Weighty Matters for Particle Physics

The HPQCD collaboration: (from Left to right) Eduardo Follana, Greg Millar, Ian Allison, Craig McNeile, Emel Gulez, Junko Shigemitsu, Peter Lepage, Elvira Gamiz, Howard Trottier, Ron Horgan, Kent Hornbostel, Christine Davies, Iain Kendall, Eric Gregory.

[This is an invited article based on a recently published work of the High Precision Quantum Chromodynamics (HPQCD) collaboration. -- 2Physics.com]

Author: Christine Davies
Affiliation: Department of Physics and Astronomy,
University of Glasgow, UK

Link to HPQCD Collaboration >>

Particle physicists at the Fermilab Tevatron and at the CERN Large Hadron Collider are engaged in an exciting race to be the first to discover the Higgs particle, a 'smoking gun' remnant of the mechanism that we believe gives mass to the other fundamental particles. Particles interact with the Higgs field pervading all of space and, rather like moving through molasses, gain a mass as result.

Meanwhile an important question is: what are these masses? A recent paper [1] by the High Precision QCD (HPQCD) collaboration answers this question accurately for up, down and strange quarks for the first time.

The masses of the electron and its cousins, the muon and tau, are very well-known since these particles can be studied by the clear tracks they leave in particle detectors.

The masses of the quarks are much less well determined. The reason for this is that the strong force interactions never allow quarks to be seen as free particles. Only their bound states called hadrons (of which the proton is an example) can be produced and studied in particle physics experiments. The quark masses must then be inferred by matching experimental results for the masses of hadrons to those obtained from theoretical calculations using the theory of the strong force, Quantum Chromodynamics (QCD). The quark mass is a parameter in the theory and so matching theory and experiment allows the quark mass to be determined.

This could only be done rather approximately for many years, particularly for the lightest up, down and strange quarks. As Figure 1 (history of the strange quark mass) shows, improvements have been very slow. Recently, however, a technique known as lattice QCD has enabled theorists to calculate the masses of some hadrons very accurately and establish mastery over QCD at last [2].

Fig.1 History of the strange quark mass: This figure shows the new result compared to earlier evaluations of the strange quark mass in the Particle Data Tables. The mass is given in units of MeV/c² - for comparison the proton mass is 938 MeV/c².

The High Precision QCD (HPQCD) Collaboration has now determined the mass of the strange quark to an accuracy of better than 2%, which improves on the evaluation of previous results given in the Particle Data Tables [3] by a factor of 10.

The technique used by HPQCD has been to determine the ratio of the mass of the charm quark to that of the strange quark. This can be done more accurately than determining the strange quark mass on its own, and gives the breakthrough in precision that has been achieved. Determining this ratio had not been possible before because previous methods had large systematic errors for the relatively heavy charm quarks, which HPQCD have now been able to overcome.

Because the charm mass is already known to 1% from several calculations, including an earlier calculation by HPQCD and others[4], this then allows an accurate determination of the strange quark mass. Similarly a determination of the ratio of the strange quark mass to that of the up and down quarks provided by the MILC collaboration[5], allows HPQCD to cascade the accuracy that they have for the charm quark mass down to all of the light quarks.

Fig. 2: Summary of quark mass values from this paper: a comparison of the new lattice QCD results for the masses of the up, down and strange quarks (from this paper) and the charm quark (from an earlier paper) to the current evaluations in the Particle Data Tables.

With this improvement in the masses of the light quarks shown in Figure 2, we now have values for the masses of all 6 quarks at the level of a few percent and a much clearer and more complete picture of what the Higgs particle has done for the quarks.

References
[1] C. T. H. Davies, C. McNeile, K. Y. Wong, E. Follana, R. Horgan, K. Hornbostel, G. P. Lepage, J. Shigemitsu, and H. Trottier (HPQCD Collaboration), "Precise Charm to Strange Mass Ratio and Light Quark Masses from Full Lattice QCD", Phys. Rev. Lett. 104:132003 (2010). Abstract.
[2] C. Davies, "Colourful calculations", Physics World 19N12:20 (2006).
[3] Particle Data Group, http://pdg.lbl.gov/
[4] I. Allison, E. Dalgic, C. T. H. Davies, E. Follana, R. R. Horgan, K. Hornbostel, G. P. Lepage, C. McNeile, J. Shigemitsu, H. Trottier, R. M. Woloshyn, K. G. Chetyrkin, J. H. Kühn, M. Steinhauser, and C. Sturm (HPQCD Collaboration), "High-precision charm-quark mass and QCD coupling from current-current correlators in lattice and continuum QCD", Phys. Rev. D78:054513 (2008) Abstract; K. G. Chetyrkin, J. H. Kühn, A. Maier, P. Maierhöfer, P. Marquard, and M. Steinhauser, C. Sturm, "Charm and bottom quark masses: An update", Phys. Rev. D80:074010 (2009) Abstract.
[5] C. Aubin, C. Bernard, C. DeTar, J. Osborn, Steven Gottlieb, E. B. Gregory, D. Toussaint, U. M. Heller, J. E. Hetrick, R. Sugar (MILC collaboration), "Light pseudoscalar decay constants, quark masses, and low energy constants from three-flavor lattice QCD", Phys. Rev. D70:114501 (2004) Abstract.

Testing the Spin-Statistics Theorem

The image shows two UC Berkeley physicists Dima Budker and Damon English. Dima Budker (left) is in a fermionic state, occupied by only one of himself. Many copies of the bosonic Damon English (right) occupy the same state at once. [image credit: Roy Kaltschmidt and Damon English /University of California, Berkeley and Lawrence Berkeley National Laboratory]

The best theory for explaining the subatomic world got its start in 1928 when theorist Paul Dirac combined quantum mechanics with special relativity to explain the behavior of the electron. The result was relativistic quantum mechanics, which became a major ingredient in quantum field theory. With a few assumptions and ad hoc adjustments, quantum field theory has proven powerful enough to form the basis of the Standard Model of particles and forces.

“Even so, it should be remembered that the Standard Model is not a final theory of all phenomena, and is therefore inherently incomplete,” says Dmitry Budker, a staff scientist in the Nuclear Science Division of the U.S. Department of Energy’s Lawrence Berkeley National Laboratory and a professor of physics at the University of California at Berkeley.

Budker has long been interested in testing widely accepted underpinnings of physical theory to their limits. In the June 25 issue of Physical Review Letters [1], he and his colleagues report the most rigorous trials yet of a fundamental assumption about how particles behave on the atomic scale.

Why we need the spin-statistics theorem

“We tested one of the major theoretical pillars of quantum field theory, the spin-statistics theorem,” says Damon English, Budker’s former student and a postdoctoral fellow in UC’s Department of Physics, who led the experiment. “Essentially we were asking, are photons really perfect bosons?”

The spin-statistics theorem dictates that all fundamental particles must be classified into one of two types, fermions or bosons. (The names come from the statistics, Fermi-Dirac statistics and Bose-Einstein statistics, that explain their respective behaviors.)

No two electrons can be in the same quantum state. For example, no two electrons in an atom can have identical sets of quantum numbers. Any number of bosons can occupy the same quantum state, however; among other phenomena, this is what makes laser beams possible.

Electrons, neutrons, protons, and many other particles of matter are fermions. Bosons are a decidedly mixed bunch that includes the photons of electromagnetic force, the W and Z bosons of the weak force, and such matter particles as deuterium nuclei, pi mesons, and a raft of others. Given the pandemonium in this particle zoo, it takes the spin-statistics theorem to tell what’s a fermion and what’s a boson.

