CMS-PAS-HIN-21-009

CMS-PAS-HIN-21-009
Observation of $\tau$ lepton pair production in ultraperipheral nucleus-nucleus collisions
CMS Collaboration
March 2022

Abstract: The first observation of $\tau$ lepton pair production in ultraperipheral nucleus-nucleus collisions, a pure quantum electrodynamics (QED) process, is presented. The measurement is based on a data sample collected by the CMS experiment at a per nucleon center-of-mass energy of 5.02 TeV, and corresponding to an integrated luminosity of 404 $\mu$ b $^{-1}$ . The photon-induced $\gamma\gamma\to\tau^{+}\tau^{-}$ production is observed with a statistical significance of at least five standard deviations for $\tau^{+}\tau^{-}$ events with a muon and three charged hadrons in the final state. The cross section is measured in a fiducial phase space region, and is found to be $\sigma(\gamma\gamma\to\tau^{+}\tau^{-}) =$ 4.8 $\pm$ 0.6 (stat) $\pm$ 0.5 (syst) $\mu$ b, in agreement with leading-order QED predictions. The measurement, produced with a fraction of the expected integrated luminosity of the LHC program, establishes the potential for a substantially more precise determination of the anomalous magnetic moment of the $\tau$ lepton, which is currently poorly constrained.
Links: CDS record (PDF) ; Physics Briefing ; CADI line (restricted) ; These preliminary results are superseded in this paper, PRL 131 (2023) 151803. The superseded preliminary plots can be found here.

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Leading-order QED diagram (and charge conjugate) for the photoproduction of a pair of $\tau$ leptons ${\gamma {}\gamma \to {\tau^{+} {}\tau^{-} {}}}$ in ultraperipheral PbPb collisions. The presence of $\gamma {}\tau {}\tau$ vertices gives sensitivity to the anomalous electromagnetic couplings of the $\tau$ lepton. A possible deviation of the anomalous magnetic moment $\delta a_\tau$ is illustrated in each vertex. The $\tau$ leptons are reconstructed in an observed final state involving one muon ( $\mu$ ) and three charged particles assumed as pions ( $\pi$ ), while neutrinos ( $\nu$ ) escape undetected. A potential electromagnetic excitation of the outgoing Pb ions is denoted by $(^{\ast})$ .
png pdf	Figure 2: Left: Transverse momentum of the muon originating from the ${\tau _\mu}$ candidate. Middle: Invariant mass of the three pions forming the $\tau _\mathrm {3prong}$ candidate. Right: $\tau \tau$ invariant mass. In all plots, the signal component (pink histogram) is stacked on top of the background component (green histogram), considering their initial normalizations as described in the text. The total is displayed by a blue line and the shaded area shows the statistical uncertainty. The data are represented with black points and the uncertainty is statistical only. The lower panels show the ratios of data to the signal plus background prediction, and the shaded bands represent the statistical uncertainty.
png pdf	Figure 2-a: Left: Transverse momentum of the muon originating from the ${\tau _\mu}$ candidate. Middle: Invariant mass of the three pions forming the $\tau _\mathrm {3prong}$ candidate. Right: $\tau \tau$ invariant mass. In all plots, the signal component (pink histogram) is stacked on top of the background component (green histogram), considering their initial normalizations as described in the text. The total is displayed by a blue line and the shaded area shows the statistical uncertainty. The data are represented with black points and the uncertainty is statistical only. The lower panels show the ratios of data to the signal plus background prediction, and the shaded bands represent the statistical uncertainty.
png pdf	Figure 2-b: Left: Transverse momentum of the muon originating from the ${\tau _\mu}$ candidate. Middle: Invariant mass of the three pions forming the $\tau _\mathrm {3prong}$ candidate. Right: $\tau \tau$ invariant mass. In all plots, the signal component (pink histogram) is stacked on top of the background component (green histogram), considering their initial normalizations as described in the text. The total is displayed by a blue line and the shaded area shows the statistical uncertainty. The data are represented with black points and the uncertainty is statistical only. The lower panels show the ratios of data to the signal plus background prediction, and the shaded bands represent the statistical uncertainty.
png pdf	Figure 2-c: Left: Transverse momentum of the muon originating from the ${\tau _\mu}$ candidate. Middle: Invariant mass of the three pions forming the $\tau _\mathrm {3prong}$ candidate. Right: $\tau \tau$ invariant mass. In all plots, the signal component (pink histogram) is stacked on top of the background component (green histogram), considering their initial normalizations as described in the text. The total is displayed by a blue line and the shaded area shows the statistical uncertainty. The data are represented with black points and the uncertainty is statistical only. The lower panels show the ratios of data to the signal plus background prediction, and the shaded bands represent the statistical uncertainty.
png pdf	Figure 3: Difference in azimuthal opening angle between the ${\tau _\mu}$ and ${\tau _\mathrm {3prong}}$ candidates. The data are represented by the points with the vertical bars showing the statistical uncertainties. The signal (background) contribution is given by the pink (green) histogram, after the application of the fit procedure. The total is displayed by a blue line and the shaded area shows the total uncertainty. The lower panel shows the ratio of data to the signal plus background prediction, and the shaded band represents the total uncertainty.
png pdf	Figure 4: The cross section, ${\sigma ({\gamma {}\gamma \to {\tau^{+} {}\tau^{-} {}}})}$ , measured in a fiducial phase space region at ${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} =$ 5.02 TeV. The theoretical predictions are computed with leading-order accuracy in QED and represented by the dark and light gray bands [3,4].
png pdf	Figure A1: Event display of a candidate $\gamma \gamma \to \tau^{+} \tau^{-}$ event measured in PbPb UPC at CMS. The event is reconstructed as having a leptonic $\tau$ decay (red), $\tau \to \mu \nu _\mu \nu _\tau$ , and a hadronic $\tau$ decay (yellow), $\tau \to \pi ^\pm \pi ^\mp \pi ^\pm \nu _\tau$ .
png pdf	Figure A2: Initial agreement between the data and the signal and background models before the fit procedure is applied. Difference in azimuthal opening angle between the $\tau _\mu$ and $\tau _\mathrm {3prong}$ candidates. The signal component (pink histogram) is stacked on top of the background component (green histogram), before the application of the fit procedure. The total is displayed by a blue line and the shaded area shows the statistical uncertainty. The data are represented by the points with the vertical bars showing the statistical uncertainties. The lower panel shows the ratios of data to the signal plus background prediction, and the shaded bands represent the statistical uncertainty.
png pdf	Figure A3: Comparison of the constraints on ${a_\tau}$ at 68% confidence level from this analysis (using the parametrization from Ref. [3]) and the DELPHI experiment at LEP. The projection to the integrated PbPb luminosity expected from the High-Luminosity LHC program is included. For the latter, we foresee a $\lesssim$ 4 ( $<$ 2)% systematic (statistical) uncertainty with the improvements originating from lepton and tracking reconstruction, and the knowledge of the luminosity.

