canonical examples of poor countries to be compared with the US are India and China. [This ir ironic. Nagel could not have known when writing that these two would be prominent members of the BRIC nations, from whom strong growth is expected in the near future. It is perhaps also worth mentioning that this growth is not coming from collective agreements but from the free interplay of markets.]

Nagel ascribes this superior development of the West as due to technology. [That is certainly one factor, but more important according to the World Bank at least are the rule of law and freedom from corruption. Since these are common goods not provided by the market, Nagel has perhaps missed an opportunity to support his views — he could argue here that only a collective agreement could provide such goods.]

The rich countries may therefore reasonably refuse to fund the poor countries to reach some type of average level in the same way that rich individuals may refuse to do the same for poor people within national boundaries. The poor may reasonably reject what is offered, while also acknowledging that the what is offered represents the most that may reasonable be demanded of the rich. [Can this be true? Is it not the case that an acknowledgment that a change is reasonable cannot also include necessary means which are themselves unreasonable? And again, do any of the poor actually think like this? Perhaps it is our job to do this for them.]

It is possible in addition for a group of entirely reasonable persons to fail to find a reasonable agreed-upon solution. The example is the last life jacket case — no parent would be unreasonable in seeking it for his child. [So the question becomes the extent to which the actual world resembles the last life jacket case. At one level, this is not the case. We could certainly feed many more people than we do currently without ourselves starving, though this would result in significant decrements to the Western lifestyle currently enjoyed. But that is not enough to resolve the issue, because it might well be the case that such an approach would in fact create the last life jacket situation. It would be a world of substantial transfers from rich countries to poor ones, for at least as long as the economies of the former could bear it. That time would be quite strictly limited by the fact that the rewards of effort and talent would not be flowing to their possessors — in fact exactly the unworkable approach Nagel seeks elsewhere. But for as long as they lasted, the additional resources would create population expansion in poor countries. Then we would be in the last life jacket situation and one moreover greatly exacerbated by our actions.]

This does not result in support for the status quo for Nagel. [He does not explain why no action is the correct course when all options for inaction appear unreasonable.] If no solutions are not reasonably rejectable by no-one, then solutions may be imposed. Revolution may be legitimate, and for Nagel current levels of inequality permit revolutions. These are correct even if they cause a radical drop in the standard of living of oneself and one’s family’. [Since this will never be accepted, are we to infer a call for the end of democracy? That would be a further though unexpected mildly Nietzschean’ note.]

A move to improved levels of international aid is as justified as the move to further domestic support. [The numbers involved here are interesting. It is indeed the case that domestic support dwarfs international aid spending. The UK is one of the few countries to meet the international aid norm of 0.7% of GNP. This amounts to some £11bn at present. Social security spending was recently £220bn but will drop probably to around the £200bn level in the next years. So we can see that if Nagel is right, we should dramatically switch the order of priorities. Setting aside the radical implausibility that the poor in the UK would vote for this, or the question as to how Nagel can balance these competing demands, it would actually appear that the force of his position could be used to support this sort of claim. He thinks that all persons have some type of equal moral value, which would mean the poor win out in virtue of their greater numbers. But arguably, they would qualify for greater support even without moral equality, whatever that means. This case can be made by noting that poor people in poor countries are dramatically less able to become rich through exercise of talent and effort than poor people in rich countries. But that type of argument supporting his position is barred to him by his refusal to countenance rewards flowing to those in possession of talent and perseverance. Nagel seems confused by the end of his paragraph, as he finally conceded that the wealthy countries may reasonably protect their wealth.]

Nagel believes that technological superiority produces strong military power. [Again, certainly a factor, but questions of manpower are also significant.] If that changes, then the economic order will also change. [This is a suggestion that poor countries with large populations would simply take the resources they want. At present, the development seems to be that military power is closely linked to economic power — as has been the case throughout history, for obvious reasons including that even if Nagel were right that technology is the key, heavier spending capacity would win out as in the Cold War he cites without much understanding.]

For these reasons, there can be no legitimate world government, and nothing can be done about injustice in other states. [Iraq and Afghanistan may be failed initiatives, but does not Nagel’s position imply that they necessarily had to be? Why would we think that?]

Cosmopolitan intellectuals’ are often less nationalistic than their less fortunate compatriots, but these are to be allowed their nationalism as one of the inalienable freedoms within the personal perspective. [Why?] Solidarity with a group means non-solidarity with outsiders. The preservation of high standards of living depends absolutely on strict controls on immigration’. [The error Nagel makes here is well known in economics; it is called the lump of labor’ fallacy’. It is not the case that imigrants take jobs’. They create employment as well. If this were not true, then countries with large populations would have higher rates of unemployment. And why would that be true? Ironically, many observers attribute a large part of the economic success of the US to its historical openness to immigration. And this is a very good reason not to allow the non-cosmopolitan non-intellectuals not to have their way here in a final closing inconsistency of which Nagel remains unaware. Lack of any economic insight or knowledge or numbers is not really excusable in political philosophy.]

## Nagel: Equality And Partiality IX

Chapter Thirteen

The chapter opens with a pair of dramatic assumptions: there are human rights, and they are currently well-protected. They include rights to medical care. These, as is well-known from the work of Buchanan and others, are in fact unfeasible. Either the level to be provided to everyone is low, in which case some will use private resources to improve on the public provision, or it is high, in which case it is unaffordable. In addition, some people are so unwell, indeed terminally so, that their health-care could cost infinite amounts. And all of that of course continues to ignore global inequalities. No mention is made of anyone’s putative right to retain their legitimately earned income and not have it arrogated by the state in pursuit of Utopian ends.

[In general, my view is that the number of rights’ is to be minimized in order to treat them properly as serious entities. Multiplying rights maximizes situations of conflicts of rights. We should aim instead for a small number taken very seriously, if we are to have any at all.]

Hume is cited with approval to the effect that it is natural’ for people to uphold rights associated with personal security. [This may be true, but how would we distinguish between a situation in which they were upheld as a result of nature or were on the other hand a product of culture? Or more simply, just pragmatism. Maybe there are no rights at all, but I refrain from physical violence merely as a way of reducing the probability that such means are used against me.]