The way to tell them apart is by their spin – not the classical spin of a whirling top but intrinsic angular momentum, a quantum concept. Quantum spin is either integer (0, 1, 2…) or half integer, an odd number of halves (1/2, 3/2…). Bosons have integer spin. Fermions have half integer spin.

“There’s a mathematical proof of the spin-statistics theorem, but it’s so abstruse you have to be a professional quantum field theorist to understand it,” says Budker. “Every attempt to find a simple explanation has failed, even by scientists as distinguished as Richard Feynman. The proof itself is based on assumptions, some explicit, some subtle. That’s why experimental tests are essential.”

Says English, “If we were to knock down the spin-statistics theorem, the whole edifice of quantum field theory would come crashing down with it. The consequences would be far-reaching, affecting our assumptions about the structure of spacetime and even causality itself.”

In search of forbidden transitions

English and Budker, working with Valeriy Yashchuk, a staff scientist at Berkeley Lab’s Advanced Light Source, set out to test the theorem by using laser beams to excite the electrons in barium atoms. For experimenters, barium atoms have particularly convenient two-photon transitions, in which two photons are absorbed simultaneously and together contribute to lifting an atom’s electrons to a higher energy state.

“Two-photon transitions aren’t rare,” says English, “but what makes them different from single-photon transitions is that there can be two possible paths to the final excited state – two paths that differ by the order in which the photons are absorbed during the transition. These paths can interfere, destructively or constructively. One of the factors that determines whether the interference is constructive or destructive is whether photons are bosons or fermions.”

In the particular barium two-photon transition the researchers used, the spin-statistics theorem forbids the transition when the two photons have the same wavelength. These forbidden two-photon transitions are allowed by every known conservation law except the spin-statistics theorem. What English, Yashchuk, and Budker were looking for were exceptions to this rule, or as English puts it, “bosons acting like fermions.”

Two opposed laser beams, identical except for polarization, attempt to excite forbidden two-photon transitions in a beam of barium atoms. [image credit: Damon English]

The experiment starts with a stream of barium atoms; two lasers are aimed at it from opposite sides to prevent unwanted effects associated with atomic recoil. The lasers are tuned to the same frequency but have opposite polarization, which is necessary to preserve angular momentum. If forbidden transitions were caused by two same-wavelength photons from the two lasers, they would be detected when the atoms emit a particular color of fluorescent light.

The researchers carefully and repeatedly tuned through the region where forbidden two-photon transitions, if any were to occur, would reveal themselves. They detected nothing. These stringent results limit the probability that any two photons could violate the spin-statistics theorem: the chances that two photons are in a fermionic state are no better than one in a hundred billion – by far the most sensitive test yet at low energies, which may well be more sensitive than similar evidence from high-energy particle colliders.

Budker emphasizes that this was “a true table-top experiment, able to make significant discoveries in particle physics without spending billions of dollars.” Its prototype was originally devised by Budker and David DeMille, now at Yale, who in 1999 were able to severely limit the probability of photons being in a “wrong” (fermionic) state. The latest experiment, conducted at UC Berkeley, uses a more refined method and improves on the earlier result by more than three orders of magnitude.

“We keep looking, because experimental tests at ever increasing sensitivity are motivated by the fundamental importance of quantum statistics,” says Budker. “The spin-statistics connection is one of the most basic assumptions in our understanding of the fundamental laws of nature.”

References
[1] Damon English, Valeriy Yashchuk, Dmitry Budker, “Spectroscopic test of Bose-Einstein statistics for photons”, Phys. Rev. Lett. 104, 253604 (2010). Abstract. arXiv:1001.1771.
[2] M.G. Kozlov, Damon English, and Dmitry Budker,“Symmetry-suppressed two-photon transitions induced by hyperfine interactions and magnetic fields,” by M.G. Kozlov, Damon English, and Dmitry Budker, Phys. Rev. A80, 042504 (2009). Abstract. arXiv:0907.3727.

[This report is written by Paul Preuss of Lawrence Berkeley National Laboratory]

Glimpse of Heavy Electrons Reveals “Hidden Order”

J.C. Séamus Davis (Photo courtesy: Cornell University)

Using a microscope designed to image the arrangement and interactions of electrons in crystals, scientists have captured the first images of electrons that appear to take on extraordinary mass under certain extreme conditions. The technique reveals the origin of an unusual electronic phase transition in one particular material, and opens the door to further explorations of the properties and functions of so-called heavy fermions. Scientists from the U.S. Department of Energy’s (DOE) Brookhaven National Laboratory, McMaster University, and Los Alamos National Laboratory describe the results in the June 3, 2010, issue of Nature.

“Physicists have been interested in the ‘problem’ of heavy fermions — why these electrons act as if they are hundreds or thousands of times more massive under certain conditions — for thirty or forty years,” said study leader Séamus Davis, a physicist at Brookhaven and the J.D. White Distinguished Professor of Physical Sciences at Cornell University. Understanding heavy fermion behavior could lead to the design of new materials for high-temperature superconductors.

In the current study, the scientists were imaging electronic properties in a material composed of uranium, ruthenium, and silicon that itself has been the subject of a 25-year scientific mystery. In this material — synthesized by Graeme Luke’s group at McMaster — the effects of heavy fermions begin to appear as the material is cooled below 55 kelvin (-218 °C). Then, an even more unusual electronic phase transition occurs below 17.5K.

[Image courtesy: Los Alamos National Laboratory] Spectroscopic imaging scanning tunneling microscopy reveals a "hidden order" of electrons, seen as bright areas, within uranium ruthenium silicate as it is cooled to very low temperatures. Seeing this hidden order for the first time has unraveled a 25-year-old physics mystery.

Scientists had attributed this lower-temperature phase transition to some form of “hidden order.” They could not distinguish whether it was related to the collective behavior of electrons acting as a wave, or interactions of individual electrons with the uranium atoms. Alexander Balatsky, a Los Alamos theoretical physicist at the Center for Integrated Nanotechnologies, provided guidance on how to examine this problem.

With that guidance, Davis’ group used a technique they’d designed to visualize the behavior of electrons to “see” what the electrons were doing as they passed through the mysterious phase transition. The technique, spectroscopic imaging scanning tunneling microscopy (SI-STM), measures the wavelength of electrons on the surface of the material in relation to their energy.

“Imagine flying over a body of water where standing waves are moving up and down, but not propagating toward the shore,” said Davis. “When you pass over high points, you can touch the water; over low points, you can’t. This is similar to what our microscope does. It images how many electrons can jump to the tip of our probe at every point on the surface.”

From the wavelength and energy measurements, the scientists can calculate the effective electron mass.

[Image credit: Mohammad Hamidian/Davis Lab, Cornell University] In this schematic diagram, individual electrons (white spheres) interact with uranium atoms (shown as yellow and blue f-electron orbitals of the uranium atoms) as they move through the URu2Si2 crystal. These interactions drastically inhibit the progress of the electrons, making them appear to take on extraordinary mass – an effect imaged for the first time in this study.

“This technique reveals that we are dealing with very heavy electrons — or electrons that act as if they are extremely heavy because they are somehow being slowed down,” Davis said.

The detection of “heavy electron” characteristics below the second transition temperature provides direct experimental evidence that the electrons are interacting with the uranium atoms rather than acting as a wave.

To visualize this, imagine a team of football players running up the field after a kickoff. If each player were free to run unimpeded, the whole team would appear to operate as a wave of relatively independent “electrons.” But imagine instead that the field is strewn with an array of chairs, and each player has to sit for an instant every time he encounters a chair before continuing up the field. In this case the chairs are analogous to the uranium atoms. Those interactions between players and chairs (or electrons and uranium atoms) clearly slow the progress.