Tables
png pdf	Table 1: Summary of the event selection, which coincides with the definition of the fiducial phase space region for the ${\sigma ({\gamma {}\gamma \to {\tau^{+} {}\tau^{-} {}}})}$ measurement.
png pdf	Table 2: Postfit contributions to the systematic uncertainty of the ${\sigma ({\gamma {}\gamma \to {\tau^{+} {}\tau^{-} {}}})}$ measurement, in percent. The last row gives the sum in quadrature of all components.

Summary

In summary, the first observation of

$\tau$ lepton pair production in ultraperipheral nucleus-nucleus collisions is reported. Events with a final state of one muon and three charged particles identified as pions are reconstructed from a lead-lead data sample collected by the CMS experiment at

${\sqrt {\smash [b]{s_{_{\mathrm {NN}}}}}} =$ 5.02 TeV in 2015, and corresponding to an integrated luminosity of 404

$\mu$ b

$^{-1}$ . The statistical significance of the signal relative to the background-only expectation is above five standard deviations. The cross section for the

$\gamma\gamma\tau\tau$ process, within a fiducial phase space region, is in agreement with predictions from quantum electrodynamics at leading-order accuracy. This measurement introduces a novel experimental strategy using heavy ion collisions already recorded by the LHC, which is expected, with the incorporation of additional data, to surpass the precision on the

$\tau$ magnetic moment attained previously at lepton-lepton colliders. Using the measured cross section and its corresponding uncertainties, we estimate a limit of (

$-$ 2.4

$< a_\tau<$ 1.7)

$\times$ 10

$^{-2}$ with 68% confidence level.