There are rights against undue interference by the state in the lives of individuals, and to have the state prevent such interference by one individual against another. The exact form of property rights will depend on the long-term economic benefits as well as the protection of individual liberty. [These of course may radically conflict, though one may hope not. It appears that strong individual property rights are a key to overall economic development; one issue hampering economic progress in developing nations has been lack of title to land. Improving this facilitates lending against collateral. But we still need to ask what would happen in the case of conflict. If there were a choice between protecting individual liberty and overall economic progress, would we not have to choose the former? To make the other decision would involve i). official certainty on the likely future effects of individual economic choices, which seems unlikely to be available and ii). mean that we vetted economic decisions for rationality. That might mean the officials would decide what was economically rational and what was unjustified risk-taking, and experience suggests that public officials are exactly the wrong people to make such decisions. Indeed, one might suspect that they entered public life precisely to avoid such an arena, seeing that their talents did not lie in the appropriate areas. Nagel does not say, but we can imagine that in such a conflict scenario, he would fall into the official’ camp rather than the individual camp’.]

The state has negative responsibilities to prevent violations it could have avoided. [This requires specification. Recently the British Prime Minister apologized for less than excellent situations obtaining in respect of the evacuation of Libya for UK citizens. Now, if those people were sent there by an oil company, one might expect that company to make arrangements for their return. But why should the state have a responsibility to bring people home who went there of their own choice aware of the risks? Why should we all cover everyone else for all risks?]

The test for limits is that they should be such as to not be capable of reasonable rejection by anyone who honestly seeks to accommodate everyone else’s point of view’. [Why is this right? Are there not a group of people whose point of view is essentially that everyone else should support them and protect them from all risks despite the fact that they make essentially no contribution at all? Why should we accommodate that? If not, does not Nagel’s entire program fail because unanimity will never be available?]

Nagel argues’ that no-one could reasonably reject a system that included taxation, because taxation is not an intolerable violation’ of personal freedom. [Why is this not an argument of the form p therefore p’? And do we not just accept taxation because it has always been there? And where are the limits? We already know that Nagel’s preferred system of providing — just — health-care to everyone at public expense is unaffordable so how would we provide the other goods as well?]

There is no expectation in advance that a society will not restrict voluntary transfers. [Why not? Why is there not an expectation in advance that a society will not restrict anything voluntary unless it impinges on the freedom of someone else?]

Nagel on balance is against restriction of freedom of expression where this is ostensibly done to prevent expression of sexist, racist or contra-religious views. [These laws exist in the UK, which would presumably mean I was committing an offense when I stated in a previous post that in my view, religious people must suffer from some form of cognitive deficit in the area of evidence assessment and would therefore in general be less suitable for occupations involving that, such as scientifically-based ones. I again think there is a mistake made in lumping together responses to the religious views of persons, which they have chosen, with responses to their sex or race. Not only have they not chosen these characteristics, but there is little or no evidence that those characteristics will in general affect employment skills in a way that could usefully be taken into account.]

Nagel deprecates the involvement of the state in suppressing sexual behavior that is offensive to the majority. [I have a rare point of total agreement with him here — but surely it prompts the question as to why he is so enthusiastic about interference and suppression of the individual in the economic sphere where he accepts this is inadvisable in the sexual one. Presumably he would respond that sexual behavior does not harm or indeed affect anyone not involved, whereas my economic decisions will harm’ others because everyone is involved’ in some tenuous way.]

It is conceded that conservatives do have an interest in preventing the behavior of others that offend them because of the cultural climate’ thereby created. [This is extraordinary, and dramatically at odds with the previous paragraph. We can see that Nagel’s brief conversion to liberty was at most skin-deep.] The conservatives needs the right cultural climate such that they can inculcate’ their values in their children [ — this is deeply disturbing and totalitarian, and the whole idea that anyone can have anything like a right to control everyone else in order to protect their environment from pollution has already sold the pass.]

The question becomes one of whether the control’ of sexual behavior should be for majority decision, or a protected area of individual rights. Homosexuality is the test case, and Nagel says persons could reasonably reject a system that prohibited it [ — with which we can agree without even going as far as questions of enforceability –] because of the personal costs to homosexuals. These costs are not outweighed by the benefits to conservatives [ — even if we accept this type of trade-off at all.] It is noted that the problem with conservatives is that they have convictions about how others should live. [This is the appeal through consistency to libertarianism, which suggests that the state should be equally uninvolved in interfering with the individual in both social and economic arenas. It is strange that conservatives wish to protect liberty in one sphere and not in the other. It is also strange that Nagel does not notice that he is making the counterpart error.]

It is stated that one murder may not be committed even to prevent five other murders. [Perhaps this is the type of case where argument is not the correct response, but other views do exist and the trolley problems produce plenty of discussion.] The argument for this is that such views lend a protected status to individuals [ — which nevertheless does not extent to their economic lives.]

Nagel will choose an increase in his likelihood of being murdered instead of abolition of his legal right not to be murdered. [This seems bizarre. Do dead people care about their legal status? Again, there seems to be a strange concentration on the abstract as against the real, the impersonal standpoint as against being alive.]

The stability of illegitimate states is noted. [The questioning of this is one of the major implications of current developments in the Middle East.] This stability follows from the tendency of people to follow rules. [Heidegger. Should we not fight against such tendencies? Otherwise we are assuming the status quo is always right.] And this leads to the German problem’, to which the solution is democracy. [Hitler was elected though.] We should aim for a situation in which officials do not avail themselves of a just following orders’ defense.

Chapter Fourteen

Different conceptions of value will lead to conflict over what the state should support [ — unless we side-step this by taking the obvious precaution of removing the state from enforcement of values.] And some of these conflicts are too severe to be resolved in the political arena, for example religious ones. This leads to the idea that some domains should be protected. [Again, why only some? And which ones? And can I have a religion that has taxation is theft’ as a holy tenet?]

Defenders of toleration often in fact support the behaviors that would be banned by intolerant legislation, so those against a ban on homosexual behavior or contraception do not see any problems with those things. [This is true. And so the response should be that banning any behavior is to be avoided — right up to the point where someone else is severely affected by it.] This is against religion and in favor of sex’. The contradiction for Nagel is that liberalism affects to protect religions. [Not my version. But Nagel is right to point up the inconsistency. The fact that some religions are opposed to homosexual behavior is an additional reason to ignore them and remove protections against discrimination for religious people that are deserved by persons who fall victim to sexism and racism.]

