DOCSLIB.ORG

Positivity of the Real Part of the Forward Scattering Amplitude

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Positivity of the Real Part of the Forward Scattering Amplitude PHYSICAL REVIEW D 97, 014011 (2018) Positivity of the real part of the forward scattering amplitude Andr´e Martin* CERN, 1211 Geneva, Switzerland Tai Tsun Wu Gordon McKay Laboratory, Harvard University, 02138 Cambridge, Massachusetts, USA (Received 5 September 2017; published 23 January 2018; corrected 26 January 2018) We prove the general theorem that the real part of the crossing even forward two-body scattering amplitude is positive at sufficiently high energies if, above a certain energy, the total cross section increases monotonically to infinity at infinite energy. DOI: 10.1103/PhysRevD.97.014011 I. HISTORICAL INTRODUCTION The perturbation character disappears in the summation. From the point of view of physics, the advantage of using In 1965, Khuri and Kinoshita published a series of quantum field theory is that the following three basic interesting papers on the real part of the forward scattering features are all satisfied: (1) relativistic kinematics, (2) uni- amplitude obtained via dispersion relations from the tarity, and (3) particle production [6]. The result found this imaginary part which is proportional to the total cross way in 1970 was a surprise: the total cross section must section [1]. Among their results was the prediction that, if increase at high energies, essentially saturating the Froissart- the Froissart bound is saturated, i.e., if the total cross 2 Martin bound, and the real part of the forward scattering section behaves at high energies like ðln sÞ where s is the amplitude does have the Khuri-Kinoshita behavior. At that square of the center-of-mass energy [2], then the real part is time, the measured proton-proton total cross section was still positive at high energies. Moreover, the ratio ρ of the real decreasing, while the real part of the forward scattering π part to the imaginary part would behave as ln s at high amplitude was still negative but increasing rapidly [7]. Three energies. At that time, nobody thought that the total cross years later, two experiments at the Intersecting Storage Ring section would increase at high energies. Instead, the general (ISR) at CERN showed that the proton-proton total cross belief was that the Froissart-Martin bound is an upper section did turn around and start rising [8]. At CERN, after a bound and that all total cross sections would approach talk by Amaldi on these experimental results, one of us (AM) constants or decrease to zero at high energies. Earlier, in “predicted” that the real part would become positive. 1960, Gribov showed that it is not possible to have at the Actually it was a guess at that time; a rigorous proof is to same time a total cross section approaching a finite nonzero be presented in the present paper. A few years later, in 1977, limit and a diffraction peak approaching a fixed shape as a an experiment at CERN showed that the real part was indeed function of the momentum transfer [3]. Instead, he pre- becoming positive [9]. Years later, the rise of the total cross ferred the total cross section to decrease to zero. In 1962, it section and the positively of the real part were both was discovered that the diffraction peak for proton-proton confirmed [10,11]. Using the shrinking of the width of the diffraction peak scattering was shrinking [4]. and the rise of the total cross section, one of us (AM) In view of this situation, Cheng and one of us (TTW) proved in 1997 that, if the differential cross section at fixed decided to learn about the high-energy behavior of total negative t, for −T<t<0, decreases to zero sufficiently cross sections by studying quantum gauge field theory, rapidly and if the total cross section increases to infinity, specifically by summing the leading terms of the perturba- then the real part must change sign at least once in this tion series [5]. It was an Abelian massive gauge theory. interval −T<t<0 [12]. Here t is as usual the negative of the square of the momentum transfer and T a positive *Corresponding author. number arbitrarily small. It is in fact in reexamining this [email protected] theorem, the proof of which still seems rather mysterious, that we were led to study again the problem of the real part Published by the American Physical Society under the terms of in the forward direction t ¼ 0. Various results were the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to obtained, the most striking one being the one presented the author(s) and the published article’s title, journal citation, in this paper. However, these considerations have failed to and DOI. Funded by SCOAP3. lead to an alternative proof of the result of reference [12]. 