CP Violation In Charm Decays: 3.5 Sigma From LHCb!
    By Tommaso Dorigo | November 15th 2011 05:59 AM | 20 comments | Print | E-mail | Track Comments
    About Tommaso

    I am an experimental particle physicist working with the CMS experiment at CERN. In my spare time I play chess, abuse the piano, and aim my dobson...

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    Today I wish to briefly discuss a recent important measurement produced by the LHCb collaboration, a measurement of CP violation in the decay of charmed mesons. Before I do, I think I need to explain some details of the LHCb experimental arrangement, because it is different from what most readers here are familiar with.

    And, update: rather than putting it at the end, I prefer to link Resonaances' post on the same subject here this time - he wrote about the matter yesterday and did a much better job than I do below. Sorry for noticing it after posting mine!

    Some pedestrian kinematics

    LHCb is one of the four detectors you may run into these days, if you are a 3.5 TeV proton. Less known than its bigger brothers ATLAS and CMS, LHCb still looks at the 7-TeV collisions delivered by LHC, but does so "sideways": only particles produced in and around the direction of one of the two beams are studied. The figure below shows a side view of LHCb, with a graph to decode the various pieces.

    When a proton moving at an energy E1=3.5 TeV hits another proton moving in the opposite direction at E2=3.5 TeV, the nominal "center-of-mass" energy is E=7 TeV: E1+E2=E, simple math. However, this is a simplified picture, since the proton is not a pointlike object, and what we are in fact observing is the hard collision of a quark or a gluon in a proton with another quark or gluon in the other proton.

    The center-of-mass energy of the hard pointlike collision is much lower than 7 TeV, and it depends on what fraction of the parent protons did the colliding constituents carry. If we take these fractions to be x1 and x2 (0<x1,x2<1), the effective collision energy in the two partons center of mass frame is 7 TeV multiplied by sqrt(x1*x2).

    Typical values of x1 and x2 range from a thousandth to some tenths: the highest collisions we observe at the LHC have therefore an effective energy of two or three TeV at most. The relative probability of softer or harder collisions is governed by the parton distribution functions (shown on the left): these are probability density functions dictating how likely it is that a parton of a given kind is found with a fraction x of the proton's momentum. These functions are high at low values of x, so very energetic collisions are quite rare. But they do occur.

    Now, to understand why physicists constructed colliding beam machines, you need to compare the center-of-mass energy of those head-on collisions with the one resulting when a single beam hits a fixed target. In the latter case, let us consider a 3.5 TeV proton hitting a proton at rest in the laboratory. The center-of-mass energy of the resulting collision can be calculated as the square root of the so-called "Mandelstam variable" s, working in four dimensions. It is actually much easier than you think. The math is the following:

    In the first row we just expressed the fact that we are interested in the squared sum of the two incoming particles' four-momenta p1, p2. In the second row we explicitate this by separating the zeroth component of the four-vectors, E1+E2, from the three-vector of four-momenta; the minus sign comes from the "metric" of four-dimensional space-time. In the third row we substitute E1->E (incoming proton) and E2->M (proton at rest in the target, of mass M and zero momentum); we also take the z axis as the one along which the beam incides on the target. In the fourth row we just expand the squared parentheses, remembering that the first proton has momentum equal to E (it is ultra-relativistic) and the second has zero momentum. The result is that the center-of-mass energy in a fixed-target collision is sqrt(2ME).

    So what would be the energy of a fixed-target collision of 3.5 TeV protons with still protons ? It would be equal to sqrt(2ME)=sqrt(2*1 GeV * 3500 GeV) = 85 GeV: quite small! We would be kinematically prevented from even producing a Z boson with such arrangement... And note that we have not even factored in the two partons fractionary momenta x1 and x2 in the calculation above. The smallness of the available energy to produce new heavy particles in fixed-target collisions is the reason of constructing particle colliders.

    Back to LHCb

    But LHCb, as I stated above, only looks at one of the two sides of the collision: it basically observes collisions which have one of the two partons much more energetic than the other. If x1>>x2, we are tantalizingly close to the kinematic regime of fixed-target collisions: the total center-of-mass energy is much smaller than the one available to central collisions, where the two partons carry similar fractions of their parents' momenta. Of course, LHCb also "sees" the one-sided view of central collisions, by intercepting the remnants of one of the two proton and the resulting fragments; but similar kinematical observations apply: the reaction energy available in the forward region is small.

    You might thus think the whole concept is a weird idea: we have spent decades trying to move away from the fixed-target arrangement and into the colliding beams configuration, making our beams more dense and intense in order to produce sufficiently high collision rates (something that fixed-target arrangements provided from day one) in order to reach higher in center-of-mass energy, and now we use these lower-rate collisions to study a lower energy regime ?