It is politically suicidal’ to defend toleration by attacking religion [ — this may be a US-centered view. Toleration of religious intolerance is another reason why Nagel’s dream of finding a system that no-one could reasonably reject is hopeless, unless we agree that religious principles are unreasonable. Which seems fine, but again, hard to sell in the US.]

Why should I take the impersonal standpoint and accept the lending of some weight to religious or moral principles when I think these same principles are wrong? [Good question.] It implies impartiality between different conceptions of the good. The defense relies on Kant’s second formulation, that we should treat no-one merely as a means, and we would be doing that if we failed to obtain unanimity.

There are four reasons for coercion: i). those accepted, ii). those that would be accepted by the reasonable, iii), those that would be accepted under an accepted principle and iv). those that are not accepted by an individual even if everyone else disagrees. Type iv). is exemplified by enforcement of religious or sexual orthodoxy. [Is state enforcement of atheism an enforcement of religious orthodoxy? Let us worry about that once we have eliminated state support for religion.]

Nagel believes that there is a distinction between cases when opponents may be described as irrational. Those who do not accept the germ theory of disease are irrational, but atheists may not describe religious people as irrational. [Why not? Belief in the germ theory rests on evidence. Religious belief does not. Why is not respect of evidence evidence of rationality?]

The role-reversal argument is appealed to as a standard for judging ethical theories — how would I like it if someone did that to me? [I would not like it, presumably. But that happens all the time. So is not the answer to reduce the amount of interaction or required interaction with others? And that means more personal autonomy.]

Restriction of freedom of worship would indeed appear justified to a religious person, because those who do not follow the true faith are damned. [Is this not further evidence of the insanity of the religious and the inadvisability of taking any account of their views?]

Is there a difference between accepting democratically decided-upon policies in defense, say, and accepting a similarly democratic policy opposing atheism? [Yes. The latter would be an argument against democracy. Why do we not have prayer instead of tanks? Alternatively, we could very simply insist that all democratic policies should be evidence-based. If a majority of a population is religious, that is another reason not to let them vote.]

Altruism generates conflicting standpoints. [Commit it then to the flames.]

Democracy is to be saved by removing conflict from the arena of discussion. [So how do we deal with what people care about?]

A common standpoint can be reached in some controversial areas such as defense because everyone sees some policy is needed. [No. A policy is arrived at despite immense disagreement because everyone sees that in fact their ability to do anything about it is effectively zero.] Religion differs from this and so everyone should be left to follow their own path. [Again, here but not economically.]

This tolerant regime could be seen as a form of coercion, being a kind of liberal sect. Would that not destroy its legitimacy? The answer is that a liberal state avoids imposing a conception of the good. [Why does this permit the state to employ taxation then?] Legitimacy trumps helping others when they may not want to be helped’. [Why do I have to help them financially when they do want that?]

Liberal toleration may allow the spread of religious orthodoxy, and so it may not be neutral as between different conceptions of the good. [Is this not an argument for doing nothing, since we cannot choose a positive position if we cannot even be sure that avoiding taking a position is neutral? At least let us not be guilty of actively choosing something wrong, even if we are already.]

Public support of an established church is wrong. [So we have plenty of work to do here. Freedom from taxation of religious charities would have to go, and the current fashion for faith-based initiatives also.]

The state should not be involved in activity which conflicts with the views of citizens about the meaning of life. [This already takes a position by assuming that there is one.]

There are some things the police should not do because individuals should not do them. [The police, though, are trained specialists expressly intended to do just things that I should not do. The power of citizen’s arrest, while it exists, is used very infrequently for various reasons, but one of them will be the general lack of understanding of the law.]

The state cannot treat criminals harshly even where doing so would reduce crime. [How do we know this? What is the argument?]

Some conceptions of the good cannot be accommodated within the Kantian position, and Nagel hopes that such fanaticism will eventually die out. [I hope not.]

## Nagel: Equality And Partiality VIII

Chapter Eleven

Individual choices which are in themselves unexceptionable’ can combine over time to produce unacceptable inequality. [How is that possible? Is not the result to be considered in the question as to what is exceptionable’ and what Draconian punishments should we imagine for such disallowed choices? Or are they fine?] The effects are grossly unequal’. [And what is the problem with that? The implied and bogus comparison in the title Partiality and Equality rears its head again.]

Family sentiment and differences in natural talent are not a problem because they are simply a reflection of the way the world is’. [This is helpful. If everything in the world is fine as it is, and is so solely in virtue of that very fact, then we can stop worrying. We have a way of arguing from is’ to ought’ — or more accurately, we do not need one since they are the same thing.]

Nevertheless, it is not possible to make a value judgment about these resulting inequalities, they are neither right nor wrong’. [Really? If the causes are unexceptionable, why are not the effects equally so? Or are we saying that the causes combine in an unacceptable fashion but because they are part of the way the world is, we cannot form a judgment on the overall picture?]

Although they do not require justification, it might be desirable to eliminate them. [Is not something it might be desirable to eliminate not exactly something that needs justification? If it had a justification, that would mean it could not be desirable to eliminate it.]

Nagel cites this as Rawls’s view in opposition to Locke with his mixing of labor’ approach to generation of property. They key difference is whether labor is the dominant factor (Locke) or social factors (Rawls).

Since we are not responsible for our talents, we are not entitled to any deriving benefits beyond the most immediate’. [What does immediate’ mean? If any are legitimate, why not all? What would be the status of borderline benefits on the boundary between legitimate derived benefits and illegitimately derived ones? What type of theory could provide such a distinction?]

Benevolence, even were it to exist, is unequal to the task of manufacturing washing machines, because such tasks are uninteresting. Only economic benefit which accrues to the those adopting a personal standpoint could persuade people to perform such necessary tasks. The market is the only source of crucial directing information via price signals. Mill is cited to observe that the closeness of the connection between a man’s labors and his rewards is directly related to the enthusiasm with which he pursues uninteresting work. [This failure to adopt the impersonal standpoint was the reason for the failure of communism.]

Such acquisitiveness need not dispel the motivation to provide a social minimum, provided this can be done at reasonable cost. [This seems possibly true, but is not relevant because the actual cost is crushing viz. UK social security spending at £220bn p.a., cf. health ca. £120bn and education ca. £80bn. And even spending at these levels is inadequate apparently.]

