Measurement of Muon Capture on the Proton to 1% Precision and Determination of the Pseudoscalar Coupling g_P
V. A. Andreev, T. I. Banks, R. M. Carey, T. A. Case, S. M. Clayton, K. M. Crowe, J. Deutsch, J. Egger, S. J. Freedman, V. A. Ganzha, T. Gorringe, F. E. Gray, D. W. Hertzog, M. Hildebrandt, P. Kammel, B. Kiburg, S. Knaack, P. A. Kravtsov, A. G. Krivshich, B. Lauss, K. R. Lynch, E. M. Maev, O. E. Maev, F. Mulhauser, C. Petitjean, G. E. Petrov, R. Prieels, G. N. Schapkin, G. G. Semenchuk, M. A. Soroka, V. Tishchenko, A. A. Vasilyev, A. A. Vorobyov, M. E. Vznuzdaev, P. Winter
MMeasurement of Muon Capture on the Proton to 1% Precision andDetermination of the Pseudoscalar Coupling g P V.A. Andreev, T.I. Banks, R.M. Carey, T.A. Case, S.M. Clayton, K.M. Crowe ∗ , J. Deutsch ∗ , J. Egger, S.J. Freedman ∗ , V.A. Ganzha, T. Gorringe, F.E. Gray,
8, 2
D.W. Hertzog,
4, 9
M. Hildebrandt, P. Kammel,
4, 9
B. Kiburg,
4, 9
S. Knaack, P.A. Kravtsov, A.G. Krivshich, B. Lauss, K.R. Lynch, E.M. Maev, O.E. Maev, F. Mulhauser,
4, 6
C. Petitjean, G.E. Petrov, R. Prieels, G.N. Schapkin, G.G. Semenchuk, M.A. Soroka, V. Tishchenko, A.A. Vasilyev, A.A. Vorobyov, M.E. Vznuzdaev, and P. Winter
4, 9 (MuCap Collaboration) Petersburg Nuclear Physics Institute, Gatchina 188350, Russia Department of Physics, University of California, Berkeley, and LBNL, Berkeley, CA 94720, USA Department of Physics, Boston University, Boston, MA 02215, USA Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Institute of Nuclear Physics, Universit´e Catholique de Louvain, B-1348, Louvain-la-Neuve, Belgium Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506, USA Department of Physics and Computational Science, Regis University, Denver, CO 80221, USA Department of Physics, University of Washington, Seattle, WA 98195, USA (Dated: October 29, 2018)The MuCap experiment at the Paul Scherrer Institute has measured the rate Λ S of muon capturefrom the singlet state of the muonic hydrogen atom to a precision of 1 %. A muon beam wasstopped in a time projection chamber filled with 10-bar, ultrapure hydrogen gas. Cylindrical wirechambers and a segmented scintillator barrel detected electrons from muon decay. Λ S is determinedfrom the difference between the µ − disappearance rate in hydrogen and the free muon decay rate.The result is based on the analysis of 1 . × µ − decays, from which we extract the capturerate Λ S = (714 . ± . stat ± . syst ) s − and derive the proton’s pseudoscalar coupling g P ( q = − . m µ ) = 8 . ± . PACS numbers: 23.40.-s, 24.80.+y, 13.60.-r, 14.20.Dh, 11.40.Ha, 29.40.Gx
We report a measurement of the rate Λ S of ordinarymuon capture (OMC), µ − + p → n + ν µ , (1)from the singlet state of the muonic hydrogen atom. Theanalysis uses the complete data set of the MuCap experi-ment, with significantly smaller systematic and statisticaluncertainties compared to our earlier publication [1].For the low momentum transfer q = − . m µ in pro-cess (1), the standard model electroweak interaction re-duces to an effective Fermi interaction between the lep-tonic and hadronic weak currents. While the leptoniccurrent has a simple γ µ (1 − γ ) structure, the hadroniccurrent between nucleon states is modified by QCD, asexpressed in a model-independent way by the introduc-tion of form factors. Since second-class currents are sup-pressed, muon capture on the proton involves g V ( q ) and g M ( q ), the vector and magnetic form factors in the vec-tor current, as well as g A ( q ) and g P ( q ), the axial andpseudoscalar form factors in the axial current [2–4]. Thefirst three are well known and contribute only around0.4% uncertainty to the determination of Λ S [5]. Our ∗ Deceased measurement of Λ S determines g P ≡ g P ( q ), the leastwell known of these form factors.The pseudoscalar term in the axial nucleon current hasplayed a significant role in the understanding of weakand strong interactions. Initial estimates were based onthe concept of a partially conserved axial current, fol-lowed by the recognition of its deeper significance as aconsequence of chiral symmetry and its spontaneous andexplicit breaking [6]. These ideas were foundations forexplaining the generation of hadronic masses and the de-velopment of chiral perturbation theory (ChPT), the ef-fective field theory of low-energy QCD. Based on well-known low-energy constants, g theory P = 8 . ± .