2470-0010=2018=97(1)=014011(4) 014011-1 Published by the American Physical Society ANDRE´ MARTIN and TAI TSUN WU PHYS. REV. D 97, 014011 (2018) II. THEOREM ON THE REAL The proof begins with the dispersion relation for fðξÞ PART AND ITS PROOF Z 2ξ2 ∞ dξ0 lm fðξÞ fðξÞ − fð0Þ¼ ð Þ The measurement of the real part of the scattering Re π ξ0 ξ02 − ξ2 5 amplitude in the forward direction is of great importance. μ In the cases of proton-proton and antiproton-proton scatter- where μ ¼ 2mamb.fð0Þ is real, since fðξÞ is real between ings, when the measured total cross sections were still the left hand cut and the right hand cut i.e. −μ < ξ < þμ. decreasing as function of energy, the first indication that Let ξo be the value of ξ such that this total cross section would turn around and increase came from the measurement of the real parts [5]. dσ ≥ 0 ξ > ξ : ð Þ Specifically, at that time the measured values were negative dξ for 0 6 but becoming less so when the center-of-mass energy increased, as expected. However, the increase (i.e., less The dispersion relation (5) can be rewritten as negative) was too fast and showed a tendency to overshoot 2 Z 2ξ ξ0 1 to become positive. Indeed, this was the first indication that fðξÞ − fð0Þ − dξ0σðξ0Þ Re 02 2 the proton-proton total cross section, among others, would π μ ξ − ξ Z increase. As already mentioned, the theoretical prediction 2ξ2 ∞ 1 of increasing total proton-proton cross section was first ¼ dξ0σðξ0Þ ð Þ π ξ02 − ξ2 7 made in 1970 and the experimental observation in 1973. ξ0 It is the purpose of the present paper to study in general In the left-hand side (LHS) of (7), for ξ → ∞ the sign of the real part of the forward scattering amplitude. 2 Z Z The specific problem is: under what general and realistic 2ξ ξ0 1 2 ξ0 dξ0σðξ0Þ ∼− dξ0σðξ0Þ; ð Þ conditions on the total cross section, the real part of the 02 2 8 π μ ξ − ξ π μ forward two-body scattering amplitude can be guaranteed to be positive at sufficiently high energies? and is therefore bounded in absolute value. Clearly, this problem should be studied through Integrating the right-hand side (RHS) of (7) by parts dispersion relations. Consider the elastic scattering process leads to Z a þ b → a þ b; ð1Þ ξ ∞ ∂ ξ0 − ξ ð7Þ¼ dξ0 σðξ0Þ RHS of π ∂ξ0 ln ξ0 þ ξ let s, t, u be the Mandelstam variables. Throughout this ξ0 paper, t ¼ 0 so that the scattering is in the forward ξ ξ0 þ ξ ¼ σðξ0Þ ln þ IðξÞ; ð9Þ direction. In this case, π ξ0 − ξ 2 2 s þ u ¼ 2ma þ 2mb ð2Þ where Z 0 0 where ma and mb are the masses of the particles a and b. ξ ∞ dσðξ Þ ξ þ ξ IðξÞ¼ dξ0 : ð Þ Thus, when t ¼ 0, the s − u symmetric variable is π dξ0 ln ξ0 − ξ 10 ξ0 1 ξ ¼ ðs − uÞ¼s − m2 − m2: ð Þ Note that the first term on the right-hand side of (9) is 2 a b 3 again bounded. This scattering amplitudes for a þ b → a þ b and a þ b¯ → a þ b¯ fðξÞ dσðξÞ are in general different. Define to If > 0 for ξ > ξ0 ð11Þ be the average of the forward scattering amplitude for these dξ two processes and σðξÞ that of the total cross sections, then IðξÞ is positive. pffiffiffi k s It only remains to show that this IðξÞ increases without fðξÞ¼ σðξÞðÞ ξ → ∞ Im 8π 4 bound for when when k is the c.m. momentum i.e. for ξ large σðξÞ → ∞ ð12Þ ξσðξÞ It follows from Im f ≃ 16π ξ0 þ ξ ξ þ ξ 2ξ The main result of the present paper is: 0 0 ln 0 ≥ ln ≥ ð13Þ Theorem: If, for sufficiently large values of ξ, σðξÞ is ξ − ξ ξ − ξ0 ξ nondecreasing and approaches infinity as ξ → ∞. Then Re fðξÞ is positive for all sufficiently large values of ξ. when ξ > ξ0 that 014011-2 POSITIVITY OF THE REAL PART OF THE FORWARD … PHYS. REV. D 97, 014011 (2018) Z ξ ξ dσðξ0Þ ξ0 þ ξ IðξÞ ≥ dξ0 The improved version of (15) is then π dξ0 ln ξ0 − ξ Z ξ0 2 ξ Z 2ξ 0 0 0 1 ξ 0 fðξÞ ≥ fð0Þþ dξ σðξ Þ ξ dσðξ Þ 2ξ0 Re 02 2 ≥ dξ0 π μ ξ − ξ π dξ0 ξ ξ0 ξ ξ þ ξ 2ξ − σðξ Þ 0 þmax 1 ½σðξÞ − σðξ Þ: 2ξ0 0 ln ξ0≤ξ1≤ξ 1 ¼ ½σðξÞ − σðξ Þ: ð Þ π ξ0 − ξ π π 0 14 ð19Þ This proves that, because of (12), IðξÞ increases without If, for example, σðξÞ saturates the Froissart-Martin bound, bound as ξ → ∞.
