We propose a method to determine the running of $\alpha_{QED}$ from the
measurement of small-angle Bhabha scattering. The method is suited to high
statistics experiments at $e^{+} e^{-}$ colliders, which are equipped with
luminometers in the appropriate angular region. We present a new simulation
code predicting small-angle Bhabha scattering. A detailed description of this
idea can be found in A.B. Arbuzov, D. Haidt, C. Matteuzzi, M. Paganoni and L.
Trentadue, The running of the electromagnetic coupling alpha in small-angle
Bhabha scattering, Eur. Phys. J. C34, 267 (2004).Comment: 4 pages, talk given at the International Conference on Linear
  Colliders - LCWS 2004, Paris, Carre' des Sciences, April 19-23, 200

Trentadue, Luca

English

arXiv

We propose a method to determine the running of $\alpha_{QED}$ from the measurement of small-angle Bhabha scattering. The method is suited to high statistics experiments at $e^{+} e^{-}$ colliders, which are equipped with luminometers in the appropriate angular region. We present a new simulation code predicting small-angle Bhabha scattering. A detailed description of this idea can be found in A.B. Arbuzov, D. Haidt, C. Matteuzzi, M. Paganoni and L. Trentadue, The running of the electromagnetic coupling alpha in small-angle Bhabha scattering, Eur. Phys. J. C34, 267 (2004).We propose a method to determine the running of $\alpha_{QED}$ from the measurement of small-angle Bhabha scattering. The method is suited to high statistics experiments at $e^{+} e^{-}$ colliders, which are equipped with luminometers in the appropriate angular region. We present a new simulation code predicting small-angle Bhabha scattering. A detailed description of this idea can be found in A.B. Arbuzov, D. Haidt, C. Matteuzzi, M. Paganoni and L. Trentadue, The running of the electromagnetic coupling alpha in small-angle Bhabha scattering, Eur. Phys. J. C34, 267 (2004).We propose a method to determine the running of $\alpha_{QED}$ from the measurement of small-angle Bhabha scattering. The method is suited to high statistics experiments at $e^{+} e^{-}$ colliders, which are equipped with luminometers in the appropriate angular region. We present a new simulation code predicting small-angle Bhabha scattering. A detailed description of this idea can be found in A.B. Arbuzov, D. Haidt, C. Matteuzzi, M. Paganoni and L. Trentadue, The running of the electromagnetic coupling alpha in small-angle Bhabha scattering, Eur. Phys. J. C34, 267 (2004).We propose a method to determine the running of $\alpha_{QED}$ from the measurement of small-angle Bhabha scattering. The method is suited to high statistics experiments at $e^{+} e^{-}$ colliders, which are equipped with luminometers in the appropriate angular region. We present a new simulation code predicting small-angle Bhabha scattering. A detailed description of this idea can be found in A.B. Arbuzov, D. Haidt, C. Matteuzzi, M. Paganoni and L. Trentadue, The running of the electromagnetic coupling alpha in small-angle Bhabha scattering, Eur. Phys. J. C34, 267 (2004)