23 (2)was derived within ChPT [2, 7], with good convergence totwo-loop order [8]. Though lattice QCD has advanced tounquenched calculations of g A and g P [9, 10], the preci-sion of the ChPT prediction in Eqn. 2 remains unmatchedand stands to be tested experimentally.Muon capture on hydrogen is the most direct means todetermine g P . Such experiments are complicated by thefact that negative muons stopped in hydrogen form notonly µp atoms, but subsequently ppµ molecules wherethe capture rate differs significantly. Prior to MuCap,the most precise capture rate was measured in liquid hy- a r X i v : . [ nu c l - e x ] J a n detector hit z y x z position from anodes y po s i t i on f r o m d r i ft z position from anodes muon a) PRODUCED BY AN AUTODESK EDUCATIONAL PRODUCTPRODUCED BY AN AUTODESK EDUCATIONAL PRODUCT P R O DUC E D BY A N A U T O D ESK E DUC A T I O N A L P R O DUC T P R O DUC E D BY A N A U T O D ESK E DUC A T I O N A L P R O DUC T eSC ePC1 ePC2 electron c) b) FIG. 1: (color online) Upper panel: (a) Cross-sectional viewof the MuCap detector showing a typical muon stop and decayelectron. Lower panels: Zoomed-in special event topologies.(b) Rare large-angle µ - p scatter event with ∼ − /µ proba-bility. c) Very rare delayed capture on impurity in µO → N ∗ ν with ∼ . × − /µ probability. The interpretation of theevent displays is described in the text. drogen (LH ) [11], where ppµ forms rapidly. The valueof g P extracted under these conditions depends criticallyon the poorly known ortho-to-para ppµ transition rate, λ op [12, 13]. The related, rare radiative muon capture(RMC) process µ − p → nνγ is less sensitive to λ op , butthe first experimental result on g P [14] disagreed withtheory. For a discussion of this puzzling situation andmuonic processes in hydrogen, see [2–4].The MuCap experiment was designed to significantlyreduce the density-dependent formation of ppµ moleculesby employing a gas density of φ ≈ .
01 (relative to LH ).In these conditions about 97% of the muon captures oc-cur in the µp singlet state. The experimental concept issketched in Figure 1(a). A 34 MeV/ c muon beam wasstopped in a time projection chamber (TPC) filled with10-bar, ultrapure hydrogen gas [15]. The TPC was usedto discriminate between muons that stop in the gas andthose that reach wall materials, where capture proceedsmuch faster than in hydrogen. Arriving muons were de-tected by an entrance scintillator ( µ SC) and a propor-tional chamber ( µ PC), and tracked in the TPC. Outgo-ing decay electrons were detected by concentric multi-wire proportional chambers (ePC1 and ePC2) and a seg-mented scintillator barrel (eSC). The decay times werehistogrammed and fit to an exponential. The differencebetween the observed disappearance rate λ µ − and thefree muon decay rate λ µ + [16] is attributed to muon cap-ture, Λ S ≈ λ µ − − λ µ + . The new data reported here were collected during the2006 (R06) and 2007 (R07) running periods in the π E3muon channel at the Paul Scherrer Institute. Propertiesof the new data sets are compared to our published result(R04) [1] in Table I. Besides the 1 . × muon-electronpairs from µ − stops in hydrogen, additional systematicdata included 0 . × µ + decays and µ − data collectedwhen the target gas was doped with elemental impurities(nitrogen, water and argon). TABLE I: Main features of MuCap production runs. Statis-tics of fully reconstructed µ - e pairs, deuterium concentration c D , water concentration c H O determined by humidity sensor(not present in R04), and observed impurity capture yield permuon, Y Z .Quantity R04 R06 R07Statistics 1 . × . × . × c D (ppb) 1440 < < c H O (ppb) · · ·
18. 8.7 Y Z (ppm) 12 6.3 3.4 Although the experimental methodology closely fol-lowed that of our first result, several hardware upgradesimplemented between R04 and R06 led to significantlyenhanced performance. In R06 the TPC was operatedwith about 2.5 times higher gas gain than in R07. Asthis affects critical chamber parameters, the comparisonof the two runs provides an invaluable consistency check.Events with multiple muons in the TPC (pileup) needto be rejected as they distort the extracted disappearancerate. The maximum rate of the dc muon beam employedin R04 was throttled to minimize pileup. In R06 andR07, the loss of events to pileup was largely eliminatedby the introduction of a 25-kV, fast-switching electro-static kicker [17]. The detection of a muon traversingthe µ SC triggered the kicker, which deflected the beamfor a period of 25.6 µ s. The beam extinction factor wasaround 100 and the rate of