    Well, it is not so weird. The fact is that a 3.5 TeV proton beam can only be produced at the LHC these days. And the resulting "lower-energy" collisions are in fact very interesting: they produce huge amounts of fast-moving heavy quarks, something that lower-energy fixed-target collisions did not do. The resulting B and D hadrons (ones containing bottom and charm, respectively) are invaluable to measure precisely some parameters of the standard model which CMS and ATLAS are less suited to study.

    One additional bit of information

    The measurement of direct CP violation in D mesons is one of these pieces of physics which LHCb is best suited to perform. The advantage of the LHCb arrangement with respect to ATLAS and CMS is that the hadrons it observes are very energetic, and thus travel long paths before decaying. Here I need to explain another bit of kinematics.

    When a particle with a lifetime t is at rest, there is a probability 1-1/e=63% that it decays in the next t seconds: this is governed by the well-known exponential decay rule. But when we see the particle moving, Einstein taught us that there is a mismatch between the time as measured in its rest frame and the time as we measure it. This mismatch is proportional to the "gamma factor" of its speed. Without going into formulas, we can get away by saying that for a particle of energy E much larger than its rest mass M, gamma=E/M is large. The 63% probability that it decays occurs now at a time t'=gamma t.

    What the above tells us is that we may see a 100-GeV charmed meson D, for which t is a few tenths of a picosecond, decaying in a time t'=50 T, since gamma is about 50 for it (its mass is M=2 GeV). Experimentally, this factor of 50 is quite important, since rather than traveling, say, 500 micrometers in the detector before disintegrating, the D meson travels one inch! We can thus "see" much more clearly its decay vertex and distinguish it from the point where it was created, rejecting backgrounds more effectively and making all of our measurements much more precise.

    In CMS and ATLAS, 100-GeV D mesons are rare, since those 100 GeV must originate from the released energy of the collision. In LHCb, instead, those 100 GeV are not so rare, since we are observing the particle moving in the same direction of the original proton: for the same reason if you are standing near somebody who is being thrown a pie, you move sideways, not behind him - remnants of the pie will be much less likely to reach you then.

    The measurement

    So it is LHCb the first experiment which measures a direct CP violation effect in the charmed meson system. The measurement we are discussing is a "3.5-sigma" one, so we are talking about a "first evidence" of a CP asymmetry: there is still a small, but not totally negligible, chance that the measurement of a non-zero asymmetry is due to a fluctuation. Before we go to a graphical illustration of the result, let us see how it came about.

    A CP asymmetry results if a particle and its antiparticle behave differently. This is possible in the standard model, due to several small effects; it can be studied best in rare decays of heavy mesons, where the CP-violating effects are relatively larger. New physics could manifest in an enhancement (by some percent) of these asymmetries with respect to the standard model prediction, so their study is a way to probe the standard model in a way which is independent on the high-energy searches that ATLAS and CMS are doing.

    LHCb tested the decay properties of neutral D mesons, particles composed of a charm quark and an anti-up quark, and anti-D mesons, which contain a up-quark and an anti-charm one. They did so in a sample of 580 inverse picobarns of proton-proton collisions collected this year (about half of their total dataset), by studying the rate of D meson decays into pairs of kaons (K+K-) or pions (pi+pi-). The identity of the D mesons (i.e., the presence of charm or anticharm in them) is first "tagged" by their production together with an additional soft pion in the decay of D* mesons (the charge of the pion discriminates the two), and then carefully studied to avoid or correct any detector-related effect which might pollute the measurement.

    The quantity that LHCb extracts from the measurement is actually not a single CP asymmetry, but the difference of two separate ones: the one of the D decay into kaon pairs minus the one of the D decay into pion pairs. Many detector-related effects cancel in the difference, so the measured quantity is much more precisely determined; but further, the "indirect" component of the asymmetries cancel in the difference, leaving only the direct part. This is a technical point which I will leave unexplained, but just mention that indirect CP violation arises from the mixing of the D mesons, and from related interference effects.

    In the end, a global fit of mass distributions as a function of the kinematics of the candidates allows to better gauge the residual detector effects. The result of LHCb is that the CP asymmetry equals -0.82+-0.21(stat)+-0.11(syst)%, a number which differs from zero by 3.5 standard deviations. The graph below illustrates what is measured in the plane spanned by direct (in the vertical axis) versus indirect (horizontal axis) asymmetry: the LHCb band is almost horizontal, indicating that the measured asymmetry is largely coming from direct CP violating sources.

    The result is compatible with the previous measurements by other experiments, but it is the first one which deviates significantly from zero, as is visually evident by looking at the "distance" of the black point from the cyan band. The black ellipses show the previous world average for the CP violating asymmetries, while the different bands illustrate the results of previous experiments, formerly dominated by the CDF result.
    LHCb will be able to improve the statistical accuracy of this result in the near future, by doubling the analyzed dataset. One might naively expect that their total uncertainty might shrink to sqrt(0.5*0.21^2+0.11^2)=0.18, which would produce, in case the central value did not move around much, a result differing from zero by over five standard deviations. Time will tell! In the meantime, I congratulate with the LHCb colleagues for this very careful and difficult analysis.