Load more

Recommended publications
  • Behaviour of Total and Elastic Cross-Sections at Very High Energies
    CERN-TH.7437/94 9 OCR Output CERN—TH-7437-94 BEHAVIOUR OF TOTAL AND ELASTIC CROSS-SECTIONS AT VERY HIGH ENERGIES Tai '1`sun WU Gordon McKay Laboratory, Harvard University, Cambridge, MA 02138, USA and Theoretical Physics Division, CERN CH - 1211 Geneva 23 CERN-TH.7437/94 September 1994 BEHAVIOR OF TOTAL AND ELASTIC CROSS SECTIONS AT VERY HIGH ENERGIES TAI TSUN WU Gordon McKay Laboratory Harvard University Cambridge, MA 02138, USA, and Theoretical Physics Division, CERM Geneva, Switzerland 1. Introduction In this talk, I would like to present an overview of the original theoretical prediction of the increasing total cross section on the basis of gauge quantum field theory, phenomeno logical predictions from this theoretical understanding, comparison with later experimental data, and expected future data from HER.A. The discussion will be limited to elastic scattering, since it is the simplest scattering process. Through the optical theorem, the total cross section—which gives the overall strength of the scattering process———is proportional to the imaginary part of the elastic scattering amplitude in the forward direction. Therefore, the theoretical understanding of elastic scattering is often of primary importance. Some of these developments can be found in an excellent book by Herbert Fried, the organizer of this workshop: Herbert M. Fried, Fhnctional Methods and Eikonal Models, Editions Frontieres (1990). A few years earlier, Hung Cheng and I also wrote a book on this subject: Hung Cheng and Tai Tsun Wu, Expanding Protons: Scattering at High Energies, The MIT Press (1987). A recent topic of current interest, of course not covered in either of these books which are a few years old, is the data from the electron-proton colliding accelerator HQERA at DESY, Hamburg, Germany.
    [Show full text]
  • Scientific and Related Works of Chen Ning Yang
    Scientific and Related Works of Chen Ning Yang [42a] C. N. Yang. Group Theory and the Vibration of Polyatomic Molecules. B.Sc. thesis, National Southwest Associated University (1942). [44a] C. N. Yang. On the Uniqueness of Young's Differentials. Bull. Amer. Math. Soc. 50, 373 (1944). [44b] C. N. Yang. Variation of Interaction Energy with Change of Lattice Constants and Change of Degree of Order. Chinese J. of Phys. 5, 138 (1944). [44c] C. N. Yang. Investigations in the Statistical Theory of Superlattices. M.Sc. thesis, National Tsing Hua University (1944). [45a] C. N. Yang. A Generalization of the Quasi-Chemical Method in the Statistical Theory of Superlattices. J. Chem. Phys. 13, 66 (1945). [45b] C. N. Yang. The Critical Temperature and Discontinuity of Specific Heat of a Superlattice. Chinese J. Phys. 6, 59 (1945). [46a] James Alexander, Geoffrey Chew, Walter Salove, Chen Yang. Translation of the 1933 Pauli article in Handbuch der Physik, volume 14, Part II; Chapter 2, Section B. [47a] C. N. Yang. On Quantized Space-Time. Phys. Rev. 72, 874 (1947). [47b] C. N. Yang and Y. Y. Li. General Theory of the Quasi-Chemical Method in the Statistical Theory of Superlattices. Chinese J. Phys. 7, 59 (1947). [48a] C. N. Yang. On the Angular Distribution in Nuclear Reactions and Coincidence Measurements. Phys. Rev. 74, 764 (1948). 2 [48b] S. K. Allison, H. V. Argo, W. R. Arnold, L. del Rosario, H. A. Wilcox and C. N. Yang. Measurement of Short Range Nuclear Recoils from Disintegrations of the Light Elements. Phys. Rev. 74, 1233 (1948). [48c] C.