The answer is to design a system that produces incentives without producing inequalities. [This is impossible because it is known from the keeping up with the Jones’s’ effect that it is in fact more the inequalities that \emph{are} the incentives. A man is very happy with a high salary up until the moment when he learns that the man at the next desk earns £5 more. And people are made dissatisfied by seeing the lifestyles of wealthier people on television in the well-known phenomenon of status anxiety’.]

Since there is (and likely to continue to be) substantial opposition to reducing inequalities due to class and talent, the choices left open to egalitarians are to attempt to move in the direction of the aim without arriving at it or hope for better people. [This seems to assume that currently no redistributive efforts are being made which is a long way from the truth. Also the implication is that class and talent are equally illegitimate sources of advantage which Nagel has previously admitted is not the case. There would be much more support for elimination of class-derived benefits than for talent-driven ones. Though of course that might just be because everyone thinks they have (some) talents while most people are aware that they are not members of the aristocracy. It would certainly be best for the rest of us if Nagel and his egalitarian cohort opts for the second choice of waiting for more egalitarian people, while we can remain optimistic that further improvement’ is unlikely. Better yet, maybe people will improve in the opposite direction and become less risk-averse.]

Nagel expresses unease about the existence of extreme poverty in relatively wealthy societies. [Is this not exactly the wrong way around? We should be most worried about poverty in poor societies because those people can do little about their situation. Poor people in the UK have been fortunate enough to be living in the fourth largest economy in a world of 200 countries and have still failed to make anything of any of the manifold opportunities for financial advantage. These are so apparent to the larger world that people make dangerous sea voyages merely to gain entry to Europe.]

Everyone is to have decent conditions’ at public expense. [Again, in the UK context, if £220bn of social security spending is inadequate in the context of government income of £500bn and total spending of £700bn, what is? What justification can there be for borrowing at those levels such amounts from future taxpayers, some of whom will be poor, to fund a social minimum today? Why are current taxpayers to be privileged so dramatically over future ones?]

A negative income tax is proposed, which would have the effect of subsidizing low wages. [How is this compatible with the admitted crucial importance of price signals in the market for efficient allocation of labor? And in any case, the current UK regime of tax credits in fact embodies this idea. And in fact we have a growing suspicion now that Nagel is arguing for the status quo. Or more accurately, since he does not fully appreciate how even the current system is too egalitarian, for a reduction in the current levels of progressiveness in the taxation system.]

The provision of the minimum would eliminate any queasiness of individuals earning far above the social minimum. [Do any such individuals actually exhibit such unease currently? Perhaps Nagel imagines that in his new utopia, such rather squeamish types could be high earners. Why would that be?] This attitude will allegedly do nothing to dampen the necessary competitive instincts that drive creativity in the economy. [This is exactly false, since progressiveness in the tax system is precisely damping those instincts. As we were previously reminded by Mill, the enthusiasm of the laborer is correlated to the closeness of the relation of reward to effort. Provision of the social minimum reduces the effects of the incentives of inequality and reduces that correlation.]

There is a task of avoiding moral hazard among the group subsidized up to the social minimum which Nagel thinks should be soluble’ without specifying the answer. [Unfortunate, this, since the problem of high marginal ‘tax’ rates has proved immensely difficult for decades with Iain Duncan Smith making the latest high-cost and and high-risk attempt to address the problem currently.] The solution will rely on the fact that most people want more than they have. [True, but that does not seem to be motivating the poor very strongly at present.]

Severe relative deprivation’ (my emphasis) is one of the worst aspects’ of inequality. [How is addressing this compatible with the recent remarks about people being free to pursue, without any pangs of conscience, earnings far above the social minimum? By doing so, they are hardly reducing relative inequality. Would not this imply that they should restrict themselves to earning amounts just above the social minimum? Presumably brain surgeons would do this by working one day a week. That might be a problem for people in need of their services, but they could take comfort from the fact that such services would be equally unavailable for persons on the social minimum. And all comfort comes from being the same as everyone else, in the same way that all distress results from difference.]

The right’ of everyone to a decent minimum is again qualified as being subject to economic feasibility. [And again, it is not noted that we already can see that it is not feasible because even the current approach to it is dramatically inadequate from the perspective of those advocating the minimum and also totally unaffordable. While we are discussing progressiveness, why do not some bad philosophers — indeed, some people not equipped or interested in pursuing the topic — receive unpaid assistance from experts so that they too can publish philosophical articles in academic journals? Why does society permit such an outrageous insult to the public sources of self-respect of many deserving individuals?]

One positive development for Nagel would be general disapproval of those who earn high wages. [We certainly see this today in the controversy around bankers’ wages. But has Nagel not noted that this very disapproval is a motivating factor for some of those receiving the wages? His positive development would in fact be counterproductive for his aims.] We would not be happy going to Italy on holiday unless everyone could. [Has Nagel actually been to a popular holiday destination recently? It is already bad enough.]

Competitive instincts are to be replaced by peer approval’. [Is it acceptable if one’s peers are denizens of an investment bank trading floor? Presumably not, although Nagel thinks that only clear definition of standards and judges are required. Nagel here admits inter alia that he is only familiar with academic life, which surprises no-one.]

Only in corrupt countries can civil servants and the military be motivated to do their work well. [This is strange. The financial rewards in the public sector are highly adequate at the higher levels and include excessively generous pension benefits. And the military as a group do not sort well with the class of civil servants.]

Market socialism with medals’ is the term for the replacement of economic incentives with peer approval. [But even Nagel does not think this is credible. Why should we?] Admitting this as impossible, Nagel retreats to the first option of gradualism. [So again, we can show him how much gradualism we already have and ask where the line is to be drawn. He thinks we are far short of it at present. What is the correct number for social security spending? £300bn? £400bn? Finally Nagel reverses himself and says that we must continue to lust after the impossible and have more egalitarianism.]

Chapter Twelve

The stated aim of the chapter is to reduce any impression that Nagel is hostile to all inequality. Nagel notes that it is difficult to prevent the disease egalitarianism from infecting’ other values. [This is surely true because if it is right in one sphere, what reasoned founded set of distinctions would prevent it from being right in all of them? Why do I not have a right to date movie stars some times, since some people do — thus, incidentally, riding rough-shod over my fragile self-esteem, based as it is on public respect.]

Educational and aesthetic stratification can also cause unease. [The plastic surgeon’s knife awaits. There is no reason why it should not move people downwards to the decent social minimum of beauty as well. And everyone should be awarded a PhD.]