    82/18 is just 4.55 so I wouldn't really call it 5 SD.

    Hi, it should be a bit lower than 5 sigma ;)
    Anyway it is a very nice results and I am looking forward to see also the time-dependent analysis.


    Yes, sorry - mistaken 0.82 for 0.92 in the rush to write the post.
    Once more, great article!

    Hi Gianluca,

    Sure, to have the CP asymmetry in the decay you need to have two contributing amplitudes with both different strong and different weak phases. But I must say I was counting on the paper (which is not out yet as far as I know) to refresh my memory on the physics of D decays...

    Is it the case that in the Standard Model, single CP violating phase CKM matrix that indirect CP violation and direct CP violation should be identical, or are those not apples to apples comparisons?

    "direct" and "indirect" refer to the source of the CP violation: "Direct" comes from the decay alone, while "indirect" is related to D0 <-> D0bar mixing. As the latter one is dominated by long-distance effects, it is tricky to compare anything here.

    Has anyone considered the implicatoins of CP violation achieved at LHCb energy levels on theories of Quantum Vacuum Decay?

    Can the SM account for this? According to a paper in Phys Lett B 222 (1989)501 (look at the date, this is called "making a prediction" in science) YES. It says that in the absence of large SU(3) breaking in these decays one should expect order 1 CP asymmetries. The authors then retract a bit and state that "This is of course very unlikely; the preferred explanation ... is that SU (3) violating effects are large in this decay." (This discussion is in the next to last paragraph in that paper). So now we know, the preferred explanation is half-way, there is some SU(3) breaking and some enhancement of the amplitude that leads to large CP violation (the one the authors call 2F+G).

    how can they disentangle the contribution to the asymmetry coming from the the strong phases difference from the contribution coming from the weak phases difference?


    Hi Gianluca,

    as far as I understand, they don't. They measure the asymmetry difference of kk and pp modes, which estimates the direct CP asymmetry, but they do not have any means to study the particular diagrams that caused it.

    Hi Tommaso,
    Actually it means that the measurement could be "strongly" affected by the strong phase difference. Indeed in both the decay channels the measured asymmetry should be proportional to sin(DW)*sin(DS), where DW and DS stay for the weak phase difference and for the strong phase difference, respectively. I would then be interested to see what they have measured for each channel separately and compare it with the 5.8 fb^-1 measurement from CDF..


    That is difficult, as the LHCb (unlike CDF) looks at proton-proton-collisions, where you have production asymmetries. To account for them, you need the ratio of D*+ to D*-, but you have to take D0 mixing into account (the decay to D+ pi0 is bad as the pi0 cannot be tracked) and have to avoid all possible CP violations in that. It is not impossible, but harder to do.
    In addition, you have to understand the pion efficiency on a permille level.

    Hi Mfb,

    thanks for the comment - I am not sure I understand where the D+ pi0 background would spoil the measurement, maybe you can make it more explicit.

    Anyway, when I see comments like yours I am both very happy and very sad. When somebody with evident insight in the topic being discussed contributes to a thread, it would be so much more valuable if they left their full name rather than a acronym. That is because by knowing who the contributors are one can exploit best their background and put together more meaningful discussions.
    Think about it (and what you would lose -practically nothing- if you abandoned anonymity).

    Hi, thanks!
    actually it seems they avoid the problem of the asymmetry, pag 9 of the presentation. This in any case does not say anything about what is measured. In the asymmetry there is a component due to the strong phase difference, and one cannot avoid it. This should be considered. One cannot claim to have observation of CP violation in charm (I really hope they will confirm it!!) if the strong phase difference has not be included as a source of asymmetry. The asymmetry may not be due to the weak phase unless the measurement is based on the assumption that only tree topologies contribute to the decay channels, in which case the strong phase cancel in the ratio of the amplitudes, but the other topologies would introduce theoretical uncertainties...
    Am I wrong?
    thanks in advance!

    @ben-hqet, this may be a good time to post your paper on the arXiv, which didn't exist in those days.

    It may also be a good time to dust your notes and improve your computation... but you already knew that

    Hi Tommaso,
    I thought that only K (s quarks) and particularly B (B quarks) mesons decayed violating CP. I'm not quite sure where I got that notion.
    Is there any relationship between the kind of quark and CP violation? Do mesons with a t quark violate CP as well?


    Mesons and baryons are composite particles.
    The standard model concerns elementary particles.
    So what does this discovery tell about the standard model?
    If you think, think twice
    Hello Hans, the SM tells us a lot about the decay modes of composite particles. There's a bunch of SM parameters in the Cabibbo-Kobayashi-Maskawa matrix, and they are needed in order to figure out the phenomenology of these decays...

    The scheme that identifies elementary particle types from ordered pairs of field sign flavors can attribute all particle properties except the generation of the particle. However, it offers an equation for computing the coupling constant m from the field configuration. See: 
    Greathings, Hans
    If you think, think twice