pileup-free data was threetimes larger in R06/7 than in R04.Another essential change was the greatly improved iso-topic and chemical purity of the TPC gas. When deu-terium is present (concentration c D ), muons can form µd atoms, which, due to a Ramsauer-Townsend mini-mum in the scattering cross section [4], can diffuse out ofthe fiducial volume and distort the disappearance rate.To separate the hydrogen into its isotopic components,a new cryogenic distillation column was installed. Peri-odic gas samples were analyzed externally using atomicmass spectrometry [18]. For the limits on c D listed inTable I, transfer to µd leads to distortions of less than0.74 s − and 0.12 s − for the R06 and R07 run peri-ods, respectively. A higher sensitivity of the atomic massspectrometer was responsible for the improved limit inR07.In the presence of Z > µp to µZ atoms, distorting thedisappearance rate. Extended baking of the TPC andincreased flux and filtering in the continuous gas purifi-cation system [19] led to a fourfold reduced impurity levelcompared to R04. Moreover, the installation of a humid-ity sensor before R06 allowed monitoring of the dominantchemical impurity.Our novel hydrogen TPC was key to the experiment.In the sensitive volume of x × y × z = 15 × ×
28 cm with an applied field of 2 kV/cm, ionization electronsfrom stopping muons drifted down towards the readoutplane with a velocity v y = − . µ s. They were am-plified in a multiwire proportional chamber region with72 anodes perpendicular and 36 strip wires parallel tothe beam. Anode and cathode signals were discriminatedwith three energy thresholds and read out by TDCs in200 ns time intervals. The event display in the center ofFigure 1(a) shows the y - z projection of a typical muonstop in the TPC. The threshold E ≈
15 keV is indi-cated by green pixels. Blue pixels denote the threshold E ≈
55 keV, which was set just below the muon’s Braggpeak. The threshold E ≈
315 keV [red pixels in Figure1(c)] was set to record nuclear recoils from muon captureson impurities. In addition to the primary TDC-basedreadout of the TPC, new 12-bit, 25 MHz flash analog-to-digital converters recorded selectively triggered events.About 30 TB of raw data were processed at the NCSAsupercomputing facility in a multistage procedure. Muonstop candidates were constructed from the µ SC time andTPC track information. Muon pileup events, flagged bythe entrance counters, were rejected. Because the com-bined inefficiency of the entrance counters was less than10 − , the residual pileup distorted the observed muondisappearance rate λ µ − by less than 0.5 s − . Contigu-ous pixel regions in the TPC were then fit to a straightline, as indicated by the black line along the muon tra-jectory in Fig. 1(a). In the case of large angle scattering[Fig. 1(b)] a two-line fit was applied. The muon stop lo-cation (red circle) was identified as the most downstream E pixel. The muon track requirements were optimizedso as to minimize possible distortions to λ µ − while sup-pressing events where the muon could have left the hy-drogen gas. Muons that stopped within a fiducial volume∆ x × ∆ y × ∆ z = 10 . × . × . were accepted.The minimum track length was 3.2 cm, and the maxi-mum fit χ was 2. λ µ − was stable against variation ofthe track length and χ cuts. However, variations in thefiducial volume boundaries produced statistically disal-lowed deviations, for which a systematic uncertainty of3 . − was assigned.Electron tracks were constructed from coincidences be-tween an eSC segment (comprising four photomultipliertubes) and hits in the two ePCs (each requiring an an-ode and at least one cathode plane). In the R06 andR07 run periods, the time and gain stabilities of the eSCwere verified by recording their signals in 8-bit, 450 MHz waveform digitizers. While the TPC gain was insuffi-cient to produce electron tracks with contiguous pixels,a virtual track in the TPC was reconstructed from hitsin the eSC and ePCs, as indicated by the red line inFigure 1(a). A cut of b ≤
120 mm was placed on theimpact parameter b between the muon stop and electronvector. This loose cut significantly reduces backgrounds(c.f. Fig. 3 in [1]) while minimizing distortions of λ µ − introduced by a time-dependent acceptance due to µp diffusion. Although µp atoms diffuse only at the mmscale, changes in λ µ − vs. b were observed. This λ µ − ( b )dependence was used to fixed the single parameter of a µp diffusion model in good agreement with theory [20]. Forthe applied cut, the model was used to determine smallcorrections ( − . ± .