Mill has attempted to address this in the context of an assumption of the equal value of persons by further assuming an unequal division of value in uses of time or pleasures. [This rather crucially depends on the definition of the undefinable term value’.] Nagel notes that this destroys the formal equality of value because some people are not fitted for or do not choose to pursue higher pleasures’. Nagel’s response is to divorce the value of some things from the pleasure of their enjoyment. And the pursuit of the more valuable is to be accorded a higher moral weight’. [This presumably means that if I can be used to work harder at the cost of my lower pleasures in order to fund your higher pleasures, that is the correct decision. But if I want to go to the opera, you can starve. Or more of you can than if I wanted to play dominoes.]

There is no evidence for the value of something beyond the value that people put on it (Mill). [How is this compatible with the existence of higher and lower pleasures?] The value of an object is distinct from the enjoyment that people derive from it. [Yes, but would not a ranking in the latter inexorably entail the same ranking in the former? Or do some people prefer less pleasure than they could have had?]

Nagel agrees that moral equality’ does not entail any other equality [ — without noting the absurdity in context of moral equality claims therefor.] Preserving natural beauty because of its value to individuals is to get things the wrong way round. [So we should be happy about a planet devoid of people but retaining the Grand Canyon.]

Artistic and educational excellence may be permitted since its products eventually benefit everyone. [What about those Nagel admitted were unfitted to appreciate the higher pleasures? The answer is that beauty is valuable even if only a few appreciate it. There is a pleasure to be had in burning cats to death, even if the relevant cognoscenti are few in number. We learn later that he judgment of experts’ is to be trusted here, so we can consult experienced cat-torturers on the best ways of furthering their enjoyment, which is not related to how much they enjoy actually watching a burning cat, but is more related to the intrinsic value of that pursuit, beyond its instantiations. Maybe thinking about burning cats is where the value lies.]

Nagel notes that there is a problem for his theory of intrinsic value in that if everyone went blind, destroying all of the paintings in the Louvre would not be a further loss [ — but does not explain how to counter this rather devastating objection. It may be that that is just true of art, he thinks.] There is value beyond value for persons. [Value for cats, for example. Paintings visible only in the ultraviolet would be unedifying for humans, but doubtless fascinating for bees.]

If these intrinsic values exist, they should be fostered by the state. [They do not. But even if they did, why? We would be removing value pursuit opportunities from individuals to pursue other value’. What would legitimize that, beyond a certainty that the public committee on value’ was more likely to be right about these questions than individuals making decisions for themselves?]

Nagel cites Rawls as being in favor of something that looks like a balanced budget argument, though he himself thinks this goes to far. [Which is just as well, because such a thing would have a catastrophic effect on social security spending, by far the largest line item in government expenditure.] Further expenditure on intrinsic values is to be allowed. [How does that work, since we are unable to afford even the provision of the social minimum Nagel wants? Are we to subsidize the opera ahead of giving everyone food who needs it or not? If not, we will never get to the opera. Nagel is dividing up some theoretical cake into seven parts each numbering 80$\%$ of available resources.]

Amazingly, Nietzsche is enlisted in support of the idea that in artistic respects, societies should be anti-egalitarian. [Why only there? Is it because of the absurd consequences in this domain of Nagel’s favored approach in economics?] Equally amazingly, the tendency towards equality in the public school system is to be distrusted’ and is inexcusable’. [How can Nagel maintain this consistently with any of the other claims he has been making?] The lower classes can not escape the mediocrity which is their lot if they are state educated. [This assumes that there are no examples of the state educated having achievements of any stature, which is false.]

The effects of class status `never depend on choice’. [What about the choice to remain in one’s original class? What about the choice to spend one’s leisure time on football rather than opera? Since the public committee has decreed that the latter is a higher and the former a lower pleasure, then it must be possible for people to make mistakes about what is valuable for them.]

We now come to the question as to why art and science are different to money [ — by way of a plea for lower academic salaries. Because scholarship is to be its own reward.] The answer is that a life of luxury and refinement is good for the person who leads it rather than good in itself. And that cannot be accepted because of the deleterious effects on those who miss out. The deleterious effects on those who miss out on a prominent scientific career can be accepted however because those careers either are intrinsically valuable or because they benefit anyone. [How does an illiterate drug addict living on social security benefit if the LHC discovers the Higgs boson? And would they vote for it?] Egalitarianism is not be allowed to eliminate haute cuisine just because not everyone can have it. [But is not that exactly what will happen if people earning well above the social minimum are deprecated and take such deprecation seriously? Or will the public values committee allow some rich people to spend their own money in restaurants providing they also have enough social achievement medals?]

## PhD Thesis Chapter X

Chapter 10

Conclusions

The performance of the ZEUS FLT has been investigated for a range of physics of interest, with special regard to the use of data from the tracking detectors. The motivation throughout this work has been to investigate the means by which signal events may be efficiently be selected by the trigger while at the same time holding leakage of beam-gas events through the trigger to a minimum. It has been shown that the RBOX will be able to successfully combine data from the FTD and the CTD in such a way as to further this aim despite the differing geometries of these two detectors.

The most important area of physics at HERA is the study of the proton structure function via the analysis of DIS NC and CC processes. An efficient trigger performance for these events is therefore essential. For this reason, the performance of the RBOX has been optimized with respect to them. The performance of the CTD alone for these events has been shown to be good which meant that it was difficult to further improve the situation. Nevertheless, it has been shown that the RBOX will be able to reduce the loss of CC events by a factor of two within the same beam-gas leakage constraints as placed on the CTD. This should greatly enhance the quality of measurements made.

While the performance of the RBOX has been shown to be good for DIS events, it is important not to lose sight of other areas of physics interest. With this in mind, other processes have been simulated with a view to examining performance in more broad terms. In particular, an investigation of heavy flavor pairs both with and without the influence of initial state gluon bremsstrahlung has been made. This has shown that transverse energy and charged multiplicity are the deciding factors which control the efficiency with which a type of event will be accepted. Also it has been shown that the effects of gluon bremmstrahlung may lead to significant changes in event characteristics for charmed pair events. Most importantly, it is now known that the RBOX will provide a good efficiency for heavy flavor events without the necessity to re-optimize the trigger parameters as designed for DIS.

Further, the efficiency of the RBOX for J/ψ events has been shown to be good. As was mentioned in the introductory chapter, these events will have a scattered electron at a very low angle. These two facts raise the prospect of using the electron calorimeter of the luminosity monitor to make precise measurements of the scattered electron which in turn will permit ZEUS to probe the gluon distribution in a kinematic domain which is completely inaccessible to other machines.