In the case of the uranium material, the electron slowdown lasts only a tiny fraction of a second at each uranium atom. But because kinetic energy and mass are mathematically related, the slowdown makes it appear as if the electrons are more massive than a free electron.

Besides revealing these interactions as the source of “hidden order” in the uranium compound, Davis’ study shows that the SI-STM technique can be used to visualize heavy electrons. That in turn opens the door to more ways to investigate and visualize this phenomenon.

The research team is continuing to probe a variety of related compounds with this new approach to further their understanding of heavy fermion systems.

“Heavy fermions remain mysterious in many ways, and it’s our job as scientists to solve the problem,” Davis said.

Reference
A. R. Schmidt,M. H. Hamidian,P. Wahl,F. Meier,A. V. Balatsky,J. D. Garrett,T. J. Williams,G. M. Luke& J. C. Davis, "Imaging the Fano lattice to ‘hidden order’ transition in URu₂Si₂", Nature, Vol 465, pp 570–576 (03 June 2010). Abstract.

[We thank Brookhaven National Laboratory for materials used in this posting]

Growing evidence of Tetraquarks

Ahmed Ali, Christian Hambrock, M. Jamil Aslam
(from Left to Right)




[This is an invited article based on a recent work by the authors. -- 2Physics.com]

Authors: Ahmed Ali¹, Christian Hambrock¹, M. Jamil Aslam²
Affiliation:
¹ Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany.
² Physics Department, Quaid-i-Azam University, Islamabad, Pakistan.

In December 2007, the Belle collaboration working at the KEKB e⁺e⁻ collider in Tsukuba, Japan, reported the first observation of the processes e⁺e⁻ → ϒ(1S)π⁺π⁻ and e⁺e⁻ →
ϒ(2S)π⁺π⁻ near the peak of the ϒ(5S) resonance at the center-of-mass energy √s of about 10.87 GeV [1]. The ϒ(nS) states (n being the principal quantum number and S stands for the orbital angular momentum l = 0, borrowing the language of atomic physics) are called “bottomonia” - bb bound states of the bottom quark and its antiparticle. Production and decays of the ϒ(nS) are popular theoretical laboratories to test Quantum Chromo Dynamics (QCD), the theory of strong interactions. In particular, the final states ϒ(1S)π⁺π⁻ and ϒ(2S)π⁺π⁻ arising from the production and decays of the lower bottomonia states, such as ϒ(4S) → ϒ(1S)π⁺π⁻, have been studied in a number of experiments over the last thirty years and are theoretically well-understood in QCD [2].

Belle measurements near the ϒ(5S), however, did not fall in line with theoretical expectations [1]. Their data were enigmatic in that the partial decay widths for ϒ(5S) →
ϒ(1S)π⁺π^- and ϒ(2S)π⁺π^- were typically three orders of magnitude larger than anticipated in QCD [2]. In addition, the dipion invariant mass distributions in these events were distinctly different from theoretical expectations as well as from the corresponding measurements at the ϒ(4S), undertaken previously by them [3]. The measurements in question are robust, with the ϒ(1S)π⁺π^- and ϒ(2S)π⁺π^- channels having a significance of 20σ and 14σ [1], respectively.

To be precise, two aspects of the Belle data had to be explained: (a) the anomalously
large partial decay rates and (b) the invariant mass distributions of the dipions. A related and important issue is whether the puzzling events seen by Belle stem from the decays of the ϒ(5S), or from another particle ϒ_b having a mass close enough to the mass of the
ϒ(5S). In the conventional Quarkonium theory, there is no place for such a nearby additional bb resonance having the quantum numbers of ϒ(5S).

Our interpretation [4] of the Belle data is that the anomalous ϒ(1S)π⁺π^- and ϒ(2S)π⁺π^- events are not due to the production and decays of the ϒ(5S), but rather from the production of a completely different hadron species, tetraquark hadrons with the quark structure Y_[bu] = [bu][b u ] and Y_[bd] = [bd][b d ], and their subsequent decays. The constituents of the tetraquarks, diquarks and antidiquarks (see the sketch below), have well-defined properties, characterized by their color and electromagnetic charges, spin and flavor quantum numbers. The tetraquark hadrons Y_[bu] and Y_[bd] are singlets in color (pictured white), and hence they participate as physical states in scattering and decay processes. This is not too dissimilar a situation from the well-known mesons, which are color singlet (white) bound states of the confined colored quarks and antiquarks.

The idea that diquarks and antidiquarks may play a fundamental role in hadron spectroscopy is rather old and goes back to well over thirty years [5]. This suggestion was lying dormant for most of this period for lack of experimental evidence. Tetraquarks resurfaced as possible explanations of the exotic hadronic states in the charm quark sector, such as X(3872) and the
Y(4660), which are interpreted as [cu][c u ] states [6]. Lately, also the perception about the light scalar mesons, such as f₀(600) and f₀(980) (there is an entire nonet of them) has changed. They are now interpreted as being dominantly tetraquark [qq′][q q′ ] states instead of the usual qq mesons [7]. Y_[bu] and Y_[bd] are the first tetraquarks in the bottom quark sector – harbingers of an entirely new world of bound and open beauty hadrons.

In an earlier paper [8], we (togeher with Ishtiaq Ahmed) were able to identify tetraquark states which can be produced in e⁺e⁻ annihilation directly. Of these, Y_[bu] and Y_[bd] are estimated to have the right masses to be produced in the vicinity of the ϒ(5S). The physical particles called Y_[b,l] and Y_[b,h], for lighter and heavier of the two, are mixed states. They have masses around 10.90 GeV and are split in mass by about 6 MeV. To search for them we analyzed the BaBar data, obtained during the energy scan of the e⁺e⁻ → bb cross section in the range of √s = 10.54 GeV to 11.20 GeV [9]. Our inference was that the BaBar data are consistent with the presence of additional bb states
Y_[b,l] and Y_[b,h] with a mass of about 10.90 GeV and a decay width of about 30 MeV, apart from the ϒ(5S) and ϒ(6S) resonances. It struck us that most of the enigmatic events in the Belle data in the final states ϒ(1S)π⁺π^- and ϒ(2S)π⁺π^- are concentrated around 10.90 GeV, and hence we tentatively identified the states in our analysis of the R_b-scan with the state Y_b(10890) in the Belle analysis.

To pursue our theoretical hypothesis, we developed a dynamical theory to make quantitative predictions and undertake an analysis of the Belle data. Explaining the larger decay rates for the transitions Y_b → ϒ(1S)π⁺π^-, ϒ(2S)π⁺π^- was not so difficult, as the decays of
Y_[b,l] and Y_[b,h] involve a recombination of the initial four quarks, as exemplified below by the process Y_[bu] ≡ [bu][b u] → (bb)(uu), with the subsequent projection (bb) → ϒ(1S) and (uu) → π⁺π^-.

Such quark recombination processes do not require the emission and absorption of gluons, and are appropriately called Zweig-allowed, after the co-discoverer of the quark-model, George Zweig. On the other hand, the dipionic transitions from a higher bottomonium state, such as ϒ(5S), to lower bottomonium states, such as ϒ(1S), are very rare QCD processes, needing the radiation of two gluons and their conversion to the π⁺π^- final state (see the sketch above).