    [Show full text]
  • Table of Contents (Print)
    PERIODICALS PHYSICAL REVIEW D Postmaster send address changes to: For editorial and subscription correspondence, American Institute of Physics please see inside front cover 500 Sunnyside Boulevard „ISSN: 0556-2821… Woodbury, NY 11797-2999 THIRD SERIES, VOLUME 56, NUMBER 11 CONTENTS 1 DECEMBER 1997 RAPID COMMUNICATIONS Can the supersymmetric flavor problem be solved by decoupling? ....................................... R6733 Nima Arkani-Hamed and Hitoshi Murayama Phenomenology of new baryons with charm and strangeness ........................................... R6738 George Chiladze and Adam F. Falk ARTICLES Studies of gauge boson pair production and trilinear couplings .......................................... 6742 S. Abachi et al. ~D0 Collaboration! New singularities in nonrelativistic coupled channel scattering. I. Second order ............................ 6779 N. N. Khuri and Tai Tsun Wu New singularities in nonrelativistic coupled channel scattering. II. Fourth order ............................ 6785 N. N. Khuri and Tai Tsun Wu Improving the signal-to-noise ratio in lattice gauge theories ............................................ 6798 Kurt Langfeld, Hugo Reinhardt, and Oliver Tennert Lattice artifacts in the non-Abelian Debye screening mass in one-loop order ............................... 6804 P. Kaste and H. J. Rothe Disorder parameter for dual superconductivity in gauge theories ......................................... 6816 A. Di Giacomo and G. Paffuti Remarks on Abelian dominance ..................................................................
    [Show full text]
  • Abstracts from Physical Review D (Print)
    PHYSICAL REVIEW C VOLUME 56, NUMBER 6 DECEMBER 1997 Selected Abstracts from Physical Review D Abstracts of papers published in Physical Review D which may be of interest to our readers are printed here. Solutions to the solar neutrino anomaly. Naoya Hata, Institute for chusetts 02138-2901 and Theoretical Physics Division, CERN, CH- Advanced Study, Princeton, New Jersey 08540; Paul Langacker, 1211 Geneva 23, Switzerland. ~Received 7 May 1997! Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104. ~Received 2 June 1997! New and surprising singularities are found in the forward scatter- ing amplitude for nonrelativistic potential scattering with coupled We present an updated analysis of astrophysical solutions, two- channels. In the simplest case of two coupled channels, these sin- flavor MSW solutions, and vacuum oscillation solutions to the solar gularities appear when the energy difference between the two chan- neutrino anomaly. The recent results of each of the five solar neu- nels is larger than the inverse range of the potential. They are simi- trino experiments are incorporated, including both the zenith angle lar to singularities recently discovered by one of us for potential ~day-night! and spectral information from the Kamiokande experi- scattering on R3 ^ S1. ment, and the preliminary super-Kamiokande results. New theoret- @S0556-2821~97!03923-4#@Phys. Rev. D 56, 6779 ~1997!# ical developments include the use of the most recent Bahcall- Pinsonneault flux predictions ~and uncertainties! and density and production profiles, the radiative corrections to the neutrino- electron scattering cross section, and new constraints on the Ga absorption cross section inferred from the gallium source experi- New singularities in nonrelativistic coupled channel scattering.