CERN Document Server

arXiv:hep-ph/0608076v1  7 Aug 2006MEASURING THE RUNNING OF THE ELECTROMAGNETICCOUPLING ALPHA IN SMALL ANGLE BHABHASCATTERINGaLUCA TRENTADUEbDepartment of Physics, CERN Theory Division, 1211 Geneva 23, SwitzerlandandINFN, Gruppo Collegato di Parma, I-43100 Parma, ItalyWe propose a method to determine the running of αQED from the measurementof small-angle Bhabha scattering. The method is suited to high statistics experi-ments at e+e− colliders, which are equipped with luminometers in the appropriateangular region. We present a new simulation code predicting small-angle Bhabhascattering. A detailed description of this idea can be found in ref.[1]1 IntroductionThe electroweak Standard Model SU(2) ⊗ U(1) contains Quantum Electro-dynamics (QED) as a constitutive part. The running of the electromagneticcoupling α is determined by the theory asα(q2) =α(0)1−∆α(q2) , (1)where α(0)=α0 is the Sommerfeld fine structure constant, which has beenmeasured to a precision of 3.7×10−9 2; ∆α(q2) positive arises from loop con-tributions to the photon propagator. The numerical prediction of electroweakobservables involves the knowledge of α(q2), usually for q2 6= 0. For instance,the knowledge of α(m2Z) is relevant to the evaluation of quantities measuredby the LEP experiments. This is achieved by evolving α from q2 =0 up to theZ-mass scale q2 = m2Z . The evolution expressed by the quantity ∆α receivescontributions from leptons, hadrons and the gauge bosons. The hadronic con-tribution to the vacuum polarization, which cannot be calculated from firstprinciples, is estimated with the help of a dispersion integral and evaluated 3by using total cross section measurements of e+e− → hadrons at low energies.Therefore, any evolved value α(q2) particularly for |q2| > 4m2pi, is affectedby uncertainties originating from hadronic contributions. The uncertainty onα(m2Z)−1 induced by these data is as small as ±0.09 3; nevertheless it turnedaWork done in collaboration with A.Arbuzov, D.Haidt, C. Matteuzzi and M. PaganonibOn leave of absence from Dipartimento di Fisica, Universita´ di Parma, 43100, Parma,Italy1out 4 that this limits the accurate prediction of electroweak quantities withinthe Standard Model, particularly for the prediction of the Higgs mass.While waiting for improved measurements from BEPC, VEPP-4M andDAFNE as input to the dispersion integral, intense efforts are made to im-prove on estimating the hadronic shift ∆αhad, as for instance5-8, and to findalternative ways of measuring α itself. Attempts have been made to measureα(q2) directly, using data at various energies, such as measuring the ratio ofe+e−γ/e+e− 9 or more directly the angular distribution of Bhabha scattering10. In this article the running of α is studied using small-angle Bhabha scatter-ing. This process provides unique information on the QED coupling constantα at low space-like momentum transfer t = −|q2|, wheret = −12s (1− cos θ) (2)is related to the total invariant energy√s and to the scattering angle θ of thefinal-state electron. The small-angle region has the virtue of giving access tovalues of α(t) without being affected by weak contributions. The cross sectioncan be theoretically calculated with a precision at the per mille level. It isdominated by the photonic t channel exchange and the non-QED contributionshave been computed11 and are of the order of 10−4; in particular, contributionsfrom boxes with two weak bosons are safely negligible.In general, the Bhabha cross section is computed from the entire set ofgauge-invariant amplitudes in both the s and t channels. Consequently, twoinvariant scales s and t govern the process. The different amplitudes are func-tions of both s and t and also the QED coupling α appears as α(s) resp. α(t)12.However, the restriction of Bhabha scattering to the kinematic regime of smallangles results in a considerable simplification, since the s channel then givesonly a negligible contribution, as is quantitatively demonstrated 1. Thus, themeasurement of the angular distribution allows us indeed to verify directly therunning of the coupling α(t). For the actual calculations, θ ≫ me/Ebeam andEbeam ≫ me must be satisfied. Obviously, in order to manifest the running,the experimental precision must be adequate. This idea can be realized byhigh-statistics experiments at e+e− colliders equipped with finely segmentedluminometers, in particular by the LEP experiments, given their large eventsamples, by SLC and future Linear Colliders. The relevant luminometers coverthe t-range from a few GeV2 to order 100 GeV2. The analysis follows closelythe procedure adopted in the luminosity measurement, which is described indetail 13, and elaborates on the additional aspect related to the measurementof a differential quantity. To this aim the luminosity detector must have a suffi-ciently large angular acceptance and adequate fine