119183444
Gravitational Self-force in a Radiation Gauge
In this, the first of two companion papers, we present a method for finding the gravitational self-force in a modified radiation gauge for a particle moving on a geodesic in a Schwarzschild or Kerr spacetime. An extension of an earlier result by Wald is used to show the spin weight ±2 perturbed Weyl scalar (ψ 0 or ψ 4 ) determines the metric perturbation outside the particle up to a gauge transformation and an infinitesimal change in mass and angular momentum. A Hertz potential is used to construct the part of the retarded metric perturbation that involves no change in mass or angular momentum from ψ 0 in a radiation gauge. The metric perturbation is completed by adding changes in the mass and angular momentum of the background spacetime outside the radial coordinate r 0 of the particle in any convenient gauge. The resulting metric perturbation is singular only on the trajectory of the particle. A mode-sum method is then used to renormalize the self-force. Gralla shows that the renormalized self-force can be used to find the correction to a geodesic orbit in a gauge for which the leading, O(ρ -1 ), term in the metric perturbation has spatial components even under a parity transformation orthogonal to the particle trajectory, and we verify that the metric perturbation in a radiation gauge satisfies that condition. We show that the singular behavior of the metric perturbation and the expression for the bare self-force have the same power-law behavior in L = l + 1/2 as in a Lorenz gauge (with different coefficients). We explicitly compute the singular Weyl scalar and its mode-sum decomposition to subleading order in L for a particle in circular orbit in a Schwarzschild geometry and obtain the renormalized field. Because the singular field can be defined as this mode sum, the coefficients of each angular harmonic in the sum must agree with the large L limit of the corresponding coefficients of the retarded field. One may therefore compute the singular field by numerically matching the retarded field to a power series in L. To check the accuracy of the numerical method, we analytically compute leading and subleading terms in the singular expansion of ψ 0 and compare the numerical and analytic values of the renormalization constants, finding agreement to high precision. Details of the numerical computation of the perturbed metric, the self-force, and the quantity h αβ u a u β (gauge invariant under helically symmetric gauge transformations) are presented for this test case in the companion paper.
118190331
RADIATION REACTION IN CURVED SPACETIME
85450376
Simple “invariance” of two-body decay kinematics
We study the two-body decay of a mother particle into a massless daughter. We further assume that the mother particle is unpolarized and has a generic boost distribution in the laboratory frame. In this case, we show analytically that the laboratory frame energy distribution of the massless decay product has a peak, whose location is identical to the (xed) energy of that particle in the rest frame of the corresponding mother particle. Given its simplicity and \invariance" under changes in the boost distribution of the mother particle, our nding should be useful for the determination of masses of mother particles. In particular, we anticipate that such a procedure will then not require a full reconstruction of this two-body decay chain (or for that matter, information about the rest of the event). With this eventual goal in mind, we make a proposal for extracting the peak position by tting the data to a well-motivated analytic function describing the shape of such an energy distribution. This tting function is then tested on the theoretical prediction for top quark pair production and its decay, and it is found to be quite successful in this regard. As a proof of principle of the usefulness of our observation, we apply it for measuring the mass of the top quark at the LHC, using simulated data and including experimental eects. PACS numbers: 11.80.Cr It is very well-known that in the rest frame of a mother particle undergoing a two-body decay, the energy of each of the daughter particles is xed in terms of mother and the daughter particle masses. Turning this fact around, we can determine the mass of the mother particle if we can measure these rest-frame energies of the daughter particles. However, often the mother particle is produced in the laboratory with a boost, that too with a magnitude and direction which is (a priori) not known. Moreover, the boost of mother particles produced at hadron colliders is dierent in each event. Such a boost distribution depends on the production mechanism of the particle and on the structure functions of the hadrons in the initial state of the collision, and is thus a complicated function. In turn, the fact that the mother has a dierent boost in each event implies that when we consider the observed energy of the two-body decay product in the laboratory frame, we get a distribution in it. Thus it seems like the information that was encoded in the rest frame energy is lost, and we are prevented from extracting (at least at an easily tractable level) the mass of the mother particle along the lines described above. We show that, remarkably, if one of the daughter particles from the two-body decay is massless and the mother is unpolarized, then such is not