    [Show full text]
  • Quantum Electrodynamics at High Energies*
    SLAC-PUB-956 W9 September 1971 QUANTUM ELECTRODYNAMICS AT HIGH ENERGIES* Hung Cheng**t Stanford Linear Accelerator Center Stanford University, Stanford, California 94305 Tai Tsun Wu Gordon McKay Laboratory Harvard University Cambridge, Massachusetts 02138 (Reported by Hung Cheng) To be presented at the 1971 International Symposium on Electron and Photon Interactions at High Energies, Cornell University, Ithaca, New York, August 23-27, 1971. *Work supported in part by the U. S. Atomic Energy Commission **Work supported in part by the National Science Foundation TPermanent address: Dept. of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. 1. INTRODUCTION Over the past four years, considerable efforts have been devoted to quantum electrodynamics at high energies D As a result of such intensive investigations, we have accumulated not only a wealth of knowledge on the interaction between electrons and photons at high energies, but also much basic understanding on the behavior of a high-energy particle in general. Today I would like to report on some of the most interesting developments here. The results I shall give are therefore of two distinct kinds: (i) those which are applicable to electrons and photons only; (ii) those which are applicable to hadrons as well. The first kind includes most of the computational results on asymptotic Feynman amplitudes e To give some examples, we have now in our possession the high-energy limit of the total and the differential cross sections for (1) the Delbrlick scattering process; (2) the photon-photon scattering process; (3) pair-creation process in electron-electron scattering or electron-positron scattering. Of these quantities, the pair-creation cross sections are already relevant to colliding beam experiments, as reported by Dr.
    [Show full text]
  • Impact Picture for the Analyzing Power a N in Very Forward Pp Elastic
    Impact picture for the analyzing power a N in very forward p p elastic scattering The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Bourrely, Claude, Jacques Soffer, and Tai Tsun Wu. 2007. “Impact Picture for the Analyzing powerANin Very Forwardppelastic Scattering.” Physical Review D 76 (5). https://doi.org/10.1103/ physrevd.76.053002. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:41555830 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA CPT-P27-2007 Impact picture for the analyzing power AN in very forward pp elastic scattering Claude Bourrely∗ Centre de Physique Th´eorique†, CNRS Luminy case 907, F-13288 Marseille Cedex 09, France Jacques Soffer‡ Department of Physics, Temple University, Philadelphia, PA 19122-6082, USA Tai Tsun Wu§ Harvard University, Cambridge, MA 02138, USA and Theoretical Physics Division, CERN, 1211 Geneva 23, Switzerland In the framework of the impact picture we compute the analyzing power AN for pp elastic scattering at high energy and in the very forward direction. We consider the full set of Coulomb amplitudes and show that the interference between the hadronic non-flip amplitude and the single-flip Coulomb amplitude is sufficient to obtain a good agreement with the present experimental data. This leads us to conclude that the single-flip hadronic amplitude is small in this low momentum transfer region and it strongly suggests that this process can be used as an absolute polarimeter at the BNL-RHIC pp collider.
    [Show full text]
  • Radiative Processes in Gauge Theories
    •247 RADIATIVE PROCESSES IN GAUGE THEORIES CALKUL Collaboration P.A.-Berends*, D. Danckaert^ , P. De Causmaecker^"', R. Gascmans^'^ R. Kleiss3 , W. Troost*'3 , and Tai Tsun WH c'4. a Instituut-Lorentz, University of Leiden, Leiden, The Netherlands V Instituut voor Theoretische Fysica, University of Leuven,B-3030 Leuven,Belgium c Gordon McKay Laboratory, Harvard University, Cambridge, Mass., U.S.A. (presented by R. Gastmans) "ABSTRACT- It is shown how the introduction of explicit polarization vectors of the radiated gauge particles leads to great simplifications in the calculation of bremsStrahlung processes at high energies. * Work supported in part by NATO Research Grant No. RG 079.80. '•. ' Navorser, I.I.K.W., Belgium. 2 Onderzoeksleider, N.F.W.O., Belgium. 3 Bevoegdverklaard navorser, N.F.W.O., Belgium. 4 " ' Work supported in part by the United States Department of Energy under Contract No. DE-AS02-ER03227. •248 I. DTTRODPCTIOK Bremsstrahlung processes play an important role in present-day high energy physics. Reactions like e e e e y and e e y y y are vital to precision tests of QED and to the determination o£ electroweak interfe- rence effects. Also, QCD processes lilce e+e~ 3 jets, 4 jets,... get con- tributions from subprocesses in which one or more gluons are radiated. In the framework of perturbative quantum field theory, there is no fundamental problem associated with the evaluation of bremsstrahlung cross sections. In practice, however, the calculations turn out to be very lengthy when one uses the standard methods. Generally, very cumbersome and untrans- parent expressions result, unless one spends an enormous effort on simpli- fying the formulae.