The measured decay distributions, such as the dipion invariant mass spectra, are also easily understood in terms of the affinity of the tetraquark states Y_[b,l] and Y_[b,h] to decay preferentially into ϒ(1S) or ϒ(2S) and lighter tetraquark states, the light 0⁺⁺ states f₀(600)and f₀(980), mentioned earlier. They are indicated in the relevant figure by the intermediate state f₀. Hence, one expects a resonant structure in the dipion invariant mass, reflecting these and other known resonances allowed by the phase space. This is indeed the case, as can be seen in the figures below adapted from our PRL paper [4]. In these plots Belle data are indicated by crosses; the shaded histograms are our theoretical calculations for the tetraquark case (best fits) and the solid curves are the shapes from the corresponding decays of the ϒ(5S), which do not fit the data. In summary, tetraquark interpretation of the Y_b(10890) provides an excellent description of the decay distributions measured by Belle.

Exciting and plausible as our interpretation of the Belle and BaBar data is, we stress that a number of measurements has to be undertaken to confirm the tetraquark interpretation of the Belle anomaly. The first and foremost is that two almost degenerate states Y_[b,l] and Y_[b,h], predicted in the tetraquark theory as members of an isodoublet, have to be confirmed experimentally. We wait anxiously for the analysis of the new data which Belle is currently accumulating around the ϒ(5S) region. Improved measurements of the cross section e⁺e⁻ → bb in dedicated energy scans, which will be carried out at the Super-B factories being planned at KEK and Frascati in Italy, may also greatly help in resolving this structure and perhaps establish other tetraquark resonances predicted in that region.

Last, but by no means least, these and other tetraquark states should be measured in
experiments at the Tevatron and the LHC. Final states -- such as seen in the Belle experiment -- are easy enough to be measured even in the noisy backgrounds in hadron colliders; calculating the production cross section requires theoretical work. We look forward to data from the ongoing run by the Belle collaboration and eventually from the two hadron colliders and the Super-B factories.

References
[1] K. F. Chen et al. [Belle Collaboration], "Observation of Anomalousϒ(1S)π⁺π^- and ϒ(2S)π⁺π^- Production near the ϒ(5S) Resonance", Phys. Rev. Lett. 100, 112001 (2008) Abstract ; K.-F. Chen et al. [Belle Collaboration], "Observation of an enhancement in e⁺e⁻ → ϒ(1S)π⁺π^-, ϒ(2S)π⁺π^-, and ϒ(3S)π⁺π^- production around √s = 10.89 GeV at Belle", arXiv:0808.2445 [hep-ex] (2010). Article.
[2] L. S. Brown and R. N. Cahn, "Separation of ψ → π⁺π^-γ from ψ → π⁺π^-π^{0 "}, Phys. Rev. Lett. 35, 1 (1975) Abstract; M. B. Voloshin, "Possible four-quark isovector resonance in the family of ϒ particles" JETP Lett. 21, 347 (1975) Pisma Zh. Eksp. Teor. Fiz. 21, 733 (1975)] Article ; K. Gottfried, "Hadronic Transitions between Quark-Antiquark Bound States", Phys. Rev. Lett. 40, 598 (1978) Abstract ; V. A. Novikov and M. A. Shifman, "Comment on the ψ′ → J/ψππ decay", Z. Phys. C 8, 43 (1981) Abstract ; Y. P. Kuang and T. M. Yan, "Predictions for hadronic transitions in the bb system", Phys. Rev. D 24, 2874 (1981). Abstract.
[3] A. Sokolov et al. [Belle Collaboration], "Measurement of the branching fraction for the decay Υ(4S)→ Υ(1S)π⁺π^-", Phys. Rev. D 79, 051103 (2009). Abstract.
[4] A. Ali, C. Hambrock and M. J. Aslam, "Tetraquark Interpretation of the BELLE Data on the Anomalous Υ(1S)π+π- and Υ(2S)π+π- Production near the Υ(5S) Resonance", Phys. Rev. Lett, 104, 162001 (2010). Abstract.
[5] R. L. Jaffe, "Multiquark hadrons. II. Methods", Phys. Rev. D 15, 281 (1977), Abstract ; R. L. Jaffe and F. E. Low, "Connection between quark-model eigenstates and low-energy scattering", Phys. Rev. D 19, 2105 (1979). Abstract.
[6] L. Maiani, F. Piccinini, A. D. Polosa and V. Riquer, "Diquark-antidiquark states with hidden or open charm and the nature of X(3872)", Phys. Rev. D 71, 014028 (2005). Abstract.
[7] G. ’t Hooft, G. Isidori, L. Maiani, A. D. Polosa and V. Riquer, "A theory of scalar mesons", Phys. Lett. B 662, 424 (2008). Abstract.
[8] A. Ali, C. Hambrock, I. Ahmed and M. J. Aslam, "A Case for Hidden bb Tetraquarks Based on e⁺e⁻ → bb Cross Section Between √s = 10.54 and 11.20 GeV", Phys. Lett. B 684, 28 (2010). Abstract.
[9] B. Aubert et al. [BaBar Collaboration], "Measurement of the e⁺e⁻ → bb Cross Section between √s=10.54 and 11.20 GeV", Phys. Rev. Lett. 102, 012001 (2009). Abstract.

Simulating the Physics of a Free Dirac Particle

Christian Roos

[This is an invited article based on a recently published work by the author and his collaborators from Austria and Spain -- 2Physics.com]

Author: Christian Roos

Affiliation: Institut für Experimentalphysik, Universität Innsbruck, Austria
and
Institute for Quantum Optics and Quantum Information
Austrian Academy of Sciences

By the mid 1920s physicists had established the dynamics of quantum particles in the non-relativistic limit. The celebrated Schrödinger equation established a framework that allowed tackling a vast range of problems in atomic, molecular and solid state physics. However, the equation is limited to the regime of particles with velocities that are small compared to the speed of light. In 1928, Dirac put forward an equation to describe electrons in a way that successfully reconciles quantum physics with special theory of relativity. The Dirac equation provides a natural explanation of spin as an intrinsic property of the electron. It has not only positive energy solutions but also solutions with negative energies which led to the prediction of anti-matter.

In 1930, at a time when the interpretation of solutions to Dirac equation was still debated, Schrödinger noticed another peculiar feature: the equation admits solutions where the centre-of-mass of a quantum particle exhibits a trembling motion, called Zitterbewegung, in the absence of external forces [1]. This effect is surprising because according to Newton’s first law, a particle that experiences no forces should move in a straight line. In real quantum particles, such as electrons, this trembling motion would have a very small amplitude (10^-13m) and an extremely high frequency (10²¹ Hz). Moreover, it arises only as an interference effect in solutions comprised of positive and negative energy components. Such solutions, which might seem irrelevant, arise, however, in the presence of external fields. For free electrons, this phenomenon does to seem to be experimentally accessible.

It is, however, possible to engineer other quantum systems such that they mimic the physics of the Dirac equation. One such system is an ion held in an ion trap and cooled and manipulated by laser light [2]. How can such a trapped non-relativistic quantum particle simulate the physics of a free Dirac particle? To answer this question, it is helpful to look first at the case of a classical particle held in a harmonic potential. The motion of this particle is described by a circle in phase space. For a particle that is resonantly excited by an external driving force, its phase space trajectory will turn into a helix. In a frame where the phase space coordinates rotate at the resonance frequency of the particle, the helix turns into a straight line which the particle follows with constant velocity, i.e. the particle looks like a free particle in the absence of forces.

The same approach can be followed in the case of a relativistic quantum particle. Using a trapped ion, internal energy levels of the ion can be used for encoding the four spinor components representing the particle’s wave function. The term that couples the particle’s momentum operator and the spinor components in the Dirac equation can be simulated in the trapped-ion case by laser beams coupling the ion’s internal states with its motion. The term representing the ion’s rest energy is simulated by another laser-ion interaction that modifies the internal-state energies. In this way, a perfect match is achieved between the form of the Dirac equation and the Schrödinger equation describing the quantum physics of the trapped ion.