Accurate knowledge of a trigger efficiency is as important as boosting that efficiency. It has been shown here that the full kinematics of a CC event need not be considered when measuring the kinematic dependence of CTDFLT efficiency. This has allowed a picture to be constructed of the likely variation of efficiency which is comprehensive in terms of range. Also, much greater precision has been obtained than would be possible within available computer resources using another method.

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## PhD Thesis Chapter IX

Chapter 9

Investigation of J/ψ Event Acceptance in the FLT

9.1 Introduction

Events containing a J/ψ can be used at HERA to probe the low-x gluon distribution of the proton[87]. In order to do this, it is necessary to know the efficiency of the FLT for these events. In this chapter, trigger efficiencies are measured for the CTDFLT, the FTDFLT and the standard parametrization of the GFLT which was described in section 8.3.

Further, a comparison was made of measured parameters for the J/ψ sample and a beam-gas sample. This enabled a first approximation to a dedicated sub-trigger to be suggested.

J/ψ event tagging methods previously suggested[88] have utilized the luminosity monitor. Here, the response of the entire detector is simulated in an effort to identify differences between signal and background.

9.2 Event Generation

The ASCII interface for the HERWIG generator described in section 8.1 was used again here in conjunction with program versions 5.2/5.3. 26,000 J/ψ events were generated.

HERWIG allows a choice of five structure functions. These were all investigated and found to produce no discernible differences in the properties of events seen in the detector. For the sake of consistency, option five was used throughout[89].

9.3 Results

Investigation then centered on the task of separating the J/ψ events from the beam-gas background. The beam-gas sample produced to allow background studies was generated using the UA5 generator. Forty thousand events were produced with a homogeneous distribution along the beam-line from z = -19 m to z = +1 m.

9.3.1 Trigger Efficiencies

Table 9.1 shows the proportions of events accepted by the full simulations of the CTDFLT, the FTDFLT and by the parametrization of the GFLT. The results for the RBOX are also shown. [At the time of this work the design of the RBOX was complete. It was felt that using the most modern version of the simulation was important. This was no longer compatible with the RBOX code so only a small event sample was passed through the RBOX code. This is why the statistical errors are larger in this case.]

Table 9.1: Event classifications from ZGANA.

The event classes have the meaning used previously in section 5.2.3 so the CTD class two and three must be summed to provide a total acceptance. This means that the CTDFLT accepts 93.1% with beam-gas leakage of 7.6%. For a leakage rate of 1 kHz m-1 this gives a background of 1528 Hz from the 20 meter source length.

The beam-gas leakage in the FTDFLT corresponds to a rate of 2100 Hz. At the time of the simulation from which results are described here, no FTD class zero was defined in ZGANA: events without diamonds were rejected. In the final system, these events will be described as unclassified. The beam-gas leakage in the parametrizations of the GFLT corresponds to a leakage rate of 1138 Hz.

9.3.2 Comparison of Signal and Background

The statistics on the plots relate to the beam-gas sample. Where relevant, the mean of the J/ψ distribution is given on the plot. The figures that are shown relating to calorimeter data (figure 9.1 to figure 9.3) show sizable differences between signal and background and therefore are useful in a dedicated sub-trigger.

Figure 9.1: Sum of visible transverse energy in the electromagnetic calorimeter.

Figure 9.2: Sum of total transverse momentum (x-direction only).

Figure 9.3: Sum of total transverse visible energy.

In particular, figure 9.3 explains why the parametrization of the GFLTB rejects some events: there are many signal events with low transverse energy deposition. These will fail the CALFLT cuts.

Figure 9.4 shows that approximately 25% of the beam-gas sample has hits in the veto-wall. Very few signal events register in the veto-wall: in a sample of 500 CC events, no hits were observed.

Figure 9.4: Veto-wall hits.

The C5 collimator is located three meters upstream (for the protons) of the interaction region and is designed to reduce the halo of off-beam particles in the beam. It is possible for good events to produce C5 hits by virtue of having tracks in the backward direction but in general, hits in the collimator are strongly indicative of a background event. It would clearly be advisable for the trigger to take advantage of this to veto events with C5 hits. Figure 9.5 shows that only a negligible fraction of signal events have C5 collimator hits whereas figure 9.6 shows that substantial discrimination against background is a prospect.

Figure 9.5: Number of hits in C5 collimator for J/ψ events.

Figure 9.6: Number of hits in C5 collimator for beam-gas events.

9.4 Discussion

Table 9.1 shows that excellent acceptance is obtained by the tracking trigger. In addition, as previously described in section 5.1, the RBOX will combine data from the FTD and the CTD and so these figures may be expected to improve. However, the table also shows that further optimization is advisable in the GFLT: some ways to produce a dedicated sub-trigger were seen to be plausible from considering the figures, many of which show substantial discrimination between signal and background. To investigate the utility of this as a first approximation to a dedicated sub-trigger was devised. It is important to emphasize that no optimization has been done on the trigger parameters: the cut values could be tuned and other sub-detectors included.

Table 9.1: Event classifications from ZGANA.

The sub-trigger was developed from a simple philosophy. Calorimeter triggers were set so that they were ‘free’: i.e. plots of measured values were studied to find cut values that would produce no beam-gas leakage but still provide some benefit in terms of J/ψ acceptance. Then if there were clear grounds to reject the event this course was taken. Finally the tracking detector triggers were applied to those events still unclassified.

The full details of this trigger are shown in figure 9.7 and the results obtained in table 9.2. It can be seen that the efficiency is comparable to that of the CTDFLT but with improved beam-gas leakage figures. The leakage rate implied here is 954 Hz. It should be noted that it is not trivial to improve on the CTDFLT because its performance is already good.

Figure 9.7: Sub-trigger decision flowchart.

Table 9.2: Event classifications for the dedicated sub-trigger.

Previous work[90] on J/ψ events in the FLT achieved an efficiency of 66% with beam-gas rates below the acceptable limit. That particular trigger is a complex entity utilizing many sub-detector components; moreover, it has been optimized. Operating here would permit cross checking of efficiencies and result in complementary data-sets for J/ψ physics.