segmentation. The variable2t (eq. 2) is reconstructed on an event-by-event basis. The cross section for theprocess e+e− → e+e− can be conveniently decomposed into three factors :dσdt=dσ0dt(α(t)α(0))2(1 + ∆r(t)). (3)All three factors are predicted to a precision of 0.1% or better. The firstfactor on the right-hand side refers to the effective Bhabha Born cross section,including soft and virtual photons11, which is precisely known, and accounts forthe strongest dependence on t. The vacuum-polarization effect in the leadingphoton t channel exchange is incorporated in the running of α and gives rise tothe squared factor in eq. 3. The third factor, ∆r(t), collects all the remainingreal (in particular collinear) and virtual radiative effects not incorporated in therunning of α. The experimental data after correction for detector effects haveto be compared with eq. 3. The t dependence is rather steep, thus migrationeffects may need attention.This goal is achieved by using a newly developed program based on thealready existing semianalytical code NLLBHA 11,14. A complete bibliography ofthis code called SAMBHA is given in ref.[1]. It is convenient to confront thefully corrected measured cross section with the Bhabha cross section, includ-ing radiative corrections in the factorized form given by eq. 3. The physicalcross section is infrared safe 11. This decomposition is neither unique nor dic-tated by a compelling physical reason; rather it allows the separation of thedifferent sources of t dependence in a transparent way without introducingany additional theoretical uncertainty. The various factors as well as the rela-tive accuracy of the QED corrections ( see for example refs [15]-[16] ) and theMonteCarlo tool to implement them are discussed in ref.[1].2 ConclusionsA novel approach to access directly and to measure the running of α in thespace-like region is proposed. It consists in analysing small-angle Bhabha scat-tering. Depending on the particular angular detector coverage and on the en-ergy of the beams, it allows a sizeable range of the t variable to be covered.The feasibility of the method has been put in evidence by the use of a newtool, SAMBHA , to calculate the small-angle Bhabha differential cross sectionwith a theoretical accuracy of better than 0.1%. The information obtainedin the t channel can be compared with the existing results of the s channelmeasurements. This represents a complementary approach, which is direct,transparent and based only on QED interactions and furthermore free of someof the drawbacks inherent in the s channel methods. The method outlined can3be readily applied to the experiments at LEP and SLC. It can also be exploitedby future e+e− colliders as well as by existing lower energy machines. As anexample the q2 values [GeV 2] as the ECenter of Mass energy varies between 0and 103 GeV within a range of acceptance for the emitted radiation betweenthe angles from 1.8 to 7.2 degrees range between 0 and 4 · 103 GeV 2.An extremely precise measurement of the loop contributions to the QEDrunning coupling ∆α(t) for small values of t may be envisaged with a dedicatedluminometer even at low machine energies.References1. A. B. Arbuzov, D. Haidt, C. Matteuzzi, M. Paganoni and L. Trentadue,Eur. Phys. J. C 34, 267 (2004) [arXiv:hep-ph/0402211].2. D.E. Groom et al.: Eur. Phys. J. C15 (2000) 13. S. Eidelman and F. Jegerlehner: Z. Phys. C67 (1995) 6024. K. Hagiwara, D. Haidt, S. Matsumoto and C.S. Kim: Z. Phys. C64(1994) 559;(ibidem)C68 (1995) 353;K. Hagiwara, D. Haidt and S. Matsumoto: Eur. Phys. J. C2 (1998) 955. F. Jegerlehner: hep-ph/03081176. M. Davier and A. Ho¨cker: Phys. Lett. B435 (1998) 427;M. Davier, S. Eidelman, A. Ho¨cker and Z. Zhang: Eur. Phys. J. C27(2003) 4977. D. Karlen and H. Burkhardt: Eur. Phys. J. C22 (2001) 39; hep-ex/0105065 (2001)8. A.A. Pankov and N. Paver, Eur. Phys. J. C29 (2003) 3139. TOPAZ Collaboration, I. Levine et al.: Phys. Rev. Lett. 78 (1997) 42410. L3 Collaboration, M. Acciarri et al.: Phys. Lett. B476 (2000) 4811. A.B. Arbuzov, V.S. Fadin, E.A. Kuraev, L.N. Lipatov, N.P. Merenkovand L. Trentadue, Small-angle electron-positron scattering with a permille accuracy, Nucl. Phys. B485 (1997) 457.12. S.J. Brodsky, G.P. Lepage and P.B.Mackenzie: Phys. Rev. D28 (1983)22813. LEP Working Group (Convenors S. Jadach and O. Nicrosini): EventGeneratorsfor Bhabha scattering, CERN Report 96-01, p. 22914. CERN Report 96-01: NLLBHA short write-up15. E.A. Kuraev and V.S. Fadin: Sov. J. Nucl. Phys. 41 (1985) 466.16. O. Nicrosini and L. Trentadue: Phys. Lett. B196 (1987) 551; Z. Phys.C39 (1988) 4794

Measuring the Running of the Electromagnetic Coupling Alpha in Small Angle Bhabha Scattering

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Measuring the Running of the Electromagnetic Coupling Alpha in Small Angle Bhabha Scattering

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