In an experiment reported in the Nature issue of the 7th January [3], this proposal is realized using a single trapped ⁴⁰Ca⁺ held in a linear ion trap (see Fig.1).

Fig.1: Experimental setup. An ion trap set up in a ultra-high vacuum system is used to store a ⁴⁰Ca⁺ ion. The ion is illuminated by laser light that serves to laser-cool, manipulate and detect the particle. (Image Credit: C. Lackner, IQOQI)

The goal of the experiment consists in observing the trembling motion predicted by Schrödinger. For this, the ion’s motion is first laser-cooled to the lowest energy state in which the ion is localized to a space of about 10 nm, the uncertainty in the position being due to the Heisenberg uncertainty relation. Then, for a certain amount of time, a suitable combination of laser beams is switched on to simulate the physics of the Dirac equation. The final step consists in a measurement that detects the change in the ion’s position. These three basic steps take no longer than 20 ms to carry out. They are repeated over and over again in order to measure the ion motion as a function of time. In perfect agreement with Schrödinger’s prediction, we indeed observe a trembling motion which is shown in Fig. 2.

Fig.2: Measured ‘Zitterbewegung’. (a) Average position of the ion as a function of time. The ion motion is composed of a uniform motion on top of which the trembling motion appears. (b) Time evolution of the ion’s wave function. Its two spinor components are shown in red and blue. The trembling motion disappears as soon as the two spinor components are no longer spatially overlapped.

Why can this experiment be called a quantum simulation? In the 1980's Richard Feynman and others proposed a new method for approaching quantum mechanical problems that are too hard to solve on ordinary computers. Their idea was to use a more accessible quantum system to simulate quantum effects of interest. To date, only a few quantum systems can be controlled well enough to act as a quantum simulator. In our experiment, we have performed a quantum simulation of a free Dirac particle using a single trapped ion manipulated with laser light. In this case, the quantum-mechanical state space has no more than 100 dimensions, a size that can be handled perfectly well by any current desktop computer. So the experiment is far from outperforming computers. But the small size of the quantum system is also an advantage because it allows us to compare experiment and theoretical prediction and in this way test the concept of a quantum simulator. The hope is that in the future systems of trapped ions or neutral atoms held in optical lattices might be used to simulate and study quantum phenomena that can no longer be analyzed by computer simulations.

References
[1] “Über die kräftefreie Bewegung in der relativistischen Quantenmechanik”, Sitz. Preuss. Akad. Wiss. Phys.-Math. Kl. 24, 418–428 (1930).
[2] “Robust Dirac equation and quantum relativistic effects in a single trapped ion”, L. Lamata, J. León, T. Schätz, E. Solano. Phys. Rev. Lett. 98, 253005 (2007). Abstract.
[3] “Quantum simulation of the Dirac equation”, R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, C. F. Roos, Nature 463, 68 (2010). Abstract.

Observation of Magnetic Monopoles in Spin Ice

Hiroaki Kadowaki, Yuji Aoki and Naohiro Doi of Tokyo Metropolitan University


[This is an invited article based on recently published work of the authors -- 2Physics.com]






Authors: H. Kadowaki¹, Y. Aoki¹, T. J. Sato², J. W. Lynn³

Affiliations: ¹Department of Physics, Tokyo Metropolitan University, Tokyo, Japan,
²NSL, Institute for Solid State Physics, University of Tokyo, Tokai, Japan,
³NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD, USA

From the symmetry of Maxwell's equations of electromagnetism, magnetic charges or monopoles would be expected to exist in parallel with electric charges. About 80 years ago, a quantum mechanical hypothesis of the existence of magnetic monopoles was proposed by Dirac [1]. Since then, many experimental searches have been performed, ranging from a monopole search in rocks of the moon to experiments using high energy accelerators [2]. But none of them was successful, and the monopole is an open question in experimental physics. Theoretically, monopoles are predicted in grand unified theories as topological defects in the energy range of the order 10¹⁶ GeV [2]. However these enormous energies preclude all hope of creating them in laboratory experiments.

Taku J. Sato of University of Tokyo

Alternatively, recent theories predict that tractable analogs of the magnetic monopole might be found in condensed matter systems [3,4,5]. One prediction [4] is for an emergent elementary excitation in the spin ice compound Dy₂Ti₂O₇ [6], where the strongly competing magnetic interactions exhibit the same type of frustration as water ice [7]. In addition to macroscopically degenerate ground states [6], the excitations from these states are topological in nature and mathematically equivalent to the Dirac monopoles [1,4]. We have successfully observed [8] the signature of magnetic monopoles in the spin ice Dy₂Ti₂O₇ using neutron scattering, and find that they interact via the magnetic inverse-square Coulomb force. In addition, specific heat measurements show that the density of monopoles can be controlled by temperature and magnetic field, with the density following the expected Arrhenius law.

Jeffrey W. Lynn of NIST, USA

In Fig. 1 we illustrate creation of a magnetic monopole and antimonopole pair in spin ice under applied magnetic field along a [111] direction. This excitation is generated by flipping a spin, which results in ice-rule-breaking "3-in, 1-out" and "1-in, 3-out" tetrahedral neighbors, simulating magnetic monopoles, with net positive and negative charges sitting on the centers of tetrahedra. The monopoles can move and separate by consecutively flipping spins in the kagome lattice.

Fig. 1. Spins of Dy₂Ti₂O₇ occupy a cubic pyrochlore lattice, which is a corner -sharing network of tetrahedra, and consists of a stacking of triangular and kagome lattices. The competing magnetic interaction brings about a geometrical constraint where the lowest energy spin configurations on each tetrahedron follow the ice rule, in which two spins point inward and two point outward on each tetrahedron. (A) By applying a small magnetic field along a [111] direction, the spins on the triangular lattices are parallel to the field, while those on the kagome lattices retain disorder under the same ice rules. This is referred to as the kagome ice state [9]. (B) Creation of a magnetic monopole (blue sphere) and antimonopole (red sphere) pair in the kagome ice state.

A straightforward signature of monopole-pair creation is an Arrhenius law in the temperature (T) dependence of the specific heat (C). This Arrhenius law of C(T) is clearly seen in Fig. 2 at low temperatures, indicating that monopole-antimonopole pairs are thermally activated from the ground state, and that the number of monopoles can be tuned by changing temperature and magnetic field.

Fig. 2. Specific heat of Dy₂Ti₂O₇ under [111] magnetic fields is plotted as a function of 1/T. In intermediate temperature ranges these data are well represented by the Arrhenius law denoted by solid lines.

A microscopic experimental method of observing monopoles is to perform magnetic neutron scattering using the neutron's dipole moment as the probe. One challenge to the experiments is to distinguish the relatively weak scattering from the monopoles from the very strong magnetic scattering of the ground state. By choosing appropriate field-temperature values, we have successfully observed scattering by magnetic monopoles, diffuse scattering close to the (2,-2,0) reflections, and that by the ground state (Fig. 3) [8].

Fig. 3. Intensity maps of neutron scattering at T = T_c + 0.05 K in the scattering plane perpendicular to the [111] field are shown for H = 0.5 T and H = H_c. The kagome ice state at H = 0.5 T (A) compared with the MC simulation (C). The weakened kagome-ice state scattering plus the diffuse monopole scattering (B) at H = H_c agree with the MC simulation (D).

Typical elementary excitations in condensed matter, such as acoustic phonons and (gapless) magnons, are Nambu-Goldstone modes where a continuous symmetry is spontaneously broken when the ordered state is formed. This contrasts with the monopoles in spin ice, which are point defects that can be fractionalized in the frustrated ground states. Such excitations are unprecedented in condensed matter, and now enable conceptually new emergent phenomena to be explored experimentally [10].