    [Show full text]
  • Expanding Protons Seen by HERA
    Centre de Physique Th´eorique∗ - CNRS - Luminy, Case 907 F-13288 Marseille Cedex 9 - France EXPANDING PROTONS SEEN BY HERA Claude BOURRELY, Jacques SOFFER and Tai Tsun WU1,2 Abstract We show that the rising total photoproduction cross section recently ob- served at HERA is entirely consistant with the impact-picture in the theory of expanding protons which was proposed more than twenty years ago. More accurate data, which is expected to be forthcoming soon, will give this pre- diction a stringent test. Key-Words : Total photon cross section, impact-picture. Number of figures : 2 arXiv:hep-ph/9409346v1 19 Sep 1994 August 1994 CPT-94/P.3060 CERN-TH/7387/94 anonymous ftp or gopher: cpt.univ-mrs.fr ∗ Unit´ePropre de Recherche 7061 1 CERN - Geneva, Switzerland and Gordon McKay Laboratory, Harvard University, Cambridge, MA 02138, U.S.A. 2 Work supported in part by the US Department of Energy under Grant N◦. DE-FG02- 84ER40158 and the Joint Service Electronics Program under Grant N00014-89-J-1023. Recently at HERA, the H1 and ZEUS detectors have measured the photo- production total cross section at an average γp center of mass energy of 180 GeV [1,2]. They confirm the previous and less accurate result of ZEUS[3] and indicate that this total cross section is rising. This rise has caused a lot of excitement and vastly different rates of increase have been proposed[4−9] which are based either on minijet contributions or on Regge - type analyses. In this letter we will present a very simple approach to this increasing γp total cross section.
    [Show full text]
  • 1999 American Physical Society Prizes and Awards
    People 1999 American Physical Society Prizes and Awards Among the 1999 American Physical Society •The Nicholson Medal to Vitaly Ginzburg of oreaux of Los Alamos, "for extensive contribu­ Prizes and Awards are: the Russian Academy of Sciences, "for coura­ tions to precision measurements science, •The Hans A Bethe Prize to Edwin Salpeter geously supporting democratic reforms in the especially searches for a permanent electric of Cornell, "for wide-ranging contributions to former Soviet Union, and for leading the Soviet dipole moment of the neutron and atoms, nuclear and atomic physics and astrophysics, scientific community in humane directions". measurements of atomic parity violation, and including the triple-alpha reaction, electron •The Lars Onsager Prize to C N Yang of SUNY, tests of spatial symmetries and quantum screening of nuclear reactions, charged-cur- Stony Brook, "for fundamental contributions to mechanics, including observation of the vac­ rent emission of neutrinos, and the form of the statistical mechanics and the theory of quan­ uum Casimir Effect". stellar initial mass function". tum fluids, including: the circle theorem, •The J J Sakurai Prize to Mikhail Shifman •The Joseph A Burton Forum Award to Free­ off-diagonal long-range order and flux quanti­ and Arkady Vainshtein of Minnesota and man J Dyson of Princeton's Institute for zation, Bose-Einstein condensation, and one- Valentine Zakharov of Michigan, "for funda­ Advanced Studies, "for his thoughtful, elegant and two-dimensional statistical mechanical mental contributions to the understanding of and widely published writings regarding the models". non-perturbative QCD, non-leptonic weak impact of diverse science and technology •The George E Pake Prize to H B G Casimir decays, and the analytic properties of super- developments on critical societal issues and of Philips, "for excellence as a leader of indus­ symmetric gauge theories".