A characteristic of J/ψ events is the presence of leptons with high transverse momentum in the opposite direction to the quark jet, as described in section 1.2.3.2. It should in general be possible to find these tracks in the CTD or the RTD and a more complex trigger, perhaps at higher levels, could search for these by correlating with the CAL or muon detectors.

9.5 Conclusions

The tracking detector FLT will provide excellent efficiency for J/ψ events since good performance has been obtained with the CTD and RBOX. Reasonable performance may be expected from the GFLT. An optimized sub-trigger along the lines suggested here would provide very good efficiency for J/ψ events.

## PhD Thesis Chapter VIII

Chapter 8

Heavy-Flavor Events in the Regional First Level Trigger

8.1 Introduction

Prior to machine turn-on, uncertainties about the details of many types of events exist. The trigger must be able to achieve high acceptances combined with good beam-gas rejection independent of the details of the final event shape. To this end, it is useful to use different generators to examine the effects of theoretical uncertainties on the trigger efficiency. An important question also concerns the effect that gluon bremsstrahlung will have on measurements in the detector.

Although DIS events are a major aspect of HERA physics, it is necessary to ensure that other important reactions are not removed at the FLT: such a reaction is the generation of bbbar and ccbar pairs by boson-gluon fusion (BGF) at low Q2 and low x (see section 1.2.3.1).

The standard ZEUS Monte Carlo for boson-gluon fusion is HFLGEN 1.3 based on the AROMA generator,[82]. Parton showers, string fragmentation and decays are carried out by JETSET[83]. A second generator HARHEA, working within the framework of the HERWIG 5.0 Monte Carlo, also produces BGF events[84–86]. HARHEA differs from HFLGEN in using a cluster hadronization model and including gluon radiation from the initial state quarks.

A HERWIG ASCII interface was written for ZEUSGeant such that the data could be read by ZGANA. This enabled direct comparison of measured parameters in the CTDFLT and the FTDFLT.

8.2 Simulation

One thousand NC ccbar and bbbar events were generated from each of the two heavy flavor generators. Also four thousand beam-gas events distributed homogeneously along the beam-line from z = -19m to z = +1m were produced using the FRITIOF generator (version 1.5).

An initial comparison of the two generators was achieved by using a parametrization of the CTD and calorimeter FLTs. This aims to provide a simple understanding of the likely response of the whole FLT to a set of events. Its philosophy is based on energy deposition and charged tracks. If tracks are found from the vertex, then only loose energy constraints are applied. On the other hand, if no tracks are found then substantial energy deposition (at high angles) is required.

In fact, if no track pointing to the vertex was found in the CTD, an event was accepted if the calorimeter registered more than 5 GeV/c in transverse momentum; if a vertex track was detected, an event was accepted if the transverse momentum was greater than 12 GeV/c. Section 4.3.1.1 explains how these quantities are measured by the CALFLT. Finally, the events were passed through the standalone CTDFLT and FTDFLT simulations and the RBOX simulation to examine the combined tracking response.

8.3 Results

Table 8.1 shows the percentage of events passing the parametrization of the FLT for the four types of events. There is a small difference in the two BGF generators for ccbar events but a major difference is seen for bbbar events. In both cases, it is much easier to trigger on the bottom pair events.

Table 8.1: Percentage of events accepted by the simple parametrization of the tracking and calorimeter first level trigger.

Table 8.2 shows the percentage of ccbar events falling into each of the tracking trigger classes and table 8.3 shows the same figures for bbbar events. These figures may be compared with those for beam-gas leakage, shown in table 6.7. As before, for the CTD standalone mode class 3 events will probably be accepted along with class 2 events so these figures must be summed to produce a final figure.

Table 8.2: FLT classifications for the full FLT simulations for ccbar events.

Table 8.3: FLT classifications for the full FLT simulations for bbbar events.

8.4 Discussion

The parametrization of the GFLT is dependent on track multiplicity and transverse energy deposition. The results obtained for GFLT efficiency are thus entirely explained by figure 8.2 and figure 8.3 which show that high acceptance is related to both high mean track multiplicity and high mean transverse energy. This may be clearly illustrated by plotting the means of the figures against the efficiencies.

This is done in figure 8.1. For comparison, figure 8.4 and figure 8.5 show the distribution of transverse energy and charged multiplicity for beam-gas events.

Figure 8.1: Effect of multiplicity and transverse energy on acceptance.

Figure 8.2: Multiplicity of charged tracks per event with a pt > 0.5 GeV/c for heavy flavor events.

Figure 8.3: Total transverse energy (GeV) per event as measured by the calorimeter for heavy flavor events.

Figure 8.4: Total transverse energy (GeV) per event as measured by the calorimeter for beam-gas events.

Figure 8.5: Multiplicity of charged tracks per event with a pt > 0.5 GeV/c for beam-gas events.

In the tracking detectors, a vertex decision is made in the triggers using essentially tracks with a transverse momentum > 0.5GeV/c. The tracking chamber triggers use the ratio of tracks from the vertex to all tracks. This ratio is therefore affected by changes in track multiplicity and transverse momentum.

The distributions in polar angle explain the event classes found. Figure 8.6 shows the polar angle of Geant tracks (tracks with energy of less than 1 GeV were omitted).

Figure 8.6: Polar angle of Geant tracks for both types of heavy flavor events in full and FTD-only angular ranges. The solid lines are HFLGEN events and the dashed lines are HERWIG events.

It can be seen that across the broad angular range, both generators are in good agreement with both giving higher multiplicities for bbbar events than for ccbar events. This explains the CTDFLT classes found, which showed both generators giving similar acceptances which were higher in the case of bbbar events. But in the FTDFLT, it can be seen that there is a significant deterioration in efficiency in HERWIG ccbar events which is not seen in bbbar events. In order to examine this more closely, figure 8.6 also shows the same plots magnified to show only the angular region covered by the FTD, 0.195 rad to 0.495 rad. It can clearly be seen that the event classes found are reflective of the observed multiplicities.

8.5 Conclusions

It has been shown that the effects of gluon bremsstrahlung may be neglected for bbbar events but become more significant in the case of ccbar. The combined FTD and CTD FLT acceptance is excellent for both bbbar and ccbar events with either generator. Higher multiplicities and higher transverse energy for bbbar events mean that they are more likely to pass the tracking trigger. The performance of the tracking triggers would not need to be optimized further in a dedicated sub-trigger. The simple parametrization of the combined calorimeter and tracking trigger indicates that a simple transverse energy cut by the calorimeter reduces bbbar acceptance by at least 10% but eliminates almost 60% of all ccbar events accepted by the tracking trigger alone. A dedicated sub-trigger would need to relax the transverse energy cut and restore beam-gas efficiency to reasonable levels by using information from other components such as collimators, the veto-wall and also timing data.

