Long Range Forces from Two Neutrino Exchange Revisited
Long Range Forces from Two Neutrino Exchange Revisited
复制标题
重新审视两个中微子交换的远程力
DOI：
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发表时间：
1992
期刊：
影响因子：
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通讯作者：
S. Hsu
中科院分区：
文献类型：
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作者：
S. Hsu
两个无质量中微子的交换产生了一种长程力，它与弱带电物质耦合。正如在以前的文献中所指出的，这种力的势是单极-单极、自旋-自旋和更复杂的相互作用的Vν(R)∝G2 F/r 5。不幸的是，这太小了，在目前的实验中观察不到。我们在弱电理论中显式地计算了Vν(R)，并表明在非常一般的假设下，由两个无质量费米子交换产生的力最多只能产生1/R5势。哈佛大学院士协会初级研究员。电子邮件：hsu@HUHEPL.bitnet，hsu@HSUNEXT.Habard.edu从理论和实验的角度来看，发现一种新的长程力耦合到普通物质的前景都是令人兴奋的。由于长程力需要无质量粒子的存在，所以在弱电理论中，一个合乎逻辑的地方是中微子的影响。单个中微子(或一般情况下，单个费米子)的交换不会产生力，因为相互作用会改变所涉及的源的角动量。然而，两个中微子的交换可能会使源的量子数保持不变，从而可能导致长程作用力。人们可以根据量纲分析推测，这种相互作用的势可以采取Vν(R)∼G2 fm/r的形式，其中m是源粒子的质量。费曼在考虑将中微子作为类引力相互作用的介体时考虑了这种形式[2]。如果这就是相互作用，那么在实验室测试中就可以观察到这种力的影响[3]。在r∼cm处，如果m是电子质量，对正常物质的作用力大约是引力的10−6倍，如果m是核子质量，则与引力相当。在r∼cm处偏离1/r电势的电流极限为10−4[3]量级。如果这两个中微子力是可测量的，它将提供关于中微子质量的实验信息，这是对标准粒子物理实验所获得的信息的补充。长程力实验对极小的质量很敏感。不幸的是，上面给出的Vν(R)的形式是不正确的。我们将在下面推导出的正确行为是1/r。这产生的影响要小得多。因此，这种相互作用的确切形式在某种程度上是理论上的，但在我们看来似乎值得计算。G.Feinberg和J.Sucher[4]以及A.de Rujula、H.Georgi和S.Glasow以前曾研究过这两个中微子力(未发表)。事实上，本文中出现的几乎所有结果都是由Feinberg和Sucher早先得到的。然而，我们的计算方法是不同的，我们认为它足够简单，值得阐述。我们是在完成自己的计算后才意识到前面的工作的。以前的作者得出了与我们类似的结论，但我们的详细结果与Feinberg和Sucher的结果略有不同。我们的势能Vν(R)比他们的小两倍，而且我们的σ1·σ2项的系数也不同。我们目前还不了解这一分歧的根源。考虑图1所示的图表。由于我们对长距离效应和相应的低动量交换感兴趣，所以将W和Z交换的效应结合到涉及中微子和弱带电粒子的四费米算符中是一个很好的近似。得到的算符可以被Fierz变换成以下形式：O4=GF√2[ν̄γμ(1−γ5)ν][ūγ(a−bγ5)u]，(1)其中a和b依赖于费米子u。
The exchange of two massless neutrinos gives rise to a long range force which couples to weakly charged matter. As has been noted previously in the literature, the potential for this force is Vν(r) ∝ G 2 F /r 5 with monopole-monople, spin-spin and more complicated interactions. Unfortunately, this is far too small to be observed in present day experiments. We calculate Vν(r) explicitly in the electroweak theory, and show that under very general assumptions forces arising from the exchange of two massless fermions can at best yield 1/r5 potentials. Junior Fellow, Harvard Society of Fellows. Email: Hsu@HUHEPL.bitnet, Hsu@HSUNEXT.Harvard.edu The prospect of discovering a new long range force coupling to ordinary matter is exciting from both the theoretical and experimental points of view [1]. Since long range forces require the existence of a massless particle, a logical place to look in the electroweak theory is at the effect due to neutrinos. The exchange of a single neutrino (or in general a single fermion) cannot give rise to a force since the interaction changes the angular momentum of the sources involved. However, the exchange of two neutrinos can leave the quantum numbers of the sources unchanged, and hence can lead to a long range force. One might guess on the basis of dimensional analysis that the potential for this interaction could take the form Vν(r) ∼ G 2 Fm /r, where m is the mass of the source particle. Feynman considered this form when contemplating neutrinos as the mediators of a gravitylike interaction [2]. If this were the interaction, the effects of such a force might be observable in laboratory tests [3]. At r ∼ cm, the resulting force on normal matter would be roughly 10−6 times smaller than that due to gravity if m is the electron mass, and comparable to that of gravity if m is a nucleon mass. The current limit on deviations from a 1/r potential at r ∼ cm are of order 10−4 [3]. If the two neutrino force were measurable, it would provide experimental information on neutrino masses which is complementary to that obtained from standard particle physics experiments long range force experiments are sensitive to extremely small masses. Unfortunately, the form given above for Vν(r) is incorrect. The correct behaviour, which we will derive below, is 1/r. This yields a much smaller effect. The exact form of the interaction is therefore somewhat academic, but seems to us worth computing. The two neutrino force was investigated previously by G. Feinberg and J. Sucher [4] and by A. De Rujula, H. Georgi and S. Glashow (unpublished). In fact, almost all of the results which appear in this paper have been obtained earlier by Feinberg and Sucher. However, our method of computation is different and we feel that it is sufficiently simple to warrant exposition. We became aware of the earlier work only after completing our own calculations. The previous authors come to conclusions similar to ours, but our detailed results disagree slightly with those of Feinberg and Sucher. Our potential Vν(r) is smaller than theirs by a factor of two, and the coefficient of our σ1 · σ2 term is also different. We do not at this time understand the origin of this disagreement. Consider the diagrams shown in figure 1. Since we are interested in a long distance effect, and correspondingly low momentum exchange, it is a good approximation to combine the effects of W and Z exchange into four-fermi operators involving neutrinos and weakly charged source particles. The resulting operator can be Fierz transformed into the following form: O4 = GF √ 2 [ν̄γμ(1 − γ5)ν][ūγ (a− bγ5)u], (1) where a and b depend on the fermion u.