References:
[1] "Quantised singularities in the electromagnetic field",
P. A. M. Dirac, Proc. R. Soc. A 133, 60 (1931). Article.
[2] "Theoretical and experimental status of magnetic monopoles",
K. A. Milton, Rep. Prog. Phys. 69, 1637 (2006). Abstract.
[3] "The anomalous Hall effect and magnetic monopoles in momentum space", Zhong Fang, Naoto Nagaosa, Kei S. Takahashi, Atsushi Asamitsu, Roland Mathieu, Takeshi Ogasawara, Hiroyuki Yamada, Masashi Kawasaki, Yoshinori Tokura, Kiyoyuki Terakura, Science 302, 92 (2003). Abstract.
[4] "Magnetic monopoles in spin ice"
C. Castelnovo, R. Moessner, S. L. Sondhi, Nature 451, 42 (2008). Abstract.
[5] "Inducing a magnetic monopole with topological surface states"
X-L. Qi, R. Li, J. Zang, S-C. Zhang, Science 323, 1184 (2009). Abstract.
[6] "Spin ice state in frustrated magnetic pyrochlore materials"
S. T. Bramwell, M. J. P. Gingras, Science 294, 1495 (2001). Abstract.
[7] "The structure and entropy of ice and of other crystals with some randomness of atomic arrangement" , L. Pauling, J. Am. Chem. Soc. 57, 2680 (1935). Abstract.
[8] "Observation of Magnetic Monopoles in Spin Ice", H. Kadowaki, N. Doi, Y. Aoki, Y. Tabata, T. J. Sato, J. W. Lynn, K. Matsuhira, Z. Hiroi, J. Phys. Soc. Jpn. 78, 103706 (2009). Abstract.
[9] "A new macroscopically degenerate ground state in the spin ice compound Dy2Ti2O7 under a magnetic field" K. Matsuhira, Z. Hiroi, T. Tayama, S. Takagi and T. Sakakibara, J. Phys. Condens. Matter 14, L559 (2002). Article; "Kagome ice State in the dipolar spin ice Dy2Ti2O7" Y. Tabata, H. Kadowaki, K. Matsuhira, Z. Hiroi, N. Aso, E. Ressouche, and B. Fåk, Phys. Rev. Lett. 97, 257205 (2006). Abstract.
[10] In Oct. 2009, in addition to [8], three experimental papers on the magnetic monopoles in spin ice have been published: "Measurement of the charge and current of magnetic monopoles in spin ice" S. T. Bramwell, S. R. Giblin, S. Calder, R. Aldus, D. Prabhakaran & T. Fennell, Nature 461, 956 (2009), Abstract; "Dirac Strings and Magnetic Monopoles in the Spin Ice Dy2Ti2O7" D. J. P. Morris, D. A. Tennant, S. A. Grigera, B. Klemke, C. Castelnovo, R. Moessner, C. Czternasty, M. Meissner, K. C. Rule, J.-U. Hoffmann, K. Kiefer, S. Gerischer, D. Slobinsky, R. S. Perry, Science 326, 411 (2009) Abstract; "Magnetic Coulomb Phase in the Spin Ice Ho2Ti2O7" T. Fennell, P. P. Deen, A. R. Wildes, K. Schmalzl, D. Prabhakaran, A. T. Boothroyd, R. J. Aldus, D. F. McMorrow, S. T. Bramwell, Science 326, 415 (2009). Abstract.

The Largest Parity Violations Ever Measured in an Atom

Dmitry Budker [Photo courtesy: UC, Berkeley]

In a paper accepted for publication in Physical Review Letters, a team of scientists from Lawrence Berkeley National Laboratory and University of California, Berkeley reported the largest effects of parity violation in an atom ever observed. Their measurements with ytterbium-174, an isotope with 70 protons and 104 neutrons, have shown a hundred times larger effect than the most precise measurements made so far, with the element cesium.

“Parity” assumes that, on the atomic scale, nature behaves identically when left and right are reversed: interactions that are otherwise the same but whose spatial configurations are switched, as if seen in a mirror, ought to be indistinguishable.

“It’s the weak force that allows parity violation,” says Dmitry Budker, who led the research team. Of the four forces of nature – strong, electromagnetic, weak, and gravitational – the extremely short-range weak force was the last to be discovered. Neutrinos, having no electric charge, are immune to electromagnetism and only interact through the weak force. The weak force also has the startling ability to change the flavor of quarks, and to change protons into neutrons and vice versa.

Protons on their own last forever, apparently, but a free neutron falls apart in about 15 minutes; it turns into a proton by emitting an electron and an antineutrino, a process called beta decay. What makes beta decay possible is the weak force.

Scientists long assumed that nature, on the atomic scale, was symmetrical. It would look the same not only if left and right were reversed but also if the electrical charges of particles involved in an interaction were reversed, or even if the whole process ran backwards in time. Charge conjugation is written C, parity P, and time T; nature was thought to be C invariant, P invariant, and T invariant.

In 1957 researchers realized that the weak force didn’t play by the rules. When certain kinds of nuclei such as cobalt-60 are placed in a magnetic field to polarize them – line them up – and then allowed to undergo beta decay, they are more likely to emit electrons from their south poles than from their north poles.

This was the first demonstration of parity violation. Before the 1957 cobalt-60 experiment, renowned physicist Richard Feynman had said that if P violation were true – which he doubted – something long thought impossible would be possible after all: “There would be a way to distinguish right from left.”

It’s now apparent that many atoms exhibit parity violation, although it is not easy to detect. P violation has been measured with the greatest accuracy in cesium atoms, which have 55 protons and 78 neutrons in the nucleus, by using optical methods to observe the effect when atomic electrons are excited to higher energy levels.

An atomic beam of ytterbium is generated in the oven at left, then passed through a chamber with magnetic and electric fields arranged at right angles—the magnetic field colinear with the atomic beam, and the electric field colinear with a laser beam that excites a "forbidden" electron-energy transition. Weak interactions between electron and nucleus contribute to the forbidden transition. [image courtesy: LBNL]

The Berkeley researchers designed their own apparatus to detect the much larger parity violation predicted for ytterbium. In their experiment, ytterbium metal is heated to 500 degrees Celsius to produce a beam of atoms, which is sent through a chamber where magnetic and electric fields are oriented at right angles to each other. Inside the chamber the ytterbium atoms are hit by a laser beam, tuned to excite some of their electrons to higher energy states via a “forbidden” (highly unlikely) transition. The electrons then relax to lower energies along different pathways.

Weak interactions between the electron and the nucleus – plus weak interactions within the nucleus of the atom – act to mix some of the electron energy states together, making a small contribution to the forbidden transition. But other, more ordinary electromagnetic processes, which involve apparatus imperfections, also mix the states and blur the signal. The purpose of the chamber’s magnetic and electric fields is to amplify the parity-violation effect and to remove or identify these spurious electromagnetic effects.

Upon analyzing their data, the researchers found a clear signal for atomic parity violations, 100 times larger than the similar signal for cesium. With refinements to their experiment, the strength and clarity of the ytterbium signal promise significant advances in the study of weak forces in the nucleus.

The Budker group’s experiments are expected to expose how the weak charge changes in different isotopes of ytterbium, whose nuclei have the same number of protons but different numbers of neutrons, and will reveal how weak currents flow within these nuclei. The results will also help explain how the neutrons in the nuclei of heavy atoms are distributed, including whether a “skin” of neutrons surrounds the protons in the center, as suggested by many nuclear models.