References
1	P. A. Steinberg for the ALICE, ATLAS, CMS, LHCb, and STAR Collaborations	Ultraperipheral collisions at RHIC and the LHC	NP A 1005 (2021) 122007
2	F. del Aguila, F. Cornet, and J. I. Illana	The possibility of using a large heavy ion collider for measuring the electromagnetic properties of the $\tau$ lepton	PLB 271 (1991) 256
3	L. Beresford and J. Liu	New physics and $\tau g-2$ using LHC heavy ion collisions	PRD 102 (2020) 113008	1908.05180
4	M. Dyndal, M. Klusek-Gawenda, M. Schott, and A. Szczurek	Anomalous electromagnetic moments of $\tau$ lepton in $\gamma{}\gamma \to \tau\tau$ reaction in $\mathrm{PbPb}$ collisions at the LHC	PLB 809 (2020) 135682	2002.05503
5	R. H. Parker et al.	Measurement of the fine-structure constant as a test of the standard model	Science 360 (2018) 191	1812.04130
6	L. Morel, Z. Yao, P. Clad\'e, and S. Guellati-Kh\'elifa	Determination of the fine-structure constant with an accuracy of 81 parts per trillion	Nature 588 (2020), no. 7836, 61
7	Muon $g-2$ Collaboration	Measurement of the positive muon anomalous magnetic moment to 0.46 ppm	PRL 126 (2021) 141801	2104.03281
8	T. Aoyama et al.	The anomalous magnetic moment of the muon in the Standard Model	PR 887 (2020) 1	2006.04822
9	M. Passera	Precise mass-dependent QED contributions to leptonic $g-2$ at order $\alpha^2$ and $\alpha^3$	PRD 75 (2007) 013002	hep-ph/0606174
10	S. Eidelman and M. Passera	Theory of the $\tau$ lepton anomalous magnetic moment	MPLA 22 (2007) 159	hep-ph/0701260
11	DELPHI Collaboration	Study of $\tau$ pair production in photon-photon collisions at LEP and limits on the anomalous electromagnetic moments of the $\tau$ lepton	EPJC 35 (2004) 159	hep-ex/0406010
12	BaBar Collaboration	Evidence for an excess of $\bar{B} \to D^{(*)} \tau^-\bar{\nu}_\tau$ decays	PRL 109 (2012) 101802	1205.5442
13	BaBar Collaboration	Measurement of an excess of $\bar{B} \to D^{(*)}\tau^- \bar{\nu}_\tau$ decays and implications for charged Higgs bosons	PRD 88 (2013) 072012	1303.0571
14	Belle Collaboration	Measurement of the branching ratio of $\bar{B} \to D^{(\ast)} \tau^- \bar{\nu}_\tau$ relative to $\bar{B} \to D^{(\ast)} \ell^- \bar{\nu}_\ell$ decays with hadronic tagging at Belle	PRD 92 (2015) 072014	1507.03233
15	Belle Collaboration	Measurement of the branching ratio of $\bar{B}^0 \rightarrow D^{+} \tau^- \bar{\nu}_{\tau}$ relative to $\bar{B}^0 \rightarrow D^{+} \ell^- \bar{\nu}_{\ell}$ decays with a semileptonic tagging method	PRD 94 (2016) 072007	1607.07923
16	Belle Collaboration	Measurement of the $\tau$ lepton polarization and $R(D^)$ in the decay $\bar{B} \to D^ \tau^- \bar{\nu}_\tau$	PRL 118 (2017) 211801	1612.00529
17	Belle Collaboration	Measurement of the $\tau$ lepton polarization and $R(D^)$ in the decay $\bar{B} \rightarrow D^ \tau^- \bar{\nu}_\tau$ with one-prong hadronic $\tau$ decays at Belle	PRD 97 (2018) 012004	1709.00129
18	Belle Collaboration	Measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^*)$ with a semileptonic tagging method	PRL 124 (2020) 161803	1910.05864
19	LHCb Collaboration	Measurement of the ratio of branching fractions $\mathcal{B}(\bar{B}^0 \to D^{+}\tau^{-}\bar{\nu}_{\tau})/\mathcal{B}(\bar{B}^0 \to D^{+}\mu^{-}\bar{\nu}_{\mu})$	PRL 115 (2015) 111803	1506.08614
20	LHCb Collaboration	Measurement of the ratio of the $B^0 \to D^{-} \tau^+ \nu_{\tau}$ and $B^0 \to D^{-} \mu^+ \nu_{\mu}$ branching fractions using three-prong $\tau$ -lepton decays	PRL 120 (2018) 171802	1708.08856
21	LHCb Collaboration	Measurement of the ratio of branching fractions $\mathcal{B}(B_c^+ \to J/\psi\tau^+\nu_\tau)$ / $\mathcal{B}(B_c^+ \to J/\psi\mu^+\nu_\mu)$	PRL 120 (2018) 121801	1711.05623
22	Belle Collaboration	Lepton-flavor-dependent angular analysis of $B\to K^\ast \ell^+\ell^-$	PRL 118 (2017) 111801	1612.05014