1) s − and ( − . ± .
1) s − for R06and R07, respectively. To check that λ µ − was insensitiveto the electron track definition, we also constructed co-incidences requiring different combinations of anode andcathode planes within the ePCs. This revealed slightlynonstatistical variations in λ µ − , which were fully coveredby a 1.8 s − systematic uncertainty.In extreme cases of example Fig. 1(b), muons scatterthrough large angles, leave the TPC volume, and stop onsurrounding materials. Because of the lower TPC gainduring R07, there were often gaps in the tracks of scat-tered muons, making it difficult to reliably identify theseevents. Moreover, the recoil proton could deposit enoughenergy in the TPC to trigger the E threshold, mimick-ing an acceptable muon stop. However, these events wereunlikely to deposit enough energy at the scattering ver-tex to exceed the E -threshold on neighboring anodes. Inthe analysis of the R06 and R07 data sets, we required atleast two consecutive E anodes at the end of the muontrack.This cut introduced a subtle systematic effect. Elec-trons that traversed the muon’s drifting ionization chargeoccasionally deposited enough additional energy to ele-vate a muon’s E signal above the E threshold. In rareinstances a muon stop with a single E anode was pro-moted to a stop with two neighboring E anodes. Suchevents would pass the µ - p scatter cut described abovewith a decay-time-dependent acceptance and thereforedistort the extracted disappearance rate. Because posi-tive muons are sensitive to the charge interference effectbut do not capture on nuclei, we were able to measure theinduced distortion [21]. The method was supplementedby neutron data collected in 8 large liquid scintillatordetectors: muons scattered into Z > − . ± .
22) s − and( − . ± .
25) s − for R06 and R07, respectively. Thecorrection was sensitive to the E threshold, which wedecreased in R07, suppressing the interference effect.As illustrated in Fig. 1(c), nuclear capture on impu-rities was identified by the presence of an E thresholdsignal in the TPC. This allowed continuous in situ mon-itoring of the yield Y Z of these events. The average val-ues for Y Z over the three data sets are given in Table Iand track well with the humidity sensor readings. Tocalibrate the necessary correction, special runs were con-ducted in which the hydrogen gas was doped with knownamounts of nitrogen or water vapor. The changes in thedisappearance rate and Y Z were measured relative to thepure, undoped hydrogen data. Scaling by the observed Y Z then determined the corrections for residual impuri-ties: ( − . ± .
87) s − and ( − . ± .
93) s − in R06and R07, respectively.To obtain the final muon disappearance rate, themuon stops and electron tracks were first sorted intomuon-electron pairs. The decay time, t ≡ t eSC − t µ SC ,was histogrammed and fit with the function N ( t ) = N wλ µ − e − λ µ − t + B over the range 160 ns < t < w was fixed at 80 ns, while N , B and λ µ − were free parameters. To avoid analysis bias, the exactclock frequency was hidden from the analyzers. After itwas revealed, we obtained λ µ − (R06) = 455 857 . ± . stat ± . syst s − , (3) λ µ − (R07) = 455 853 . ± . stat ± . syst s − . (4)Because the fit χ / DOF = 1 . ± . S -factorprescription [5]. The three-parameter fitting procedurewas complemented by applying a full kinetics fit whichincluded all atomic- and molecular-state effects as well aswater and nitrogen impurities; the result was consistentwithin 0.2 s − .In order to check the consistency of our result, we ex-amined changes in λ µ − with respect to variations in dataselection. The fit start and stop times were varied overa range of several microseconds and the parameters re-mained stable. Only statistical variations were observedwhen the data were sorted chronologically by run num-ber. Since many of the subtle couplings between themuon and electron definitions are geometrical, the ob-served stability of the result with respect to azimuth wasa critical cross-check.Table II summarizes the aforementioned corrections toour λ µ − result as well as the systematic uncertainties.Two additional corrections are required to correctly ex-press λ µ − as: λ µ − = (cid:0) λ µ + + ∆ λ µp (cid:1) + Λ S + ∆Λ ppµ . (5)Here ∆ λ µp is a calculable µp bound-state effect [22, 23],while ∆Λ ppµ accounts for the around 3% of muons thatcapture from molecular states. The latter depends on λ op and λ ppµ and is derived from fits to simulated datagenerated with the precise experimental conditions (gasdensity φ = 0 . ± . λ op =(6 . ± . × [4] and a newly determined value of TABLE II: Applied corrections and systematic errors.Effect Corrections and uncertainties [s − ]R06 R07 Z > − . ± . − . ± . µ - p scatter removal − . ± . − . ± . µp diffusion − . ± . − . ± . µd diffusion ± . ± . ± . ± . ± . ± . ± . ± . λ µ − corr. − . ± . − . ± . µp bound state: ∆ λ µp − . ± . − . ± . ppµ states: ∆Λ ppµ − . ± . − . ± . λ ppµ = (1 . ± . × s − [24], which was measuredby admixing 19 . ± . . ± .