“The neutron skin is very hard to detect with charged probes, such as by electron scattering,” says Budker, “because the protons with their large electric charge dominate the interaction.” He adds, “At a small level, the measured atomic parity violation effect depends on how the neutrons are distributed within the nucleus – specifically, their mean square radius. The mean square radius of the protons is well known, but this will be the first evidence of its kind for neutron distribution.”

Measurements of parity violation in ytterbium may also reveal “anapole moments” in the outer shell of neutrons in the nucleus (valence neutrons). As predicted by the Russian physicist Yakov Zel’dovich, these electric currents are induced by the weak interaction and circulate within the nucleus like the currents inside the toroidal winding of a tokamak; they have been observed in the valence protons of cesium but not yet in valence neutrons.

Yacov Zel'dovich proposed that the weak force induces electrical currents in the nucleus, which flow like currents in a tokamak. This anapole moment has been detected in nuclear valence protons but not yet in valence neutrons.[image courtesy: LBNL]

Eventually the experiments will lead to sensitive tests of the Standard Model – the theory that, although known to be incomplete, still best describes the interactions of all the subatomic particles so far observed.

“So far, the most precise data about the Standard Model has come from high-energy colliders,” says Budker. “The carriers of the weak force, the W and Z bosons, were discovered at CERN by colliding protons and antiprotons, a ‘high-momentum-transfer’ regime. Atomic parity violation tests of the Standard Model are very different – they’re in the low-momentum-transfer regime and are complementary to high-energy tests.”

Since 1957, when Zel’dovich first suggested seeking atomic variation in atoms by optical means, researchers have come ever closer to learning how the weak force works in atoms. Parity violation has been detected in many atoms, and its predicted effects, such as anapole moments in the valence protons of cesium, have been seen with ever-increasing clarity. With their new experimental techniques and the observation of a large atomic parity violation in ytterbium, Dmitry Budker and his colleagues have achieved a new landmark, moving closer to fundamental revelations about our asymmetric universe on the atomic scale.

Reference
“Observation of a large atomic parity violation in ytterbium”,
K. Tsigutkin, D. Dounas-Frazer, A. Family, J. E. Stalnaker, V. V. Yashchuck, and D. Budker,
Accepted for publication in Physical Review Letters. arXiv:0906.3039

[We thank Lawrence Berkeley National Laboratory for materials used in this posting]

The Shadows of Gravity

Jose A. R. Cembranos

[This is an invited article based on the author's recently published work -- 2Physics.com]

Author: Jose A. R. Cembranos
Affiliation: William I. Fine Theoretical Physics Institute, University of Minnesota in Minneapolis, USA

Many authors have tried to explain the dark sectors of the cosmological model as modifications of Einstein’s gravity (EG). Dark Matter (DM) and Dark Energy (DE) are the main sources of the cosmological evolution at late times. They dominate the dynamics of the Universe at low densities or low curvatures. Therefore it is reasonable to expect that an infrared (IR) modification of EG can lead to a possible solution of these puzzles. However, it is in the opposite limit, at high energies (HE), where EG needs corrections from a quantum approach. These natural ultraviolet (UV) modifications of gravity are usually thought to be related to inflation or to the Big Bang singularity. In a recent work, I have shown that DM can be explained with HE modifications of EG. I have used an explicit model: R² gravity and study its possible experimental signatures [1].

Einstein’s General Relativity describes the classical gravitational interaction in a very successful way by the metric tensor of the space-time through the Einstein-Hilbert action (EHA). This theory is particularly beautiful and the action particularly simple, since it contains only one term proportional to the scalar curvature. The proportionality parameter which multiplies this term, defines the Newton’s constant of gravitation and the typical scale of gravity. This magnitude is known as the Planck scale and its approximated energy value is 10¹⁹ Giga-electronvolts, which is equivalent to a distance of 10^-35 meters.

However, the inconsistency of quantum computations within the gravitational theory described by the EHA demands its modification at HE. Quantum radiative corrections produced by standard matter provide divergent terms that are constant, linear, and quadratic in the Riemann curvature tensor of the space-time. The constant divergence can be regularized by the renormalization of the cosmological constant, which may explain the Dark Energy. The linear term is absorbed in the renormalization of the Planck scale itself. On the contrary, the quadratic terms are not included in the standard gravitational action. If these quantum corrections are not cancelled by invoking new symmetries, these terms need to be taken into account for the study of gravity at HE [2]. Indeed, these terms are also produced by radiative corrections coming from the own EG. Unfortunately, the gravitational corrections do not stop at this order as the associated with the matter content. There are cubic terms, quartic terms, etc. All these local quantum corrections are divergent and the fact that there is a non finite number of them implies that the theory is non-renormalizable. We know how to deal with gravity as an effective field theory, working order by order, but we cannot access higher energies than the Planck scale by using this effective approach [2]. In any case, the Planck scale is very high, and unreachable experimentally so far.

Inspired by this effective field theory point of view, which identifies higher energy corrections with higher curvature terms, I have studied the viability of a solution to the missing matter problem from the UV completion of gravity. As I have explained above, the first HE modification to EG is provided by the inclusion of quadratic terms in the curvature of the space-time geometry. The most general quadratic action supports, in addition to the usual massless spin-two graviton, a massive spin-two and a massive scalar mode, with a total of eight degrees of freedom (in the physical gauge [3]). In fact, this gravitational theory is renormalizable [3]. However, the massive spin-two gravitons are ghost-like particles that generate new unitarity violations, breaking of causality, and important instabilities.

In any case, there is a non-trivial quadratic extension of EG that is free of ghosts and phenomenologically viable. It is the so called R² gravity since it is defined by the only addition of a term proportional to the square of the scalar curvature to the EHA. This term by itself does not improve the UV behaviour of EG but illustrates the idea in a minimal way. This particular HE modification of EG introduces a new scalar graviton that can provide the solution to the DM problem.

In this model, the new scalar graviton has a well defined coupling to the standard matter content and it is possible to study its phenomenology and experimental signatures [1] [3][4]. Indeed, this DM candidate could be considered as a superweakly interacting massive particle (superWIMP [5]) since its interactions are gravitational, i.e. it couples universally to the energy-momentum tensor with Planck suppressed couplings. It means that the new scalar graviton mediates an attractive Yukawa force between two non-relativistic particles with strength similar to Newton’s gravity. Among other differences, this new component of the gravitational force has a finite range, shorter than 0.1 millimeters, since the new scalar graviton is massive.

This is the most constraining lower bound on the mass of the scalar mode and it is independent of any supposition about its abundance. On the contrary, depending on its contribution to the total amount of DM, its mass is constrained from above. I have shown that it cannot be much heavier than twice the mass of the electron. If that is the case, this graviton decays in an electron-positron pair. These positrons annihilate producing a flux of gamma rays that we should have observed. In fact, the SPI spectrometer on the INTEGRAL (International Gamma-ray Astrophysics Laboratory) satellite, has observed a flux of gamma rays coming from the galactic centre (GC), whose characteristics are fully consistent with electron-positron annihilation [6].

If the mass of the new graviton is tuned close to the electron-positron production threshold, this line could be the first observation of R² gravity. The same gravitational DM can explain this observation with a less tuned mass and a lower abundance. For heavier masses, the gamma ray spectrum originated by inflight annihilation of the positrons with interstellar electrons is even more constraining than the 511 keV photons [7].

On the contrary, for lighter masses, the only decay channel that may be observable is in two photons. It is difficult to detect these gravitational decays in the isotropic diffuse photon background (iDPB) [8]. A most promising analysis is associated with the search of gamma-ray lines from localized sources, as the GC. The iDPB is continuum since it suffers the cosmological redshift, but the mono-energetic photons originated by local sources may give a clear signal of R² gravity [1].