23	LHCb Collaboration	Measurement of form-factor-independent observables in the decay $B^{0} \to K^{*0} \mu^+ \mu^-$	PRL 111 (2013) 191801	1308.1707
24	LHCb Collaboration	Differential branching fractions and isospin asymmetries of $B \to K^{(*)} \mu^+ \mu^-$ decays	JHEP 06 (2014) 133	1403.8044
25	LHCb Collaboration	Test of lepton universality using $B^{+}\rightarrow K^{+}\ell^{+}\ell^{-}$ decays	PRL 113 (2014) 151601	1406.6482
26	LHCb Collaboration	Angular analysis of the $B^{0} \to K^{*0} \mu^{+} \mu^{-}$ decay using 3 fb $^{-1}$ of integrated luminosity	JHEP 02 (2016) 104	1512.04442
27	LHCb Collaboration	Angular analysis and differential branching fraction of the decay $B^0_s\to\phi\mu^+\mu^-$	JHEP 09 (2015) 179	1506.08777
28	LHCb Collaboration	Test of lepton universality with $B^{0} \rightarrow K^{*0}\ell^{+}\ell^{-}$ decays	JHEP 08 (2017) 055	1705.05802
29	LHCb Collaboration	Search for lepton-universality violation in $B^+\to K^+\ell^+\ell^-$ decays	PRL 122 (2019) 191801	1903.09252
30	CMS Collaboration	The CMS Experiment at the CERN LHC	JINST 3 (2008) S08004	CMS-00-001
31	CMS Collaboration	Performance of the CMS level-1 trigger in proton-proton collisions at $\sqrt{s} =$ 13 TeV	JINST 15 (2020) P10017	CMS-TRG-17-001 2006.10165
32	CMS Collaboration	The CMS trigger system	JINST 12 (2017) P01020	CMS-TRG-12-001 1609.02366
33	CMS Collaboration	Performance of electron reconstruction and selection with the CMS detector in proton-proton collisions at $\sqrt{s} =$ 8 TeV	JINST 10 (2015) P06005	CMS-EGM-13-001 1502.02701
34	CMS Collaboration	Performance of the CMS muon detector and muon reconstruction with proton-proton collisions at $\sqrt{s}=$ 13 TeV	JINST 13 (2018) P06015	CMS-MUO-16-001 1804.04528
35	CMS Collaboration	Performance of photon reconstruction and identification with the CMS detector in proton-proton collisions at $\sqrt{s}=$ 8 TeV	JINST 10 (2015) P08010	CMS-EGM-14-001 1502.02702
36	CMS Collaboration	Description and performance of track and primary-vertex reconstruction with the CMS tracker	JINST 9 (2014) P10009	CMS-TRK-11-001 1405.6569
37	CMS Collaboration	Particle-flow reconstruction and global event description with the CMS detector	JINST 12 (2017) P10003	CMS-PRF-14-001 1706.04965
38	CMS Collaboration	Performance of reconstruction and identification of $\tau$ leptons decaying to hadrons and $\nu_\tau$ in pp collisions at $\sqrt{s}=$ 13 TeV	JINST 13 (2018) P10005	CMS-TAU-16-003 1809.02816
39	CMS Collaboration	Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV	JINST 12 (2017) P02014	CMS-JME-13-004 1607.03663
40	CMS Collaboration	Performance of missing transverse momentum reconstruction in proton-proton collisions at $\sqrt{s} =$ 13 TeV using the CMS detector	JINST 14 (2019) P07004	CMS-JME-17-001 1903.06078
41	J. Alwall et al.	The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations	JHEP 07 (2014) 079	1405.0301
42	T. Sjostrand et al.	An introduction to $PYTHIA$ 8.2	CPC 191 (2015) 159	1410.3012
43	GEANT4 Collaboration	GEANT4--a simulation toolkit	NIMA 506 (2003) 250
44	CMS Collaboration	Measurement of Tracking Efficiency	CMS-PAS-CMS-PAS-TRK-10-002
45	CMS Collaboration	Measurement of exclusive $\Upsilon$ photoproduction from protons in pPb collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}=$ 5.02 TeV	EPJC 79 (2019) 277	CMS-FSQ-13-009 1809.11080
46	Particle Data Group Collaboration	Review of Particle Physics	PTEP 2020 (2020) 083C01
47	CMS Collaboration	Precision luminosity measurement in proton-proton collisions at $\sqrt{s} =$ 13 TeV in 2015 and 2016 at CMS	EPJC 81 (2021) 800	CMS-LUM-17-003 2104.01927
48	CMS Collaboration	Evidence for light-by-light scattering and searches for axion-like particles in ultraperipheral PbPb collisions at $\sqrt{s_\mathrm{NN}} =$ 5.02 TeV	PLB 797 (2019) 134826	CMS-FSQ-16-012 1810.04602