46 s − [5, 16], we determine the singletcapture rates:Λ S (R06) = 717 . ± . stat ± . syst s − , (6)Λ S (R07) = 713 . ± . stat ± . syst s − . (7)We also update slightly our previous publication [1] us-ing the latest values for λ µ + , λ op , and λ ppµ , to obtainΛ S (R04) = 713 . ± . stat ± . syst s − . Accounting forcorrelated systematics among these three data sets, wereport a final, combined resultΛ
MuCap S = 714 . ± . stat ± . syst s − . (8)This new result is in excellent agreement with recent the-ory [25–27]. From the latest calculation [27], we deriveΛ Th S ( g A , g P ) = (712 . ± . ± . × (cid:2) . g A − g PDG A ) − . g P − g Th P ) (cid:3) s − , (9)where all form factors are evaluated at q . Equation (9)quantifies the dependence of the theoretical capture rateon the choice of g P , relative to value g Th P = 8 . g A , relative to the latest g PDG A (0) =1 . ± . g A and radiativecorrections. Setting Λ Th S ( g PDG A , g MuCap P ) to Λ MuCap S gives g MuCap P ( q = − . m µ ) = 8 . ± . ± . , (10)where the two uncertainties arise from the error propaga-tion of Λ MuCap S and Λ Th S , respectively. If we would haveupdated g A (0) to 1.275, as advocated in [28] and sup-ported by recent measurements of the neutron β -decay ) -1 s (10 op l ) m = - . m ( q P g Ex1op l Thop l Ex2op l O M C R M C MuCap Avg
FIG. 2: Extracted values for g P as a function of the poorlyknown molecular transition rate λ op [12, 13, 31]. In con-trast to earlier experiments (OMC [11], RMC [14]), MuCapis rather insensitive to this parameter. asymmetry [29, 30], the g P extracted from MuCap wouldhave increased to 8.34.Figure 2 illustrates the excellent agreement with thetheoretical prediction, Eq. (2), and highlights MuCap’sreduced sensitivity to the molecular parameter λ op . Thisanswers the long-standing challenge of an unambiguousmeasurement of g P , generated by the mutual inconsis-tency of earlier experiments (OMC, RMC) and theirstrong sensitivity to λ op . Corroborating values for g P are obtained in recent analyses [32, 33] of an earlier 0.3%measurement of muon capture on He [34], with uncer-tainties limited by theory. MuCap provides the mostprecise determination of g P in the theoretically clean µp atom and verifies a fundamental prediction of low-energyQCD.We are grateful to the technical staff of the collabo-rating institutions, in particular of the host laboratoryPSI. We thank M. Barnes, G. Wait, and A. Gafarov forthe design and development of the kicker, the Demoncollaboration for providing neutron detectors, the AMSteam at the ETH Z¨urich for the deuterium measure-ments, and A. Adamczak, N. Bondar, D.B. Chitwood,P.T. Debevec, T. Ferguson, J. Govaerts, S. Kizilgul, M.Levchenko, and C.S. ¨Ozben for their contributions. Thiswork was supported in part by the U.S. NSF, the U.S.DOE and CRDF, PSI, the Russian Academy of Sciencesand the Grants of the President of the Russian Federa-tion. NCSA provided essential computing resources. [1] V. A. Andreev et al. (MuCap Collaboration), Phys. Rev.Lett. , 032002 (2007), arXiv:0704.2072. [2] V. Bernard, L. Elouadrhiri, and U.-G. Meissner, J. Phys. G28 , R1 (2002).[3] T. Gorringe and H. W. Fearing, Rev. Mod. Phys. , 31(2004).[4] P. Kammel and K. Kubodera, Annual Review of Nuclearand Particle Science , 327 (2010).[5] J. Beringer et al. (Particle Data Group), Phys. Rev. D86 ,010001 (2012).[6] Y. Nambu, Phys. Rev. Lett. , 380 (1960).[7] V. Bernard, N. Kaiser, and U.-G. Meissner, Phys. Rev. D50 , 6899 (1994).[8] N. Kaiser, Phys. Rev.
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