In conclusion, I have analyzed the possibility that the DM origin resides in UV modifications of gravity [1]. Although, strictly speaking, my results are particular of R² gravity, I think they are qualitatively general with a minimum set of assumptions about the gravitational sector. In any case, different approaches to try to link our ignorance about gravitation with the dark sectors of standard cosmology can be taken [9], and it is a very interesting subject which surely deserves further investigations.

This work is supported in part by DOE Grant No. DOE/DE-FG02-94ER40823, FPA 2005-02327 project (DGICYT, Spain), and CAM/UCM 910309 project.

References

[1] J. A. R. Cembranos, ‘Dark Matter from R² Gravity’ Phys. Rev. Lett. 102, 141301 (2009). Abstract

[2] N. D. Birrell and P. C. W. Davies, 'Quantum Fields In Curved Space’ (Cambridge Univ. Pr, 1982); J. F.Donoghue, ‘General Relativity As An Effective Field Theory: The Leading Quantum Corrections’ Phys. Rev. D 50, 3874 (1994) Abstract; A. Dobado, et al., ‘Effective lagrangians for the standard model’ (Springer-Verlag, 1997).

[3] K. S. Stelle, ‘Renormalization Of Higher Derivative Quantum Gravity’ Phys. Rev. D 16, 953 (1977) Abstract; K.S. Stelle, ‘Classical Gravity With Higher Derivatives’ Gen Rel. Grav. 9, 353 (1978) Abstract.

[4] A. A. Starobinsky, ‘A New Type of Isotropic Cosmological Models Without Singularity’ Phys. Lett. B 91, 99 (1980) Abstract; S. Kalara, N. Kaloper and K. A. Olive, ‘Theories of Inflation and Conformal Transformations’ Nucl. Phys. B 341, 252 (1990) Abstract; J. A. R. Cembranos, ‘The Newtonian Limit at Intermediate Energies’ Phys. Rev. D 73, 064029 (2006) Abstract.

[5] J. L. Feng, A. Rajaraman and F. Takayama, ‘Superweakly-Interacting Massive Particles’ Phys. Rev. Lett. 91, 011302 (2003) Abstract; J. A. R. Cembranos,Jonathan L. Feng, Arvind Rajaraman, and Fumihiro Takayama,‘SuperWIMP Solutions to Small Scale Structure Problems’ Phys. Rev. Lett. 95, 181301 (2005) Abstract.

[6] B. J. Teegarden et al., 'INTEGRAL/SPI Limits on Electron-Positron Annihilation Radiation from the Galactic Plane’ Astrophys. J. 621, 296 (2005) Article.

[7] J. F. Beacom and H. Yuksel, ‘Stringent Constraint on Galactic Positron Production’ Phys. Rev. Lett. 97, 071102 (2006) Abstract.

[8] J. A. R. Cembranos, J. L. Feng and L. E. Strigari, ‘Resolving Cosmic Gamma Ray Anomalies with Dark Matter Decaying Now’ Phys. Rev. Lett. 99, 191301 (2007) Abstract; J. A. R. Cembranos and L. E. Strigari, ‘Diffuse MeV Gamma-rays and Galactic 511 keV Line from Decaying WIMP Dark Matter’ Phys. Rev. D 77, 123519 (2008) Abstract.

[9] J. A. R. Cembranos, A. Dobado and A. L. Maroto, ‘Brane-World Dark Matter’ Phys. Rev. Lett. 90, 241301 (2003) Abstract; ‘Dark Geometry’ Int. J. Mod. Phys. D 13, 2275 (2004) arXiv:hep-ph/0405165.

5 Most Important Breakthroughs That My Field of Research Needs -- Nathan Seiberg

Nathan Seiberg [photo courtesy: Institute for Advanced Study, Princeton]

[Our guest today in the feature ‘5-Breakthroughs’ is Nathan Seiberg, Professor at the Institute for Advanced Study in Princeton, NJ. Prof. Seiberg’s work has spanned a wide spectrum of research revolving around particle physics phenomenology, field theory, gauge theory, Matrix theory, string theory, and supersymmetry.

In early 1990s, he formulated the application of holomorphy to calculations in gauge theories with supersymmetry. In his famous 1994 article “Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories” (Abstract link) he conjectured a new kind of Strong-Weak duality or S-duality relating two different supersymmetric QCDs which are not identical, but agree at low energies. This is now well-known as Seiberg duality.

Working with Edward Witten, he also devised a series of partial differential equations that simplified the classification of 4-dimensional manifolds. The invariants of such compact smooth 4-manifolds are now known as Seiberg–Witten invariants. Later, they analyzed the appearance of non-commutative geometry in theories containing open strings, and identified a low energy limit of open string dynamics as a noncommutative quantum field theory.

Prof. Seiberg also made pioneering contribution in Matrix Theory, M Theory and various subfields of particle physics. Here is link to his list of publications: Google Scholar.

He received his Ph.D from the Weizmann Institute of Science in Israel in 1982. Before joining the Institute for Advanced Study, he had been a Professor of Physics at the Weizmann Institute for Science and at Rutgers University.

Prof. Seiberg is a member of National Academy of Sciences and Fellow of American Academy of Arts and Sciences. He received The John D. and Catherine T. MacArthur Fellowship (Genius Grant) in 1996. In 1998, American Physical Society awarded Dannie Heineman Prize for Mathematical Physics to Nathan Seiberg and Ed Witten "for their decisive advances in elucidating the dynamics of strongly coupled supersymmetric field and string theories. The deep physical and mathematical consequences of the electric-magnetic duality they exploited have broadened the scope of Mathematical Physics (quote from the citation)."

It’s an honor and privilege on our part to present 5 most important breakthroughs that Prof. Seiberg would like to see in his fields of research.
— 2Physics.com ]

1. Origin of electroweak symmetry breaking. This will shed light on the origin of mass of elementary particles. An effective description of this phenomenon in terms of the Higgs mechanism is known. The Large Hadron Collider (LHC) will explore it in detail and perhaps will point to a deeper structure. One possibility is that the LHC will discover supersymmetry – a new kind of symmetry which extends our understanding of space and time. Alternatively, it will find new particles which might have a description in terms of new space dimensions. If only the Higgs particle is discovered, its mass might be set anthropically. Is this true?

2. Origin of the elementary particles. What determines the properties of the quarks and the leptons (their quantum numbers)? Why do they appear in 3 generations? Most of the parameters of the Standard Model of particle physics are associated with the quark and lepton masses. It is possible that the underlying structure which controls them exists at very high energies which will not be explored soon. One possible explanation of the properties of the quarks, the leptons, and their interactions is the idea of grand unification. Is this idea correct?

3. Dark matter and dark energy of the Universe. Is the dark matter weakly interacting massive particles? This question could be settled soon either by detecting these particles, or the product of their interactions, or by creating them at the LHC. Is the dark energy a cosmological constant? What sets the value of the cosmological constant today? Is it anthropic?

4. Inflation. It seems that in the past the Universe had a period of rapid expansion known as inflation, during which the cosmological constant was large. What is the detailed description of this phenomenon? The study of inflation naturally leads to the idea of a multiverse – the Universe is a lot larger than what we observe and different parts of the Universe have different physics. How should we think about physics in such a setup? What are the correct observables? What is the precise role of anthropic ideas in this context?

5. Theory of quantum gravity. The correct theory of quantum gravity appears to be string theory. At the moment we do not have a clear conceptual formulation of the theory, nor do we have clear experimentally verifiable predictions of string theory. Can we solve these problems? Presumably, a deeper understanding of string theory will show that space and time are emergent concepts which are not present in the fundamental formulation of the theory. This could have important implications for the mysteries of the Big Bang.