the case. Specically, in this case, we demonstrate that the distribution of the daughter particle’s energy in the laboratory frame has a peak precisely at its corresponding rest-frame energy. This result is interesting per se. Furthermore, we expect that it will lead to formulation of new methods for mass measurements. Obviously, for this purpose, we need to be able to determine the location of this peak accurately from the observed energy distribution of the massless daughter. To this end, we propose and motivate an analytic function that can be used to t the data on the energy distribution and thus extract the peak position. We show that this function is a suitable one using the top quark decay, t! W b, as a test case, namely, it ts very well the theory prediction for energy spectrum of the resulting b-jets. Simulating a realistic experimental situation, we then show that we can extract the value of the top mass from the position of the peak in the b-jet energy distribution along with the well-measured mass of the W boson. Let us consider the decay of a heavy particle B of mass mB, i.e., B! Aa where a is a massless visible particle. For the subsequent arguments, the properties of the particle A (other than its mass denoted by mA) are irrelevant. In the rest frame of particle B, the energy of the particle a is simply given by E = m 2 m 2 2mB :
59435944
UsingMT2to distinguish dark matter stabilization symmetries
We examine the potential of using colliders to distinguish models with parity (Z_2) stabilized dark matter (DM) from models in which the DM is stabilized by other symmetries, taking the latter to be a Z_3 symmetry for illustration. The key observation is that a heavier mother particle charged under a Z_3 stabilization symmetry can decay into one or two DM particles along with Standard Model (SM) particles. This can be contrasted with the decay of a mother particle charged under a parity symmetry; typically, only one DM particle appears in the decay chain. In arXiv:1003.0899, some of us studied the distributions of visible invariant mass from the decay of a single such mother particle in order to highlight the resulting distinctive signatures of Z_3 symmetry versus parity symmetry stabilized dark matter candidates. We now describe a complementary study which focuses on decay chains of the two mother particles which are necessarily present in these events. We also include in our analyss the missing energy/momentum in the event. For the Z_3 symmetry stabilized mothers, the resulting inclusive final state can have two, three or four DM particles. In contrast, models with Z_2 symmetry can have only two. We show that the shapes and edges of the distribution of M_T2-type variables, along with ratio of the visible momentum/energy on the two sides of the event, are powerful in distinguishing these different scenarios.
122541104
Progress report on the Bates parity experiment
We are performing an experiment at the MIT Bates Linear Accelerator Center to measure the parity‐violating asymmetry in the elastic scattering of polarized electrons from carbon. The asymmetry, which is due to the isoscalar piece of the neutral weak current, is predicted to be about one part per million for our experimental conditions. We have recently obtained preliminary data with polarized electrons. This paper discusses the status of the experiment, with emphasis on our understanding of the most important systematic errors.
116401557
Test beam results from prototype scintillating tile calorimeters with fiber readout
43932193
Using energy peaks to measure new particle masses
A bstractWe discussed in arXiv:1209.0772 that the laboratory frame distribution of the energy of a massless particle from a two-body decay at a hadron collider has a peak whose location is identical to the value of this daughter’s (fixed) energy in the rest frame of the corresponding mother particle. For that result to hold we assumed that the mother is unpolarized and has a generic boost distribution in the laboratory frame. In this work we discuss how this observation can be applied for determination of masses of new particles, without requiring a full reconstruction of their decay chains or information about the rest of the event. We focus on a two-step cascade decay of a massive particle that has one invisible particle in the final state: C → Bb → Aab, where C, B and A are new particles of which A is invisible and a, b are visible particles. Combining the measurements of the peaks of energy distributions of a and b with that of the edge in their invariant mass distribution, we demonstrate that it is in principle possible to determine separately all three masses of the new particles, in particular, without using any measurement of missing transverse momentum. Furthermore, we show how the use of the peaks in an inclusive energy distribution is generically less affected (as compared to other mass measurement strategies) by combinatorial issues. For some simplified, yet interesting, scenarios we find that these combinatorial issues are absent altogether. As an example of this general strategy, we study SUSY models where gluino decays to an invisible lightest neutralino via an on-shell bottom squark. Taking into account the dominant backgrounds, we show how the mass of the bottom squark, the gluino and (for some class of spectra) that of the neutralino can be determined using this technique.