## PhD Thesis Chapter VII

Chapter 7

Investigation of Kinematic Dependence of CTDFLT Efficiency

7.1 Introduction

The motivation behind the work described in this chapter was the desire to know to high precision the CTDFLT efficiency across the whole of the accessible phase space. This is important for measurement of cross-sections as mentioned in the previous chapter. The naıve approach of simply generating large numbers of events in kinematic bins is not a suitable one since the constraints of available computer resources mean that the requisite precision cannot be obtained over all phase-space. For this reason, a method of simplifying the problem was searched for. For CC events, it is inherently plausible that the efficiency of the CTDFLT depends only on the polar angle of the current jet theta-jet. This hypothesis was shown to be consistent with the data by generating a large sample of events in small regions of phase space with fixed theta- jet.

The results for each angle were combined to produce high-precision efficiency data. These were then used to plot a map in x – Q2 space by assuming the same efficiency for all points in the phase space with the same jet angle. The method was also investigated with respect to NC events. As would be expected however, it was found to be unsatisfactory due to the scattered electron which plays an important part in triggering these events.

7.1.1 Special Jacquet-Blondel Kinematics

It is possible to manipulate the usual kinematic equations (see equation 1.26 in section 1.2.2.3) so that the theta-jet dependency becomes more explicit; in particular using half angle formulae and setting E_e = 30GeV gives equation 7.1:

So for a fixed jet angle, various different combinations of values of x and Q^2 are available for a given y. Contours of fixed y are shown in the x=theta-jet plane in figure 7.1 and for the Q^2 – theta-jet plane in figure 7.2.

Figure 7.1: Contours of fixed y in the x – theta-jet plane.

Figure 7.2: Contours of fixed y in the Q^2 – theta-jet plane.

We may define a SL polar angle such that a track from the nominal interaction point at this angle will leave the sensitive volume of the CTD at a position on the end-plate midway between where the two central wires are attached. The minimum angles for the instrumental SLs are 11. degrees, 18.9 degrees, 25.4 degrees for SL1, SL3 and SL5 respectively.

It is obvious that there will be no information from the CTDFLT concerning tracks with angles smaller than 11.6 degrees (or greater than 168.4 degrees). In fact, there will be some spread of tracks around the nominal jet angle so that some proportion of events have no tracks within the sensitive volume of the CTD. Clearly one expects this proportion to increase as the nominal jet angle is changed such that the tracks are expected to be closer to the beam-pipe.

7.2 Event Generation

A low-statistics pass across the whole of the angular range was made. Fifty events were generated in angular bins of two degrees. The information needed to produce bins in x and Q^2 corresponding to the required angular range is shown graphically in figure 7.1 and figure 7.2.

The events were generated with 10 degrees < theta-jet < 90 degrees. It was not necessary to generate any events with jet angles of larger than 90 degrees because symmetry means that eta(theta – 90 degrees) = eta(theta). Below 10 degrees there is not expected to be any activity in the detector. A similar sample was generated for NC events.

A selected set of five angles were chosen for high statistics runs. These angles were 13 degrees, 23degrees, 33degrees, 43degrees and 63 degrees. These were chosen with reference to the super-layer polar angles mentioned above. They correspond to the cases in which one expects the jet to pass through the one or two instrumental SLs for the two lowest angles and all three instrumented SLs for the remaining three angles.

Angular bins with a a range of one degree either side of the nominal value were defined for the low-statistics run. To measure the variation with respect to y from 0.1 to 0.9 were defined. Approximately one thousand events were generated in each bin so that in total 36250 events were used in this study. The CTDFLT simulation was run to find the efficiency.

7.3 Results

The results for theta-jet = 63 degrees are shown in table 7.1, for theta-jet = 43 degrees in table 7.2, for theta-jet = 33 degrees in table 7.3, for theta-jet = 23 degrees in table 7.4 and for theta-jet = 13 degrees in table 7.5.

Table 7.1: CTDFLT efficiencies in the kinematic bins for theta-jet = 63 degrees +/- 1 degree.

Table 7.2: CTDFLT efficiencies in the kinematic bins for theta-jet = 43 degrees +/- 1 degree.

Table 7.3: CTDFLT efficiencies in the kinematic bins for theta-jet = 33 degrees +/- 1 degree.

Table 7.4: CTDFLT efficiencies in the kinematic bins for theta-jet = 23 degrees +/- 1 degree

Table 7.5: CTDFLT efficiencies in the kinematic bins for theta-jet = 13 degrees +/- 1 degree

7.4 Discussion

Figure 7.3 shows that the results are consistent with the hypothesis that there is a smooth dependence of efficiency on jet angle. From the numbers in the tables it can be seen that efficiency is constant for a given angle independent of all other kinematic variables. Also the expected deterioration in efficiency is seen as the jet angle becomes closer to the beam-line.

Figure 7.3: Low statistics full angle pass for CC events.

For NC events however, figure 7.4 shows that the pattern does not show the same simple dependency on jet angle only. This is due to the presence of the scattered electron. It is unsafe therefore to attempt to proceed further with the method for this type of event.

Figure 7.4: Low statistics full angle pass for NC events.

Returning to the CC sample, it is now plausible to combine the various tables of results at the same jet angles to produce high-precision results. Since the results represent statistically independent measurements of the same quantity, they may be combined by taking the mean and dividing the error by root n where n is the number of entries in the relevant table. This yields the figures in table 7.6.

Table 7.6: Final combined figures for CTDFLT efficiency.

These figures may be used to generate contours of constant trigger efficiency in the x – Q^2 plane, remembering that symmetry allows the same efficiencies to be plotted for 180 degrees – theta also. This is shown in figure 7.5.

Figure 7.5: Efficiency for CC events.

7.5 Conclusions

It has been shown that CTDFLT CC efficiency is dependent on theta-jet only. Precise knowledge of the expected efficiency may now be obtained over a large part of the accessible phase space by deducing the jet angle from the kinematics of a given event if that event lies on or near one of the angles studied with high statistics. Otherwise, an interpolation may be made.