    [Show full text]
  • Rahlung in the Deep Quantum Regime
    BEAMSTRAHLUNG IN THE DEEP QUANTUM REGIME I M. Jacob and Tai Tsun Wu I Abstract Electron—positron linear colliders working in the multi—TeV range cannot achieve the very high luminosities which are required, without bunch densities which imply an abundant bremsstrahlung. We discuss this radiation in the deep quantum regime, where such machines are likely to operate. Bringing radiation losses to a tolerable level is an interesting challenge to the design of such linear colliders. At present there is much interest in electron—positron linear The question of electron radiation in a strong field has a long colliders which could operate in the TeV and multi—TeV ranges. history. One may start with the seminal work of Schwinger [7], While no design can yet be proposed for such machines, followed by extensive studies of synchrotron radiation and more extensive studies being carried out at CERN and at SLAC in recent calculations [8,9]. The topical nature of the problem stems particular should lead to interesting developments [1]. The from the fact that the parameter I", well known in synchrotron energy range covered by such machines should open up radiation, and which gives the ratio between the typical radiation fascinating perspectives [2]. While a great deal of physics should energy and the beam energy in the classical case, may become probably be learned first with proton—proton colliders, the much larger than 1. One has relative clarity of the event structure in e+e— collisions should be 2 an invaluable asset for detailed studies [2]. r = L . (2) mpc However, there is no point in reaching very high energy if the luminosity is not high enough.
    [Show full text]
  • Transverse Momentum Distribution of the Z Produced at the Large Hadron Collider and Related Phenomena
    Transverse momentum distribution of the Z produced at the Large Hadron Collider and related phenomena The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Gastmans, R., Sau Lan Wu, and Tai Tsun Wu. 2010. “Transverse Momentum Distribution of the Z Produced at the Large Hadron Collider and Related Phenomena.” Physics Letters B 693 (4) (October): 452–455. doi:10.1016/j.physletb.2010.08.075. Published Version doi:10.1016/j.physletb.2010.08.075 Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:26516680 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#OAP Transverse Momentum Distribution of the Z Produced at the Large Hadron Collider and Related Phenomena R. Gastmans¤,1 Sau Lan Wuy,2 and Tai Tsun Wu3, 4 1Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium 2Department of Physics, University of Wisconsin, Madison WI 53706, USA 3Gordon McKay Laboratory, Harvard University, Cambridge MA 02138, USA 4Theory Division, CERN, CH-1211 Geneva 23, Switzerland From the recent theoretical result on the production of the Higgs boson at the large Hadron Collider, it follows that other particles will also be produced with small transverse momentum, of the order of 1 GeV=c. The leptonic decay mode of the Z is especially suited for a ¯rst observation of this phenomenon.
    [Show full text]
  • Onwisconsin Summer 2019
    FOR UNIVERSITY OF WISCONSIN–MADISON ALUMNAE AND FRIENDS SUMMER 2019 Our Monumental Women How Badger alumnae shape the world Vision Next-generation Badger stars? Inspired young fans greet the UW women’s hockey team on its return from winning the national championship in March. It was the team’s fifth title since 2006. Photo by Bryce Richter On Wisconsin 3 Contents Volume 120, Number 2 UW women’s basketball was popular from the get-go. See page 32. UW ARCHIVES 24/2/2, 48441-C DEPARTMENTS 2 Vision 7 Communications 9 First Person Women’s Issue OnCampus 11 News FEATURES 13 Bygone Ladies’ Halls 14 Calculation Women in 22 A Pioneer’s Perseverance Leadership Born in war-torn Hong Kong to a prominent but absent father 17 Conversation #MeToo in and his sixth concubine, UW physicist Sau Lan Wu has over- Science come stunning obstacles on her path to three major scientific 18 Exhibition Swoon discoveries. By Preston Schmitt ’14 20 Contender Terry Gawlik on Title IX 28 Leaving Madison in a Model T An adventurous summer road trip turned the UW’s first female engineering grad, Emily Hahn ’26, into one of America’s most storied travel writers. By Sandra Knisely Barnidge ’09, MA’13 OnAlumni 32 The Women and the Goat Soon after basketball was invented, women at the UW picked 49 News up the sport — even before the men. Intramural teams quickly 50 Tradition Women’s Studies grew in popularity and competed for an unusual (and some- 51 Class Notes times bleating) trophy. By Tim Brady ’79 59 Diversions 60 Conversation Steadfast Activist 36 A Driving Force 61 Exhibition Southern Physicist Fatima Ebrahimi PhD’03 believes that if efforts to Exposures control nuclear fusion pay off, it will provide unlimited energy MILLER JEFF 62 Honor Roll Florence Bascom that will change the world.
    [Show full text]